Macro 1 Theory and background - rel 108 OM format.pdf

8/11/2019 Macro 1 Theory and background - rel 108 OM format.pdf

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Rockfall protection system

MACRO 1

THEORY AND BACKGROUND MANUAL

Version 1.08 JANUARY 2014


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MACRO 1 THEORY AND BACKGROUND Page | 2

MACRO 1

THEORY AND BACKGROUND

INDEX

1 INDRODUCTION 6

2 BASIC DEFINITONS 7

3GENERAL CONCEPTS 8

3.1 COEXISTENCE OF ANCHOR AND MESH 8

3.2 CONCEPTUAL SOLUTION 9

3.3 DESIGN APPROACH 9

4 NAIL DIMENSIONING 11

4.1 FORCE INTO THE GEOMECHANICAL SYSTEM 11

4.2 STABILIZING CONTRIBUTION OF ANCHORS 16

4.3 EVALUATION OF NAIL LENGTH 17

5MESH DIMENSIONING 18

5.1 ULTIMATE LIMIT STATE 18

5.2 MAXIMUM ROCK VOLUME VSPUSHING ON THE MESH 21

5.3 MESH DEFORMATION UNDER PUNCH LOAD AND SCALE EFFECT 21

5.4 MESH DIMENSIONING:SERVICEABILITY LIMIT STATE 23

6GENERAL BIBLIOGRAPHY 24

7 END NOTES 26

LIST OF THE FIGURES

Figure 1 - Typical configuration of the secured drapery 6Figure 4 - Conceptual solution for the calculation of anchors and mesh 9Figure 5 - Thickness of the unstable slope "s" evaluated with geomechanical

survey (left), or with rough estimation of the detachment niches and

size boulders (right) 12Figure 6 Rock masses with different lithology; left: non homogeneous rock mass

(for example flysch); right: homogeneous rock mass (for example

mudstone) 13


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Figure 7 Left: the weathering quickly denudates the anchors. Right: despite of the

heavy jointed rock mass, the weathering is slow. If the weathering

velocity is negligible, the anchor length Le1 and Le2 into the sound

rock is enough to hold the unstable surficial portion for a long time. 13Figure 8 - Left: even slope morphology: the mesh lies in contact to the slope

surface. Right: uneven slope morphology: the mesh touches the slope

surface in few points 14Figure 9 - Left: even slope morphology: the mesh lies in contact to the slope

surface. Right: uneven slope morphology: the mesh touches the slope

surface in few points 14Figure 10 - Anchor bar in the rock mass. Li = length crossing the unstable mass; Lp

length in the plasticized rock mass; Ls length in stable rock mass 17Figure 12 - Scheme of the forces acting on the mesh 20Figure 13 Shapes of the rock volumes that can move among the anchors:

triangular (left) and trapezium (right) 20Figure 14 - Geometry of the volume between the anchors 20Figure 15 - Volumes B and C between the anchors 21Figure 16 - Sketch of the geometry of the mesh with punching load 22Figure 17 - Plan view of the punch test according to UNI 11437:2012. Legend: 1 =

tested mesh; 2 = punching device (1.0 m in diameter); 3 = perimeter

constraint between the mesh and the frame. 22Figure 18 - Example of a curve load-displacement used for the design of the mesh

at the Serviceability Limit State 23

LISTS OF THE TABLES

Table 1 - Recap of the safety coefficients for the reduction of the destabilizing

forces and of the resistances ............................................................................... 15

Table 2 - Global safety coefficients applied to the stabilizing end driving forces ................. 15


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LIST OF THE MAIN SYMBOLS

Factor of safety Factor applied to Symbol used

in the

formulas

showed

below

Partial factor

applied on the

nail

Yield stress of the steel ST

Adhesion grout-rock GT

Partial factor

applied on the

mesh

Longitudinal tensile strength of the mesh M

Maximum displacement admitted on the mesh M-BULG

Partial factorapplied on the

instability/rock

Thickness of the instability T

Unit weight of the rock W

Rock behavior (i.e. weathering of the rock) B

Load factor Slope morphology MO

External loads OL

Category of data Data and typical unit of measure Symbol used in

the formulas

shown below

Geotechnical andgeomechanical

data

Slope inclination [deg]

Thickness of instability [m] s

Unit weight of the rock [kN/m3]

Inclination of the most critical joint set [deg]

Roughness of the most critical joint set [-] JRC0

Compressive strength of the most critical joint set [MPa] JCS0

Nails Horizontal distance between nails [m] ix

Vertical distance between nails [m] iy

Nominal external diameter [mm] e

Nominal internal diameter [mm] (if the bar is hollow) i

Potential thickness of corrosion on the bar diameter [mm] tc

Yield stress of the steel [N/mm2] ST

Inclination from the perpendicular to the slope [deg] 0

Grout-rock adhesion (bond stress) [MPa] LIM

Mesh Type of mesh i.e. commercial

name

Ultimate longitudinal tensile strength [kN/m] Tm

Curve load displacement [kN / mm] P / PUNCH

Seismic action Horizontal seismic acceleration coefficient [-] c


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Parameter of the

joint

In-situ tool to define the parameter Typical values

JRC (roughness) Barton Comb Smooth joint: 0 to

2; Very rough joint:

18 to 20

JCS (jointcompressive

strength)

Schmidt Hammer From 3 to 200 MPadepending on the

strength of the rock

(JCS is approx. 1/3

of UCS*)

Inclination () Geological compass Can vary from 0

deg to 90 deg


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MACRO 1

THEORY AND BACKGROUND

1 INDRODUCTION

Macro 1 is the software of Officine Maccaferri aimed at calculating the pin drapery systems

for rockfall protection.

