1

CIVL 111 CONSTRUCTION MATERIALS

Chapter 1 Introduction 1.1. Materials for construction The world is composed of various materials. The materials science and engineering serves as ground for all technology branches such as electronics, energy, communication, environment, and healthy engineering. Construction materials are the most widely used materials and their usage is the largest in tonnage in the world.

Through the history of human civilization, many materials have been used in the construction of buildings, bridges, roads and other structures. The focus of our study is on modern construction materials including concrete, steel, wood, bituminous materials as well as polymers and fibrous composites. Among these materials, concrete will receive the most attention in this course, for two reasons. First, the civil engineer is responsible for designing the concrete he/she uses and for ensuring its long term performance. On the other hand, steel and wood products are designed by material and mechanical engineers, who supply them to us according to our specifications. Second, concrete (reinforced concrete) is the most widely used construction material in the world and of course in Hong Kong, too. For any civil engineer who will be practicing in Hong Kong, a good knowledge of concrete behaviour is essential. Besides concrete, steel and wood are the other two most commonly used construction materials in the world. In the US, for example, most residential houses are built with wood and over half of the office buildings are constructed with steel. This is due to the abundant supply of both materials, making them economical. Steel, besides its use as structural members on its own, is also used as reinforcements or prestressing tendons for concrete structures. Understanding steel behaviour is hence an important component in the studying of reinforced concrete and prestressed concrete design. Bituminous materials are used all over the world in the construction of road pavements. In recent years, polymers and polymeric composites have been gaining popularity in the construction industry, due to their light weight and good durability. Polymers have been used in pipes, fabrics for large roofing as well as geotextiles for slope protection. Reinforcing bars and grids have been made with fiber reinforced composites to replace metals in corrosive environments. Soil is also an important construction material, but it is covered in a separate course. Masonry (bricks and blocks) are widely used in building walls. Since they are not the primary load carrying components, we will not discuss them here. In buildings, many non-structural materials are also employed. These include floor and wall coverings, tiles, glass, insulation materials, sealants etc. Most of them are specified for aesthetic purposes by the architect or the interior designer. They will not be studied in this course. 1.2. Construction materials and structural design

2

Construction materials and structural design are two closely related fields. To design a building or a bridge, we often starts with a given structural form. Once the loading on the structure is determined, structural analysis allows us to obtain the moments and shear forces in each of the members. We then choose member sizes to ensure that failure or excessive deflection will not occur. Moreover, in case failure occurs, we want it to be gradual, rather than sudden and without warning. In order to perform this task, two questions need to be answered. First, how can one relate the maximum stress and deflection of a member to the applied moment and shear as well as the member size and material stiffness. The answer to this question is provided by the theories in mechanics of materials. Second, what is the strength (or maximum stress capacity) and stiffness of the material, and what is its failure mode. The answer lies in the study of the behaviour of construction materials, and is best presented in terms of the stress-strain diagram (or constitutive relation) of the material (Fig.1.1).

(a) (b)σ σ

εε Fig.1.1 Stress Strain Diagrams for (a) Brittle and (b) Ductile Materials

The initial slope of the stress strain diagram reflects the stiffness of the material. The higher the slope, the more difficult it is to deform the material. If a structural member is made with a stiffer material, its deflection will be reduced. Fig.1.1 (a) shows the stress strain relation for a brittle material such as glass. Once a critical stress value (the strength) is reached, failure will occur suddenly with no warning. The stress strain relation shown in Fig.1.1 (b) represents that of mild steel (up to a certain strain level). After the critical value is reached, the material can still carry stress on further deformation. This deformation capability is called ductility. The implication is that the structural member will undergo significant deflections before failure occurs, providing warning to people in and around the structure. In the above discussion, we start with the structure form, and then consider the relevance of material stress-strain relation in choosing the member size. In reality, the stress-strain relation of a material often determines the structural form. For example, due to the high compressive strength but low tensile strength of natural stone, historical stone structures are built in the arch form. With the development of high strength steel, cable suspended and cable stayed bridges are designed. The fact that structural form is affected by material behaviour is usually taken for granted, since we have sufficient experience with materials like concrete, wood and steel to prescribe the structural form. When new materials (such as fiber reinforced composites) are introduced, civil engineers should come up with new structural forms which would take full advantage of the materials.

3

In recent years, due to the infrastructure decay problem in many developed countries, the long term performance of structures has become an important concern. In other words, we are interested in knowing how the stress-strain relation may change with time. For example, under chemical attack and repeated loading from the traffic, would the strength of concrete or steel be reduced over time. Under sustained loading over many years, would the stiffness of polymers become a lot lower, hence leading to excessive deflection. These are important issues to be addressed and will be one of the major foci of discussion throughout the course. Besides the mechanical properties, physical properties and chemical properties of construction materials are also important. The weight of materials governs the dead load on a structure. Its porosity governs water and gas penetration that affects material durability. The chemical properties govern the likelihood of chemical reaction and deterioration under various environments, and are clearly important in the study of long term performance of materials. Before closing of the introduction chapter, let’s mention the fact that construction materials are always evolving. Forty years ago, concrete of 50 MPa is considered high strength. Today, 50 MPa concrete can be easily produced anywhere and 130 MPa concrete has been employed in the construction of high rise buildings. Thirty years ago, polymeric composites are only commonly used in the aerospace industry. Today, composite reinforcing bars are commercially available, at a price only slightly higher than epoxy-coated steel (which is widely used in bridges in the U.S. - the epoxy coating is to provide corrosion protection). Readers of civil engineering magazines will notice advertisements of new materials all the time, some used on their own, while others used as additives to improve the properties of concrete. With knowledge developing at an ever-increasing rate, civil engineers of this generation will likely encounter new construction materials in their career. How, then, can a sound judgement be made regarding the use of such a material? The answer lies again in the behaviour of the material. With a good understanding of the physical basis of material behaviour, factors that may affect it and its relation to structural behaviour, we will be able to ask the right question about any new material, and perform the right tests to assess its applicability. The second chapter will provide a concise summary of mechanical properties of materials. This will provide a background for the understanding of material behaviour in general, and be helpful in the study of specific construction materials in the later chapters.

5

CIVL 111 CONSTRUCTION MATERIALS

Chapter 2 Mechanical Behaviour of Materials

2.1 Elastic behaviour

2.1.1 Introduction

Under a small load, all materials behave in an elastic manner. When stress is applied, strain will be resulted. Once the stress is removed, the material returns to its original state (i.e., the strain goes back to zero). Moreover, before a certain critical state is reached, the stress and strain are linearly dependent on one another. Linear elastic behaviour is the basic assumption of many engineering analyses. In this section, we are going to investigate the physical basis of linear elastic behavior, define the Young’s modulus and describe how it affects structural design. Then, we will study the elastic behaviour of composite materials (i.e., when two or more materials are used in combination to carry the load). This will provide a foundation for the understanding of reinforced concrete design, which will be taught in another class.

2.1.2 Physical Basis of Elastic Behaviour

To most of us, the first manifestation of elastic behaviour is perhaps the behavior of a spring. On loading, the deformation is clearly visible and on unloading, the spring returns to its original length. The elastic behaviour of all materials can be explained in terms of the simple spring. As we all know, materials consist of atoms that are held in equilibrium positions by bonds. Since the bond force is linearly dependent on interatomic distance, bonds can be considered as small springs placed between atoms (Fig.2.1). When loading is applied, the atoms will move relative to one another. The movement will stop once the bond force (resulting from change in interatomic distance) is in balance with the applied force. Once the loading is removed, the atoms will move back to the original equilibrium positions. The behaviour of the whole material is therefore linear elastic. In Fig.2.1, for simplicity, we have only considered the presence of bonds along the direction of the loading. In reality, there are interactions between neighbouring atoms at all directions. (Actually, the interaction may extend beyond the first layer of neighbours, but this is beyond the scope of our discussion here). Fig.2.2 shows an example of such kind of interaction. Again, if we consider the bond to be a spring, when loading is applied in the direction shown in Fig.2.2, the stretching of the spring results in forces with two components, one parallel to the applied load and the other perpendicular to it. As a result, under loading, materials not only deform parallel to the loading direction, but will also deform perpendicular to it. This deformation is called the Poisson’s effect and is important in understanding the effect of confinement on material behaviour, a topic of importance in reinforced concrete column design.

6

Displacement of atom asbond stretch under load

Bond behaves like spring

Figure 2.1 Displacement of atoms under applied loading

Vertical component of spring forcepulls atoms away from one another

Horizontal component of spring forcemoves atoms closer to one another

Figure 2.2 Illustration of the Poisson’s Effect

2.1.3 Young’s Modulus: Definition, Typical Values and Significance to Structural Design

In the linear elastic regime, the stress (σ) and strain (ε) are directly proportional to one another. The Young’s modulus, E, is defined as: E = σ / ε The Poisson’s ratio ν is defined as: ν = - (strain perpendicular to loading direction) / (strain along loading direction)

7

Note the negative sign in the equation for ν: with this definition, the situation illustrated in Fig.2.2 will result in a positive value of ν. As examples, ν = 0.28 for steel and range from 0.14 to 0.20 for concrete. In some applications, which involve the shear deformation of materials, the shear modulus G is used. For an isotropic material, which is defined as a material with equal properties in all directions, G is related to E and ν through: G = E / 2(1+ν) A high value of E means that a high level of stress is required to produce a given strain. The material is then said to have a high stiffness. Physically, the magnitude of E is governed by the intensity of the bond between atoms. Primary bonds such as covalent, ionic and metallic bonds result in high E values. Secondary bonds, including hydrogen bond and van der Waal’s force, give rise to low values of E. The Young’s moduli for common materials are given in Table 2.1. The covalent bonded diamond is the stiffest material in the world and included here as a reference. Steel, which is held by metallic bonds, has a high modulus of around 200 GPa. Wood and polymers have a low modulus of 16 GPa or below. Both wood and polymers are built up of long chains of carbon atoms. Along the chain, the atoms are covalent bonded and therefore the stiffness is very high. However, individual chains are held together by either the weak secondary bonds or occasional cross-links. It is therefore quite easy for the chains to slide relative to one another, resulting in the low E values. The modulus of concrete, depending on mix proportions, is around 20 to 40 GPa. Concrete consists of many different chemical phases, fine and coarse aggregates as well as pores. Its modulus is affected by many factors and we postpone the discussion to the chapter on concrete.

It is important for us not to confuse between the two concepts of strength and stiffness. For example, aluminum and glass both have a modulus of 69 GPa. That is, they have comparable stiffness. However, their strength and failure modes are completely different.

Table 2.1 Reference E values (in GPa) for common materials

Diamond 1,000 Wood ( // grain ) 9 - 16 Steel 190 - 210 Wood ( | grain) 0.6-1 Aluminum 69 Polyesters 1 - 5 Glass 69 Epoxies 3 Concrete 20 - 40 Ice (H2O) 9.1 The Young’s modulus is the material parameter governing the deformation of a structure (Note: deformation is of course also affected by the member size). When material of a lower E is used to replace one with a higher E (e.g. aluminum is employed to replace steel to reduce environmental corrosion), the deflection should be checked to make sure that it is not excessive. A reduction of E will also increase the likelihood of buckling failure, which is the sudden lateral deflection of a slender member under compression (This can be easily illustrated by compressing a thin plastic ruler). It should be noted that when a material is damaged, its E value is always reduced. Since the speed of stress wave propagation in a material is proportional to the square root of E, the wave speed in a damaged material will also be reduced. By sending a wave into a structural member and measure the time for it to

8

travel between two points, the damage condition of a structure can be assessed in a non-destructive manner.

2.1.4 Modulus of Composite Materials: Application to Reinforced Concrete Column In this section, we will consider the elastic behavior of composite materials. This is of relevance because: (i) the same concepts apply to the analysis of reinforced concrete members, (ii) there is increasing interest in the use of fiber reinforced composites in civil engineering applications. Our discussions will be limited to composites with two phases, but they can be easily extended to more general cases. Only two simple cases will be considered. In both cases, the two phases are considered to be planar and aligned in the same direction (Fig.2.3). In case 1, the loading is applied parallel to the aligned direction, and in case 2, the loading is applied perpendicularly. The analysis of each case is given below. Case 1: Loading along aligned direction Assume a total load carrying area of A, and an average applied stress of σ. The total applied force is therefore given by Aσ. Let Va be the volume fraction of phase A, and Vb (= 1 - Va) be the volume fraction of phase B. Phases A and B are bonded together. When loaded in parallel, they must deform by the same amount (otherwise, they will not be fitted together any more). In other words, the strain in each phase (along the loading direction) must be the same, i.e., εa = εb = ε. The stress in the phases is then given by: σa = Eaεa = Eaε

σb = Ebεb = Ebε The force carried by each phase is equal to the stress in each phase multiplied by the

area: Fa = VaA σa = VaA Eaε Fb = VbA σb = VbA Ebε Force equilibrium requires F = Fa + Fb, which gives: Ασ = (VaA Ea + VbA Eb) ε

or, E = σ/ε = (VaEa + VbEb) This is called the parallel model, which states that the composite modulus is simply the weighted average of the phase moduli, with the corresponding volume fraction used as the weight.

9

CASE 1

Loading along aligned directionCASE 2

Loading perpendicular to aligned direction

H

Figure 2.3 Calculation of composite modulus for two different cases

Case 2: Loading perpendicular to the aligned direction In this case, since the two phases are loaded in series, the stress on each phase must be the same in order for equilibrium to be satisfied. That is, σa = σb = σ, where σ is the applied stress. The strain in each of the two phases are:

εa = σ / Ea

εb = σ / Eb

Assuming the thickness of composite to be H. The total extension in phases A and B are given by: ea = εa Va H eb = εb Vb H For the composite, the total extension is given by e = εH. Since e = ea + εb, ε = σ ( Va/Ea + Vb/Eb ) or E = σ/ε = ( Va/Ea + Vb/Eb )-1

It should be noted that cases 1 and 2 give the upper and lower bound for the elastic modulus of a composite system. In a composite with any arbitrary arrangement of the two phases, the modulus will always lie between the values given by the two expressions derived above. Example: Elastic Behavior of a Reinforced Concrete Column A 200 mm x 400 mm rectangular concrete column is reinforced with six 25 mm diameter bars. The length of the column is 3 m. An axial load of 1000 kN is applied. How much would the column be shortened and what are the stresses in the concrete and the steel? (Take Es =200 GPa, Ec = 26.7 GPa) Solution: The volume fraction of steel is given by: 6π(12.5)2/(200x400) = 0.0368 Since steel and concrete are loaded in parallel, the effective modulus is given by: E = (0.0368) (200) + (1-0.0368) (26.7) = 33.08 GPa Shortening of the column = [1000 x 103 (N) / (200 x 400 (mm2)x 33.08 x 103 (N/mm2) )] x 3000 (mm)

10

= 3.78 x 10-4 x 3000 (mm) = 1.134 mm Stress in steel = 3.78 x 10-4 x 200 x 103 (N/mm2) = 75.6 N/mm2 (or 75.6 MPa) Stress in concrete = 3.78 x 10-4 x 26.7 x 103 = 10.1 MPa NOTE: When reinforced concrete members are subjected to bending, the strain varies over the depth of the member. To analyze its behavior, we make a similar assumption: the strain in the steel is equal to that in the adjacent concrete. Details will be left to the class on reinforced concrete design.

11

2.2 Plastic behaviour

2.2.1 Phenomenon of Plastic Yielding When loading on a piece of metal is continuously increased, yielding will eventually occur. Plastic yielding is indicated by a significant increase in deformation with a relatively small increase in load (or, in the case of mild steel, with no increase in load). The ultimate load carrying capacity, however, is higher than the load at which yielding first occurs. As a result, the large deformation after yielding serves as warning before final failure occurs. Materials that yield are often referred to as ductile materials, and ductility is a desirable feature for all structures. The stress-strain behaviour of a typical metal is shown in Fig.2.4 below. From the figure, the following can be defined: σy : yield strength, the point where a sudden change in slope occurs σ0.1% : the 0.1% proof stress, obtained from a line starting from 0.1% ε and extending parallel to the initial slope. This is often used when an abrupt change in slope is difficult to identify. One can also report the proof stress at other strain levels (0.2%, 0.3%) based on the same concept. σTS: ultimate strength of the material εf : tensile ductility or the plastic strain after failure

ε0.001(0.1%)

σ0.1%

σ yUnloading line

following initial slope

Onset of Necking

Tensile Fracture

σ TSHardening

ε f

σ

Figure 2.4 Stress-Strain Curve for most Metals

For most metals, once the yield strength is reached, continuous straining will be accompanied by a more gradual increase in stress. This stress increase is referred to as hardening. During the hardening state, the deformation is still uniform along the member (i.e., the strain is the same at all points). Once the ultimate strength is reached, localization of deformation starts to occur at a particular section. On further straining, the area of this section becomes smaller and smaller. This phenomenon is called ‘necking’ as strain localization leads to the formation of a ‘neck’ along the loaded member (see illustration in Fig.2.4). Final failure is due to plastic fracture, and the member breaks into two parts. When the two parts are fitted back together, the length (L) is often significantly above the original

12

length (Lo). The ratio (L - Lo)/Lo is called the tensile ductility. For steel, this value can range from 0.1 to 0.6, depending on the grade. The stress strain curve shown in Fig.2.4 is applicable to most metals. However, it does not represent the behaviour of mild steel, a material widely used in construction. The stress strain curve of mild steel is shown in Fig.2.5. The curve exhibits an upper yield point and a lower yield point. With further straining beyond the lower yield point, a constant stress region (called the yield plateau) is observed before the material starts to harden like other metals. It should be noted that the upper yield point depends on loading speed and specimen type, while the lower yield point stays constant. As a result, the lower yield stress is taken to be the yield strength of mild steel and is the value used in structural design.

