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CHAPTER 1: Introduction
1
CHAPTER ONE
GENERAL INTRODUCTION
1.1. GENERAL
The stability and improvement of underground excavation and surface slopes mining
during and after the excavation is a big concern to designers as any kind of instability
may result in damage to the environment, high cost in repair work as well as time
consumption. The forms of instability and their mechanism and the factors and
conditions associated with them must be clearly understood so that a correct way to
the stabilisation and reinforcement of the structure can be undertaken. Rock
reinforcement is a specific technique with in the general category of rock
improvement methods. And rock improvement concludes all techniques which
looking for increasing the strength or decreasing the deformability characteristics of
a rock mass. Rock mass stabilisation by bolting has now been used for more than a
century all over the world (Snyder 1983). In civil and mining engineering projects
various kinds of rock bolt; mechanically, grouted, anchored, are recently considered
one of the principal support members in rock structure.
Rock bolting in various types has been used as early as the nineteenth century. An
early use of bolts in a coal mine reported in 1918 in Germany (Lang et al 1979). The
bolt was made out of wood and used preventing small pieces of rock from falling
between the face and the main support system. Palmer and et al (1976) evaluated
limiting displacement as the key parameter of the bolting action.
CHAPTER 1: Introduction
2
In the past, because of the lack of understanding on the behaviour of rock mass and
rock bolt as well as their complicate interaction, the use of rock bolt was not
developed like today. However, in the recent years, the range of using of rock bolt
systems has been extended both in mining and civil structures and has been become a
dominant measure for rock support in mining engineering. This is because of
advances made in the understanding of bolt failure as well as the improvement
attained in strata control technology. To decrease roof failure of a mine fully grouted
bolts are used more than mechanically anchored bolts, it is due to fully grouted bolts
have greater area of anchorage capacity. The majority of the 100 million roof bolts
installed each year in the United States are fully grouted resin bolt (Maleki 1992).
They can create the great reinforcement on rock walls around underground
excavation and also are very effective in closely jointed rocks and in soft rocks. Rock
reinforcement system will increase the factor of safety against crack initiation, and
will influence the orientation of critical existing crack. The idea of a resin
reinforcement system leads directly to the load transfer of the load from unstable
rock through the reinforcement system to stable rock. The reinforcement system and
load transfer concepts have been used to define three fundamental types of
reinforcement system (Windsor and Thomson 1993):
1-Continous mechanically coupled (CMC) systems,
2-Continious frictionally coupled (CFC) systems and
3-Discretly mechanically or frictionally coupled (DMFC) system.
The load transfer between the rock bolt and the borehole is dependent on some
parameters such as borehole dimeter, annulus thickness, bolt profile and so on .In a
fully grouted rock bolt, the load transfer mechanism is dependent on the shear stress
CHAPTER 1: Introduction
3
attained on the interfaces of bolt-resin and resin –rock. The shear stress capability of
the interfaces and the rate of shear stress generation determine the response of the
bolts to the strata behaviour. The researches on rock bolts, gained momentum
following the introduction of new Austria tunnelling method (NATM) in the early
sixties and since its introduction more than 30 years ago, resin grouting has
significantly improved the effectiveness of roof bolting and this process is
continuing. Many researchers have worked on application of fully grouted rock bolts
both theoretically and experimentally, but a little research has become on load
transfer mechanism. Littlejohn and Bruce (1975) conducted the first systematic study
on the failure of rock bolt system and suggested three modes of failure of rock bolts
system include:
- Failure of rock mass,
- Failure of rock bolt and
- Failure of bolt-grout-rock interface.
Hollingshead (1971), Pells (1974), Farmer (1975), Xueyi (1983), Aydan et al (1985),
Serbousek and Singer, (1987), Aydan (1989), Singer (1990), Hyett et al. (1992),
Skybey (1992), Gray et al. (1998) Li and Stillborg (1999), Fabyznchic et al. (1992,
1998), Thompson and Finn (2001), Kilic and et al. (2002, 2003), Aziz (2003),
Ivanovic (2003) and Campbell and Mould (2005) carried out the theoretical and the
experimental approaches to define the bolt behaviour under axial loading conditions.
They tried to describe the bolt/grout/rock interaction under axial loading conditions.
In majorities of the above research, the bolt profile was ignored.
In case of bolt bending behaviour and the load transfer mechanism subjected to
lateral loading conditions, following researchers carried out the analytical and
CHAPTER 1: Introduction
4
experimental study. Dulascka (1972) then Bjurstrom (1974), Haas (1976,1981),
Azuar (1977), Hibino and Motojima (1981), Egger and Fernands (1983) and Ludvig
(1983), Gerard (1983), Dight (1982), Bjornfot & Stephansson (1983), Larsson
(1983), Schubert (1984), Yoshinaka et al. (1987), Spang and Egger, (1990), Stillberg
(1994), Holmberg (1992), Egger and Zabuski (1991), Ferrero (1995), Pellet and
Egger (1995), Goris et al. (1996), Grasselli (2005) and Mahoni et al (2005). All
experimental testing of grouted bolts were performed as a single shear test without
applying tensile loads on the bolt. However, in some research, only confining
pressure on the moving block was applied.
To the best of author’s knowledge, no suitable literature was available at the time of
writing this thesis to report on the effect of bolt profile on bending behaviour of
perpendicular bolts to the joints and also the effect of pretensioning in this situation.
1.2. BACKGROUND FOR PRESENT RESEARCH
The present research including; laboratory tests, numerical design, field tests and
some theoretical design, by the author was carried out because of following reasons:
1- Load transfer capacity of bolt types in particular with different profiles and
ribs has not been evaluated before.
2- All previous shear tests have been carried out by single shear test, giving
difficulties in shear joint due to non-equilibrium situation and un-uniformity
distributed load on shear joint (twisting due to movement) So, new method is
designed in present research. Due to virtue of symmetry, no moment in the
moving block can be induced, while such forces undoubtedly are available in
single shear apparatus, which were used so far.
CHAPTER 1: Introduction
5
3- No shear test and failure mechanism have been reported yet on high strength
steel, which are main applicable bolts in Australia and all around the world.
4- There was lake of understanding in axial and shear behaviour and load
transfer of bolts and also some ambiguous reports in their failure mechanism.
5- New available high strength steel bolts in market have not previously
importantly tested.
6- There is lack of quality data available on the exact nature of fully grouted bolt
under shearing, subjected to pretensioning.
7- There are no reported results in case of diversity of resin thickness and
quantitative significance of shear resistance mechanism in different
surrounding rock strengths.
8- There is no reported result in load transfer mechanism subjected to axial
loading, regarding different bolt profile such as rib height and rib spacing.
9- There is no valuable numerical design in both axial and shear behaviour of
the bolts, especially in profile behaviour and bolt/grout/concrete contact
interfaces.
1.3. KEY OBJECTIVE
1- The evaluating of the shear behaviour mechanism in bolt-grout and grout-
rock interfaces both in the laboratory and field,
2- To design and develop a shear testing machine which meets and removes the
relevant problems in previous machines,
3- The study of the load transfer capacity in bolt-grout-rock interface both field
and laboratory, in different Types of bolts,
CHAPTER 1: Introduction
6
4- The effect of resin thickness on shear behaviour of bolts and load transfer
evaluation, subjected to axial and shear behaviour,
5- The effect of rock strength on bending behaviour of bolts,
6- The effect of bolt pretensioning on shear behaviour and load transfer
mechanism,
7- The effect of bolt profile and thread rebar specifications on load transfer
under various level of pretensioning and different strength surrounding
materials.
8- To better understanding the exact nature and quantitative significant of load
transfer mechanism for shear resistance,
9- The evaluation of rib height and rib spacing and resin thickness in different
bolt profile on load transfer mechanism subjected to axial loading,
10- Numerical design of bolt/ joint/ concrete and contact elements in both axial
and lateral applied loads and
11- The verification of results by numerical simulation.
1.4. RESEARCH METHODOLOGY
The laboratory tests and numerical modelling were chosen as the main methods for
this research project. DSS (Double shearing system) was used for laboratory tests
subjected to bolt bending behaviour, pull and push tests were used to define load
transfer mechanism subjected to axial loading conditions and 3D finite element
program, Ansys, was used to find the stress-strain behaviour in bolt-grout-concrete,
bolt/grout and grout/concrete interfaces and their interactions, which have not been
considered in previous researches.
CHAPTER 1: Introduction
7
1.5. SCOP OF THE THESIS
In spite of many research including theoretically and experimentally on bond
strength of fully grouted rock bolts have been done, still lack of understanding of
load transfer mechanism on fully resin grouted bolts is recognised. In other words the
lack of published results on bolt bending behaviour in different bolt profile
characteristics and surrounding materials in various pretension loads, writer of the
thesis seeking the method to evaluate the load transfer under both axial and lateral
loading conditions. This thesis consists of 10 chapters. The flowchart of the
arrangement of the thesis is shown in Figure 1.1.
CHAPTER 1: Introduction
8
Figure 1. 1. Structure of Chapters in the thesis
• Chapter 1 presents the general purpose of the research, background of the
research in field of rock bolt and methodology of the research and key
objectives.
CHAPTER FIVE DOUBLE SHEARING OF BOLTS ACROSS JOINTS
CHAPTER SIX ROLE OF BOLT ANNULUS THICKNESS ON BOLT SHEARING
CHAPTER SEVEN NUMERICAL DESIGN IN FULLY GROUTED ROCK BOLTS
CHAPTER FOUR
FAILURE MECHANISM OF BOLT RESIN INTERFACE SUBJECTED TO AXIAL LOAD
CHAPTER THREE REVIEW OF SHEAR BEHAVIOUR OF BOLTS AND MECHANICAL PROPERTIES OF
THE MATERIAL USED
CHAPTER TWO ROCKBOLT SYSTEM AND REVIEW OF BOLT BEHAVIOUR UNDER AXIAL LOADING
CHAPTER ONE INTRODUCTION
CHAPTER EIGHT ANALYTICAL BEHAVIOUR OF FUULY GROUTED BOLT
CHAPTER NINE FIELD INVESTIGATION
CHAPTER TEN CONCLUSION AND RECOMMENDATION
CHAPTER 1: Introduction
9
• Chapter 2 includes the general knowledge of the rock bolt system, rock bolts
application and reinforcement mechanism in particular fully grouted rock bolt
and the advantages of this type of bolt. And also highlights the bolt theories,
rock bolt types and their descriptions. Moreover, it gives a brief view of the
bolt behaviour and load transfer mechanism subjected to axial loading
conditions in both analytical and experimental methods.
• Chapter 3 deals with the brief view of the bolt bending behaviour subjected to
lateral loading conditions both theoretically and experimentally. In additions,
it evaluates the mechanical and physical properties of the material used such
as; bolt, grout and concrete.
• Chapter 4 describes the load transfer mechanism when bolt axially is loaded.
And also different types of bolts in terms of different profile characteristics in
both pull and push tests are discussed.
• Chapter 5 deals with shear behaviour of bolts across joints. It describes the
experimental procedure and double shearing system. Six different types of
bolts in terms of mechanical and physical characteristics and three material
strengths; 20, 40 and 100 MPa were considered to evaluate the load transfer
mechanism under various pretension loads, 0, 5, 10, 20, 50 and 80 kN.
• Chapter 6 describes effect of the resin thickness on bolt shear performance.
For this reason, tests are carried out on the same type of bolt, pretension load
and the concrete strength.
• Chapter 7 gives a brief view of finite element application in rock bolt. In
addition, it presents the validation of the numerical modelling results with the
laboratory results. 32 models are created to define the effect of concrete
strength, resin thickness, different pretension loads on the load built up along
CHAPTER 1: Introduction
10
the bolt, grout and concrete during the shearing process. Moreover, the stress,
strain developed along the bolt subjected to the axial behaviour are discussed
in this chapter.
• Chapter 8 deals with a brief review of the analytical methods of the bolt
bending behaviour and prediction of the hinge point location in both elastic
and plastic condition. In addition, the axial load distribution along the elastic
bolt installed in elasto plastic rock mass in a circular tunnel is evaluated
numerically. A program was written for this reason. It was tried to use the
material properties of the Metropolitan colliery mine in the model.
• Chapter 9 illustrates the fieldwork description. Two different bolt types,
which are considered in experimental work, selected for field investigation
practically. They were instrumented by 18 strain gauges in both sides of the
bolt along the 2.1 m bolt length. During several months the bolt monitoring
was carried out and load distribution along the bolt was recorded.
• Chapter 10 summarise the results and principal conclusions of the research
work presented in this thesis and the recommendations for further research.
CHAPTER 2: Rock bolt system and review of bolt behaviour under axial loading
11
CHAPTER TWO
ROCK BOLT SYSTEM AND REVIEW OF BOLT
BEHAVIOUR UNDER AXIAL LOADING
2.1. INTRODUCTION
This chapter concludes two main parts; first, general description of rock bolts,
particularly fully grouted rock bolts and then followed by the review of the bolt
behaviour subjected to axial loading conditions.
Rock bolting technology has advanced rapidly during the past three decades due to
better understanding of load transfer mechanisms and advances made in bolt system
technology. Bolts are used both as temporary and permeant support systems, in
tunnelling and mining operations. In surface mining they are used for slope stability
operations and in underground working in a variety of purposes, which include
roadway development, shaft sinking and stoping operations. Rock bolts are basically
installed to prevent the movement of discontinuity planes, depending upon the
direction of installation and nature of discontinuity surface. Bolts provide a tensile
effect to transfer the load from one side to another when relative strata layer
movement takes place with separation. Basically rock bolts provide a reinforcement
zone in rock mass and the main aim of rock reinforcement is to make greater use of
inherent rock mass strength to enable the rock media to support themselves.
2.2. HISTORICAL
The application of bolts as a mean of ground control was first reported in 1918 in a
coal mine in Germany (Lang.T.A et al. 1979). In the united kingdoms the earliest
reporting came from the slate quarry located in North Wales in 1872 (Schach et al
CHAPTER 2: Rock bolt system and review of bolt behaviour under axial loading
12
1979). Bolstad and Hill (1983) reported the use of mechanical rock bolt in a metal
mine in the United States (1927). However, the development of rock bolting as a
practical and economical technology began with the Norwegian in the late 1940’s.
To reduce the number of fatal accidents caused by roof falls, the U.S Bureau of
Mines (USBM) begun the use of roof bolting technology in 1947. The use of rock
bolt was significantly spread throughout of U.S., which by 1952; the annual roof bolt
consumption had reached 25 million. The practices of rock bolting technology for
Australian condition took place with the snowy mountain hydroelectric Scheme
(1949-1969). It was during this period that the use of grouted rock bolts for
permanent reinforcement was pioneered.
2.2.1. History of bolting Australian mines
In Australia the application of roof bolting in conjunction with normal timber support
was reported from Elrington Colliery, New South Wales in 1949. This was soon
turned into fully scale bolting operation that mine in April 1950 (Gardner 1971).
Since 1983, bolts have become the main method of support in most of the
underground openings in Australia mines. Near 5 million of different bolt type are
installed in the Australia mining industry per year.
2.3. ROOF BOLT PRACTICE AND APPLICATION
Nowadays, the application of rock bolts for ground reinforcement and stabilisation is
of worldwide scale, and the level of bolt usage has contributed to increased
variations in design and purpose. In the US coal mines, every year around 15000 km
entries are excavated and about 100 million roof bolts are installed in these entries
(Yassein et al 2004). Similarly the application of Hundreds of million of units are
CHAPTER 2: Rock bolt system and review of bolt behaviour under axial loading
13
installed each year in Australia, and a recent survey revealed that the worldwide
usage of rock bolts was in excess of 500,000,000 annually (Windsor, 1997). Figure
2.1 displays the usage of rock bolts in the past decades in the coal mining industry
(Junlu 1999). Rock bolts are installed as an active support system, as they are loaded
from the time of installation. This is achieved by the pretensioning process. Bolt
pretensioning can clamp individual bedding planes together and closes the small gaps
that might have occurred due to sagging after excavation. Pretensioning of the fully
grouted bolt can create much higher level of active support than the point anchored
bolts such as the mechanically anchored bolts.
Figure 2. 1. Usage of rock bolts in the world
2.4. REINFORCEMENT MECHANISM
The main aim of rock reinforcement is to make greater use of inherent rock mass
strength to enable the rock media to support themselves (Biniawski 1984). Rock
reinforcement depends upon the type of rock bolt and anchorage system. The rock-
bolt interaction is affected by the rock type, strata lithology and encapsulation
Year
1920 1930 1940 1950 1960 1970 1980 1990 2000
0
20
40
60
80
100
120
Num
ber o
f bol
ts c
onsu
med
in m
illio
n
CHAPTER 2: Rock bolt system and review of bolt behaviour under axial loading
14
characteristics. The development of the load on the bolt or a section of its length is
affected by the strata lithology with other parameters being equal.
Rock mass in general is insufficiently strong in tension or in shear. These properties
can be strengthened by bolting. Supporting of the ground with bolts allows the
application of compression to the strata, which will aid to increase the shear and
tension resistance through effective binding of the strata layers. The increase of these
strengths can thus be achieved by the friction effect. Another mechanism of bolt
reinforcement is by beam composite action.
2.5. BOLT THEORIES
Table 2.1 lists the various theories proposed for ground support using rock bolts. As
can be seen from the Table 2.1, the selection of any prosed theory is dependent upon
the methodology of bolt application and the geological conditions. The proposed
terminology used fro each theory is influence by the geological conditions; normally
the suspension theory is dead weight transfer of the lowered and separated beds to
the upper and stronger and commitment beds. Full column grouted bolts reinforce the
bedded roof strata by resisting slip along bedding planes (Stimpson 1983).
CHAPTER 2: Rock bolt system and review of bolt behaviour under axial loading
15
Theory Description Shape Comments Reference
Suspension
The dead weight load of the strata transferred between the bolt head and the anchor.
The upper layer should be strong enough to anchre the bolts
Peng (1984) Stillborg (1986)
Beam
building
Bolts bind the strata layers together, which prevents or greatly reduce the movements. The frictional effect generated by bolt pretensioning increases the shear strength between the layers,
The tensile failure is prevented because of the increase in binding strength and stiffness effect However, failure may still occur by shearing at the two ends. Hence bolts a and b are most effective in this method.
Peng (1984) Panek (1956) Xiu (1997) Snyder (1983) Stillborg 1986)
Keying effect
When the roof strata are highly fractured and blocky, or planes of weakness intersect the immediate roof strata, keying effect roof support may be used. Roof bolting provides significant frictional forces along fractures, cracks, and weak planes
Confinement is provided by way of tensioned roof bolts, and then the strata material will be locked or keyed together.
Peng (1986)
Arching Action
The main aim of the arching theory is to increase the value of compressive stresses in the roof so that the tensile stress is ignored and the shear resistance increased. Arching provides very strong roof profile, which is one of the strongest roof profiles
To support the weakened zones between bolts, the use of wire mesh and shotcrete is recommended
Wagner (1997)
Table 2. 1 Bolt theories
a b
CHAPTER 2: Rock bolt system and review of bolt behaviour under axial loading
16
2.6. TYPE OF ROCK BOLTS
Rock bolts are classified into three main groups, according to their anchorage
systems Hoek and Wood, (1988) and Franklin and Dusseault (1989). Table 2.2
shows the types of rock bolts presented preliminary by Peng (1984). The first group
is the mechanically anchored rock bolts that can be anchored by a slit and wedge
mechanism or an expansion shell. The second group is the friction anchored rock
bolts, split set and swellex. The third group is the fully grouted rock bolts that can be
anchored by cement or resin. Table 2.2 and Table 2.3 show the different type of rock
bolts and their accessaries respectively.
CHAPTER 2: Rock bolt system and review of bolt behaviour under axial loading
17
Types of
bolts Types of anchor Applicability Capacity
(t) Advantages Disadvantages Typical diagram
Slot and wedge
Expansion shell Hard rock
Resin grout Universal
Point
anchored bolts
(tensioned
Combination anchor[NIA1] Most strata
10-16
• Inexpensive •Immediate support possible • High capacity in hard rocks.
• Limited to use in soft rock condition •Long-term stability is affected by slippage.
Cement
Injection
Cartridge
Most strata
Resin
Injection
Fully length grouted bolt
(untensioned)
Cartridge
All strata
Seedsman (2005)
15-25
-High corrosion resistance - Durable - Consistent. -Increased use recently specially for weak rocks
-Shrinkage of cement, longer setting time -Installation is time critical -Costlier than mechanical bolt.
Table 2.2 Descriptions of various boltsTable 2.2. Bolt types and description
CHAPTER 2: Rock bolt system and review of bolt behaviour under axial loading
18
Types of bolts
Types of anchor Applicability Capacity
(t) Advantages Disadvantages Typical diagram
Roof truss Expansion shell Adverse roof
Suitable at intersection and high pressure area
This Type of support should be used if bolt are not pretensioned
Flexible
Bulb
Grouted Cable
Heiten
Universal
Up to 50 ton
Same as grouted bolt -Capability up to 15 m
Special procedure has to apply for tensioning
Friction Split set Swellex
Weak to moderate strata
10-14
Cheap, Simple installation - Capability of large displacement -Reusable.
- Relatively expensive - Hole diameter is critical for installation -Not very corrosion resistive.
Threaded Fibre glass
Resin Anchor Weak to moderate strata
Up to33 ton
Does not prevent mucking up
Only drill bit rotary
Table 2.2 Continued
CHAPTER 2: Rock bolt system and review of bolt behaviour under axial loading
19
Types of bolts
Type of anchor
Applicability Capacity (t) Advantages Disadvantages Typical diagram
Helical rock bolt (Giralo
2005)
Fully grouted /
point anchored
Weak rock
0.92tone/in HRB can be implemented with any size, grade and length of bar
Needs modification to the bolter hydrulic system
Hilti onestep bolt
www.Hilti.com
Resin anchor
Weak to moderate
rocks
>20 t Faster bolt installation- increased working safety
Limitation of bolt length- Higher price compar
Cone bolt (Big Bell1999)
Resin anchor
Rock burst zone
Up to 20 t Easy to install- Effective even in high deformation
The preformance heavily dependes on grout specifications
Posimix 4 (Mikula 2004)
Resin anchor
Moderate strengths
Up to 12.5 t Constant annulus
-Spin torque for mixing resin is high -Spring can catch on mesh during insertion
Table 2.2 Continued Table 2.2 Continued
CHAPTER 2: Rock bolt system and review of bolt behaviour under axial loading
20
Accessories Usage Diagram Comments
Face plate To uniformly distribute the load at bolt
collar.
Used with all types of bolt.
Dome shape is the most
common.
Anti friction
washer
To reduce the friction between the nut
and faceplate.
Increases the torque-tension
ratio. Common for all bolt
types.
Nuts and
spherical
seats
To prevent the bolt from pulling and
applying pretension load
Common for all bolt types
W-strap Pulled into rock surface by the bolt to
conform major irregularities.
Provide a large surface
confinement to any loose rock
between bolts.
Wire mesh To prevent injury to personnel and
damage to equipment from small
pieces of rock or spalled flakes.
Used right up to the face to
avoid any accident at intervals
between 1 to 1.5 m.
welded Chainlink
Table 2.3. Bolt accessories
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
21
2.7. LOAD TRANSFER IN ROCK BOLTS
The performance of any reinforcement system is limited by the efficiency of load
transfer. Basically the load transfer process begins when the movement of a block of
rock reinforced has occurred. The concept of the load transfer is composed of three
basic mechanisms; Stille (1992) and Windsor (2004).
i. Rock movement, which requires load transfer from the unstable rock to the
reinforcing element.
ii. Transfer of load via reinforcing element from the unstable zone to a stable
zone.
iii. Transfer of the reinforcing element load to the stable rock mass.
There are a wide variety of methods by which the load transfer between the rock and
reinforcing element may be achieved and many reinforcing devices have been
developed.
Fabjanczyk and Tarrant (1992) identified load transfer as a mechanism by which
force is generated and sustained by a supporting tendon as a consequence of strata
deformation Windsor (1996, 97), Windsor and Thomson (1993, 1996) refined this
concept as the transfer of load from unstable rock within the reinforcement system to
stable rock. They classified the current reinforcement devices into three groups:
-Continuous mechanically coupled (CMC),
-Continuous frictionally coupled (CFC) and,
-Discretely mechanically or frictionally coupled”(DMFC).
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
22
2.7.1. Load Transfer Concept in Fully Grouted Rock Bolts
A fully grouted bolt is a passive roof support system, which is activated by the
movement of the surrounding rock. Fully grouted bolting system consists of three
components; the bolt, the grout, and the surrounding rock. The relationship between
these three is similar to continuous mechanically coupled bolt system (CMC) shown
in Figure 2.2. The efficiency of load transfer is affected by the type and the grout
properties (cementitious or resin), profile of the rock bolt (see Chapter Four), hole
and bolt diameter, anchorage length, rock material, confinement pressure, over/under
spinning and installation procedures. As Figure 2.3 shows, the fully grouted bolt
provides greater shear surface for the transmission of the load from the rock to the
bolt and visa versa (Snyder 1983). The main utility of the grout is to supply a
mechanism for the load transfer between the rock and the reinforcing element. The
redistribution of forces along the bolt is the result of movement in the rock mass,
when the movements occur, the load is transferred to the bolt via shear resistance in
the grout. This resistance could be the result of adhesion and /or mechanical
interlocking.
Figure 2. 2. Continuous mechanically coupled rock bolt
Section C-C Rock
Bolt GGrout
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
23
Figure 2.3. Load transfer in fully grouted rock bolts
Adhesion is the actual bonding between the grout, the steel and the rock, and the
mechanical interlocking is a keying effect created when grout fills irregularities
between bolt and the rock. It is practically recommended use of 25 % to 30 % more
resin than the theoretical annulus volume (Aziz et al. 1992).
The bolt will help to prevent failure of the weak zone if there is sufficient anchorage
length and if failure does not occur in one of the component (grout or bolt) when the
load develops in the bolt. Stress concentration is induced between the hole wall
roughness and the bolt surface profile. This localized stress concentration could go
over the strength of the grout and rock, resulting in localized crushing that allows
additional deformation in the steel.
Singer (1990) demonstrated that there is no adhesion between the grout-bolt and
grout-rock interface. However, in most cases, which have been reported, there is very
little adhesion between grout/rock and grout/bolt, Aziz and Webb (2003). In general,
only resinous grouts can meet the high strength requirements for short anchorages.
The grouted bolt has an advantage which is greater load transfer compared with the
expansion shell or wedge type bolt anchorages. This may be essential in weaker rock
strata where transfer of high loads over a short length of borehole may commence
failure at the rock interface.
Stable area Join Unstable area
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
24
Serbousek and Singer, (1987) found that the rate of load transfer from the bolt to the
rock exponentially is decayed. This exponentially reduction in load transfer is
dependent upon the material properties of the bar, the grout, and the rock interfaces.
Figure 2.4 shows the rate of load transfer along the bolt. Based on several pull out
tests they found the load transfer between the bolt, grout and rock is controlled by
mechanical interlocking. The significant tests, which were carried out in the current
research in both pull and push tests showed that mechanical interlocking and bolt
profile configuration play a great role on load transfer mechanism, is discussed in
Chapter Four.
Figure 2.4 Rate of load transfer along the fully grouted rock bolts
2.8. SELECTION OF FULLY GROUTED BOLTS
Carr (1971), Parker (1973), Reed (1974), Gerdeen et al (1977), Wittaker and grant
(1980), Dight (1982), Snyder (1983), Maleki (1992), Gray and et al (1998) Siab
0
2
4
6
8
10
12
14
0 10 20 30 40 50
Distance from bolt head
Load
(K
ips)
Resin grout
Gypsum grout
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
25
(2001) and Yassein et al. (2002) found that fully grouted bolts were much more
successful in supporting roof strata than mechanically anchored bolts. The reason
behind is following advantages.
1- Fully grouted bolt can create a full contact with the surrounding rock and
because of high stiffness is able to increase the rock stiffness by joining the
roof layers together and also reducing the roof sagging.
2- The fully grouted bolts are loaded as long as the surrounding rock deformation
is continuing.
3- It has capability to sustain high peak load (see Figure 2.6).
4- Fully grouted bolt can provide greater support to the rock mass than point
Anchored Bolts even with the same steel strength (Gray et al. 1998).
5- They can produce the higher degree of load transfer in comparison to the other
types of bolts (Whitaker 1998).
6- Fully grouted rock bolts can be about 5 times more effective than mechanical
bolts in reduction of roof beam deflection, when the roof is suspended from
component rock. (Gerdeen et al 1977).
7- The axial stiffness for fully grouted bolts is 10-20 times larger than for
mechanical bolts (Gerdeen et al 1977).
8- Resin grouted bolts does not fail suddenly. They undergo at least 100 mm of
movement prior to failure (Harrison 1987).
9- Fully grouted bolts are more effective than mechanical bolts in ground control
in thinly layered deposit (Snyder 1983).
10- Fully grouted bolts can be used on or close to the face for normal tunnel
blasting without any damaging effect on the functioning of the rock bolt (Stjern
and Myrvang 1998).
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
26
2.8.1. Fully Grouted Bolt Failure
Various types of axial failure can occur when using grouted bolts. Failure can take
place in one or more of the following modes. This was considered by Littlejohn
(1993) as well.
-The bolt,
-The grout,
-The rock,
-The bolt-grout interface or
-Grout rock interface.
The type of axial failure depends on the properties of individual elements. The steel
bar governs the axial behaviour of the bolt, which is much stiffer and stronger than
the grout and rock. If the bolt has sufficient length to transfer the entire bolt load to
the rock, then the bolt will fail if the ultimate strength of the bolt is less than what is
necessary to support. The maximum capacity of the steel depends upon the bolt
diameter and steel grade. It should be noted that it might be failure in the steel bolt
occurs under the shear load. The shear failure happens if a section along the bolt is
subjected to a shear load, which exceeds its shear strength. The shear stress at the
bolt-grout interface is greater than the shear stress at the grout-rock interface; it is
because of the smaller effective area. It can be understood that if the grout and rock
have similar strengths and if the required anchorage length is inadequate, then failure
could occur at the bolt-grout interface. If the surrounding rock is softer, then the
failure could happen at the grout –rock interface.
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
27
2.8.2. Load Transfer Measurement
In a fully grouted rock bolts, the load transfer mechanism is dependent on the shear
stress continued on the bolt/resin and resin/rock interfaces. The peak shear stress
capability of the interfaces and the rate of shear stress generation determine the
reaction of the bolt to the strata behaviour. Load transfer is determined by
measurement of the peak shear stress capacity and system stiffness.
Figure 2. 5 The mechanism of the load transfer
Fabjanczyk and Tarrant (1992) conducted several pull tests and evaluated the rate of
load transfer. They pointed out that the most important aspect of good load transfer is
the utilisation of the full load capacity of the bolt and they also indicated that the load
build up was a function of displacement.
Stillborg (1994) carried out a number of tests on different kinds of rock bolts
installed across a simulated joint using two blocks of high strength reinforced
concrete (Figure 2.6). It significantly reveals that the rate of load transfer in resin
grouted rock bolt is higher than other kinds of bolts.
Rock •
Grout
• • •
•
• • • •
• • •
• •
•
• • •
• •
• •
• •
•
• •
•
•
• •
•
•
• • •
• •
• •
• •
•
• •
•
• • • •
•
• • •
• • • • •
• •
•
• • •
• • •
•
• •
Bolt
load
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
28
Figure 2.6. Load deformation results in different bolts (Stillborg 1994)
2.9. EFFECT OF BOLT IN CONTINUUM MEDIUM
Not only the shear resistance parameters in jointy rock can increase by fully grouted
rock bolts but also the mechanical properties of the medium (deformation modulus,
strength, etc.) can be improved by rock bolt reinforcements. Basically the main effect
of roof bolting is in post failure properties of materials. When the bolts are installed,
the bolt behaviour depends upon the axial and shear stiffness (Brian and Chappel
Loa
d (T
on)
Resin grouted 22 mm diameter fiberglass rod
Cement grouted 20 mm diameter steel rebar
Resin grouted 20 mm diameter steel rebar
EXL Swellex dowel
Expansion shell anchored 17.3 mm diameter steel rock bolt
Type SS 39 split set stabilizer
To 150 mm
To 150 mm
Deformation (mm)
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
29
1989), which is varied in different surrounding situations and reinforming bar
characteristics.
2.10. THE EFFECT OF BOLT ON DISCONTINUITY
Rock bolts are basically installed to prevent the movement of discontinuity planes.
The effectiveness of the bolt reinforcement is dependent upon the direction of
installation and the nature of discontinuity surface. Rock bolts can provide a tensile
effect to transfer the load from one side to another when movement takes place with
separation. Also, bolts contribute to shear strength because of the increasing
frictional effect thus creating high tensile resistance to the discontinuity layers.
Peng (1984) investigated the reinforcing effect of keying in underground
excavations. The orientation of the bolts installed in relation to the fracture plane is
illustrated in Figure 2.7. The following relationships were established for bolting at
(a) normal to fracture plane and (b) normal to the roofline of a rectangular
underground headings.
Incline bolt (2.5)
Perpendicular bolt (2.6)
where;
pσ = Horizontal stress;
β =Angle between the normal to the fracture plane and the horizontal plane;
ϕ = Friction angle of the fracture.
ϕβϕβϕββσ
σtagtag
tagpb )sin(cos
)cos(sin
+−
=
ϕϕβββσ
σtag
tagpb
)coscos(sin 2−=
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
30
a: perpendicular
b: incline
Figure 2.7. Bolt installation to the joint a: perpendicular, b: incline (After Obert and Duvall 1967) Peng clearly related the relationship between the fracture and roof line with
horizontal stress and coefficient of friction in the case (a) suggesting that for
effective bolting (sp) must be very small and that β >ϕ . However, the stability
conditions for (b) is obtainable when the bolt is installed perpendicular to the roof
line prescribed by Figure 2.7 b. and that (sp) is small
βσσ 2cospb +
ββσ cossinp
β pσpσ
bσ
bσ
Joint
Roof
βσσ 2cospb +
bσ
βσβσ 22 cossin pb +
β
ββσσ cossin)( pb −pσ pσ
bσ
Roof
Joint
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
31
2.11. SUMMARY
Rock bolts by increasing frictional effects through the fractures and discontinuities
can provide high shear strength. Bolt pretensioning is one of main factor to increase
friction effect, and reducing the tensile stress within the layers below the tensile
strength of the rock. It makes all the layers more together. Primarily the shear
resistance at the bolt/grout or grout/rock interfaces provides the bearing capacity of
the fully grouted rock bolts. The efficiency of the grouted bolts depends upon the
shear strength of the bolt/grout interface and the grout/rock interface and different
bolt types in terms of profile characteristics.
The performance of any reinforcement system is limited by the efficiency of the load
transfer. Basically load transfer process initiates when the block movement of a rock
reinforced is occurred. The result of movement in the rock causes the forces to
redistribute along the bolt. Load is transferred to the bolt via shear resistance in the
grout. And this resistance could be the result of adhesion and /or mechanical
interlocking. Mechanical interlocking is a keying effect created when grout fills
irregularities between bolt and the rock. Stress concentration induces between the
hole roughness and the rolled ribs of the steel. Valuable research has been reported
that the rate of load transfer from the bolt to the rock is similar an exponential decay
curve and is dependent upon the material properties of the bar, the grout, the rock
and interfaces.
From the significant investigations which are mentioned above, it was found that
fully grouted bolts were much more successful in supporting roof strata than other
types of bolts. So for those mentioned advantages, the fully grouted bolts were only
selected bolts to evaluate the load transfer mechanism and affecting parameters on it.
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
32
2.12. REVIEW OF FAILURE MECHANISM OF BOLT RESIN
INTERFACE SUBJECTED TO THE AXIAL LOAD
Most rock masses include natural discontinuities, which may cause stability
problems, therefore most underground openings need to be stabilized to protect their
integrity during their service life.
Laboratory and field studies are the common methods used to study the bonding
strength, the bearing capacity of rock bolts and the load and hence the load transfer
characteristics of bolts. Often these tests overlook the role of the bolt profiles and
hence they are neglected from any analysis.
2.12.1. Theoretical behaviour of the bolt under axial load
The behaviour of fully grouted bolt has been investigated experimentally,
numerically and theoretically by several researches. When modelling a one
dimensional resin grouted anchor, Farmer (1975) proposed a theoretical solution to a
circular elastic anchor surrounded by an elastic grout confined by a rigid borehole.
He derived a homogeneous linear differential equation describing the distribution of
force along the anchor. His solution predicted that the axial stress of the bolt and
shear stress of the interface decreases exponentially from the point of loading to the
far end of the bolt before decoupling occurs. The shear stress in resin annulus was a
function of the grout as:
gx
x GaR )( −
=ξτ When R-a < a (3.1)
gx
x G
aR
a ln
ξτ = When R-a > a (3.2)
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
33
where;
xτ = shear stress in resin annulus
xξ = extension in the bolt
a = radius of bolt
x = distance along the length of bolt starting at free end of grout
R = radius of the borehole
Gg = shear modulus of grout
Figure 2.8 shows a sketch of the stress situation around a bolt when the bolt is loaded
axially. An approximate indication of the shear distribution along a typical resin
anchor was given by the following equation and is shown in Figure 2.9.
)2.0(exp1.00 a
xx −=στ
(3.3)
where;
0σ = Axial stress at the free end = 0 stress on bolt at x = 0,
To compare theoretical results, Farmer carried out a series pull tests in concrete,
limestone and chalk. The results showed good correlation for low axial loads in
concrete, but were different in weaker limestone and chalk. These discrepancies were
attributed to the lack of a model to account for the effect of slip at the bolt-grout
interface. The anchors in concrete closely simulated the assumed theoretical
conditions of the rigid rock boundary, and the stress distribution along the bolt was
variable as the maximum stress values were at the free end of the bolt as in Figure
2.9.
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
34
Figure 2. 8. Stress situation in a grouted anchor (after Farmer, 1975)
Figure 2. 9. Theoretical stress distribution along a resin anchor in a rigid hole with thin resin annulus (after Farmer 1975)
0στ
ax
e2.0
0
1.0−
=στ
ax
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
35
Figure 2.10 shows the load displacement, strain distribution, and computed shear
stress distribution curves in concrete.
Figure 2. 10. Load displacement, strain distribution, and computed shear stress distribution curves in concrete, a) strain distribution at the specified anchor load, b) theoretical shear-stress distribution curves. (After Farmer 1975)
The only limitation of the Farmer’s theory was the elastic behaviour assumption of
the system, which is not the case in real in-situ situation.
A more realistic analytical treatment of Farmer’s work was presented by Aydan et al
(1985). An idealized elastic-softening plastic behaviour was adopted for the anchor /
grout interface, and the analytical solution by the differential equation for the load-
displacement curve was found to be in closed agreement with the finite element
(a)
Shea
r str
ess
(kN
/m^2
)
Str
ain
()
L
oad
(kN
)
Distance along rod, x (mm)
(a)
(b)
Distance along rod, x (mm)
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
36
results obtained by Hollingshead (1971). In a further development Aydan (1989)
dropped the assumption of an elastic bolt by assuming a bi-linear elasto-plastic
behaviour for the bolt and elastic –softening-residual plastic behaviour for both the
grout and the rock. Indraranta and Kaiser (1990 a,b) described an analytical
approach to model a reinforced circular tunnel in a homogeneous, isotropic medium
with fully grouted bolts. Using the theory of elasto-plasticity, the equivalent material
properties for supported ground were calculated and the effect of bolt density on the
stress and displacement field near the opening was determined.
Xueyi (1983) expressed a simple theoretical model to predict stress distribution along
the bolt based on field studies in yielding rocks. The concept of neutral point was
subsequently introduced. The shear stress distribution is characterized by the division
of the bolt into a pick-up length and an anchor length on either side of the neutral
point. Neutral point is the point where there is zero relative displacement between the
bolt and the rock, in this situation a positive frictional force, generates between rock
and bolt interface towards the rock and a negative frictional force forms from the
rock to the bolt due to the rock deformation. He derived the equation 3.4 for the
shear stress distribution. It should be noted that bolts in situ have both a pick up
length and an anchor length, which bolts in pull out test have only anchor length, and
it is expected that the axial load distribution in two cases will produce different
results.
))(()( uxwxukx +−=τ (3.4)
where;
xτ = Shear stress distribution along the bolt
k = Long term shear deformation modulus of rock (kg/cm^3)
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
37
)(xw = Expression for bolt displacement (cm)
)(xu = Bolt displacement due to strain (cm)
u = Neutral point displacement (cm)
Yu and Xian (1983) investigated the location of the neutral point along the bolt by the
equilibrium equation 3.5. They supposed that the model of the shear and axial stress
distribution along the bolt behaves according to Figure 2.11.
(3.5)
Where;
P = Radial distance to the neutral point and
a = Tunnel radius
Figure 2. 11. Stress distribution model for grouted bolt (after Yu and Xian, 1983)
)](1ln[al
lp
+=
Shear stress Axial stress Tunnel
Neutral point
Pick -up length
Anchor length
Dep
th
Dep
th
aLaL
pln)ln( −+
=P
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
38
Following Hyett and et al. (1996), Li and Stillborg (1999) developed an analytical
model for predicting the behaviour of rock bolts under three different conditions; a)
for bolts subjected to a concentrated pull load in pull out tests, b) for bolts installed in
a uniformly deformed rock massed and c) for bolts subjected to the opening of
individual rock joints.
The development of these models was based on the description of the mechanical
coupling at the interface between the bolt and the grout medium for the grouted tests
or between the bolt and the rock for frictionally coupled tests as shown in Figure
2.12. The shear stress along the bolt, at two levels of applied load, was given by
Equation (3.6).
(3.6)
where;
A = Bolt cross section area
d = Bolt diameter
bσ = Applied stress
bτ = Shear stress at interface
b = Shear length
Figure 2. 12. Stress Component in a small section of a bolt (after Stillberg & Li, 1999)
Li and Stillborg suggested that for bolts in pull out tests, the shear stress of the
interface attenuates exponentially with increasing distance from the point of loading
when the deformation is compatible across the interface. Decoupling was found to
start at the loading point when the applied load was large enough, and then
dxd
dbA b
b
σπ
τ .−=
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
39
propagated towards the far end of the bolt with an increase in the applied load. The
section of the bolt close to the loading point was completely decoupled with a zero
shear stress at the bolt interface. Figures 2.13 and 2.14 show the shear stress
distribution before and after decoupling respectively. The magnitude of the shear
stress on the decoupled bolt section depended on the decoupling mechanism at the
interface and the shear stress attenuated exponentially towards the far end of the bolt.
The shear stress at the decoupled interface is lower than the ultimate shear strength
of the interface. The calculated results showed that the decoupled length of the bolt
was shorter with a face plate than without a face plate, and the axial stress in the
decoupled section is larger for the bolt with a face plate than the bolt without a face
plate. This means that rock bolts with a faceplate have better reinforcement effect
than those without a faceplate. The shear stress between the bolt grout interface is
exponentially reduced from outside end of the bolt towards the inner end. However,
Li and Stillborg, did not specify the bolt decoupled length. This is the subject of
further research discussion to be reported in the thesis.
Figure 2. 13. Shear stress along a fully coupled rock bolt subjected to an axial load before decoupling
Shea
r str
ess
)(xbτ
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
40
Figure 2. 14. Distribution of shear stress along a fully grouted rock bolt subjected to an axial load in coupled rock bolt
2.12.2. Experimental behaviour of the bolt under axial load
Various experimental studies have been carried out to examine various parameters
influencing the effective load transfer characteristics of bolt installations. These
studies include the works of Pells (1974), Farmer (1975), Serbousek and Singer,
(1987), Aydan (1989), Singer (1990), Fabyznchic et al. (1992, 1998), Hyett et al.