Pin drapery (called also secured drapery, or cortical strengthening, or superficial

stabilization) is composed of anchors and steel mesh (rockfall net). The goal of this system is

improving the surficial rock face stability and maintaining the debris/rock on place (Figure 1).

Figure 1 - Typical configuration of the secured drapery

The pin draperies could be included into the active protection measures, because they are

directly applied on the unstable zone in order to prevent the rockfall. In these terms they

absolutely differ from the rockfall barriers that are placed far from the detachment area and

can only mitigate the effect of the rockfall. But from the geomechanical point of view they

should be classified as passive interventions because they generate forces as the rockfall

displacement takes places1.

The design of secured drapery is not at all easy because of numerous variables, including

topography, rock mass properties, joint geometry and properties, mesh type and related

restraint conditions. Often the solution to the problem may require complex numerical

modelling which is not practical for every project, especially if the design is aimed at

interventions of modest size. Because of that, at the present, limit equilibrium models are

preferable. Taking this into consideration and incorporating field experience, Officine

Maccaferri has developed MacRo1, the limit equilibrium approach for the design of secured

drapery. The procedure is quite rough, but it is sufficient when considering the low accuracy

level of the input data, the reliability of the results and the speed of the calculations.


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2 BASIC DEFINITONS

The materials intended to the software are the following:

Mesh: steel meshes produced by Officine Maccaferri. The software contains a library with

the behaviour of the mesh under punch and tensile load. The knowledge of these behaviours

derives from a series of laboratory test carried out in accordance with standard UNI

11437:20122. The software does not allow inserting any other mesh type.

Anchors: in the description the terms anchors, and nail are interchangeable. The steel

bars used for pin drapery applications are preferably full threaded. They are installed in a

drilled hole, previously realized with specific drilling machines. They have to be centred into

the hole and then grouted along their entire length. Normally the grout has a compression

resistance of 20 to 50 MPa in order to guarantee an efficient bond stress between the steelbar and the rock3. The grout has also the function to protect the steel against corrosion. The

diameter of these bars is generally 20 to 50 mm. Frequently the drilling diameter is approx.

2.0-2.5 times the diameter of the bar. The length of the nails (L) in most of the cases is

between 2.5 to 4.0 m, and the spacing (ix and iy 4 see Figure 1) ranges between 2.0 and

4.0 m. On the rock slopes, nails mainly works in shear condition, because often they are

installed perpendicular to the sliding surface. Thus, the nail design requires the definition of

the type of steel and diameter. The software admits any steel anchor type.

Pin drapery: in these text pin drapery, secured drapery, cortical strengthening, areinterchangeable. In the pin drapery the anchor and the mesh should cooperate, and the

anchor should really stabilize the slope face. Very frequently the effective anchor spacing

ranges between 2 and 3 m: The designer should remember that the larger the spacing is, the

lower the interlocking between the instable block. Large anchor spacing means frequent

rockfall and heavy loads on the mesh facing. It is always possible choose spacing larger

than 3.0 m, but the intervention progressively loose effectiveness and smokes to something

else.


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3 GENERAL CONCEPTS

3.1 Coexistence of anchor and mesh

The calculation approach considers that on the slope there is a surficial weathered (or heavy

jointed, blasted, or disturbed) rock mass. The weathered mass is conveniently approximated

as pseudo continuous5; this continuous body most frequently generates shallow instabilities

and rockfalls. It has thickness s and inclination parallel to the slope. Several sets of

joints cross the surficial body; the most unfavourable has inclination (Figure 2).

The forces of mesh and nails are passively generated when one of these two conditions

happens:

- the whole weathered body slides down on the plane inclined . This is the problem of

the global stability of the weathered surface; it is solved by the raster of anchors

(Figure 3 on the left).

- one or more block move out from the weathered body. The dynamic of the instabilitycould be any one (planar or wedge sliding, toppling, bucking, fall). The software only

considers the planar sliding on the plane , which is the most unfavourable case.

Because this instability can happen only among the nails, it can be defined as local

instability of the weathered surface; the mesh fixed with the anchors answers to the

local instability (Figure 3 on the right).

-

Figure 2 - Slope with the weathered unstable surface


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3.2 Conceptual solution

Both mesh and anchors can only develop reactions as the rock mass moves (passive

system). Macro 1 separately analyses the mechanisms anchors and mesh facing. But

because the spacing between the anchors dramatically changes the load on the mesh

facing, the user follows this iterative process (Figure 4):

Figure 4 - Conceptual solution for the calculation of anchors and mesh

3.3 Design approach

The adopted design approach only follows the general concepts of Eurocodes (UNI ENV

1997-1:2005). In these terms Macro 1 allows increasing the destabilizing forces and

reducing the resistances by mean of suitable safety coefficients, which should be calibrated

with probabilistic methodology. Unfortunately the Eurocodes cannot correctly be applied on

the geomechanical field6, and the secured draperies are quite far from the standard

problems. That is why the coefficients of Macro 1 have been based on specific parameterslike the slope morphology or the mesh behaviour. The user has to find out the suitable

Figure 3 - Elements of the pin drapery systems. Nails (left) stabilize the superficial portion. Mesh(right) keeps in place the unstable material between the nail.


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coefficients considering what he has directly seen on site. This approach is more realistic

and helps in designing the secured draperies.

Macro 1 calculates the raster of anchors in order to get a more favourable equilibrium

condition of the weathered rock mass.