ε

Unloading line following

initial slope

Hardening

σ Upper and LowerYield Points

Figure 2.5 Stress Strain Curve for Mild Steel

2.2.2 Physical Basis of Plastic Behaviour The physical origin of plasticity has remained a puzzle for many years. Considering the simple spring model in Fig.2.1, plastic behaviour will be resulted if each spring behaves in a plastic manner. In other words, the bond force has to vary with distance in a way similar to the stress strain curve. Analysis of inter-atomic interactions based on electrostatic theory indicates that this is not the case. Moreover, analysis shows that the stress required to break the bond is about one order of magnitude lower than the Young’s modulus. For most metals, however, the yield strength (and tensile strength) is about two to three orders of magnitude lower. How can this be explained? The answer to this interesting question also provides a basis for explaining plastic behaviour. A key in understanding plastic behaviour is the observation that atomic bonds do not all break at the same time. Since only a small fraction of bonds are broken at a given time, the applied stress at which bond breakage occurs is a lot lower than the theoretical value. When forces are applied along bonds to pull them apart (as in Fig.2.1), there is no mechanism for bonds to break one by one. However, if shear stress is applied, bonds can easily break and re-

13

A C

B D

A

B

C

D

A

B

C

D

E

F

G

H

A

B

C

D

E

F

A C E G

B D F H b

Fig.2.6 Illustration of Plastic Deformation due to Dislocation Movement

form one after another. This process is difficult to explain in words but is illustrated in Fig.2.6. One can observe from the figure that shearing leads to the stretching of bonds between two horizontal layers (between atoms A and B, C and D). Eventually, these bonds will be broken and replaced by a new bond between atoms A and D. The breaking and re-formation of bonds (between different pair of atoms) result in an extra plane of atoms in the atomic lattice. Such an extra plane is called a ‘dislocation’. On further shearing, additional bond breaking and re-formation move the dislocation from one side to the other side of the atomic block. A ‘step’ equal to the atomic spacing is then created. Continuous application of the shear stress can result in another series of bond breaking and re-formation, leading to additional displacement between the upper and lower blocks. The relative sliding between the two blocks is the cause of the large strain after yielding. In Fig.2.6, for illustration, we show the formation of a dislocation under applied stress. In real materials, dislocations pre-exist everywhere inside the atomic lattice. When shear stress of a sufficient magnitude is applied, dislocation movements occur all over the material. The material can then be considered as consisting of many separate ‘blocks’ trying to slide relative to one another. The strain in the material is therefore made up of two parts: the elastic stretch of bonds within each block, and the relative sliding between the blocks. The elastic part of the strain is completely recoverable on unloading, while the sliding leads to the irrecoverable plastic strain. This is the reason the unloading line after yielding is parallel to the loading line. Since dislocations can move in different directions, the blocks also tend to slide in different directions and can eventually get into the way of one another, making movement more difficult. This explains the existence of the hardening regime, where increased stress is required to continue the yielding process. The dislocation theory described above implies that yielding is resulted from shear stresses. When there is no shear stress (e.g., equal tension is applied in all directions),

14

yielding will not occur. As a result, a criterion for yielding should be based on the shear stress. A discussion of common yield criterion will be postponed to the chapter on steel. To increase the yield strength (or, to ‘harden’ the material), the resistance to dislocation movement has to be improved. Since many hardening techniques can lead to a reduction in ductility of the material, the potential compromise between strength and ductility of metals should be kept in mind. Specific hardening methods for steel and their effect on ductility will also be presented in a later chapter.

2.2.3 Modelling of Plastic Behaviour Fig.2.7 shows two models for plastic behaviour. In structural analysis, the elastic/perfectly plastic model is often used for two reasons. First, it is a good approximation for mild steel, which is commonly used in construction. Second, for a hardening material, it simplifies the analysis and provides conservative results. The rigid perfectly plastic model is employed for the calculation of ultimate collapse load for a ductile structure. Since collapse occurs at a strain much higher than the yield strain, the initial elastic part can be neglected in such an analysis.

ε

σ

Elastic/Perfectly Plastic Model

Rigid/Perfectly Plastic Model

Figure 2.7 Models for Plastic Behaviour

2.2.4 Illustration of Plastic Behaviour with a Parallel System

To illustrate plastic behaviour of structures, we will consider the parallel system shown in Fig.2.8 below. The simple system consists of several members working together to carry the applied load. One of the members will yield before the others. Real structures consists of many members to carry the load (e.g., a building with many columns plus an internal core to carry wind load, a bridge with multiple spans, each contributing to carrying the traffic load on other spans). Each individual member will generally yield at a different load. The qualitative behaviour of the simple system in Fig.2.8 therefore resembles that of a real structure. By studying the simple system, post-yielding behaviour of real structures can be understood.

15

yσ

yε

2LL

u : applied displacement

12

3

RigidBar

σ

ε

Figure 2.8 A Parallel System to Illustrate Plastic Behaviour

In Fig.2.8, let’s assume all members to have the same cross sectional area A. The

objective is to find the load (F) corresponding to a given displacement (u). The members do not yield at the same displacement.

For members 1 and 3, yielding occurs when: u = 2Lεy For member 2, yielding occurs when: u = Lεy Elastic Stage: 0 < u/L < εy F = AEu/L + 2AEu/(2L) = 2(AE/L)u The first term is the contribution from member 2 and the second term is from 1 and 3. Bar 2’s yielding Bar 2’s yielding occurs when: u = uy = Lεy Fy = 2AEεy After First Yielding: εy < u/L < 2εy F = AEεy + 2AEu/(2L) = AEεy + 2AEεy/2 + 2AE(u-Lεy)/(2L) = Fy + (AE/L) (u - uy) Before bar 2’s yielding, the load increment is proportional to 2AE/L. After yielding, the increment is proportional to AE/L (Fig.2.9). With bar 2’s yielding, the structure becomes more flexible on further loading. This is a general feature observed in any structure with plastic members.

F

uu y

Fy

2AE/L

AE/L

u - u y

Fig.2.9 Load vs Displacement for a Parallel system with Elastic/Perfectly Plastic Members

16

Whole system’s yielding When the deformation of the whole system reaches 2 Lεy , bar1 and 3 will yield. Thus the whole system is yielded. The ultimate load capacity of the system is reached when the whole system yields. The ultimate load is given by 3AEεy. Let’s compare this with the ultimate load of a brittle member system. The strength and failure strain of the brittle material are taken to be σy and εy. Since the material is brittle, once εy is exceeded, the stress will drop to zero immediately. At ε = εy, failure occurs in member 2. The load at this moment is F = 2AEεy. After failure, member 2 cannot carry any load. The remaining load carrying capacity of members 1 and 3 is also 2AEεy. In other words, once the middle member fails, the system cannot carry additional load and the whole system collapses. This illustrates another advantage of ductile materials over brittle materials. Even if the materials possess the same strength (σy in this case), the ultimate load carrying capacity of the ductile system can be significantly higher than that of the brittle system. 2.3 Time Dependent Behaviour - Creep 2.3.1 Phenomenon of Time Dependent Behaviour For many materials (e.g. polymers, wood, concrete), the response to stress or strain has a time dependent component. For example, when a fixed stress is applied, after an instantaneous elastic response, the strain will continue to increase with time. This phenomenon is called creep and is illustrated in Fig.2.10(a). On the other hand, when a fixed strain is applied (e.g., by stretching a member and then fixing its ends), the stress in the member will decrease with time (Fig.2.10(b)). This phenomenon is called relaxation. If creep and relaxation are linear (e.g., if the stress is doubled, the strain at a particular time is also doubled), we can define the following two parameters: Creep compliance, J(t) = ε(t)/σ Relaxation modulus, Er(t) = σ(t)/ε The creep compliance can be obtained from a test with a fixed load applied to a specimen. Knowing J(t), the time dependent behaviour of the material under arbitrary loading history can be obtained from superposition (see section 2.3.5).

ε

Time

instantaneouselastic strain

creepstrain

(a)σ

Time

(b)

Fig.2.10 (a) Creep Behaviour, (b) Relaxation Behaviour

17

For materials exhibiting creep behaviour, when a stress is applied, the strain will increase with time. If stress is applied at a slower rate (i.e. over a longer period of time), the resulted strain will be more than that due to a stress applied at a rapid rate. Fig.2.11 shows the loading/unloading behaviour for two general cases. For creeping materials, the loading and unloading curve do not overlap with one another. The area between the two curves (called the hysteresis loop) reflects the energy absorped by the material over a loading/unloading cycle. This energy absorption varies with loading rate, and is highest at intermediate loading rate.

Fig.11 Hysteresis Behaviour under High and Low Loading Rates

2.3.2 Implications to Structural Design When materials exhibit time dependent behaviour, it will affect structural behaviour in a number of ways. The important effects of time behaviour are summarized below: (1) Due to creeping effects, the long term deformation of structures may be significantly

above the short term deflection. Therefore, we should provide enough allowance between panels and other attachments to the primary structure. For large structure, the long term differential creep in different parts of a structure needs to be checked to ensure no problems will be caused.

(2) The hysteresis loop as shown in Fig.2.11 indicates that energy can be absorbed during cyclic loading. The energy absorption results in damping of a structure as it is set under vibration (e.g., during an earthquake or typhoon). Note that the damping is frequency dependent, although this is often not considered in civil engineering designs, as damping is difficult to quantify in practice.

(3) In prestressed concrete design, the creeping of concrete and relaxation of steel can lead to the loss of prestress. This has to be accounted for in design, and in some cases, re-stressing of the prestressed tendon has to be carried out.

(4) Relaxation of a restrained member may lead to stress reversal. This is best illustrated by Fig.2.12, which shows a beam between two very stiff walls. As temperature increases, the beam tends to expand but its expansion is restrained by the walls. With this restraint, the beam is put under compression. Keeping the beam at the high temperature, it will eventually relax to a lower stress level. On cooling, the walls prevent the beam from contracting. As a result, tension is introduced.

σ

ε

Intermediate Loading Rate High Loading rate

Low Loading Rate

18

Beam

Stiff Walls

Fig. 2.12 A Beam constrained by Stiff Walls

2.3.3 Physical Basis of Time Dependent Behaviour Time dependent behaviour is due to the need of time for atoms or molecules to re-arrange themselves under load. For example, when a polymer is under stress, the polymeric chains tend to slide relative to one another. A finite time is required for the chains to go from one state (i.e., a given arrangement) to another. When loaded for a longer time, more movement will be resulted, leading to the phenomenon of creep. Relaxation can be explained in a similar way. When a strain is suddenly applied, there is little time for the polymer chains to move relative to one another. Most of the strain is then carried by the polymer chains themselves, resulting in high stress. As time progresses, the relative movement between the chains allows them to relax. The stress will then be significantly reduced. The rate at which molecular re-arrangement can occur depends on the thermal energy of the molecules. As temperature increases, the energy also increases and creeping (or relaxation) occurs at a higher rate. For metals and ceramics, the significance of creeping can be assessed by looking at the homologous temperature defined by T/Tm, where T is the current temperature and Tm is the melting point of the material. Both temperatures should be measured in the absolute scale (i.e., degree C plus 273). If T/Tm > 0.3 - 0.4 for metals, or if T/Tm > 0.4 - 0.5 for ceramics, creeping will start to become important. For polymers, the melting point is not well defined. Creeping becomes significant when the temperature goes above the glass transition temperature (TG) of the material. Physically, this is the temperature above which the van der Waal’s forces between polymer chains start to break. In other words, the chains start to slide after TG is exceeded. Creep and relaxation behaviour then comes into the scene. At room temperature, common materials that may creep significantly include concrete, wood, most polymers as well as lead, tin and glass. In general, the creep rate (i.e., the rate of strain increase under a given stress) increases with applied stress. Creep behaviour is not necessarily linear. For many metals and ceramics, the creep rate at high temperature is proportional to the stress raised to a high power. However, at room temperature and working stress levels, the creep strain of many common materials (polymers, wood, concrete) are linearly dependent on stress. In such a case, material behaviour can be described by models combining springs and dashpots. The studying of these models will constitute the subject matter of the next section.

19

2.3.4 Modelling of Creep at Low Temperature (Viscoelastic Models) Models with spring and dashpots can be used to describe linear creep behaviour. The spring (Fig.2.13(a)) is a linear elastic element with direct proportionality between stress and strain. For the dashpot (Fig.2.13(b)), the rate of straining is directly proportional to the applied stress. This is similar to the behaviour of viscous liquid, the strain rate of which is directly proportional to the applied shear stress. Since the material can be considered as a combination of linear elastic and viscous elements, it is called a linear viscoelastic material.

(a) Spring (b) Dashpot

ε = σ/E dε/dt = σ/η

Fig. 2.13 Spring and Dashpot for the Modelling of Viscoelastic Behaviour

Using one spring and one dashpot, two different models can be created by putting the elements either in series or in parallel. The behaviour of each of these simple models will be studied below. (I) Maxwell Model: (Spring and Dashpot in Series)

E η

Fig.2.14 Maxwell Model

In the Maxwell model, the material is considered to be made up of two parts in series. The elastic (time independent) part is represented by a spring with modulus E, and the viscous (time dependent) part is represented by a dashpot of viscosity η. The equation relating stress and strain (as well as time) for this model is dervied below. Under an applied stress σ, the strain in the spring (ε1) and the strain rate are given by: ε1 = σ/E ; dε1/dt = (1/E) dσ/dt The strain rate in the dashpot is given by: dε2/dt = σ/η The total strain, ε, is the sum of strain in the elastic and viscous parts. ε = ε1 + ε2 ; dε/dt = dε1/dt + dε2/dt which gives: (1/E) dσ/dt + σ/η = dε/dt as the governing equation for the material.

20

(1) Creep Behaviour under constant stress applied from 0 < t < t1 Under constant stress, dσ/dt = 0 dε/dt = σ/η; ε = (σ/η)t + ε(0) It takes finite time for the dashpot to respond to loading. Therefore, at t = 0, ε2(0)= 0 and the dashpot acts as if it is rigid. The initial strain is then resulted from the spring alone. ε(0) = σ/E ; ε = σ/E + (σ/η)t At t = t1, the load is completely removed. The spring shortens by an amount equal to σ/E. The remaining strain is (σ/η)t1. After load removal, σ = dσ/dt = 0, implying dε/dt = 0. The strain will stay constant for t > t1. The stress and strain are plotted against time in Fig.2.15 below.

σ ε

t1 t 1t t

Fig.2.15 Creep Behaviour under Constant Stress for the Maxwell Model

(2) Relaxation Behaviour (Constant Strain applied at t = 0) Under constant strain, dε/dt = 0. The governing equation gives: (1/E) dσ/dt = - σ/η Integrating both sides, and noting that σ(0) = Eε (dashpot stays undeformed) at t = 0, we have: σ = Eε exp(-Et/η)

ε σ

t t

Fig.2.16 Relaxation Behaviour of the Maxwell Model

(II) Kelvin-Voigt Model (Spring and Dashpot in parallel)

η

E

Fig.2.17 Kelvin-Voigt Model

21

For this model, the spring and dashpot are put under the same strain ε. Stress in the spring: σ1 = Eε Stress in the dashpot: σ2 = ηdε/dt The total stress (σ), which is the sum of σ1 and σ2, is related to ε through: ηdε/dt + Eε = σ The above is the governing equation for the Kelvin-Voigt model. (1) Creep Behaviour under constant stress applied from 0 < t < t1 The governing equation is a first order differential equation, which can be solved by the following procedure: Multiplying each side of the governing equation by exp(Et/η), we have dε/dt exp(Et/η) + (E/η) exp(Et/η) ε = (σ/η) exp(Et/η), The left hand side of the equation can be written as: d [ε exp(Et/η)]/dt. Carrying out the integration, and noting that ε(0) = 0 (because the dashpot takes a finite time to respond), the strain is given by: ε = (σ/E) [1 - exp(-Et/η)] If the stress is removed at t = t1. Then σ = 0 for t > t1. The governing equation becomes: ηdε/dt = - Eε Integrating, with ε = ε(t1) at t = t1 as the initial condition, gives: ε = ε(t1) exp[-E( t - t1)/η] The behaviour is illustrated in Fig.2.18

σ ε

t1 t 1t t

Fig.2.18 Relaxation Behaviour of the Kelvin-Voigt Model

(2) Relaxation Behaviour (Constant Strain applied at t = 0) At t = 0, dashpot is theoretically rigid. In other words, the strain should be zero. To force the strain to reach a finite value, infinite stress is required. For t > 0, the strain is constant, implying dε/dt = 0. The governing equation gives σ = Eε. The relaxation response is shown in Fig.2.19.

22

ε σ

t t

Infinite stress at t = 0

Fig.2.19 Relaxation Behaviour of the Kelvin-Voigt Model

In describing the creep/relaxation behaviour of real materials, each of the two models above has its own shortcomings. For the Maxwell model, the strain rate is constant, and after stress is removed, there is no time-dependent gradual strain recovery. For the Kelvin-Voigt model, no instantaneous material response is allowed, thus producing the artifact of infinite stress when a finite strain is suddenly applied. For real materials, applied stress is always accompanied by an instantaneous response. Subsequently, the strain will increase with time but at a decreasing rate. After stress is removed, part of the strain is recovered immediately, while another part will be slowly recovered after a period of time. To describe the behaviour of real materials, the two simple models can be combined as in Fig.2.20. This combined model is called the Burger’s body and can be used to describe the time-dependent behaviour of both concrete and wood.

E1 η1

η2

InstantaneousResponse

SteadyState Creep

TransientResponse

ε

t

InstantaneousResponse

TransientResponse

Steady StateCreep

Fig.2.20 The Burger’s Body and its Response to Constant Stress

2.3.5 Strain Response under Arbitrary Stress History – Superposition The creep strain for a unit stress, or creep compliance J(t), can be obtained experimentally from a single test (under constant stress). Once the compliance is known, the creep behaviour under a non-constant stress can be obtained by superposition as illustrated in Fig. 2.21. To apply superposition, any increase in stress level is replaced by a new constant stress applied at the time when stress change takes place. Decrease in stress level is replaced

23

by the removal of a constant stress. In the figure, the stress is shown to increase by discrete amounts. For a continuously changing stress, the stress history can be approximated with discrete stress increments occurring over very small time steps. This is the same principle behind numerical integration.