(1992), Skybey (1992), Ebisu et al (1993), `Gray et al. (1998), Thompson and Finn
(2001), Kilic and et al. (2002, 2003), Aziz (2003), Hagan (2003, 2004), Compton and
Oyler (2005) and Campbell and Mould (2005). The push and pull tests can be
informative to understand the effect of various parameters on the mechanical
behaviour of the bolt system, but they are not suitable to determine the material
behaviour for the evaluation of the mechanical performance of rock bolts under
various state of stress. The push and pull methods are considered the acceptable
methods to investigate the bolt/grout/rock interaction under axial loading. A great
S
hear
str
ess
rb s=τ
0=bτ
pb s=τ
)(xbτ
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
41
deal of experimental studies was carried out in order to describe the bolt/grout/rock
interaction under axial loading conditions. A summary of the various research works
is as follows:
Serbousek and Singer, (1987) conducted a series of experimental pull tests in grouted
rock bolts and compared the results with analytical and numerical modelling, their
tests were conducted on 1.2 m (4. 2ft) and 0.3 m (1 ft) bolts in holes of 25.4 mm,
44.4 mm dimeters. In their tests the applied load was limited to the elastic response
of the system so that failures did not occur and examination of resin bond showed no
chemical adhesion of the grout. Basically, as movement takes place, the irregularities
on the surface of the bolt and the hole cause mechanical interlock and the interlock
will cause shear resistance to be transferred from one medium to another until the
maximum shear strength is reached. The experimental results showed that hole size
and grout type did not have a large influence on the elastic-load transfer rates. This
result was not in agreement with the results reported by Fabyznchic et al (1998), Aziz
(2004), and in the results reported in this
thesis discussed in Chapter 4. Serbousek and Singer also proposed an analytical
model (Equation 3.7), which had various restrictions that were unrealistic. They
considered the existence of the complete bonding between the bolt /grout and grout
/rock interfaces, rock deformation was zero and also the elastic deformation takes
place both in the bolt and in the grout. However, numerical simulation and laboratory
tests in this thesis have shown that grout being crushed in bolt elastic region and
experiences non-linear situation. Besides, in the complete bonding, bolt and grout
move equally, which is not real case.
(3.7) lEdb
pyy ee ∆
−− == 2
4
00πα σσσ
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
42
where;
σ = Stress in the bolt at a distance y, psi
0σ = Stress at the point of applied force, psi
α = Decay coefficient 1/in which depends on the stiffness of the system
y = Distance along the bolt from the applied load, in
p = Load applied at the bolthead, lb
E = The modulus of the bolt
Db = The dimeter of the bolt
∆ l = The deflection at the head of the bolt, in.
The schematic diagram of the bolt, grout, and rock with above variables is shown
in Figure 2.15. Serbousek and Singer proposed an additional numerical model to
evaluate the load transfer of fully grouted bolt.
Figure 2. 15. Variables used in closed-form solution (after Serbousek and Singer 1987)
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
43
The model was based on linear elastic behaviour, which is not the realistic case of
actual behaviour in particular for the grout interface, follows the non-linear
behaviour.
Kilic and et al. (2002, 2003) carried out a direct pull out test using different types of
rock bolts having different shapes of lugs. The bolts used were single, double and
triple conical lugged (Figure 2.16). They found, there was the influence of bolt shape
on the load bearing capacity and deformational behaviour of bolts. In addition, the
yield load in single and triple conical lugs was lowest and highest value respectively.
In all the cases in single and double conical, failure occurred in grout column and in
some cases in triple conical, failure occurred in the steel bolt. This meant the number
of lugs had some bearing on the load bearing capacity of rock bolts.
a) Single conical lugged bolt b) double conical lugged bolt
Figure 2. 16. Schematic illustration of different conical lugged bolts: (a) Single, (b) Double and (c) Triple c) Triple conical lugged bolt
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
44
Also, it was found that both the bolt length and diameter increased the bearing
capacity of the bolt. However, this increase is limited to the ultimate tensile strength
of the bolt materials.
2.12.3. Bolt –grout-rock interface mechanism
Aydan (1989) carried out a series of push and pull out test to investigate the
anchorage mechanism of the grouted rock bolts and the effect of various parameters
such as bolt / borehole dimeter ratio and bolt/grout interface behaviour under triaxial
stress state. Two types of steel bars 13mm and 19 mm in diameter were tested.
The test results showed that the load bearing capacity of rock bolts was 25% higher
in the case of push-out tests than those in the case of pull out test. This increase in
push test values was attributed to the poison ratio effect (The radial stress is of
compressive character in the push out case while it tends to become tensile in the
case of pull out tests). His investigation showed that the increase of the bearing
capacity was attributable to the normal stress of compressive character resulting from
the geometric dilatancy of the bolt surface. Aydan suggested that shearing might
occur along one of the surface of weakness in the rock bolt system (grout-rock
interface and bolt –grout interface), and classified the failure modes in push/pull test
as follows:
1. Failure along the bolt –grout interface: This type of failure was observed in
all tests on steel bars with a smooth surface and in the case of deformed
bars installed in large borehole.
2. Failure along the grout –rock interface: This type of failure was observed in
the case of deformed bars only installed in smaller dimeter boreholes.
3. Failure by splitting of grout and rock annulus
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
45
Aydan observed that although shearing failure along one of the interfaces was the
main cause of failure, some samples were found to have failed by splitting without
confining pressure. This was attributed to geometrical dilatancy of the bolt-grout
interface during shearing which causes an internal pressure on the borehole.
The geometrical dilatancy of the surface is probably one of the most important
parameters in determining overall load bearing capacity. However, bolt profile
configurations, which affect severely the load transfer mechanism and interlocking
effect, was not substantiated by the Aydan’s tests. Further tests by Aydan included
the study of the least shear resistance, which was reported by the grout-smooth steel
interface followed in grout-rock interface and the largest shear resistance offered by
the grout steel interface of ribbed type corresponding to 19 mm ribbed bolt surface
(Figure 2.17).
It should be noted that the axial failure in the steel bar might occur if the axial load
exceeds the ultimate capacity of the steel bar. However, in short encapsulation tests
failure usually happens from the interfaces. In addition to this the failure mechanism
of fully grouted bolt depends on the grout-rock-bolt interface, which are affected by
various parameters including; contact interface stiffness, the nature of the bond
between interfaces, cohesion and angle of friction of interfaces and shear strength of
the interfaces. In numerical design method all of these parameters, are evaluated
which are ignored in previous works. Aydan’s tests were conducted under the
constant normal load condition (CNL) but in reality when shearing surface is smooth
enough or insignificant dilation then the testing under CNL condition is adequate to
evaluate the shear behaviour, for Non planar discontinuities shearing often results in
dilation as one asperity rides over another. So a realistic outcome of such study was
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
46
considered possible if the tests were conducted under constant normal stiffness
(CNS) condition (Figures 2.18).
Figure 2. 17. Shear stress versus shear displacement in bolt /grout interface at different bolt diameter (after Aydan 1989)
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
47
No dilation Dilation
Smooth surface Rough Surface
Figure 2. 18. Dilation behaviour of joint plane a) two smooth plane, b) bolt and resin interface. Singer (1990) conducted a series of field pull tests to investigate the transfer of
applied load from the bolthead to the rock. Figure 2.19 shows the pull test gear
arrangement force, which was applied to the head of the bolt by a hydraulic ram.
When the load was applied to the system, the bolthead would deflect. These
deflections were measured at the end of the pull gear by a dial gauge. Increasing the
pull load resulted in higher stiffness, indicating that the effectiveness of the
Joint plane
Bolt
= Rock and bolt stiffness = Joint dilation
Behaviour of bolted joint under constant normal stiffness
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
48
mechanical interlock among the bolt/grout and the rock mass and the primary
mechanism for transference of load.
Figure 2. 19. Pull test gear arrangement (after Singer 1990) Singer also carried out a series of laboratory tests over a series of bolts and his results
indicated that 0.56 m (22 in) of bolt length was required to transfer 90% of the load
from the bolt to the rock .He used polyester resin and gypsum grout with a 19mm
bolt and 25.4 mm hole dimeter. Figure 2.20 shows a comparison of load distribution
in different methods along the length of the bolt. Results showed that the load
applied during a standard pull test is dissipated into the rock with, 0.61m of the bolt
head, however the anchorage at the end of the bolt, which is critical for proper
support was not tested, and that it is difficult to evaluate properly the capacity of the
grouted bolt by the pull test. Furthermore the results showed that if there is sufficient
length of the bolt past the yield zone, then the load will transfer from the bolt to the
Pressure gauge
Hydraulic jack Pressure transducers
Crow’s foot
Strain gauge lead wires
Deflection gauge Adjusting nut Hydraulic ram
Pull cellar Grouted bolt
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
49
rock. This means that the grouted bolt can still be an effective support past the yield
point of the steel.
Figure 2.20. Comparison of load distribution along the bolt length
2.12.4. Load transfer mechanism
Yazici and Kaiser (1992) conducted studies on the bond strength of a conceptual
model for fully grouted cable bolts called bond strength model (BSM). According to
their theory, the bond strength of bolts depended upon the pressure at the bolt-grout
interface. The increased pressure at the interface was a function of the grout dilation
or radial movement, which was caused by the rough surfaces of the cable bolt. The
bolt surface was assumed to be zigzag in shape as shown in Figure 2.21. The bond
strength was expressed in terms of friction and dilation angle:
Distance from bolt head (in)
Bol
t loa
d (1
0^3
Ib)
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
50
])(1[lim
0 ϕσσστ β +−= itag (3.8)
where;
i = Apparent dilation angle
β = Reduction coefficient of dilation angle
limσ = Limiting stress
ϕ = Friction angle between the bolt and grout
Consequently, the ultimate bond strength at the bolt-grout interface was limited by
the grout strength, for a rough bolt. The bond strength significantly increases when
the pressure on the bolt /grout interface builds up due to dilation created as the rough
edges of the bolt push the grout laterally against the confining rock. The theory of
Yazicic and Kaiser was not valid for bolts with different surface geometry. They
assumed only zigzag surface for bolt.
Figure 2. 21. Schematic diagram reflecting the geometry of a rough bolt (after Yazici and Kaiser, 1992)
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
51
Skybey (1992) evaluated the load transfer mechanism between bolt/resin/rock with
sky bolt concept. This bolt concept was point anchored with resin in large diameter
holes of 38 mm and 45 mm. He carried out pull out tests and obtained, the load
transfer mechanism values, which maximised the loading capacity of the resin from 6
kN/mm to 12 KN/mm.
Fabjanczyk and Tarrant (1992) investigated the load transfer mechanism in pull and
push out tests. They found that smooth and lower profiled bolts had minimum
stiffness (Figure 2.22). It was found that the load transfer was the function of various
parameters such as, hole geometry, resin properties and bar surface configurations. In
addition, it showed the role of confinement generated within the annulus as being
critical to the load transfer performance. However, they neglected the effect of bolt
rib spacing, which significantly affects the load transfer capacity of the bolt system.
Peng and Guo (1992) reported from the filed study that debonding occurred between
the resin annulus and wall rock.
Figure 2. 22. Load/displacement curves for rebar with various amounts of bar deformation removed (after Fabjanczyk and et al, 1992)
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
52
It should be noted that in the field situation, if failure doesn’t happen in steel bolt, it
is likely that it will occur in the resin grout and wall rock as the bolt profile creates
higher level of interlocking. This is supported by the experimental test observations,
which is discussed later in the thesis (Chapter 4).
Benmokrane et al (1996) carried out a series of laboratory short encapsulation pull
tests. They used six types of cement-based grouts and two types of rock anchors. The
following empirical equation was derived for the estimation of anchor pull out
resistance for the embedment length.
(3.9)
where;
P = ultimate pull out load
l∆ = anchorage length
d = dimeter of anchor and a, b = constants, depends on grout and anchor type.
Benmokrane et al stated that the bond strength from the laboratory tests was higher
than that from the field study.
From the tests it was investigated that the slip at the unload end began at near 80% of
the failure load and also they proposed an analytical model for the bond -stress -slip
relationship for the threaded bars and the standard cables.
tsk += .τ (3.10)
where;
τ = Shear bond stress at anchor grout interface
s = Slip between anchorage and grout
k,t = Coefficients which depend on the type of anchor, grout and stages of shear.
dl
bap∆+=
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
53
Mark et al (2002) conducted a series of pull tests on fully grouted rock bolts. They
found that short encapsulation pull testing (SEPT)(the international consensus seems
to be that at least 0.3m of the bolt should be grouted to minimize the effect of the
zones of poor mixing at the top and the bottom of the resin) could be used to make a
simple evaluation of resin bolt anchorage. They proposed that poor anchorage could
be an issue, particularly where the roof rock is very weak. In their results they
expressed when anchorage is poor, roof movements near the top of bolt, within the
anchorage zone, can pull the bolt out of the upper portion of the hole at loads less
than the yield strength of the rod. It was supposed that the two most likely causes of
poor anchorage are weak rock and poor installation quality. They found that if short
encapsulation tests have confirmed that the anchorage is poor, the following steps
could improve it:
1. Check the quality of the installation (such as grout-hole-bolt),
2. Reduce the hole annulus, as most of the tests have found that the optimum
difference between the diameter of the bolt and the diameter of the hole is
no greater than 6.35mm, giving an anulus of about 3.17mm,
3. In very serious condition, the only way to increase the anchorage strength
would be to increase both the hole dimeter and the bar dimeter. This
enlarges the area of the grout-rock contact surface that increases the total
shear resistance.
2.12.5. Conclusion
From the numerous research studies undertaken around the world in pull and push
tests, it is concluded that the bolt interacts with the host rocks via shear stresses at the
contact interfaces between them. Accordingly, shear resistance of the interfaces have
Chapter 3: Rock bolt system and review of bolt behaviour under axial loading
54
to be strong enough to transfer the load from the bolt to the rock. This is affected by
several parameters such as resin annulus, grout strength, bolt profile characteristics,
rock roughness, rock strength and mechanical properties of the steel bolt.
There is a lack of significant research in terms of bolt profile specification, and load
transfer capacity in different profiles. This is an important parameter, which requires
further research, and therefore it forms a significant part of the research study carried
out by this study, which will be discussed in the later chapters.
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
55
CHAPTER THREE
REVIEW OF SHEAR BEHAVIOUR OF BOLTS AND
MECHANICAL PROPERTIES OF THE MATERIAL
USED
3.1. INTRODUCTION
Rock bolts are main elements of support in the modern stabilization techniques for
geotechnical engineering. Generally bolts work as an additional resistance against the
shear failure along joints and weakness planes. The steel bar within the rock bolt
system is the main element to resist to both the axial load under suspension
conditions and transverse the shear loads due to beam bending and slip on joints. The
axial force in the bolt is made of two components; the perpendicular component to
the shear joint, contributes to the frictional strength and the other component, parallel
to shear joint plane in the shear direction, which contributes to the dowel effect.
When rock bolts are used to support rock slope and underground excavations, they
are affected by both the axial and shear loadings during any movement on the blocks
(Figure 3.1). The bolt behaviour under both loads and how the load is transferred
along the bolt length is significantly important. These are discussed in this chapter.
This chapter consists of two main parts; First part explains a summary of significant
studies undertaken by various workers on shear behaviour and second part describes
the conducted laboratory tests to define the material properties used in the next
chapters.
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
56
Figure 3.1. Stability issues in rock mass reinforced by fully grouted bolts
These studies were first initiated by Dulascka (1972), she was then followed by
Bjurstrom (1974), Haas (1976,1981), Azuar (1977,79), Hibin and Motojim (1981),
Egger and Fernands (1983) and Ludvig (1983), Gerard (1983), Dight (1983),
Bjornfot & Stephansson (1984), Larsson (1984), Schubert (1984), Lorig (1985),
Yoshinaka et al. (1987) Spang and Egger, (1990), Stillberg (1991), Holmberg
(1991), Egger and Zabuski (1991), Ferrero (1995), Pellet and Boulon (1995), Pellet
et al. (1995, 1996), Goris et al. (1996), Grasselli et al (1999), Grasselli (2005) and
Mahoni (2005) worked on the mechanical behaviour of rock bolts. All experimental
testing of grouted bolts were performed as a single shear test using single shear
apparatus, which results difficulties in the shear joint due to non-equilibrium
situation and un-uniformity distributed load on the shear joint. None of works
included applying tensile loads on the bolt. However, in several studies, only
confining pressure on the moving block was applied. Thus, new method is designed
in present research to evaluate the bolt bending behaviour in proper manner, which is
discussed later.
Tunnel axis
Rock Joint
Bolt
• •
• •
• •
Ground surface
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
57
3.2. DESCRIPTION OF PAST RESEARCHES
Dulascka (1972) established the following expression to find the shear force carried
by bolt, based on idealised stress distribution at the bolt contact. Her theory was
based on the development of a plastic hinge at the point of maximum moment given
by;
(3.1)
where;
T = Shear force carried by bolt
cσ = Uniaxial compressive strength of rock
bD = Bolt diameter
yσ = Yield stress of bolt
β = Angle between bolt and normal to the joint
The crushing strength of the concrete was at least four times greater than the
compressive strength of the concrete. As shown in Figure 3.2 there is no static
equilibrium condition in both sides of the shear joint, which is the limitation of the
system.
Bjurstrom (1974) direct shear test on cement-grouted bolts in granite blocks was
aimed to evaluate the influence of various factors affecting the shear strength of rock
joints. The bolts had inclinations of between 30o-90o with respect to the joint surface.
He found that, for angle <40o bolts failed in tension and for angles >40o the bolts
failed in a combination of both shear and tension.
]1)sin03.0
(1[2.0 22 −+=
βσσσ
y
cybDT
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
58
Figure 3. 2. The shear test arrangement in (a) and (b) probable load generation (after Dulasck 1972)
Bjurstrom provided an analytical solution based on the equilibrium of the forces
acting on the system and expressed that the total shear strength of a bolt reinforced
joint was dependent on the following three parameters:
i) Shear resistance due to reinforcement effect:
)sin(cos ϕββ tagpTb += (3.2)
where;
bT = The reinforcement effect in shear resistance due to bolting
p = Axial load corresponding to the yield strength due to shear displacement
= Initial angle between bolt and joint direction
= The friction angle of the joint
(a) (b)
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
59
ii) Shear resistance due to the dowel effect:
5.02 )(67.0 cybd dT σσ= (3.3)
where;
bd = Bolt diameter
yσ = Bolt yield strength
cσ = Uniaxial compression strength of the rock
iii) Shear resistance due to friction of joint:
jnjf tagAT ϕσ= (3.4)
where;
jA = Joint area
nσ = Normal stress on joint and
jϕ = Joint friction angle
Figure 3. 3. Components of shear resistance offered by a bolt (after Bjurstrom, 1974)
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
60
According to Bjurstrom, the total contribution from the bolt to the shear strength of
the joint, shown in Figure 3.3, is given as:
5.02 )(67.0)sin(cos cybt DtagpT σσϕββ ++= + jnj tagA ϕσ (3.5)
Bjurstrom’s estimate of the contribution to the increase in strength reveals at first
glance to be acceptable. However, the mode of failure in surrounding materials was
neglected which is a limitation.
Hass (1976) carried out a series of single shear tests on chalk and limestone and
reported the splitting of the sheared block in the shearing process. The stresses on
both sides of the shear joint were suggested to be different, which is not a realistic
situation around the shear joint plane (Figure 3.4a). If the loading were truly
symmetrical there would be an equal probability of either block splitting. To better
distribute the shear load Hass applied a large bearing plate on the moving block, but
it was unsuccessful. Figure 3.4b shows the deformed bar subjected to lateral loading.
It obviously reveals that there is non-uniform situation along the joint plane. It is
clearly understood that the single shear test has difficulties in equal load distribution
in the shear joint. One method of minimising this problem was to by maintaining
high confining pressures in order to reduce the unbalance situation in the vicinity of
the shear joint plane. Non-uniform stress distribution across the shear joint plane was
also investigated by the numerical analysis (Afridi and et al, 2001), and thus
confirming the existence of non-equilibrium condition across the shear joint sides
(Figure 3.5).
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
61
Figure 3. 4. (a) block splitting in one side of shear joint (b) non equilibrium situation in vicinity of shear joint
Figure 3. 5. (a) Finite element mesh and (b) deviatoric of stress distribution across the joint (Afridi and et al. 2001)
Azuar (1977) found that for bolt installed perpendicular to the joint, the frictional
effect is negligible. This finding is not consistent with the confining theories, which
contribute part of the strength increase to a frictional component. Azuar also found;
Normal load
Shea
r loa
d
a b
a b
Hole diameter
Fracture
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
62
i. The maximum contribution of a rock bolt to the shear resistance of a joint is
influence by bolt orientation with respect to the joint surface. It ranges from
60 to 80 % of the ultimate tension load of the bolt installed perpendicularly
and 90 % for the inclined bolt.
ii. The friction characteristics of the joint do not influence the contribution of
the bolt.
iii. For a given shear displacement, the dilatancy increases the resistance of the
bolted joint.
Hibino and Motojima (1981) reported on shear tests on un-grouted 2 mm diameter
bolts installed in concrete blocks. They considered bolts placed in 2 mm and 40 mm
borehole for fully bonded and point anchored respectively and reported that:
i. For a given shear displacement the shear resistance of fully bonded bolts
was significantly higher than that of point anchored ones.
ii. The shear resistance did not increased by bolt inclination. This is in
contrast with others investigators.
iii. Pretensioning of the bolt reduced the shear displacement but did not
influence the shear resistance. This result is not consistent with the
laboratory and numerical results obtained by this author and discussed later
in the thesis.
Hass (1981) reported on the laboratory tests on limestone with artificially cut joints
reinforced by different types of bolts and different orientations (0o, +45o and -45o) to
the shear plane as shown in Figure 3.6. He suggested that bolts would act more
effectively when they are inclined at an acute angle to the shear surface than the
opposite direction, as they tend to elongate as shearing progress.
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
63
The total shear strength offered by a bolt was given by the summation of the bolt
contribution and the frictional strength along the shear surface, resulting from the
stress on the shear plane. Hass could not apply the bolt pretensioning effect, because
of incapability of the designed device. With increasing shear displacement, the bars
started to pull into the rock and consequently bolt resistance was reduced. However,
for bolts with bearing plate, the shear resistance was increased around 23%.
Figure 3. 6. Arrangement for bolt shear testing (after Hass, 1981) Dight (1982) conducted a theoretical analysis of the grouted bolt performance. Dight
assumed that the bolt contribution to the strength of a sheared joint was the resultant
of the tensile force in the bolt and the dowel effect (Figure 3.7). The angle of dilation
was given by the following relationship:
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
64
Angle of Dilation = iv
tag =− )(1
δδ
Figure 3. 7. General deformation patterns for a dowel in shear
The dowel force was determined by Eq (3.6)
))(1(7.14
22
yuyp t
tp
dt −= πσ (3.6)
where; up = The bearing capacity of the grout or rock
t = Axial bolt load in the position of the plastic moment,
yt = Axial load corresponding to the yield strength
yσ = Yield stress of the steel,
Reinforcing bar
Grout
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
65
d = Bolt diameter
And at the magnitude of pt , the location of plastic hinge was as follows:
))(1(58.0 2
yu
ypg t
tp
dl −=σ
(3.7)
Dight did not make any predictions on bolt behaviour in elastic conditions, if tension
behaviour prevails then the yield strength develops immediately. He considered the
Eq (3.8) for component of the axial load in shear direction and suggested the bolt
contribution would be the summation of Eqs (3.6) and (3.8).
)(cos(sin itagtt byc ++= ϕθθ (3.8)
where;
θ = The angle between the normal vector to the joint and the bolt, and bϕ is the
basic joint friction angle.
Dight reported:
i. The normal stress acting on the joint plane does not influence the shear
resistance, which is against the criterion of joint confining effect and results
reported by Saeb and Amadei (1992).
ii. Joints with inclined bolts had stiffer behaviour than those perpendicular
ones. The deformed length of the bolt was related to the deformability of
the rock.
Egger and Fernandez (1983) carried out bolted samples of concrete blocks in a high
capacity press. They found:
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
66
i. The optimum angle of bolt inclination with respect to the joint varied from
30o to 60o. However, Sharma and Pande (1988) found that the best direction
of reinforcement is normal to the major joint direction.
ii. Perpendicular bolts have appeared to have the lowest shear resistance.
iii. Shear displacements at failure were minimal for bolt inclinations between
40o and 50o.
Ludvig (1983) performed tests on swellex bolts, split sets and two sizes ungrouted
bars. The bolts were performed at 45o and 90o to the shear joint. Under shear
condition the tube bolts, in general, were weaker than the solid bars. He suggested
that the swellex bolt has approximately the same shear resistance as a solid 14 mm
diameter ungrouted bar.
Schubert (1984) proposed an analytical analysis based on the equilibrium of the
forces acting on the deformed system and conducted shear tests on bolted concrete
and limestone blocks. The sketch of the shear device, which was used by Schubert, is
shown in Figure 3.8. His results lead to the following findings:
i. The deformability of the surrounding rock is important for the bolt
reaction.
ii. Bolts embedded in harder rock require smaller displacements for attaining
a given resistance those in softer rock.
iii. Soft steels improve the deformability of the bolted system in soft rock.
Yoshinaka et al. (1987) study on the direct shearing of 16 mm bolt diameter
suggested 35o –55o angles as most favourable bolt angle against the joint plane. In
addition, a perpendicular bolt showed lowest bolt contribution to shearing compared
with low angles (Figure3.9). Moreover, no pretensioning was considered.
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
67
Figure 3. 8. Shear test machine used by Schubert (1984)
Figure 3. 9. Relation between shear stress and shear displacement (After Yoshinaka 1987) Spang and Egger (1990) made an extensive series of shear tests of grouted bolt
performance and used three different rock qualities, sandstone, concrete and granite.
Shea
r Str
ess
(MPa
)
Shear displacement (mm)
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
68
They found the maximum bolt contribution to the shear strength of the joint was a
function of the ultimate strength of the bolt, Tu.
)45.085.0()](sin01.055.1[14.0207.1 φσβσ tagiTT ccuo +++= − (3.9)
where;
uT = Ultimate strength of the bolt
cσ = The uniaxial compressive strength of the rock,
= Inclination between the bolt and the shear surface
i = Dilation
d = Dimeter of the bolt
= Friction angle of the joint and following Eq (3.10 ) was expressed for the
shear deformation of the bolt.
]cos
)70
(1)[2.562.552.15( 125.028.014.0
ββ
σσσ tag
duc
cco −+−= −− (3.10)
But this theory was limited to:
i. Steel bolts grouted with cement,
ii. Borehole dimeter approximately twice that of the bolt diameter,
iii. A uniaxial strength of rock between 10-70 MPa,
iv. Deformation formula is not accepted for bolts perpendicular to the joint (
=90o) and,
v. Bolt not subjected to pretensioning
Egger and Zabuski (1991) carried out a single shear test on small bolt diameters of
between 2.5 mm to 5 mm. Tests were made without the normal pressure and no
pretensioning across the joint. Figure 3.10 shows the direct shear test apparatus.
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
69
Bolts failed under the combination of both the shear and axial forces. Only low
strength steel was used in the test, as the technique was not suitable for high strength
steel, because of non-equilibrium and un-uniformity of the load distributed on the
shear joint.
Figure 3. 10. Direct shear test device (after Egger and Zabuski 1991)
Holmberg (1991) theoretically examined the mechanical behaviour of untensioned
grouted rock bolts in elastic and yielding conditions. His analytical model was based
on the equilibrium of the forces acting on the deformed system. He expressed three
stages and ultimate condition of bolt-grout interaction. These stages are shown in
Figure 3.11 and were distinguished as following:
i Bolt and surrounding medium are in elastic state,
ii Bolt is in elastic and surrounding medium in yielding state,
iii Bolt and surrounding medium are yielded,
iv Ultimate condition.
Holmberg’s theory disregarded the influence of the grout material. The following
conclusions were drawn:
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
70
a: Elastic condition b: Elastic bolt and yielding subgrade
c: Yielding bolt and yielding subgrade
Figure 3. 11. Bolt grout behaviour sketch (after Holmberge 1991)
yl up
y
yuy =
tyT
tT
d: Ultimate condition
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
71
i. The bolt contribution to the shear resistance of a bolted joint from dowelling
effect and axial load can be determined as a function of the deformation for
different load conditions,
ii. The initial bolt angle with respect to the direction of deformation is of minor
importance with regard to the maximum resistance of the bolted joint,
iii. The initial bolt angle has great influence on the maximum deformation of the
bolt,
iv. A bolt inclination of 60o with respect to the direction of deformation reduces
the total deformation by 4 folds compared to a bolt perpendicular to the
direction of deformation,
v. When the steel bolt crushes into the rock mass and develops a shape similar to
a crank handle, the ability to resist larger deformations before failure is
increased significantly,
In jointed rock mass, the bolt shear resistance becomes important where the bolt
intersects the joint. When deformation occurs in the rock mass the grouted rock bolt
will be subjected to loading, which generates both the axial and lateral forces in the
bolt (Figure 3.12). Factors influencing include; bolt and hole diameter, steel quality,
bolt elongation, rock and grout strength.
The angle between the bolt and the joint is very important for the behaviour of the
bolted joint surface, especially in determining bolt failure type. If the angle is less
than 35o, the failure seems to be a tension failure, and if the angle is approximately
90o, the failure is in shear.
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
72
Figure 3. 12. A grouted rock bolt subjected to lateral force
Ferrero (1995) proposed a shear strength model for reinforced rock joints based on
the numerical and laboratory studies on large size shear blocks. He suggested that the
overall strength of the reinforced joint could be attributed to the combination of both
the dowel effect and the incremental axial force due to the bar deformation. Figure
3.13 shows the shear test apparatus. The apparatus tend to suffer from unbalance-
distributed load on the shear joint plane. Ferrero’s analytical model was applicable to
the bolts installed perpendicular to the joint surface in stratified bedding planes. As
shown in Figure 3.14, the proposed analytical model was expressed by
F = ϕαααα tagQtQt rr )cossin(sincos −−− (3.11)
where;
ϕ = Joint friction angle
rt = Load induced in the bolt
Q = Force due to dowel effect
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
73
α = Angle between the joint and the dowel axis and
F = Global reinforced joint resistance.
According to his experimental and modelling evidence Ferrero suggested failure
could possible occur in one of the following ways, depending on the prevalent type
of stress:
Figure 3. 13. Ferrero’s shear test machine
Figure 3. 14. Resistance mechanism of a reinforced rock joint (after Ferrero 1995)
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
74
i. Failure due to the combination of the axial and shear force acting at the
bar joint intersection.
ii. Failure due to the axial force following the formation of hinge points.
The first yielding mechanism is likely to occur with stiffer and stronger rock at the
bar-joint plane intersection under a combination of the shear and normal forces.
As shown in Figure 3.15, the bolt is loaded by both the axial force the frictional
forces that develop between bolt and the surrounding grout.
The following equations were developed to describe the relationship between the bar
tension at the point of maximum moment and bolt-joint intersection respectively.
0
20
2 yx
Dpt bur = (3.12)
5.12
0
20
0
20 )
41(
2 x
yy
xDpt bur += (3.13)
The second failure mechanism occurs when the maximum computed bending
moment in A exceeds the maximum yielding moment of the bar. Usually this kind of
failure occurs in weak and less stiff rocks. The yielding conditions propagate from
the plastic hinges up to the joint intersection and, consequently, the steel bar is
affected by tensile stress.
However, Ferrero stated that pretension does not influence the maximum resistance
of the system. This appeared to be in contrast with both the experimental and
numerical studies undertaken in current thesis, which is discussed later in the
Chapters 5 and 7 of this thesis.
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
75
Figure 3. 15. Forces acting on the failure mechanism 1 (after Ferrero 1995)
Pellet and Egger (1995) analytical model for the contribution of bolts to the shear
strength of a rock joint, took into account the interaction between the axial and the
shear forces mobilised in the bolt and large plastic displacements of the bolt
occurring during the loading process. The description of the bolt behaviour must be
divided in two sections. The first one concerns the elastic range (from the beginning
of the loading process) and the second one deals with the plastic range (from the
yield to the failure of the bolt). The shape of the stressed bolt and the failure
envelope for both elastic and plastic deformations are shown in Figure 3.16 and
Figure 3.17 respectively. They used Tresca criterion as a failure criterion of the bolt.
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
76
a)
b)
Figure 3. 16. Force components and deformation of a bolt, a) in elastic zone, and b) in plastic zone (after Pellet and Eager 1995)
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
77
a)
b)
Figure 3. 17. Evolution of shear and axial forces in a bolt, a) in elastic zone, and b) in plastic zone (after Pellet and Egger, 1995)
The shear forces at the end of both the elastic limit and plastic region are obtained
from Eq 3.14 and Eq 3.15 respectively.
)4
(5.0 oeelb
buoe ND
DpQ −=σπ
(3.14)
22
2
)(1618 ecb
ofec
bof
D
NDQ
σπσπ
−= (3.15)
where;
oeQ = Shear force acting at point O at the yield stress of the bolt
Relationship between axial and shear forces in elastic conditions
Axial and shear forces at the yield limit
Yield limit
Failure criterion
Axial and shear forces at failure
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
78
oeN = Axial force acting at shear plane at the yield stress of the bolt
elσ = Yield stress of the bolt
bD = Dimeter of the bolt
ofQ = Shear force acting at shear plane at failure of the bolt
ofN = Axial force acting at shear plane at failure of the bolt
ecσ = Failure stress of the bolt
The displacement of the bolt in elastic and plastic stages were expressed by the
following equations:
βπ sin
8192344
4
ub
oeoe
pDE
bQU = (3.16)
)sin(
sin
opu
opoeof p
QU
ωβω∆−
∆= (3.17)
Where opω∆ = )sin)(1(cossinarccos[ 2222 βββf
e
f
e
ll
ll
−± (3.18)
where:
el = Distance between bolt extremity (point O) and the location of the maximum
bending moment (point A)
fl = The length of the part O_A at failure
Pellet and Eager evaluations showed that bolt inclination has a significant influence
on the maximum joint displacement. The greatest displacement is reached when the
bolt is normal to the joint. As the angle between the bolt and the joint decreased, the
displacement drops rapidly (Figure 3.18).
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
79
Figure 3. 18. Joint displacement as a function of angle for different UCS value (after Pellet 1994)
Pellet’s theory is valid for the inclined bolts less than 90o and is not acceptable for
bolts sharply perpendicular to the joints.
Robert (1995) reported shear tests on smooth bars and cone bolts by his double shear
apparatus. He found that failure only happened in one of the joint intersection. His
results showed non-symmetric situation in both side of the shear joint, which is likely
due to the generation of unbalance forces in three pieces blocks and is contradicted
with results from DSS in this research (see experimental results in Chapter 5).
Goris et al (1996) carried out a direct shear tests on 69 MPa concrete blocks with
joint surface area of 0.078 m2 (Figure 4.19). The test consisted of installing
perpendicularly a 15.24 mm diameter cable bolt (258 kN yield strength) into a 25.9
mm diameter hole. It was found that the yield occurred at 220 kN with 4 mm of
displacement which is higher than the double shear test carried out on the same type
of cable bolt. It appears that the single shear test has higher shear resistance than the
double shear test. This is due to inequilibrium load distribution on the shear joint and
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
80
concentration of the load through the blocks in front of the bolt, which pushes the
blocks together (zone A) resulting in the higher shear resistance which is not an
actual bolt contribution. Another limitation of the test setup was the maximum shear
displacement available being limited to 46 mm, which prevented the cabled from
failure.
Figure 3. 19. Shear block test assembly (After Goris and et al 1996)
3.3 PRETENSIONING EFFECT IN FULLY GROUTED BOLTS
Bolt tensioning places the rock into compressive state. Although pretension is very
effective in preventing bed separation and creating frictional forces between layers,
but this does not mean that higher bolt pretension always create better stability.
When a bolt is pretensioned, it would influence the shear strength of the joint with
forces acting both perpendicular and parallel to the sheared joint, this is created by
inducing confining pressure. A general rule for determining the maximum pretension
A
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
81
is that the pretension load should not exceed 60% of the bolt yield strength or 60% of
the anchorage capacity.
Nearly all the tests that were conducted by various authors related to the bolt
behaviour under the shear were accomplished in the absence of pretensioning.
However, in field studies and numerical simulations, pretensioning was applied and
it was unanimously agreed that pretensioning contributes to increase reinforcement
effect and improve stability, Lang et al. 1979, Maleki 1992, Peng and Guo 1992,
Jafari and Vutukuri 1994, 1998, Stankus and Guo 1997, Unrug and Thompson 2002,
Zhang and Peng 2002, and Hebblewhite 2005. However, Numerical studies placed
limitations on bolt / grout / rock contact interfaces. In addition, no experimental tests
have conducted to apply pretension in fully encapsulated high strength bolts. In
particular the evaluation of the effect of bolt profile on shear resistance under various
level of pretensioning is neglected. In current research care was taken into account to
remove the whole assumptions and limitations from both laboratory and numerical
design. Pretensioning was conducted in four different load, 0, 20, 50, and 80 kN in
both laboratory and numerical simulations. In numerical chapter a new design of bolt
model and contact interfaces is discussed. As it was discussed above, there are pros
and cons, in each method, which was used so far. A brief view of the methods is
shown in Table 3.1.
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
82
Author Base of the method Advantages Disadvantages
Dulascka
(1972)
Development of
plastic hinge after
max. Moment
Prediction of shear
force by bolt
Non static equilibrium
condition in shear joint
Bjurstrom
(1973)
Equilibrium forces
acting on the
system
Estimation of shear
resistance: due to
dowel, reinforcement
and friction effect,
Mode of failure in
surrounding materials was
neglected
Hass
(1976)
Single shear test Test were performed
on real rocks
Non-uniform stress
distribution along the shear
joint
Azuar
(1977)
Single shear test Different bolt angles
were considered
Influence of friction effect
could not properly
considered
Hibino
(1981)
Single shear test Pretensioning was
applied
Pretensioning and bolt’s
inclination could not
considered properly
Hass
(1981)
Single shear test Real rocks with
different bolt angles
were considered
Pretensioning was not
applied
Dight
(1982)
Theoretical analysis The prediction of
dowel effect and hinge
point was considered
Neglecting the bolt
behaviour in elastic range,
poor effect of normal stress
on joint
Egger and
Fernandz
(1983)
Single shear test Different bolt angles
was applied
Pretensioning was not
applied
Ludvige
(1983)
Single shear test Different bolt angles
was applied
No fully grouted bolt was
tested
Schubert
(1984)
Equilibrium forces
acting on the
deformed system
Real rocks was tested
Pretensioning was not
considered
Table 3.1. A brief comparison of the used methods in bolt shear behaviour
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
83
Author Base of the method Advantages Disadvantages Yashinaka
(1987)
Direct shear test Different bolt angles
was considered
Pretensioning could not
apply
Spang and
Egger
(1990)
Single shear test Real rocks was tested,
max bolt contribution
and displacement was
predicted
Limited in: grout types,
annulus thickness, rock
strength and
pretensioning
Egger and
Zabuski
(1991)
Single shear test Prediction of bolt
failure at a combination
of axial and shear
No joint confinement and
bolt pretensioning was
considered
Holmberge
(1991)
The equilibrium of
forces acting on the
deformed bar
Bolt behaviour was
analyzed in both elastic
and plastic stages
The effect of grout was
disregarded
Ferrero
(1995)
Single shear test The plastic stage of the
system was considered
In-capability of the
method to show the
effect of pretensioning
Pellet and
Egger (1995)
Theoretical analysis Both elastic and plastic
stages was analyzed
The effect of grout
material was neglected
Goris et al.
(1996)
Single shear test Perpendicular bolts
was analyzed
Non-equilibrium load
distribution on the shear
joint, Max. Displacement
was up to 46 mm
Grasselli
(2005)
Double shear test Symmetric situation
around the shear joint
Bolt pretensioning was
not considered
Mahoni, et
al. (2005)
Single shear test Lengthy bolt-grout-
concrete anchorage
-
Aziz et al
(2005)
Double shear test
Symmetric situation
around the shear joint,
pretension effect, bolt
profile, any grout, bolt
& hole diameter
The size of the shear box
is small for large bolt
diameters and strong
steel bolts
Table 3.1. Continued
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
84
3.4. SUMMARY
In can be inferred from this review that:
i. For rock /concrete samples reinforced with bolt inclined at an angle to the
normal of the joint plane, two hinges are developed on either side of the
joint plane. The great majority of the inclined bolts failed in tension near
the shear surface.
ii. For samples with a bolt forming a small angle to the normal of the joint
plane, bending of the bolts becomes predominant even when the shear force
is small, which will create two hinges above and below the joint plane.
iii. The vertical height of the bended bolt is about 2-4 times the bolt diameter
called effective height, corresponding to an effective length.
iv. Large bolt diameter reduces shear displacement required for obtaining a
given shear force.
v. The effect of dilatancy contributed to the stiffness of the bolted joint.
vi. Inclined bolts are stiffer and contributes significantly to the shear strength
of the bolted blocks than the perpendicular bolts.
vii. Bolt pretensioning reduces shear displacement, but not the shear resistance.
viii. The deformed length of the bolt is related to the deformability of the host
rock.
ix. Shear displacement at failure is minimal for inclinations between 40o and
50o.
To avoid the related problems for direct shear test and evaluating the load transfer
mechanism in stable situation, in this research, a new approach is evaluated as bolts
can experience both lateral and axial loads in equilibrium situation at both sides of
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
85
the shear joint without any moment generation through the testing machine and
surrounding materials. However, direct shear can provide the valuable information
on the strength parameters of rock joints but when is applied to evaluate the load
transfer mechanism of bolt, is inferior because of non-uniform distribution of stress
concentration on the shear joint and along the bolt in direct shear machine. Afridi and
et al. (2001) also have emphasised on this problem and pointed out that when the
applied shear load is not in the line with the shear plane (it is somewhat above) it
produces overturning moments, which produce rotation in the shear box and create a
non –uniform stress profile.
The following work reported in the next chapter examines the interaction of rock /
resin / bolt and focuses on the following issues specifically to get proper knowledge
in the load transfer capacity and bolt / joint interaction in different situations:
i Evaluating of the shear behaviour mechanism in bolt-grout and grout-
rock interfaces.
ii Evaluating of different bolt profile on the load transfer of fully
grouted bolts, that is the main factor in load transfer capacity, which
was ignored in all above works.
iii Study of the load transfer and bending behaviour in bolt-grout-rock
interface in different material strength.
iv The effects of resin thickness on shear behaviour of bolts and load
transfer evaluation,
v The effects of bolt pretensioning on shear resistance and load transfer
of bolts.
So to achieve the above parameters and conditions extensive laboratory tests were
conducted and the results are presented in the next chapter.
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
86
It should be noted that in spite of extensive research which has been done in this
field- due to a huge number of involved factors affected – on the bolt behaviour such
as, intact and rock mass strength, joint geometry and their characteristics, mechanical
bolt properties, bolt surface configuration, grout annulus thickness, grout strength,
pretensioning and relative orientation of joint with bolt, there is no overall theory to
evaluate thoroughly the bolting behaviour. Only each experiment and new or
modified idea extends the range of experience and knowledge in this field.
In the next section, it was tried to define the mechanical properties of the whole
material used- bolt, resin and concrete- in the experimental tests, which are described
in the next chapters.
3.5. MECHANICAL PROPERTIES OF REINFORCING
MATERIALS
In this part, the strength properties of bolts, resin and concrete are studied. All the
tests were carried out in the laboratory, and under controlled conditions. Parameters
examined include, the uniaxial compression strength, shear strength, and modulus of
deformations. Then parameters are pertinent to the overall study of load transfer
mechanism of bolts, resin, and concrete interactions.
3.5.1. Bolt Types
Seven different bolt types were tested for tensile strength. Three bolts are the popular
types that are used widely by the Australian mining industry. Figure 4.20 shows the
photographs for various bolts and Table 3.2 list the physical specification of all the
bolts. The bolts are of similar diameter core size, but of different profile heights and
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
87
spacings. Also included in the test is a seven-strand cable bolt used for double
shearing test. Figure 3.21 shows the general profile details of the bolts.
Tensile, bending and shear strengths of the steel bolt are the most important
mechanical parameters that influence its behaviour when loaded axially and in shear.
Figure 3. 20. Different Bolt Types used for axial and shear behaviour tests Figure 3. 21. Profiles specification
Rib Spacing (mm) Rib Width
Outer Diam. (mm)
Core Diam. (mm)
Rib Height
T1 T2 T4 T5 T6 T3
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
88
3.5.2. Bolt strength tests
Three kinds of laboratory tests were carried out on different Types of bolts (Table
3.2). They are:
• Tensile strength
• Bending strength
• Direct shear test
Table 3.2. Physical specifications of different bolt types
Bolt
Bolt
Commercial
name
Rib
Spacing
(mm)
Core
diameter
(mm)
Rib
height
(mm)
T1 AX 11.5 21.7 1.0
T2 AXR 11.5 21.7 1.5
T3 JX 24.0 21.7 1.2
T4 9.7 19.6 1.3
T5 1.4 10.3 0.6
T6 N12 7.74 11.7 0.8
3.5.2.1. Tensile strength test
A 33 cm bolt length, was cut and tested for tensile strength by pull testing. A
universal Instron tensile testing machine was used to carry out the tensile test. The
tensile test, on all rebar specimens, were carried out in accordance with the
Australian Standards for tensile tests No AS 1391. A typical tensile test arrangement
is shown in Figure 3.22. The test specimen was installed between the two large grips
of the testing machine and then loaded in tension. The computer-controlled tensile
test loaded the specimen at a constant rate until failure. While the test progressed,
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
89
load and displacement values were monitored by the computer. The load
displacement curves in Figure 3.24 to 3.27 show a typical behaviour of the steel with
elastic behaviour in the beginning of the test and small displacement till yielding
point. Beyond the yield point, the bolt will deform without further increase in the
load until the bolt is strain hardened. Finally the steel bolt fails with contraction of
the cross section area, which is in the form cap and cone known as (necking). It
should be noted that the cable bolt failed by the tensile failure of the individual
strands.