According to the common design practice, Macro 1 purposes the calculation of the mesh

facing for the ultimate and the serviceability limit states. The ultimate limit state allows

understanding if the mesh can be broken because of the load, whereas the serviceability

allows foreseeing the facing deformation perpendicular to the mesh plane. The knowledge of

deformation is very useful because:

- when the deformation reaches the design limit, it means that the maintenance

(cleaning) of the secured drapery is needed before that further displacements

determine the mesh rupture. A simple visual monitoring let the owner programs the

interventions.

- Too much deformed mesh implicates easy stripping on the anchors and lower

durability of the intervention. The designer must be aware of this and foresee the

right mesh type accordingly.

- Since the meshes are largely deformable, the facing of the secured drapery could

interfere with close infrastructures or vehicles.


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4 NAIL DIMENSIONING

4.1 Force into the geomechanical system

Considering passive behaviour, the nail calculation must assume the unstable portion of the

slope lies in condition of limit equilibrium, where the safety factor is equal to 1.0. Therefore,

the resisting forces have the same value of the driving forces and the following equation is

true (Figure 4):

Resisting forces = W sin

= driving forces [1]where

W = weight of the unstable rock mass to be consolidated

= inclination of the slope surface, where the sliding of the unstable rock mass can

occur.

Using the resistance criteria of Barton-Bandis7for the joints, equation [1] can be rewritten to

describe the improved stability condition:

W (sin c sintan ) + R W (sin + c cos ) [2]

assuming

R = stabilizing contribution of the nails

c = seismic coefficients

= residual friction angle of the joint

The equation [2] is written in accordance with the concept of passive intervention 8.

Setting tan 1 (friction angle = 45)9, and posing the safety factors for reducing the

stabilizing forces (RW) and increasing the driving ones (DW), the stability condition simply

becomes:

Wsin (1- c) / RW + R W DW(sin + c cos ) [3]

or

FSslp> = FDslp [4]

assuming

FDslp= W (sin + c cos ) DW = Sum of the driving forces [5]

and

FSslp= W sin (1- c) / RW+ R = Sum of stabilizing forces [6]

Equation [3] allows determining the nail force that consolidates a rock mass in the limit

equilibrium state. It is a conservative equation and it is simple to be used since it basically

requires simple geometric variables.

The safety coefficients (RW, DW) depend on several factors. The rock mass features affect

the size of the stabilizing forces, so that their safety coefficient can be described as


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RW= THl WG BH [7]

where10

- THl describes the uncertainties in determining the surficial instability thickness s.

Its value ranges between 1.20, when the estimation is based on a geomechanicalsurvey, and 1.30, when it is based on rough estimation (Figure 5). It must be

considered that the thickness of the unstable layer is not homogeneous, locally its

thickness could be thicker.

- WG describes the uncertainties in the unitary weight determination of the rock

mass. Usually it is assumed to equal 1.00, but if there are severe uncertainties it

can be assumed to equal 1.05. For instance it can be noticed that for non

homogenous rocks (e.g. flysch rock masses where there are thin layered clay

stone alternated to hard mudstone), the mesh and the nails can locally be heavy

loaded, whereas in other places the load is lower being the same volume ofinstability (Figure 6).

- BHdescribes the uncertainties related to the rock mass behaviour. High erodibility

of the rock surface can cause stripping of the nails and weakness of the whole

system (Figure 7). One consequence is that the unstable portion held by the nails

(or by the mesh) could become quickly deeper. Usually the value is assumed

equal to 1.00, but if there are severe environmental conditions or the rock mass is

easily weathered (it is the case of several rock types containing clay), it can be

assumed to equal 1.05.

Figure 5 - Thickness of the unstable slope "s" evaluated with geomechanical survey (left), or with rough

estimation of the detachment niches and size boulders (right)


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Figure 6 Rock masses with different lithology; left: non homogeneous rock mass (for example flysch);

right: homogeneous rock mass (for example mudstone)

Figure 7 Left: the weathering quickly denudates the anchors. Right: despite of the heavy jointed rock

mass, the weathering is slow. If the weathering velocity is negligible, the anchor length Le1 and Le2

into the sound rock is enough to hold the unstable surficial portion for a long time.

External conditions, especially slope morphology, play an important role in the magnitude ofthe driving forces, whose safety coefficient is defined as

DW= MO OL [8]

where:

- MO describes the uncertainties related to slope morphology. If the slope is very

rough, then the mesh facing is not in continuous contact with the surface, and the

unstable blocks can freely move; in that case a safety coefficient of 1.30 should

be applied. If the slope surface is even, the mesh facing lies in better contact with


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the ground; in the case, the unstable block movement is limited, and a safety

coefficient of 1.10 is used (Figure 8 and Figure 9).

- OL describes the uncertainties related to additional loads applied on the facing

system. The additional loads could be related to the presence of ice or snow, or to

vegetation growing on the slope. Usually it is assumed to equal 1.00, but if severeconditions are foreseen, it can be assumed to equal 1.20.

Figure 8 - Left: even slope morphology: the mesh lies in contact to the slope surface. Right: uneven slope

morphology: the mesh touches the slope surface in few points

Figure 9 - Left: even slope morphology: the mesh lies in contact to the slope surface. Right: uneven slope

morphology: the mesh touches the slope surface in few points


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Table 1 - Recap of the safety coefficients for the reduction of the destabilizing forces and of the

resistances

The above safety coefficients (formula [7] and [8]) have been calibrated in order to get the

following range of values (Table 2):

Table 2 - Global safety coefficients applied to the stabilizing and driving forces

Safety coefficient Minimum value Maximum value

For stabilizing forces 1.20 1.43

For driving forces 1.10 1.56

With this procedure the global safety coefficient applied on the geomechanical system very

roughly ranges between 1.5 and 3.2 according to the most common experience and design

codes.