σ ε

t t

1

2

3

1

1 + 2

1 + 2 - 3

Fig.2.21 Illustration of the superposition principle

24

2.4 Fracture and fatigue

2.4.1 Introduction Fracture is the failure of materials due to the propagation of a crack. In the discussion of ductile behaviour, we have mentioned that the final failure in tension is due to fracture after the onset of necking. In such a case, a large elongation can be observed before final fracture takes place. We are therefore given plenty of warning. In many materials, however, failure occurs by fast fracture. When loading increases, the material (and hence the structure) behaves in an elastic manner. Then, fracture suddenly occurs without any warning. This failure mode, referred to as brittle failure, is exhibited by many common materials such as glass, rock and plain concrete. (Note: due to the presence of aggregates that act as bridges in the crack, fracture in concrete is often considered “quasi-brittle”. This will be further discussed in a later chapter.) Moreover, even for materials that normally behave in a ductile manner (e.g., steel, especially high strength steel), fast failure may occur under some circumstances. Indeed, the unexpected fracture failure of tanks, bridges and ships earlier in this century has resulted in a series of investigations leading to the present day understanding of fracture processes. Fast fracture is due to the sudden propagation of a crack inside a structural component at a load level below that required for yielding of a complete cross section. (Otherwise, yielding will occur instead.) Cracks pre-exist in many materials due to a number of reasons. When solid materials are formed, the densification may not be perfect. Trapped air in the molten or liquid state can turn into pores and cracks in the solidified material. During handling of materials, such as transportation of structural components and their installation, surface damages can be introduced. One common example is the scratch on the surface of window glass. When members are welded together, cracks may form around the weld due to residual stresses and phase changes in the material (this will be further discussed in the Steel chapter). Also, under repeated loading, cracks may nucleate in materials and grow larger with each loading cycle. The slow growth of crack in this manner is referred to as fatigue crack growth. In the following, the physical basis of fracture and a simple way to model fast fracture are first described, followed by a discussion of the various parameters affecting the change in failure mode. Then, our focus will turn to the studying of fatigue. Material fatigue leads to the gradual weakening of structural members and can often convert the failure mode from ductile to brittle. An understanding of fatigue is therefore essential in the assessment of long-term safety of structures.

2.4.2 Fast Fracture: Physical Basis and Modelling When loading is applied to a material, the stress at the tip of a sharp crack is infinite if elastic behaviour is assumed. Since no real material can stay elastic at very high stress levels, an inelastic zone will always be present in front of the crack tip (see Fig.2.22). In metals, inelastic behaviour is due to material yielding. For concrete, this is due to the formation of micro-cracks in front of the main crack. When the load is increased, the inelastic zone grows in size. Ultimately, the crack will propagate suddenly at a very high speed. An important question to address is: what is the criterion for fast fracture to occur?

25

Fig.2.22 Stress Distribution and Inelastic Zone in front of a Sharp Crack

To answer the above question, we need to consider the energy balance of a system when crack propagation occurs. Crack propagation requires energy. When a crack extends by a small amount (∆a) (Fig.2.23), new surfaces are formed. Since atoms on the material surface contain more energy than those in the bulk, surface energy needs to be provided. Also, when the crack propagates, energy is required to extend the inelastic region (see Fig.2.23).

additional Crack Area formeddue to Crack Propagation

Extension ofInelastic Zone

Fig.2.23 Energy Absorbing Mechanisms during Crack Propagation

To see where the required energy may come from, we can look at the structural

component after the crack has propagated by a small amount (Fig.2.24). With a slightly larger crack, the component becomes less stiff (i.e., it is easier to deform). If it is fixed on both ends, the stress will decrease all over the member and energy is released (Fig.2.24a). If it is under fixed load, the displacement at the loading points will increase (Fig2.24b). Additional work is therefore done on the member. Part of the work is converted into additional strain energy stored in the member (Note: in this case, the strain in the uncracked part of the member increases and more energy is stored). The rest is available for extending the crack. In summary, for the two limiting cases described above, and all other cases in between, crack propagation will be accompanied by a release of energy from the system. If this energy is sufficient for the formation of new surfaces and the extension of the inelastic zone, fracture will occur.

Distance from Crack Tip

Stress

Critical Stress

Inelastic Zone

Loading Direction

Crack

26

Under general conditions, the mathematical modelling of the fracture process is very difficult. However, if the inelastic zone is much smaller in size than the specimen, we can define a parameter called critical energy release rate (Gc) and use the following fracture criterion:

Fracture occurs when: G = Gc, where G is the energy release rate of the system under a given loading condition, which can be obtained in terms of the applied load and the specimen geometry. In many cases, instead of calculating G, we compute a parameter K defined by K = (EG)1/2. The fracture criterion is then converted into the form: Fracture occurs when: K = Kc = (EGc)1/2

K is a parameter of physical significance because it characterizes the stress concentration in front of the crack tip (Fig.2.25). Along the crack direction, the tensile stress (acting perpendicular to the crack) is given by: σ = K/(2πr)1/2

where r is the distance from the crack tip. K is called the stress intensity factor. Kc is called the critical stress intensity factor or simply the fracture toughness of the material.

Loading Direction

Distance fromCrack Tip, r

Stress

σ = K2πr

Fig.2.25 Variation of Stress in front of Crack Tip Values of K have been obtained for many common loading configurations. Some

examples are given in Fig. 2.26. Kc is a material parameter (i.e., it stays the same for the same material) and can be obtained from standard specimens in the laboratory.

27

2a

W

σ

σ

W

P

a

P/2 P/2S

P

W

a

P

K = σ πa (sec )πaW

1/2K =

PSBW 3/2 [ 2.9(a/W) - 4.6(a/W) + 21.8(a/W)

- 37.6(a/W) + 38.7(a/W) ]9/27/2

5/23/21/2

K =P

BW 1/2 [ 29.6(a/W) - 185.5(a/W) + 655.7(a/W) - 1017(a/W) + 63.9(a/W) ]9/27/2

5/23/21/2

Fig.2.26 Stress Intensity Factor for a few Common Loading Configurations

2.4.3 Failure of Metal: Ductile or Brittle

As we mention earlier, metals can sometimes fail in a brittle manner. In this section, we will look at the various factors affecting the failure mode of metals. (Note: similar arguments can be made for other materials though the analysis is often more complicated.) Consider a steel plate with a small internal crack of size 2a, under uniform tensile stress. If the width W is very large compared with 2a, sec(2a/W) is very close to unity. The stress intensity factor is then given by (see Fig.2.26): K = σ(πa)1/2 Fast fracture occurs when K=Kc, or at an applied stress of: σ = σF = Kc/(πa)1/2

Material failure can also occur in a ductile manner when σ = σy. Gross yielding will then occur over the whole cross section of the material. Whether failure will be brittle or ductile depends on the relative magnitude of σF and σy. Since σF decreases with increasing crack size, for a member with a relatively large crack, failure will be brittle. For a member with a small crack, ductile failure will occur. This is illustrated in Fig.2.27. The transition crack size (aT) is given by: aT = (1/π)(Kc/σy)2

28

Crack Size, a

σ

BrittleFracture

GrossYielding

σ = σ y

σ = K / πac

a T Fig.2.27 Transition between Brittle and Ductile Failure Modes

The transition crack size is a function of the fracture toughness and yield strength of

the material. For a tough metal with low yield strength, the failure can stay ductile at a larger crack size. For strong metals with low toughness, failure is brittle even if only a small crack exists. The transition crack size depends on temperature and strain rate. Yielding is due to the movement of dislocations in the atomic lattice, which requires a finite amount of time. When loading is very rapid, or when temperature is very low (so the atoms are at very low energy levels), it is more difficult for dislocations to move and the yield strength tends to increase. With less yielding, the inelastic zone in front of the crack tip becomes smaller. As the crack propagates, the newly formed inelastic region (shaded area in Fig.2.23) will also be smaller in size. The energy required for crack propagation then also decreases, leading to a lower material toughness. With higher yield strength and reduced fracture toughness, the transition crack size can decrease significantly. In other words, for a given structural member with a fixed crack size, brittle fracture is more likely to occur at low temperatures or under impact loading. With an understanding of the relation between yield strength and fracture toughness, we can also explain why the strengthening of metals (through alloying, for example) will often reduce the fracture toughness. When very high strength metals are used in structures, extra care should be taken to make sure that failure will not occur in a brittle manner (e.g., the structure can be inspected for crack size to ensure that the maximum crack size is below the transition value).

2.4.4 Fatigue - Phenomenon and Empirical Expressions

When cyclic loading is applied to a material, failure may occur at a stress much lower than the strength under static loading. This apparent weakening of the material is called fatigue. The strength reduction with the number of load cycles is illustrated in Fig.2.28 with the S-N diagram. This diagram, which can be obtained experimentally, is useful for component design. Once we know the number of load cycles a structural component is expected to endure over its life span, the appropriate strength value can be chosen. It should be noted that the strength approaches a constant value for very large N. This value is called the fatigue threshold. If applied stress is kept below this value, the material can sustain an infinite number of cycles.

29

Number of Cycles, N

Stre

ngth

Fig.2.28 The S-N Curve under Cyclic Loading

Besides reading off the strength from the S-N curve, various empirical expressions have been proposed to relate the magnitude of cyclic loading or stress range (∆σ) to the number of cycles to failure (Nf). Here, ∆σ is defined as the difference between the maximum applied stress (σmax) and the minimum applied stress (σmin). Also, we can define σm to be the mean stress during load application. These definitions are illustrated in Fig.2.29. In equation form, they are: ∆σ = σmax - σmin σm = (σmax + σmin)/2

time

σ

∆σmaxσ

minσmσ

Fig.2.29 Definition of terms for Cyclic Loading

In the study of fatigue behaviour, we have to distinguish between high cycle and low cycle fatigue. In high cycle fatigue, the applied stress is often low so neither σmax nor σmin are high enough to cause gross yielding (in tension and compression respectively). The number of cycles to failure is then high. In low cycle fatigue, one or both of σmax and σmin exceed the yield strength. Failure will then occur after a small number of cycles. For high cycle and low cycle fatigue under zero mean stress (σm = 0), the following expressions have been proposed: Basquin’s Law for high cycle fatigue: ∆σ (Nf)a = C1 where C1 and ‘a’ are constants. For common materials, ‘a’ range from about 1/8 to 1/15. Coffin-Manson Law for low cycle fatigue: ∆εPL (Nf)b = C2

30

where C2 and b are constants, with ‘b’ varying between 0.5 and 0.6. After yielding has occurred, the variation of plastic strain (∆εPL), rather than the stress variation itself, is found to govern fatigue behaviour. When the mean stress is non-zero, the number of cycles to failure will decrease for a given stress range. To keep the same number of cycles to failure, the stress range ∆σο needs to be reduced to ∆σσm in accordance with Goodman’s Rule: ∆σσm = ∆σο ( 1 - |σm| / σTS ) In the equation, |σm| is the absolute value of the mean stress and σTS is the ultimate strength in tension. When the magnitude of cyclic loading is not constant, the lifetime can be predicted with Miner’s rule: Σ(Ni/Nfi) =1 where Ni is the number of cycles under ∆σο and Nfi is the number of cycles to failure under ∆σο. Physically, the equation means that every time load cycles are applied, a part of the structural life is used. Eventually, when all the lifetime is used up, failure will occur. It should be noted that the expressions presented in this section are all based on experimental data. The constants in Basquin’s law and Coffin-Manson law are dependent on loading configuration (e.g., direct tension-compression or bending) as well as specimen type (e.g., rod vs plate). These empirical laws are useful when a component is tested in the same way as it will be used in practice. For example, the fatigue results for a steel reinforcing bar under direct tension and compression can be used directly in practice because this is the way a reinforcing bar will be loaded in a real structure. In more general cases, the prediction of fatigue failure requires an understanding of the fatigue process. This will be the focus of the next section.

2.4.5 Physical Basis of Fatigue and K-Based Modelling For an initially uncracked component, the formation of cracks under cyclic loading is illustrated in Fig.2.30(a). At locations of stress concentrations (e.g. bends, corners), local yielding may occur. Dislocation movements lead to sliding of materials at an angle to the applied stress. In some locations, sliding will lead to the formation of extrusions on the surface while in some other locations, intrusions will be present. An intrusion will act like a sharp notch to initiate the propagation of a crack. The crack, which is originally parallel to the sliding direction, eventually orients itself perpendicular to the applied stress. Fig.2.30(b) illustrates the growth of an existing crack. When the maximum stress is applied, the crack opens. Yielding and the associated material sliding result in the formation of new surface at the crack tip. When stress decreases, the crack starts to close (fully or partially) and the new surface folds forward to extend the crack. Note that the area that can fold forward depends on the difference in crack openings at maximum and minimum stress. This explains the significance of stress range ∆σ in fatigue behaviour. Slow crack growth under cyclic loading leads to the gradual weakening of a structural component, because the fracture stress decreases with crack size. Also, as the crack grows larger, the failure mode may change from ductile to brittle.

31

Extrusions

Intrusions producesa Sharp Notch

Crack Initiated from Notch Tip

(a) (b)

Kmin

Kmax

Kmin

New SurfaceFormed

New SurfaceFolds Forward

Preferred SlidingDirection

Fig.2.30 Mechanisms for (a) Crack Initiation and (b) Crack Propagation during Fatigue

The modelling of crack initiation (Fig.2.30a) is very difficult. However, for many

large structures used in civil engineering (such as bridges, storage tanks, pressure vessels, etc), cracks are almost always present at the joints, especially when welding is carried out. We can therefore focus on the modelling of crack propagation. The design strategy is as follows. For a structural component, we calculate (using the approach described in 2.4.3) the critical crack size before fast fracture occurs. Then, after the structure is built, important components are inspected for the initial crack size. If no cracks are found, we use the resolution of inspection as the initial crack size. For example, if the inspection can only reveal cracks 1mm in size or larger, 1 mm is used as a conservative estimate of initial crack size. Knowing the initial and critical crack sizes, the number of cycles to failure can be calculated with the help of Paris’ law, which states: da/dN = A(∆K)n da/dN is the growth in crack size per unit cycle A and n are constants obtained from experiments ∆K = Kmax - Kmin is the change in stress intensity factor during the loading cycle. Note that ∆K is a function of crack size ‘a’. The equation can be re-arranged in the following form: dN = da / [A(∆K)n] N goes from zero to Nf when the crack grows from the initial size to the critical. Nf can therefore be obtained through direct integration.

where ai is the initial crack size and ac is the critical crack size when fast occur occurs under the applied load.

∫∆

=c

i

a

a nf])K(A[

daN

CIVL 111 CONSTRUCTION MATERIALS Chapter 3 Aggregates

3.1 Introduction Aggregates are defined as inert, granular, and inorganic materials that normally consist of stone or stone-like solids. Aggregates can be used alone (in road bases and various types of fill) or can be used with cementing materials (such as Portland cement or asphalt cement) to form composite materials or concrete. The most popular use of aggregates is to form Portland cement concrete. Approximately three-fourths of the volume of Portland cement concrete is occupied by aggregate. It is inevitable that a constituent occupying such a large percentage of the mass should have an important effect on the properties of both the fresh and hardened products. As another important application, aggregates are used in asphalt cement concrete in which they occupy 90% or more of the total volume. Once again, aggregates can largely influence the composite properties due to its large volume fraction. 3.2 Classification of aggregate Aggregates can be divided into several categories according to different criteria. a) In accordance with size:

Coarse aggregate: Aggregates predominately retained on the No. 4 (4.75 mm) sieve. For mass concrete, the maximum size can be as large as 150 mm.

Fine aggregate (sand): Aggregates passing No.4 (4.75 mm) sieve and predominately retained on the No. 200 (75 μm) sieve.

b) In accordance with sources:

Natural aggregates: This kind of aggregate is taken from natural deposits without changing their nature during the process of production such as crushing and grinding. Some examples in this category are sand, crushed limestone, and gravel.

Manufactured (synthetic) aggregates: This is a kind of man-made materials produced as a main product or an industrial by-product. Some examples are blast furnace slag, lightweight aggregate (e.g. expanded perlite), and heavy weight aggregates (e.g. iron ore or crushed steel).

c) In accordance with unit weight

Light weight aggregate: The unit weight of aggregate is less than 1120 kg/m3. The corresponding concrete has a bulk density less than 1800 kg/m3. (cinder, blast-furnace slag, volcanic pumice).

36

Normal weight aggregate: The aggregate has unit weight of 1520-1680 kg/m3. The concrete made with this type of aggregate has a bulk density of 2300-2400 kg/m3. Heavy weight aggregate: The unit weight is greater than 2100 kg/m3. The bulk density of the corresponding concrete is greater than 3200 kg/m3. A typical example is magnesite limonite, a heavy iron ore. Heavy weight concrete is used in special structures such as radiation shields.

3.3 Properties of aggregate 3.3.1 Moisture conditions The moisture condition of aggregates refers to the presence of water in the

pores and on the surface of aggregates. There are four different moisture conditions:

a) Oven Dry (OD): This condition is obtained by keeping aggregates

at temperature of 1100C for a period of time long enough to reach a constant weight.

b) Air Dry (AD): This condition is obtained by keeping aggregates

under room temperature and humidity. Pores inside the aggregate are partly filled with water.

c) Saturated Surface Dry (SSD): In this situation the pores of the

aggregate are fully filled with water and the surface is dry. This condition can be obtained by immersion in water for 24 hours following by drying of the surface with wet cloth.

d) Wet (W): The pores of the aggregate are fully filled with water and

the surface of aggregate is covered with a film of water.

Saturated Oven Dry Air Dry Surface Dry Wet OD AD SSD

37

3.3.2 Moisture content (MC) calculations

a) Relative to oven dry condition

%100W

WW)OD(MCOD

ODstock −=

where Wstock = weight of aggregates in stock WOD = weight of oven dry aggregates b) Relative to saturated surface dry condition

%100W

WW)SSD(MCSSD

SSDstock −=

where Wstock = weight of aggregates in stock WSSD = weight of aggregates in SSD condition c) Absorption capacity

%100W

WWAbsorptionOD

ODSSD −=

To make concrete, aggregates are mixed with water and cement. Since concrete properties at both the fresh and hardened states are strongly affected by the water content, it is very important to ensure that the right amount of water is added to the mix. In designing concrete mix, the moisture content under SSD condition is used as reference because that is an equilibrium condition at which the aggregates will neither absorb water nor give up water to the paste. Thus, if MCSSD value for a batch of aggregates is positive, there is surface moisture on the aggregates. If it is negative, it means that the pores in aggregates are only partly filled with water. Since the aggregates may give out or absorb water, the amount of water added to the mix need to be adjusted according to the MCSSD value. This is particularly important for concrete with low water content as the amount of adjusted water can be a significant portion of the total amount. 3.3.3 Density and specific gravity Definitions Density (D): weight per unit volume (excluding the pores inside a

single aggregate)

solidVweightD =

Bulk density: the volume includes the pores inside a single

aggregate.