Figure 3. 22. Bolt clamped in Instron Universal testing Machine
As can be seen from the loading profile of the tested bolt (Figure 3.23) the following
features were deduced;
a) Elastic range
b) Yield point
c) Elasto-plastic range
d) Failure range
The yield strength of the steel bar is an important factor in the determination of bolt
tension, thus influences the effectiveness of the bolt performance. It should be noted
Bolt
Grips
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
90
that although a roof bolt of high yield strength is desirable, however, it is use in situ
should be avoided.
The high strength bolt when fails, the bar is most likely to shoot out of the hole with
such high speed that it could severely injure anyone in its path (Peng 1986).
According, the current bolts strength used in mines are of strength 320 kN. The value
of the yield and ultimate failure loads in all types of bolt is described in Table 3.3.
Table 3.3. Bolt tensile strength
Figure 3. 23. Stretching of the bolts after tensile test
Bolt Yield Point (kN)
Tensile Strength
(kN)
Yield stress (MPa)
Ultimate stress (MPa)
T1 260 328 683 862
T2 256 342 673 900
T3 210 358 552 942
T4 163 194 518 617
T5 38 44 365 423
T6 57 67 501 593
Necking/Yielding/Failure
T1 T2 T3 T4 T5 T6
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
91
Figure 3.1. Load- deflection curve at tensile test in various bolts
Figure 3.25. Load- deflection curve at tensile test of Bolt Type T5 and T6
Figure 3.26. Load- deflection curve at tensile test in cable bolt
Figure 3.27. Load- deflection curve at tensile test of Bolt Type T4
3.5.2.2. Three point load bending test
For better understanding of bending behavior of rock bolts used, several bending
tests were carried out in 3PLBT (three point load bending test). Figure 3.28 shows
the three-point load bending test set up. Three types of bolts, which were used for
axial and double shearing tests, were tested under pure bending load by this method.
Three types of bolts, which were tested under pure bending load condition. The
bending behaviour of Bolt Types T1, T2 and T3 is displayed in Figure 3.29. Bolt
T
T6
T5
T3
0
50
100
150
200
250
300
350
400
0 20 40 60 80
Displacement (mm)
Tens
ile L
oad
(kN
) . T1
T2
0
50
100
150
200
250
300
0 5 10 15
Displacement (mm)
Ten
sile
load
(kN
)
.
0
50
100
150
200
250
0 10 20 30 40 50 60
Displacement (mm)
Ten
sile
load
(kN
)
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
92
Type T1 has the lowest bending strength While Bolt Types T2 and T3 exhibited
higher bending loads
Figure 3.28.Three point load bending test set up
Figure 3.29. Load- displacement behaviour of 3PLBT
3.5.2.3. Direct shear test
The direct shear tests on bolts were carried out guillotine test. The guillotine
apparatus is especially designed for rock bolt testing with replaceable bushing to
ensure proper fit and no possibilities for initial bending of the bolt being tested. The
shear forces are the resultant of the shear stresses distributed over the cross sectional
area of the bolt. These stresses act parallel to the cut surface. Figure 3.30 shows the
average shear load versus shear displacement for Bolt Type T1 and T3 respectively.
Table 3.4 shows the results of direct shear tests two types of bolts. The direct shear
test was conducted in an Instron 8033 Servo Controlled 50 tone Compression Testing
Machine.
0
10
20
30
40
50
60
0 10 20 30 40
Displacement (mm)
Load
(K
N)
AXRJABAX
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
93
Figure 3. 30. direct shear test trend in Bolt Types T1 and T3 Table 3.4. Specification of bolts shear test
Bolt type Shear load (kN)
Shear strength (MPa)
Displacement (mm)
T3 236.3 638.12 6.5 T3 237.2 641.3 6 T3 237 640.8 7.3
Average 236.83 640 6.6 T1 237 641 7.2 T1 241.5 653 7 T1 239.8 648.4 6.6
Average 239.43 647.5 6.93
3.5.3. Resin grout
Epoxy and polyester resins are the most commonly forms of chemicals used in bolt
installation in Australian Mines. The most popular type used is the resin combination
sausage capsule supplied by Minova Australia (formerly known as Fosrock Mining).
A program of strength properties tests was carried out on resin. These include, the
uniaxial compression tests, the double shear tests and modulus deformation tests.
These tests were carried out on slow setting (20 minutes) PB1 Mix and Pour resin.
0
50
100
150
200
250
0 2 4 6 8
Shear displacement (mm)
Shea
r Loa
d (k
N)
.
T1T3
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
94
The longer duration of setting time was essential to conduct the strength tests. The
diameter of the prepared samples was different for different tests carried out.
a) Uniaxial Compression Test: A uniaxial compression test is the most
common test performed on rock and other types of samples – in this case, resin. The
samples prepared for this batch of tests had 50 mm diameter and the length to
diameter tests were in the order of 2.5: 1. The samples were cast in a special plastic
mould specifically fabricated for the test. The tests were accomplished by Instron
machine, 500 kN capacity. A constant displacement rate of 0.25 mm/min was used to
load the samples to failure. In reality, tested samples break similar Figure 3.31 and
sometimes the failure cracks are parallel to axial direction. Figure 3.32 shows the
compression test set up and subsequent tests undertaken. Although simple, care must
be taken when carrying out the test so that errors are minimised, and interpretations
are as accurate as possible. The procedure for conducting a UCS test was carried out
in accordance with International Rock Mechanics Standards. Samples were polished
and cut till the height to diameter ratio 2.5 –3 was achieved. Table 3.5 list the details
of the samples tested and the UCS values obtained. A total of seven samples were
tested. The average UCS values were in the order of 70.8 MPa with SD of +/-
XXXX. The UCS Value obtained was in agreement with the manufacturer’s
specified strength of 71 MPa. Figure 3.33 shows the relationship between stress and
strain in resin. Figure 3.34 displays the load versus displacement. Some of sample
was instrumented with strain gauges to monitor, axial and lateral deformation of the
sample during loading process.
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
95
Figure 3.31. Typical fracture plane and fracture angle for compression test samples
Figure 3.32. Compression test set up
α
Fracture Plane
Angle of Fracture
Hemispherical Seating
Resin Sample
Strain gauge
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
96
Table 3.5. Summary of the results obtained from UCS test
Sample Length (mm) Failure load (KN) Ucs (MPa)
S1 72.74 146.12 74.42 S3 79.54 142.74 72.7 S4 99 133.5 68 S5 79.5 143 72.7 S6 99 134 68 S7 97.75 136 69 S8 89.8 140 71
Average 70.8
b) Shear Strength: The shear strength tests were undertaken using Double
shear tests using a 50 tone capacity Avery testing machine as shown in Figure 3.35.
The samples were prepared by casting in specially prepared moulds of 32 mm
diameter, which fitted snuggly in the double shear barrel. A total of four tests were
carried out, with the average shear strength value in the order of 16.2 MPA +/- XXX.
Standard deviation. The resin was different with the sausage type as it had setting
time in the order of 20 minutes thus allowing a sufficient time for proper preparation
of the samples for various tests.
Figure 3.33. Stress strain curve for resin
UCS=73 MPa, E= 10500 MPa Poisson ratio=0.26
0
10
20
30
40
50
60
70
80
-0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04
strain
Axi
al s
tress
(MPa
)
.
axiallateral
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
97
Figure 3.34 . Load versus displacement
3.5.3.1. Double shear test
32mm diameter samples of resin were cast in PVC tube to a length of 100mm. Each
sample was placed within the double shear-testing rig and then loaded by the Avery
testing machine until failure at a standard rate of 2.5kN per minute.. The double
shear test rig is outlined in Figure 3.35. There are two shear locations to accurately
determine the shear properties of the material being tested. From the dial reading on
the Avery testing machine, the peak load at failure was read.
A total of four double shear tests were conducted in order to accurately determine the
peak shear force of the resin and to ensure consistency of both testing methods and
results. Sample measurements are shown in Table 3.6.
0
20
40
60
80
100
120
140
160
0 1 2 3 4 5 6
Axial displacement (mm)
Com
pres
sive
load
(kN
)
.
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
98
a b Figure 3.35. Double shear test set up a: shear box set up b: induced loads
Table 3.6. Double shear test specifications
Sample Diameter
(mm)
Sample area
(mm*2)
Failure load
(kN)
Shear strength
(MPa)
S1 31.95 801.7 25 15.6
S2 31.88 798.2 26.2 16.4
S3 31.95 801.7 28.5 17.7
S4 31.9 800 24.6 15.3
Average 16.2
3.5.4. Concrete
3.5.4.1. Uniaxial compressive strength
Four nominal concrete strengths, 20, 40, 50 and 100 MPa, were used in the double
shearing tests. These strengths compare well with the range of rock strength. From
each batch, which was prepared some cylindrical samples, were cast to measure the
concrete strength. Concrete was tested in compression to ensure that the required
32 mm
Location of Shear Failure
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
99
strength has been obtained. Figure 3.36a & b show the concrete sample during the
test and the concrete blocks after taking out from the water tank.
The modulus of elasticity was calculated from equation which was expressed from
Australia standard AS3600 (1994) and also the typical value of Poisson’s ratio
specified by AS3600 is 0.2.
(3. 19)
A suitable expression, which applies for concrete excess of 50 MPa, has been
recommended by ACI Committee 363 (1992):
(3. 20)
where;
cE = Modulus of elasticity (MPa)
ρ = Concrete density )/( 3mkg
cmf = Mean value of the concrete compressive strength at the relevant age (MPa)
a b
Figure 3.36. Concrete sample: a) concrete under the test b) concrete after 30 days
cmc fE 5.1043.0 ρ=
69003320 += cmc fE
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
100
3.5.4.2. Concrete joint surface properties
In order to estimate the strengthening effects of bolting one has to know the friction
properties of unbolted joints. For this reason, a series of direct shear tests was
performed on specimens of broken and intact concrete, and under a variety of normal
loads. All samples were tested in direct shear, using direct shear machine. By this
method some important parameters can obtain such as, peak shear strength, residual
shear strength, cohesion and angle of internal friction (See Moosavi and Bawden
2003). The specimen properly positioned and then the lower half of the sample was
potted in the shear box ring with the potting compound. After the compound
hardened the appropriate thickness of Plexiglas spacer sheets was placed on top of
the lower shear box to form the shear plane. Whereas, the specimen being tested had
a weakness plane (concrete-concrete interface) it was placed in the shear machine
such that the plane of joint was coincided with the plane of the machine. The friction
angle of joint can be estimated by performing repeated shear tests under different
normal loads. To estimate shear resistance of a joint Barton (1966) developed an
empirical model (Brady and Brown 1985). Which can be written as following.
(3.21)
Where, pτ =peak shear stress, nσ = normal stress, JRC = joint roughness coefficient,
JCS = joint compressive strength, and bϕ basic friction angle.
From the data analysis it was found that the joint surface cohesion in both concrete
20 and 40 MPa was zero and the angle of friction was 31 and 38 degree respectively
(Figure 3.37 a and b). As Figure 3.38 shows, once the peak shear strength was
overcome, there was considerable loss of shear resistance. From the analysed
+= b
nnp
JCSJRCtg ϕ
σστ )(log10
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
101
laboratory results the concrete specifications were found as shown in Table 3.7.Also
it was found that the relation between shear stress and normal stress was nearly 0.9 to
1.7 normal stress in 20 and 40 MPa concrete respectively.
a b Figure 3.37. Variation of peak shear stress versus different normal stress in shear joint plane in a: 20 MPa and b: 40 MPa concrete Table 3.7. Concrete joint properties
Ucs Strength (MPa)
Modulus of Elasticity (MPa)
Poisson ratio Friction angle(o)
20 21000 0.2 31 40 30000 0.2 38 50 30500 0.2 -
100 40100 0.2 -
Figure 3.38. Shear load –versus shear displacement in joint plane in 40 MPa concrete
00.5
11.5
22.5
33.5
44.5
5
0 2 4 6
Normal stress (MPa)
She
ar s
tress
(M
Pa)
.
0
2
4
6
8
10
12
0 2 4 6
Normal stress (MPa)
She
ar s
tress
(MP
a)
.
0
5
10
15
20
25
0 5 10 15 20 25
displacement (mm)
She
ar lo
ad (
kN)
2.5 kN7.5 kN5 kN
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
102
3.5.5. Summary
There is no doubt that the load transfer mechanism in fully grouted bolts is highly
affected by mechanical properties of bolt, surrounding materials, and contact
interfaces. Tensile, bending and shear strengths of steel bolt are the most important
mechanical parameters, which play a great role on load transfer mechanism, when
bolt is axially and laterally loaded. It was concluded that the highest and lowest value
of tensile strength were recorded for bolt Types T3 and T5 respectively. From the
analysing the load- displacement curves, it was found that bolts have three stages of
behaviour in axial loading which includes, elastic, plastic and elasto-plastic.
However, in bending behaviour bolt shows elastic and elasto-plastic behaviour. This
trend continues till failure occurs in the bolt.
The choice of grout is of great importance to access high shear resistance. From the
laboratory tests it was found that the uniaxial compressive strength and shear
strength of resin are approximately 70 and 17 MPa respectively. Thus resin grout can
experience high shear resistance and interlocking effect. This type of resin with
qualified specifications which being used is the main character to transfer the load
from bolt to rock.
Concrete is used in lieu of rocks as regular sample for experimental tests, which are
carried out for bolt purposes. An understanding of mechanical behaviour of concrete
used as surrounding material is essential for the safe and sure design. Bolt bending is
highly affected by rock/concrete strength, especially at the vicinity of shear joint,
which are the critical zones. Thus to find the mechanical properties of involved
materials in experimental tests concrete has major effect on load transfer mechanism
and bending behaviour. Consequently, the concrete properties, especially, uniaxial
Chapter 3: Review of shear behaviour of bolts and mechanical properties of the material used
103
compressive strength, and shear joint parameters are the main factor, which were
accurately found before the relevant tests. The above mechanical properties were
used in the numerical modelling and analysing the experimental data accurately,
which are discussed in the two next Chapters.
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
104
CHAPTER FOUR
FAILURE MECHANISM OF BOLT RESIN
INTERFACE S DUE TO AXIAL LOAD
4.1. INTRODUCTION
In recent years, fully encapsulated rock bolt have become a key element in the design
of ground control systems especially in the Australian coal mining industry. The
main reason the acceptance of fully grouted bolts is that they offered the maximum
shear resistance to bed separation. Load transfer mechanism of a fully grouted bolt is
a function of the bolt surface condition. The surface roughness of bolt dictates the
rate of interlocking between the bolt and the resin surface. Shear stress of interfaces
rather than the grouting material is of great importance in the overall resistance of
rock bolt system. There are limitations to pull test in determining the resistance of
interfaces as stress distribution in the system is significantly affected by the geometry
of the bolt, borehole, the embedment sample and their material properties. These are
the subjects of discussion in this chapter.
4.2. LOAD TRANSFER MECHANISM
During rock movement the load is transferred from the bolt to the rock via the grout
by the mechanical interlocking acting between the surface irregularities at the
interface. When shearing is taking place due to rock movement, the load is
transferred to the bolt by shearing of the grout interface (Serbousek, 1987). The
ability to transfer the load between bolt/grout/rock depends upon several parameters
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
105
such as; resin annulus, grout strength, bolt profile characteristics, rock roughness,
rock strength and the mechanical properties of the steel bolt.
The nature of bolt failure in field test is different from laboratory test. In field test,
the failure is dependent upon the characteristics of the system, the material properties
of the individual elements and anchorage length. Slippage may occurs at either of
rock-grout or grout-bolt interfaces, which is called decoupling behaviour.
Decoupling takes place when the shear stress exceeds the interface strength. In
laboratory test, the failure usually takes place along the bolt-grout interface and if
real rock is used instead of the steel tube as outer casing element, then the failure
may happen along the rock-grout interface and depending on the rock strength. If the
rock is soft then the failure occurs along the grout rock interface, as the mechanical
interlock breaks down at low loads and the frictional resistance comes into account.
In hard rock on the other hand, the mechanical interlock would be dominant. Kilic
(1999) reported that when surface friction of a borehole decrease, slippage occurs at
the grout-rock interface. In addition, when the bolt and borehole length exceeds a
critical length for a bolt size of 21 mm in a 27 mm hole diameter, failure takes place
at the bolt. This has been demonstrated by the laboratory tests (Aziz 2004). Figure 4.1
shows the schematic representation of the influence load transfer generation at the
interface, together with bolt profile configuration. It displays that the mechanical
interlocking occurs when the irregularities move relative to each other (wedges are
created). Surface interlocking will transfer the shear forces from one element to
another. When the shear forces exceed the maximum capacity of the medium, failure
occurs and only frictional and interlocking resistance will control the load transfer
characteristics of the bolt.
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
106
Figure 4. 1. Sketch of real bolt profile specifications and interfaces
4.3. BOND CHARACTERISTIC
The mechanisms of effective bonding between bolt, resin and rock can be attributed
to adhesion, friction and mechanical interlock. The effectiveness of each parameter
on bond strength is variable and depends on the test conditions. Normally the
effectiveness of adhesion is almost negligible, and this was clearly demonstrated by
sawing axially a column of resin block cast on a bolt as shown in Figures 4.2 a and b.
The cut two halve sections of the resin detached clean from the bolt core surface in
the force applied. Such finding was also supported by the interpretation of the results
Geometrical configuration of bolt grout interface (bolt T1)
Rock •
Grout
• • •
•
• • • •
• • •
• •
•
• • •
• •
• •
• •
•
• •
•
•
• •
•
•
• • •
• •
• •
• •
•
• •
•
• • • •
•
• • •
• • • • •
• •
•
• • •
• • •
•
• •
Bolt
Load
0.75mm
• •
•
• • •
• • •
• •
• •
•
•
• • • •
•
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
107
of bolt /resin shearing tests carried out under constant normal stiffness conditions
(Aziz 2003). The bonding strength is almost near zero when the normal stress is
reduced. It should be noted that the frictional effect is also dependent on the bolt
surface roughness as discussed later in this chapter. It is obvious that the applied
confining pressure has a major influence on the level of friction and interlocking
action at the bolt /resin interface. Kaiser et al. (1992) reported that the mining
induced stress change is one of the most important parameters controlling the bond
strength.
Figure 4. 2. (a) resin/bolt load transfer under various confining pressures (b) resin bolt separation after post encapsulation
4.4. PULL AND PUSH ENCAPSULATION TESTS
The installation and subsequent performance of bolts in-situ, results in the bolt being
placed in often in both tension and shear. There will be a general reduction in bolt
cross section as a result of bolt tensioning, causing premature bolt resin surface
contact failure and loss of the grip. The common method of evaluating the
competence of any bolt installation is to conduct pull tests on a short section of the
anchored bolt. This encapsulation length is in the order of 300 mm long. Another
method, which has gained acceptance by the industry, is short encapsulation push or
Resin normal confining stress (MPa)
Res
in p
eak
shea
r str
engt
h
(M
Pa)
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
108
pull test of a short length of the bolt installed in short steel cylinder tube. This kind of
test is usually carried out in the laboratory, using between 50 to 75 mm steel tube.
Concerns are often raised about the validity of the short encapsulation push test as it
does not realistically reflect on the true load transfer capability of the bolt/grout
interface. The sort encapsulation push test was developed to examine the peak load
transfer performance, without due consideration given to the possible reductions in
bolt diameter, due to pushing, which would influence the load transfer mechanism.
By pushing the bolt out of the cylindrical steel tube it would contradict the realities
of bolt functioning in-situ. The shear load developed at the bolt/ grout interface
would be in compression rather than in tension. In contrast, the short encapsulation
pull testing is considered as a more acceptable method of testing as the pulled bolt is
undergoing extension and deformation, similar to in-situ bolt condition.
Accordingly, a series of short encapsulation pull and push tests were undertaken on
three common types of bolts to examine the influence of test method on load transfer
characteristics of the bolt. These bolts were known as T1, T2 and T3 Bolt Types. For
obvious reasons all three bolt types were given identification designations. The general
characteristics of the various bolts were discussed in chapter 2. The following
parameters were examined under both pull and push test conditions:
1. Bolt-grout bond strength between bolt-grout in various bolt profiles
2. Rock-resin bond strength between rock-resin interact the interface
3. Bond stiffness between grout and bolt interface
4. Bond stiffness between rock-resin interface
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
109
Bond strength and bond stiffness between bolt and grout are best determined by
laboratory tests and the bolt/grout interface is the main bond in encapsulation pull
and push tests. However, bond and stiffness strength between grout and rock can be
determined in the field.
4.4.1. Push Encapsulation Test
Figure 4.3 shows the details of the short encapsulation push test cell. The cell is 75
mm long, which is 50% greater than that reported by Fabjanczyk and Tarrant (1992),
50 mm long steel tube. The longer length cell was selected in order to permit a
sufficient number of bolt surface profiles to be encapsulated in the cell. The cell
consisted of a machined steel cylinder tube with an internal groove. The groove
provides grip for the encapsulation medium and prevents premature failure on the
cylinder / resin interface. As opposed to pull testing, push testing involves pushing of
the bolt under constant normal load conditions through the hardened resin. With the
use of a digital load cell and LVDT, a full load / displacement history could be
obtained. All the bolt samples were each cut to lengths of 120mm using a
mechanised saw. The equal lengths ensured that all the samples of the same type had
an equal number of profile ribs and that the ends of each sample were square. All
bolts were encapsulated into the push test cells using Minova PB1 Mix and Pour
resin grout. The grout and bolt properties are illustrated in Table 4.1. As can be seen
from Figure 5.4 the bolts were centrally located with uniform resin annulus
thickness. Every effort was made to ensure the bolts were set axially parallel to the
hole axis. Figure 4.5 shows post-test sheared bolt out of the steel tube. All failures
occurred along the bolt grout interface
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
110
Figure 4. 3. (a) The actual push test configuration (b) the shematic of the test
Table 4.1 Grout and steel properties
Figure 4. 4. Preparing the bolt resin samples
Parameter Grout Steel
UCS (MPa) 71 -
Ave. Shear strength
(MPa) 16.2 600 (tensile test)
E (Gpa) 12 200
Poisson ratio 0.25 0.3
Universal platen
Bolt
Test cell
Spacer ring
75 mm
27 mm
48 mm
LVDT
Load cell
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
111
Figure 4. 5. Post-test sheared Bolt Type T2 out of steel cylinder in push test
4.4.2 Pull Encapsulation Test
In order to encounter the much criticism of the push test, a series of short
encapsulation pull tests were then under taken using the same 75 mm steel tubes.
Each tested bolt was cut to a 300 mm in length, and Figure 4.6 shows the general set
up of pull testing. As can be seen from Figure 4.7 a and b, the grout is clearly been
sheared off within the ribs of the bolt, which is a clear indication of the shear failure
across the grout annulus.
The pulling force and displacement were measured by pressure and displacement
gauges automatically as they were interfaced with a data logger and a PC. The load
and displacement were incrementally recorded at every 0.2 kN until the failure
occurred in bolt/grout interface.
As can bee seen from the load displacement values, there was a significant reduction
in the peak load values in comparison to failure by push test. For bolt T1 the
reduction was 11%, and for T3 it was 7%. Also the failure loads were higher in T2
bolts. There are a number of reasons for the reduction in pulling load as compared to
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
112
push test, and these are further analysed later in the chapter. Additional figures of
the tested samples are listed in Appendix A.
Figure 4. 6. Pull test arrangement
(a) Steel sleeve (b) Bolt
Figure 4. 7. Post-test sheared bolt out of steel cylinder
4.5. DISCUSSION
Table 4.2 shows the load transfer pull and push test results of all three bolts. Figures
4.8 and 4.9 show typical load-displacement graphs of both pull and push test results
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
113
respectively. Additional results of tests are listed in Appendix A. All profiles are
characterized with an initial linear load-displacement zone, the peak shear load or
failure zone and the post peak displacement or failure zone. Post peak load /
displacement profile was considered plastic stage as the bonding has failed between
the bolt and resin. It must be stressed that the load displacement relationship of
pull/push test of bolt/resin interaction cannot be considered as elasto-plastic
relationship similar to loading to failure of a steel bar. This is because the load
displacement of the bolt/resin/rock combination is merely concerned with shearing of
the bolt from resin and hence involves separating one material from another. The
general load-displacement profiles were the same for all three types of bolts tested.
Bolt Type T3 has higher shear load and lower stiffness, its post peak load-
displacement profile was, in general, higher than the other two Bolt Types T2 and T3
respectively. This is an advantage for Bolt Type T3, as it is considered to tolerate
greater displacement before reaching the peak load, and hence is considered as an
advantage in soft coal measure rock reinforcement. Each of the Bolt Types T1 and
T3 has greater stiffness than Bolt Type T3 and thus accommodates less displacement.
They are considered as an effective support system in strong and competent rocks.
Thus the bolt anchorage stiffness is important factor prior to the bolt-grout bond
failure. Figure 4.10 provides an explanation of the load displacement profile
behaviour.
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
114
Table 4.2. The load transfer laboratory results of the bolts in both pull and push tests
Pull Push
Bolt type Bolt type
Measured parameters
T1 T2 T3 T1 T2 T3
Ave Profile Height (mm) 0.75 1.35 1.2 0.75 1.35 1.2
Ave Profile Spacing (mm) 11.0 12.0 23.5 11.0 12.0 23.5
Ave Max Load (kN) 114.8 131.7 160 129.2 139.2 172
Ave Max Displacement
(mm) 4.10 4.55 8.2 3.3 3.86 7.4
Ave Shear Stress Capacity
(MPa) 22.2 25.4 30.9 24.8 26.85 33.6
Maximum effective shear
stress capacity (MPa)* 23.8 26.6 35.6 25.7 30 37.8
Average System Stiffness
(kN/mm) 28.3 28.93 19.5 39.1 36.3 23.2
Figure 4. 8. Shear load as a function of displacement in pull test
0
20
40
60
80
100
120
140
160
180
0 5 10 15 20 25 30
Bond displacement (mm)
Shea
r loa
d (k
N)
.
T1T2T3
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
115
Figure 4. 9. shear load as a function of displacement in push test
Figure 4. 10. General trend of push and pull test view
4.5.1. Effect of bolt profile
The magnitude of the shear stress and stiffness developed along the bolt/resin/rock
interface is influenced by the bolt profile configurations. Both bolt profile spacing
and profile height are important parameters which affect the level of load build up
0
20
40
60
80
100
120
140
160
180
200
0 5 10 15 20 25
Bond displacement (mm)
Shea
r loa
d (k
N)
.
T1T2T3
Axial displacement
Axi
al lo
ad
Elastic behaviour
Bond failure
•
Action wedge • Exceeds shear strength point
Interlocking and friction effect
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
116
along the bolt /grout interface, pre and post peak load. After decoupling, different
profiled rock bolts, behave differently. This is clearly illustrated by the load
displacement graphs shown in Figures 4.8, and 4.9.
High post-peak load residual strength feature, at the resin-bolt interface, was found to
suit Bolt Type T3 in soft formations, such as coal measure rocks, as it accommodates
greater rock deformation than the other two closely spaced bolts. Bolt Type T2 had
higher profile height than Bolt Type T1. From pull and push test results it was
found that, the higher profile bolt, with same spacing had higher level of both load
transfer capacity and stiffness values. The shear stiffness caused the transfer of the
load from one layer to another. It was found that the larger the rib, the greater was
the failure load of the rock bolt. Moreover, the higher load transfer, the greater was
the load developed over a relatively short encapsulation length of the bolt.
The total bonding failure was considered to occur, when the shear stress exceeded
the shear strength. From Figures 5.8 and 5.9 it can be seen that Bolt Type T1 before
achieving peak load was slightly higher in shear stiffness. A strong interaction
between the bolt and the grout has attributed to this high level of stiffness. From the
shear load versus shear displacement in all types of bolts it is understood that in the
Bolt Type T3, the final bond has failed at about 7-8 mm of displacement which is
nearly double to that obtained from other bolts with profile spacing 50% of the Bolt
Type T3 spacing. Such level of performance was also true to shear resistance of all
bolts tested of the same type. However, shear displacement before failure was larger
for bolt type T3. The main advantage of Bolt Type T3 is that, shear load is gradually
decreased after failure, which is suitable for soft ground conditions.
The profile spacing of the bolt was found to have significant influence on load
transfer characteristics. As stated before, the increased profile spacing allowed
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
117
greater displacement at peak load and increased load transfer at post peak range as
well. Figure 4.11 shows the relationship of shear load and rib spacing. This
relationship was based on the analysis of the laboratory test results shown in Table
5.2 in Appendix A.
27.5)ln(6.52max −= sDT 12.005.0 <<sD
a (4.1)
where;
maxT = The peak shear load at bolt-grout interface (kN)
a = Height of rib
sD = Rib spacing
Figure 4.11. The effect of Rib spacing on shear load
No studies are carried out to examine the effectiveness of profile spacing beyond 25
mm range as reported in this thesis. Bur all indications suggest that, at greater profile
spacing beyond 25 mm range there will be a gradual decline in the effectiveness of
the bolt load bearing characteristics with increased spacing as extrapolated in Figure
0
50
100
150
200
250
0 5 10 15 20 25 30 35
Rib spacing (mm)
Shea
r loa
d (k
N)
.
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
118
4.11. Similarly, no studies been carried out to determine the effectiveness of closer
spacings less than 12 mm. It is however sufficient to report that reduced spacing
would lead to reduced load transfer characteristics of the bolt irrespective of bolt
profile height. This statement can be supported by the loss of peak load and reduced
post peak load displacement shown in Figure 4.12. This was also reported by Aziz
and Webb (2003).
Figure 4. 12. The shear load versus shear displacement in smooth bolt
4.5.2. Bolt yielding/necking
In all the tests, slip and yield occurred at the bolt grout interface and there was not
physical failure of the bolt. Bolt yielding and necking was unlikely to occur in bolts
tested in 75 mm long steel sleeves as the level of load applied actually was around
40% of the maximum tensile strength of the steel, which is far less than that required
for the bolt to yield. For the bolts to undergo necking it must be gripped firmly at
both ends. However, it should be noted that by pulling the bolt, the diameter of the
0
2
4
6
8
10
12
14
16
18
20
0 1 2 3 4 5 6
Shear displacement (mm)
Shea
r loa
d (k
N)
.
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
119
bolt continues to reduce along the bolt length and results into elongation according to
Poisson effect. The elongation characteristics of the bolt would obviously affect the
load transfer capacity of the bolt. Figure 4.13 shows the process of debonding in pull
test. The excessive tapering of the bolt end drawn on the pull side is merely intended
to show the possible small reduction in bolt diameter and is not aimed to depict bolt
necking. This debonding and bolt reduction occurs after the load displacement rises
linearly in the bolt. Based on the numerical analysis discussed later in Chapter 7
there is a high level of load induced in top head of the bolt, which is reduced
exponentially along the bolt. By increasing the load, the debonded area propagates
and expands proportionally. From this time, the load decreases and hinge point in the
curve, is named the maximum bearing capacity of the bolt, is formed. After the peak
point, the shear load - shear displacement depends upon the interlocking phenomena,
which is function of bolt profile specifications, resin grout properties and resin
thickness.
During pull testing of the bolt, the embedded or encapsulated bolt section in the steel
sleeve enclosure would undergo a gradual reduction along its length, being relatively
greater at the pulled side of the bolt, gradually reducing towards the bottom and free
end. The reduction or increase in the bolt cross-section would depend on the test
type, which is whether the test was carried out in pull or push. Such difference in
diameter change would obviously affect the level of pulling or push force required to
mobilize bolt shear.
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
120
Figure 4. 13. Debonding at pull test
4.5.3. Effective Shear Stress at the Bond Interface
Effective bond shear strength capacity ( Eτ ) is calculated by Equation 4.1. Eτ is
calculated by the load at each step divided by the surface area of the bolt grout
contact interface. The contact bond length reduces with increasing the load, and this,
obviously affect the shear strength value.
(4.2)
where;
D = the bolt diameter,
L = the embedded length and
U = the shear displacement at each step of loading.
Based on the double shear tests on cylindrical resin samples, (see Chapter 5), and the
above results, the pure resin shear strength at the bolt grout interface is between 45 to
)()(
)(uLD
NLoadMPaE −
=π
τ
Debonding
Pull load
Excessive bolt tapering drawn for clarity
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
121
70 % of the maximum shear strength generated. The reason is, the bond strength is
affected by the combination of shear and compressive strength of the resin grout,
which has come to act during the interlocking process. It is known that the
compressive strength of the grout is around 70 MPa, which is approximately 5 times
of the grout shear strength. Therefore, the bond strength of the ribbed bolt is between
5 to 8 times of the smooth surface bolt depends upon the profile characteristics.
Figures 4.14 and 4.15 show the shear stress developed along the bolt/grout interface
in both push and pull tests respectively. The minimum and the maximum yield
stresses occurred at the lowest and highest rib profile Bolt Types T1 and T2
respectively. However, the maximum shear strength generated in bolt / grout contact
interface was induced in Bolt Type T3. Such high values were considered to be
attributed to the effects of both the rib height and rib spacing causing greater
interlocking effect (see details in Appendix A).
Figure 4.14. Shear stress versus bond displacement in Push test
0
5
10
15
20
25
30
35
40
0 5 10 15 20 25
Bond displacement (mm)
Shea
r stre
ss (M
Pa)
.
T1T2T3
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
122
Figure 4.15. Shear stress versus bond displacement in pull test The point where the shear load tapers away at the end of the range is defined as the
yield load. The yield and failure stress, elastic and peak shear displacements are
shown in Appendix 4.1. Table 4.3 shows various strength properties laboratory
results in both pull and push test results for three bolt types.
Table 4.3. Comparison of the laboratory results in pull and push tests
Type
of bolt
Ave.
Peak pull
load (kN)
Ave. Peak
push load
(kN)
Ave. Diff
%
Ave. Peak
disp in
pull (mm)
Ave. Peak
disp in
push (mm)
Ave.
Diff
%
T2 131.7 139.2 5.4 4.55 3.86 15.16
T1 114.8 129.2 11 4.1 3.3 19.5
T3 160 172 7 8.2 7.4 9.75
0
5
10
15
20
25
30
35
40
0 5 10 15 20 25 30
Bond displacement (mm)
Shea
r stre
ss (M
Pa)
.
.
T1T2T3
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
123
The following were deduced from Tables 4.2 and 4.3 results:
1. The average shear load values in push test were greater than the pull test,
irrespective of the bolt type,
2. The average shear stress capacity of the bolt in push test was in general
greater than the pull test,
3. The displacement at peak shear load were greater in pull test,
4. The shear stiffness of resin / bolts interface is an important factor in resisting
shear along the joint planes. As a consequence, the average system stiffness
for various bolts was greater in push than in pull tests. The difference in the
average stiffness values between push and pull tests, for all three Bolt Types
T1, T2 and T3, were in the order of 27.6, 20.3, and 16 % respectively.
5. The profile spacing appears to play a significant role in load transfer
mechanism characterisation for different bolts, and this supports the earlier
study findings under constant normal stiffness conditions reported by Aziz
(2002).
6. Bolt Type T3 can resist 25 % higher shearing force than Bolt Type T2. The
maximum peak load in Bolt T3 occurred at greater displacement. In residual
behaviour almost all bolts have the same trend in load displacement.
However, the residual shear load in Bolt T3 was twice than that of Bolt T2.
7. Bolt Type T3 losses its grip much more gradually than the other two bolts.
This is an advantage particularly in softer formation. In a way, it behaves in
an elasto-plastic manner.
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
124
4.5.4. Bolt core behaviour subjected to axial loading
In order to understand the bolt core behaviour during the shearing and also to
evaluate the Poisson effect in both pull and push tests, the mathematical calculation
was used and elastic parameters were calculated. Basically, when load is applied to
the bolt, it stretches in axial direction and contracts in the lateral direction because of
Poisson effect. When contraction occurs, the bond initiates breaking at the interface.
The stretching and contractions are calculated in both pull and push tests during
loading process. Table 4.4 shows the poison effect calculations in all three types of
bolts. There are small changes in axial and lateral strain values in push and pull test
results in all types of bolt. As expected, the pull test caused a diameter reduction
while push test caused diameter increase.
Table 4.4 axial and lateral strains along the bolt in pull and push tests
Bolt Type
Max. Stress (MPa)
Axial strain (%)
Diameter reduction
(mm)
Lateral strain (%)
T1 302 0.151 0.008 0.04 T2 346 0.173 0.011 .052
Pull
T3 421 0.21 0.013 0.06 T1 340 0.17 0.011 +0.051 T2 366 0.18 0.011 +0.054
Push
T3 452 0.22 0.014 +0.066
4.5.5. Effect of annulus
In an endeavor to examine the role of increased annulus encapsulation thickness on
resin anchorage strength, a comparative push test was made using two different
encapsulation thicknesses in equal length steel tubes. One tube had the internal
diameter of 27 mm while the other had 45 mm internal diameter. As can be seen in
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
125
Figure 4.16 there was a dramatic reduction in pulling force between the two-
encapsulation thicknesses (48 % reduction in load when annulus increases from 3.5
mm to 11 mm). In both cases the same profile type of bolt was used. As reported by
Campoli et al (2002) the size of the resin annulus is one of the critical variables
affecting resin bolt performance. Hagan (2003) found that there is little significant in
shear load with resin annulus size of 4 mm or less. Hagan’s results showed there is
26% reduction in shear load with annulus from 3 mm to 5 mm. Ulrich (1991) found
the optimum annulus thickness is 3.1mm in 25.4 mm hole diameter.
Figure 4.16. Annulus thickness effect
4.6. SUMMARY
• Short encapsulation pull test represent a better and a realistic method of
evaluating the load transfer mechanism of bolt in comparison with the pull test
method.
• Bolt profile configuration is an important parameter in load transfer capacity
of bolt. Both profile height and profile spacing have important and distinct role
Push test, ID= 27mm v ID 45 mm in short encapsulation push test
0
20
40
60
80
100
120
140
160
0 5 10 15
Displacement (mm)
She
ar L
oad
(kN
)
T2 ID 27mm
T2 ID 45mm
Chapter 4: Failure mechanism of bolt resin interfaces due to axial load
126
for bolt integrity. Profile spacing dictates the level of peak load displacement,
which intern accommodates a relatively greater level of strata movement. Such
characteristics of wider spaced profile bolts like Bolt Type T3 make them
suitable for strata reinforcement in soft rocks like coal measure rocks. Increased
profile spacing beyond 25 mm has not been tested experimentally but is likely to
act detrimentally to bolt performance. Like wise the reduction of bolt profile
spacing below the tested range of 12.5 mm would not be beneficial for bolt
performance.
• High profiles increases load transfer capacity of the bolt.
• Yielding and necking is unlikely to occur in bolts tested in 75 mm long steel
sleeves as the peak shear load was around 40% of the maximum tensile strength
of the steel. For the bolts to undergo necking it must be gripped firmly at both
ends.
• The average shear stress capacity of bolt in push test was greater than the pull
test. However the shear stiffness of the bolts were generally lower with pull test
in comparison to push test.
• Bolt- resin interface failure occurred by initially shearing of the grout at the
profile tip in contact with the resin. Naturally, the load failure of the resin / bolt
surface contact is dependent on the profile height as well as spacing.
• Increasing resin annual thickness reduces the load transfer capability of bolt,
and is also detrimental economically. Therefore it would be beneficial to install
the bolts effectively if the annulus resin thickness is kept to minimum.
Chapter 5: Double shearing of bolts across joints
127
CHAPTER FIVE
DOUBLE SHEARING OF BOLTS ACROSS JOINTS
5.1. INTRODUCTION
Bolts installed in jointed rock undergo axial and shear loading when sheared. Figure
5.1 shows a typical bolt bending due to bedding displacement. To gain a better
understanding of the effectiveness of bolt reinforcements, a series of laboratory
based double shear tests were carried out. Using different bolt types, and different
concrete strengths, the study examined the influence of various parameters on the
load transfer characteristics of different bolts in strata reinforcement installations.
Figure 5. 1. Bolt bending behaviour (after Indraratna et al. 2000)
Shear force
Rock
Local crushing
Shear fracture Rotation
Segregation
Inside failure
Bolt
Joint separation
Normal load
Pretension load
Shear failure
Chapter 5: Double shearing of bolts across joints
128
5.2. EXPERIMENTAL PROCEDURE
5.2.1. Block Casting
Double-jointed concrete blocks were cast for each double shearing test. Four
different strengths concrete blocks were cast, 20MPa and 40MPa, 50MPa and
100MPa strengths to simulate four different rocks. The solid ingredients components
of the concrete comprised mainly sand and cement, and occasionally aggregates were
also added. The concrete mix for the low strength batch consisted of ordinary
Portland cement, mixed with Nepean River sand. However, in higher strength
concrete of 50 and 100 MPa, aggregate was added to the mix.
Once mixed the concrete was poured into greased wooden moulds measuring
600mm x 150mm x 150mm,which were divided into three sections separated by two
metal plates, A length of plastic conduit 24 mm in diameter was set through the
centre of the mould lengthways to create a hole for the bolt. Figure 5.2shows the
general view giving the actual dimensions of concrete blocks used for double
shearing tests. The concrete was left for 24hrs to set and then removed from the
moulds and placed in a water bath for a period of 30 days to cure. The plastic
conduit was removed from the centre of the blocks and the hole was reamed to the
desired hole size, ready for the appropriate diameter bolt installation. The purpose of
the reaming the hole to larger diameter was to produce rifled hole surface for
effective bolt installation anchorage. Rifling was achieved by a specially machined
tip of a wing bit shown in Figure 5.3.
Chapter 5: Double shearing of bolts across joints
129
Figure 5. 2. Laboratory and numerical model
Figure 5.3. Hole reaming for hole rifling
Shear joint
Shear joint
Symmetric planes
300mm
150 mm 150mm
150 mm
Chapter 5: Double shearing of bolts across joints
130
5.2.2. Bolt Installation in Concrete Blocks
1400 mm long bolt, threaded 100 mm on both ends was then fixed in the concrete
specimen using Minova PB1 Mix and Pour resin grout. Prior to bolt installation, the
concerete blocks were clamped together with straight metal pieces place down the
sides to keep the blocks lined up and even. The blocks were placed in an upright
position and a series of rubber stoppers and steel plates, were attached to the concrete
hole-end to prevent the resin from pouring out from the bottom of the vertically
assembled block. The rubber stopper had a hole that the rock bolt could fit through,
thus allowing minimal resin escape. A funnel was placed over the top of the hole to
guide resin and reduce spillage. In addition, two thick steel rings were inserted at the
top and bottom of the hole collars to keep the bolt centrally positioned.
Care was taken to ensure the encapsulation resin fully mixed for maximum strength.
The rock bolts had their threads taped up to prevent the resin from clogging up the
thread. Initially the resin was poured in the hole and the bolt was then pushed
through the stopper plates. Further resin was applied as required while rotating the
bar to reduce the possibility of voids and filling the space between the bolt and the
sides of the hole along the entire length of the bolt through the blocks.
The instruction for resin mixing proportion was 100 grams of resin against 2 grams
of catalyst. Care was taken to install all the bolts in their respective concrete blocks
with uniform profile /flash orientation. The bolted blocks were left for at least half an
hour to allow the resin to cure before moving them for the place of storage. Most
bolted specimens were left to cure for a minimum of seven days before being
mounted on the steel frame double shear box and tested.
Chapter 5: Double shearing of bolts across joints
131
5.3. DOUBLE SHEAR BOX
Figure 5.4 shows the steel frame shear box. The three section box was made from
20 mm steel plates machined into three box, and held assembled with a total of
34 cap screws, each 300 mm thread length. The box plates were cad coated to
prevent them from corrosion. When assembled the internal dimension of the
shear box was such that the concrete specimen fitted snugly in the shear box.
One of the unique features of double shear system was that it was a symmetric
system of load application and shearing of the bolt. This symetricity was relevant
particularly when the bolt was subjected to axial loading.