Partial/Load

factor

Description Value

T If the superficial instability thickness is defined by:- geomechanical survey:

- rough/visual estimation: 1.20

1.30

W If the rock unit weight is:

- homogeneous:

- not-homogeneous (i.e. flysh):

1.00

1.05

B If the rock:

- does not present any anomalous behavior (i.e. compact rock):

- is subjected to erosion and/or environmental condition that can create

weakness of the rock mass (i.e. weathering rock):

1.00

1.05

MO If the morphology of the rock is:

- regular (the mesh lies in better contact with the slope, thus the rock

movement are limited):

- rough (the mesh cannot be in adherence with the slope, thus the unstable

block can easily move):

1.10

1.30

OL If there are/are not external loads acting on the system:

- not significant loads are applied:

- additional external loads are applied (i.e. snow, ice, vegetation, etc.)

1.00

1.20


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4.2 Stabilizing contribution of anchors

The reinforcing nail bars work principally in proximity to the sliding joint, where it is

subjected to shear stresses together with tensile stresses. The resisting force R, due to the

bar along the sliding plane11, is derived utilising the maximum work principal12:

[9]

where:

m = cotg (+ ) [10]

= angle between the bar axis and the horizontal. It is equal to

= 90 - o , [11]

where ois the angle between the bar axis and the normal to the sliding plane.

= sliding surface dilatancy

Ne= bar strength (elasticity limit condition) = ESS adm= ESS ST /ST [12]

ST = coefficient of reduction for the steel resistance.

ESS = effective area of the steel bar = / 4 ((fe - 2 fc)2- fi2) [13]

fe = external diameter of the steel bar

fc = thickness of corrosion on the external crown

fi = minor diameter of the steel bar

In accordance with the Barton Bandis resistance criteria, the value is approximated as13

[14]

where 14:

[15]

= inclination of the most unfavourable sliding plane

plan= sliding plane normal stress

JRC = joint roughness coefficient15 = [15]

JCS = joint uni-axial compression resistance 16= [16]

JCS0 = joint compression strength referred to the scale joint sample

JRC0 = roughness referred to scale joint sampleL0= joint length (assumed to be 0.1 m for lack of available data)

Lg= sliding joint length (assumed to be equal to vertical nail spacing.

eNm

m

R

+

+

=

2

1

2

2

41

161

JRC log JCS

plan

#

$%&

'(

3

( )002.0

0

0

JRCg

L

L

JRC

( )003.0

0

0

RCJg

L

LJCS

plan =ixiy s cos

ixiy


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The equations from [14] to [16] are exclusively aimed at determining the dilatancy that

increases the stabilizing contribution R of the anchor especially when it is put perpendicular

to a very rough plane17. Macro 1 must adopt a conservative approach because on surficial

rock masses the joints are often opened, or with filling of clay, sometime with advanced

weathering process, the uniaxial compressive strength is very low; other times the rock mass

is disturbed by the excavation18. In these conditions the anchors mostly works with the shear

resistance of the anchor bar. In lack of input data, the user should remember the followings:

- the roughness JRC and the uniaxial compression resistance JCS should be estimated

on the most unfavourable joints inclined . Macro 1 assumes that the joint (parallel to

the slope face) has such most unfavourable resistance, and the anchors are calculated

accordingly.

- If JRC is unknown19it can be set at 0.

- If JCS is unknown20, it can be set at 5 MPa.

- If the joint inclination is unknown, it can be assumed between 40 and 50 in order to

get al large volume sliding on a very steep plane.

4.3 Evaluation of nail length

The evaluation of nail length should consider the following:

a) The nail plays the most important role in superficial consolidation of the slope. Its

length must be deeper than the instability thickness, and should allow the bar to

reach into the stable section.

b) The steel bar and the grout are exposed to weathering actions (ice, rain, salinity,

temperature variations, etc.).

c) The steel bar can develop the shear resistance because rock and grout develop the

same opposite strength. But because rock and grouting are weaker than the steel,

generally the rock plasticizes close the sliding plane21. The plasticized volume

depends on the rock type.

Figure 10 - Anchor bar in the rock mass. Li = length crossing the unstable mass; Lp length in the

plasticized rock mass; Ls length in stable rock mass


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The minimum theoretical length is derived by

Lt = Ls+ Li + Lp [17]

assuming:

Ls= length in the stable part of the mass = P / (drill lim/ gt) [18]Li= length in the weathered mass = s / cos dw [19]

LP = length of hole with plasticity phenomena in firm part of the rock mass. The values

ranges between 0.05 m for hard rock (e.g. granite or basalt) up to 0.30 m for weak rock (e.g.

marl), and exceptionally up to to 0.45 m for very weak rock (e.g. claystone or tuff).

With

drill = diameter of the hole for the bar

lim= bound stress (adherence tension) between grout rock22

gt= safety coefficient of the adhesion grout rock. According to the Eurocode EC7, it

should not be taken lower than 1.823.

P = pullout force; it is the greater of the following:

PMesh = ((WSbar- WDbar) cos (+ o)) ix = pull out due to the mesh [20]

PRock = (FSslp R FDslp) cos (+ o) = pull out due to the slope instability[21]

The length of the nail must be intended as a preliminary value. The final suitable length of

the bars has to be evaluated while drilling and confirmed with pull out tests.