38

poressolid VVweightBD+

=

BD can be either BDSSD or BDAD according to the moisture condition of aggregate when it is weighed.

Specific gravity (SG): mass of a given substance divided by unit

mass of an equal volume of water (it is the density ratio of a substance to water).

Depending on the definition of volume, the specific gravity can be

divided into absolute specific gravity (ASG) and bulk specific gravity(BSG).

w

solid D waterof density

Vparticle of weight

ASGρ

==

and

w

poressolid BD waterof density

VVparticle of weight

BSGρ

=+

=

In practice, the BSG value is the realistic one to use since the effective volume that aggregate occupies in concrete includes its internal pores. The BSG of most rocks is in the range of 2.5 to 2.8. Similar to BD, BSG can be either BSGSSD or BSGAD according to the moisture condition of aggregates. The BSG can be determined using the displacement method. In this method, Archimedes’ principle is utilized. The weight of aggregate is first measured in air, e.g. under SSD condition, this is denoted as WSSD in air. Then, the weight of the sample is measured in water, the value being denoted as WSSD in water. Thus, we have:

waterin SSDair in SSD

air in SSD

ntdisplaceme

air in SSDSSD

W-WW

WWBSG

=

=

Where, Wdisplacement is the weight of water displaced by the aggregates.

39

3.3.4 Unit Weight (UW) (except for pores inside every aggregate, the bulk volume includes the spacing among aggregate particles).

The unit weight is defined as weight per unit bulk volume for bulk aggregates. Besides the pores inside each aggregate, the bulk volume also includes the space among the collection of particles. According to the weight measured at different conditions, the unit weight can be divided into UW (SSD) and UW (OD).

spacingporessolid

SSD

VVVW)SSD(UW

++=

and

spacingporessolid

OD

VVVW)OD(UW

++=

The percentage of spacing (voids) among the aggregates can be calculated as

%100BD

UWBD)void(Spacing −=

3.4 Grading of aggregates

3.4.1 Grading - size distribution The particle size distribution of aggregates is called grading. The grading determine the paste requirement for a workable concrete since the amount of void requires needs to be filled by the same amount of cement paste in a concrete mixture. To obtain a grading curve for aggregate, sieve analysis has to be conducted. The commonly used sieve designation is as follows: Sieve designation Nominal size of sieve opening 3" 75 mm 1.5" 37.5 mm 3/4" 19 mm 3/8" 9.5 mm No. 4 4.75 mm No. 8 2.36 mm No. 16 1.18 mm No.30 600 μm No.50 300 μm No.100 150 μm No.200 75 μm

40

Five different kinds of size distributions, dense graded, gap-graded, uniformly graded, well graded and open graded are illustrated in the figure below. Dense and well-graded aggregates are desirable for making concrete, as the space between larger particles is effectively filled by smaller particles to produce a well-packed structure. Gap-grading is a kind of grading which lacks one or more intermediate size. Gap-graded aggregates can make good concrete when the required workability is relatively low. When they are used in high workability mixes, segregation may become a problem. For the uniform grading, only a few sizes dominate the bulk material. With this grading, the aggregates are not effectively packed, and the resulting concrete will be more porous, unless a lot of paste is employed. The open graded contains too much small particles and easy to be disturbed by a hole.

A wide range of grading curves is acceptable for the economic production of concrete with good quality. Both British Standards (B.S.) and American Standards of Testing and Measurements (ASTM) provide grading limits (which are essentially upper and lower bounds of the grading curve) that can be used in practice. As long as the grading curve lies within the recommended grading limits, the aggregate can be employed.

41

3.4.2 Fineness modulus To characterize the overall coarseness or fineness of an aggregate, a concept of fineness modulus is developed. The Fineness Modulus is defined as

100)percentage retained ve(Cummulati

modulus Fineness ∑=

To calculate the fineness modulus, the sum of the cumulative percentages retained on a definitely specified set of sieves needs to be determined, and the result is then divided by 100. The sieves specified for the determination of fineness modulus are No. 100, No. 50, No. 30, No. 16, No. 8, No. 4, 3/8", 3/4", 1.5", 3", and 6". The following table provide an example for calculating the fineness modulus.

Table 3-1 Sieve analysis of aggregate

The Fineness Modulus for fine aggregates should lie between 2.3 and 3.1. A small number indicates a fine grading; whereas a large number indicates a coarse material. The fineness modulus can be used to check the constancy of grading when relatively small change is expected; but it should not be used to compare the grading of aggregates from two different sources. The fineness modulus of fine aggregates is required for mix proportion since sand gradation has the largest effect on workability. A fine sand (low fineness modulus) needs more water for good workability. ASTM specifies that the variation of fineness modulus for different batches of a given mix should not exceed 0.2.

3.4.3 Fineness modulus for blending of aggregates

Blending of aggregates is undertaken for a variety of purposes, for instance, to remedy deficiencies in grading. The fineness modulus of blended aggregates can be calculated if the values for the component aggregates are known. If two aggregates,

42

designated as A and B, with fineness moduli of FMA and FMB, respectively, are mixed, the resultant blend will have the following fineness modulus:

100PFM

100PFMFM B

BA

Ablend +=

where, PA and P are the percentages, by weight, of aggregate A and B in the blend. B 3.5 Shape and texture of aggregate Aggregate shape and surface texture influence the properties of freshly mixed concrete more than the properties of hardened concrete. Rough-textured, angular, and elongated particles require more water to produce workable concrete than smooth, rounded compact aggregate. Consequently, the cement content must also be increased to maintain the water-cement ratio. However, with rough aggregates, there is better mechanical bond in the hardened concrete, so strength is higher (if concrete with the same w/c ratio is compared). Hence, when smooth aggregates are replaced with rough aggregates, concrete of similar flow properties and strength can be produced by adding a little bit more water. In the following figure, both rounded (the first row) and angular (second row) aggregates are shown. The surface/volume ratio of spherical aggregates is the smallest. Near-spherical aggregates need less water for mixing and are desirable. Flat, needle-shaped and elongated particles should be avoided, as they require more water and are prone to segregation. When used in concrete, these aggregates can also lead to high stress concentrations and hence a reduction in strength. Generally, flat and elongated particles should be limited to about 15 percent by weight of the total aggregate.

43

CIVL 111 CONSTRUCTION MATERIALS

Chapter 4 Portland Cement Concrete is made by portland cement, water and aggregates. Portland cement is a hydraulic cement that hardens in water to form a water-resistant compound. The hydration products act as binder to hold the aggregates together to form concrete. The name portland cement comes from the fact that the colour and quality of the resulting concrete are similar to Portland stone, a kind of limestone found in England. 4.1 Manufacture of Portland cement

Portland cement is made by blending the appropriate mixture of limestone and clay or shale together and by heating them at 1450oC in a rotary kiln. The sequence of operations is shown in following figure. The preliminary steps are a variety of blending and crushing operations. The raw feed must have a uniform composition and be a size fine enough so that reactions among the components can complete in the kiln. Subsequently, the burned clinker is ground with gypsum to form the familiar gray powder known as Portland cement.

44

The raw materials used for manufacturing Portland cement are limestone, clay and Iron ore. a). Limestone (CaCO3) is mainly providing calcium in the form of calcium oxide (CaO) CaCO3 (1000oC) → CaO + CO2 b). Clay is mainly providing silicates (SiO2) together with small amounts of Al2O3 + Fe2O3 Clay (1450oC) → SiO2 + Al2O3 + Fe2O3 + H2O c). Iron ore and Bauxite are providing additional aluminum and iron oxide (Fe2O3) which help the formation of calcium silicates at low temperature. They are incorporated into the raw mix. Limestone 3 CaOoSiO2 High temperature 2 CaOoSiO2 Clay (1,450 oC) 3 CaOoAl2O3 Iron Ore, Bauxite 4 CaOoAl2O3

oFe2O3 d). The clinker is pulverized to small sizes (< 75 μm). 3-5% of gypsum (calcium sulphate)

is added to control setting and hardening. The majority particle size of cement is from 2 to 50 μm. A plot of typical particle size distribution is given below. (Note: “Blaine” refers to a test to measure particle size in terms of surface area/mass)

45

4.2 Chemical composition a). Abbreviation: CaO = C, SiO2 = S, Al2O3 = A; Fe2O3 =F, Ca(OH)2 = CH, H2O = H, SO3 = S (sulphur trioxide)

Thus we can write 3 CaO = C3 and 2 CaOoSiO2 = C2S. b). Major compounds Compound Oxide colour Common name Weight percentage composition Tricalcium Silicate C3S white Alite 50% Dicalcium Silicate C2S white Belite 25% Tricalcium aluminate C3A white/grey --- 12% Tetracalcium Aluminoferrite C4AF black Ferrite 8% Since the primary constituents of Portland cement are calcium silicate, we can define Portland cement as a material which combine CaO SiO2 in such a proportion that the resulting calcium silicate will react with water at room temperature and under normal pressure. c). Minor components of Portland cement The most important minor components are gypsum, MgO, and alkali sulfates. Gypsum (2CaSO4

o2H2O) is an important component added to avoid flash set (to be discussed in a latter section). Alkalies (MgO, Na2O, K2O) can increase pH value up to 13.5 which is good for reinforcing steel protection. However, for some aggregates, such a high alkaline environment can cause alkali aggregate reaction problem.

46

4.3 Hydration The setting and hardening of concrete are the result of chemical and physical processes that take place between Portland cement and water, i.e. hydration. To understand the properties and behavior of cement and concrete some knowledge of the chemistry of hydration is necessary. A). Hydration reactions of pure cement compounds The chemical reactions describing the hydration of the cement are complex. One approach is to study the hydration of the individual compounds separately. This assumes that the hydration of each compound takes place independently of the others. I). Calcium silicates Hydration of the two calcium silicates give similar chemical products, differing only in the amount of calcium hydroxide formed, the heat released, and reaction rate.

2 C3S + 7 H → C3S2H4 + 3 CH

2 C2S + 5 H → C3S2H4 + CH The principal hydration product is C3S2H4, calcium silicate hydrate, or C-S-H (non-stoichiometric). This product is not a well-defined compound. The formula C3S2H4 is only an approximate description. It has amorphous structure making up of poorly organized layers and is called glue gel binder. C-S-H is believed to be the material governing concrete strength. Another product is CH - Ca(OH)2, calcium hydroxide. This product is a hexagonal crystal often forming stacks of plates. CH can bring the pH value to over 12 and it is good for corrosion protection of steel. II). Tricalcium aluminate

Without gypsum, C3A reacts very rapidly with water:

C3A + 6 H → C3AH6

The reaction is so fast that it results in flash set, which is the immediate stiffening after mixing, making proper placing, compacting and finishing impossible.

With gypsum, the primary initial reaction of C3A with water is :

C3A + 3 (C S H2) + 26 H → C6A S 3H32

The 6-calcium aluminate trisulfate-32-hydrate is usually called ettringite. The formation of ettringite slows down the hydration of C3A by creating a diffusion barrier around C3A. Flash set is thus avoided. Even with gypsum, the formation of ettringite occurs faster than the hydration of the calcium silicates. It therefore contributes to the initial stiffening, setting and early strength development. In normal cement mixes, the ettringite is not stable and will further react to form monosulphate (C4A S H18).

47

B) Kinetics and Reactivities The rate of hydration during the first few days is in the order of C3A > C3S > C4AF >C2S. Their reactivities can be observed in the following figures.

48

C). Calorimetric curve of Portland cement

A typical calorimetric curve of Portland cement is shown in the following figure. The second heat peaks of both C3S and C3A can generally be distinguished, although their order of occurrence can be reversed.

From the figure, five stages can be easily identified. Since C3S is a dominating component in cement, the five stages above can be explained using the reaction process of C3S by the following table.

49

On first contact with water, calcium ions and hydroxide ions are rapidly released from the surface of each C3S grain; the pH values rises to over 12 within a few minutes. This hydrolysis slows down quickly but continues throughout the induction period. The induction (dormant) period is caused by the need to achieve a certain concentration of ions in solution before crystal nuclei are formed for the hydration products to grow from. At the end of dormant period, CH starts to crystallize from solution with the concomitant formation of C-S-H and the reaction of C3S again proceeds rapidly (the third stage begin). CH crystallizes from solution, while C-S-H develops from the surface of C3S and forms a coating covering the grain. As hydration continues, the thickness of the hydrate layer increases and forms a barrier through which water must flow to reach the unhydrated C3S and through which ions must diffuse to reach the growing crystals. Eventually, movement through the C-S-H layer determines the rate of reaction. The process becomes diffusion controlled. D). Setting and Hydration Initial set of cement corresponds closely to the end of the induction period, 2-4 hours after mixing. Initial set indicates the beginning of forming of gel or beginning of solidification. It represents approximately the time at which fresh concrete can no longer be properly mixed, placed or compacted. The final set occurs 5-10 hours after mixing, within the acceleration period. It represents approximately the time after which strength develops at a significant rate. In practice, initial and final set are determined in a rather arbitrary manner with the penetration test. While the determination of initial and the final set has engineering significance, there is no fundamental change in hydration process for these two different set conditions.

4.4 Types of Portland cements

According to ASTM standard, there are five basic types of Portland cement. Type I regular cement, general use, called OPC

Type II moderate sulphate resistance, moderate heat of hydration, C3A < 7%

Type III With increased amount of C3S, High early strength

Type IV Low heat

Type V High sulphate resistance

(Note: sulphates can react with C4A S H18 to from an expansive product. By reducing the C3A content, there will be less C4A S H18 formed in the hardened paste)

50

Their typical chemical composition is given in the following table:

From the above table, we can evaluate the behavior of each type of cement and provide the standard in selecting different cement types. The following figures show the strength and temperature rise for the different types of cement.

51

These graphs provide the basic justification in selecting the cement for engineering

application. For instance, for massive concrete structure, hydration heat is an important consideration because excessive temperature increase (to above 50-60oC) will cause expansion and cracking. Hence, type IV cement should be the first candidate and Type III should not be used. For a foundation exposed to groundwater with high concentration of sulphates, high sulphate resistance is needed. Thus, type V should be selected. If high early strength is needed, type III will be the best choice. But, generally, type I is the most popular cement used for civil engineering.

4.5 Porosity of hardened cement paste and the role of water Knowledge of porosity is very useful since porosity has a strong influence on strength and durability. In hardened cement paste, there are several types of porosity, trapped or entrained air (0.1 to several mm in size), capillary pores (0.01 to a few microns) existing in the space between hydration products, and gel pores (several nanometers or below) within the layered structure of the C-S-H. The capillary pores have a large effect on the strength and permeability of the hardened paste itself. Of course, the presence of air bubbles can also affect strength.

From experiments, the porosity within the gel for all normally hydrated cements is the same, with a value of 0.26. The total volume of hydration products (cement gel) is given by Vg = 0.68α cm3/g of original cement where α represents the degree of hydration.

52

The capillary porosity can be calculated by

α36.0cwPc −= cm3/g of original cement

where w is the original weight of water and c is the weight of cement and w/c is the water-cement ratio. It can be seen that with increase of w/c, the capillary pores increase. The gel / space ratio (X) is defined as

c/w32.068.0

porescapillary of volumegel of volumepores) gel (including gel of volmeX

+=

+=

αα

The minimum w/c ratio for complete hydration is usually assumed to be 0.36 to 0.42. It should be indicated that complete hydration is not essential to attain a high ultimate strength. For pastes of low w/c ratio, residual unhydrated cement will remain.

To satisfy workability requirements, the water added in the mix is usually more than that needed for the chemical reaction. Part of the water is used up in the chemical reaction. The remaining is either held by the C-S-H gel or stored in the capillary pore. Most capillary water is free water (far away from the pore surface). On drying, they will be removed, but the loss of free water has little effect on concrete. Loss of adsorbed water on surfaces and those in the gel will, however, lead to shrinkage. Movement of adsorbed and gel water under load is a cause of creeping in concrete 4.6 Basic tests of Portland cement a). Fineness (= surface area / weight): This test determines the average size of

cement grains. The typical value of fineness is 350 m2 / kg. Fineness controls the rate and completeness of hydration. The finer a cement,

the more rapidly it reacts, the higher the rate of heat evolution and the higher the early strength.

I III V Fineness (m2 / kg) 350 450 350

f’c 1-day (MPa) 6.9 13.8 6.2 b). Normal consistency test: This test is to determine the water required to achieve

a desired plasticity state (called normal consistency) of cement paste. It is obtained with the Vicat apparatus by measuring the penetration of a loaded needle.

c). Time of setting: This test is to determine the time required for cement paste to

harden. Initial set can not be too early due to the requirement of mixing,

53

conveying, placing and casting. Final set can not be too late owing to the requirement of strength development.

Time of setting is measured by Vicat apparatus. Initial setting time is defined as the time at which the needle penetrates 25 mm into cement paste. Final setting time is the time at which the needle does not sink visibly into the cement paste.

d). Soundness: Unsoundness in cement paste refers to excessive volume change

after setting. Unsoundness in cement is caused by the slow hydration of MgO or free lime. Their reactions are MgO +H2O = Mg(OH)2 and CaO + H2O = Ca (OH)2. Another factor that can cause unsoundness is the delayed formation of ettringite after cement and concrete have hardened. The pressure from crystal growth will lead to cracking and damage. The soundness of the cement must be tested by accelerated methods. An example is the Le Chatelier test (BS 4550). This test is to measure the potential for volumetric change of cement paste. Another method is called Autoclave Expansion test (ASTM C151) which use an autoclave to increase the temperature to accelerate the process.

e). Strength: The strength of cement is measured on mortar specimens made of

cement and standard sand (silica). Compression test is carried out on a 2" cube with S/C ratio of 2.75:1 and w/c ratio of 0.485 for Portland cements. The specimens are tested wet, using a loading rate at which the specimen will fail in 20 to 80 s. The direct tensile test is carried out on a specimen shaped like a ∞. The load is applied through specifically designed grips. Flexural strength is measured on a 40 x 40 x 160 mm prism beam test under a center-point bending.

f). Heat of hydration test. (BS 4550: Part 3: Section 3.8 and ASTM C186).