Figure 5.4. An assembled bolt fitted with load cells on both ends of the bolt
5.4. TESTING
Figure 5.5a shows the sketch of the double shear box and bolt bending. Figure 5.5b
shows the assembled shear box in 5000 kN capacity Avery testing machine. A base
platform that fitted into the bottom ram of the testing machine was used to hold the
shear box between the loading plates. Steel blocks about 55mm thick were placed
beneath the two outer concrete blocks to allow for centre block vertical displacement
when sheared. The two outer ends of the shear box were then clamped tightly with
Chapter 5: Double shearing of bolts across joints
132
the base platform to avoid toppling of the blocks during shearing. A predetermined
tensile load was applied to the bolt prior to shear loading. This acted as a
compressive/confining pressure to simulate different forces on the joints within the
concrete. The predetermined tension loads were 0, 5 KN, 10 KN, 20KN, 50KN and
80KN. The maximum applied pretension load was nearly 40% of the maximum
tensile strength of the bolt. Axial tensioning of the bolt was accomplished by
tightening simultaneously the nuts on both ends of the bolt manually. Simultaneous
manual tensioning was preferred on mechanical /hydraulically operated loading so
that equal loading of the bolt can be maintained on either side of the bolt, thus
avoiding any possibility of differential loading application at any stage of the bolt
tensioning, which could influence the encapsulation integrity. The applied axial loads
were monitored by two hollow load cells mounted on the bolt on either side of the
block. During testing, load-cell readings were taken every 10 kN at 0.04 sec /minute
loading rate. The outer sections of the shear box remained fixed as the central block
was pushed down.
Double shear testing was carried out using either 500 kN capacity Intestron
Universal Testing Machine (Figure 5.6) or 5000 kN Avery Testing Machine (Figure
5.5 b). The selection of the machine type was dependent on the bolt type and extent
of bolt shearing range required.
Information gathered from the test included the applied load, bolt vertical
displacement, axial load generated on the bolt due to shearing. It must be stressed
that the axial load cell readings were manually read from GEOKON read out unit
strain indicator P-3500, made from Vishay measurements group, and then processed.
Chapter 5: Double shearing of bolts across joints
133
Figure 5.5. Schematic of post failed assembled shear box (a), and a set up of the high strength capacity machine -Avery machine (b)
Figure 5.6. The set up of the Instron machine with load cell connection
A Load cell E Load cell F Shear Box G Bolt
GI will fix it later
b a
Tensile zone
Compression zone
Chapter 5: Double shearing of bolts across joints
134
5.5. BOLT TYPES
Six types of bolts were tested in various combinations with respect to the concrete
strength, and are shown in Figure 5.7. These bolts were of different diameters and
profile configurations as shown in Table 3.2 in chapter 3.
Figure 5.7. Different bolt types
The range of double shearing tests carried out in this programme of study
consisted of the following:
a) Testing of bolts in 20 MPa concrete, representing soft rocks
b) Testing of bolts in 40 MPa concrete representing medium strength rocks
c) Testing of bolts in 100 MPa concrete representing high strength rocks
d) Testing of bolts in different encapsulation annual thickness
e) Testing of bolts without resin thickness
f) Strain gauge installed along the bolt
g) Testing of bolts for complete failure
f) A comparative study of bolts of different diameters.
T1 T2 T4 T5 T6 T3
Chapter 5: Double shearing of bolts across joints
135
g) Bolt contribution in different bolt characteristics
All the above tests were carried out under different pretension loads as stated
previously. Tables 5.1 to 5.3 show various tests conducted in different concrete
strengths combinations and the number of tests for each bolt type in different
pretensioning. It shows a total of 72 bolts in different situations were tested.
Table 5.1. Experimental Schedule indicating the number of samples tested per bolt in 20 MPa concrete
Table 5.2. Experimental Schedule indicating the number of samples tested per bolts in 40 and 100 MPa concrete
Pretension load (kN) Bolt Type
Strength (MPa)
0 20 50 80
Total Comments
40 2 2 2 2 8 With resin
40 2 1 1 1 5 Without resin T1
100 1 1 1 1 4 With resin
T2 40 3 3 2 2 10 With resin
T3 40 2 2 2 2 8 With resin
T4 40 1 - 1 - 2 φ19 mm bolt
Total 12 9 11 8 40
Pretension load (kN)
Bolt Type
0 20 50 80
Total
Remark
T1 2 9* 2 2 15
T2 2 2 2 2 8
T3 - 2 2 2 6 Total 4 13 6 6 29
*7 out of 9 tests on Bolt
Type T1 were tested in
different resin thickness
Chapter 5: Double shearing of bolts across joints
136
Table 5.3. Experimental Schedule indicating the number of samples tested per bolts T5 and T6 (low strength steel) in 40 MPa concrete
Pretension load (kN)
Bolt Type
0 5 10
Total
T5 1 2 2 5
T6 0 0 1 1
Total 1 2 3 6
5.6. RESULTS AND DISCUSSION
5.6.1. Shear Load and Shear Displacement
5.6.1.1. Profile description
Figure 5.8 shows a general load-displacement profile of the double shearing test.
Three distinct stages of the shear profile is shown. This is similar to the profile three-
point load bending of a steel bar. These are; elastic stage, non-linear stage and
plastic stage. Generally, the profiles are of similar configurations irrespective of the
test conditions, however the level of the load build up and the resultant
displacements were found to be influenced by various factors, such as; Bolt diameter,
concrete strength, profile configuration, resin thickness and bolt axial pretension.
i) Elastic Stage
This part of the graph is associated with the elastic behaviour of the sheared system.
The sheared joint surfaces start sliding against each as the shear load applied. This
linear section of the graph is characterised with a rapid increase of the shear load at a
relatively small displacement of less than 5 mm. On most cases the highest stiffness
and the elastic recovery of the system, upon the removal of the shearing load, will
Chapter 5: Double shearing of bolts across joints
137
depend on the level of the confining pretension load initially applied on the bolt.
There will be some minor fracturing of the grout /concrete, while is not significant to
cause the loss of bonding. The displacement level at the elastic yield stage reduces as
the bolt pretension load increases
Figure 5.8. Typical shear displacement profile of the sheared bolt
ii) Non-linear Stage
This stage is the transitional zone between the elastic and plastic zones. It is also
called the elasto - plastic stage. There is a sharp drop in the rate of shear stiffness
post the peak elastic yield load (P). The displacement / deflection at this stage can be
the same rate or slightly greater than the linear stage section of < 6 mm and also
depends upon the strength of material, bolt profile type and axial pretension load
level. The system stiffness decreases towards the plastic range and the bolt undergoes
irreversible bending particularly post peak yield point (P). Occasionally, a small drop
in the shear load values occurs beyond the elastic peak yield load point. This is due
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50
shear displacement ( mm )
Shea
r loa
d (k
N)
.
1
2 3
•
Chapter 5: Double shearing of bolts across joints
138
to the axial fractures developing in the concrete and along the bolt axis. The elastic
peak yield point (P) is likely to occur at reduced displacement with increased bolt
pretension.
iii) Plastic Stage
The plastic limit of the bolt is characterised by low rate of shear loading at increased
vertical displacement, in other words the low stiffness of the system. The hinge
points are clearly created in the bolt on both sides of the shear joint because of the
reduced shear stiffness. Concrete and grout are completely damaged at the
compression zones with excessive fracturing along the bolt axis in all three blocks
(Figure 5.19).
5.6.1.2. Shear loading for a limited displacement
Tables 5.4 and 5.5 show the test results of three types of bolts tested in both 20 and
40 MPa concrete in different pretension loads. Also included in the table are test
results of non-pretensioned bolts (i.e., 0 kN pretension load). The load-displacement
profiles of the tests conducted on three types of bolts T1, T2 and T3 are shown in
Figure 5.9 (a-f). Figure 5.10 (a-f) shows the comparative shear load and vertical
displacement (deflection) profiles in both 20 and 40 MPa concrete medium for the
given pretension loads as indicated. Individual comparative results between 20 and
40 MPa in different profiles bolt are presented in Appendix B. However, Bar charts
5.11 shows the comparative results in different bolt type and concrete medium.
Additional tests on Bolt Type T4 are listed in Appendix B.
Chapter 5: Double shearing of bolt across joints
139
Table 5.4. Yield point shear load values for different bolts under different environment
Shear load at yield
point (kN)
Shear displacement at
yield point (mm)
Shear stiffness
(kN/mm)
Comments Concrete
Strength
(MPa)
Pretension
load (kN)
Type
T1
Type
T2
Type
T3
Type
T1
Type
T2
Type
T3
Type
T1
Type
T2
Type
T3
Type
T1
Type
T2
Type
T3
0 102 71 - 3.3 5.53 - - 12.83 -
20 110 160 80 4.9 7.75 6.5 22.4 20.6 12.3
50 150 190 140 5.69 8.2 4.8 26.3 23.2 29
20
80 200 218 160 4.58 5.8 2.92 43.6 37.5 54
Hole diameter 27
mm
0 116 160 157 4.6 5.13 5.4 25 31 29
20 173 240 240 3.3 5.84 3.65 52 41 65
50 205 240 300 4.2 4.86 3.86 49 49 77
40
80 280 260 - 4.34 5.23 - 64 50 -
Hole diameter 27 mm
Chapter 5: Double shearing of bolt across joints
140
Table 5. 5. Yield point shear load values for bolt Type T1 under different environment Concrete
Strength (MPa)
Pretension
load (kN)
Hole
diameter
(mm)
Shear load at
yield point
(kN)
Shear load
at failure
point (kN)
Shear
displacement at
yield point (mm)
Shear
displacement at
failure (mm)
Shear
stiffness
(kN/mm)
Comments
20 25 163 762 6.23 91.7 26
20 27 168 813 5.83 80.7 29
20 28 177 821 5.37 86 33
20
20 36 198 756 4.57 75 43
Bolt diameter
21.7 mm
0 25 85 - 7.6 - 11.18 Without end
plate 0 25 110 - 7.4 - 14.86
20 25 212 - 12 - 17.6
50 25 209 - 8.86 - 23.6
40
80 25 274 10.57 - 26
With end
plate
100 Tests carried out in 0, 20, 50 and 80 kN and are discussed in related section
Tests carried
out without
resin
Chapter 5: Double shearing of bolts across joints
141
Figure 5.9 (a-f). All bolt shear load and vertical displacement profiles in both 20 and 40 MPa concrete medium
(a) Bolt Type T1 in 20 MPa concrete (d) Bolt Type T1 in 40 MPa concrete
050
100150200250300350400450
0 20 40 60 80 100
shear displacement ( mm )
Shea
r loa
d (k
N)
.
20kn50KN80KN0 kN
0
100
200
300
400
500
600
0 10 20 30 40 50
Shear displacement ( mm )
Shea
r Loa
d (k
N)
.
20 kN50 kN80 kN0 kN
(b) Bolt Type T2 in 20 MPa concrete (e) Bolt Type T2 in 40 MPa concrete
0
50
100
150200
250
300
350
400
0 10 20 30 40 50
Shear displacement (mm)
Shea
r lo
ad (
kN)
.
0kN50kN80kN20 kN
0
100
200
300
400
500
600
0 10 20 30 40 50
Shear displacement (mm)
Shea
r Loa
d (k
N)
. 20kN 50kN80kN0 kN
(c) Bolt Type T3 in 20 MPa concrete (f) Bolt Type T3 in 40 MPa concrete
0
100
200
300
400
0 10 20 30 40 50
Shear displacement (mm)
Shea
r Loa
d (k
N)
.
20kN80kN50 kN
0
100
200
300
400
500
600
0 10 20 30 40 50
Shear displacement (mm)
Shea
r loa
d (k
N)
.
20 kN50 kN0kN
Chapter 5: Double shearing of bolts across joints
142
Figure 5.10 (a-f). Comparative results of all bolts shear load and vertical displacement profiles in both 20 and 40 MPa concrete medium
(a) 20 MPa concrete (d) 40 MPa concrete
050
100150200250300350400
0 10 20 30 40 50
Shear displacement (mm)
shea
r loa
d (k
N)
.
T3- 20 kNT2-20 kNT1-20 kN
0
100
200
300
400
500
600
0 10 20 30 40 50
Shear displacement (mm)
Shea
r loa
d (k
N)
.
T1-20 kNT3-20 kNT2-20 kN
(b) 20 MPa concrete (e) 40 MPa concrete
050
100150200250300350400
0 10 20 30 40 50
Shear displacement (mm)
Shea
r loa
d (k
N)
.
T1-50 kNT3-50 kNT2-50 kN
0
100
200
300
400
500
600
0 10 20 30 40
Shear displacement (mm)
Shea
r Loa
d (k
N)
.T1-50 kNT3-50 kNT2-50 kN
(c) 20 MPa concrete (f) 40 MPa concrete
0
100
200
300
400
500
0 10 20 30 40 50
Shear displacement (mm)
Shea
r loa
d (k
N)
.
T1-80 kNT3-80 kNT2-80 kN
0
100
200
300
400
500
600
0 10 20 30
Shear displacement (mm)
Shea
r Loa
d (k
N)
.
T1-80 kNT2-80 kN
Chapter 5: Double shearing of bolts across joints
143
Figure 5.11. Shear yield load difference in different concrete strength and bolt types and various pretension loads
The following can be induced from the load /displacement data and graphs:
1. The elastic peak load (P) for non-pretension bolts in Bolt Type T1 did not
change significantly with changes in the concrete strength (see Figure 5.9 a
and d), However, there was a difference in “P“ value in Bolt Type T2. Only
one test was made at no Pretension load in Bolt Type T3, which was in 40
MPa concrete. A possible explanation for the difference can be attributed to
the profile configurations between these two bolt types.
2. For the increase in pretension load from 20 kN to 80 kN, the peak elastic
shear load “P” values for the three Types of bolts increased by 81% for Bolt
Type T1, 45% for Bolt Type T2 and 100% for Bolt Type T3. In 40 MPa
concrete the respective “P”values were 55 % increase in Bolt Type T1, and 9
% in Bolt Type T2. No tests were made for Bolt Type T3 in 80 kN.
However, “P” value in Bolt Type T3 increased 25 % from 20 to 50 kN
0
50
100
150
200
250
300
350
0 20 50 80
Pretension load (kN)
Pret
ensi
on-Y
ield
load
(kN
)
. Pretension load40 MPa-T120 MPa-T140 MPa-T220 MPa-T340 MPa-T320 MPa-T2
Chapter 5: Double shearing of bolts across joints
144
pretension load. This means that the tensioned bolt acts as an active support
system and provided the confining pressure to the sheared joint surfaces.
3. The peak elastic shear load displacement level for the given axial pretension
load was dependent on the bolt type. This displacement was more likely to
decrease with increased pretension load.
4. The strength of the medium has influenced the shear load level but not the
trend. Shear load values for all bolts were generally less in 20 MPa concrete
medium in comparison to the shear load values of bolts tested in 40 MPa
concrete.
5. Bolt Type T2 displayed closer and consistent shear load/displacement profiles
at all three levels of bolt pretension loads (20, 50, and 80 kN) particularly in
40 MPa strength. This consistency was relatively less in 20 MPa concrete,
and remained less scattered than the other two Bolt Types T1 and T2.
6. Bolt Type T3 load - displacement profiles were inconsistent and diverse at
different pretension load, this was expected in view of the large profile
spacing configurations of this bolt.
7. As shown in Figure 5.12, shearing of the bolt without bolt pretension can lead
to an early loss of resin/bolt bonding and inward pulling and bending of the
bolt, leading to excessive gap formation. This situation became worse when
the bolt ends were not fitted with nuts and plates to hold against the concrete
block ends. The presence of end plat plays importance role in providing better
structure reinforcement (see Tadolini and Ulrich 1986).
As can be seen from Figure 5.13 the gap created as a result of bolt bending,
was different for different test environment. The gap height varied under
different concrete type, pretension load values, and bolt type. The effective
Chapter 5: Double shearing of bolts across joints
145
gap (Chen 1999) was determined from testing of each of the bolt types T5
and T6 and was in the order of 1.35 and 3 times the bent bolt diameter (Db)
respectively. The formation of the gap is shown in Figure 5.33.
9. Figures 5.9 to 5.11 show the peak elastic yield load “P” values in different
bolt types in both 20 and 40 MPa concrete. Obviously, no definite
conclusions can be made on different bolt behaviour without bolts being
pretensioned in 20 MPa concrete. However, “P” value in Bolt Type T2
showed 38 % more than Bolt Type T1 in 40 MPa concrete and almost the
same with Bolt Type T3. What is obvious is the trend, which was also
showed in Figures 5.10 (a-f), that bolt pretensioning can contribute to
increased elastic peak yield load, and that the value of the peak yield load is
dependent on the level of pretensioning and concrete strength
10. Peak elastic yield point values changed with changes in resin annulus
thickness. This is clearly evident when testing bolts installed in different
diameter holes in 20 MPa concrete shown in Table 5.5 (Details in the next
chapter).
Figure 5.12. Bolt slippage along the bolt -grout interface in case of non-pretensioning and non- plate
Type T1
Chapter 5: Double shearing of bolts across joints
146
Figure 5.13. Axial fracture along the concrete and broking off of the grout in tensile zone in bolt type T1 in 40 MPa concrete with 80 kN pretensioning
5.6.1.3. Shear loading of bolt to ultimate failure
Next, a series of tests were carried out to examine the effect of increased shear
displacement until the bolt was completely sheared (failed). Two approaches were
adopted:
i. Shearing of small diameter bolts. The bolts used in these tests were Bolt
Types T5 and T6, tested in 40 MPa concrete.
ii. Shearing of the 23 mm bolt in 100 MPa high concrete. Only Bolt Type T1
was used in this test.
The above tests were undertaken at different confining pressures similar to tests
carried out under limited displacement. The general descriptions of these bolts are
shown in Table 3.1.
Tables 5.6 shows the test results on Bolt Types T5 and T6. Figures 5.14 shows the
load displacement profiles of the bolts tested under different axial load conditions.
The level of maximum shear loads and displacement were different because of
Chapter 5: Double shearing of bolts across joints
147
different pretension loads, and bolt types as indicated in Figure 5.15. The relationship
between shear yield load and pretensioning in Bolt Type T5 is shown in Figure 5.16a
and failed sheared bolt Type T6 is shown in Figure 5.16 b.
Table 5.7 shows the results of the tests carried on Bolt Type T1 tested in 100 MPa
concrete. Figure 5.17 shows the load displacement profiles of the bolt Type T1 in
different pretensioning in 100 MPa concrete. The excessive bolt necking in 100 MPa
concrete is shown in Figure 5.18. Figure 5.19 shows the failed bolt across the joint
planes and the crushed zones within the vicinity of the sheared planes in Bolt Type
T1 in 100 MPa concrete. Figure 5.20 shows the sheared failure resin imprint.
Chapter 5: Double shearing of bolts across joints
149
Table 5.6. Test results at Bolt Types T5 and T6 surrounded by 40 MPa concrete
* Displacement at failure and gap in bolt Type T5 is between 1.25 to 2 times bolt diameter
** Displacement at failure and gap in bolt Type T6 is around 3 times bolt diameter
*** Hinge distance in two types of bolts is between 2.8 to 3.3 times bolt diameter
Bolt Type
Concrete strength Preload
(kN)
Yield point (kN)
Displ at yield (mm)
Failure load (kN)
Displ at failure (mm)
Gap (mm)
Hinge distance
(mm) (***)
Angle of bolt
bending (0)
Stiffness (kN/mm)
40 0 48.7 6.3 76.5 23.8* 16* 34 28 7.75
40 5 70 4.23 100.8 18.4* 15* 37 28 16.55 T5
40 10 83 3.96 118.9 21.1* 18* 40 30 21
T6 40 10 98 4.33 172 36** 35** 40 44 22.6
Chapter 5: Double shearing of bolts across joints
150
Table 5.7. Bolt type T1 in 100 MPa concrete
Pretension-load (kN)
Yield load (kN)
Displ. at
yield (mm)
Peak load (kN)
Displ. at
failure (mm)
Bolt deflection
(mm)
Max displ. (mm)
Hinge distance (mm))
Angle of
rotation (o)
Stiffness (kN/mm
0 219 8.9 272 - 22 31.65 65 14 24.6
20 260 7 770 69.6 50 69.6 - - 37.15
50 300 11 500 - 22.5 34 60 - 27.3
80 329 7.25 799 53.5 48 53.5 45 45 45.4
Remarks
20 kN pretension
load is carried
out in 36 mm hole diameter
Failure was
occurred only in 80 kN
CHAPTER 5: Double shearing of bolts across joints
151
Figure 5.14. Shear load versus shear displacement in 0, 5 and 10 kN pretension load in Bolt Types T5 and T6 in 40 MPa concrete
Figure 5.15. The bolt failure view in different pretensioning
0
20
40
60
80
100
120
140
160
180
200
0 10 20 30 40 50
Shear displacement (mm)
Shea
r loa
d (k
N)
.
T5-0 kNT5-5 kNT5-10 kNT6-10N12
1
2
3
4
Curve 1 Curve 2
Curve 3 Curve 4
Failure
Failure
CHAPTER 5: Double shearing of bolts across joints
152
Figure 5.16. (a) Relationship between failure load and maximum tensile strength of the single shear on bolt type T5, (b) bolt failure angle Figure 5.17. Shear load versus shear displacement in 100 MPa concrete and different pretensioning in Bolt Type T1
0
100
200
300
400
500
600
700
800
900
0 10 20 30 40 50 60
Shear displacement (mm)
Shea
r loa
d (k
N)
.
0 kN50 kN80 kN
0
20
40
60
80
100
120
140
160
0 5 10
Pretensioning (kN)
fail
ure
load
ove
r Max
. ten
sile
load
(%)
.
12o
23o
CHAPTER 5: Double shearing of bolts across joints
153
Figure 5.18. Excessive bolt necking in concrete 100 MPa in 80 kN pretension load Figure 5.19. Bolt/ joint concrete interaction at shear joint in concrete 100 MPa and 80 kN pretension load
Confining effect on joint surface
Created gap between bolt -grout interface
Overwhelmed grout under high pressure
L ≈AB 60 mm L AB
A B
B
A
O
Failure location
Bolt Type T1
CHAPTER 5: Double shearing of bolts across joints
154
50kN 80kN with bolt failure
Figure 5.20. Bolt imprint on resin in concrete 100 MPa at 50 and 80 kN pretension loads
The following were deduced from both sets of tests stated above:
A) Testing of Bolt Types T5 and T6 in 40 MPa Concrete:
i. The snapping or failure of the bolt across joint planes, were the results
of both shearing and tensile loading. This is because the failed surfaces
of the bolt were not vertical and parallel to the sheared vertical joint
planes. The failed sheared bolt surface angle was in the order of 12o
from the sheared joint plane shown in Figure 5.16b.
ii. The peak elastic yield point “P” in the bolt has gradually moved from
the plastic hinge point (first yield point in the bolt) towards the bolt /
joint intersection.
iii. Bolt necking initiated around the peak elastic yield point “P”.
Noticeable necking was evident because of the predominately tensile
load at the bolt joint intersection. When necking commences, the bolt
CHAPTER 5: Double shearing of bolts across joints
155
diameter decrease severely on the effective length, which is between the
hinge points in the vicinity of the shear joint.
iv. For the pretension load of 80 kN, the shear displacement at failure for
Bolt Type T6 was 40% higher than the corresponding shear
displacement for Bolt Type T5. As Figure 5.16a shows the relationship
between the failure load and the maximum tensile strength of the Bolt
Type T5 in different pretension, indicating that the slope of the
relationship was in the order of 18o. These results contradicted Ferrero’s
result (1995), which stated that the pretension does not influence the
maximum shear resistance of the system. Ferrero’s tests were
undertaken in a single shear test box, whereby the pretension loads were
applied to one side of the bolt.
B) Testing in 100 MPa Concrete.
As shown in Table 5.7 and Figures 5.17, the following were noted:
i. The displacement rate of the sheared bolted block in 100 MPa strength
concrete was, as expected, lower than in both 20 and 40 MPa concrete
respectively.
ii. The failure load for Bolt Type T1 with Pretension load of 80kN was in
the order of 799 kN. This was in excess of the axial tensile failure load
of the bolt at around 340 kN.
iii. The crushed zones in 100 MPa concrete were less that those obtained in
40 MPa concrete. The length of the crushed zone was in the order of 60
mm on either side of the joint plane. This clearly demonstrated that
CHAPTER 5: Double shearing of bolts across joints
156
during shearing there was significant resistance concrete and hence less
vertical displacement.
iv. No failure occurred at 50 kN pretension load, however the failure was
achieved at 80 kN. The level of concrete crashing and sheared failed
resin imprints are shown in Figure 5.20.
v. During shearing, the bolt failed at around 66 % of the maximum tensile
strength of the bolt. The bolt could not have failed at this level on
purely the axial load, and this demonstrates again that the failure was a
combination of both shear and axial loads at the bolt joint intersection
(see Figures 5.21).
Figure 5.21. The ratio of axial load developed along the bolt over ultimate tensile strength of the bolt versus shear displacement in concrete 100 MPa with 80 kN pretension load
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 10 20 30 40 50 60
Shear displacement (mm)
Axi
al lo
ad /
Ulti
mat
e te
nsile
load
.
CHAPTER 5: Double shearing of bolts across joints
157
5.6.2. Influence of Shearing Load on Pretension Load
Figure 5.22 shows a typical shear load versus bolt pretension load developed along
the bolt installed in a 20 MPa concrete medium. Point A is known as the Limit of
Maximum Frictional Bonding Strength (LMFBS) which indicates shear load values
whereby the pretension load values, monitored by the load cells mounted on either
sides of the bolt, began to increase from the initial applied load. This level of shear
load is significantly higher than the peak elastic yield point (P) shown in Figures 5.9
and 5.10 respectively, and discussed in previous section (5.6.1). The level of shear
load increase was dependent on the initial axial tensile load on the bolt, concrete type
and bolt profile pattern. Figure 5.23 (a-f) shows different shear load and load cell
readings for various bolts. The graph profiles were different for different bolt types.
Figure 5.22. Shear load versus load cell readings on tensile load applied on a bolt installed in a 20 MPa concrete
0
50
100
150
200
250
300
350
400
0 20 40 60 80 100 120 140
Axial load developed along the bolt(kN)
Shea
r loa
d (k
N)
.
LMFBS
• A
CHAPTER 5: Double shearing of bolts across joints
158
Figure 5.23 (a-f). Shear load and pretension loads (load cell readings) for various bolts with initial pretension load of 20, 50 and 80 kN
(b) Bolt Type T2 in 20 MPa concrete (e) Bolt Type T1 in 40 MPa
0
100
200
300
400
500
600
0 50 100 150
Axial load along the bolt (kN)
Shea
r loa
d (k
N)
.20 kN50 kN80 kN
050
100150200250300350400
0 20 40 60 80 100 120 140
Axial load along the bolt (kN)
Shea
r loa
d (k
N)
.
20 kN50 kN80 kN
• A
B C
• •
(a) Bolt Type T1 in20 MPa concrete (d) Bolt Type T1 in 40 MPa concrete
0
100
200
300
400
500
600
0 50 100 150
Axial load along the bolt (kN)
Shea
r loa
d (k
N)
.
20 kN50 kN80 kN
0
100
200
300
400
500
0 50 100 150 200
Axial load along the bolt (kN)
Shea
r loa
d (k
N)
.
20 kN50 kN80 kN
A B C • •
•
(c) Bolt Type T3 in 20 MPa (f) Bolt Type T3 in 40 MPa
050
100150200250300350400
0 50 100 150 200
Axial load along the bolt (kN)
Shea
r loa
d (k
N)
.
20 kN50 kN80 kN
A
B
C
•
•
•
0
100
200
300
400
500
600
0 50 100 150
Axial load along the bolt (kN)
Shea
r loa
d (k
N)
.
CHAPTER 5: Double shearing of bolts across joints
159
The following can be observed from the shear load versus axial load built up
along the bolt in different pretension load and concrete strengths.
i. The level of initial confining axial load applied to bolts had profound
influence on the applied shear load at the LMFBS between the bolt and
the resin. The higher was the initial tensioning load, the greater was the
shear load at the LMFBS.
ii. The shear load values at the LMFBS were greater than P at the shear load
shear displacement curve in all levels of pretensioning and concrete
strengths.
iii. Back sloping of the load cell-shear load graph prior to the failure of the
frictional bonding strength in high pretension load (80 kN) was attributed
to the crushing of the concrete blocks as indicated in Figure 5.24. Clearly
the bolt appears to have pulled through the concrete as the shear load was
increased. This phenomenon was more common in weaker concrete such
as in 20 MPa concrete medium. Thus 20 MPa concrete was too weak for
testing 22 mm core diameter bolts.
iv. Bolt Type T2 installed in the 40 MPa concrete had comparatively greater
shear load at LMFBS point than the other two bolts.
v. The level of shear displacement at the LMFBS point was dependent on
the level of initial pretension load. As can be seen from Figure 5.25. The
shear displacement was greater in 80 kN pretension load than the other
two profiles with 20 and 50 kN pretension loads.
CHAPTER 5: Double shearing of bolts across joints
160
Figure 5.24. End crushing of the concrete in high pretensioning load
Figure 5.25. Axial load developed along the bolt versus shear displacement in Bolt Type T2 in 40 MPa concrete
5.6.3. Load Transfer Level In Different Profile
Figure 5.26 shows the comparison of the peak P values as a function of pretensioning
in different bolt profiles and the concrete strength. From the graph it can be seen that
the level of P has increased with increasing the concrete strength in different bolt
0
20
40
60
80
100
120
140
0 5 10 15 20 25 30 35
Shear displacement (mm)
Axi
al lo
ad a
long
the
bolt
(kN
) .
20kN50 kN80 kN
5.8 mm
7.7 mm
8.6 mm
Compressed
CHAPTER 5: Double shearing of bolts across joints
161
profiles. Bolt Types T3 and T2 had the lowest and highest (P) levels respectively in
20 MPa concrete. The graph also show that, in 20 MPa strength, the effect of
pretensioning in lower pretension load was much more effective than the higher
pretension load. In addition, it shows that Bolt Type T2 in 40 MPa concrete has
almost constant trend. In all the laboratory tests it was noted that the yielding of the
bolt bar begins at the plastic hinge point, which is positioned between 20 and 40 mm
from the shear joint plane, was dependent on the materials properties and test
conditions.
Figure 5.26. Effect of pretension load, bolt profile and concrete strength on the bolt resistance What is also obvious is that the failed area in the concrete mass was two or three
order of magnitude greater than the cross sectional area of the bolt. Once again this is
a clear indication that the bolt has failed under the combination of both shear and
axial load conditions.
0
50
100
150
200
250
300
350
0 20 40 60 80 100
Pretensioning (kN)
Yie
ld lo
ad (k
N)
.
T1, 20 MPa
T3, 20 MPa
T2, 20 MPa T1, 40 MPa
T2, 40 MPa
T1, 100 MPa
CHAPTER 5: Double shearing of bolts across joints
162
5.6.4. Double Shearing of Instrumented Bolt
To gain a clear understanding of the pattern of build up of loads and stresses along
the bolt, two tests were carried out on strain gauged instrumented bolts (Bolt Type
T2), one test was made with bolt not subjected to pretension load (zero pretension)
and the other with a pretension load of 20 kN. Figures 5.27 and 5.28 show the
location of the strain gauges in Bolt Type T2. In each designated locations 1 to 6,
strain gauges were mounted on a side of the bolt surface. However, there were only
single strain gauges at locations 7 and 8, which were situated at the lower side of the
bolt. The spots where the strain gauge located had the bolt profile ground flat and
smoothed. The 21.7 mm core diameter bolts were installed in 27 mm holes as per
previous tests. Both tests were carried out in 40 MPa concrete. Details of strain
gauges positions are clearly marked in Figure 5.27. The strain gauge measurements
revealed that both the tensile and compression stresses were generated along the bolt
length during the shearing process.
By comparing the axial strain at each location along the bolt, the axial stress could be
determined by equation 5.1:
(5.1)
and the shear stress distribution can be given by:
lr
Erl
Aajaib
baijij 2
).(2
.εε
πσ
τ −== (5.2)
where;
aijσ = Change in axial stress between two adjacent gauges
bE = Bolt modulus of elasticity (MPa)
)( ajaibaij E εεσ −=
CHAPTER 5: Double shearing of bolts across joints
163
a) Without pretension load
b) 20 kN pretension load and the distance measurements
Figure 5.27. Schematic diagram of the strain gauges locations in the reinforcing element (a) without pretension load and (b) 20 kN pretension load
Strain gauges gauges
•
2 3 4 5 6
1
Tension
Compression Tension
Joint
Bolt
• • • • •
Grout
Load cell
150mm 300mm 150mm
• • • • • • 1 2 3 4 5 6
Strain gauges Tension
CompressioTension
Joint
Bolt
• • 7 8
Joint
grout
Load cell
30 30
60 60
90
• • • • • • • •
30 30
CHAPTER 5: Double shearing of bolts across joints
164
aiε = Axial strain at gauge 1( sµ )
ajε = Axial strain at gauge 2( sµ )
l = Distance between gauges (mm)
r = Bolt radius (mm)
Using the above equations in un-loaded conditions, it was found that, for a 30 kN
shear load, the maximum tensile and shear stresses, between the strain gauges 3 and
4 at the bolt / grout interface were 196 MPa and 35 MPa respectively. Beyond this
load, the stresses were reduced, indicating the bond failure between bolt and grout.
The minimum axial and shear stresses were recorded at 50 kN shear load, which are
approximately 18 and 3.25 MPa respectively. Further analyses are presented in
Appendix B. This situation is occurred at the elastic region of the shear load-shear
displacement curve, which is supported by experimental and numerical results. It
should be noted that the distribution of the shear stress prior to the yield point is in
agreement with Farmer’s theory (1995). Load build up registered for the rest of the
strain gauges are shown in Figure 5.28. Figure 5.29 shows a section of the bolt with
strain gauges mounted on its outer surface. Figure 5.30 shows the variation of the
strain changes along the bolt.
The following were observed:
i. Strain gauge No 3 in non-pretension case, located in the compression zone
and placed 60 mm away from the shear joint, produced 2.5 % strain at 60 kN
shear load (one half of the total shear load acting of two joint planes). This
value of strain is in the range of the plastic region (higher than 0.3 % at the
end of the elastic region). This yield situation has occurred around 20% of the
maximum tensile strength of the bolt.
CHAPTER 5: Double shearing of bolts across joints
165
ii. The formation of two plastic hinges in the bolt symmetrically opposite to
either side of the sheared joint plane was determined by strain measurements.
Beyond the hinge point and towards the bolt ends there was a gradual decline
in the rate of bolt strain. This was in line with the findings obtained from the
numerical simulation. From the strain gauges located in the vicinity of the
hinge points, it was found that very small shear loads (12 kN at strain gauge
no 5) were needed to subject the outer profiles to strain. Thus it was clearly
evident from Figure 5.28 that both the tensile and the compression zones are
initiated in the bolt during the early process of shearing.
iii. From the pretension case it was found that the hinge point is located around
30 mm from the shear joint. The location of the hinge points depends on the
strength of the concrete. In week concrete, there will be excessive crushing of
the concrete in the vicinity of the sheared joint faces leading to higher
distance between the hinge point and joint spacing. However, the hinge point
location will be closer in high strength concrete.
Figure 5.28. The shear load versus strain measurements in non-pretension load
0
20
40
60
80
100
120
140
160
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1
Strain %
Shea
r Loa
d (k
N)
.
strain 3
strain 1
strain 4
strain 5
CHAPTER 5: Double shearing of bolts across joints
166
Figure 5.29. The bolt surface with strain gauges installed
Figure 5.30. The strain rate along the bolt, drawn by strain measurements in non-pretension load Figures 5.31 and 5.32 show the relationship between the applied shear load and
strains developed along the bolt in 20 kN pretension load.
Figure 5.31. Shear load versus strain gauge measurements along the bolt in 20 kN pretensions.
0
50
100
150
200
250
300
350
400
450
500
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Strain %
Shea
r loa
d (k
N)
.)
gauge 1
gauge 2
gauge 3
gauge 4
gauge 5
gauge 9
gauge 7
gauge 6
Joint
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
-10 -8 -6 -4 -2 0 2 4
Length along the bolt (cm)
Stra
in %
Right side of the joint Left side of the joint
CHAPTER 5: Double shearing of bolts across joints
167
Figure 5.32. The variation of the strain gauge measurements along the bolt at 20 kN pretension load It is clear from the strain gauge measurements that the higher values of the strain
occurred within the distance of 30 mm from either side of the shear joint plane. Thus
it is reasonable to assume that the location of the hinge points are likely to be in these
zones and this finding is in agreement with the numerical studies discussed later in
Chapter 7. Further analysis of the strain variations along the bolt as shown in
Appendix B.
5.6.5. Medium (Concrete and resin) Reaction
When a bolted joint is sheared, the surrounding materials (concrete and grout)
deform and induce support reaction against the shear load along the bolt’s length.
This reaction depends upon the mechanical properties of the rock and grout. It is
noted that at early stages of shearing, the surrounding materials behave elastically,
which ends at around 10-20% of the loading time- as determined from the numerical
analysis- discussed later in the numerical chapter 7. The severities of these changes
Bolt axis
-0.5
0
0.5
1
1.5
2
-10 -5 0 5 10
Distance from shear joint (cm)
stra
in %
Right side of the joint Left side of the joint
CHAPTER 5: Double shearing of bolts across joints
168
depend upon several parameters, such as the mechanical and physical properties of
the bolt, rock and grout strength and bolt pretension load. Yield in the surrounding
materials will begin in the vicinity of the shear joint and propagates with increasing
bolt deformation. The grout annulus yields when the shear load (lateral bolt pressure)
at the bolt/joint intersection becomes equal to the grout yield strength. Grout
separation will start from the hinge point towards the shear joint and completely
separates from the bolt in the tension zone. Due to the axial bolt load, the yield in the
grout can be determined when the actual bond stress, τ between bolt and grout is
equal to the grout yield strength yτ as:
1=yτ
τ
When the yield occurs in the surrounding material, the axial bond strength between
the bolt/grout will change and on the yielding length the residual bond strength is
considered to be frictional and a function of the lateral pressure. This relationship can
be written as:
)( xres pµτ = where; τ = Bond shear stress (MPa)
yτ = Grout shear strength (MPa)
resτ = Residual bond strength (MPa)
µ = Friction coefficient between bolt-grout interface
)( xP = Support reaction (MPa)
(5.3)
(5.4)
CHAPTER 5: Double shearing of bolts across joints
169
For bolt lateral deformation, the rock is affected by the bolt pressure and the yield
in concrete is initiated from the pressure zone, which is in the vicinity of the bolt
joint intersection. In other words, the yield appears in the concrete when the
maximum elastic deformation of the concrete is exceeded. Gradually yield is
developed and expanded through the rock with increasing the bolt deformation.
Figure 5.33 shows the concrete block being split axially along the bolt, due to the
high stresses induced along the shear direction through the concrete blocks.
These fractures originate from the compression zone (critical zone in the vicinity
of the shear joint) and propagate into the upper side of the concrete block. By
splitting the concrete, the reaction pressure reduces and then the bolt deformation
increases with increasing the shear load. It is noted that block fracturing was
observed in all of the double shear tests performed. Figure 5.34 displays the gap
created between the bolt and the grout in the plastic stage, which was around 0.8-
1.0 Db (Db= bolt diameter). It is reasonable to conclude that the contact surface
area from the shear joint plane along the bolt between bolt/grout/concrete
interfaces gradually decreases to form the gap in the vicinity of the shear joint.
Figure 5.33. Axial fracture developed along the bolt through the 20 MPa concrete
Axial fracture
CHAPTER 5: Double shearing of bolts across joints
170
Figure 5.34. The created gap in plastic stage
5.6.6. Prediction Of The Bolt Contribution
Bolt contribution to the shear strength of the reinforced shear joint plane depends
upon the rock/ concrete strength, grout strength, bond strength between the
interfaces, mechanical and physical properties of the steel bolt, joint specification
and bolt pretension loads. Each of these parameters, as discussed in previous
chapters, plays significant role in affecting the shear resistance and the failure
mechanism. Some of the affected parameters on the bolt contribution are inherent
specification for the shear joint which were found by direct shear tests on 20 and 40
MPa concrete joint planes. Based on the laboratory studies and shown in Table 3.6,
the value of the friction angle for 20 and 40 MPa concrete were measured as 31o and
38o respectively. Thus the confining effect can be calculated as;
ϕtanncN c += (5.5)
where;
cN = Confining load (kN)
Gap height
CHAPTER 5: Double shearing of bolts across joints
171
c = Cohesion between block joints (kN) n = Normal force (kN) ϕ = Angle of friction (o) When the bolt is subjected to shearing, the total shear resistance is a combination of
the joint without reinforcement element and bolt contribution. According to Mohr
Coulomb criterion, the shear joint contribution under the confining pressure can be
expressed as in Equation 5.6. Also the bolt contribution can be expressed as in
Equation 5.7.
(5.6)
(5.7)
where;
)(tf = Bolt contribution
vT = Shear load
)(2
tan2
2tan2
tan2
max
max
tfFNT
T
FT
T
NTT
NT
T
cvb
tb
cvt
cv
t
=−=
=
−=
−=
ϕ
ϕ
ϕ
CHAPTER 5: Double shearing of bolts across joints
172
tT = Joint contribution
maxF = Maximum tensile strength of the bolt
b
b
Du
uf =)(
)(uf = Dimensionless factor in terms of shear displacement,
bu = Shear displacement and
bD = Bolt diameter.
Table 5.8 shows the confining force value in different concrete strength and various
level of pretensioning. By using the above equations in different rock strength and
various level of pretensioning, the bolt contribution is calculated
Table 5.8. Joint confining specification
The bolt contribution in bolt Types T1, T2, T3, T4, T5 and T6 in different concrete
strength and bolt pretension loads are presented in Appendix B.
Concrete strength (MPa
Pretension load (kN)
Joint angle of friction
(o)
Confining load (kN)
20 31 12
50 31 30 20
80 31 48 20 38 15.6
50 38 23.4 40 80 38 62.5
CHAPTER 5: Double shearing of bolts across joints
173
Based on the laboratory results in different concrete strength, pretension load and
steel strength, the following relationships were established among the related
parameters;
(5.8) (5.9)
where;
bT = Yield point at shear load- displacement curve
cσ = Uniaxial compressive strength of the rock (MPa)
tyf = Pretension load (kN)
yu = Joint movement (mm), which is usually twice bolt deflection
bD = Bolt diameter (mm) From the equation it can be envisaged that the increase in the rate of the bolt
contribution reduces when concrete strength increases. Figure 5.35 shows the effect
of concrete strength on factor of the shear movement in both the numerical and
experimental analysis. The numerical results were conducted without pretension
load. Clearly as the concrete strength increased the shear displacement factor f(u)
tapers of exponentially reaching a constant level of around 0.5 beyond the concrete
strength of 60 MPa.
239)(058.0)(014.0)ln(5.120 2 −++= tytycb ffT σ
96.4)ln(06.1 +−= cb
y
D
uσ
CHAPTER 5: Double shearing of bolts across joints
174
Figure 5.35. Effect of concrete strength on the factor of movement
With the inclusion of the resin thickness and the strength properties of the steel while
maintaining the other parameters constant, the following relationship was stabled
using the statistical method SPSS V.7 software with 77 % correlation factor;
(5.10) where;
bT = Shear yield load (kN)
yσ = Maximum tensile strength of bolt (kN)
bD = Bolt diameter (mm)
hD = Hole diameter (mm)
Pr = Pretension load (kN)
cσ = Uniaxial compressive strength of the rock (MPa)
53.0)(005.0(Pr)004.0)(36.0 +++−= ch
b
y
b
DDT σ
σ
0
0.5
1
1.5
2
2.5
0 20 40 60 80 100 120
Conrete strength (MPa)
numeric
Lab
)(uf
CHAPTER 5: Double shearing of bolts across joints
175
Figure 5.36 shows the relationship between the expected and observed results, which
show good agreement between predicted and observed results.
Figure 5.36. Expected cumulative results versus observed cumulative results
The following were deduced from the bolt contribution in all types of bolts.
• From the results in bolt Type T1, T2 and T3 it is concluded that the
maximum bolt contribution of the bolts depends upon the concrete strength
and bolt pretension load.
• In 40 MPa concrete, for instance, in bolt Type T1, it was found that in case of
un-pretensioned load, there was no significant change in the level of bolt
contribution. However, the bolt contribution was increased to around 70 % in
20 MPa concrete when the bolt was pre-tensioned.
• The bolt Type T3 has shown lower level of contribution in comparison with
bolt Types T1 and T2 in 20 MPa concrete.