5 MESH DIMENSIONING

5.1 Ultimate limit state

Some secondary blocks could slide among the nails on a plane with inclination , where is

smaller than the slope inclination , and push on the mesh facing. The maximum block size

pushing per horizontal linear meter of facing depends on the thickness s and the vertical

spacing iybetween two nails. Since the load pushing is asymmetric and the mesh deforms

unevenly, the forces acting on the facing are represented with the following simplified

scheme (Figure 11 and Figure 12):

Figure 11 - Deformed mesh with forces


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F - the force developed by the blocks sliding between the nails on a plane inclined at

.

T - the force acting on the facing plane, which rises when the sliding blocks push on

the facing. The force can develop because there is a large friction between mesh

and blocks, and a pocket is formed. The facing, which is considered to be nailedon the upper part only, reacts to T with the tensile resistance of the mesh.

M the punch force developed by the blocks perpendicular to the facing plane. The

force is developed since there are several lateral restraints, like the nailing (strong

restraint) and the next meshes (weak restraint). The magnitude of M largely

depends on the stiffness of the mesh: the higher the membrane stiffness of the

mesh is, the more effectiveness the facing is.

In the case of the mesh, the ultimate limit state is satisfied when

Tadm- T > = 0 [22]

where

Tadm= admissible tensile strength of the mesh

which is

Tadm = Tm/ MH [23]

where

Tm= Tensile resistance of the mesh

MH= safety coefficient for the reduction of the tensile resistance of the mesh. Taking into

account the inhomogeneous stress acting on the loaded mesh, the minimum safety

coefficient should be not lower than 2.50. This safety coefficient is based upon

empirical observations on the punch tests carried out in Pont Boset with Torino TechUniversity24 and Lab IUAV Venice University25, where it has been noticed that the

mesh between the anchors does not give a full contribution to hold the lower facing,

and the stress basically is absorbed by the nails. Those last hold a force Q ranging

between 30 and 55 kN per anchor26.

The real distribution of the stress has been seen with numerical analysis27. The stress acting

on the mesh depends on the membrane stiffness: the higher the stiffness is, the higher the

capacity of the mesh to be like a restrain between the anchors is. The stiffer mesh is more

effective, accordingly. From the theoretical point of view, the lower the stiffness is, the higher

the safety coefficient should be, since the stress in mainly concentrated on the anchors andnot homogenously distributed on the mesh.

The stress T on the mesh depends on the force pushing on the mesh (M Figure 12), which

can be calculated using the same principles as formula [3]:

M = F sin () ix= (Mbdrv Mbstb) sin () ix [24]


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Figure 12 - Scheme of the forces acting on the mesh

Where:

Mbdrv= Mb (sin + c cos ) DW = driving forces [25]

Mbstb= (Mb sin (1- c)) RW = resisting forces [26]

Mb = V = weight of the unstable rock mass [27]

V = maximum unstable volume between nails (Figure 13, Figure 14, Figure 15) which

is calculated in accordance with the next paragraph 5.2.

Figure 13 Shapes of the rock volumes that can move among the anchors: triangular (left) and

trapezium (right)

Figure 14 - Geometry of the volume between the anchors


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Figure 15 - Volumes B and C between the anchors

5.2 Maximum rock volume VS pushing on the mesh

Macro 1 assumes that the maximum volume pushing on the mesh has the following

boundaries (Figure 14):

- top: top and anchor (for simplicity the anchors are always considered perpendicular to

the sliding plane)

- bottom: sliding surface inclined . The plane intersects the surface at the head of the

lower anchor.

- Back: sliding surface inclined

There are several procedures for the calculation of the maximum rock volume that could

move among the anchors. Hereby is described the one followed by the analytical algorithm

of Macro 1.

If (arctan (s/iy)) and < [28]

Then the volumes simply becomes (triangular shape in Figure 13 left)

Volume A [29]

else, if < arctan (s/iy) [30]

can be distinguished the following volumes (Figure 15)

Volume B V = iys - s2/ tan () [31]

And volume C V = 0.5 s2 / tan () [32]

Macro 1 determines the maximum theoretical volume as the sum ofV = Volume A + Volume B + Volume C [33]

5.3 Mesh deformation under punch load and scale effect

Macro 1 assumes that in any case the punch load on the mesh can be greater than the

weight of the rock volume among the anchors. Then Macro 1 check if

M/ix/sin ( p) < Mb sen [34]

then

T = M / ix/ sin ( p)else

)tan(2

1 2 = yiV


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T = Mb sen [35]

With

Zbulg= displacement related to the punch load M.

p = angle of deformation of the mesh arctg (2 bulg / i) [36]

= average spacing between the anchors = (ix * iy)

0.5

[37]

Figure 16 - Sketch of the geometry of the mesh with punching load

Figure 17 - Plan view of the punch test according to UNI 11437:2012. Legend: 1 = tested mesh; 2 =

punching device (1.0 m in diameter); 3 = perimeter constraint between the mesh and the frame.

When the load induces the maximum displacement Zbulg, the process of the mesh rupture

stars. The maximum punch displacement Zbulg is related to the sample size: in accordance

with the results of the tests carried out28, it is possible to roughly say that the larger the

sample size is, the larger the displacement is (scale effect). The general law of the scale

effect is assumed in the simplified form

x = x0x [38]y = y0y [39]

where

(x, y) = generic coordinate of the scaled graphic

(x0, y0) = generic coordinate of the reference graphic

(x, y) = constants correlating the scaled to the reference graphic

As the curves have been determined following the standard UNI 11437 (a sample size 3.0 x

3.0 m), the reference size for the description of scale effect is 3.0 m (Figure 17).