Cement hydration is a heat releasing process. The heat of hydration is usually defined as the amount of heat evolved during the setting and hardening at a given temperature measured in J/g. The experiment is called heat of solution method. Basically, the heat of solution of dry cement is compared to the heats of solution of separate portion of the cement that have been partially hydrated for 7 and 28 days. The heat of hydration is then the difference between the heats of solution of dry and partially hydrated cements for the appropriate hydration period. This test is usually done on Type II and IV cements only, because they are used when heat of hydration is an important concern. Excessive heating may lead to cracking in massive concrete construction.

g). Other experiments. Including sulphate expansion and air content of mortar. h). Cement S. G and U. W.: The S.G. for most types of cements is 3.15, and UW

is 1000-1600 kg /m3.

54

CIVL 111 CONSTRUCTION MATERIALS Chapter 5 Concrete

5.1 Introduction 5.1.1 Concrete: definition and composition Concrete is a composite material composed of coarse granular material (the aggregate or filler) embedded in a hard matrix of material (the cement or binder) that fills the space between the aggregate particles and glues them together. We can also consider concrete as a composite material that consists essentially of a binding medium within which are embedded particles or fragments of aggregates. The simplest representation of concrete is: Concrete = Filler + Binder. According to the type of binder used, there are many different kinds of concrete. For instance, Portland cement concrete, asphalt concrete, and epoxy concrete. In concrete construction, the Portland cement concrete is utilized the most. Thus, in our course, the term concrete usually refers to Portland cement concrete. For this kind of concrete, the composition can be presented as follows Cement (+ Admixture) → Cement paste + Water + → mortar fine aggregate + → concrete coarse aggregate Here we should indicate that admixtures are almost always used in modern practice and thus become an essential component of modern concrete. Admixtures are defined as materials other than aggregate (fine and coarse), water, fibre and cement, which are added into concrete batch immediately before or during mixing. The widespread use of admixture is mainly due to the many benefits made possible by their application. For instance, chemical admixtures can modify the setting and hardening characteristic of cement paste by influencing the rate of cement hydration. Water-reducing admixture can plasticize fresh concrete mixtures by reducing surface tension of water, air-entraining admixtures can improve the durability of concrete, and mineral admixtures such as pozzolans (materials containing reactive silica) can reduce thermal cracking. A detailed description of admixtures will be given in latter sections. 5.1.2 Advantages and limitations Concrete is the most widely used construction material in the world. It is used in many different structures such as dam, pavement, building frame or bridge. Also, it is the most widely used material in the world, far exceeding other materials. Its worldwide production exceeds that of steel by a factor of 10 in tonnage and by more than a factor of 30 in volume. The present consumption of concrete is over 10 billion tons a year, that is, each person on earth consumes more than 1.7 ton of concrete per year. It is more than 10 times of the consumption by weight of steel. Concrete is neither as strong nor as tough as steel, so why is concrete so popular?

55

Advantages: a) Economical: Concrete is the most inexpensive and the most readily available

material. The cost of production of concrete is low compared with other engineered construction materials.

Three major components: water, aggregate and cement. Comparing with steel, plastic and polymer, they are the most inexpensive materials and available in every corner of the world. This enables concrete to be locally produced anywhere in the world, thus avoiding the transportation costs necessary for most other materials.

b). Ambient temperature hardened material: Because cement is a low temperature

bonded inorganic material and its reaction occurs at room temperature, concrete can gain its strength at ambient temperature.

c) Ability to be cast: It can be formed into different desired shape and sizes right at

the construction site. d) Energy efficiency: Low energy consumption for production, compare with steel

especially. The energy content of plain concrete is 450-750 kWh / ton and that of reinforced concrete is 800-3200 kWh/ton, compared with 8000 kWh/ton for structural steel.

e) Excellent resistance to water. Unlike wood and steel, concrete can harden in

water and can withstand the action of water without serious deterioration. This makes concrete an ideal material for building structures to control, store, and transport water. Examples include pipelines (such as the Central Arizona Project, which provide water from Colorado river to central Arizona. The system contains 1560 pipe sections, each 6.7 m long and 7.5 m in outside diameter 6.4 m inside diameter), dams, and submarine structures. Contrary to popular belief, pure water is not deleterious to concrete, even to reinforced concrete: it is the chemicals dissolved in water, such as chlorides, sulfates, and carbon dioxide, which cause deterioration of concrete structures.

f). High temperature resistance: Concrete conducts heat slowly and is able to store

considerable quantities of heat from the environment (can stand 6-8 hours in fire) and thus can be used as protective coating for steel structure.

g). Ability to consume waste: Many industrial wastes can be recycled as a substitute

for cement or aggregate. Examples are fly ash, ground tire and slag. h). Ability to work with reinforcing steel: Concrete and steel possess similar

coefficient of thermal expansion (steel 1.2 x 10-5; concrete 1.0-1.5 x 10-5). Concrete also provides good protection to steel due to existing of CH (this is for normal condition). Therefore, while steel bars provide the necessary tensile strength, concrete provides a perfect environment for the steel, acting as a physical barrier to the ingress of aggressive species and preventing steel corrosion by providing a highly alkaline environment with pH about 13.5 to passivate the steel.

i) Less maintenance required: No coating or painting is needed as for steel

structures.

56

Limitations: a) Quasi-brittle failure mode: Concrete is a type of quasi-brittle material. (Solution:

Reinforced concrete) b) Low tensile strength: About 1/10 of its compressive strength. (Improvements:

Fiber reinforced concrete; polymer concrete) c) Low toughness: The ability to absorb energy is low. (Improvements: Fiber

reinforced concrete) d) Low strength/BSG ratio (specific strength): Steel (300-600)/7.8. Normal

concrete (35-60)/2.3. Limited to middle-rise buildings. (Improvements: Lightweight concrete; high strength concrete)

e) Formwork is needed: Formwork fabrication is labour intensive and time

consuming, hence costly (Improvement: Precast concrete) f). Long curing time: Full strength development needs a month. (Improvements:

Steam curing) g). Working with cracks: Most reinforced concrete structures have cracks under

service load. (Improvements : Prestressed concrete). 5.1.3 Classification of concrete Based on unit weight Ultra light concrete <1,200 kg/m3

Lightweight concrete 1200- 1,800 kg/m3

Normal-weight concrete ~ 2,400 kg/m3

Heavyweight concrete > 3,200 kg/m3

Based on strength (of cylindrical sample) Low-strength concrete < 20 MPa compressive strength Moderate-strength concrete 20 -50 MPa compressive strength

High-strength concrete 50 - 200 MPa compressive strength Ultra high-strength concrete > 200 MPa compressive strength Based on additives: Normal concrete Fiber reinforced concrete Shrinkage-compensating concrete Polymer concrete

57

5.2 Three-phase theory for Concrete 5.2.1 Three phases in concrete Concrete consists of three phases, aggregate (coarse and fine), hardened cement paste (hcp) and transition zone. Each phase can be further divided into multiple phases. For example, the aggregate contains various minerals, voids and micro cracks. Since we have discussed the properties of the first two phases, here we will concentrate on the properties of transition zone. 5.2.2 Transition zone a). Structure of transition zone: The transition zone is defined as the region between large aggregate particles and the hcp (or mortar). It exists as a thin shell, typically 10-50 micron thick. Formation of transition zone can be attributed to poor packing and the formation of water films around large particles during mixing. Owing to higher w/c ratio, the transition zone is more porous than the bulk cement paste or mortar matrix. Also, due to low strength, micro-cracks often form within the transition zone even before loading is applied.

58

b). Influence on concrete properties: The transition zone is generally weaker than both the aggregate and the hcp. Although the transition zone occupies much less volume than the other two phases, its influence on concrete properties is very large. The existence of transition zone can be used to explain why:

. Cement paste or mortar will always be stronger than concrete provided that they have the same w/c ratio and be tested at same age. . The permeability of concrete is much higher than cement paste. . Under the same loading, components of concrete (aggregate and hcp) can show linear behaviour while concrete itself shows a nonlinear behaviour.

The first two questions can be easily explained by the high porosity and existing of micro-cracks in transition zone. For the third question, we should note that it does not take a lot of energy for the propagation of pre-existing micro-cracks in the transition zone. Even at 40 percent of the ultimate strength of concrete, nonlinear behaviour can be observed. Scanning electron microscopy indicates the following: HCP and transition zone have the same constituent phases but at different fractions. The transition zone is more porous and large CH crystals are present, providing smooth planes for cracks to go through. This observation cast light on the ‘engineering’ of microstructure to improve concrete strength. By adding silica fume, a very small particle that can react with CH to form additional C-S-H, the CH crystals are removed and the interface becomes much denser. Indeed, silica fume is a very common constituent in high strength concrete used in practice.

59

5.3 Fresh concrete 5.3.1 Definition Fresh concrete is defined as concrete at the state when its components are fully mixed but its strength has not yet developed. This period corresponds to the cement hydration stages 1, 2, and 3. The properties of fresh concrete directly influence the handling, placing and consolidation, as well as the properties of hardened concrete. 5.3.2 Workability a) Definition Workability is a general term to describe the properties of fresh concrete. Workability is often defined as the amount of mechanical work required for full compaction of the concrete without segregation. This is a useful definition because the final strength of the concrete is largely influenced by the degree of compaction. A small increase in void content due to insufficient compaction could lead to a large decease in strength. The primary characteristics of workability are consistency (or fluidity) and cohesiveness. Consistency is used to measure the ease of flow of fresh concrete. And cohesiveness is used to describe the ability of fresh concrete to hold all ingredients together without segregation and excessive bleeding. b). Factors affecting workability

. Water content: Except for the absorption by particle surfaces, water must fill the spaces among particles. Additional water "lubricates" the particles by separating them with a water film. Increasing the amount of water will increase the fluidity and make concrete easy to be compacted. Indeed, the total water content is the most important parameter governing consistency. But, too much water reduces cohesiveness, leading to segregation and bleeding. With increasing water content, concrete strength is also reduced.

. Aggregate mix proportion: For a fixed w/c ratio, an increase in the aggregate/cement ratio will decrease the fluidity. (Note that less cement implies less water, as w/c is fixed.) Generally speaking, a higher fine aggregate/coarse aggregate ratio leads to a higher cohesiveness.

. Maximum aggregate size: For a given w/c ratio, as the maximum size of aggregate increases, the fluidity increases. This is generally due to the overall reduction in surface area of the aggregates.

. Aggregate properties: The shape and texture of aggregate particles can also affect the workability. As a general rule, the more nearly spherical and smoother the particles, the more workable the concrete.

. Cement: Increased fineness will reduce fluidity at a given w/c ratio, but increase cohesiveness. Under the same w/c ratio, the higher the cement content, the better the workability (as the total water content increases).

60

. Admixtures: Air entraining agent and superplasticizers can improve the workability.

. Temperature and time: As temperature increases, the workability decreases. Also, workability decreases with time. These effects are related to the progression of chemical reaction. c). Segregation and bleeding

. Segregation (separation): Segregation means separation of the components of fresh concrete, resulting in a non-uniform mix. More specifically, this implies some separation of the coarse aggregate from mortar.

. Bleeding (water concentration): Bleeding means the concentration of water at certain portions of the concrete. The locations with increased water concentration are concrete surface, bottom of large aggregate and bottom of reinforcing steel. Bleed water trapped under aggregates or steel lead to the formation of weak and porous zones, within which microcracks can easily form and propagate.

5.3.3 Measurement of workability a). Slump test (BS 1881: 102, ASTM C143):

Three different kinds of possible slumps exist, true slump, shear slump, and collapse slump. Conventionally, when shear or collapse slump occur, the test is considered invalid. However, due to recent development of self compact concrete, the term of collapse slump has to be used with caution.

61

b). Compaction factor test (BS 1881: Part 103): The compacting test was developed in Great Britain in 1947. As shown in the figure, the upper hopper is completely filled with concrete, which is then successively dropped into the lower hopper and then into the cylindrical mould. The excess of concrete is struck off, and the compacting factor is defined as the weight ratio of the concrete in the cylinder, mp, to the same concrete fully compacted in the cylinder (filled in four layers and tamped or vibrated), mf (i.e., compacting factor = mp/mf). For the normal range of concrete the compacting factor lies between 0.8 to 0.92 (values less than 0.7 or higher than 0.98 is regarded as unsuitable). This test is good for very dry mixes. Three limitations: (i) not suitable for field application; (ii) not consistent; (iii) mixes can stick to the sides of the hoppers.

62

c). Vebe test (BS 1881: Part 104): The Vebe consistometer was developed in 1940 and is probably the most suitable test for determining differences in consistency of very dry mixes. This test method is widely used in Europe and is described in BS 1881: Part 104. It is, however, only applicable to concrete with a maximum size of aggregate of less than 40 mm. For the test, a standard cone is cast. The mould is removed, and a transparent disk is placed on the top of the cone. Then it is vibrated at a controlled frequency and amplitude until the lower surface of the disk is completely covered with grout. The time in seconds for this to occur is the Vebe time. The test is probably most suitable for concrete with Vebe times of 5 to 30s. The only difficulty is that mortar may not wet the disc in a uniform manner, and it may be difficult to pick out the end point of the test.

63

d). Ball-penetration test A measure of consistency may also be determined by ball penetration (ASTM C360). Essentially, this test consists of placing a 30-lb metal cylindrical weight, 6" in diameter and 4-5/8" in height, having a hemispherically shaped bottom, on the smooth surface of fresh concrete and determining the depth to which it will sink when released slowly. During penetration the handle attached to the weight slides freely through a hole in the center of the stirrup which rests on large bearing areas set far enough away from the ball to avoid disturbance when penetration occurs. The depth of penetration is obtained from the scale reading penetration of the handle, using the top edge of the independent stirrup as the line of reference. Penetration is measured to the nearest 1/4", and each reported value should be the average of at least three penetration tests. The depth of concrete to be tested should not be less than 8". This test is quickly made and is less prone to personal errors. The ratio of slump to penetration is usually between 1.3 and 2.0.

64

5.3.4 Setting of concrete a). Definition: Setting is defined as the onset of rigidity in fresh concrete. It is

different from hardening, which describes the development of useful and measurable strength. Setting precedes hardening although both are controlled by the continuing hydration of the cement.

b). Abnormal setting

False setting: If concrete stiffens rapidly in a short time right after mixing but

restores its fluidity by remixing, and then set normally, the phenomenon is called false setting. The main reason causing the false setting is crystallization of gypsum. In the process of cement production, gypsum is added into blinker through inter-grinding. During grinding, the temperature can rise to about 120oC, thus causing the following reaction:

CS H2 → CS H1/2

The CS H1/2 is called plaster. During mixing, when water is added, the plaster will

re-hydrate to gypsum and form a crystalline matrix that provides ‘stiffness’ to the mix. However, due to the small amount of plaster in the mix, very little strength will actually develop. Fluidity can be easily restored by further mixing to break up the matrix structure.

Flash setting: Flash setting is caused by the formation of large quantities of monosulfoaluminate or other calcium aluminate hydrates due to quick reactivities

65

of C3A. This is a rapid set with the development of strength and thus is more severe than false setting. However, as we mentioned before, flash setting can be eliminated by the addition of 3-5% gypsum into cement.

Thixotropic set is due to the presence of abnormally high surface charges on the cement particles. It can be taken care of by additional mixing.

As the hydration reaction progresses with time, the concrete becomes less flowable, and the slump value will naturally decrease. However, if the slump value decreases at an abnormally fast rate, the phenomenon is called “slump loss”. It is often due to the use of abnormal setting cement, the unusually long time taken in the mixing and placing operations, or the high temperature of the mix (e.g., when concrete is placed under hot weather, or when ingredients have been stored under high temperature). In the last case, ice chips can be used to replace part of water to lower the temperature.

66

5.3.5 Placing, Compacting and Curing

Concrete should be placed as close to its final position as possible. To minimize segregation, it should not be moved over too long a distance. After concrete is placed in the formwork, it has to be compacted to remove entrapped air. Compaction can be carried out by hand rodding or tamping, or by the use of mechanical vibrators. For concrete to develop strength, the chemical reactions need to proceed continuously. Curing refers to procedures for the maintaining of a proper environment for the hydration reactions to proceed. It is therefore very important for the production of strong, durable and watertight concrete. In concrete curing, the critical thing is to provide sufficient water to the concrete, so the chemical reaction will not stop. Moist curing is provided by water spraying, ponding or covering the concrete surface with wet sand, plastic sheets, burlaps or mats. Curing compounds, which can be sprayed onto the concrete surface to form a thin continuous sheet, are also commonly used. Loss of water to the surrounding should be minimized. If concrete is cast on soil subgrade, the subgrade should be wetted to prevent water absorption. In exposed areas (such as a slope), windbreaks and sunshades are often built to reduce water evaporation. For portland cement concrete, a minimum period of 7 days of moist curing is generally recommended.