• Bolt contribution was increased around 15 % with existence of the resin grout
compared with absence of the grout at the same conditions.
CHAPTER 5: Double shearing of bolts across joints
176
• Despite the lower shear load developed at the bolt- joint intersection in bolt
Type T5 compared with bolt Type T6, the overall bolt /joint contribution in
bolt Type T5 is higher than the bolt Type T6- 125% of the maximum tensile
strength of the bolt against 135%. This means that the bolt contribution
significantly depends upon the maximum tensile strength of the bolt.
• The axial and shear loads are at their maximum at the bolt - joint intersection.
However, it has to be considered that for those cases in which the resistance
factor is less than 1, the shear stress is dominant. In particular for case
without pretensioning the resistance factor is around half of the maximum
tensile strength of the bolt, which bolt has likely failed in the pure shearing
condition. The reason for this is when the bolt is moving down -as there is no
axial load against axial movement, it can move easily and no axial stress
develops along the bolt. Then the bolt failure is due to the only shear stresses.
• From the bolt Type T1 in 100 MPa concrete it was found that the maximum
bolt-joint contribution at failure is about 120 % of the maximum tensile
strength of the bolt.
• The value of bolt contribution at yield point in concrete 20, 40 and 100 MPa
in Bolt Type T1 was about 0.24, 0.3 and 0.52 respectively.
5.7. SUMMARY
The double shearing study has demonstrated its importance in better understanding
of the role that a bolt would play in real ground reinforcements particularly in
sheared zones. The double shear system represented a better method of shearing
CHAPTER 5: Double shearing of bolts across joints
177
system as it enabled to allow a symmetric study of bolt shearing analysis, which is
not possible with available systems.
Accordingly the following were deduced from the study:
• Bolt profiles plays a significant role in load transfer mechanism,
• Bolt pretensioning contributes to increased level of shear resistance,
• The resistance of the bolt will dependent on the concrete strength
• Increasing the concrete strength reduces significantly the joint shear
displacement and contributed to increased shear stiffness.
The study demonstrated that the current size of the double shearing apparatus is
insufficient to conduct tests with larger diameter bolts. It thus recommended that the
size of the system to be doubled for effective results.
CHAPTER 6: Role of bolt annulus thickness on shearing
178
CHAPTER 6
ROLE OF BOLT ANNULUS THICKNESS ON BOLT
SHEARING
6.1. INTRODUCTION
The effect of resin thickness when bolt is axially loaded was investigated extensively
which was mentioned in Chapter 4. It was concluded that the optimum resin annular
spacing of 3-4 mm provides the safe installation and interlocking effect while bolt is
subjected to axial loading, Skybey (1992). In this method of loading, the anchorage
capacity decreases dramatically with increased annular spacing. However, there exist
no reported results in terms of resin thickness so far when bolt is subjected to lateral
loading (bending). Here, the effect of annulus on the shear resistance and shear
stiffness is considered.
6.2. TEST METHOD
To investigate the effect of resin thickness on load transfer mechanism and bending
behaviour of the fully grouted rock bolts, only bolt type T1 was selected through the
various types of bolts tested in previous section. Tests were carried out in two
concrete strengths, 20 and 100 MPa, in 25, 27, 28, and 36 mm hole diameter. All
tests were accomplished at the same pretensioned load - 20 kN. From the
investigations the following results were established.
CHAPTER 6: Role of bolt annulus thickness on shearing
179
6.3. EXPERIMENTAL RESULTS AND DISCUSSION
Tables 6.1 and 6.2 show the results of experimental tests in different resin
thicknesses. From the tables, it can be found that the yield load of the bolt-joint
reinforced system has increased 21% with an increase of annulus from 1.6 to 7.1
mm. In this situation, shear displacement has showed a 36 % reduction. Thus, the
bolt-joint stiffness has increased up to %65, which revealing the high effectiveness of
resin thickness in particular when the concrete strength is lower than resin strength.
Table 6.1. The results of bolt tested in type T1-20MPa strength with 20 kN pretension load
Db (mm)
Dh (mm)
Annulus (mm)
Hinge distance
(mm)
Bolt deflection
(mm)
Bolt bending
(o)
Comment
21.7 25 1.6 60 63 42
21.7 27 2.6 59 60 38
21.7 28 3.1 50 65 40
21.7 36 7.1 45 67 50
20 MPa
21.7 36 7.1 27.5 49 51 100MPa
Table 6. 2. The results of shear test in different resin thickness and concrete strength
Db
(mm) Dh
(mm) Annulus
(mm) Yield
load (kN) Yield
displacement (mm)
Failure load (kN)
Stiffness (kN/mm)
Remarks
21.7 25 1.6 163 6.23 762 26 21.7 27 2.6 168 5.83 813 29 21.7 28 3.1 177 5.37 821 33 21.7 36 7.1 198 4.57 756 43 * 21.7 36 7.1 259 6.53 784 40 100MPa
* This test stopped at plastic range and after dropping the load again was loading.
CHAPTER 6: Role of bolt annulus thickness on shearing
180
6.3.1. Shear load/ shear displacement
Figure 6.1 presents the comparison of shear load versus shear displacement in
different resin thickness. The shear load shear displacement for individual resin
thickness is presented in Appendix C.
Bar charts 6.2 and 6.3 show the effect of hole diameter on shear yield displacement,
yield load respectively. The shear stiffness is one of the important factors in resisting
shear along the joint surfaces.
In all the tests after the yield point, it can be seen that there is a gradual significant
increase in the shear load with high value of the shear displacement until failure
reached in the bolt at the bolt/joint intersection. In 27 mm hole diameter bolt was not
snapped. However, there was 5.6 % bolt diameter reduction at the bolt joint
intersection. Bolt yielded at 168 kN with 5.8 mm displacement.
Figure 6. 1. Shear load as function of shear displacement in different resin thickness
25 mm
0
100
200
300
400
500
600
700
800
900
0 20 40 60 80 100
Shear displacement (mm)
Shea
r loa
d (k
N)
.
27mm25mm28mm36mm
CHAPTER 6: Role of bolt annulus thickness on shearing
181
Figure 6. 2. Effect of resin thickness on shear displacement
Figure 6.3. The effect of resin thickness on shear load shear displacement yield point
25 27 28 36
163 168177
198
0
50
100
150
200
250
1 2 3 4
Parameter
Hol
e si
ze a
nd Y
ield
load
(mm
-kN
) .
.
Dh
yield Load
0
5
10
15
20
25
30
35
40
1 2 3 4parameter
Hol
e si
ze a
nd y
ield
dis
pl.(m
m)
.
Dh
yield displ
Parameter
CHAPTER 6: Role of bolt annulus thickness on shearing
182
In addition, it reveals that beyond the yield load, there was significant increase in
shear load- approximately four times before failure- due to reaction pressure, the
confining effect and the bolt pretensioning.
In case of 36 mm hole diameter the hinge point distance is lower than the lower resin
thickness, about 45 mm, which is 70% of thin resin annulus. In addition, the higher
resin thickness showed the higher shear yield load, which is due to the resin annulus.
It should be noted that the resin strength was more than triple concrete strength (see
chapter 3). This makes a stronger beam around the bolt and finally a stronger system,
that shows lower overall resistance and lower shear displacement.
With increase of the resin annulus, shear yield displacement was reduced, yield load
and shear stiffness was increased. Figure 6.4 shows the shear load versus the shear
displacement in different resin thickness and concrete strength. With comparison to
20 MPa concrete in different resin thickness it was found that there is a high level of
shear load in higher resin thickness and lower overall resistance in higher resin
thickness, which is expected. In addition it revealed that higher concrete strength
appears to have lower overall resistance. Besides, this shows that lower resin
thickness in high concrete strength has lower overall resistance, because the lower
resin annulus in high strength concrete makes it stronger as resin strength is 60% of
the concrete strength. Also it shows there is a high level of the shear yield load in the
lower resin annulus compared with higher resin annulus in stronger concrete. This
means stronger and stiffer surrounding material tends to have a higher shear
resistance to be induced in the bolt and lower overall resistance in the system. It is
inferable that overall bolt contribution in lower strength concrete is slightly higher
than the high strength concrete. The reason, in soft concrete strength, the bolt can
mobilized a greater axial force due to its ability to be deformed.
CHAPTER 6: Role of bolt annulus thickness on shearing
183
Figure 6.4. Shear load and shear displacement in concrete 20 and 100 MPa and 20 kN pretension load and different resin thickness in Bolt Type T1 Figure 6.5 and 6.6 show the resin breaking and gap creation in high and thin resin
thickness at the vicinity of the bolt joint intersection in concrete 20 and 40 MPa
respectively with 20 kN pretension load. From the Figure 6.5 it can be seen that grout
is separated from the bolt in the tension zone, and is crushed by pressing in the
compression zone. In higher concrete strength in Figure 6.6, resin has broken off but
is not separated, due to harder concrete.
Figure 6.5. Gap creation between bolt grout at high resin thickness in concrete 20 MPa with 20 kN preload (5 mm thick)
0
100
200
300
400
500
600
700
800
900
0 20 40 60 80
Shear displacement (mm)
Shea
r loa
d (k
N)
.
80 kN-27mm-10020kN-36mm-100
20kN-36mm-2020kN-27mm-20
Easily will be separated due to tension cracks
CHAPTER 6: Role of bolt annulus thickness on shearing
184
Figure 6.6. Gap creation between bolt grout at high resin thickness in concrete 40 MPa with 20 kN preload (5 mm thick)
6.3.2. Axial load built up
Figure 6.7 presents the shear load as a function of axial load build up along the bolt.
As stated in chapter 5, point A is called LMFBS.
Figure 6.7. Shear load and axial load build up along the bolt in concrete 20 MPa and 20 kN pretension load and thin resin thickness in bolt Type T1 (25mm)
The trend of axial load generation can be classified into three sections. In the first
part, the increase in axial load is negligible. At the end of this part, which is LMFBS,
A
0
100
200
300
400
500
600
700
800
900
0 50 100 150 200 250
Axial load along the bolt (kN)
Shea
r loa
d (k
N)
.
1
2
3
LMF•
CHAPTER 6: Role of bolt annulus thickness on shearing
185
the axial load begins to increase and continues gradually with high shear
displacement. This means when failure occurs in the surrounding materials, grout
and rock, the bolt can penetrate through its base bottom. As it is pretensioned, the
axial load increases along the bolt.
The third section usually will start from 70% of the shear failure load, while the
increase rate of axial load is decreasing with higher shear displacement rate. This is
more likely around the bolt necking. This behaviour continues until complete failure
in the bolt at the bolt joint intersection. Figure 6.8 shows the axial load developed
along the bolt as a function of the shear displacement in different resin thickness.
Figure 6.9 shows the axial load shear displacement in 27 mm hole diameter. The
same trend was found in all resin thickness (see appendix). It shows that the smooth
behaviour at the beginning is due to the elastic behaviour of the materials and their
strength, which don’t transfer much load on the bolt.
Figure 6.8. Shear load versus axial load developed along the bolt in different resin thickness in 20 MPa concrete
0
100
200
300
400
500
600
700
800
900
0 20 40 60 80 100 120 140 160 180 200 220
Axial Load along the bolt (kN)
Shea
r loa
d (k
N)
.
27 mm25 mm28 mm36 mm
CHAPTER 6: Role of bolt annulus thickness on shearing
186
The smooth end has resulted for the bolt necking and reaches to the failure, causing
reduction in bolt resistance and higher rate of the shear displacement.
Figure 6.9. Axial load versus- shear displacement in bolt T1 and 20 kN preload in 27 mm hole diameter surrounded by 20 MPa concrete
6.3.3. Failure mechanism of reinforced element
Those bolts, which reached failure, continued very lengthy plastic behaviour and
finally failed due to the applied shear load and generated axial load. This ductile
behaviour happens in the bending region, which is located between hinge points. By
increasing shear load, the axial load is increased at the straight length of the bolt in
the bending region and then by combination of the axial and shear load at the vicinity
of the shear joint, the bolt was failed.
Figure 6.10 presents the axial stress along the bolt versus shear displacement in high
resin thickness. It shows in nearly half of the maximum deflection, the shear stress
developed five times which is due to the acceleration of the load generation along the
0
50
100
150
200
250
0 20 40 60 80 100
shear displacement (mm)
Axi
al lo
ad a
long
the
bolt
(kN
)
.
Axial load
Smooth trend
Smooth trend Low rate of axial load
Low rate of axial load
CHAPTER 6: Role of bolt annulus thickness on shearing
187
bolt. This occurrence happens beyond the LMBFS. From the figure it can be seen
that the maximum stress build up along the bolt is about 600 MPa, which is nearly
equal of tensile yield point of the bolt. However, the bolt failed in this test. If we
accept that the bolt should fail only by axial load, bolt should not be failed in this
stress, which is less than tensile yield point of the bolt, while bolt was failed and
snapped in this level of the stress. Thus it is inferred that bolt failure is combination
of the axial and shear loads developed in the bolt joint intersection. Figure 6.11
shows the axial resistance factor (axial load build up, over ultimate bolt tensile
strength) versus shear displacement. It depicted that after the yield point, the axial
load generation in all different resin thickness is approximately the same. However,
beyond the yield point, the higher resin thickness appeared to have higher resistance
factor, being 13% of the maximum tensile strength of the bolt compared with 9% in
lower resin thickness. In all of these tests the bolt failed during the shearing process.
However, the maximum load generation along the bolt is 67% of the maximum
tensile strength of the bolt.
Figure 6.10. Axial stress versus shear displacement in bolt Type T1 in 20 kN preload in 36 mm hole diameter surrounded by 20 MPa concrete
0
100
200
300
400
500
600
700
800
900
0 20 40 60 80
Shear displacement (mm)
Axi
al s
tress
(MPa
) .
stress
CHAPTER 6: Role of bolt annulus thickness on shearing
188
Figure 6.11. Comparison of the axial load induced in bolt in different resin thickness in 20 MPa strength (axial resistance factor is equal axial load over ultimate tensile strength of the bolt)
This means that, at least 33% of the failure load is applied by shear load. So it can be
again inferred that the bolt has failed under a combination of the axial and shear load.
Figure 6.12 shows the side profile of the failed rock bolt embedded in 36 mm hole
diameter and 20 MPa surrounding concrete in 20 kN pretensioning. Inspection of the
failed reinforcing element showed that the failed surface causes the axial and
shearing failures, which initiates with small cracks from the center. However, it is
supposed that after the yield point, the shear stress generation in the vicinity of the
shear joint through the reinforced bar is almost constant and the bolt fails with the
increase of the axial load along the bolt due to much bending with combination of
shear load developed. It shows the shear lip in the failed bolt has created an ellipsoid
shape. This was found by Mahony et al. (2005) as well.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 20 40 60 80 100
Shear displacement (mm)
Axi
al re
sist
ance
fact
or
.
36mm28mm25mm
CHAPTER 6: Role of bolt annulus thickness on shearing
189
(a) (b) Figure 6.12. Side profile of failed bolt Type T1 surrounded by concrete 20 MPa and 36 mm hole diameter at 20 kN pretension load b) typical end profile of a failed reinforcing element The following can be found from shear load/shear displacement and axial load
results in different resin annulus.
• At given shear load the axial load developed along the bolt in low resin
thickness is higher than the high resin thickness
• As the resin strength is significantly higher than the surrounding material in
soft concrete (20 MPa) higher resin annulus makes the stronger system
• Higher resin thickness showed high level of shear yield load and a low level
of maximum axial load on the bolt
• Hinge point distance was reduced with increase of resin annulus surrounded
by soft concrete
• Shear displacement was reduced at the shear yield load in high resin
thickness
• Shear stiffness was increased with increase of resin thickness
• Higher resin thickness shows higher LMFBS (Limit of maximum frictional
bonding strength).
CHAPTER 6: Role of bolt annulus thickness on shearing
190
• As in soft concrete, bolt bending generates extensive stress on resin /
concrete interface and failure occurs by shearing of the concrete at the resin /
concrete interface. It is assumed that bolt and resin strengths are more than
adequate to transfer the required load. Thus, to distribute the concentrated
shear stress on the rock and also to obtain larger and stronger anchorage,
increasing the hole diameter is a recommended option. However, in strong
surrounding material (rocks) increasing the resin thickness is not suitable
option as it decreases shear stiffness. Sakurai and Kawashima (1992)
reported that the stiffness of rock mass increases when rock bolts are
installed. This increase in stiffness is more dominant in hard rocks than in
soft rocks.
Consequently it can be concluded that in lower rock strength, to obtain the higher
bolt-joint stiffness/shear resistance, increasing the grout annulus is so important to
achieve this goal. It should be noticed that this is when the resin strength is higher
than the rock strength. However, in higher concrete strength and lower resin strength,
the shear stiffness reduces as resin thickness increases.
6.3.4. Effect of resin thickness on shear stiffness
Bar charts 6.13 show the effect of hole diameter on shear stiffness. The shear
stiffness is one of the important factors in resisting shear along the joint surfaces.
It shows the shear stiffness in higher resin thickness is higher than the lower resin
thickness. It has to be mentioned that the stiffness value by numerical simulation was
found to be 12 and 19 kN/mm without a pretensioning load at 27 and 36 mm hole
diameter respectively.
CHAPTER 6: Role of bolt annulus thickness on shearing
191
Figure 6.13. The effect of hole diameter versus stiffness
From the experimental results it can be inferred that the effective stiffness of a fully
grouted rock bolt depends on the mechanical properties and physical configuration of
the bolt, grout and rock and annulus thickness. (Gerdeen 1997) expressed an
analytical method to find the effective stiffness of the bar, assuming a rigid rock
mass as following equation. In the case of rigid rock mass and high resin thickness,
the above equation almost can offer the acceptable prediction as compared with
experimental results. However, as the rock property, which plays the great role on
the reaction pressure and shear load level, is neglected, this equation in soft rock
predicts incorrect results.
(6.1)
(6.2)
(6.3)
(6.4)
Stiffness
H
ole
diam
eter
2527 28
36
13 14.416.5
21.6
0
5
10
15
20
25
30
35
40
1 2 3 4
Parameter ( hole diameter and Stiffness)
Stif
fnes
s-H
ole
size
(kN
/mm
-mm
)
.
Dh
stifness
)(
2
64
4
4
4
3
bh
g
b
s
DD
EK
DI
EIK
EIK
−=
=
=
=
π
α
α
CHAPTER 6: Role of bolt annulus thickness on shearing
192
where;
E = Modulus elasticity of the bar
gE = Modulus of elasticity of the grout
hD = Hole diameter
bD = Bolt diameter
I = Bolt moment of inertia
In 36 mm hole size when the resin is three times stronger than the concrete, it
predicts shear stiffness 21 kN/mm against 21.6 kN/mm from laboratory.
As resin thickness reduces, whereas the overall strength of the surrounding material
changes to softer material, the stiffness will change, this model cannot predict it and
again gives higher shear stiffness, which is unrealistic prediction.
The empirical method to find the reinforcement system stiffness is calculated
according to the equation below.
(6.5) (6.6) where;
sK = Bolt stiffness (kN/mm)
at = Resin thickness (mm)
bD = Bolt diameter (mm)
hD = Hole diameter (mm)
)068.0137.0ln(1.24 bas DtK +=
2bh
a
DDt
−=
CHAPTER 6: Role of bolt annulus thickness on shearing
193
By expanding the equation in a larger range of hole diameter it was concluded that
the angle of stiffness declines gradually.
6.4. NUMERICAL SIMULATION IN DIFFERENT RESIN
THICKNESS
Numerical finite element method in different resin thickness and different concrete
strength was carried out with ANSYS 9.1, which was discussed properly in
numerical chapter. In this investigation different hole diameter, namely 25, 27, 32
and 36 mm in 20 and 40 MPa concrete was simulated. Figure 6.14 and 6.15 show the
effect of hole size and concrete strength on shear displacement.
From the numerical analyses it was found that the relation between shear
displacement and concrete strength in 27 and 36 mm hole diameter (2.5 and 7 resin
annulus) is according to the following equations respectively.
(6.7)
(6.8)
Where, yU is shear displacement (mm) and cσ is uniaxial compressive strength of
the concrete (MPa)
Table 7.3 displays the effect of concrete strength on shear displacement in different
resin thickness. It shows there is slightly decrease in displacement in elastic
behaviour compared with significant displacement reduction in non-linear behaviour
in different concrete strength.
6.0
74.0
)(160
)(310
−
−
=
=
cy
cy
U
U
σ
σ
CHAPTER 6: Role of bolt annulus thickness on shearing
194
Figure 6.14. Effect of hole diameter and resin thickness on shear displacement in numerical design
Figure 6.15. Effect of resin thickness and concrete strength on shear displacement in numerical design in un-pretension load
Numerical
27
3633.97
26.38
0
5
10
15
20
25
30
35
40
1 2hole diameter and displacement
hole
zis
e an
d di
spla
cem
ent
(mm
)
Dhdispl (mm)
0
10
20
30
40
0 20 40 60 80 100 120
Concrete strength (MPa)
shea
r dis
plac
emen
t (m
m)
.
36mm
27mm
CHAPTER 6: Role of bolt annulus thickness on shearing
195
Table 6.3. Concrete strength effect on shear displacement reduction in different resin thickness
Percent of displacement reduction (%) Hole diameter
(mm) Concrete strength
(MPa) Elastic behaviour
Non-linear behaviour
27 20 to 60 12.4 55
36 20 to 100 16 60
6.5. THE EFFECT OF RESIN ANNULUS ON INDUCED
STRESSES
The value of the generated stresses in the vicinity of the joint intersection was
evaluated in different resin thickness of 1.6, 2.6 and 5 mm, concrete and grout
modulus of elasticity and following results was established. It is noted that in these
analyses the concrete and grout were assumed to be linearly elastic, homogenous,
and isotropic. The behaviour of steel bolt was assumed non-linear hardening
behaviour discussed in numerical chapter.
6.5.1. Induced Shear Stress
Figure 6.16 shows the relationship between shear stress developed on the bolt in
vicinity of joint plane and concrete modulus of elasticity. The analyzed were carried
out in three resin thickness. As can be seen the shear stress decreased with increasing
level of concrete modulus. The rate of decrease was greater in thicker encapsulation
annulus layer. The results of medium concrete strength are presented in Appendix C.
CHAPTER 6: Role of bolt annulus thickness on shearing
196
6.5.2. Induced Tensile Stress
Tensile stress is a more critical stress than the compression stress, since the most
possibility of the failure happens because of tensile /combination of tensile and shear
which are located in vicinity of hinge point and bolt joint intersection. The effect of
grout and concrete elasticity modulus were evaluated. It was found that the induced
tensile stresses are reduced with increase of concrete modulus. Figure 6.17 displays
the induced tensile stress as a function of grout modulus. In general, there was a
gradual decline in tensile stress with increasing grout modulus in both concrete soft
and medium. In addition, small resin thickness has produced higher tensile stress
along the bolt.
Figure 6.16. Induced shear stress versus concrete modulus of elasticity in different annulus size (grout modulus is considered 12 GPa)
285
290
295
300
305
310
315
320
325
330
335
340
0 10 20 30 40 50
Concrete Modulus (GPa)
Shea
r stre
ss in
bol
t int
erse
ctio
n (M
Pa)
.
27mm32mm25mm
CHAPTER 6: Role of bolt annulus thickness on shearing
197
Figure 6. 17. Induced tensile stress versus grout modulus of elasticity in soft concrete (20 GPa)
6.5.3 Induced Compression Stress
Induced compression stresses are not so important for the bolt under compression, as
it cannot fail under the compression. Figure 6.18 shows the amount of compression
stresses as a function of concrete modulus of elasticity in different resin thickness.
There is no significant change in compression stress after 10 GPa modulus of
elasticity. From the simulated models it is possible to suggest that, the greater the
elastic modulus of concrete, the less the magnitude of induced stresses in/along the
bolt.
6.6. Effect Of Concrete Modulus Of Elasticity On Shear
Displacement
Figure 6.19 shows the effect of concrete modulus of elasticity on shear displacement
under different resin thickness. There is an exponential relationship between concrete
620
630
640
650
660
670
680
690
700
0 5 10 15 20 25 30
Grout modulus (GPa)
Ten
sile
stre
ss a
long
the
bolt
(MPa
) .
32mm27mm25mm
CHAPTER 6: Role of bolt annulus thickness on shearing
198
modulus of elasticity and shear displacement. The shear displacement is reduced
dramatically in range of the lower concrete modulus. The drop in shear displacement
tapers of to a near constant rate post-E value of approximately 15 GPa. Also it shows
there is no significant change between different resin thicknesses.
Figure 6.18. Induced compression stress versus concrete modulus of elasticity
However, in low concrete modulus of elasticity, higher thickness causes less
displacement but in higher concrete modulus of elasticity (stiff rock or hard rock)
thin resin appeared lower displacement, so it is concluded that, it is better to use in
soft rock higher resin thickness and in hard rock lower resin thickness. The reason
behind this is when debonding occurs and grout is broken, the bolt can move through
the resin on contact interface. When the resin thickness is reasonable value and low,
the interlocking effect is activated and resists against interface movement, so
displacement is reduced. From the simulated models it is possible to conclude that,
the greater the elastic modulus of concrete, the less the magnitude of shear
displacement.
0
200
400
600
800
1000
1200
0 10 20 30 40 50
Concrete modulus (GPa)
Com
pres
sion
stre
ss a
long
the
bolt
(MPa
) .
32mm
27mm25mm
CHAPTER 6: Role of bolt annulus thickness on shearing
199
Figure 6.19. Shear displacement versus concrete modulus of elasticity in different resin thickness, grout modulus is 12 GPa
It should be noted that in non-linear behaviour of concrete and resin, different resin
thickness definitely appears a significant difference in shear displacement.
6.7. Effect of grout modulus of elasticity on shear displacement
In this section a variety of grout modulus of elasticity was evaluated in different
concrete strength and in different annulus thicknesses. It was observed that there was
an exponential relationship between the modulus of elasticity and the shear
displacement in both concrete strengths of 20 and 40 MPa. Higher resin thickness
produced relatively lower shear displacement. As Figures 6.20 shows the shear
displacement is increased with increasing the resin thickness in both 20 and 40 MPa
concrete. However, this trend is reduced with increasing the grout modulus of
elasticity.
0
2
4
6
8
10
12
14
0 10 20 30 40
Concrete modulus (GPa)
Shea
r dis
plac
emen
t (m
m)
. Eg=12,32mm
Eg=12,27mm
Eg=12,25mm
CHAPTER 6: Role of bolt annulus thickness on shearing
200
Figure 6.20. Shear displacement versus grout modulus of elasticity in different resin thickness, concrete modulus is 20 GPa and constant
6.8. EFFECT OF BOLT MODULUS
The variety of bolt modulus of elasticity is evaluated in different modulus of
elasticity and 12 GPa grout modulus of elasticity. Figure 6.21 shows the effect of
bolt modulus of elasticity on shear displacement. It shows that the shear
displacement is reduced with increasing bolt modulus of elasticity. This trend is
lower in high concrete strength. The effect of bolt modulus on shear displacement is
analytically discussed in analytical section, which shows acceptable agreement with
numerical results. In addition the results showed there is no significant changes in
induced stresses along the bolt in different modulus of elasticity. It is noted that this
part of the simulation is only in 2.5-resin thickness.
0
1
2
3
4
5
6
0 10 20 30 40
Grout modulus (GPa)
Shea
r dis
plac
emen
t (m
m)
. Ec=20,32 mm
Ec=20, 27 mm
Ec=20, 25 mm
CHAPTER 6: Role of bolt annulus thickness on shearing
201
Figure 6.21. Shear displacement as a function of bolt modulus variations in different rock strength
The following can be noted from the numerical simulation:
• The higher annulus thickness appears lower displacement in case when resin
strength is stronger than the surrounding material,
• Low concrete modulus is more sensitive than the high concrete modulus on
shear displacement,
• Shear displacement is reduced with increase of bolt, grout and concrete
modulus of elasticity,
• Beyond the 15 GPa concrete modulus, there was not observed significant
changes on induced compressive stress on the bolt, and
• With increasing grout modulus of elasticity, tensile and shear stress built up
along the bolt are reduced
y = 3.9086x-0.114
R2 = 0.9663
y = 5.5495x-0.1479
R2 = 0.9203
1.5
1.8
2.1
2.4
2.7
3
3.3
0 50 100 150 200 250
Bolt modulus (GPa)
Shea
r dis
plac
emen
t (m
m)
.
Ec=40Ec=20Power (Ec=40)
CHAPTER 6: Role of bolt annulus thickness on shearing
202
6.9. SUMMARY
• When concrete strength is significantly higher than the resin strength, the
larger annulus size shows higher shear displacement and lower shear
stiffness. This means the strength of the rock and resin -in terms of shear
stiffness and shear resistance of fully grouted bolts subjected to transversely
loading - is more effective than the resin annulus.
• In soft strength materials (20 MPa) as the resin strength is significantly higher
than the surrounding material, higher resin annulus makes the stronger system
• Hinge point distance was reduced with increase of resin annulus, when
surrounding material is weaker than the resin strength
• Shear displacement was reduced at the shear yield load in higher resin
thickness
• Shear stiffness was increased with increase of resin thickness
• Higher resin thickness shows higher LMFBS (Limit of maximum frictional
bonding strength).
As in soft concrete, bolt bending generates extensive stress on resin / concrete
interface and failure occurs by shearing of the concrete at the resin / concrete
interface. It is assumed that bolt and resin strengths are more than adequate to
transfer the required load. Thus, to distribute the concentrated shear stress on the
rock and also to obtain larger and stronger anchorage, increasing the hole diameter is
a recommended option. However, in strong surrounding material (rocks) increasing
the resin thickness is not suitable option as it decreases shear stiffness.
Consequently it can be concluded that in lower rock strength, to obtain the higher
bolt-joint stiffness/shear resistance, increasing the grout annulus is so important to
CHAPTER 6: Role of bolt annulus thickness on shearing
203
achieve this goal. It should be noticed that this is when the resin strength is higher
than the rock strength. However, in higher concrete strength and lower resin strength,
the shear stiffness reduces as resin thickness increases.
CHAPTER 7: Numerical analyses in fully grouted rock bolts
204
CHAPTER 7
NUMERICAL ANALYSES IN FULLY GROUTED
ROCK BOLTS
7.1. INTRODUCTION
The current chapter consists of several parts, which are presented as follows. It is
aimed to describe a literature survey of the fundamentals of numerical modelling, the
application of numerical modelling in mining particularly in field of rock bolt,
developing of the FE model for the bolt/grout/rock and two interfaces, verification of
the model and finally analysing the stresses and strains developed in the rock bolt,
surrounding materials and related investigations.
Numerical methods represent the most versatile computational method for the
various engineering disciplines. The fundamental characteristic of numerical
methods is that a structure is discritised into small elements. Then the constitutive
equations that describe the individual elements and their interactions are constructed.
Finally these equations, which are large in number, are solved simultaneously and
interactively using computers. The results from this procedure include the stress
distribution and displacement pattern within the structure. Numerical modelling
includes several analysis techniques such as, finite elements, boundary elements,
distinct elements and other numerical approaches that depend upon the material and
the structure base numerical methods into three major models.
CHAPTER 7: Numerical analyses in fully grouted rock bolts
205
7. 2. FE IN ANSYS
The ANSYS software is a commercial Finite element analysis program, which has
been in use for more than thirty years (Pool et al. 2003). The software is capable to
analyse the stress and strain build up in the verity of problems, specially designing
roof bolts and long wall support systems.
The original code, developed around a direct frontal solver has been expanded over
the years to include full featured pre- and post- processing capabilities, which
support a comprehensive list of analysis capabilities including linear static analysis,
multiple non-linear analyses, modal analysis, contact interface analyses and many
other analysis types. Ansys is a powerful nonlinear simulation tool, Bhashyam.G.R
(2002).
In this study only structural analysis was used. Structural analyses are available in
the ANSYS Multiphysics, ANSYS Mechanical, ANSYS Structural, and ANSYS
Professional programs only. Static analysis is used to determine displacements,
stresses, and strains under static loading conditions. (Both linear and non-linear static
analyses). Nonlinearities can include plasticity, stress stiffening, large deflection,
large strain, hyperelasticity, contact surfaces, creep. A brief description of numerical
techniques, finite element method, basic theory of finite element method, non-linear
solution in Ansys and failure criteria in Ansys are presented in Appendix D.
7.3. A REVIEW OF NUMERICAL MODELING IN ROCK BOLT
A number of computer programs have been developed for modelling civil and
geotechnical problems. Some of these programs can be used partially to design and
analyse roof-bolting systems. It is noted that to simulate the whole characters of a
CHAPTER 7: Numerical analyses in fully grouted rock bolts
206
model, such as modelling of the joints, bedding planes, contact interface and failure
criterion, the use of 3D software is necessary. Several numerical methods are used in
rock mechanics to model the response of rock masses to loading and unloading.
These methods include the finite element method (FEM), the boundary element
method (BEM), finite difference method (FDM) and the discrete element method.
A few research was carried out on bolt behaviour in FE field; such as, Coats and Yu
(1970), Hollingshead (1971), Aydan (1989), Saeb and Amadei (1990), Aydan and
Jawamoto (1992), Swoboda and Marence (1992), Moussa and Swoboda (1993),
Chen et al. (1994, 1999, 2004), Surajit (1999), and Marence and Swoboda (1995).
One of the earliest attempts to use standard finite elements to model the bolt and
grout was done by Coats and Yu (1970). The research was carried out on the stress
distribution around a cylindrical hole with the finite element model either in tension
or compression. It was found that the stress distribution was a function of the bolt
and rock moduli of elasticity. The presence of grout between the bolt and the rock
was not considered and also any allowance was not given for yielding. The analysis
was also accomplished only in linear elastic behaviour with two phase materials,
which were the limitation of the model.
Hollingshead (1971) solved the same problem using a three-phase material (bolt-
grout and rock) and allowed the penetration of a yield zone into the grout using an
elastic –perfectly plastic criterion, according to the Tresca yield criterion, for the
three materials (Figure 7.1). In the model the interface behaviour was not considered.
John and Dillen (1983) developed a new one-dimensional element passing through a
cylindrical surface to which elements representing the surrounding material are
attached (Figure 7.2). They considered three important modes of failure of fully
grouted bolts. In this model, for axial behaviour a bi-linear elasto-plastic model and
CHAPTER 7: Numerical analyses in fully grouted rock bolts
207
for the bonding material an elastic-perfectly plastic-brittle-residual plastic model was
assumed. Although this model had eliminated many previous limitations and had
shown a good agreement with the experimental results, it has neglected rock stiffness
and in situ stress effects around the borehole. They claimed the critical shear stress
has occurred at the grout-rock interface, which is not always the case in the field or
in laboratory.
Figure 7. 1. FE Simulation of bolted rock mass (After Hollingshead, 1971)
Figure 7. 2. Three-Dimensional rock bolt element (After John and Dillen, 1983)
Rock
Grout Bolt
CHAPTER 7: Numerical analyses in fully grouted rock bolts
208
Aydan (1989) presented a finite element model of the bolt. He assumed a cylindrical
bolt and grout annulus is connected to the rock and was a three-dimensional 8-nodal
points. Two of these nodes are connected to the bolt and six nodes are connected to
the rock mass. The use of boundary element and finite element techniques to analyse
the stresses and deformations along the bolt was conducted by Peng and Guo (1988)
(Figure 7.3). The effect of the faceplate was replaced by a boundary element. The
effect of reinforcement because of the assumption of perfect bonding was
overestimated.
Figure 7. 3. Bolt-Rock interaction model (Peng and Guo, 1988)
Stankus and Guo (1996) investigated that in bedded and laminated strata, point
anchor and fully grouted bolts are very effective especially where they are installed
at high tension quickly after the excavation. They used three different lengths 3300,
2400 and 1500 mm and three different tensions; 66, 89, and 110 kN and found that:
- Bolts with higher pretension, induce a smaller deflection
- The longer the bolt, the larger the load,
Tension in bolt
Reaction force bolt
Shear force in bolt Shear force in wall rock
Bearing plate
Bolt head
CHAPTER 7: Numerical analyses in fully grouted rock bolts
209
- In bolts with the same length and high tension, there is small deflection,
- Large beam deflection was observed at long bolt, and small beam deflection
at the short bolt.
They developed a method to achieve the optimum beaming effect (OBE). However,
there were some assumptions in their methodology, such as: the problem in gap
element, which is not flexible for any kind of mesh especially when the grout
thickness is low. Many relevant parameters about contact interface cannot be defined
in gap element. The whole materials were modelled in elastic region.
Marence and Swoboda (1995) developed a special element, Bolt Crossing Joint
(BCJ) element. It connects the bolt elements on both sides of the shear joint. This
element has only two nodes, each on one side of the discontinuity. The model can not
predict the debonding length along the bolt grout interface and hinge point position.
Kharchafi et al. (1998) simulated the behaviour of bolted rock joints in a three-
dimensional method. However, they did not analyse the bolt behaviour in large
displacements. Also bolt pretensioning was not considered in their model.
It was realized and required that in order to further facilitate the data analysis and
stress, strain build up along the bolt surrounding by composite material and their
interaction, a powerful computer simulation is needed. The finite element modeling
is considered the only tool to accomplish this goal. Although, still there is lack of an
adequate global model of grouted bolt to analyze the bolt behaviour properly, in
particular contact interface behaviour.
In this study, three-dimensional formulations and non-linear deformations of rock,
grout, bolt and two interfaces are taken into account in the reinforced system. A
description of the numerical model developed is presented below.
CHAPTER 7: Numerical analyses in fully grouted rock bolts
210
7.4. MATERIAL DESIGN MODEL
Finite element method is the most suitable computational method to evaluate the real
behavior of the bolt, grout and surrounding rock when there are composite materials
with different interfaces in the model. Three dimensional finite element model of the
reinforced structure subjected to the shear loading was used to examine the
behaviour of bolted rock joints. Three governing materials (steel, grout, and
concrete) with two interfaces (bolt/grout and grout/concrete) were considered for 3D
numerical simulation. To create the best possible mesh, symmetry rules should be
applied to the model. To reduce the computing demand and computing time (when a
fine mesh is used) the density of the mesh has been optimised during the meshing
process. The division of zones into elements was such that the smallest elements
were used in where details of stress and displacement were required. The process of
FE analysis is shown in Figure 7.4.
CHAPTER 7: Numerical analyses in fully grouted rock bolts
211
Figure 7.4. The process of FE simulation (Dof = degrees of freedom)
Improve Mesh
Geometry of the model
Element type
Material properties
Decide and analysing the problem
Select 3D Software
Start
Mesh generation
Contact interface properties
Boundary condition
Dof Condition Symmetric Condition Loading
Determine load step, sub step, time step and solution method
Analyse nodal and Element
solution
Compare with laboratory tests
Check penalty stiffness
Modify contact and material properties
Convergence Yes No
OK END
Unacceptable
Acceptable Increase sub step No
OK
No
CHAPTER 7: Numerical analyses in fully grouted rock bolts
212
7.4.1 Modelling of Concrete and Grout
Care was taken to develop the best model for concrete and grout that could offer an
appropriate behaviour. 3D solid elements, Solid 65 that has 8 nodes was used with
each node having three translation degrees of freedom, that tolerates irregular shapes
without significant loss in accuracy. The element is capable of plastic deformation,
cracking in three orthogonal directions, and crushing. The geometry and node
locations for this element type are shown in Figure 7.5 a. The solid element not only
is capable of plastic deformation, cracking in tension and crushing in compression,
creep nonlinearity and large deflection geometrical nonlinearity but also includes the
failure criteria of concrete; Fanning (2001), Feng et al (2002) and Ansys (2004).
Concrete can fail by cracking when the tensile stress exceeds the tensile strength or
by crushing when the compressive stress exceeds the concrete compressive strength.
A finite element mesh for concrete is shown in Figure 7.5b. Figure 7.6 shows the
finite element mesh for grout. Due to symmetry only a quarter of the model need to
be treated.
Figure 7.5. (a) 3D concrete Solid 65 (b) Concrete mesh
2 3
1
5 4
6
k
J
I
M
L
N
O P
Y X
Z
CHAPTER 7: Numerical analyses in fully grouted rock bolts
213
Figure 7.6. Finite element mesh for grout
7.4.2 Modelling the Bolt
The steel bar is the main element within the rock bolt system to resist both axial and
shear loads during the loading process due to rock movements. So care was taken to
model the steel bar properly, in particular the type of element designed and bolt
behaviour in both linear and non-linear region. 3D solid elements, solid 95 that has
20 nodes was used to model the steel bar, with each node having three translation
degrees of freedom. The approach is adopted in this study, is to reveal that the
experimentally verified shear resistance effect of fully grouted bolt can be
investigated by numerical design. Elastic behavior of the elements was defined by
Young’s Modulus and Poisson’s ratio of the various materials. The stress-strain
relationship of steel is assumed as bilinear kinematics hardening model and the
modulus of elasticity of strain hardening after yielding is accounted as a hundredth of
the original one, Cha et al. (2003), Hong et al. (2003) and Abedi et al. (2003). Yield
strength of the steel was obtained from laboratory tests, 600 MPa. Figure 7.7 displays
the finite element mesh for bolt
Fine mesh at vicinity of shear joint
CHAPTER 7: Numerical analyses in fully grouted rock bolts
214
Figure 7.7. Finite element mesh for bolt
7.4.3. Contact Interface Model
The main difficulties of numerical simulation of reinforced shear joint are the
simulation of the bolt/grout and grout/rock interfaces. An important parameter
controlling the mechanism of load transfer from the bolt to the rock through resin, is
bond behaviour between the interfaces. If these interfaces are not designed properly,
it is certainly difficult to understand the bonding behaviour and when and where
debonding occurs and how gap is created between interfaces and how the load is
transferred. Thus, care was taken to design the contact interfaces as they behave
realistically. To study the stress-strain generation through numerical modelling, it is
very important to model the interfaces accurately (Pal et al. 1999). Ostreberge (1974)
also emphasized on the bond strength influence between two adjacent mediums on
the accurate load transfer. Nietzsche and Hass (1976) proposed a model for bolt-
grout -rock and assumed a linear elastic behaviour for all materials and perfect
bonding for all contact interfaces (bolt/grout and grout/ rock). It has to be noted that
perfect bonding particularly between bolt/grout interface could not consider the right
behaviour, as there is no cohesion strong enough between them. In addition, there is
Fine mesh around shear joint
CHAPTER 7: Numerical analyses in fully grouted rock bolts
215
large stresses and strains concentration at the vicinity of the shear joints, which
restricts the perfect bonding. The interface behavior of the grout-concrete was
considered as a standard contact behaviour, where the normal pressure changes to
zero when separation occurs. As found from laboratory results the low value of
cohesion (150 kPa) was adopted for contact interface, which was determined from
the test results under constant normal condition.
3D surface-to-surface contact element (contact 174) was used to represent the contact
between 3D target surfaces (steel-grout and rock-grout). This element is applicable to
3D structural contact analysis and is located on the surfaces of 3D solid elements
with midside nodes. This contact element is used to represent contact and sliding
between 3-D "target" surfaces (Target 170) and a deformable surface, defined by this
element. The element is applicable to three-dimensional structural and coupled
thermal-structural contact analysis. This element is also located on the surfaces of 3-
D solid or shell elements with midside nodes. It has the same geometric
characteristics as the solid or shell element face with which it is connected. Contact
occurs when the element surface penetrates one of the target segment elements on a
specified target surface. The contact elements themselves overlay the solid elements
describing the boundary of a deformable body and are potentially in contact with the
target surface. This target surface is discritised by a set of target segment elements
(Target170) and is paired with its associated contact surface via a shared real
constant set.
7.4.4. Geometrical Model
The model bolt core diameter ( bD ) of 22 mm and the grouted cylinder ( hD ) of 27
mm had the same dimensions as those used in the laboratory test. Due to the
CHAPTER 7: Numerical analyses in fully grouted rock bolts
216
symmetry of the problem, only one fourth of the system was considered here. Figure
7.8 shows the geometry of the FE model with mesh generation.
Figure 7.8. Geometry of the model and mesh generation
7.5. VERIFICATION OF THE MODEL
A numerical representation model for fully grouted reinforcement bolt has been
developed. Then, validity of the developed model has been assessed with laboratory
data, which were conducted in a variety of rock strengths and pretensioning. The
comparison of experimental results with numerical simulations displayed that the
model is capable of predicting the bolt-grout-concrete interaction and interfaces
behaviour. The consistency of the experimental observation with numerical design
model is presented by typical shear load-shear displacement curves shown in Figure
15 cm
15 cm
7.5cm
C T
T C
Shear load Shear joint
Grout
Bolt
Concrete 15 cm
75mm 150 mm
150 mm
150 mm
CHAPTER 7: Numerical analyses in fully grouted rock bolts
217
7.9. More comparison results are shown in Appendix D. It is clear that when the
concrete strength was doubled, there was a twice reduction in the shear displacement.