Macro 1 automatically modifies the typical load vs displacement curves considering the

scale effect.


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Figure 18 - Example of a curve load-displacement used for the design of the mesh at

the Serviceability Limit State

5.4 Mesh dimensioning: serviceability limit stateThe serviceability limit state provides information concerning the following:

- required maintenance activity on the facing;

- risks of stripping because of anchor necking;

- interference between infrastructure and facing as consequence of excessive

displacements.

The serviceability limit state is satisfied if

Bulg- Zbulg >= 0

where

Bulg = Dmbulg/mbulg = admissible displacement

Dmbulg = maximum design displacement

mbulg = safety coefficient. Its value ranges between291.50 (facing installed properly on a

slope with an even surface) and 3.00 (facing installed improperly on a slope with

uneven morphology). The safety coefficient decreases the desired maximum

deformation and automatically gets the related admissible load.

bulg = deformation of the facing as derived from the results of Maccaferri tests on the

base due to punch force M (Figure 18).


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6 GENERAL BIBLIOGRAPHY

AICAP, (1993): Anchor in soil and rock: recommendations (in Italian).

Bertolo P. , Giacchetti G., 2008 - An approach to the design of nets and nails for surficial

rock slope revetment in Interdisciplinary Workshop on Rockfall Protection, June 23-25

2008, Morshach, Switzerland.

Bertolo P., Ferraiolo F., Giacchetti G., Oggeri C., Peila D., e Rossi B., (2007): Metodologia

per prove in vera grandezza su sistemi di protezione corticale dei versanti GEAM

Geoingegneria Ambientale e mineraria, Anno XLIV, N. 2, Maggio-Agosto 2007.

Besseghini F., Deana M., Di Prisco C., Guasti G., 2008 Modellazione meccanica di un

sistema corticale attivo per il consolidamento di versanti di terreno, Rivista GEAM

Geoingegneria ambientale e Mineraria, Anno XLV, N. III dicembre 2008 (125) pp. 25-30

(in Italian)

Bonati A., e Galimberti V., (2004): Valutazione sperimentale di sistemi di difesa attiva dalla

caduta massi in atti Bonifica dei versanti rocciosi per la difesa del territorio - Trento

2004, Peila D. Editor.

Brunet G., Giacchetti G., (2012) - Design Software for Secured Drapery- Proceedings of the

63rd Highway Geology Symposium, May 7-10, 2012, Redding, California.

Castro D., (2008) Proyetos de investigacin en la Universidad de Cantabria - II Curso

sobre proteccin contra caida de rocas Madrid, 26 27 de Febrero. Organiza STMR

Servicios tcnicos de mecnica de rocas.

Cravero M., Iabichino G., Oreste P.P., e Teodori S.P. 2004: Metodi di analisi e

dimensionamento di sostegni e rinforzi per pendii naturali o di scavo in roccia in atti

Bonifica dei versanti rocciosi per la difesa del territorio Trento 2004, Peila D. Editor.

Ferrero A.M., Giani G.P., Migliazza M., (1997): Interazione tra elementi di rinforzo di

discontinuit in roccia - atti Il modello geotecnico del sottosuolo nella progettazione

delle opere di sostegno e degli scavi IV Conv. Naz. Ricercatori universitari

Hevelius pp. 259 275.

Flumm D., Ruegger R. (2001): Slope stabilization with high performance steel wire meshes

with nails and anchors International Symposium Earth reinforcement, Fukuoka, Japan.

Goodman, R.E. and Shi, G. (1985), Block Theory and Its Application to Rock Engineering,

Prentice-Hall, London.

Jacob V., (2009): Engineering, unpublished thesis, Technical University Torino.

LCPC, (2001) : Parades contre les instabilits rocheuses - Guide technique - Paris.

Phear A., Dew C., Ozsoy B., Wharmby N.J., Judge J., e Barley A.D., (2005): Soil nailing

Best practice guidance - CIRIA C637, London, 2005.

Ribacchi R., Graziani A. e Lembo Fazio A. (1995). Analisi del comportamento dei sistemi di

rinforzo passivi in roccia, XIX Convegno Nazionale di Geotecnica: Il Miglioramento e il

Rinforzo dei Terreni e delle Rocce, Pavia, pp. 239-268

Ruegger R., e Flumm D., (2000): High performance steel wire mesh for surface protection in

combination with nails and anchors Contribution to the 2 ndcolloquium Contruction in

soil and rock Accademy of Esslingen (Germany).


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Saderis A., (2004): Reti in aderenza su versanti rocciosi per il controllo della caduta massi:

aspetti tecnologici e progettuali Tesi di Laurea in Ingegneria per lAmbiente e il

Territorio, unpublished thesis, Technical University Torino.

Torres Vila J.A., Torres Vila M.A., e Castro Fresno D., (2000): Validation de los modelos

fisicos de analisis y diseno para el empleo de membranas flexibile Tecco G65 como

elemento de soporte superficial en la estabilizacion de taludes.

Valfr A., (2007): Dimensionamento di reti metalliche in aderenza per scarpate rocciose

mediante modellazioni numeriche GEAM Geoingegneria Ambientale e mineraria,

Anno XLIII, N. 4, Dicembre 2006.


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7 END NOTES

1

See pag. 570 of Turner A.K, Schuster R.L. Editors (2012) Rockfall CharacterizationRockfall Characterization and control Transportation Research Board, Washington D.C.