Under normal curing (at room temperature), it takes one week for concrete to reach about 70% of its long-term strength. Strength development can be accelerated with a higher curing temperature. In the fabrication of pre-cast concrete components, steam curing is often employed, and the 7-day strength under normal curing can be achieved in one day. The mold can then be re-used, leading to more rapid turnover. If curing is carried out at a higher temperature, the hydration products form faster, but they do not form as uniformly. As a result, the long-term strength is reduced. This is something we need to worry about when we are casting under hot weather. The concrete may need to be cooled down by the use of chilled water or crushed ice. In large concrete structures, cooling of the interior (e.g., by circulation of water in embedded pipes) is important, not only to prevent the reduction of concrete strength, but also to avoid thermal cracking as a result of non-uniform heating/cooling of the structure. After concrete is cast, if surface water evaporation is not prevented, plastic shrinkage may occur. It is the reduction of concrete volume due to the loss of water. It occurs if the rate of water loss (due to evaporation) exceeds the rate of bleeding. As concrete is still at the plastic state (not completely stiffened), a small amount of volume reduction is still possible, and this is accompanied by the downward movement of material. If this downward movement is restraint, by steel reinforcements or large aggregates, cracks will form as long as the low concrete strength is exceeded. Plastic shrinkage cracks often run perpendicular to the concrete surface, above the steel reinforcements. Their presence can affect the durability of the structure, as they allow corrosive agents to reach the steel easily. If care is taken to cover the concrete surface and reduce other water loss (such as absorption by formwork or subgrade), plastic shrinkage cracking can be avoided. If noticed at an early stage, they can be removed by re-vibration

67

5.4 Admixtures used in concretes Historically, admixtures are almost as old as concrete itself. It is known that the Romans used animal fat, milk, and blood to improve their concrete properties. Although these were added to improve workability, blood is a very effective air-entraining agent and might well have improved the durability of Roman concrete. In more recent times, calcium chloride was often used to accelerate hydration of cement. The systematic study of admixtures began with the introduction of air-entraining agents in the 1930s when people accidentally found that cement ground with beef tallow (grinding aid) had more resistance to freezing and thawing than a cement ground without it. Nowadays, as we mentioned earlier, admixtures are important and necessary components for modern concrete technology. The concrete properties, both in fresh and hardened states, can be modified or improved by admixtures. In some countries, 70-80% of concrete (88% in Canada, 85% in Australia, and 71% in US) contains one or more admixtures. It is thus important for civil engineers to be familiar with commonly used admixtures. 5.4.1 Definition and classifications Admixture is defined as a material other than water, aggregates, cement and reinforcing fibers that is used in concrete as an ingredient and added to the batch immediately before or during mixing. Admixtures can be roughly divided into the following groups. i). Air-entraining agents (ASTM C260): This kind of admixture is used to improve the frost resistance of concrete (i.e., resistance to stresses arising from the freezing of water in concrete). ii). Chemical admixtures (ASTM C494 and BS 5075): This kind of admixture is mainly used to control the setting and hardening properties for concrete, or to reduce its water requirements. iii). Mineral admixtures: They are finely divided solids added to concrete to improve its workability, durability and strength. Slags and pozzolans are important categories of mineral admixtures. iv). Miscellaneous admixtures include all those materials that do not come under the above mentioned categories such as latexes, corrosion inhibitors, and expansive admixtures.

68

5.4.2 Chemical admixtures This includes soluble chemicals that are added to concrete for the purpose of modifying setting times and reducing the water requirements of concrete mixes. 5.4.2.1 Water reducing admixtures Water reducing admixtures lower the water required to attain a given slump value for a batch of concrete. The use of water reducing admixture can achieve different purposes as listed in the following table.

Water-reducing admixture are surface-active chemicals. It can separate the cement particles by increasing the static charge on the particle surfaces and thus releasing the water entrapped by cement particle clusters (see Figure below). More water is then available to ‘lubricate’ the mix.

A water-reducing admixture lowers the water required to attain a given workability. This means an effective lowering of the w/c ratio that leads to high strength, low permeability, and improved durability. According to their efficiency, water-reducing admixtures can be divided into two categories, normal range and high range water- reducing admixture. The normal range water reducing admixtures or conventional water-reducing admixtures can reduce 5-10% of water at normal dosages. The high range water- reducing admixture, also called superplasticizer, can reduce water requirement by 15-30%. Superplasticizers were initially developed in Japan and Germany. They are long-chained molecules with a large number of polar groups attached to the main hydrocarbon chain.

69

Once they are adsorbed on a cement particle, strong negative charge is introduced on the particle surface. The surface tension of the surrounding water is hence greatly reduced and the fluidity of the system is significantly improved. In normal applications, the dosage of superplasticizer ranges from 0.6 to 3.0% the weight of cement. Superplasticizers are used for two main purposes: a). To produce high strength concrete at w/c ratio in a range of 0.23-0.3. b). To create "flowing" concrete with high slumps in the range of 175 to 225 mm.

(useful in applications involving: rapid pumping of concrete, areas with congested reinforcements or poor assess – placing can be done with reduced vibration effort )

Associated with the reduced w/c ratio, additional benefits on hardened concrete include better durability and lower creep and shrinkage. The major drawbacks of superplasticizer are: (i). retarding of setting (especially at high dosage)

- introduction of surface charges makes it more difficult for hydration products to ‘bond’ together

(ii). cause more bleeding - dispersion of cement grains releases ‘trapped’ water (iii). entrained too much air - reduced surface tension of water makes it easier for bubbles to form. 5.4.2.2 Setting control admixtures a). Mechanism

The setting and hardening phenomena of Portland cement paste are derived from the progressive crystallization of the hydration products. As discussed before, setting, or the start of significant crystallization of hydration products, occurs at the end of the induction period, when the concentration of ions (calcium, aluminate and silicates etc) has reached a critical state. Since the solubility of ions is sensitive to the presence of other ions in solution, it is possible to change the dissolution rate of ions from the cement, by introducing other ions. This is the principle behind retarding and accelerating admixtures. Retarding admixtures are chemicals that can slow down the dissolution of ions from the cement, thus extending the induction period and delaying initial set. However, the overall strength development (during stages 3 and 4) may not be much slower than that without the retarder. Accelerating admixtures have opposite effect to retarding admixtures. They often reduce the induction period, and also increase the hardening rate at stages 3 and 4.

b) Applications i) Retarding admixtures: Mainly used to: 1. Offset fast setting caused by ambient temperature particularly in hot weather; 2. Control setting of large structural units to keep concrete workable throughout the entire placing period. Examples include:

70

lignosulfonic acids and their salts, hydroxycarboxylic acids and their salts as well as sugars and their derivatives.

ii)Accelerators: Used for plugging leaks, emergency repair, shotcreting and winter construction in cold region. They are mostly soluble inorganic salts. Calcium chloride is by far the best known and most widely used accelerator, and its effect is illustrated in the figure below. However, the introduction of chloride ions can accelerate the corrosion of steel. Other common accelerators include calcium acetate and calcium formate.

71

5.4.3 Air-entraining admixtures (0.05% of air entraining agent by weight of cement) Air-entraining admixtures entrain air in concrete. Air-entraining admixture contain surface-active agents concentrated at the air-water interface. By lowering the surface tension, bubbles can form more readily, and remains more stable after they are formed. With air-entraining admixtures, the mixing water tends to foam and the foam is locked into the paste during hardening. The entrained air voids is different from entrapped air voids. The entrained air void is formed on purpose while the entrapped air void forms by chance when air gets into the fresh concrete during mixing. Entrapped air voids may be as large as 3 mm; entrained air voids usually range from 50 to 200 microns. The size distribution of the solids and pores in a hydrated cement paste is give in the following figure.

Air is entrained into concrete to provide resistance against frost action, or the freeze/thaw of water in the capillary pores. When freezing occurs, there is a net increase in volume. If the saturation of the pores is below 91%, the volume increase can be accommodated. With a higher saturation, however, the volume of ice will be larger than the pore size. Internal stresses are hence introduced, and cracking may occur. With the presence of closely spaced air bubbles in the hardened cement paste, when ice starts to form and grow, the remaining water in the capillary pore can move (through smaller ‘channels’ in the paste) into the air bubbles. The air bubbles thus act as a water reservoir and help to relieve internal stress arising from water freezing. The effectiveness of air-entrainment depends on the spacing among the air bubbles. As shown in the following figure, the smaller the spacing factor (which is defined as the average maximum distance from any point in the paste to the edge of a void), the more durable the concrete. For spacing factor beyond 0.3 mm, the entrained air has little effect on durability.

The presence of entrained air also reduces the effective modulus of the hardened cement paste. With a more flexible paste, the resistance to internal expansion is improved. The concrete is hence more durable against expansive reactions in general. Also, small air bubbles act like ‘bearings’ between aggregates. Their size compensates for the lack of fine particles in sand. Air-entrainment can hence improve both consistency and cohesion.

72

(Note: durability factor is defined as the percentage of original Young’s modulus retained after 300 freeze/thaw cycles)

With entrained air, the improved workability allows the reduction of w/c ratio. This can partly compensate for the reduced strength due to the presence of air bubbles. In normal air-entrained concrete, the strength loss is in the order of 10-20%.

With increasing entrained air content, the internal stress due to freezing is reduced.

However, the strength of the concrete itself is also decreasing, making it easier for damage to occur. Hence, there exists an optimal air content that provides the highest durability.

73

The volume of air required to give optimum durability is about 4-8% by volume of concrete as observed from the above figure. The actual fraction depends on the maximum size of aggregate. With larger aggregate size, the required air content is reduced (see the Table below). This is because less paste is required to provide workable concrete with larger size (and hence smaller surface area per unit weight) of the coarse aggregates. Maximum Recommended Concrete Mortar Paste Spacing aggregate size Air Content factor (mm) 63.5 mm 4.0% 4.5% 9.1% 16.7% 0.18 38 5.0 4.5 8.5 16.4 0.20 19 6.0 5.0 8.3 16.9 0.23 9.5 7.5 6.5 8.7 19.7 0.28 If entrained air is added into cement paste, the formula for the gel space ratio has to be modified as follows.

air entrainedc/w32.068.0

air entrained porescapillary of volume gel of volumepores) gel (including gel of volumeX

++=

++=

αα

5.4.4 Mineral admixtures Mineral admixtures are finely divided siliceous materials that are added into concrete in relatively large amounts (above 10% the weight of the cement). Industrial by-products are the primary source of mineral admixtures. Common mineral admixtures include fly ash, condensed silica fume and blast furnace slag. Typical oxide compositions are given in the table below: Oxide Fly Ash Blast Furnace Silica Fume Portland

Low Ca High Ca Slag Cement _____________________________________________________________________

(% by weight) SiO2 48 40 36 97 20

Al2O3 27 18 9 2 5

Fe2O3 9 8 1 0.1 4

MgO 2 4 11 0.1 1

CaO 3 20 40 --- 64

Na2O 1 --- --- --- 0.2

K2O 4 --- --- --- 0.5

_____________________________________________________________________

74

When low-calcium fly ash (<10% CaO) and silica fume are added to cement, the

following reaction occurs. S + CH + H → C-S-H The pozzolanic reaction given by the above equation is of great significance in concrete technology. The chemical reaction between silicon dioxide (S), and calcium hydroxide (CH) results in the formation of additional C-S-H. In other words, a weak phase is converted into a stronger phase. As a result, the ultimate concrete strength is improved. Materials with no cementing property on its own, but can react with CH at ordinary temperature to form cementitious compounds, are called pozzolans. It should be noted that the conversion of CH to C-S-H is also beneficial to concrete durability, as the permeability of concrete is reduced (due to a denser microstructure) and the resistance to acidic chemicals and alkali-aggregate reactions is improved (as there is less alkalis). With high calcium content, blast furnace slag is mainly cementitious on its own. High calcium fly ash has both cementing and pozzolanic properties. In the following, our discussion will focus on silica fume and low-calcium fly ash. Behaviour of concrete with high-calcium fly ash and blast furnace slag is intermediate between that of portland cement concrete and concrete with low-calcium fly ash. A) Condensed silica fume Silica fume is a by-product of the induction arc furnaces in the silicon metal and ferrosilicon alloy industries. Reduction of quartz to silicon at temperature up to 2000oC produces SiO vapours, which oxidize and condense in the low temperature zone to tiny spherical particles consisting of noncrystalline silica. The material removed by filtering the outgoing gases in bag filters. A size distribution of silica fume, relative to portland cement and fly ash, is shown in the following figure.

75

More accurately, the size distribution of a typical silica fume product is provided as: 20% below 0.05 micron 70% below 0.10 micron 95% below 0.20 micron 99% below 0.50 micron.

The surface area is around 20 m2/g and its average bulk density is 586 kg/m3. Compared with normal portland cement and typical fly ashes, silica fume is two orders of magnitude finer. With such a small size, the pozzolanic reaction can occur very fast. The incorporation of silica fume in concrete can hence increase concrete strength at both early age (due to rapid pozzolanic reaction) and later stage. Besides the pozzolanic reaction, the development of a denser C-S-H structure through better packing (achievable with the small silica fume particles) also contributes to the strength improvement. Indeed, the use of silica fume is an effective way to produce high strength concrete. For strength over 100 MPa, the addition of silica fume is mandatory. The small size of silica fume creates problems of handling. It is often mixed in water to avoid inhalation, which is detrimental to human health. Also, with its large surface area, the water requirement to make workable concrete is significantly increased. A superplasticizer must be used together with silica fume. B) Fly ash Fly ash (pulverized fuel ash) is a by-product of electricity generating plant using coal as fuel. During combustion of powdered coal in modern power plants, as coal passes through the high temperature zone in the furnace, the volatile matter and carbon are burned off, whereas most of the mineral impurities, such as clays, quartz, and feldspar, will melt at the high temperature. The fused matter is quickly transported to lower temperature zones, where it solidifies as spherical particles of glass. Some of the mineral matter agglomerates to form bottom ash, but most of it flies out with the flue gas stream and thus is called fly ash. This ash is subsequently removed from the gas by electrostatic precipitators. Fly ash can be divided into two categories according to the calcium content. The ash containing less than 10% CaO (from bituminous coal) is called low-calcium fly ash (Class F) and the ash typically containing 15% to 30% of CaO (from lignite coal) is called high-calcium fly ash (Class C). By replacing cement with low calcium fly ash, the cohesiveness is improved (small particles are always helpful to prevent segregation). The water requirement to achieve the same consistency is reduced, as the near-spherical fly ash particles makes it easier for the concrete mix to flow. As the pozzolanic reaction does not occur until later, the early strength of concrete is reduced, with a corresponding reduction in heat of hydration. Fly ash can hence be used in mass concrete construction. The ultimate strength is higher than that for concrete without fly ash replacing part of the cement. This is due to the conversion of CH to C-S-H in the long term.

76

5.5 Hardened concrete 5.5.1 Strength of hardened concrete

5.5.1.1 Introduction A). Definition Strength is defined as the ability of a material to resist stress without failure. The failure of concrete is due to cracking. Under direct tension, concrete failure is due to the propagation of a single major crack. In compression, failure involves the propagation of a large number of cracks, leading to a mode of disintegration commonly referred to as ‘crushing’. The strength is the property generally specified in construction design and quality control, for the following reasons: (1) it is relatively easy to measure, and (2) other properties are related to the strength and can be deduced from strength data. The 28-day compressive strength of concrete determined by a standard uniaxial compression test is accepted universally as a general index of concrete strength. 5.5.1.2 Compressive strength and corresponding tests a). Failure mechanism

a. b. c. d.

a. At about 25-30% of the ultimate strength, random cracking (usually in transition zone around large aggregates) are observed

b. At about 50% of ultimate strength, cracks grow stably from transition zone into paste. Also, microcracks start to develop in the paste.

c. At about 75% of the ultimate strength, paste cracks and bond cracks start to join together, forming major cracks. The major cracks keep growing while smaller cracks tend to close.

d. At the ultimate load, failure occurs when the major cracks link up along the vertical direction and split the specimen

The development of the vertical cracks result in expansion of concrete in the lateral

directions. If concrete is confined (i.e., it is not allow to expand freely in the lateral directions), growth of the vertical cracks will be resisted. The strength is hence increased, together with an increase in failure strain. In the design of concrete columns, steel stirrups are placed around the vertical reinforcing steel. They serve to prevent the lateral displacement of the interior concrete and hence increase the concrete strength. In composite construction (steel + reinforced

77

concrete), steel tubes are often used to encase reinforced concrete columns. The tube is very effective in providing the confinement.

The above figure illustrates the case when the concrete member is under ideal

uniaxial loading. In reality, when we are running a compressive test, friction exists at the top and bottom surfaces of a concrete specimen, to prevent the lateral movement of the specimen. As a result, confining stresses are generated around the two ends of the specimen. If the specimen has a low aspect ratio (in terms of height vs width), such as a cube (aspect ratio = 1.0), the confining stresses will increase the apparent strength of the material. For a cylinder with aspect ratio beyond 2.0, the confining effect is not too significant at the middle of the specimen (where failure occurs). The strength obtained from a cylinder is hence closer to the actual uniaxial strength of concrete. Note that in a cylinder test, the cracks propagate vertically in the middle of the specimen. When they get close to the ends, due to the confining stresses, they propagate in an inclined direction, leading to the formation of two cones at the ends.

(b) Specimen for compressive strength determination

Note that the cube specimen is popular in U.K. and Europe while the cylinder specimen is commonly used in the U.S.

i) Cube specimen BS 1881: Part 108: 1983. Filling in 3 layers with 50 mm for each layer (2

layers for 100 mm cube). Strokes 35 times for 150 mm cube and 25 times for 100 mm cube. Curing at 20±5 0C and 90% relative humility.

ii) Cylinder specimen ASTM C470-81. Standard cylinder size is 150 x 300 mm. Curing condition

is temperature of 23±1.7 0C and moist condition. Grinding or capping are needed to provide level and smooth compression surface.

78

(c). Factors influencing experiment results

(i) End condition. Due to influence of platen restraint, cube's apparent strength is about 1.15 time of cylinders. In assessing report on concrete strength, it is IMPORTANT to know which type of specimen has been employed.

(ii) Loading rate. The faster the load rate, the higher the ultimate load obtained. The standard load rate is 0.15 -0.34 MPa / s for ASTM and 0.2-0.4 MPa/s for BS.

(iii)Size effect: The probability of having larger defects (such as voids and cracks) increases with size. Thus smaller size specimen will give higher apparent strength. Standard specimen size is mentioned above. Test results for small size specimen needs to be modified.

5.5.1.3 Tensile strength and corresponding tests a). Failure mechanism

a. b. c.

a. Random crack development (microcracks usually form at transition zone) b. Localization of microcracks

c. Major crack propagation

It is important to notice that cracks form and propagate a lot easier in tension than in compression. The tensile strength is hence much lower than the compressive strength. An empirical relation between ft and fc is given by:

79

ft = 0.615 (fc)0.5 (for 21 MPa < fc < 83 MPa) Substituting numerical values for fc, ft is found to be around 7 to 13% of the compressive strength, with a lower ft/fc ratio for higher concrete strength. In the above formula, fc is obtained from the direct compression of cylinders while ft is measured with the splitting tensile test, to be described below. b). Direct tension test methods

Direct tension tests of concrete are seldom carried out because it is very difficult to control. Also, perfect alignment is difficult to ensure and the specimen holding devices introduce secondary stress that can not be ignored. In practice, it is common to carry out the splitting tensile test or flexural test. c). Indirect tension test (split cylinder test or Brazilian test)

BS 1881: Part 117:1983.

Specimen 150 x 300 mm cylinder. Loading rate 0.02 to 0.04 MPa/s

ASTM C496-71: Specimen 150 x 300 mm cylinder. Loading rate 0.011 to 0.023 MPa/s The splitting test is carried out by applying compression loads along two

axial lines that are diametrically opposite. This test is based on the following observation from elastic analysis. Under vertical loading acting on the two ends of the vertical diametrical line, uniform tension is introduced along the central part of the specimen.