Figure 7.9. Load-deflection in 80 kN pretension bolt load and 40 MPa concrete
7.6. MODELLING OF FULLY GROUTED ROCK BOLTS
An extensive series of laboratory tests to analyse the bending behaviour of fully
grouted bolts in different rock strength, bolt pretensioning and resin thickness were
carried out. Three governing materials (steel, grout, and rock) with two interfaces
(bolt grout and grout-rocks) were considered for 3D numerical simulation.
By this three-dimensional FEM, characteristics of elasto - plastic materials and
contact interfaces behaviour are simulated. The numerical modelling in different rock
strengths (20, 40, 50 and 80 MPa) and different pretension loads (0, 20, 50, and 80
kN) were carried out and the results were analysed in the following sections. Table
7.1 shows a total of 32 numerical models in different rock strengths, pretensioning,
and resin thicknesses.
0
50
100
150
200
250
300
350
400
0 5 10 15 20
Shear displacement (mm)
Shea
r loa
d (k
N)
.
Laboratory
Numeric
CHAPTER 7: Numerical analyses in fully grouted rock bolts
218
Table 7.1. Summery of created models Concrete strength (MPa)
Pretension load (kN)
Bolt diameter
(mm)
Hole diameter
(mm)
Resin thickness (mm)
Number of models
22 25 1.5 22 27 2.5
0
22 32 5
3
22 25 1.5 22 27 2.5
20
22 32 5
3
22 25 1.5 22 27 2.5
50
22 32 5
3
22 25 1.5 22 27 2.5
20
80
22 32 5
3
22 25 1.5 22 27 2.5
0
22 32 5
3
22 25 1.5 22 27 2.5
20
22 32 5
3
22 25 1.5 22 27 2.5
50
22 32 5
3
22 25 1.5 22 27 2.5
40
80
22 32 5
3
0 22 27 2.5 20 22 27 2.5 50 22 27 2.5
50 80 22 27 2.5
4
0 22 27 2.5 20 22 27 2.5 50 22 27 2.5
80 80 22 27 2.5
4
CHAPTER 7: Numerical analyses in fully grouted rock bolts
219
7.7. RESULTS AND DISCUSSION
The numerical simulation was carried out in a variety of concrete strength and
different pretensioning. However, because of large output results, only the main
results of 0 and 80 kN pretensioning are presented here and the rest of the analyses
are shown in Appendix D.
7.7.1. Bolt Behaviour
7.7.1.1. Stress developed along the bolt
When a beam with a straight longitudinal axis is loaded laterally, its longitudinal axis
is deformed into a curve, the resulting stresses and strains are directly related to the
curvature of the deflection curve, which is affected by the surrounding materials.
Figure 7.10 shows a quarter of the model with induced loads along the shear joint.
When the beam is bent, there were both deflection and rotation at each point. The
angle of rotation α is the angle between the bolt axis and the tangent to the
deflection curve, shown as point o. α is measured for the bent bolts tested. The
deflection trend in 20 MPa concrete is shown in Figure 7.11. Also to find the
relationship between the bolt deflection and each point along the bolt axis, the output
raw data from the numerical simulation were classified and entered, as an input data
to Maple software (Ver. 9.1). Equation 7.3 and Figure 7.12 were established.
CHAPTER 7: Numerical analyses in fully grouted rock bolts
220
Figure 7.10. Numerical model (s = symmetric planes, c = compression zone, T = tension zone
(7.1) (7.2)
Figure 7. 11. Bolt displacement in 20 MPa, without Pretensioning
dxdv
dxdv
arctan
,tan
=
=
α
α
Confining pressure
T C C
T S
S
S
S
Concrete
Shear joint
Bolt
Grout
Shear load
Tensioning load
S
α o
dv
dx
Shear joint location
CHAPTER 7: Numerical analyses in fully grouted rock bolts
221
Figure 7.12. Shear displacement as a function of bolt length sections in 20 MPa concrete (7.3) where;
yU = Shear displacement (mm)
X = distance from the bolt centre to the end (mm), from A to B.
The relationship between vertical displacement at the bolt - joint intersection and
hinge point is:
Uy (hinge) = (0.15-0.2) Uy (joint) Which is consistent with laboratory results. Figure 7.13 shows the bolt deflection in
40 MPa concrete.
)tan(2676.40 )2.705.0( −+−= xy eArcU
Distance from centre to end (mm)
Shea
r dis
plac
emen
t (m
m)
A B
Effective height
CHAPTER 7: Numerical analyses in fully grouted rock bolts
222
Figure 7.13. Bolt deflection at the moving side and hinge point versus loading process, in 40 MPa concrete without pretension load
Figure 7.14 shows the contours of stress developed along the bolt in 20 MPa
concrete. It shows the stresses in the top part of the bolt and towards the perimeter
are tensile and it is compressive at the centre. However, the stress conditions at the
lower half section of the bolt are reverse. In addition, the shape of the bolt between
the hinges can be considered as linear. The rate of stress changes in post failure
region is plotted in Figure 7.15. It can be seen that the induced stresses at these
zones are high and the bolt appears in yield state. At the two hinges the yield limit of
the bolt is reached quickly. However, further increase of the shear load has no
apparent influence on the stress built up at the hinge point. From this stage
afterwards, only the tensile stresses are developed and expanded between the hinge
points and may lead the bolt to fail at distance between the hinge points which are
located at the vicinity of the shear joint, as the maximum stress and strain occurre
between the hinge points.
Loading steps
Sh
ear d
ispl
acem
ent (
mm
)
Bolt deflection at moving side
Bolt deflection around hinge point
CHAPTER 7: Numerical analyses in fully grouted rock bolts
223
Figure 7.14. Stress built up along the bolt axis in 20 MPa concrete without pretensioning
Figure 7.15. The trend of stress built up along the bolt axis 20 MPa concrete with 80 kN pretensioning From analysing the results in different pretensioning it was found that there are no
significant changes in induced stresses along the bolt with increase of the pretension
load in the tension zone. However, there is a slight reduction in the compression
stresses with increasing the pretension load. Induced stresses are higher than the
Shear joint
Bolt axis
Stre
ss a
long
the
bolt
(MPa
)
Distance from centre to end (mm)
O A
Tensile zone
Compression zone
Compression zone
Tensile zone Shear joint
O
A
CHAPTER 7: Numerical analyses in fully grouted rock bolts
224
yield point and less than the maximum tensile strength of the steel bolt in both
situations (without and with pretensioning in all concrete strengths). Moreover, in
different concrete strength it was observed that the strength of the concrete, affects
greatly shear displacement and bolt contribution. However, there was not observed
meaningful changes in induced stresses beyond the yield point along the bolt axis
with increasing the rock strength. But, the value of stresses was slightly reduced in
high level of pretensioning and high concrete strength.
The rate of stress generation and Von Mises stresses along the bolt in 40 MPa
concrete are presented in Appendix D. The Von Mises stress trend along the bolt axis
perpendicular to the shear joint in 20 MPa concrete is plotted in Figure 7.16.
Figure 7.16. Von Mises stress trend in 20 MPa concrete without pretensioning
Comparing the results in both pretensioning and non-pretensioning in 20 MPa
concrete it was found that the Von Mises stress is slightly decreased with increase of
the bolt pretension. However, this difference is not significant.
O A
Shear joint
Von
Mis
es s
tres
s al
ong
the
bolt
(MPa
)
Distance from centre to end (mm)
CHAPTER 7: Numerical analyses in fully grouted rock bolts
225
Figure 7.17 shows the shear stress concentration along the bolt. The rate of shear
stress changes along the bolt axis is displayed in Figure 7.18. Figure 7.19 shows the
shear stress trend along the length of the bolt in one side of the joint surrounded with
soft concrete.
Figure 7.17. Shear stress contour in the concrete 20 MPa without pretensioning As it shows the maximum shear stress is concentrated at the vicinity of the joint
plane and according to structural analysis, bending moment in this point is zero.
These stresses slowly increase, beginning with the plastic deformation and ending
with a stable situation. The value of shear stress dramatically reduces from the shear
joint towards the bolt end. This trend likely reaches to zero at the hinge point. In the
two hinges, the yield limit of the steel is reached quickly, at about 0.3 P and 0.4 P in
concrete 20 and 40 MPa respectively, (P is the maximum given applied load).
Further increase of the shear force has no apparent influence on the stresses in the
hinges. The distance between the hinge points is reduced with increasing the strength
of the concrete.
O
A Shear joint
Max Stress concentration
CHAPTER 7: Numerical analyses in fully grouted rock bolts
226
Figure 7.18. The rate of shear stress along the bolt axis in concrete 20 MPa without pretensioning Figure 7.19. The rate of shear stress along the bolt axis in concrete 20 MPa without pretensioning in one side of the joint plane
Bolt axis
y = 430.07e-0.1052x
R2 = 0.9399
0
50
100
150
200
250
300
350
400
450
500
0 10 20 30 40 50 60
Distance from joint (mm)
Shea
r stre
ss (M
Pa)
.
Joint plane
Shear joint Shear joint
τ
Shear stress distribution
Distance from centre to end (mm)
Shea
r str
ess
tren
d al
ong
the
bolt
(MPa
)
CHAPTER 7: Numerical analyses in fully grouted rock bolts
227
Figure 7.20 shows the trend of shear stress changes in stress profile with the shear
stress tapering off to a stable state past the yield point. It displays the shear stress
trend is not exceeded during further loading after the yield point. Eventually, the
combination of this stress with induced tensile stress at the bolt-joint intersection
lead the bolt to failure. By increasing the bolt initial tensile load, the shear stress was
decreased and this was also observed in different concrete strength. However, there
was not observed significant changes with increasing shear load after the yield point.
Any reduction in shear stress causes an increase in the bolt resistance to shear. It can
be noted that the shear stress was slightly increased with increasing concrete
strength. The details results are presented in Appendix A7.I.
Figure 7. 20. Shear stress trend in bolt –joint intersection in concrete 20 MPa at post failure region without pretension load
Sh
ear s
tres
s (M
Pa)
Loading steps
CHAPTER 7: Numerical analyses in fully grouted rock bolts
228
7.8.1.2. Strain developed along the bolt
Simultaneously with increasing the shear load, strains were generated along all the
surrounding materials, in particular along the bolt axis. With increase of the bolt
deflection, plastic strain is induced in the critical locations in all three materials (bolt,
resin and concrete). Figure 7.21 shows the location of the maximum plastic
deformation along the bolt while bending. It shows there are two hinge points around
the shear plane with approximately 50 mm distance from the shear joint in 20 MPa
concrete. However, increasing pretension load has not affected significantly hinge
points distances, which are around 2.3Db. This value in the laboratory test is around
44mm that is 2 Db. The strains and the rate of strain changes along the bolt in 20
MPa concrete are shown in Figures 7.22 and 7.23. As the Figure 7.22 shows the
outer layer of the bolt material has yielded, whereas the middle part of the bolt
crosses section remains in the elastic state.
Figure 7. 21. Deformed bolt shape in post failure region in 20 MPa concrete
Shear load
+13
-11.3
+14.6
-9.7
CHAPTER 7: Numerical analyses in fully grouted rock bolts
229
Figure 7.22. The plastic strain contour along the bolt axis in concrete 20 MPa without pretensioning
Figure 7.23. Strain trend along the bolt axis in concrete 20 MPa without pretensioning in upper fibre of the bolt Figure 7.24 shows the beginning of plastic strain during the shearing and trend of the
strain development as a function of the time stepping. It notes that both the tensile
and the compression strain around the bolt were started approximately 27-30 % of
O
A Shear joint
Compression strain
Tensile strain
Bolt axis
Shear joint
CHAPTER 7: Numerical analyses in fully grouted rock bolts
230
loading time and increased with increasing of the shearing load. However, the rate of
increase in the tensile zone is higher than the compression zone. As Figure 7.25
shows these strains appeared in early stage of loading and small displacement
(around 3 mm) and increased with increasing the shear deflections.
Figure 7. 24. The yield strain trend as a function of time stepping concrete 20 MPa in 20 kN pretension With increase of the loading, the shear displacement was increased. It was found that
there is a significant increase in the shear displacement after 35% of the loading time.
Bending of the bolt is predominant at the low loading time. The generation of the
Von Mises strain at the hinge point as a function of the loading time is shown in
Figure 7.26. It displays the plastic strain is initiated at the hinge point around 35 % of
loading. Figures 7.27 and 7.28 show Von Misses strain and the rate of yield strain
changes along the bolt in 20 MPa concrete.
Tensile strain trend
Compression strain
Com
pres
sion
& te
nsio
n st
rain
Time of loading
CHAPTER 7: Numerical analyses in fully grouted rock bolts
231
Figure 7. 25. Tension and pressure strain along the bolt in 20 MPa concrete and 20 kN pretension
Figure 7.26. The Von Mises strain trend along the bolt axis in concrete 40 MPa and 80 kN pretensioning
Compression strain
Tension strain
Com
pres
sion
& te
nsio
n st
rain
Shear displacement (mm)
Plas
tic s
trai
n
Von Mises strain rate
Shear strain rate
Loading steps
CHAPTER 7: Numerical analyses in fully grouted rock bolts
232
Figure 7.27. Von Mises strain along the bolt in concrete 20 MPa concrete without pretensioning Figure 7.28. Von Mises strain trend in concrete 20 MPa without pretensioning in upper fibre of the bolt With comparison of the data analysing, (pretensioning and non-pretensioning) it
shows that the intensity of the strain along the bolt axis is slightly reduced with
increase of the pretension load. However, the affected area in the tensile zone is
O
A Shear joint location
O A
Shear joint location
Stra
in a
long
the
bolt
Distance from centre to end (mm)
CHAPTER 7: Numerical analyses in fully grouted rock bolts
233
expanded towards the shear joint. In addition, it was found that the strains in both the
compression and tension zones were reduced in higher concrete strength.
7.7.2. Concrete
7.7.2.1. Stress developed in concrete
The behaviour of concrete under the shear load was analysed in different concrete
strength and different pretension loads. During the shearing process the middle part
of the concrete assembled system was moved down with increasing the shear load.
Figure 7.29 shows the concrete deflection rate after concrete failure. During the
concrete movement, the reaction forces are developed and increased in critical
locations (at the vicinity of the shear joint), which are affected by the steel bolt. So,
stresses and strains are induced and propagated in such zones.
Figure 7.29. The concrete displacement in non-pretension condition in 20 MPa concrete
O A
C
oncr
ete
disp
lace
men
t (m
m)
Distance from centre to end (mm)
CHAPTER 7: Numerical analyses in fully grouted rock bolts
234
Figure 7.30 shows the high-induced stress in the vicinity of the shear joint as the
maximum reaction forces are expected in these areas. It is considered that when the
induced stress in concrete is larger than the ultimate stress of the concrete, the
concrete will be crushed. Figure 7.31 displays the rate of induced stresses in concrete
interface at the vicinity of the shear joint. It shows the induced stresses are much
higher than the compressive strength of the concrete and concrete at this location
would be severely crushed. From the figure it can be seen that the length of the high
stress distribution is propagated approximately 60 mm from the shear plane. At an
early stage of the loading, concrete was crushed and stresses propagated through the
concrete, the yielding of the concrete started around 2 mm deflection from the
intersection edge. Beyond this point stresses are increased quickly through the
concrete especially at the vicinity of the joint intersection and reaction zones. From
the pretensioning results it was found that the induced stresses in the vicinity of shear
joints were reduced slightly with increase of the bolt pretension load.
Figure 7.30. Yield stress induced in 20 MPa concrete without pretensioning condition
Maximum reaction stresses
O
A
CHAPTER 7: Numerical analyses in fully grouted rock bolts
235
Figure 7.31. Induced stress and displacement trend in 20 MPa concrete without pretensioning
In addition, the trend of the induced stresses and strains built up along the concrete
interface in higher concrete, 40 MPa, was the same as the soft concrete, 20MPa.
However, the value of stresses and strains were slightly reduced in higher concrete.
7.7.2.2. Strain developed in concrete
As discussed in the section above, in the vicinity of the shear joint, there was highest
level of induced stresses. Consequently it is expected that the strain would be highest
around such zones. Figure 7.32 shows the induced strain contours at the high-
pressure zone. The rate of the strain changes in the concrete interface along the bolt
axis is presented in Appendix D. Figure 7.33 shows the induced strain in terms of
loading time in grout and concrete. It reveals that the strain generation is initiated in
the concrete prior to the resin grout. This is due to the lower concrete strength, as the
concrete strength is one third of the grout strength. Figure 7.34 shows the rate of the
Shear joint location
Stress trend
Deflection trend
O A
D
ispl
. (m
m)-
indu
ced
stre
ss (M
Pa)
Distance from centre to end (mm)
CHAPTER 7: Numerical analyses in fully grouted rock bolts
236
shear displacement in concrete block at the shearing side and bolt - joint intersection
in 20 and 40 MPa without pretension load. Figure 7.35 shows the rate of strain
variations along the contact interface through the concrete versus loading time in 40
MPa concrete without pretension load. It shows there is approximately exponential
relation in the strain trend with increasing the loading process. In addition, also after
20% of loading steps, the plastic strain is induced along the contact interface at the
vicinity of the shear joint. This value in soft concrete (20MPa) is at an earlier stage,
which is around 15% of loading step. In addition, it shows the strain built up along
the bolt axis is lower than the shear direction. With comparison of the induced strain
along the joint interface in both pretensioning and non-pretensioning it was found
that the value of strain in shear direction is reduced (around 15%) with increasing the
pretensioning. In both axial and shear direction the strain concentration was
generated at vicinity of the shear joint.
Figure 7.32. The produced strain contours in 20 MPa concrete without pretensioning (in shearing direction)
CHAPTER 7: Numerical analyses in fully grouted rock bolts
237
Figure 7.33. Induced strain in concrete 20 MPa in grout and concrete versus loading in non-pretension load and 27 mm hole diameter
Figure 7.34. Concrete displacement versus loading time in concrete (a) 20 and (b) 40 MPa in non-pretension condition
Stra
in in
gro
ut-c
oncr
ete
Grout Concrete
St
rain
in g
rout
and
con
cret
e
Loading steps
Con
cret
e di
spla
cem
ent (
mm
)
Loading steps
Shearing block
Intersection edge Intersection edge
Moving block
Loading steps
C
oncr
ete
disp
lace
men
t (m
m)
(a) (b)
CHAPTER 7: Numerical analyses in fully grouted rock bolts
238
Figure 7.35. Induced strain rate along the contact interface in 40 MPa concrete and non pretension condition
Figure 7.36 shows the deformational behaviour of both concrete medium and bolt.
The plastic deformation of the concrete occurs at nearly 15 % of the maximum shear
load, while the deformation of the bolt occurs at 33% of the loading steps.
Figure 7.36. Induced strain in concrete and bolt as a function of loading steps in 20 MPa concrete with 80 kN pretensioning
Stra
in in
bol
t and
con
cret
e
Loading steps
Strain in concrete
Strain in bolt
Loading steps
C
oncr
ete
stra
in
Minimum principal strain
Strain in shear direction
Strain along the bolt axis
CHAPTER 7: Numerical analyses in fully grouted rock bolts
239
From the graphs it can be seen that in very low values of the bolt deflection and time
steps, fractures happened in the concrete, which is in elastic range of the bolt. Any
further increase in the shearing force appears not to influence the stresses at the
hinges points, however the induced stresses in the concrete blocks causes extensively
fractures propagation and eventually leading the concrete to failure.
7.7.3. Grout
7.7.3.1. Stress developed in grout
It is known that the grout bands the bolt shanks to the surrounding ground making
the bolt an integral part of the rock mass itself, and the efficiency of the grouted bolts
depends on the shear strength of the bolt-grout interface and the grout-rock interface.
Figure 7.37 shows the induced stress contours through the resin layer surrounded by
20 MPa concrete without pretensioning. It was revealed that the induced stress
exceeded the uniaxial compressive strength of the grout at the vicinity of the bolt –
joint intersection causes crushing of the grout in this zone. It shows the value of
induced stress in the grout layer in vicinity of the shear joint is much higher than the
uniaxial strength of the grout and grout in this location can be crushed. Observation
of the broken assembled sample after test displayed that grout was intensively
crushed around this zone. The damaged area in upper side of the grout was
approximately 60 mm from the shear joint. Figures 7.38 and 7.39 show both the gap
formation after bending in the numerical and laboratory methods respectively. It is
noted that the induced stresses were reduced with increasing the pretensioning.
(Nearly 10 %). However, it shows they are slightly expanded).
CHAPTER 7: Numerical analyses in fully grouted rock bolts
240
Figure 7.37. Induced stress contours in grout layer in un-pretension condition and 20 MPa
Figure 7.38. Created gaps in post failure region in 20 MPa concrete in the Numerical simulation
High stress zone
Created gap between grout and bolt
CHAPTER 7: Numerical analyses in fully grouted rock bolts
241
Figure 7.39. Created gaps in post failure region in 20 MPa concrete in the laboratory test Figure 7.40 shows the rate of the grout deflection versus loading time in different
grout locations: moving block, intersection and hinge point. It shows that at the hinge
points there is almost no lateral deflection as the grout layer is separated from the
bolt/grout interface (See Figure 7.39).
Figure 7.40. The grout displacement in different location along the bolt axis in 40 MPa concrete
S
hear
dis
plac
emen
t (m
m)
at hinge point
at Intersection
at shearing block
Loading steps
Created gap
CHAPTER 7: Numerical analyses in fully grouted rock bolts
242
7.7.3.2. Strain Developed in Grout
While shearing tacking place, strains are induced through the grout particularly at the
vicinity of the shear joint and the reaction zones. The value of strain in the grout
layer was around 10 times greater than the linear region at critical zones. This means
that the grout in those areas had broken off the sides that were in tension (as was
shown in Chapter 6, Experimental Results). The rate of induced strain along the
grout layer in axial direction is displayed in Figure 7.41.
Comparison of the results of strain along the joint interface in the grout layer showed
that the value of strain was decreased around 3 % and 5 % in the compression and
tension zones with increasing pretensioning to 80 kN which is due to higher shear
resistance and low lateral displacement. Figure 7.42 shows the grout shear
displacement in moving side of the shear block and the bolt -joint intersection versus
induced plastic strain.
Figure 7.41. The rate of induced strain along the grout layer in non-pretension condition in axial direction
Tensile zone
Compression zone
Distance from centre to end (mm)
S
trai
n al
ong
the
grou
t
CHAPTER 7: Numerical analyses in fully grouted rock bolts
243
It displays the grout layer at the bolt -intersection will start to crush after slightly
movement along the joint and causes the plastic strain generation in the grout layer.
Figure 7.42. The grout displacement as a function of plastic strain generated in bolt-joint intersection through the grout in non-pretension condition In high concrete strength, the value of induced stress was slightly reduced and also
pretensioning causes reduction in level of induced stresses along the bolt grout
interface. The induced stress and strain and the rate of changes along the grout layer
in different concrete strength and pretension loads are presented in Appendix D.
7.7.4. Contact Pressure
Contact pressure contours were found to increase with increasing the shear load.
However, contact pressure has slightly reduced with increase of the pretension load.
Figure 7.43 shows the rate of induced contact pressure along the grout-concrete and
bolt –grout. It displays that in vicinity of the shear joint there is high level of contact
0
5
10
15
20
25
30
35
40
0 0.1 0.2 0.3 0.4
Plastic strain at intersection
grou
t she
ar d
ispl
acem
ent (
mm
) .
Moving side
Intersection
Plastic strain at the intersection
Gro
ut s
hear
dis
plac
emen
t (m
m)
CHAPTER 7: Numerical analyses in fully grouted rock bolts
244
pressure in both interfaces. However, this value in bolt –grout contact interface is
much higher than grout –concrete interface.
Figure 7.43. The rate of contact pressure changes between (a) grout – concrete interface (b) bolt-grout interface in 20 MPa concrete in non-pretension condition Figures 7.44 shows the rate of contact pressure generation in the concrete-grout and
grout - bolt interfaces respectively in 20 MPa concrete in 36 mm hole diameter with
80 kN pretension load. They show there is exponential relation between contact
pressure and loading process at the bolt - grout interface, which started after around
15% of the loading process. However, the contact pressure trend in the concrete -
grout interface has formed by 2 parts, from beginning to around 15% of the loading,
there is an approximate linear relation then followed by an exponential relation till
the end of the load stepping process. Figure 7.45 depicts the shear load versus
contact pressure at the bolt - grout interface. It shows that the significant contact
pressure is initiated after 50 kN shear load.
Con
tact
pre
ssur
e (M
Pa)
Distance from centre to end (mm)
C
onta
ct p
ress
ure
(MPa
)
Distance from centre to end (mm)
Shear joint
(a) (b)
CHAPTER 7: Numerical analyses in fully grouted rock bolts
245
Figure 7.44. Contact pressure at the (a) bolt - grout interface (b) concrete - grout interface in 20MPa concrete in high resin thickness (36mm hole diameter) in 80kN pretension load
Figure 7.45. Shear load versus bolt-grout contact pressure at 36 mm hole and 20 MPa and 80kN preload
7.8. SUMMARY
The numerical analysis of the grout/concrete/bolt interaction has demonstrated that:
• There were no significant changes in induced stresses along the bolt with
increasing pretension load, particularly in the tension zone. However, there
was a small reduction in the compression stresses.
0
50
100
150
200
250
300
350
400
0 50 100 150 200
Contact pressure (MPa)
She
ar lo
ad (
kN)
Contact pressure (MPa)
S
hear
load
(kN
)
Loading steps
C
onta
ct p
ress
ure
(MPa
)
Loading steps
C
onta
ct p
ress
ure
(MPa
) (a) (b)
CHAPTER 7: Numerical analyses in fully grouted rock bolts
246
• The yield limit of the bolt occurs first at the hinge point at about 0.3 P and 0.4
P in 20 MPa and 40 MPa concrete respectively, (P is the maximum given
applied load). Further increase in the shear force has no apparent influence on
the stresses in the hinges. The distance between the hinge points reduced with
increasing the concrete strength.
• The strength of concrete, affect greatly shear displacement and bolt
contribution. However, no significant change was observed in the induced
stresses beyond the yield point along the bolt axis with increasing the
concrete strength.
• The maximum shear stress was concentrated in the vicinity of the bolt-joint
intersection.
• There was an exponential relationship between the value of the shear stress
and the distance from the shear joint.
• The shear stress value was not exceeded during further loading after the yield
point. Eventually, the combination of this stress with induced tensile stress at
the bolt-joint intersection lead the bolt to failure.
• By increasing the bolt pretension load, the shear stress was decreased and this
was also observed in different concrete strength.
• The shear stress at the bolt joint intersection slightly increased with
increasing the concrete strength.
• There was no observed significant change in the hinge point distances with
increase of the bolt pretension.
• There was significant increase in the shear displacement beyond 35 % of the
loading step, which is likely the yield point.
CHAPTER 7: Numerical analyses in fully grouted rock bolts
247
• The value of strain in shear direction along the concrete was reduced (around
15%) with increasing the pretensioning. In both axial and shear direction the
strain concentration was generated in the vicinity of the shear joint.
• The induced stresses exceeded the uniaxial compressive strength of the grout
in the vicinity of the bolt –joint intersection, causing grout crushing.
• The damaged area in the upper side of the grout was approximately 60 mm
from the shear joint.
• The induced stresses along the grout were reduced with increasing the
pretension load, nearly 10 %. However, it shows they have slightly expanded.
• The value of strain was decreased by around 3 % and 5 % in both the
compression and tension zones where the bolt pretension load increased to 80
kN.
7.9. NUMERICAL MODELLING OF FAILURE MECHANISM OF
BOLT RESIN INTERFACE SUBJECTED TO AXIAL LOADING
7.9.1. Introduction
A numerical model was developed to find the contact interface behaviour during
shearing under both pull and push tests. The same 3D solid elements and surface-to-
surface contact elements were used for grout and steel simulations. The numerical
simulation of the actual bolt cross-section area and its ribs was a complicated one,
and is almost impossible with the range of software available in the market today.
However, an attempt was made to model the bolt profile configurations by taking
into account the realistic behaviour of the rock-grout and grout-bolt interfaces, based
on the laboratory observations. To achieve this task, the coordinates of all nodes for
CHAPTER 7: Numerical analyses in fully grouted rock bolts
248
all the materials were firstly defined, then all these coordinates were inter-connected
to form the elements and finally the elements were extruded, in several directions, to
obtain real shape of the bolt.
7.9.2. Results and Discussion
Figure 7.46 shows the finite element mesh. Figure 7.47 shows the Bolt Type T1
under pull test condition. Two main fractures produced as a result of shearing of the
bolt from the resin. The first one begins at the top of the rib, with an angle of about
53 degrees running almost parallel to the rib orientation, and the second one has an
angle of less than 40 degree from the bolt axis. When these fractures intersect each
other, they cause the resin to chip away from the main resin body as it is
overwhelmed by the rib surface roughness while shearing.
Figure 7. 46. Finite element mesh: a quarter of the model
Grout
Bolt
Outer plate
CHAPTER 7: Numerical analyses in fully grouted rock bolts
249
Figure 7.47. The bolt movement in pulling test
The produced internal pressure by the bolt profile irregularities causes tangential
stress inducement in the grout. The grout fractures and shears when the induced
stress exceeds the shearing strength of the grout material, thus allowing the bolt to
slide easily along the sheared and slikenside fractures in the grout interface surface.
7.9.2.1. Bolt Behaviour
Figure 7.48 shows the bolt displacement trend. The maximum bolt displacement
occurs at the top collar on the pulling side of the bolt, causing a reduction in bolt
diameter. As a result, there will be an increase in grout-bolt surface debonding as
discussed in Chapter 4. The decrease in the bolt diameter, due to the Poisson effect in
the steel, contributes to an axial elongation of about 0.084 mm at the top collar of the
Shear and tensile fractures
1
Bolt Grout
Rock
2
Bolt
Outer plate Grout
Pull
CHAPTER 7: Numerical analyses in fully grouted rock bolts
250
bolt where the load is applied. This value in push test is around 0.05 mm as shown in
Figure 7.49.
Figure 7. 48. Rate of the bolt displacement
Figure 7. 49. Bolt displacement contour in Bolt Type T1 in case of push test
Distance from end to top (mm)
Axi
al d
ispl
acem
ent (
mm
)
0.08 mm length elongation
Outer plate
bolt
grout
Push load
CHAPTER 7: Numerical analyses in fully grouted rock bolts
251
Figures 7.50 and 7.51 show the maximum induced strain, located in the vicinity of
the applied load position in both the pull and push results respectively. The strain
value is around the elastic strain range and therefore the bolt is unlikely to yield.
Figure 7.50. Induced strain along the bolt profiles
Figure 7.51. Shear strain in bolt ribs in push test
Movement direction
Concentrated stress and strain
CHAPTER 7: Numerical analyses in fully grouted rock bolts
252
Figure 7.52 shows the stress trend along the bolt profile, which shows the maximum
stress being concentrated at the pulling end of the bolt, gradually reducing towards
its free end. Similar results were found by Karanam (2005). Also it shows the shear
and tensile stress trends along the bolt. The maximum tensile stress along the bolt is
330 MPa. This value is in the order of one half of the elastic yield point strength of
600 MPa. This means the bolt behaves elastically and is unlikely to reach the yield
and situation. The axial stress developed along the bolt is given by:
(7.4) (7.5)
Where, tσ is the tensile stress, T is the axial load, D is the bolt diameter and yσ is
the yield strength of the bolt. The bolt behaves elastically as long as the following
expression is satisfied:
tσ < yσ (7.6)
So in this situation with failure along the bolt / grout interface, bolt never experience
yield situation. The shear stress and strain contours along the bolt/grout interface in
case of push test are shown in D.
4*
4
2
2
t
t
DT
and
DT
σπ
πσ
=
=
CHAPTER 7: Numerical analyses in fully grouted rock bolts
253
Figure 7.52. Von Mises Stress and shear stress along the bolt axis
7.9.2.2. Grout Behaviour
The behaviour of interface grout anulus is assumed to be elastic-softening-residual
plastic flow type. This behaviour was developed by Aydan (1989), and is given as:
(7.7)
(7.8)
(7.9)
Where; = Shear modulus of grout interface = Shear strain at any point in the interface
Distance from end to top head of the bolt (mm)
S
tres
s al
ong
the
bolt
(MPa
)
Axial stress
Von Mises stress
Shear stress
O A
γτ G=maxττ <
)( maxmax
maxmax r
r
ττγγγγττ −
−−
−=
rττ =
G
γ
CHAPTER 7: Numerical analyses in fully grouted rock bolts
254
= Shear strain at residual shear strength = Shear strain at peak shear strength
= Residual shear strength of the interface = Peak shear strength of interface = Shear stress at any point in interface
The grout material is in elastic conditions if the following expression is satisfied;
yt TT < (7.10) where; =tT Actual bond stress in the grout
yT = Yield stress of the grout in shear
From the strain generated along the grout interface it was found that the surface of
the grout layer was disturbed by the shear stress induced at the interface and this
strain is higher than the elastic strain range that caused the grout to be damaged at the
contact surface. Figure 7.53 displays the shear stress contour at the grout interface.
The whole contact area of the grout surface was affected by the shear stress and
consequently the induced shear strain was highly dominated. The maximum bonding
stress was approximately 38% of the uniaxial compressive strength of the resin grout.
The stress produced along the grout contact interface was greater than the yield
strength of the grout of 16 MPa and beyond the yield point only a slight increase in
load increment is enough to damage the whole contact surface. Also, the shear
displacement increased as a result the bonding failure occurred. The shear stress at
rγ
maxγ
rτ
maxτ
τ
CHAPTER 7: Numerical analyses in fully grouted rock bolts
255
the bolt grout interface can be calculated by Equation (7.11), which shows a close
agreement with the results from the numerical simulation.
Thus,
(7.11)
where; τ = Shear stress in the grout –bolt interface (MPa)
f = Axial force in the bolt (kN)
A = Contact interface area (mm2)
D = Bolt diameter (mm) Using Farmer (1974) equation the shear strength was equal to 27 MPa.
(7.12)
where; τ = Shear stress along the bolt grout interface
σ = Axial stress a = Bolt radius During the shearing process, the bolt’s outer plate was influenced by the stresses and
strains of the resin contact surface. Also these were small amount of generated over
the contact surface. From the analyses it was found that the induced stress along the
surface of the outer plate was insignificant, at about 30% of the yield stress, which is
not sufficient to reach the outer plate to yield. In addition, the grout debonding
MParlD
Af
2.238
2
===π
σπτ
)2.0
(1.0 a
x
e−
=στ
CHAPTER 7: Numerical analyses in fully grouted rock bolts
256
occurred around 50 to 60 kN in different applied load levels. The details results are
listed in Appendix D.
Figure 7.53. Shear stress contours along the grout interface
7.9.3. Modulus of Elasticity Effect
The Young's modulus is the intrinsic property of an undamaged material, which has
main effect on shearing behaviour of the elasto-plastic contact interface. To define
the influence of this main factor, numerical simulations, with different grout modulus
of elasticity, were carried out to obtain the function coefficients. In the proposed
model the behaviour of the resin grout was assumed isotropic, homogeneous and
linear. However, the behaviour of contact interface was assumed non-linear with
perfect bonding between grout and outer plate and standard bonding between the
grout and bolt including a small cohesion and friction which was calculated from the
bolt - grout interface under constant normal stiffness condition tests (Aziz 2003).
Figures 7.54 to 7.55 show the shear displacement as a function of grout modulus of
elasticity in push, pull and their combination respectively. This relationship was
CHAPTER 7: Numerical analyses in fully grouted rock bolts
257
based on the data produced by the numerical model. There is a power function
between the shear displacement and grout modulus of elasticity.
Figure 7.54. The effect of grout modulus of elasticity on shear displacement in push test
Figure 7.55. The effect of grout modulus of elasticity on shear displacement in pull test
0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
0 5 10 15 20 25 30
Grout modulus of elastisity (GPa)
Shea
r dis
plac
emen
t (m
m)
.
0
0.3
0.6
0.9
1.2
1.5
1.8
2.1
2.4
2.7
3
0 5 10 15 20 25 30
Grout modulus of elastisity (GPa)
Shea
r dis
plac
emen
t (m
m)
.
CHAPTER 7: Numerical analyses in fully grouted rock bolts
258
Equations 7.13 and 7.14 show the shear displacement as a function of grout modulus
of elasticity for push and pull respectively.
(7.13)
(7.14)
By combining Equations 7.13 and 7.14, the following relationship was established.
(7.15)
Where, gE is grout modulus of elasticity, de and du are changes in grout modulus of
elasticity and shear displacement in interface respectively.
Figure 7.56. The shear displacement as a function of grout modulus of elasticity in case of push and pull test
0)(0
4.2
6.1
71.0
68.0
≥ >
−
−u
E
E
yg
g
g
dUdE
0
0.5
1
1.5
2
2.5
3
0 5 10 15 20 25 30
Grout modulus of elastisity (GPa)
Shea
r dis
plac
emen
t (m
m)
.
pull
push
71.0
68.0
4.2
6.1
−
−
=
=
gy
gy
EU
EU
CHAPTER 7: Numerical analyses in fully grouted rock bolts
259
It was found that the value of Equation 7.15 is always positive. The energy required
to exceed the shear strength of the interface is therefore higher than in the pull test.
The reason behind is because of Poisson effect and increasing the lateral pressure.
7.10.4. Summary
Both the experimental and numerical simulation has lead to the following
conclusions:
• The average shear stress capacity of a bolt in a push test was greater than
that in a pull test.
• Yielding and necking is unlikely to occur in bolts tested in 75 mm long
steel sleeves as the peak shear load was around 40% of the maximum
tensile strength of the steel. For the bolts to undergo necking it must be
gripped firmly at both ends.
• Bolt-resin interface failure occurred by initially shearing of the grout at
the profile tip in contact with the resin.
• Numerical simulation provided an opportunity to understand better the
stresses and strains generated as a result of bolt resin interface shearing.
Such understanding supported clearly both analytically as well as by
simulation.
• The experimental test findings were in agreement with the numerical
simulations and analytical results.
CHAPTER 8: Analytical aspect of fully grouted bolts
260
CHAPTER 8
ANALYTICAL ASPECT OF FULLY GROUTED BOLT
8.1. REACTION FORCES DURING THE SHEARING
Numerous investigators have proposed analytical models and tried to evaluate the
bolt behaviour subjected to shearing, which are presented in following sections.
However, according to nature of theoretical solution, accepting of the some
assumptions is inevitable. When a bolted rock joint is subjected to shearing, the bolt
is deformed with increasing joint displacement and this can mobilizes a normal and a
shear force in the bolt, Swoboda and Marence (1992). And also with applying load to
a beam, its longitudinal axis is deformed into a curve and two components are
produced. A lateral load Q and an axial load N and two critical points: one in bolt-
joint intersection with zero bending moment and another in the maximum bending
moment (hinge point) with zero shear stress. these loads produce stress resultants in
the form of bending moments M, shear force Q and axial forces N throughout the
beam. Since both the axial force N and bending moment M produce normal stresses,
we need to combine those stresses to obtain the final stress distribution. Based on the
beam’s theory the axial stress produces a uniform stress distribution AN=σ and the
bending moment produces a linearly varying stress IMy−=σ with compression on the
upper part of the beam and tension on the lower part and inverse in other side of the
joint. Figure 8.1 shows the assembled concrete, grout and steel model. Figure 8.2
displays the load generation along the bolt under shearing. The final distribution of
CHAPTER 8: Analytical aspect of fully grouted bolts
261
normal stresses is obtained by superposing the stresses produced by the axial force
and the bending moment.
(8.1)
A = 4
2dπ (8.2)
I = 64
4dπ (8.3)
Note that N is negative when it produces tension and positive bending produces
compression in the upper part of the beam.
Figure 8. 1. Assembled model (concrete, grout and steel bolt) Figure 8. 2. Load generation along the bolt during the shearing
IMy
AN −=σ
Joint
N1 N1
grout bolt
Rock
N1
N1
M M
N1
Q (x) Q (x)
Q (x)
• • D E C
cfQcfN
•
M Shear joint
CHAPTER 8: Analytical aspect of fully grouted bolts
262
As the loading increase, the surrounding medium concrete or grout supplies a
reaction. This reaction acts on the bolt length, which progressively increases until the
bolt reaches the yield situation, this reaction pressure depends on medium strength
and medium stiffness, which is discussed later.
),,()( byy DUKfxQ = (8.4)
where; yk = Medium stiffness, yu = Displacement along the joint and bD = Bolt
diameter.
8.2. STEEL BOLT BEHAVIOUR
8.2.1. Plastic Design
Steel has predictable structural behaviour in the stress range in excess of the yield
point, i.e, the plastic range. Within this range, stress is no longer proportional to
strain and permanent deformation takes place. Plastic design implies a design
procedure based upon behaviour of the structure or element stressed within the
plastic range of the material (Crawley et al 1984).
There are two principal aspects of plastic theory. The first involves the stress pattern
at a single cross section and the developed stress resultant. The second aspect
involves the element as a whole the entire length of a series of continuous beam.
8.2.2. Plastic Theory
Whereas steel is ductile material, it is able to withstand deformation under load
without fracture. Figure 8.3 shows the normal stress strain curve for structural steel.
When the yield point, yF , is first reached, it has a corresponding strain yε . Any
CHAPTER 8: Analytical aspect of fully grouted bolts
263
slight increase in stress beyond this point will cause the steel to behave plastically.
However, its ductile quality allows it to be strained or stretched 15 times its yield
point strain without a noticeable increase in stress.
Figure 8. 3. Stress strain relationship for bolt type T1
This is frequently referred to as a large flow of the material at a constant stress. If
this phenomenon is applied to a member in bending, the stress patterns illustrated at
Figure 8.4 a,b,c and d,e are those resulting from successively higher bending
moments. Rock bolts act as flexible support and redistribute the bending moment on
it, Moussa and Swoboda (1995).
Figure 8. 4. Elastic – plastic stress sequence in bending
yF
yF yF
yF
yF
yF
a b c d e
0
50
100
150
200
250
300
350
400
0 10 20 30 40 50 60 70
Axial displacement (mm)
Axi
al L
oad
(kN
) .
yF
yε
CHAPTER 8: Analytical aspect of fully grouted bolts
264
From elastic theory, stress is proportional to distance from the neutral axis, and
triangular stress patterns are formed such as those shown in Figure 8.4-b and c, the
outermost fibre has reached the yield point, and the corresponding stress resultant or
yield bending moment would be My= yF . (r). Any additional moment would cause
the outermost fibre to flow but at the same time maintain the yield stress.
Consequently the adjacent fibres undergo an increase in strain with corresponding
increase in stress up to a maximum of yF . This condition is shown in Figure (8.4.d).
For still larger moments, the process continues until the entire section is stressed up
to yF as shown in Figure 8.4 e. This is the maximum stress on the entire section. In
this stress condition, plastic hinge is formed, and the corresponding moment is
referred to as the plastic moment. Since the stress almost is constant in both the
tension and compression regions, the areas and internal forces must be equal.
8.2.3. Basic Equation For A Grouted Rock Bolt Subjected To
Lateral Deformation
According to beam’s theory on an elastic foundation the mechanical performance of
the grouted rock bolt is as following equation, Hetenyi (1961).
(8.5)
where;
y = deflection of the bolt
E = modulus elasticity of the bolt
I = moment of inertia of the bar
0)4( =+ yEIDk
y bm
CHAPTER 8: Analytical aspect of fully grouted bolts
265
mK = Stiffness of subgrade reaction, which is function of annulus thickness, rock
mass surrounding materials.
bD = bolt diameter
mE = Modulus of subgrade
It is assumed that transversely loaded bolts behave according to Figure 8.5, which
shows the reaction forces supply, shear force, a bending moment and shear
displacement diagrams. The resulting strains and stresses in the beam are directly
related to the curvature of the deflection curve. This is discussed primarily by
Crawley and Dillon (1984). The bolt bending creates a bending stress in the bolt,
Koshti (2002 a,b).
Two points M1 and M2 are identified on the deflection curve. Point M1 is selected at
an arbitrary distance x from the axis y and point M2 is located a small distance (ds)
further along the curve. From each of these points a line normal to the tangent to the
deflection curve is drawn that is normal to curve itself. These normal intersect at
point o, which is the center of curvature of deflection curve. The distance M1o from
the curve to the center of curvature is called the radius of curvature ( ρ ). Curvature is
a measure of how sharply a beam is bent. If the load on a beam is small, the beam
will be nearly straight, the radius of curvature will be very small. If the load is
increased, the amount of bending will increase, the radius of curvature will become
smaller, and the curvature will become larger. When yield in both subgrade and bolt
has occurred the bolt angle then changes towards the directions of deformation and
an axial load will develop in the bolt.