2 UNI 11437 (2012). Rockfall protection measures : Tests on meshes for slope coverage -UNI Ente Nazionale Italiano di Unificazione. It is the first worldwide norm that describes theprocedures for the two basic resistances of a mesh (punch and tensile). It considers andextends the pre existing standards (ASTM 975-97 2003 and EN 15381:2008).

3The following graph shows the effect of water content on the compressive strength, bleedand flow resistance of grout mixes (Littlejohn and Bruce, 1975, from pag 322 of Wyllie D.C.(1999) Foundations on Rock Second edition E & FN SPON, London and New York).

4In Macro 1 the notation of the anchor spacing is referred to the horizontal inter-axis i xandthe vertical one iy(measured on the slope face). The Figure 1shows the configuration of theanchor pattern spaced ix and iy. In reality the anchor pattern could be also diamond, asrepresented in following figure. Macro 1 only accepts the input with the concept of squarepattern (left in the figure). If the user wants to change from square to diamond, he has toinput a fictitious square pattern that respects the anchor density (number of anchor per area

unit).Area per 1 anchor in the squared pattern Area = iy ixIf iy =ix, the squared area can be rewritten Area = ix

2Area per 1 anchor in the diamond pattern Area = dy dx / 2It must be that ix

2= dy dx / 2And then ix= (dy dx / 2)

0.5The last relationship allows adopting the diamond pattern in Macro 1 too.

Example: the diamond pattern to be calculated is dy = 5.5 m and dx = 2.9 m. The equivalentsquare pattern to be inserted in Macro 1 isix= iy= (dy dx / 2)

0.5= (5.5 2.9/ 2)0.5= 2.8 m


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The best position of the anchors happens when they can cooperate each other and interferewith the rock mass. Then the best theoretical pattern should be the diamond one, withanchor axis spaced in order to form an equilateral triangle. But more simply, it is importantthat the areal distribution of the anchor is as homogeneous as possible. In these terms it isstrongly recommended to avoid irregular pattern (examples: diamond 3.0 m x 8.0 m orrectangular 2.5 m x 4.8 m).For practical reasons many contractors prefer the squared pattern.

5 Ferraiolo F., Giacchetti G. (2004) Rivestimenti corticali: alcune considerazionisullapplicazione delle reti di protezione in parete rocciosa, in proceedings Bonifica diversanti rocciosi per la protezione del territorio Trento 2004 Peila D. editor. In Italian.

6At the present has been instituted a work group for the proposal of a new Eurocode for therock masses. For instance see: Alejano L.R., Bedi A., Bond A., Ferrero A.M., Harrison J.P.,Lamas L., Migliazza M.R., Olsson R., Perucho ., Sofianos A., Stille H., Virely D. (2013).Rock engineering design and the evolution of Eurocode 7. In Rock Mechanics for

Resources, Energy and Environment Kwasniewsky & Lydzba (eds.) 2013 Taylor & FrancisGroup, London, ISBN 978-1-138-00080-3, pag. 777-782

Anyway, with special reference to the DIN 1054:2010-12 (Subsoil Verification of the safetyof earthworks and foundations Supplementary rules to DIN EN 1997-1 - table A 2.1 for theapproach B-SP, GEO-2), and more generally to the EC7 concepts, the user can introducethe coefficients 1.35 for the estimation of the stabilizing forces, and 1.00 for the estimation ofthe driving ones (see Tabelle Teilsicherheitsbeiwerte F1 bzw. E2 fr Einwirkungen undBeanspruchungen, B-SP, STR und GEO-2: Grenzzustand des Versagens von Bauwerken,Bauteilen und Baugrund, pag 30 DIN EN 1997-1). This approach implicate that theefficiency for the system (Maccaferri internal report):

= FDslp / FSslp

is equals or greater than 0.77 (see equations [5] and [6]). In order to respect this efficiency,the safety coefficient DWand RW(see Table 2) have to respect at least the following value:

DW = (W sen / RW + Rd / W sen )

(for the meaning of W, and R, please see the symbol list table)


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The relation between DWand RW has been plot in the above graph for immediate use, as thefollowing examples shows:

Example 1: if DWis equals to 1.20, in order to get an efficiency not lower than 0.77,RW shall not be lower than 1.25.

Example 2: if RWis equals to 1.50, in order to get an efficiency not lower than 0.77,DWshall not be lower than 1.10.

The user can modulate the partial safety coefficients (see Error! Reference source notfound.) according to his knowledge of the slope until DWand RW (see the input data menu ofsafety coefficients in the software) do not satisfy the required efficiency of the system, as perthe graph above.

7The Barton-Bandis criteria does not consider the cohesion on the joints, but a peak frictionangle, which depends on a base friction angle (related to the rock type) and an incrementangle (related to JRC and JCS).Main references: Barton, N.R. and Choubey, V. (1977). The shear strength of rock joints in theory and

practice. Rock Mech. 10(1-2), 1-54. Barton, N.R. and Bandis, S.C. (1982). Effects of block size on the shear behaviour of

jointed rock. 23rd U.S. symp. on rock mechanics, Berkeley, 739-760

Practical synthesis can be found in- chapter 2 of Hoek E. (2000). Course Notes for Rock Engineering (CIV 529S) inwww.rocscience.com

8see pag. 352 354 of Hoek, E. and Bray, J.W. 1981. Rock Slope Engineering . 3rd edn.London: Institution of Mining and Metallurgy 402 pages.

9According to the Barton-Bandis failure criteria, the friction angle commonly ranges between28 and 70. Most frequently the value of 45 can be considered conservative.