80

The splitting tensile strength can be obtained using the following formula:

LDP2fst π

=

According to the comparison of test results on the same concrete, fst is

about 10-15% higher than direct tensile strength, ft.

d) Flexural strength and corresponding tests

BS 1881: Part 118: 1983. Flexural test. 150 x 150 x 750 mm or 100 x 100 x 500 (Max. size of aggregate is less than 25 mm). The arrangement for modulus of rupture is shown in the above figure. From Mechanics of Materials, we know that the maximum tension stress should occur at the bottom of the constant moment region. The modulus of rapture can be calculated as:

2bt bdPlf =

This formula is for the case of fracture taking place within the middle one third of the beam. If fracture occurs outside of the middle one-third (constant moment zone), the modulus of rupture can be computed from the moment at the crack location according to ASTM standard, with the following formula.

2bt bdPa3f =

However, according to British Standards, once fracture occurs outside of the constant moment zone, the test result should be discarded.

81

Although the modulus of rupture is a kind of tensile strength, it is much higher than the results obtained from a direct tension test. This is because concrete can still carry stress after a crack is formed. The maximum load in a bending test does not correspond to the start of cracking, but correspond to a situation when the crack has propagated. The stress distribution along the vertical section through the crack is no longer varying in a linear manner. The above equations are therefore not exact. 5.5.1.4 Factors affecting concrete strength

Water/Cement Ratio In the discussion of cement hydration, it has been pointed out that the density of hardened cement (in terms of a gel/space ratio) is governed by the water/cement ratio. With higher w/c ratio, the paste is more porous and hence the strength is lower. An empirical formula relating fc and w/c was proposed by Abrams in 1919:

)c/w(5.1c BAf =

For 28 day strength, A is approximately 100 MPa. B is usually taken to be 4. It should be noted that the equation gives very conservative estimates for concrete with low w/c ratio (below about 0.38). Also, the strength continues to increase with decreasing w/c ratio only if the concrete can be fully compacted. For concrete with very low w/c ratio, if no water-reducing agent is employed, the workability can be so poor that a lot of air voids are entrapped in the hardened material. The strength can then be lower than that for concrete with higher w/c ratio. While w/c ratio is the most important parameter governing the strength of concrete, it is not the only parameter. Strictly speaking, the above equation is not correct. However, with no test results available, an estimation of fc from w/c is a good first approximation. Indeed, under the American practice of mix proportioning (ACI 211.1), the compression strength is estimated (in a conservative way) from the water/cement ratio. Under British practice, design tables and charts that take into consideration the types of cement and aggregate are employed. More details will be provided in a later section on concrete mix design.

Age and Curing Condition The effect of curing temperature on concrete strength has already been discussed before. Provided the concrete is properly cured, the strength increases with time due to the increased degree of hydration. As a rule of thumb, for type I cement, the 7 day strength can range from 60 – 80% of the 28 day strength, with a higher percentage for a lower w/c ratio. After 28 days, the strength can continue to go up. Experimental data indicates that the strength after one year can be over 20% higher than the 28 day strength. The reliance on such strength increase in structural design needs to be done with caution, as the progress of cement hydration under real world conditions may vary greatly from site to site.

82

Aggregates

For the same w/c ratio, mixes with larger aggregates give lower strength. This is due to the presence of a weak zone at the aggregate/paste interface, where cracking will first occur. With larger aggregates, larger cracks can form at the interface, and they can interact easier with paste cracks as well as other interfacial cracks. With the same mix proportion, rougher and more angular aggregates give higher strength than smooth and round aggregates. However, with smooth aggregates, a lower w/c ratio can be employed to achieve the same workability. Therefore, it is possible to achieve similar strength with smooth and rough aggregates, by adopting slightly different w/c ratios. For a fixed w/c ratio, the strength increases slightly with the aggregate/cement ratio. This is because aggregates are often denser than the cement paste. With less paste in the concrete, the overall density is increased. For normal strength concrete, the aggregate strength is seldom a concern. However, in the development of high strength concrete, it is important to select aggregates with strength higher than that of the hardened paste.

Admixtures Air-entraining agents decrease concrete strength by incorporation of bubbles. Set-retarding and accelerating agents affect the early strength development but have little effect on ultimate strength. Incorporation of mineral admixtures increases ultimate strength through the pozzolanic reaction. 5.5.1.5 Rate effect on concrete strength and creep rupture

83

The strength of concrete is found to decrease with decreasing loading rate. At slower

loading rates, more time is allowed for the crack to propagate, and hence a lower stress

is required for the joining of cracks to cause failure. Indeed, concrete failure can occur

if loading is increased to 70-80% of the ultimate short-term strength and then kept

constant for a period of time. This phenomenon is referred to as creep rupture or static

fatigue.

5.5.1.6 Fatigue strength of concrete

The fatigue of concrete is often analyzed using empirical approaches, following the

same concept of the Goodman’s law, i.e., the allowable stress oscillation decreases

linearly with the mean stress. An example design diagram is shown in the figure

below.

106 cycles

60

80

100 100

80

40

20

0

Minimum stress as a percentage

of static strength

Maximum stress as a percentage

of static strength 60

40

20 0 For a life of 106 cycles, if the minimum stress is zero, the allowable maximum

stress is 50% the static strength. If the minimum stress is non-zero, the allowable maximum stress can be found in a way illustrated by the arrows in the figure. Note that the above diagram gives conservative estimates of life time.

84

5.5.2 Stress-strain curve and modulus of elasticity

The elastic modulus of concrete is usually determined from test data up to about 40% of the ultimate strength (i.e., within or slightly beyond the linear range). Since concrete is a composite material making up of the hardened paste (with pores) and the aggregates, its modulus can be predicted from composite models. The modulus of the paste increases with decreasing porosity so paste with lower w/c ratio is stiffer. Empirically, the paste modulus is found to vary with (1-p)3, where p is the porosity. To obtain the concrete modulus Ec from the paste modulus Ep and aggregate modulus Ea, three models have been proposed. (i) Parallel model (aggregate and paste under the same strain)

Ec = VaEa + VpEp Va: volume fraction of aggregate Vp = 1 – Va = volume fraction of paste

(ii) Series model (aggregate and paste under the same stress)

1

p

p

a

ac E

VEV

E−

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

(iii) Square in square model

Aggregates are assumed to be completed surrounded by cement, and the composite is simplified into a system of square in square. To find the concrete modulus, the system is assumed to be one made of two layers of pure paste in series with a layer consisting of paste and aggregate in parallel. This is illustrated in the figure below.

Paste Aggregate

Unit length

Va0.5

Pastealone

Paste andAggregatein Parallel

Pastealone

85

For the square in square system,

)V1(EVEV

EV1

E1

apaa

a

p

a

c −++

−=

Concrete modulus predicted from this model is found to agree much better with experimental results than predictions from the parallel and series models.

Concrete modulus generally increases with strength. To achieve higher strength, the water/cement ratio is reduced, and hence the hardened cement paste is denser and stiffer. The composite modulus will therefore also increase. For high strength concrete, the higher modulus is also due to the use of high quality (and hence strong and stiff) aggregates in the mix.

In practice, the concrete modulus is usually not measured, but estimated from the

concrete compressive strength using empirical formula. According to the British Standard for the structural used of concrete (BS 8110: part 2), the Young's Modulus of concrete (in GPa) can be related to the cube compressive strength (in MPa) by the expression

33.0

cc f1.9E =

for concrete with density of 2320 kg/m3, i.e. for typical normal weight concrete. If the density of concrete is between 1400 and 2320 kg/m3, the expression for Young's modulus is

633.0

c2

c 10f7.1E −×= ρ

where ρ is the density of concrete in kg/m3. According to ACI Building Code 318-83, the Young's Modulus of normal weight concrete is,

5.0

cc f70.4E =

where fc is the cylinder compressive strength. For concrete with density from 1,500 to 2,500 kg/m3, the relationship changes to

65.0

c5.1

c 10f43E −×= ρ

86

5.5.3 Dimensional stability--Shrinkage and creep Dimensional stability of a construction material refers to its dimensional change over a long period of time. If the change is so small that it will not cause any structural problems, the material is dimensionally stable. For concrete, drying shrinkage and creep are two phenomena that compromise its dimensional stability. Shrinkage and creep are often discussed together because they are both governed by the deformation of hydrated cement paste within concrete. The aggregate in concrete does not shrink or creep, and they serve to restrain the deformation. 5.5.3.1 Drying shrinkage After concrete has been cured and begins to dry, the excessive water that has not reacted with the cement will begin to migrate from the interior of the concrete mass to the surface. As the moisture evaporates, the concrete volume shrinks. The loss of moisture from the concrete varies with distance from the surface. The shortening per unit length associated with the reduction in volume due to moisture loss is termed the shrinkage. Shrinkage is sensitive to the relative humidity. For higher relative humidity, there is less evaporation and hence reduced shrinkage. When concrete is exposed to 100% relative humidity or submerged in water, it will actually swell slightly. Shrinkage can create stress inside concrete. Because concrete adjacent to the surface of a member dries more rapidly than the interior, shrinkage strains are initially larger near the surface than in the interior. As a result of the differential shrinkage, a set of internal self-balancing forces, i.e. compression in the interior and tension on the outside, is set up. In additional to the self-balancing stresses set up by differential shrinkage, the overall shrinkage creates stresses if members are restrained in the direction along which shrinkage occurs. If the tensile stress induced by restrained shrinkage exceeds the tensile strength of concrete, cracking will take place in the restrained structural element. If shrinkage cracks are not properly controlled, they permit the passage of water, expose steel reinforcements to the atmosphere, reduce shear strength of the member and are bad for appearance of the structure. Shrinkage cracking is often controlled with the incorporation of sufficient reinforcing steel, or the provision of joints to allow movement. After drying shrinkage occurs, if the concrete member is allowed to absorb water, only part of the shrinkage is reversible. This is because water is lost from the capillary pores, the gel pores (i.e., the pore within the C-S-H), as well as the space between the C-S-H layers. The water lost from the capillary and gel pores can be easily replenished. However, once water is lost from the interlayer space, the bond between the layers becomes stronger as they get closer to one another. On wetting, it is more difficult for water to re-enter. As a result, part of the shrinkage is irreversible.

Gel pore

Internal Structure Interlayer space

of C-S-H

87

The magnitude of the ultimate shrinkage is primarily a function of initial water content of the concrete and the relative humidity of the surrounding environment. For the same w/c ratio, with increasing aggregate content, shrinkage is reduced. For concrete with fixed aggregate/cement ratio, as the w/c ratio increases, the cement becomes more porous and can hold more water. Its ultimate shrinkage is hence also higher. If a stiffer aggregate is used, shrinkage is reduced. The shrinkage strain, εsh, is time dependent. Approximately 90% of the ultimate shrinkage occurs during the first year. Both the rate at which shrinkage occurs and the magnitude of the total shrinkage increase as the ratio of surface to volume increases. This is because the larger the surface area, the more rapidly moisture can evaporate.

Based on a number of local investigations in Hong Kong, the value of shrinkage strain (after one year) for plain concrete members appears to lie between 0.0004 and 0.0007 (although value as high as 0.0009 has been reported). For reinforced concrete members, the shrinkage strain values is reduced, as reinforcement is helpful in reducing shrinkage. 5.5.3.2 Creep Creep is defined as the time-dependent deformation under a constant load. Water movement under stress is a major mechanism leading to creeping of concrete. As a result, factors affecting shrinkage also affect creep in a similar way. Besides moisture movement, there is evidence that creep may also be due to time-dependent formation and propagation of microcracks, as well as microstructural adjustment under high stresses (where stress concentration exists). These mechanisms, together with water loss from the gel interlayer, lead to irreversible creep. Creeping develops rapidly at the beginning and gradually decreases with time. Approximately 75% of ultimate creep occurs during the first year. The ultimate creep strain (after 20 years) can be 3-6 times the elastic strain. Creep can influence reinforced concrete in the following aspects. i). Due to the delayed effects of creep, the long-term deflection of a beam can be 2-3 times larger than the initial deflection. ii). Creeping results in the reduction of stress in pre-stressed concrete which can lead to increased cracking and deflection under service load. iii). In a R.C column supporting a constant load, creep can cause the initial stress in the steel to double or triple with time because steel is non-creeping and thus take over the force reduced in concrete due to creep. Creep is significantly influenced by the stress level. For concrete stress less than 50% of its strength, creep is linear with stress. In this case, the burger’s body, which is a combination of Maxwell and Kelvin models, is a reasonable representation of creep behaviour. For stress more than 50% of the strength, the creep is a nonlinear function of stress, and linear viscoelastic models are no longer applicable. For stress level higher than

88

75-80% of strength, creep rupture can occur. It is therefore very important to keep in mind that in the design of concrete column, 0.8 fc is taken to be the strength limit. Factors affecting Creep of concrete

a). w/c ratio: The higher the w/c ratio, the higher is the creep.

b). Aggregate stiffness (elastic modulus): The stiffer the aggregate, the smaller the

creep.

c). Aggregate fraction: higher aggregate fraction leads to reduced creep.

d). Theoretical thickness: The theoretical thickness is defined as the ratio of section area to the semi-perimeter in contact with the atmosphere. The higher the theoretical thickness the smaller the creep and shrinkage.

e). Temperature: with increasing temperature, both the rate of creep and the ultimate creep increase. This is due to the increase in diffusion rate with temperature, as well as the removal of more water at a higher temperature.

f). Humidity: with higher humidity in the air, there is less exchange of moisture between the concrete and the surrounding environment. The amount of creep is hence reduced.

g). Age of concrete at loading: The creep strain at a given time after the application of loading is lower if loading is applied to concrete at a higher age. For example, if the same loading is applied to 14 day and 56 day concrete (of the same mix), and creep strain is measured at 28 and 70 days respectively (i.e., 14 days after load application), the 56 day concrete is found to creep less. This is because the hydration reaction has progressed to a greater extent in the 56 day concrete. With less capillary pores to hold water, creep is reduced.

89

5.5.4 Durability Almost universally, concrete has been specified principally on the basis of its compressive strength at 28 days after casting. Since reinforced concrete structures are usually designed with a sufficiently high safety factor, it is rare for concrete structures to fail due to lack of intrinsic strength. However, gradual deterioration caused by the lack of durability reduces the safety margin of concrete structures to an extent that serious concerns have been raised. The extent of the problem is such that concrete durability has been recently described as a "multimillion dollar opportunity". In the U. S. A., the cost of repairing the interstate highway bridges alone is 20 Billion U.S. dollars. In developed countries, it is estimated that over 40% of the total resources of the building industry are applied to repair and maintenance of existing structures. In Hong Kong, steel corrosion and chemical attack on concrete have created a lot of problems. Some new pipelines can not even last for five years. Steel corrosion has led to the collapse of canopies, resulting in death and injury of people. Durability of concrete can be defined as its ability to resist weathering action, chemical attack, abrasion, or any other process of deterioration, and hence to retain its original shape, dimension, quality and serviceability. 5.5.4.1 Causes of deterioration and main durability problems The causes of concrete deterioration is grouped into two categories Physical causes: Surface wear (abrasion, erosion and cavitation) Cracking (Volume changes, loading damage, and extreme

temperature damage) Chemical causes: Alkali-aggregate reaction Sulphate attack Steel corrosion The most severe durability problems always involve the penetration of water (with corrosive agents) into the concrete. Physical action (e.g., water freezing) or chemical reaction (e.g., alkali-aggregate reaction) will then lead to internal expansion, resulting in significant cracking/spalling of the concrete. Durability of concrete is hence related to the ease of ingress of water and chemicals. Concrete permeability and diffusivity are hence important parameters to be considered.

90

5.5.4.2. Basic factors influencing the durability The durability of concrete depends, to a large extent, on permeability, K, and diffusivity, D. Permeability is defined as the property that governs the rate of flow of a fluid into a porous material under a hydraulic gradient. For steady-state flow, the Darcy’s law states:

xhKu x ∂∂

−=

where ux is the velocity of flow in the x-direction, h the pressure head and K the coefficient of permeability. Obviously the permeability is a function of pores inside materials. It is affected by both the percentage of porosity and size distribution of pores. Porosity(%) Average pore size Permeability coefficient Hardened 40 110 x 10-12 cm/sec. Cement 30 20 x 10-12 cm/sec. Paste 20 100 nm 6 x 10-12 cm/sec. Agg. 3 - 10 10 μm 1-10 x 10-12 cm/sec. Concrete 20 - 40 nm-mm 100 - 300 x 10-12 cm/sec. Diffusivity is defined by Fick's law, and it is the rate of moisture migration under a concentration gradient at the equilibrium diffusion condition.

xCDQ p ∂∂

−=

wher Q is the mass transport rate (kg/m2.s); Dp the diffusion coefficient (m2/s); C the concentration of a particular ion or gas (kg/m3). The two parameters apply to different situations. When water is flowing through a piece of concrete, or from one part to another part under a hydraulic gradient, permeability is the governing parameter. When gases (e.g. oxygen) move through concrete (either dry or wet) or ions (e.g. chloride) move through the pore solution, the process is governed by the diffusion coefficient (or diffusivity). Note that the diffusion coefficient varies for different diffusing substances. Generally speaking, since both the permeability and diffusivity are related to the pore structure of concrete, concrete with low permeability will also possess low diffusivity. Means to reduce permeability and diffusivity (e.g. use lower w/c ratio to reduce capillary porosity, specification of cement content high enough to ensure sufficient consistency and hence proper compaction, proper curing to reduce surface cracks) are generally helpful to concrete durability.

91

5.5.4.3 Alkali-Aggregate Reaction

Alkali-Aggregate Reaction (AAR) is the reaction between alkalis from cement and constituents present in some aggregates. It can be further classified into alkali-silica reaction (ASR) and alkali-carbonate reaction. The small amounts of Na2O and K2O present in the cement clinker are responsible for the reaction. In the cement paste, these form hydroxides and raise the pH level from 12.5 to 13.5. In such highly alkaline solutions, reaction can occur for some aggregates. ASR occurs if an aggregate contains glassy silicates. Examples include chert, flint, opal, cristoballite, chalcedony and volcanic glasses. The reaction products absorb water and expand. Stresses induced by the expansion lead to cracking and spalling. Alkali-carbonate reaction occurs for dolomite. In this case, the reaction products do not expand, but the reaction exposes clay minerals that tend to absorb water and expand. Cracking will then occur. In Hong Kong AAR has only been observed for one source of aggregates from mainland China used in some projects in Northern New Territories.