CHAPTER 8: Analytical aspect of fully grouted bolts
266
Figure 8. 5. Deformed shape, shear force, bending moment and shear displacement diagrams According to Egger and Spang (1990) the deformed shape of the bolt shows two
singular point: one in the bolt-joint intersection, and another one in the point of
maximum bending moment (hinge point).
The failure of the bar may happens in one of these two locations; joint-bolt
intersection (affected by contribution of normal and transversal forces at the point C)
or at the point D, occurring by the combination of the axial force and the bending
moment (hinge point), where the bending moment is maximum and shear force is
zero. The failure equations can be determined by following interaction formula,
Pellet (1994).
D E C
M
N0
ds
M1 M2
Q (x)
Hinge point distance
Lhg
Bolt with reaction forces
Bolt bending
Shear force diagram =
Bending moment diagram
Shear displacement
ρ
cfQcfN
Hinge point
Max bending
y
//y
///y
o •
• •
CHAPTER 8: Analytical aspect of fully grouted bolts
267
Failure at the bolt-joint intersection and in the maximum bending moment are
presented in Equations 8.9 and 8.10 respectively
(8.9) (8.10)
where;
cfN = Normal force at yield limit
pN = Normal force at failure
cfQ = Shear force at yield limit
pQ = Shear force at failure
DM = Bending moment at yield limit
pM = Bending moment at plastic limit
DN = Axial force in hinge point
According to beam theory both the bending moment and curvature of the bolt at
point C are zero. However, the axial force and shear force in this point are maximum.
By using the above equations, pellet (1996) carried out an analytical formulation and
obtained following equations to determine the failure forces at bolt-joint intersection
and maximum bending moment. The axial force and shear force at bolt-joint
intersection are calculated by Equations 8.11 and 8.12:
1)(
1)()(
2
22
=+
=+
p
D
p
D
p
cf
p
cf
NN
MM
Q
Q
N
N
CHAPTER 8: Analytical aspect of fully grouted bolts
268
(8.11)
(8.12)
where;
bA = Bolt cross section area,
fσ = Failure stress at bolt material and
eQ = Shear force acting at point C in elastic limit
cfQ = Shear force acting at point C at failure of the bolt material
Axial force and shear force at point maximum bending moment are calculated from
Equations 8.13 and 8.14.
(8.13) (8.14)
According to the analysing it was found that the amount of shear load at bolt joint
intersection is higher than that at hinge point, which is consistent with the numerical
design as the maximum shear stress concentration was found at bolt –joint
intersection.
2)(12 fb
cff
bcf A
NAQ
σσ −=
fu
cffbDf
DP
QAN
σπσ 3
2
69.1(161−=
])(1[16
69.1 23
fb
cffuDf A
NDPQ
σσ
π−=
2)(41fb
efbcf A
QAN
σσ −=
CHAPTER 8: Analytical aspect of fully grouted bolts
269
8.3. BOLT - JOINT CONTRIBUTION
In reality when the bolt - joint is perpendicularly oriented (near 90 degree) bolt
would fail under combination of the shear and tension as it was found from the
experimental and numerical results. Whereas in small angles bolt is affected by
stretching load, failure is occurred under the tension, this occurrence was originally
investigated by Bjurstrom (1973). In a simple analytic procedure the contribution of
the bolt is calculated as following (Figure 8.6).
Figure 8. 6. Applied loads on joint intersection T j = tf cos β + sf sin β (8.15)
vT = tf sin β - sf cos β (8.16)
bT = T j + T v φτag (8.17)
bT = tf cos β + sf sin β + ( tf sin β - sf cos β ) φτag (8.18)
bT = tf (cos β + sin β φτag ) + sf (sin β -cos β φτag ) (8.19)
where;
β
Joint
Bolt
β
sf
β
β
T j
T v
tf
CHAPTER 8: Analytical aspect of fully grouted bolts
270
sf = Shear load
tf = Axial load, which could be summation of axial load due to pretensioning
along the bolt ( 1T ) and axial load developed due to shearing movements ( 2T ), so it
can be written as:
yt TTTf ≤+= )( 21 (Maximum tensile strength of bolt)
β = Joint slope
φ = Joint friction angle
bT = Bolt contribution
From the equation it can be seen that bolt contribution depends upon the bolt angle,
angle of friction, confining effect and axial load developed along the bolt.
In this equation if angle is great (perpendicular bolt), it can be expressed as;
bT = tf φτag + sf (8.20)
With comparison of two equations for inclined and perpendicular bolt, it is found
that the role of confining in case of perpendicular is significant.
In other words, pretensioning can increase the confining effect and consequently bolt
contribution. In reality a coefficient of the pretensioning may affect as confining,
then,
bT = ( 21 TKN + ) φτag + sf (8.21)
1N = Pretensioning
K = interface load transfer factor, it can be assumed equal coefficient of friction
angle
CHAPTER 8: Analytical aspect of fully grouted bolts
271
In absence of confining pressure and pretensioning, the only resistance forces are
shear resistance between bolt-grout:
T
b= sf + rlπτ 2. φτag (8.22)
where;
τ = Shear stress between bolt-grout interface
l = embedded length
r = bolt radius
Without pretensioning or end plate bolt is pulling along the bolt with applying the
shear load, however, if there is end plate, tensile stresses are produced along the bolt
and bolt contribution will increase. As it shows when pretensioning or confining
pressure increases contribution of the bolt will increase. This occurrence was
observed by laboratory and numerical results.
8.4. REACTION FORCES
A grouted bolt subjected to lateral deformation induces a support reaction that will
develop in both the grout and the rock mass. When the bolt is laterally loaded it is
assumed that the response from the subgrade depends on the mechanical properties
of the rock mass. Because of the small width of the grout annulus, probably should
be disregarded and the influence of the grout material is insignificant. However, if
the resin thickness is high and stronger than the surrounding rock, the effect is
CHAPTER 8: Analytical aspect of fully grouted bolts
272
significant as was confirmed by laboratory results. Besides, the effect of resin
thickness was compared with the case without resin. It was found that bolt
contribution would increase. (See laboratory chapter). There is a high value of lateral
deformation and pressure reaction in vicinity of the bolt-joint intersection. Thus the
yield in the subgrade will start in locations next to the shear joint and will expand
with increasing the bolt deformation progressively.
8.4.1. Basic Equation for Rock and Subgrade Material
The reaction of lateral bolt deformation can express by following equations (in
elastic situation).
(8.23)
where,
up = Support reaction
mK = Lateral stiffness, this is function of annulus thickness, rock and resin
mechanical properties.
yu = Lateral deformation
Terzaghi (1955) found one equation for lateral stiffness in elastic material. However
he neglected the effect of grout properties:
mK =b
m
DE35.1
(8.24)
mE = Modulus of elasticity of subgrade
bD = Diameter of the bolt
ymu ukp =
CHAPTER 8: Analytical aspect of fully grouted bolts
273
Based on rock mechanics equations mE is equal (0.3-0.4) iE or equal 400 cσ and
iE = Modulus of elasticity of intact subgrade
So it is concluded that the reaction force can be measured as a function of bolt
deflection, subgrade modulus of elasticity and strength of material, which these
parameters are evaluated in numerical simulation chapter. According to the
Holmberg (1991) analysis, the support reaction of subgrade can be expressed as.
b
ycu D
up
σ300= (8.25)
And according to Pellet’s discussion
uP = bc D.σ (8.26)
8.6. ANALYTICAL APPROACH TO DEFINE THE HINGE
POINT LOCATION REGARDING AXIAL LOAD ALONG THE
BOLT
8.6.1. Elastic behaviour
When lateral force acts on the bar, then the axial force and bending moment are
induced along the bolt. Figure 8.7 displays the induced loads around the bolt during
shearing.
Figure 8. 7. Reaction forces in bolt loaded laterally
No D E C
M
Bolt with reaction forces
cfQcfN
uP
pL
CHAPTER 8: Analytical aspect of fully grouted bolts
274
(8.37)
A =4
2dπ (8.38)
S = 32
3dπ (8.39)
where,
DM = bending moment,
N cf = axial force,
A = area of bar cross section
d = bolt diameter,
S = section modulus.
maxσ = normal stress acting on the bolt
The bending moment at point D can calculated as Equation 8.41. Point D is the hinge
point, which carries zero shear stress and maximum bending moment. With assuming
the equilibrium situation in this part of the beam, it can be expressed as follows:
(8.40)
(8.41)
By substituting Eq (8.40) in Eq (8.41) and simplify, it can be written:
2/2puD lpM = (8.42)
and, by substituting the Equations 8.38, 8.39, 8.42 in Equation 8.37, hinge point
distance to the shear joint can be expressed as a following equation.
SM
A
NDcf ±=maxσ
pucfy LPQF *0 ==
2
.*0
2. pu
pcfDD
LPLQMM −==
CHAPTER 8: Analytical aspect of fully grouted bolts
275
(8.43)
where;
cfQ = shear force
cpL = reaction length
uP = reaction fore, which can be equal bc D.σ according to Pellet’s discussion
yσ = elastic yield stress
cσ = uniaxial compressive strength of rock
Figure 8.8 shows the effect of hinge point distance as a function of the axial force
along the bolt. As figure shows in the higher level of axial force, close to the tensile
yield point of the bolt, there is not significant difference in hinge point in different
rock strength. Yield tensile load is around 230 kN. According to the laboratory tests
and recording of axial load along the bolt, it was observed that there is no significant
change in value of the axial load in elastic region, so with this assumption the hinge
point length, distance from maximum bending moment to the shear joint, can be
expressed as Equation 8.44. Figure 8.9 shows the variation of the bolt diameter as a
function of hinge point location. It displays that the hinge point location is increased
with increasing bolt diameter. In addition, higher rock strength, has shown lower
hinge point distance.
(8.44)
u
cfbybp p
NDDl
)4(
41
2 −=
πσ
u
byp p
Dl
3
41 πσ
=
CHAPTER 8: Analytical aspect of fully grouted bolts
276
Figure 8. 8. Hinge point distance versus axial force Figure 8. 9. Bolt diameter versus hinge point distance in different rock strength
8.6.2. Plastic Behaviour
As discussed earlier the failure of the bar may happens in one of these two locations;
bolt - joint intersection or at the maximum bending moment, The failure equation in
0
50
100
150
200
250
0 10 20 30 40 50 60
Hinge point distance (mm)
Axi
al lo
ad a
long
the
bolt
(kN
)
.
20 MPa-Elastic40 MPa-elastic
0
5
10
15
20
25
30
35
40
45
0 20 40 60 80 100 120
Hinge point distance (mm)
Bol
t dia
met
er (m
m)
.
20 MPa
40 MPa
CHAPTER 8: Analytical aspect of fully grouted bolts
277
maximum bending moment can be determined by Equation 8.45, which was
described in Eq (8.10).
(8.45)
According to beam theory both the bending moment and curvature of the bolt at the
bolt- joint intersection are zero. With validation of Tresca’s failure criterion for the
bolt behaviour, the value of plastic bending moment and axial force at failure can be
expressed as follows:
(8.46)
(8.47)
By substituting Equations 8.43, 8.47 and 8.48 in Equation 8.46, it can be written as:
(8.48)
After simplification, and substituting the uP = bc D.σ hinge point distance can be
expressed as follows:
ybc
Dybp
D
NDl
σπσσπ
.
)16(32.0 2
2242 −= (8.49)
Figure 8.10 presents the effect of axial load on hinge point distance in plastic
situation at both 20 and 40 MPa concrete. It indicates that there is no significant
influence in hinge point distance in different rock strength at high level of axial load.
However, the hinge point distance is reduced with increasing the strength of
1)( 2 =+p
D
p
D
NN
MM
4
32
7.1
2
3
ybp
ybp
DN
DM
σπ
σπ
=
=
1).
4(
.4.3
32 223
2
=+yb
D
yb
pu
D
N
D
lp
σπσπ
CHAPTER 8: Analytical aspect of fully grouted bolts
278
surrounding material. This was consistent with the laboratory results (Figure 8.12)
Moreover, the hinge point distance was increased with decreasing the axial load in
the bolt with polynomial trend. Thus, it can be inferred that when axial load
increases, the hinge point distances reach closer. This means the maximum axial load
moves towards the bolt-joint intersection and eventually lead the bolt to failure with
combination of axial and shear load at this area. Figure 8.11 shows the comparison of
hinge point distance and axial load in both elastic and plastic situation.
In other words, increase of the axial load is due to the lateral load increase, which
induces higher axial deformation. So with increasing the axial deformation, yield
position will move towards the bolt joint intersection, which was observed, from
laboratory results (Bolt Type T5). After stopping the test it was observed that the rib
distance at hinge point were increased which is due to yield at this point.
Figure 8. 10. The relationship between axial load and hinge point distance in different rock strength in plastic situation
0
50
100
150
200
250
0 10 20 30 40 50 60 70 80
Hinge point distance (mm)
Axi
al lo
ad a
long
the
bolt
(kN
)
.
20 MPa
40 MPa
CHAPTER 8: Analytical aspect of fully grouted bolts
279
Figure 8. 11. The relationship between the axial load and hinge point distance in both elastic and plastic situation Figure 8. 12. Hinge point position in different concrete strength
However, other test after dramatic reduction in load, they were continuing till failure
occurred with bolt separation at the bolt joint intersection, this means that initially
0
50
100
150
200
250
0 10 20 30 40 50 60 70 80
Hinge point distance (mm)
Axi
al lo
ad a
long
the
bolt
(kN
)
. 20 MPa-Plastic40 MPa-Plastic20 MPa-Elastic40 MPa-elastic
Higher strength
Lower strength
CHAPTER 8: Analytical aspect of fully grouted bolts
280
failure will occur at yield point and then with increasing axial load and axial
deformation this yield moves towards the joint intersection and results the failure at
that point with combination of the axial and shear load.
Holmberge (1991) developed an equation to define hinge point location in case of
yielding bolt and yielding subgrade as following:
2)1(58.0 tu
ybh ku
pDl −=
σ (8.50)
where;
K = factor depends upon the modulus of elasticity , bolt yield strength and grout
condition
According to this equation when axial displacement increases, hinge point position
moves towards the bolt joint intersection (Figure 8.13), which was discussed earlier.
Figure 8. 13. Relationship between hinge point position and axial deformation
0
2
4
6
8
10
12
14
16
0 0.2 0.4 0.6 0.8 1 1.2
Axial deformation (mm)
Hin
ge p
oint
pos
ition
(mm
)
.
CHAPTER 8: Analytical aspect of fully grouted bolts
281
8.7. ANALYTICAL APPROACH TO DEFINE THE HINGE
POINT LOCATION REGARDING SHEAR DISPLACEMENT
According to previous sections in elastic region the Equation 8.51 was found to
define the hinge point location with strength of material and axial force induced in
the bolt.
(8.51)
Based on a semi - empirical expression, which was derived regarding the subgrade
support reaction in elastic conditions, the Equation 8.51 can be written as Equation
8.53:
(8.52)
(8.53)
By simplification of Equation 8.53, the hinge point location can be expressed as
Equation 8.54. Hinge point location gets stable situation with increasing the shear
displacement along the joint. Moreover, the hinge point location is decreased in
higher rock strength. (Figure 8.14)
(8.54)
From the previous sections, it is concluded that first yield point will be in hinge point
and by increasing shear load, shear displacement, axial load and axial deformation
u
byp p
Dl
3
41 πσ
=
yc
byp u
Dl
σπσ
30041
4
=
b
ycu D
uP
σ300=
21
2 )(025.0yc
ybp u
Dlσσ
=
CHAPTER 8: Analytical aspect of fully grouted bolts
282
will increase. Then due to these changes, failure position will move towards the joint.
This effect was evaluated by laboratory tests in Bolt Type T5 clearly. The hinge
point location was initially investigated by Dight (1982).
Figure 8. 14. Hinge point location as a function of shear displacement in elastic region
8.8. ANALYTICAL METHOD TO DEFINE THE SHEAR
DISPLACEMENT IN CASE OF BOLT MODULUS OF
ELASTICITY
By substituting Eq (8.39) in Eq (8.40), which were expressed in previous section and
simplifications, bending moment at hinge point can be written:
ucfD PQM 2/2= (8.55)
and, By substituting the Equations 8.38, 8.39 and 8.55 in Equation 8.37, Equation
8.56 is expressed.
0
10
2030
40
50
60
7080
90
100
0 2 4 6 8 10 12
Shear displacement (mm)
Hin
ge p
oint
dis
tanc
e (m
m)
.
20 MPa40 MPa100 MPa
CHAPTER 8: Analytical aspect of fully grouted bolts
283
cfQ = 5.0)]4
2([5.0 cf
ybbu N
ddP −
σπ (8.56)
where;
cfQ = shear fore
cpL = reaction length
uP = reaction force
yσ = elastic yield stress
In elastic limit, axial force along the bolt is negligible, this assumption was
confirmed from the laboratory results, which was discussed in previous chapter. So,
the shear force can be written as following equation:
cfQ = 5.03
)16
*( uyb Pd σπ
(8.57)
By substituting the Equation 8.57 in Equation 8.58, which was expressed by pellet in
elastic limit for determining the shear displacement, Equation 8.60 is developed.
Pellet’s theory was according to the beam’s theory on an elastic foundation the
mechanical performance of the grouted rock bolt:
(8.58)
up = bcdσ (8.59)
(8.60)
where;
cσ = Uniaxial compressive of surrounding material
βsin.17.22 34
4
ubcfoe pdE
Qu =
βσσσπ
sin)(.1)(08.0 34
23
bcbbcyboe dDE
ddu =
CHAPTER 8: Analytical aspect of fully grouted bolts
284
E = bolt modulus of elasticity
β = angle between bolt and joint
In this equation the value of axial load is reduced as it is in elastic range. in this range
as laboratory tests showed there was no axial load on the bolt, so it can be removed
from the equation.
Following Equation comes from numerical simulations:
14.05.5 −= boe EU (8.61)
As the Figure 8.15 shows the small difference which is distinguished between the
analytical and numerical curves is due to some assumptions in analytical method
such as defining the same strength for surrounding materials and neglecting of
contact interfaces. However, in numerical simulation, two surrounding materials,
grout and concrete, with different strength and also contact interface properties are
defined, so this small difference is reasonable.
Figure 8. 15. Comparison of the numerical and analytical results, concrete 20 MPa,
1.5
2
2.5
3
3.5
4
4.5
0 50 100 150 200 250
Bolt modulus (GPa)
Shea
r dis
plac
emen
t (m
m)
.
Numerical
Analytical
CHAPTER 8: Analytical aspect of fully grouted bolts
285
8.9. Analysis of a Fully Grouted Elastic Bolt in Plastic
Rock Mass
Following Farmer (1975), the equilibrium of a fully grouted rock bolt may be
written:
xFA xxb ∆−=δσ (8.62)
b
xx
AF
x−
=∆
∆σ (8.63)
where;
bA is bolt cross section area
xF is the shear load due to bond per unit length in elastic behaviour
dxdu
E xbx =σ (8.64)
Then substituting (8.64) into (8.63):
bb
xx
EAF
dxud −
=2
2
(8.65)
In other words, the shear force due to the bolt can be assumed as a linear function of the relative slip between the bolt and the rock, Moosavi (1997).
Then,
)( xrx uuKF −= (8.66)
where;
K = shear stiffness of interfaces (N/mm^2)
CHAPTER 8: Analytical aspect of fully grouted bolts
286
ru = Rock displacement along the bolt (mm) which decreases with distance from the
surface of the excavation and depends of many in situ parameters.
By combining (6.66) and (6.67) the following equation, where is distribution of the
displacement along the bolt is found.
bb
r
bb
xx
EAKu
EAKu
dxud −
=−2
2
(8.67)
The above Equation was considered by Moosavi (1997) as well. However, he
considered both bolt and rock mass in elastic condition. In this model the bolt and
rock mass behaviours are considered elastic and plastic respectively.
ru can be represented by an analytical function of the geometry of the tunnel and
rock surface movement.
xr
ruu
o
orr
o
+=
. (8.68)
where;
or = Tunnel radius, rou is the total deformation of the excavation wall, which
depends on the property of the rock mass, maybe, written (Stille et al. 1989):
)]1()(2[1
1 −++
= + frr
fBr
u f
o
eoro (8.69)
(8.70)
(8.71)
bbPok
r
rPoE
B
e
er
−++
=
−+=
)(1
2
)(1
σ
σν
CHAPTER 8: Analytical aspect of fully grouted bolts
287
And parameters b, k and f can be found from following equations. (8.72) (8.73)
(8.74)
where;
ν = poison ration of rock mass
Po = in situ stress
c = cohesion
ϕ = friction angle
er = the boundary between the zone of plastic and elastic
By substituting Eq (8.69) into Eq (8.68) and then Eq (8.68) into Eq (8.64) a
numerical method has been developed as following.
To solve the Equation (8.64) a numerical method is obtained in which the bolt length
was divided into small equal sections. It should be noted that the bond stiffness was
considered constant. Then the load distribution can be calculated by linking these
small sections together.
As we have,
bb
r
bb
xx
EAKu
EAKu
dxud −
=−2
2
(8.75)
To solve the equation dimensionless quantities are defined.
)245tan(
)245tan(
)2
45(tan
tan
2
ψϕ
ϕ
ϕ
ϕ
−+
+=
+=
=
f
k
cb
CHAPTER 8: Analytical aspect of fully grouted bolts
288
orx
x =′ , ro
xx u
uu =′ ,
ro
xr u
uu =′
Then it can be written,
rbb
ox
bb
ox uEA
Kru
EAKr
xdud ′−
=′−′′
′′
22
2
2
(8.76)
bb
o
EA
Kr 2
is a dimensionless quantity. By defining bb
o
EAKr
2
=γ it can be written as,
rxx uu
xdud ′−=′−′′
′′ γγ2
2
(8.77)
By dividing the bolt to the n equal sections (Figure 8.16) and defining
)(1o
ii nrLxxx =′−′=′∆ + and using the following expressions for derivatives of xu ′′
at ixx ′=′
Figure 8. 16. Notation for numerical formulation
xxuxu
xdud ixixx
′∆′′−′′
=′′ −′+′′
2)()( 11 (8.78)
or
xxuxu
xdud ixixx
′∆′′−′′
=′′ ′+′′ )()( 1 (8.79)
• • •
Nodal point 1+il1−il
1+ixix1−ix•
CHAPTER 8: Analytical aspect of fully grouted bolts
289
211
2
)()()(2)(
xxuxuxu
xdud ixixixx
′∆′′+′′−′′
=′′ −′′+′′ (8.80)
Equation (8.77) for i = 2, • • •, n can be written as;
)()()()(])(2[)( 21
21 irixixix xuxxuxuxxu ′′′∆−=′′+′′′∆+−′′ +′′−′ γγ
These n — 1 equation with two boundary conditions will form a tridiagonal
system of n + 1 linear algebraic equations with n + 1 unknowns, )( ix xu ′′ ′ ,
which can be solved.
xur ′+
=′1
1 (8.81)
The solution is conducted for two cases;
Case 1: two free ends of the bolt Fx =0 at x =0 and Fx =0 at x=L, where
xdud
ru
EAF x
o
robbx ′
′= ′)(
Defining normalized force xF ′ = Fx/ (AbEb) the above boundary conditions will be
equivalent to;
0)()( 12 =′′−′′ ′′ xuxu xx and 0)()( 1 =′′−′′ ′+′ nxnx xuxu
Case 2: Faceplate attached to one end —> ux = ur0 at x = 0 and Fx = 0 at x = L,
or
1)( 1 =′′ ′ xu x and 0)()( 1 =′′−′′ ′+′ nxnx xuxu
CHAPTER 8: Analytical aspect of fully grouted bolts
290
Figures 8.17 to 8.23 show the distribution of axial load developed along the bolt and
the normalised displacement, without face plate, installed in plastic surrounding
materials. The input data for surrounding materials are used according to SCT report.
The initial stress and rock modulus of elasticity are considered 25 and 15000 MPa
respectively. The effect of bolt length, rock modulus, initial stress and shear stiffness
of the interface are evaluated on the axial load built up along the bolt. Figure 8.17
shows the axial load along the bolt in different bolt length. It displays with increasing
the bolt length, axial load is increased and also the peak point of the load moves
towards the end of the bolt. In addition, the bolt load is concentrated near the
excavation surface. Figure 8.18 shows the normalised displacement as function of
bolt length. It shows with increase of the bolt length, rock displacement is reduced.
Figures 8.19 and 8.20 show the normalised displacement as function of bolt length,
for a 2.1 m bolt, in same rock strength, but different initial stress with various
interface shear stiffness. It shows there are no significant changes on the normalised
displacement at different stress. However, with increase of interface stiffness,
displacement is reduced. It should be noted that according to Equation 8.69 to 8.74,
the value of rou in 15 and 25 MPa initial stress is 6.3 and 10 mm respectively.
Figure 8. 17. Axial load along the bolt versus bolt length, in case of unplated with 25 MPa initial stress and 15 GPa modulus of surrounding rock
po=25 MPa
0
5
10
15
20
25
30
35
0 2 4 6 8 10
Bolt length (m)
Loa
d al
ong
the
bolt
(kN
) .
XL=5mXL=10mXL=2.1 m
CHAPTER 8: Analytical aspect of fully grouted bolts
291
Figure 8. 18. Normalised displacement versus bolt length in case of unplated with 25 MPa initial stress and 15 GPa modulus of surrounding rock Figure 8. 19. Normalised displacement versus bolt length in case of unplated with 25 MPa initial stress and 15 GPa modulus of surrounding rock at different k values Figure 8. 20. Normalised displacement versus bolt length in case of unplated with 15 MPa initial stress and 15 GPa modulus of surrounding rock at different k values
po=25 MPa
00.10.20.30.40.50.60.70.8
0 2 4 6 8 10 12
Bolt length (m)
Nor
mal
ised
dis
plac
emen
t .
XL=5mXL=10mXL=2.1 m
Po=25 MPa, E=15 GPa
0.55
0.6
0.65
0.7
0.75
0.8
0 0.5 1 1.5 2 2.5
Bolt length (m)
Nor
mal
ised
dis
plac
emen
t
k=10k=10k=1
po=15
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0 0.5 1 1.5 2 2.5
Bolt length (m)
Nor
mal
ised
dis
plac
emen
t .
k=100k=10k=1
CHAPTER 8: Analytical aspect of fully grouted bolts
292
Figure 8.21 shows the distribution of axial load along the bolt length (2.1 m) in
different interface stiffness. It displays with increase of stiffness the load developed
is increased. Figure 8.22 shows load developed along the bolt increased with increase
of initial stress. This is considered at constant stiffness. Figures 8.23 and 8.24 show
load distribution along the bolt 2.1m and 10 m respectively at 25 MPa initial stress
for different values of rock modulus of elasticity. It displays softer rocks generate
higher value of load along the bolt.
Figure 8. 21. Load developed along the bolt versus bolt length in case of unplated with 15 MPa initial stress and 25 GPa modulus of surrounding rock at different k values Figure 8. 22. Load developed along the bolt versus bolt length in case of unplated with 15 GPa modulus of surrounding rock at different initial stresses
Po=25 MPa, E=15 GPa
01020304050607080
0 0.5 1 1.5 2 2.5
Bolt length (m)
Loa
d al
ong
the
bolt
(kN
) .
k=1k=10k=100
k=10
02468
10121416
0 0.5 1 1.5 2 2.5
Bolt length (m)
Loa
d al
ong
the
bolt
(kN
) .
po=35 M Pa
Po=25 M Pa
P0=15 M Pa
CHAPTER 8: Analytical aspect of fully grouted bolts
293
Figure 8. 23. Load developed along the bolt versus bolt length in case of unplated with 25 MPa initial stress and different modulus of surrounding rock at k=10 Figure 8. 24. Load developed along the bolt versus bolt length in case of unplated with 25 MPa initial stress and different modulus of surrounding rock at k=10, L=10 m
Case 2: End plate attached to end
Using Eq 8.76 and boundary conditions in case 2(using end plate), the axial load
built up along the bolt and distribution of the bolt displacement for different bond
strength, rock mass modulus of elasticity, bolt length in various initial stress are
analyzed as follows. Figures 8.25 and 8.26 show the axial load and distribution of the
bolt displacement in two different bond stiffness respectively. It shows the bond
Po=25 MPa
05
1015
2025
3035
0 0.5 1 1.5 2 2.5
Bole length (m)
Loa
d al
ong
bolt
(kN
) . E=5GPa
E=15GPaE=25GPaE=50GPa
0
20
40
60
80
100
120
0 2 4 6 8 10 12
Bolt length (m)
Axi
al lo
ad a
long
bol
t (kN
) .
E=5GPa
E=15GPa
E=25GPa
CHAPTER 8: Analytical aspect of fully grouted bolts
294
strength plays a major role on increasing the bolt load and reducing the bolt
displacement.
Figure 8. 25. Load developed along the bolt versus bolt length in case of using end plate with 25 MPa initial stress and different k, at Er = 5GPa
Figure 8. 26. Normalised displacement versus bolt length in case of using end plate with 25 MPa initial stress and different k, at Er = 5GPa Figures 8.27 and 8.28 show the distribution of axial load and bolt displacement in
different rock modulus and different bolt length. It displays that higher rock modulus
of elasticity generates lower axial load along the bolt. This trend is reduced
exponentially towards the bolt end in both bolt length. Figure 8.29 shows the axial
load distribution along the bolt in different initial stress conditions. It reveals that
020406080
100120140160
0.00 0.50 1.00 1.50 2.00 2.50
Bolt length (m)
Axi
al lo
ad (k
N)
.k=1
k=10
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
0.00 0.50 1.00 1.50 2.00 2.50
Bolt length (m)
Nor
mal
ised
dis
plac
emen
t .
k=1
k=10
CHAPTER 8: Analytical aspect of fully grouted bolts
295
surrounding rocks involved with higher initial stress induces higher axial load along
the bolt. As Figure 8.30 shows, the axial load reduces with decreasing the radius of
plastic zone around the tunnel.
Figure 8. 27. Axial load versus bolt length in case of using end plate with 25 MPa initial stress and different rock modulus and bolt length, k=10
Figure 8. 28. Normalized displacement versus bolt length in case of using end plate with 25 MPa initial stress and different rock modulus and bolt length, k=10
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0.00 2.00 4.00 6.00 8.00 10.00 12.00
Bolt length (m)
Nor
mal
ised
dis
plac
emen
t
E=15GPa,l=2.1m
E=5GPa,l=10m
050
100150200
250300
350400
0.00 2.00 4.00 6.00 8.00 10.00 12.00
Bolt length (m)
Axi
al lo
ad (k
N)
.
E=5GPa,L=2.1m
E=15GPa,l=2.1m
E=5GPa, L=10m
E=15GPa,l=10m
CHAPTER 8: Analytical aspect of fully grouted bolts
296
Figure 8. 29. Axial load versus bolt length in case of using end plate in different initial stress with 5 GPa rock modulus, k=10
Figure 8. 30. Axial load versus bolt length in case of using end plate in different plastic zone radius with 5 GPa rock modulus, k=10 From the above analyses in both cases; with and without end plates, it can be inferred
that:
• Higher value of k generates higher value of axial loads
• Axial load increases with increasing value of initial stress
• Higher value of rock modulus of elasticity induces higher value of axial
loads.
020406080
100120140160
0.00 0.50 1.00 1.50 2.00 2.50
Bolt length (m)
Axi
al lo
ad (k
N)
.
E=5GPa,po=25MPaE=5GPa,po=15MPaE=5GPa,po=5MPa
020
40
60
80
100
120
140
160
0.00 0.50 1.00 1.50 2.00 2.50
Bolt length (m)
Axi
al lo
ad (k
N)
.
E=5GPa, re=4m
E=5GPa, re=2
CHAPTER 8: Analytical aspect of fully grouted bolts
297
• Higher bond strength and bolt length generates the distribution of bolt
displacement reduces with increasing bond strength and bolt length
• Lower value of the plastic zone reduces the value of bolt load generation
along the bolt
8.10. CONCLUSION
At hinge point when the elastic limit is reached, bending moment cannot increase
further. Thus the shear force remains constant at very low level. However, maximum
shear stresses are concentrated at bolt joint intersection and numerical design showed
that after elastic limit it cannot increase significantly and remains almost constant. So
as the deflection at bolt joint intersection is higher than hinge deflection around 85%.
Thus the axial stresses at bolt joint intersection will increase and finally with
combination of axial load and shear load bolt will break at bolt joint intersection (see
the laboratory chapter).
From the axial load developed along the elastic bolt surrounded in the elasto plastic
materials in circular tunnel it can be inferred that, bond strength, rock mass modulus
and initial stress affects significantly the load distribution level.
CHAPTER 9: Field investigations
298
CHAPTER 9
FIELD INVESTIGATIONS
9.1. INTRODUCTION
To verify the experimental findings, with respect to the influence of bolt profile
characteristics on load transfer mechanism, a program of field study were undertaken
in two local coal mines Collieries in the Southern Coalfields of Sydney Basin, NSW,
Australia.
The aim of the study was to compare the load transfer capabilities of two different
profiled bolts. The comparative study was carried out by strain gauge
instrumentation of each bolt. In Metropolitan site, the instrumented bolts were
installed at the travelling road with 255 m away from the retreating longwall face at
the time of installation.
In Appin, the instrumented bolts were installed at the belt road, 700 m away from the
retreating longwall face at the time of installation. Two different types of fully
instrumented bolts were installed in each site. The methodology of their installation,
positioning, and regular monitoring is the subject of discussion in this chapter.
9.2. SITE DESCRIPTION
9.2.1. Metropolitan Colliery
Metropolitan Colliery is an underground coal mine situated in the Southern
Coalfields of Sydeny Basin, NSW, Australia, around 35 km north of Wollongong
(Figure 9.1). It is a sophisticated mine, utilising longwall method with continuous
miner development of main headings and longwall gate roads. The average seam
CHAPTER 9: Field investigations
299
thickness of the Bulli Seam in the instrumented site is around 3 m. Underground
access is performed by drift and shaft. A representative geological section and related
strength of materials close to the experimental site, illustrating the immediate roof
stratification above the Bulli seam is shown in Figure 9.2. The roof rock consists
mainly of sandstone and mudstones, and is classified as moderate to strong roof. The
detailed layout of the mine and location of the longwall panel is shown in Figure 9.3.
The maximum horizontal stress at Metropolitan Collier based on measurements in G
panel (Tarrant 2002) is between parallel to the gateroads (030/150 relative to GN) to
30o West of the gateroads (060/120 relative to GN).
Figure 9. 1. Geographical location of (a) Metropolitan and (b) Appin Colliery
Metropolitan Colliery currently drives gateroads N-S and extracts longwall S-N.
From the stress measurements it was found that the vertical stress, 1σ = 25 MPa,
oriented between parallel with the current heading direction and 30 west of the
heading direction. 2σ = 15 MPa to 17 MPa and 3σ = 12.5 MPa vertical. It should
Metropolitan Colliery
a b
CHAPTER 9: Field investigations
300
be noted that these measurements were conducted within sandstone of modulus 16
GPa. Six, 2.1 m long instrumented bolts were installed at the instrumented site. Three
bolts were of Bolt Type T1 and the other three were Bolt Type T3, which installed in
the longwall panel between C/T 7 and 8. Figure 9.4 shows the bolt installation at the
site.
Figure 9. 2. Modelled geological section and strength profiles (SCT report 2002)
Figure 9.5 shows the details of the instrumented bolt installation pattern. The regular
pattern of bolting in the site was 6 bolts in a row with spacing between the rows 1.2
m. In addition to the instrumented bolts, three extensometer probes were installed
between the two rows of instrumented bolts. However, no extensometer monitoring
was carried, because of the readout box malfunction.
Sandstone
Sandstone
Sandstone
Sandstone
Mudstone
Mudstone
Sandstone Sandstone Siltstone
Siltstone
Laboratory UCS (MPa)
Coal Bulli Seam
Dep
th (m
) H
eigh
t (m
)
CHAPTER 9: Field investigations
301
Figure 9.3. The detailed layout of the panel under investigation indicating instrumentation site at Metropolitan Colliery
Figure 9.4. Photograph of the site with installed bolts
C/ T
7
C/ T
8 Maingate
Tailgate Relief
Concentration of major horizontal stress on maingate side
Assumed insitu stress direction
CHAPTER 9: Field investigations
302
Figure 9. 5. Detail site plane of the instrumented bolts at Metropolitan Colliery
9.2.2. Appin Colliery
…….
9.3. INSTRUMENTATION
9.3.1. Instrumented Bolts
An instrumented rock bolt with electrical strain gauges placed at discrete points
along the 2.1 m bolt length. The first step involved in the bolt instrumentation
process was to cut two identical, diametrically opposite channels of 6 mm wide and 3
mm deep each along the bolt axis (see Signer and Rains 2001), leaving outer 100 mm
intact as shown in Figures 9.6. The intact bolt configuration without any channel in
the first 100 mm ensured the stability and integrity of the strain gauges and the
Ordinary bolt
Mega bolt
Instrumented bolts
Direction of Development
C/ T
7
C/ T
8
Long wall retreat
TRT1-3
TRT1-2
TRT1-1
TRT3-3
TRT3-2
TRT3-1
CHAPTER 9: Field investigations
303
corresponding wirings during the installation of bolt in the field. This has been the
normal practice in bolt instrumentation, Signer and Jones (1990). Figure 9.7 shows a
section of a bolt with engraved channels.
Once the channels were cut, they were smoothened with sand paper and wiped clean
with alcohol solvents. A total of 18 strain gauges were mounted on each bolt (9 in
each channel). The spacing between the strain gauges mounted on 2.1 m bolt, was
200 mm. The slots were then filled with silicon gel to cover up the strain gauges, and
allowed to harden for a week prior to installation in the field. Figure 9.8 shows a
section of an instrumented bolt with strain gauges and wirings visible through the
silicon cover.
CHAPTER 9: Field investigations
304
Figure 9. 6. Strain gauge and bolt layout
Figure 9. 7. Bolt segment showing channels
200
200
200
200
200
200
200
300
100
200
11
22
33
44
55
77
88
99
Cross Section
Slot : 6 mm x 2.5 mmSlot Area : < 10 %
All Strain Gauges are 5 mm, 120 , Gauge Factor 2.15All Strain Gauges are 5 mm, 120 , Gauge Factor 2.15
Long Section
66
Strain Gauges
21.8
6
200200
2100
Ω
CHAPTER 9: Field investigations
305
Figure 9. 8. A section of an instrumented bolt showing the strain gauge and wirings through the silicon gel.
9.3.2. Intrinsically Safe Strain Bridge Monitor
An intrinsically safe Strain Bridge Monitor (SBM), IS2000, was used for the
underground measurement of strains developed in the instrumented bolts. The
following description of the SBM is based on an operation handbook prepared by
Strata Control Technology Operations Pty Ltd. The SBM is an electronic instrument
(readout box) that is used for:
• Stress monitoring
• Measuring bolt loads
• Measuring shear displacements
• Other strain gauge monitoring applications
The SBM is fully approved for use in Australian Coal Mines. The instrument is
portable and battery powered requiring recharging periodically. When used
underground, the SBM is connected to the instrumented bolts by electrical leads.
Measures were taken throughout the experiment to protect the SBM, leads and
connections from ingress of moisture and dust as these could seriously affect the
measured results. The SBM is set to operate with the more commonly used 120Ω
strain gauges. By choice of appropriate bridge circuit, it was possible to measure the
strain in a single gauge, two gauges or four gauges. The quarter bridge
CHAPTER 9: Field investigations
306
configuration, used in this experiment, was restricted to 120Ω strain gauges only. As
the SBM had a fixed gauge factor setting of 2.00, the actual strain measurement,
indicated by the display, could be calculated as follows. A general view of the SBM,
while taking reading in underground is shown in Figure 9.9.
GV
E d2= For quarter bridge configuration (9.1)
GV
E d= For half bridge configuration (9.2)
GV
E d
2= For full bridge configuration (9.3)
where;
E = the mean actual strain measured by an active gauge,
Vd = the change in SBM reading, and
G = the gauge factor of the strain gauge.
Figure 9. 9. A general view of the SBM, while taking readings in underground
CHAPTER 9: Field investigations
307
9.4. FIELD MONITORING AND DATA ANALYSING
9.4.1. Metropolitan Colliery
Following of the bolt installation, site monitoring was carried out at regular periods,
until the site was over run by the approaching longwall face.
When rock bolts are installed in the tunnel, the load generation initiates at the bolt /
grout / rock structure. The whole full length of the bolt can experience loading. In
reality, when adjacent rock blocks are sheared, due to joint roughness dilation occurs
and this generates tensile forces in the bolt. After decoupling rock bolts according to
their profile configurations behave differently.
Figures 9.10 and 9.11 Show the load developed on both bolt Types T1 and T3
respectively with respect to the approaching longwall positions, right, middle and left
bolts of the traveling road. The details results are presented in Appendix.
Despite the mega bolt installation at the right side of the road, there was higher shear
loading as compared to the bolts at other side of road, which is due to the direction,
and impact of the horizontal stresses. In addition, it shows that Bolt Type T3 had
higher load developed at the left and right side as compared to Bolt Type T1 (30 kN
in Bolt Type T3 against 28 kN in Bolt Type T1). However, the load transferred at the
middle of the section was almost the same in both types of bolts. It is to be noted
that, because of the increased distance between the longwall face position and the
location of the instrumented site, the load developed on each bolt was not maximum
at this stage and that the final load developed would be significantly greater than the
recorded amount.
CHAPTER 9: Field investigations
308
Figure 9. 10. Load transferred on the bolt Type T1 installed at the right side of the TR, Metropolitan Colliery.
TRA1
0
500
1000
1500
2000
2500
0 2 4 6 8 10 12
Load on bolt (kN)
Roo
f hei
ght (
mm
) .
255.0221.0140.090.025.01.0-110.0-163-260
(Installed at the left)
TRA6
0
500
1000
1500
2000
2500
-5 0 5 10 15 20 25 30
Load on bolt (kN)
Roo
f hei
ght (
mm
) .
255.0221.0140.090.025.01.0-110.0-163-260
(Installed at the right) TRT1-1
TRA5
0
500
1000
1500
2000
2500
-10 0 10 20 30 40
Load on bolt (kN)
Roo
f he
ight
(m
m)
.
25522114090251-110-163-260
(Installed at the middle) TRT1-2
TRT1-3
CHAPTER 9: Field investigations
309
Figure 9.11. Load transferred on the bolt Type T3 installed at the right side of the TR, Metropolitan Colliery.
TRJ1
0
500
1000
1500
2000
2500
-10 0 10 20 30 40
Load on bolt (kN)
Roo
f hei
ght (
mm
)
.
255.0
221.0
140.0
90.0
25.0
1.0
-110
-163
-260
(Installed at the right) TRT3-1
TRJ3
0
500
1000
1500
2000
2500
-5 0 5 10 15 20 25
Load on bolt (kN)
Roo
f hei
ght (
mm
)
.
255.0221.0140.090.025.01.0-110.0-163-260
(Installed at the middle) TRT3-2
TRJ6
0
500
1000
1500
2000
2500
-5 0 5 10 15 20 25 30
Load on bolt (kN)
Roo
f he
ight
(m
m)
.
255.0221.0140.090.025.01.0-110.0-163-260
(Installed at the left)
TRT3-3
CHAPTER 9: Field investigations
310
Figures 9.12 and 9.13 show the corresponding shear stresses at the bolt resin
interface for both bolt Types T1 and T3 respectively. The shear stress developed at
the bolt resin interface was calculated by using the following equations:
∆τπ
=−F Fd l
1 2 (9.4)
where;
∆τ = average shear stress at the bolt-resin interface,
F1 = axial force acting in the bolt at strain gauge position 1, calculated from
strain gauge reading,
F2 = axial force acting in the bolt at strain gauge position 2, calculated from
strain gauge reading,
d = bolt diameter, and
l = distance between strain gauge position 1 and strain gauge position 2.
From the results it was found that the shear stress sustained by the bolt/resin
interface had almost the same magnitude in Bolt Types T1 and T3 in the middle
and right side of the roadway, at approximately 1.1 MPa. However, the
magnitude of the shear stress developed in the Bolt Type T2 at the left side of the
roadway was nearly four times of the Bolt Type T1 (1.2 against 0.3). This is due
to the wider profile spacing and higher profile height, which is consistent with
the laboratory results found from pull and push results. (See chapter 4). It should
be noted that if shear stress is negative, it would indicate that the shear stress is
towards the tunnel wall, and plus would have meat that it is against the tunnel
wall (Cai et al 2004).