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10Grimod A., Giacchetti G. and Peirone B., 2013. A new design approach for pin draperysystems. Proceedings of GeoMontreal 2013. 29thSpetember 3rd October 2013, Montreal(QC). Paper n. 491.

11The stabilizing contribution of a steel bar crossing a sliding plane can be described withthe following typical graphics:

The graph, developed for a specific type of steel bar, shows the effect of the dilatancy on the

stabilizing contribution R is higher when the bar perpendicular the sliding plane.See also pag. 337- 339 of Giani G. P. (1992), Rock slope stability analysis Balkema,Rotterdam

12pag. 95 96 of Pellet F., e Egger P., (1995): Analytical model for the behaviour of boldedrock joints and practical applications. In proceedings of international symposium Anchorstheory and practice. Widmann R. Editor, Balkema, Rotterdam.

13Giani G. P.see note 1114see the following references:

Singh B., Goel R.K. (1999) Rock mass Classification A practical approach in civil

engineering- Elsevier pag 69 of Bell F.G. (2007). Engineering Geology Elsevier BH


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15See pag 37 38 of Barton N. (1992): Scale effects or sampling bias?Proc. Int. WorkshopScale Effects in Rock Masses, Balkema Publ., Rotterdam

16

Barton N. - see note 1517 See pag. 169 171 of Goodman, R.(1989) - Rock Mechanics Second edition. JohnWiley.

18An idea of grade of disturbance can be found on the chapter describing the rock massproperties of Hoek E. (2000). Course Notes for Rock Engineering (CIV 529S) inwww.rocscience.com

19The value of JRC can be measured by the Barton comb and comparing the roughnessprofile to the typical of the table (from Barton, N.R. and Choubey, V. , 1977 see note 7).

20The value of JCS can be measured with the Schmidt hammer, or in lack o information,

deduced from the uniaxial compressive strength (UCS = c) of the rock. The following tablegives the compressive frame of the most common values (from Appendix 3 of Palmstrom A.,(1995) RMi - a system for characterization of rock masses for rock engineering purposes.Ph. Thesis, University of Oslo, Norway. In www.rockmass.net)


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21 See the references:

pag 139-141 of Wyllie D.C., e Mah C.W., (2004): Rock slope engineering civil andmining- 4th edition Spon Press London and New York.

ITASCA (2004). UDEC universal distinct element Code User manual: Specialfeatures Minneapolis, USA.

22 The following table the approximate relationship between rock type and working bond shearstrength for cement grout anchorages (from pag 331 of Wyllie D.C. (1999) Foundations on Rock

Second edition E & FN SPON, London and New York.)


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See also:

Littlejohn, G.S. and Bruce, D.A. (1975a) Rock anchors state of the art. Part 1: Design.Ground Eng., 8(4), 418.

Littlejohn, G.S. and Bruce, D.A. (1975b) Rock anchors - state of the art. Part 2: Construction.Ground Eng., 8(4), 3645.

Littlejohn, G.S. and Bruce, D.A. (1976) Rock anchors state of the art. Part 3: Stressing andtesting. Ground Eng., 9(5), 33141.

23UNI ENV 1997-1:200524 Bertolo P., Oggeri C., Peila D., 2009 Full scale testing of draped nets for rock fall

protection- Canadian Geotechnical Journal, No. 46 pp. 306-317.

25The typical load vs displacement curves of the mesh have been implemented in the libraryof Macro 1.

26The values have been seen with specific tests in Cottbus University test i.e. Test 2011-MPZ05SG/B-06 13/ May 2011

27See the following references:

Muhunthan B., Shu S., Sasiharan N., Hattamleh O.A., Badger T.C., Lowell S.M.,Duffy J.D., (2005): Analysis and design of wire mesh/cable net slope protection -

Final Research Report WA-RD 612.1 - Washington State Transportation CommissionDepartment of Transportation/U.S. Department of Transportation Federal HighwayAdministration.

Sasiharan N., Muhunthan B., Badger T.C., Shu S., Carradine D.M.(2006) Numerical analysis of the performance of wire mesh and cable net rockfall protectionsystems. Engineering Geology 88, 121-132. Elsevier

28See the following references: Majoral R., Giacchetti G., Bertolo P., 2008 Las mallas en la estabilizacin de

taludes II Curso sobre proteccin contra caida de rocas Madrid, 26 27 deFebrero. Organiza STMR Servicios tcnicos de mecnica de rocas.

Grimod A., Giacchetti G. , 2013, New design software for rockfall simple draperysystems. Proceedings 23nd World Mining Congress & Expo, Montreal. Paper No.


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255.

29The safety coefficients for the diplacement normal to the mesh plane should be alwaysquite large in order to compensate for all the uncertainties that affect the mesh. Theinstallation accuracy generates one of the largest uncertainties. The most relevant researchto analyze the performance of the mesh stressed by a punch test was done by thePolytechnic of Turin (see note 24 and the figures below with the cross section of the punchdevice acting on the tested meshes). The goal of the research was to study the real behaviorof different type of mesh installed on a rock slope. The meshes were anchored to the rock by4 nails distributed in a squared configuration. The distance between the nails was 3m x 3m.The falling block was simulated by a piston connected to a punch device (diameter = 1.5 m);the piston was installed in order to develop a 45 degree pressure against the mesh. Themaximum elongation of the piston was approx. 1.2 m ! The best way to reduce thedeformation is inserting cables into the mesh as suggested by Muhunthan ( see note 26).

.

Documents

Macro 1 Theory and background - rel 108 OM format.pdf