Although it is possible to tell (through mineral identification) if an aggregate will

react with cement, it is impossible to predict whether its use will result in excessive expansion or not. Various tests for AAR have therefore been developed. In the chemical test (ASTM C289), powdered aggregate is put into sodium hydroxide, and the solubility is measured to assess the reactivity of aggregate with an alkali. Since the presence of various minerals may affect the solubility, the result is not reliable. In the mortar bar test (ASTM C227), crushed aggregates are used to cast mortar bars of standard size. The bars are stored moist at 38 oC to accelerate the reaction. Expansion should not exceed 0.05% after 3 months or 0.1% after 6 months. Since significant expansion may start after 6 months, the test should ideally be continued further. However, the time involved may make it impractical. Recently, a few rapid testing methods have been developed, such as dynamic modulus test, and gel fluorescence test. Dynamic modulus, measured from pulse velocity (Note: v = (E/ρ)1/2) is a good indication of deterioration due to AAR. The measurement can even detect deterioration before any expansion and visible cracking occurs. In the gel fluorescence test, 5% solution of uranyl acetate is applied on the specimen surface, and the specimen is then viewed under ultraviolet (UV) light. A yellowish green fluorescent glow means that reaction products from AAR are present. The new rapid testing methods are promising but they are yet to be standardized.

To minimize the risk of AAR, one can:

A) Use non-deleterious aggregate when the alkali content of the cement is high;

B) Use low-alkali cement (<0.6% Na2O equivalent) when the silica content of aggregate is high

C) Keep concrete dry (relative humidity of the concrete < 80%).

The choice on types of cements and aggregates at a construction site is usually

very limited, and the environment surrounding the concrete is obviously unchangeable. Therefore, the above guidelines may not be practical in a real world. In such cases, the only effective way to reduce the risk of AAR is to control moisture migration in the concrete. No AAR will occur in dry concrete even if reactive aggregates are present. Control of moisture flow can be achieved with external coating on the structural member,

92

or local diffusion coating around the aggregates (formed by placing the aggregates into a slurry of the protective material before casting).

5.5.4.4 Sulphate Attack

Sulphates may be present in ground water, particularly from clay soils. Underground concrete members such as foundations and pipes are therefore subject to sulphate attack. The severity of sulphate attack depends on the type of sulphate present. Calcium sulphate reacts with monosulphate (formed from C3A in the cement) to form ettringite. Since the reaction products occupy a higher volume, internal stresses are generated to disrupt the concrete. (Note: when ettringite is initially formed during the first few hours of cement hydration, expansion also occurs. However, since the concrete is still plastic, the expansion can be accommodated.) When sodium sulphate is present, it also reacts with calcium hydroxide to form gypsum, leading to a loss in strength and stiffness. Magnesium sulphate can react with calcium hydroxide and attack the C-S-H as well. The resulting degradation is hence even more serious. Sulphate is also present in seawater. However, in the presence of chloride ions (which are also abundant in seawater), the resulting ettringite stays in solution. Hence, there will be no expansion and internal stresses. Therefore, sulphate attack in seawater is not as severe as that in ground water.

To minimize sulphate attack, several approaches can be employed. Firstly, the

C3A content of the cement can be reduced. This is the rationale behind using type V (sulphate resistant) cement. Secondly, a lower w/c ratio can be used to reduce the permeability of concrete. While reducing the w/c ratio, it is important to keep a minimum cement content. Otherwise, the water content may become too low for the concrete to be properly compacted. Thirdly, fly ash and silica fume can be added to reduce the permeability. Replacement of cement with pozzolans can also ‘dilute’ the C3A. 5.5.4.5 Corrosion of Steel Reinforcement The high pH in concrete offers a protective environment to the corrosion of steel. In such an environment, steel oxidizes to form Fe(OH)2 first. Part of the oxide will further react to form FeO.OH. With pH > 11.5, and in the absence of chloride ions, both oxides are stable. They form a thin protective film on top of the steel surface to prevent further corrosion. Steel is said to be ‘passivated’ under such a condition. The initiation of steel corrosion is usually due to either carbonation of the concrete, or the penetration of chloride ions. Carbonation is the reaction between carbon dioxide in the air, and calcium hydroxide in the hardened cement to form calcium carbonate. With calcium hydroxide removed by this reaction, the pH drops to below 11.5. When carbonation proceeds to the level of the steel reinforcement, the protective layer is no longer stable. Steel is then ‘depassivated’ and significant rusting will start. In this case, relatively uniform rusting occurs on the steel. In cities near the ocean, such as Hong Kong, or in cold regions where salt is used for deicing of road pavements, the penetration of chloride ions is a major cause for steel corrosion. When the chloride concentration at the steel level reaches a critical value (0.6 to 0.9 kg/m3 of concrete for pH value of 12-13), it will react with the Fe(OH)2 (the remaining ferrous oxide that has not converted into FeO.OH) to form a water soluble compound. The protective surface is hence destroyed. Since the part of the surface covered with FeO.OH is not affected, corrosion only occurs at isolated spots where the

93

Fe(OH)2 formerly exists. This type of corrosion is referred to as ‘pitting’ corrosion, and it is more dangerous than uniform corrosion, as large reduction in steel cross section can occur locally with little loss in total mass.

Once steel is depassivated, corrosion occurs through an electrochemical process, consisting of both oxidation and reduction reactions. Four components must be present for corrosion to occur. The four components include anode, cathode, electrolyte and metallic path. The anode is the electrode at which oxidation occurs. Oxidation involves the loss of electrons and formation of metal ions. Hence, material is lost at the anode. The cathode is the electrode where reduction occurs. Reduction is the gain of electrons in a chemical reaction. The electrolyte is a chemical mixture, usually liquid, containing ions that migrate in an electric field. A metallic path between anode and cathode is essential for electron movement between the anode and cathode. For steel corrosion in concrete, the anode and cathode are both on the steel and the steel itself is the metallic path. The electrolyte is the moisture in concrete surrounding the steel. The specific reactions are given below.

At the anode:

Fe → Fe++ +2e-

At the cathode:

4e- +O2 +2H2O → 4(OH)-

In the electroyte:

Fe++ + 2(OH)- → Fe(OH)2

4 Fe(OH)2 + 2 H2O + O2 → 4 Fe(OH)3

(further reaction with sufficient water supply)

As steel oxidizes, the corrosion products occupy a higher volume. The unit volume

of Fe can be doubled if FeO is formed. The unit volume of the final corrosion product, Fe(OH)3

. 3H2O, is as large as six and a half times of the original Fe. Expansion leads to cracking and surface spalling of concrete. Once the concrete cover spalls and steel is exposed to the atmosphere, the corrosion rate will increase significantly. Eventually, the excessive loss of steel area, if left unnoticed, can lead to collapse of the structure.

94

Based on the above discussions on the corrosion process, various approaches for corrosion control can be proposed. The most cost-effective corrosion control method is to use a low w/c concrete and a relatively thick cover on the steel. (Note: the cover cannot be excessive thick as this will significantly increase the member size. Also, a thick unreinforced cover can easily crack due to shrinkage or thermal effects.) With thick cover and low concrete diffusivity, it takes a long time for carbon dioxide or chloride ion to reach the reinforcing steel. Corrosion initiation is therefore greatly reduced. Also, with low water permeability associated with low w/c ratio, once water is used up in the corrosion reactions, it takes a longer time for it to be replenished. In other words, the electrolyte, a critical component in the electrochemical reaction, is removed. Similarly, with low oxygen diffusivity, the replenishment of reacted oxygen is slow. The corrosion rate after initiation is hence reduced. Another approach to stop corrosion is to isolate the anode and cathode from the electrolyte. This is the principle behind epoxy-coated rebars (reinforcing bars). In general, epoxy-coated rebars have performed well in bridge decks and parking garages. When epoxy coated rebars are used, it is important to minimize damage to the coating during the casting procedure. Training is thus necessary for proper handling of epoxy-coated bars. Recently, notable problems with corrosion of epoxy-coated bars were reported for bridge columns in Florida. Epoxy coating, though intact, was found to separate from the steel. Further research is hence required to understand the degradation mechanism and to improve the coating performance. Instead of isolating steel from the electrolyte, one can also connect steel to either a voltage supply, or a metal higher in the electrochemical series (and hence have a higher tendency to oxidize, e.g. zinc), so the whole piece of steel becomes the cathode. This technique is called cathodic protection. Further discussions on cathodic protection will be given in the section on steel. Corrosion can also be controlled through chemical means, through the incorporation of corrosion inhibitors. The most common corrosion inhibitor is calcium nitrite. Its presence facilitates the conversion of Fe(OH)2 to FeO.OH. In other words, it is competing with chloride ions for Fe (II) ions. If the nitrite/chloride concentration is high, the chloride cannot react with Fe(OH)2 to turn it into a water soluble compound. Therefore, pitting will not occur.

95

5.6 Concrete Mix Design Procedures In the previous chapters, we have discussed the various concrete properties and the factors influencing the properties. Now, we are ready to apply this knowledge to design a concrete mix. Mix design, or mix proportioning, is a process by which one arrives at the right combination of cement, aggregate, water, and admixtures to produce concrete to satisfy given specifications. It should be indicated that this process is considered an art rather than a science. 5.6.1. Principal requirements for concrete The main purpose of mix design is to obtain a product that will perform according to predetermined requirements. These requirements include the following concrete properties: i). Quality (strength and durability) Strength and permeability of hydrated cement paste are mutually related through the capillary porosity that is controlled by w/c ratio and degree of hydration. Since durability of concrete is controlled mainly by its permeability, there is a relationship between strength and durability. Consequently, routine mix design usually focuses on strength and workability only. When the concrete is exposed to special environmental conditions, provisions on durability (e.g. limit on w/c ratio, minimum cement content, minimum cover to steel reinforcement, etc) will also be considered. ii).Workability As we mentioned earlier, workability is a complicated concept for fresh concrete and embodies various properties including consistency and cohesiveness. There is still not a single test method that can fully reflect workability. Since the slump represents the ease with which the concrete mixture will flow during placement, and the slump test is simple and quantitative, most mix design procedures rely on slump as a crude index of workability. Sometimes, the Vebe time may be employed. iii).Economy Among all the constituents of the concrete, the admixture has the highest unit cost, followed by cement. The cost of aggregates is about one-tenth that of cement. Admixtures are often used in small amounts, or they are required to achieve certain properties. To minimize cost of concrete, the key consideration is the cement cost. Therefore, all possible steps should be taken to reduce the cement content of a concrete mixture without sacrificing the desirable properties, such as strength and durability. The scope for cost reduction can be enlarged further by replacing a part of the portland cement with cheaper materials such as fly ash or ground blast-furnace slag. As mentioned earlier, under normal conditions, it is sufficient to consider workability and strength for concrete design. For special conditions, additional considerations on dimensional stability and durability have to be taken.

96

5.6.2 Fundamentals of mix design i) w/c ratio

Water/cement ratio is the most important factor influencing various kinds of concrete properties. For the strength of concern, the Abrams's law states:

)c/w(5.1c BAf =

where fc is the compressive strength, A is an empirical constant (usually about 100 MPa), and B is a constant depends mostly on the cement properties (usually 4). In practice, tables or charts are available for the determination of fc from w/c, as well as cement and aggregate type. ii) cement content At a given w/c ratio, increasing the cement content will increase workability and durability. However, the cost and hydration heat will also be increased. To solve such a problem, part of the cement can be replaced with fly ash or slag. iii) major aggregate properties a) maximum aggregate size: The maximum aggregate size influences the paste requirement and optimum grading. The larger the maximum size, the lower the paste requirement to achieve a given workability. However, the larger the maximum aggregate size, the lower the strength. The following considerations should be taken into account when choosing maximum aggregate size: (a). For reinforced concrete, the maximum size should not exceed one-fifth of the minimum dimension, or three-fourths of the minimum clear spacing between bars. (b) For slabs on grade, the maximum size may not exceed one-third the slab depth. b) aggregate grading The grading of aggregate is important to concrete because a good grading will decrease the cement content and void in concrete and thus produce economical and better concrete. For practical purpose it is adequate to follow grading limits specified by various organizations (e.g. British Standards, ASTM), which are not only broad and therefore economically feasible, but are also based on practical experience. 5.6.3 Weight method and volume method

Usually the unit weight of fresh concrete can be known from previous experience for the commonly used raw materials. Thus we have,

W(wet concrete) = W(cement)+W(water)+W(aggregate)+W(sand) The unit weight of wet concrete is usually ranged from 2300 to 2400 kg/m3.

In the case of the absolute volume method the total volume (1 m3) is equal to the sum of volume of each ingredient (i.e., water, air, cement, and coarse aggregate). Thus we have

1)%( =++++ airvolumeWWWW

sand

sand

aggregate

saggregate

water

water

cemen

cement

ρρρρ

Since the weight of each ingredient is easy to measure than volume, the design proportion of concrete is usually expressed as a weight ratio. Hence, the proportion obtained in volume method have to be converted to weight units by multiplying it by the density of material.

97

5.6.4 Design procedures There are many different methods for designing concrete mix. For example, ACI method and UK method. However, there is no fundamental difference among these methods. Thus, it is sufficient to introduce one method. Here, the method adopted in U. K. (Department of the Environment, DoE, 1988) is introduced. Step 1. Set a target mean compressive strength, fm

Two terms about strength are important in concrete design. One is target mean strength, fm, and another is specified design (characteristic) strength, fc. The characteristic strength, fc, is the strength to be used in structural design, and is hence the objective strength to be achieved. The target strength is the strength to be obtained with the concrete mix design. Due to the variations of concrete quality, characteristic strength, fc, is defined for a permissible percentage of failure. For example, a characteristic strength, fc, of 30 MPa with 5% failures, implies that 95% of test results have to be equal to or higher than 30 MPa. Thus, the target mean strength (fm) should be higher than the characteristic strength, fc, and can be obtained from the following equation

ksff cm +=

where k is a factor dependent on the failure percentage and s is the standard deviation. k and s can be obtained from the following table and figure.

98

Step 2. Obtain required material information, including availability of materials (what kind of aggregate and cement available), sieve analysis of both coarse and fine aggregate, BD, UW and MC of aggregate, and maximum size of aggregate.

Step 3. Determine the w/c ratio according to the following empirical table and figures.

To do this, first get a predicted compressive strength according to the type of cement and type of coarse aggregate for a w/c ratio of 0.5 from the following table. Then, plot this value on the following figure on the w/c =0.5 vertical line. Draw a curve through this point, parallel to the printed curves, until it intercepts a horizontal line passing through the ordinate of predetermined mean strength. The value of the w/c ratio corresponding to mean strength can then be obtained.

99

Step 4. Specify the slump value. Usually, slump values of the concrete to be designed will be specified according to the job nature of the concrete construction. For an inexperienced person, the following table shall provide sufficient information.

100

Step 5. The free water content is then obtained from the following table according to the type of aggregate and the specified workability.

Step 6 The cement content can then be calculated by dividing the water content by w/c

ratio.

cw /mcontent / Water mcontent / Cement

33 =

Compare this value with the specified minimum required cement content

determined by durability consideration. If it is below such a value, the value specified must be used and the modified w/c ratio calculated.

101

Step 7. The total aggregate content is then obtained by estimating the wet density of the fully compacted mix from following figure. The total SSD aggregate content is then equal to (wet density - cement content - free water content) for 1 m3 concrete.

Step 8. Determine the proportion of sand. The proportion of fine aggregate to total

aggregate depends on the grading of the sand and maximum aggregate size, the workability and w/c ratio. The value can be determined from the following figures, which plot the percent of fine aggregate versus w/c ratio for different maximum aggregate size, workability, and the aggregate zone (represented by the percentage of fine aggregates going through the 600 μm sieve).

For a given slump, as the w/c ratio increases (with fixed water content), a

higher percentage of fine aggregates is employed as there is less cement in the mix. For the same w/c, when one goes from one figure to another figure of higher slump (for the same max. aggregate size), the water content increases, and the percentage of fines can also increase. When the maximum aggregate size increases (e.g. going from Fig. (a) to (b) below), the amount of water decreases, so the percentage of fines (for the same slump and w/c ratio) decreases.

102

103

104

105

Step 9. The proportion of coarse aggregate is then the total aggregate content minus the amount of fine aggregate.

Step 10. Obtain the mix proportion for the standard material conditions. Usually, take

cement as 1 and other materials and the ratio of the weight of cement. Step 11. For field applications, make adjustment for moisture in the aggregates. For stock aggregate with surface moisture, the actual weight of stock aggregate

for mixing should be more than the weight of aggregate specified in the proportion while the amount of water (available for achieving desired workability) should be decreased. For stock aggregate with absorption capability, the actual weight of aggregate for mixing should be less than the weight of above proportioned aggregate while the amount of water should be increased.

Step 12. Calculate the quantities in kg per cubic meter for the raw materials. Step 13. Make the trial batch to check the validity of the concrete design.

The calculated mix proportions should be checked by making trial mixes. Only a sufficient amount of water to produce the required workability should be used, regardless of the amount calculated. Trial mix should be tested for flow ability, cohesiveness, finishing properties and air content, as well as for yield and density (unit weight). If any one of these properties, expect the last two, is unsatisfactory, adjustments to the mix proportions are necessary. For example, lack of cohesiveness can be corrected by increasing the fine aggregate content at the expense of the coarse aggregate content. The ‘rules of thumb’ are as follows: (a) If the correct slump is not achieved, the estimated water content is increased (or

decreased) by 6 kg/m3 for every 25 mm increase (or decrease) in slump. (b) If the desired air content is not achieved, the dosage of the air-entraining admixture

should be adjusted to produce the specified air content. The water content is then increased (or decreased) by 3 kg/m3 for each 1 per cent decrease (or increase) in air content.

(c) If the estimated density (unit weight) of fresh concrete by mass method is not achieved and is of importance, mix proportions should be adjusted, allowance being made for a change in air content.

Step 14. Finalize the mix proportion based on the adjustment of the trial batch.

106