CHAPTER 9: Field investigations
311
Figure 9. 12. Shear stress developed at the bolt/resin interface of the Bolt Type T1, in Metropolitan Colliery.
TRA6
0
500
1000
1500
2000
2500
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Shear stress (MPa)
Roo
f hei
ght (
mm
) .
255.0
221.0
140.0
90.0
55.0
25.0
1.0
-110.0
-163
-266
Installed at the right
TRT1-1
TRA5
0
500
1000
1500
2000
2500
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Shear stress (MPa)
Roo
f hei
ght (
mm
) . 255
221140
9025
1-110
-163-260
Installed at the middle TRT1-2
TRA1
0
500
1000
1500
2000
2500
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4
Shear stress (MPa)
Roo
f hei
ght (
mm
)
. 255.0
221.0
140.0
90.0
25.0
1.0
-110
-163
-260
Installed at the left TRT1-3
CHAPTER 9: Field investigations
312
Figure 9. 13. Shear stress developed at the bolt/resin interface of the Bolt Type T3, in Metropolitan Colliery.
Appin
TRJ6
0
500
1000
1500
2000
2500
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Shear stress (MPa)
Roo
f hei
ght (
mm
)
. 255.0
221.0
140.0
90.0
25.0
1.0
-110.0
-163
-260
Installed at the left
TRT3-3
TRJ3
0
500
1000
1500
2000
2500
-1.0 -0.5 0.0 0.5 1.0
Shear stress (MPa)
Roo
f hei
ght (
mm
)
.
255.0
221.0
140.0
90.0
25.0
1.0
-110
-163
-260
Installed at the middle TRT3-2
TRJ1
0
500
1000
1500
2000
2500
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5
Shear stress (MPa)
Roo
f hei
ght (
mm
) . 255.0
221.0
140.0
90.0
25.0
1.0
-110-163
-260
Installed at the right TRT3-1
CHAPTER 10: Conclusions and recommendations
313
CHAPTER 10
CONCLUSIONS AND RECOMMENDATIONS
10.1. SUMMARY
The load transfer mechanism and reinforcement system behaviour has been
comprehensively investigated during the course of this research. The thesis has
presented methods and results of experimental testing in both axial and lateral
loading conditions, finite element analyses and field investigations carried out over
three years. The main them and philosophy throughout the work was: (i) The
evaluating of the shear behaviour mechanism in bolt-grout and grout-rock interfaces
in the laboratory, numeric and field in different Types of bolts, resin thickness and
different concrete strength, (ii) design and develop a shear testing machine which
meets and removes the relevant problems in previous machines, (iii) The effect of
bolt pretensioning, bolt profile and thread rebar specifications on shear behaviour
and load transfer mechanism, (iv) Numerical analyses of bolt-joint-concrete and
contact elements in both axial and lateral applied loads.
10.2. CONCLUSIONS
A number of important parameters have been identified which affect the load transfer
mechanism and bolt behaviour subjected to axial and lateral loading conditions.
Accordingly, a series of experimental studies, numerical techniques and field
investigations were undertaken. The following sections describe the main
conclusions drawn from this research.
CHAPTER 10: Conclusions and recommendations
314
10.2.1. Literature survey
In can be inferred from this review that:
• For rock /concrete samples reinforced with bolt inclined at an angle to the
normal of the joint plane, bolts failed in tension near the shear surface. In
addition, inclined bolts are stiffer to the shear strength of the bolted blocks
than the perpendicular bolts. Moreover, shear displacement at failure is
minimal for inclinations between 40o and 50o.
• For samples with a bolt forming a small angle to the normal of the joint
plane, bending of the bolts becomes predominant even when the shear force
is small,
• The vertical height of the bended bolt is about 2-4 times the bolt diameter
called effective height, corresponding to an effective length.
• Large bolt diameter reduces shear displacement required for obtaining a
given shear force.
• Bolt pretensioning reduces shear displacement, but not the shear resistance.
• Direct shear test produces overturning moments, which produce rotation in
the shear box and create a non –uniform stress profile. Accordingly it is
inferior because of non-uniform distribution of stress concentration on the
shear joint and along the bolt in direct shear machine.
10.2.2. Experimental investigations
• Bolt profile configuration is an important parameter in load transfer
capacity of bolt.
CHAPTER 10: Conclusions and recommendations
315
• Profile spacing dictates the level of peak load - displacement, which intern
accommodates a relatively greater level of strata movement.
• High profiles increases load transfer capacity of the bolt.
• Yielding and necking is unlikely to occur in bolts tested in 75 mm long
steel sleeves as the peak shear load was around 40% of the maximum
tensile strength of the steel.
• Push test showed the higher value of shear stress capacity of bolt compared
with pull test.
• The load failure of the resin / bolt surface contact is dependent on the
profile height as well as spacing.
• Increasing resin annual thickness reduces the load transfer capability of bolt
subjected to axial loading conditions. However, it depends upon the
surrounding material strengths subjected to lateral loading conditions.
• The double shear system represented a better method of shearing system as
it enabled to allow a symmetric study of bolt shearing analysis.
• The maximum bolt contribution of the bolts significantly depends upon the
concrete strength and bolt pretension load.
• Bolt contribution was increased around 15 % with existence of the resin
grout compared with absence of the grout at the same conditions.
• Physical and mechanical properties of the bolt types affect the bolt –joint
contribution.
• The axial and shear loads are at their maximum at the bolt - joint
intersection.
CHAPTER 10: Conclusions and recommendations
316
• From the bolt Type T1 in 100 MPa concrete it was found that the maximum
bolt-joint contribution at failure is about 120 % of the maximum tensile
strength of the bolt.
• The value of bolt contribution at yield point in concrete 20, 40 and 100
MPa in Bolt Type T1 was about 0.24, 0.3 and 0.52 respectively.
• Increasing the concrete strength reduces significantly the joint shear
displacement and contributed to increased shear stiffness.
• In lateral loading conditions, the effect of resin and concrete strength is
more effective than the resin thickness.
• Hinge point distance was reduced with increase of the resin annulus, when
surrounding material was weaker than the resin strength
• An extensive stress and strain was developed on the resin / concrete
interface in soft concrete during the bolt bending.
• In all bending situations, axial fractures were created along the concrete
blocks after the yield point.
• Shear stress in softer concrete was lower than the harder concrete due to the
excessive deformation. Then the tensile load develops while the dowel
component reduces.
• The dowel effect in harder concrete is strong due to the higher shear
resistance. It results bolt to cut before excessive deformation. So, it prevents
the excessive axial load generation along the bolt.
CHAPTER 10: Conclusions and recommendations
317
10.2.3. Numerical analyses
• The yield limit of the bolt first begins from the hinge points at both sides of
the shear joint.
• Further increase in the shear force beyond the yield point has no apparent
influence on the stresses in the hinges.
• The distance between the hinge points reduced with increasing the concrete
strength.
• During the shearing process the tension and the compression stresses and
strains were generated in the upper and lower fibre of the bolt in the vicinity
of the shear joint.
• Bolt profile in the vicinity of the bolt-joint intersection experienced the
maximum shear stress value. In addition, there was an exponential
relationship between the value of the shear stress and the distance from the
shear joint.
• The shear stress value was not exceeded during further loading after the yield
point. Eventually, the combination of this stress with induced tensile stress at
the bolt-joint intersection lead the bolt to failure.
• By increasing the bolt pretension load, the shear stress was decreased and this
was also observed in different concrete strength.
• The value of strain along the concrete and grout was reduced with increasing
the pretensioning.
• The induced stresses exceeded the uniaxial compressive strength of the grout
and concrete in the vicinity of the bolt –joint intersection, causing them
crushing.
CHAPTER 10: Conclusions and recommendations
318
• The average shear stress capacity of a bolt in a push test was greater than that
in a pull test.
• Bolt-resin interface failure occurred by initially shearing of the grout at the
profile tip in contact with the resin.
• Numerical simulation provided an opportunity to understand better the
stresses and strains generated as a result of bolt resin interface shearing.
10.2.4. Field investigations
……
10.3. SUGGESTIONS FOR FURTHER RESEARCH
This research provided a comprehensive understanding of some of the significant
factors that affects the load transfer mechanism, such as; bolt profile characteristics,
mechanical and physical bolt property, different surrounding concrete strength and
resin thickness, various pretension loads. However, still it needs more and further
research in this field.
• Double shearing system (DSS) provides the better understanding of the
bolt/joint interaction. However, it is recommended that the size of the double
shearing apparatus system to be doubled for effective results. The design of
the new shear box is completed and the apparatus is under construction for
future research (Figure 10.1).
• To better understanding of the resin thickness subjected to lateral loading
conditions, more tests needs to be undertaken in different concrete strength.
CHAPTER 10: Conclusions and recommendations
319
• Further studies on hard concrete strength (more than 100 MPa) are
recommended to obtain better understanding of the load transfer in hard rock
conditions.
• In very hard rock conditions, the use of real rocks instead of concrete is
recommended.
• To find the actual load transfer mechanism in high profile spacing in different
bolt types, the use of longer steel sleeve is recommended.
• Effect of bolt, grout and concrete modulus of elasticity in different concrete
strength and resin thickness in non-linear condition is recommended by
numerical simulations.
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vii
CHAPTER ONE .....................................................................................................1
GENERAL INTRODUCTION ..............................................................................1
1.1. GENERAL.....................................................................................................1
1.2. BACKGROUND FOR PRESENT RESEARCH ...........................................4
1.3. KEY OBJECTIVE .........................................................................................5
1.4. RESEARCH METHODOLOGY....................................................................6
1.5. SCOP OF THE THESIS.................................................................................7
CHAPTER TWO ..................................................................................................11
ROCK BOLT SYSTEM AND REVIEW OF BOLT BEHAVIOUR UNDER
AXIAL LOADING ...............................................................................................11
2.1. INTRODUCTION........................................................................................11
2.2. HISTORICAL..............................................................................................11
2.2.1. History of bolting Australian mines .......................................................12
2.3. ROOF BOLT PRACTICE AND APPLICATION ........................................12
2.4. REINFORCEMENT MECHANISM............................................................13
2.5. BOLT THEORIES .......................................................................................14
2.6. TYPE OF ROCK BOLTS ............................................................................16
2.7. LOAD TRANSFER IN ROCK BOLTS .......................................................21
2.7.1. Load Transfer Concept in Fully Grouted Rock Bolts .............................22
2.8. SELECTION OF FULLY GROUTED BOLTS............................................24
2.8.1. Fully Grouted Bolt Failure.....................................................................26
2.8.2. Load Transfer Measurement ..................................................................27
2.9. EFFECT OF BOLT IN CONTINUUM MEDIUM .......................................28
2.10. THE EFFECT OF BOLT ON DISCONTINUITY ......................................29
2.11. SUMMARY..............................................................................................31
2.12. REVIEW OF FAILURE MECHANISM OF BOLT RESIN INTERFACE
SUBJECTED TO THE AXIAL LOAD...............................................................32
2.12.1. Theoretical behaviour of the bolt under axial load................................32
2.12.2. Experimental behaviour of the bolt under axial load ............................40
2.12.3. Bolt –grout-rock interface mechanism .................................................44
viii
2.12.4. Load transfer mechanism.....................................................................49
2.12.5. Conclusion ..........................................................................................53
CHAPTER THREE..............................................................................................55
REVIEW OF SHEAR BEHAVIOUR OF BOLTS AND MECHANICAL
PROPERTIES OF THE MATERIAL USED......................................................55
3.1. INTRODUCTION........................................................................................55
3.2. DESCRIPTION OF PAST RESEARCHES..................................................57
3.3 PRETENSIONING EFFECT IN FULLY GROUTED BOLTS .....................80
3.4. SUMMARY.................................................................................................84
3.5. MECHANICAL PROPERTIES OF REINFORCING MATERIALS............86
3.5.1. Bolt Types.............................................................................................86
3.5.2. Bolt strength tests ..................................................................................88
3.5.3. Resin grout ............................................................................................93
3.5.4. Concrete ................................................................................................98
3.5.4.2. Concrete joint surface properties.......................................................100
3.5.5. Summary.............................................................................................102
CHAPTER FOUR...............................................................................................104
FAILURE MECHANISM OF BOLT RESIN INTERFACE S DUE TO AXIAL
LOAD ..................................................................................................................104
4.1. INTRODUCTION......................................................................................104
4.2. LOAD TRANSFER MECHANISM...........................................................104
4.3. BOND CHARACTERISTIC......................................................................106
4.4. PULL AND PUSH ENCAPSULATION TESTS........................................107
4.4.1.Push Encapsulation Test .......................................................................109
4.4.2. Pull Encapsulation Test .......................................................................111
4.5. DISCUSSION............................................................................................112
4.5.1. Effect of bolt profile ............................................................................115
4.5.2. Bolt yielding/necking ..........................................................................118
4.5.3. Effective Shear Stress at the Bond Interface.........................................120
ix
4.5.4. Bolt core behaviour subjected to axial loading.....................................124
4.5.5. Effect of annulus .................................................................................124
4.6. SUMMARY...............................................................................................125
CHAPTER FIVE ................................................................................................127
DOUBLE SHEARING OF BOLTS ACROSS JOINTS....................................127
5.1. INTRODUCTION......................................................................................127
5.2. EXPERIMENTAL PROCEDURE .............................................................128
5.2.1. Block Casting......................................................................................128
5.2.2. Bolt Installation in Concrete Blocks.....................................................130
5.3. DOUBLE SHEAR BOX ...........................................................................131
5.4. TESTING...................................................................................................131
5.5. BOLT TYPES............................................................................................134
5.6. RESULTS AND DISCUSSION .................................................................136
5.6.1. Shear Load and Shear Displacement....................................................136
5.6.1.1. Profile description ............................................................................136
5.6.1.2. Shear loading for a limited displacement...........................................138
5.6.1.3. Shear loading of bolt to ultimate failure ............................................146
A) Testing of Bolt Types T5 and T6 in 40 MPa Concrete: .............................154
5.6.2. Influence of Shearing Load on Pretension Load...................................157
5.6.3. Load Transfer Level In Different Profile.............................................160
5.6.4. Double Shearing of Instrumented Bolt .................................................162
5.6.5. Medium (Concrete and resin) Reaction................................................167
5.6.6. Prediction Of The Bolt Contribution....................................................170
5.7. SUMMARY...............................................................................................176
CHAPTER 6 .......................................................................................................178
ROLE OF BOLT ANNULUS THICKNESS ON BOLT SHEARING .............178
6.1. INTRODUCTION.....................................................................................178
6.2. TEST METHOD........................................................................................178
6.3. EXPERIMENTAL RESULTS AND DISCUSSION..................................179
x
6.3.1. Shear load/ shear displacement ............................................................180
6.3.2. Axial load built up...............................................................................184
6.3.4. Effect of resin thickness on shear stiffness...........................................190
6.4. NUMERICAL SIMULATION IN DIFFERENT RESIN THICKNESS......193
6.5. THE EFFECT OF RESIN ANNULUS ON INDUCED STRESSES ...........195
6.5.1. Induced Shear Stress............................................................................195
6.5.2. Induced Tensile Stress .........................................................................196
6.5.3 Induced Compression Stress .................................................................197
6.6. Effect Of Concrete Modulus Of Elasticity On Shear Displacement............197
6.7. Effect of grout modulus of elasticity on shear displacement.......................199
6.8. EFFECT OF BOLT MODULUS...............................................................200
6.9. SUMMARY...............................................................................................202
CHAPTER 7 .......................................................................................................204
NUMERICAL ANALYSES IN FULLY GROUTED ROCK BOLTS..............204
7.1. INTRODUCTION......................................................................................204
7. 2. FE IN ANSYS..........................................................................................205
7.3. A REVIEW OF NUMERICAL MODELING IN ROCK BOLT .................205
7.4. MATERIAL DESIGN MODEL .................................................................210
7.4.1 Modelling of Concrete and Grout .........................................................212
7.4.2 Modelling the Bolt................................................................................213
7.4.3. Contact Interface Model ......................................................................214
7.4.4. Geometrical Model..............................................................................215
7.5. VERIFICATION OF THE MODEL...........................................................216
7.6. MODELLING OF FULLY GROUTED ROCK BOLTS ............................217
7.7. RESULTS AND DISCUSSION .................................................................219
7.7.1. Bolt Behaviour ....................................................................................219
7.7.1.1. Stress developed along the bolt .........................................................219
7.8.1.2. Strain developed along the bolt .........................................................228
7.7.2. Concrete ..............................................................................................233
7.7.2.1. Stress developed in concrete .............................................................233
7.7.2.2. Strain developed in concrete .............................................................235
xi
7.7.3. Grout...................................................................................................239
7.7.3.1. Stress developed in grout ..................................................................239
7.7.3.2. Strain Developed in Grout ...............................................................242
7.7.4. Contact Pressure..................................................................................243
7.8. SUMMARY...............................................................................................245
7.9. NUMERICAL MODELLING OF FAILURE MECHANISM OF BOLT
RESIN INTERFACE SUBJECTED TO AXIAL LOADING ............................247
7.9.1. Introduction.........................................................................................247
7.9.2. Results and Discussion ........................................................................248
7.9.2.1. Bolt Behaviour .................................................................................249
7.9.2.2. Grout Behaviour ...............................................................................253
7.9.3. Modulus of Elasticity Effect ................................................................256
7.10.4. Summary...........................................................................................259
CHAPTER 8 .......................................................................................................260
ANALYTICAL ASPECT OF FULLY GROUTED BOLT...............................260
8.1. REACTION FORCES DURING THE SHEARING...................................260
8.2. STEEL BOLT BEHAVIOUR ....................................................................262
8.2.1. Plastic Design......................................................................................262
8.2.2. Plastic Theory......................................................................................262
8.2.3. Basic Equation For A Grouted Rock Bolt Subjected To Lateral
Deformation..................................................................................................264
8.3. BOLT - JOINT CONTRIBUTION.............................................................269
8.4. REACTION FORCES................................................................................271
8.4.1. Basic Equation for Rock and Subgrade Material ..................................272
8.6. ANALYTICAL APPROACH TO DEFINE THE HINGE POINT
LOCATION REGARDING AXIAL LOAD ALONG THE BOLT....................273
8.6.1. Elastic behaviour .................................................................................273
8.6.2. Plastic Behaviour.................................................................................276
8.7. ANALYTICAL APPROACH TO DEFINE THE HINGE POINT
LOCATION REGARDING SHEAR DISPLACEMENT ..................................281
xii
8.8. ANALYTICAL METHOD TO DEFINE THE SHEAR DISPLACEMENT IN
CASE OF BOLT MODULUS OF ELASTICITY..............................................282
8.9. Analysis of a Fully Grouted Elastic Bolt in Plastic Rock Mass
.........................................................................................................................285
8.10. CONCLUSION........................................................................................297
CHAPTER 9 .......................................................................................................298
FIELD INVESTIGATIONS...............................................................................298
9.1. INTRODUCTION......................................................................................298
9.2. SITE DESCRIPTION.................................................................................298
9.2.1. Metropolitan Colliery ..........................................................................298
9.2.2. Appin Colliery.....................................................................................302
9.3. INSTRUMENTATION..............................................................................302
9.3.1. Instrumented Bolts ..............................................................................302
9.3.2. Intrinsically Safe Strain Bridge Monitor ..............................................305
9.4. FIELD MONITORING AND DATA ANALYSING..................................307
9.4.1. Metropolitan Colliery ..........................................................................307
CHAPTER 10......................................................................................................313
CONCLUSIONS AND RECOMMENDATIONS .............................................313
10.1. SUMMARY.............................................................................................313
10.2. CONCLUSIONS......................................................................................313
10.2.1. Literature survey................................................................................314
10.2.2. Experimental investigations...............................................................314
10.2.3. Numerical analyses............................................................................317
10.2.4. Field investigations...........................................................................318
10.3. SUGGESTIONS FOR FURTHER RESEARCH ......................................318
xiii
LIST OF FIGURES
Figure 1. 1. Structure of Chapters in the thesis ..........................................................8
Figure 2. 1. Usage of rock bolts in the world ……………………………………….13
Figure 2. 2. Continuous mechanically coupled rock bolt ........................................22
Figure 2.3. Load transfer in fully grouted rock bolts................................................23
Figure 2.4 Rate of load transfer along the fully grouted rock bolts........................24
Figure 2. 5 The mechanism of the load transfer.......................................................27
Figure 2.6. Load deformation results in different bolts (Stillborg 1994)...................28
Figure 2.7. Bolt installation to the joint a: perpendicular, b: incline (After Obert and
Duvall 1967) ...................................................................................................30
Figure 2. 8. Stress situation in a grouted anchor (after Farmer, 1975) ......................34
Figure 2. 9. Theoretical stress distribution along a resin anchor in a rigid hole with
thin resin annulus (after Farmer 1975).............................................................34
Figure 2. 10. Load displacement, strain distribution, and computed shear stress
distribution curves in concrete, a) strain distribution at the specified anchor load,
b) theoretical shear-stress distribution curves. (After Farmer 1975) .................35
Figure 2. 11. Stress distribution model for grouted bolt (after Yu and Xian, 1983) ..37
Figure 2. 12. Stress Component in a small section of a bolt (after Stillberg & Li,
1999)...............................................................................................................38
Figure 2. 13. Shear stress along a fully coupled rock bolt subjected to an axial load
before decoupling............................................................................................39
Figure 2. 14. Distribution of shear stress along a fully grouted rock bolt subjected to
an axial load in coupled rock bolt ....................................................................40
Figure 2. 15. Variables used in closed-form solution (after Serbousek and Singer
1987)...............................................................................................................42
Figure 2. 16. Schematic illustration of different conical lugged bolts: (a) Single, (b)
Double and (c) Triple c) Triple conical lugged bolt .............................................43
Figure 2. 17. Shear stress versus shear displacement in bolt /grout interface at
different bolt diameter (after Aydan 1989) ......................................................46
Figure 2. 18. Dilation behaviour of joint plane a) two smooth plane, b) bolt and resin
interface. .........................................................................................................47
Figure 2. 19. Pull test gear arrangement (after Singer 1990) ...................................48
xiv
Figure 2.20. Comparison of load distribution along the bolt length..........................49
Figure 2. 21. Schematic diagram reflecting the geometry of a rough bolt (after Yazici
and Kaiser, 1992) ............................................................................................50
Figure 2. 22. Load/displacement curves for rebar with various amounts of bar
deformation removed (after Fabjanczyk and et al, 1992) .................................51
Figure 3.1. Stability issues in rock mass reinforced by fully grouted bolts...............56
Figure 3. 2. The shear test arrangement in (a) and (b) probable load generation (after
Dulasck 1972) .................................................................................................58
Figure 3. 3. Components of shear resistance of bolt (after Bjurstrom, 1974)............59
Figure 3. 4. (a) block splitting in one side of shear joint (b) non equilibrium situation
in vicinity of shear joint...................................................................................61
Figure 3. 5. (a) Finite element mesh and (b) deviatoric of stress distribution across
the joint (Afridi and et al. 2001) ......................................................................61
Figure 3. 6. Arrangement for bolt shear testing (after Hass, 1981)...........................63
Figure 3. 7. General deformation patterns for a dowel in shear................................64
Figure 3. 8. Shear test machine used by Schubert (1984).........................................67
Figure 3. 9. Relation between shear stress and shear displacement (After Yoshinaka
1987)...............................................................................................................67
Figure 3. 10. Direct shear test device (after Egger and Zabuski 1991) .....................69
Figure 3. 11. Bolt grout behaviour sketch (after Holmberge 1991) ..........................70
Figure 3. 12. A grouted rock bolt subjected to lateral force .....................................72
Figure 3. 13. Ferrero’s shear test machine ...............................................................73
Figure 3. 14. Resistance mechanism of a reinforced rock joint (after Ferrero 1995).73
Figure 3. 15. Forces acting on the failure mechanism 1 (after Ferrero 1995)............75
Figure 3. 16. Force components and deformation of a bolt, a) in elastic zone, and b)
in plastic zone (after Pellet and Eager 1995)....................................................76
Figure 3. 17. Evolution of shear and axial forces in a bolt, a) in elastic zone, and b) in
plastic zone (after Pellet and Egger, 1995).......................................................77
Figure 3. 18. Joint displacement as a function of angle for different UCS value
(after Pellet 1994) ...........................................................................................79
Figure 3. 19. Shear block test assembly (After Goris and et al 1996).......................80
Figure 3. 20. Different Bolt Types used for axial and shear behaviour tests.............87
xv
Figure 3. 21. Profiles specification..........................................................................87
Figure 3. 22. Bolt clamped in Instron Universal testing Machine.............................89
Figure 3. 23. Stretching of the bolts after tensile test ...............................................90
Figure 3. 24. Load- deflection curve at tensile test in various bolts ……………… 91
Figure 3.25. Load- deflection curve at tensile test of Bolt Type T5 and T6………...91
Figure 3.26. Load- deflection curve at tensile test in cable bolt ……………………91
Figure 3.27. Load- deflection curve at tensile test of Bolt Type T4……………….. 91
Figure 3.28.Three point load bending test set up ………………………………….. 92
Figure 3.29. Load- displacement behaviour of 3PLBT……………………………..92
Figure 3. 30. direct shear test trend in Bolt Types T1 and T3……………………...93
Figure 3.31. Typical fracture plane and fracture angle for compression test samples95
Figure 3.32. Compression test set up………………………………………………..95
Figure 3.33. Stress strain curve for resin………………………………………… 96
Figure 3.34 . Load versus displacement…………………………………………….97
Figure 3.35. Double shear test set up a: shear box set up b: induced loads……… 98
Figure 3.36. Concrete sample: a) concrete under the test b) concrete after 30 days..99
Figure 3.37. Variation of peak shear stress versus different normal stress in shear
joint plane in a: 20 MPa and b: 40 MPa concrete…………………………....101
Figure 3.38. Shear load –versus shear displacement in joint plane in 40 MPa concrete
Figure 4. 1. Sketch of real bolt profile specifications and interfaces………………106
Figure 4. 2. (a) resin/bolt load transfer under various confining pressures (b) resin
bolt separation after post encapsulation .........................................................107
Figure 4. 3. (a) The actual push test configuration (b) the shematic of the test .......110
Figure 4. 4. Preparing the bolt resin samples .........................................................110
Figure 4. 5. Post-test sheared Bolt Type T2 out of steel cylinder in push test.........111
Figure 4. 6. Pull test arrangement..........................................................................112
Figure 4. 7. Post-test sheared bolt out of steel cylinder ..........................................112
Figure 4. 8. Shear load as a function of displacement in pull test...........................114
Figure 4. 9. shear load as a function of displacement in push test ........................115
Figure 4. 10. General trend of push and pull test view...........................................115
Figure 4.11. The effect of Rib spacing on shear load .............................................117
Figure 4. 12. The shear load versus shear displacement in smooth bolt..................118
xvi
Figure 4. 13. Debonding at pull test ......................................................................120
Figure 4.14. Shear stress versus bond displacement in Push test............................121
Figure 4.15. Shear stress versus bond displacement in pull test .............................122
Figure 4.16. Annulus thickness effect ...................................................................125
Figure 5. 1. Bolt bending behaviour (after Indraratna et al. 2000)..........................127
Figure 5. 2. Laboratory and numerical model ........................................................129
Figure 5.3. Hole reaming for hole rifling...............................................................129
Figure 5.4. An assembled bolt fitted with load cells on both ends of the bolt .........131
Figure 5.5. Schematic of post failed assembled shear box (a), and a set up of the high
strength capacity machine -Avery machine (b) ..............................................133
Figure 5.6. The set up of the Instron machine with load cell connection ................133
Figure 5.7. Different bolt types .............................................................................134
Figure 5.8. Typical shear displacement profile of the sheared bolt.........................137
Figure 5.9 (a-f). All bolt shear load and vertical displacement profiles in both 20 and
40 MPa concrete medium..............................................................................141
Figure 5.10 (a-f). Comparative results of all bolts shear load and vertical
displacement profiles in both 20 and 40 MPa concrete medium.....................142
Figure 5.11. Shear yield load difference in different concrete strength and bolt types
and various pretension loads..........................................................................143
Figure 5.12. Bolt slippage along the bolt -grout interface in case of non-pretensioning
and non- plate ...............................................................................................145
Figure 5.13. Axial fracture along the concrete and broking off of the grout in tensile
zone in bolt type T1 in 40 MPa concrete with 80 kN pretensioning ...............146
Figure 5.14. Shear load versus shear displacement in 0, 5 and 10 kN pretension load
in Bolt Types T5 and T6 in 40 MPa concrete.................................................151
Figure 5.15. The bolt failure view in different pretensioning .................................151
Figure 5.16. (a) Relationship between failure load and maximum tensile strength of
the single shear on bolt type T5, (b) bolt failure angle ...................................152
Figure 5.17. Shear load versus shear displacement in 100 MPa concrete and different
pretensioning in Bolt Type T1.......................................................................152
Figure 5.18. Excessive bolt necking in concrete 100 MPa in 80 kN pretension .....153
xvii
Figure 5.19. Bolt/ joint concrete interaction at shear joint in concrete 100 MPa and
80 kN pretension load ...................................................................................153
Figure 5.20. Bolt imprint on resin in concrete 100 MPa at 50 and 80 kN pretension
loads .............................................................................................................154
Figure 5.21. The ratio of axial load developed along the bolt over ultimate tensile
strength of the bolt versus shear displacement in concrete 100 MPa with 80 kN
pretension load..............................................................................................156
Figure 5.22. Shear load versus load cell readings on tensile load applied on a bolt
installed in a 20 MPa concrete.......................................................................157
Figure 5.23 (a-f). Shear load and pretension loads (load cell readings) for various
bolts with initial pretension load of 20, 50 and 80 kN....................................158
Figure 5.24. End crushing of the concrete in high pretensioning load ....................160
Figure 5.25. Axial load developed along the bolt versus shear displacement in Bolt
Type T2 in 40 MPa concrete .........................................................................160
Figure 5.26. Effect of pretension load, bolt profile and concrete strength on the bolt
resistance ......................................................................................................161
Figure 5.27. Schematic diagram of the strain gauges locations in the reinforcing
element (a) without pretension load and (b) 20 kN pretension load................163
Figure 5.28. The shear load versus strain measurements in non-pretension load ....165
Figure 5.29. The bolt surface with strain gauges installed......................................166
Figure 5.30. The strain rate along the bolt, drawn by strain measurements in non-
pretension load..............................................................................................166
Figure 5.31. Shear load versus strain gauge measurements along the bolt in 20 kN
pretensions. ...................................................................................................166
Figure 5.32. The variation of the strain gauge measurements along the bolt at 20 kN
pretension load..............................................................................................167
Figure 5.33. Axial fracture developed along the bolt through the 20 MPa concrete169
Figure 5.34. The created gap in plastic stage .........................................................170
Figure 5.35. Effect of concrete strength on the factor of movement.......................174
Figure 5.36. Expected cumulative results versus observed cumulative results .......175
Figure 6. 1. Shear load as function of shear displacement in different annulus.......180
Figure 6. 2. Effect of resin thickness on shear displacement ..................................181
xviii
Figure 6.3. The effect of resin thickness on load - displacement yield point ..........181
Figure 6.4. Shear load and shear displacement in concrete 20 and 100 MPa and 20
kN pretension load and different resin thickness in Bolt Type T1 ..................183
Figure 6.5. Gap creation between bolt grout at high resin thickness in concrete 20
MPa with 20 kN preload (5 mm thick) ..........................................................183
Figure 6.6. Gap creation between bolt grout at high resin thickness in concrete 40
MPa with 20 kN preload (5 mm thick) ..........................................................184
Figure 6.7. Shear load and axial load build up along the bolt in concrete 20 MPa and
20 kN pretension load and thin resin thickness in bolt Type T1 (25mm)........184
Figure 6.8. Shear load versus axial load developed along the bolt in different resin
thickness in 20 MPa concrete ........................................................................185
Figure 6.9. Axial load versus- shear displacement in bolt T1 and 20 kN preload in 27
mm hole diameter surrounded by 20 MPa concrete .......................................186
Figure 6.10. Axial stress versus shear displacement in bolt Type T1 in 20 kN preload
in 36 mm hole diameter surrounded by 20 MPa concrete...............................187
Figure 6.11. Comparison of the axial load induced in bolt in different resin thickness
in 20 MPa strength (axial resistance factor is equal axial load over ultimate
tensile strength of the bolt) ............................................................................188
Figure 6.12. Side profile of failed bolt Type T1 surrounded by concrete 20 MPa and
36 mm hole diameter at 20 kN pretension load b) typical end profile of a failed
reinforcing element .......................................................................................189
Figure 6.13. The effect of hole diameter versus stiffness .......................................191
Figure 6.14. Effect of hole diameter and resin thickness on shear displacement in
numerical design ...........................................................................................194
Figure 6.15. Effect of resin thickness and concrete strength on shear displacement in
numerical design in un-pretension load .........................................................194
Figure 6.16. Induced shear stress versus concrete modulus of elasticity in different
annulus size (grout modulus is considered 12 GPa) .......................................196
Figure 6. 17. Induced tensile stress versus grout modulus of elasticity in soft concrete
(20 GPa) .......................................................................................................197
Figure 6.18. Induced compression stress versus concrete modulus of elasticity .....198
Figure 6.19. Shear displacement versus concrete modulus of elasticity in different
resin thickness, grout modulus is 12 GPa.......................................................199
xix
Figure 6.20. Shear displacement versus grout modulus of elasticity in different resin
thickness, concrete modulus is 20 GPa and constant......................................200
Figure 6.21. Shear displacement as a function of bolt modulus variations in different
rock strength .................................................................................................201
Figure 7. 1. FE Simulation of bolted rock mass (After Hollingshead, 1971) ..........207
Figure 7. 2. Three-Dimensional rock bolt element (After John and Dillen, 1983) ..207
Figure 7. 3. Bolt-Rock interaction model (Peng and Guo, 1988) ...........................208
Figure 7.4. The process of FE simulation (Dof = degrees of freedom)...................211
Figure 7.5. (a) 3D concrete Solid 65 (b) Concrete mesh .................212
Figure 7.6. Finite element mesh for grout..............................................................213
Figure 7.7. Finite element mesh for bolt................................................................214
Figure 7.8. Geometry of the model and mesh generation......................................216
Figure 7.9. Load-deflection in 80 kN pretension bolt load and 40 MPa concrete ...217
Figure 7.10. Numerical model (s = symmetric planes, c = compression zone, T =
tension zone ..................................................................................................220
Figure 7. 11. Bolt displacement in 20 MPa, without Pretensioning........................220
Figure 7.12. Shear displacement as a function of bolt length sections in 20 MPa
concrete ........................................................................................................221
Figure 7.13. Bolt deflection at the moving side and hinge point versus loading
process, in 40 MPa concrete without pretension load.....................................222
Figure 7.14. Stress built up along the bolt axis in 20 MPa concrete without
pretensioning.................................................................................................223
Figure 7.15. The trend of stress built up along the bolt axis 20 MPa concrete with 80
kN pretensioning...........................................................................................223
Figure 7.16. Von Mises stress trend in 20 MPa concrete without pretensioning.....224
Figure 7.17. Shear stress contour in the concrete 20 MPa without pretensioning ...225
Figure 7.18. The rate of shear stress along the bolt axis in concrete 20 MPa without
pretensioning.................................................................................................226
Figure 7.19. The rate of shear stress along the bolt axis in concrete 20 MPa without
pretensioning in one side of the joint plane....................................................226
Figure 7. 20. Shear stress trend in bolt –joint intersection in concrete 20 MPa at post
failure region without pretension load ...........................................................227
xx
Figure 7. 21. Deformed bolt shape in post failure region in 20 MPa concrete ........228
Figure 7.22. The plastic strain contour along the bolt axis in concrete 20 MPa
without pretensioning....................................................................................229
Figure 7.23. Strain trend along the bolt axis in concrete 20 MPa without
pretensioning in upper fibre of the bolt..........................................................229
Figure 7. 24. The yield strain trend as a function of time stepping concrete 20 MPa in
20 kN pretension...........................................................................................230
Figure 7. 25. Tension and pressure strain along the bolt in 20 MPa concrete and 20
kN pretension................................................................................................231
Figure 7.26. The Von Mises strain trend along the bolt axis in concrete 40 MPa and
80 kN pretensioning ......................................................................................231
Figure 7.27. Von Mises strain along the bolt in concrete 20 MPa concrete without
pretensioning.................................................................................................232
Figure 7.28. Von Mises strain trend in concrete 20 MPa without pretensioning in
upper fibre of the bolt....................................................................................232
Figure 7.29. The concrete displacement in non-pretension condition in 20 MPa
concrete ........................................................................................................233
Figure 7.30. Yield stress induced in 20 MPa concrete without pretensioning
condition.......................................................................................................234
Figure 7.31. Induced stress and displacement trend in 20 MPa concrete without
pretensioning.................................................................................................235
Figure 7.32. The produced strain contours in 20 MPa concrete without pretensioning
(in shearing direction) ...................................................................................236
Figure 7.33. Induced strain in concrete 20 MPa in grout and concrete versus loading
in non-pretension load and 27 mm hole diameter...........................................237
Figure 7.34. Concrete displacement versus loading time in concrete (a) 20 and (b) 40
MPa in non-pretension condition...................................................................237
Figure 7.35. Induced strain rate along the contact interface in 40 MPa concrete and
non pretension condition ...............................................................................238
Figure 7.36. Induced strain in concrete and bolt as a function of loading steps in 20
MPa concrete with 80 kN pretensioning ........................................................238
Figure 7.37. Induced stress contours in grout layer in un-pretension condition and 20
MPa ..............................................................................................................240
xxi
Figure 7.38. Created gaps in post failure region in 20 MPa concrete in the Numerical
simulation .....................................................................................................240
Figure 7.39. Created gaps in post failure region in 20 MPa concrete in the laboratory
test ................................................................................................................241
Figure 7.40. The grout displacement in different location along the bolt axis in 40
MPa concrete ................................................................................................241
Figure 7.41. The rate of induced strain along the grout layer in non-pretension
condition in axial direction............................................................................242
Figure 7.42. The grout displacement as a function of plastic strain generated in bolt-
joint intersection through the grout in non-pretension condition ....................243
Figure 7.43. The rate of contact pressure changes between (a) grout – concrete
interface (b) bolt-grout interface in 20 MPa concrete in non-pretension
condition.......................................................................................................244
Figure 7.44. Contact pressure at the (a) bolt - grout interface (b) concrete - grout
interface in 20MPa concrete in high resin thickness (36mm hole diameter) in
80kN pretension load ....................................................................................245
Figure 7.45. Shear load versus bolt-grout contact pressure at 36 mm hole and 20 MPa
and 80kN preload..........................................................................................245
Figure 7. 46. Finite element mesh: a quarter of the model .....................................248
Figure 7.47. The bolt movement in pulling test .....................................................249
Figure 7. 48. Rate of the bolt displacement ...........................................................250
Figure 7. 49. Bolt displacement contour in Bolt Type T1 in case of push test ........250
Figure 7.50. Induced strain along the bolt profiles.................................................251
Figure 7.51. Shear strain in bolt ribs in push test ...................................................251
Figure 7.52. Von Mises Stress and shear stress along the bolt axis ........................253
Figure 7.53. Shear stress contours along the grout interface ..................................256
Figure 7.54. The effect of grout modulus of elasticity on shear displacement in push
test ................................................................................................................257
Figure 7.55. The effect of grout modulus of elasticity on shear displacement in pull
test ................................................................................................................257
Figure 7.56. The shear displacement as a function of grout modulus of elasticity in
case of push and pull test...............................................................................258
xxii
Figure 8. 1. Assembled model (concrete, grout and steel bolt)...............................261
Figure 8. 2. Load generation along the bolt during the shearing.............................261
Figure 8. 3. Stress strain relationship for bolt type T1 ...........................................263
Figure 8. 4. Elastic – plastic stress sequence in bending ........................................263
Figure 8. 5. Deformed shape, shear force, bending moment and shear displacement
diagrams .......................................................................................................266
Figure 8. 6. Applied loads on joint intersection .....................................................269
Figure 8. 7. Reaction forces in bolt loaded laterally...............................................273
Figure 8. 8. Hinge point distance versus axial force...............................................276
Figure 8. 9. Bolt diameter versus hinge point distance in different rock strength ...276
Figure 8. 10. The relationship between axial load and hinge point distance in
different rock strength in plastic situation......................................................278
Figure 8. 11. The relationship between the axial load and hinge point distance in both
elastic and plastic situation............................................................................279
Figure 8. 12. Hinge point position in different concrete strength ...........................279
Figure 8. 13. Relationship between hinge point position and axial deformation.....280
Figure 8. 14. Hinge point location as a function of shear displacement in elastic
region............................................................................................................282
Figure 8. 15. Comparison of the numerical and analytical results, concrete 20 MPa,
.....................................................................................................................284
Figure 8. 16. Notation for numerical formulation .................................................288
Figure 8. 17. Axial load along the bolt versus bolt length, in case of unplated with 25
MPa initial stress and 15 GPa modulus of surrounding rock ..........................290
Figure 8. 18. Normalised displacement versus bolt length in case of unplated with 25
MPa initial stress and 15 GPa modulus of surrounding rock ..........................291
Figure 8. 19. Normalised displacement versus bolt length in case of unplated with 25
MPa initial stress and 15 GPa modulus of surrounding rock at different k values
.....................................................................................................................291
Figure 8. 20. Normalised displacement versus bolt length in case of unplated with 15
MPa initial stress and 15 GPa modulus of surrounding rock at different k values
.....................................................................................................................291
xxiii
Figure 8. 21. Load developed along the bolt versus bolt length in case of unplated
with 15 MPa initial stress and 25 GPa modulus of surrounding rock at different
k values.........................................................................................................292
Figure 8. 22. Load developed along the bolt versus bolt length in case of unplated
with 15 GPa modulus of surrounding rock at different initial stresses ............292
Figure 8. 23. Load developed along the bolt versus bolt length in case of unplated
with 25 MPa initial stress and different modulus of surrounding rock at k=10
.....................................................................................................................293
Figure 8. 24. Load developed along the bolt versus bolt length in case of unplated
with 25 MPa initial stress and different modulus of surrounding rock at k=10,
L=10 m .........................................................................................................293
Figure 8. 25. Load developed along the bolt versus bolt length in case of using end
plate with 25 MPa initial stress and different k, at Er = 5GPa .........................294
Figure 8. 26. Normalised displacement versus bolt length in case of using end plate
with 25 MPa initial stress and different k, at Er = 5GPa..................................294
Figure 8. 27. Axial load versus bolt length in case of using end plate with 25 MPa
initial stress and different rock modulus and bolt length, k=10 ......................295
Figure 8. 28. Normalized displacement versus bolt length in case of using end plate
with 25 MPa initial stress and different rock modulus and bolt length, k=10..295
Figure 8. 29. Axial load versus bolt length in case of using end plate in different
initial stress with 5 GPa rock modulus, k=10.................................................296
Figure 8. 30. Axial load versus bolt length in case of using end plate in different
plastic zone radius with 5 GPa rock modulus, k=10.......................................296
Figure 9. 1. Geographical location of (a) Metropolitan and (b) Appin Colliery ......299
Figure 9. 2. Modelled geological section and strength profiles (SCT report 2002) .300
Figure 9.3. The detailed layout of the panel under investigation indicating
instrumentation site at Metropolitan Colliery.................................................301
Figure 9.4. Photograph of the site with installed bolts ...........................................301
Figure 9. 5. Detail site plane of the instrumented bolts at Metropolitan Colliery....302
Figure 9. 6. Strain gauge and bolt layout ...............................................................304
Figure 9. 7. Bolt segment showing channels..........................................................304
xxiv
Figure 9. 8. A section of an instrumented bolt showing the strain gauge and wirings
through the silicon gel. ..................................................................................305
Figure 9. 9. A general view of the SBM, while taking readings in underground ....306
Figure 9. 10. Load transferred on the bolt Type T1 installed at the right side of the
TR, Metropolitan Colliery. ............................................................................308
Figure 9.11. Load transferred on the bolt Type T3 installed at the right side of the
TR, Metropolitan Colliery. ............................................................................309
Figure 9. 12. Shear stress developed at the bolt/resin interface of the Bolt Type T1, in
Metropolitan Colliery. ...................................................................................311
Figure 9. 13. Shear stress developed at the bolt/resin interface of the Bolt Type T3, in
Metropolitan Colliery. ...................................................................................312