Advanced-Concrete-Technology-2

Vat Lieu k51

Advanced-Concrete-Technology-2

Vat Lieu k51

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The book, based on the Institute of Concrete Technology's Advanced Concrete Technology (ACT) course syllabus, explores critical aspects of concrete's properties, performance, and durability. It emphasizes self-learning and accessibility through a web-based format. The text covers constituent materials, different types of concrete, and their application in construction, along with testing and quality control processes.

Figures (234)

Figure 1.1 The slump test (BS 1881 Part 102: 1983; BS EN 12350-2: 2000; ASTM C 143-90a).

Figure 1.7 The relationship between slump and flow table measurements. The relationships between slump and flow table results from three sources are shown in Figure 1.7; two of these indicate an S-shaped relationship showing the increased sensitivity of the flow table test at higher slumps, but the third is linear between slumps of 100 and 250 mm. However, the scatter is sufficiently wide to encompass both forms of the relationship.

The situation is further complicated by the fact that, in some instances, if different ests are used to either rank or differentiate between mixes, conflicting results can be obtained. For example, Table 1.3 gives the slump, Vebe and compacting factor values of Table 1.2 Consistence classes according to BS EN 206-1: 2000

Figure 1.8 The relationship between slump and slump flow measurements. concrete (it has been standardized for this purpose in Japan). The only extra complication over the slump test is that the result is more sensitive to the surface condition of the board on which the test is performed. The relationship between slump amd slump flow from three test programmes is shown in Figure 1.8. Not surprisingly this shows that, at slumps above about 200 mm, the latter is much more sensitive to changes in the concrete fluidity. The best-fit relationships diverge at higher slumps, which may reflect differences in practice, e.g. in the measurement of slump as discussed above.

Figure 1.9 Typical spread of results from single-point workability tests (data from Ellis, 1977). Table 1.3 Slump, Vebe and compacting factor results from four mixes (data from Ellis, 1977)

where Tp is the intercept on the shear stress axis, and a and n are constants. The three lines shown have different values of n. In shear thinning behaviour, the curve is convex to the Le LIUW UVUOlIiadVIUUL. The other forms of flow curves in Figure 1.11 all intercept the shear stress axis at some positive, non-zero value, i.e. flow will only commence when the shear stress exceeds this threshold value, which is often called the yield stress. This is a characteristic of solid suspensions, i.e. solid particles in a liquid phase, of which cement paste, mortar and concrete are good examples. A wide range of equations have been proposed to model the various shapes of flow curves found in practice, but for our purposes it is sufficient to consider a general equation of the form:

Figure 1.12 A coaxial cylinder viscometer. Instruments that measure the relationship between shear stress and strain rate are called viscometers or rheometers (the two terms are, in effect, interchangeable). There are several forms of such instruments, and a coaxial cylinder viscometer, as illustrated in Figure 1.11, is perhaps the most common. In the version shown in Figure 1.12, the inner cylinder is rotated and the torque imposed on the stationery outer cylinder is measured; other rotating and measuring arrangements are possible. For testing most liquids, the

Figure 1.13 Flow curves for cement pastes with varying water/cement ratio.

subtracting water produces similar proportional changes in both properties. First, taking the simplest mixture of cement and water, varying the water/cement ratio produces a fan-shaped family of flow curves such as that in Figure 1.13, which shows that both the yield stress and plastic viscosity reduce with increasing water content. Figure 1.14 shows some values for Portland cement mixes, from which it can be seen that the magnitude of the changes of both the yield stress and plastic are similar, i.e. adding or subtracting water produces similar proportional changes in both properties.

Figure 1.15 Typical effect of superplasticizer on Bingham constants for cement paste (Domone and Thurairatnam, 1988).

The data of Figures 1.14 and 1.15 can be combined into a single diagram of yield stress versus plastic viscosity, as in Figure 1.16. From the individual data points lines of equal water/cement ratios and superplasticizer dosages can be drawn. The latter are much steeper than the former and indeed, are near vertical over much of the range. Clearly the mechanisms of fluidity increase by water and superplasticizer must be different — both make the flow easier to initiate, i.e. they reduce the yield stress, but superplasticizers maintain the viscosity. Such diagrams are extremely useful in showing these interactive effects, and we will use them later to describe the more complicated behaviour of concrete.

Figure 1.17 The BML viscometer (Wallevik and Gjorv, 1990; RILEM, 2002) (the dimensions are those of the most commonly used system).

Figure 1.18 The BT RHEOM rheometer (de Larrard et a/., 1997; RILEM 2002).

Figure 1.19 The two impeller systems for the two-point workability test (Domone, Xu and Banfill, 1999; RILEM, 2002).

Figure 1.21 Variation of the Bingham constants of mixes containing microsilica (Gjorv, 1997). Also, it is difficult to predict the interactive effects of two or more variables; an example of this is shown in Figure 1.21 for mixes containing varying cement and microsilica contents. Small amounts of microsilica reduce the plastic viscosity, with almost no effect on the yield stress; however, above a threshold level of microsilica, which depends on the cement content, there is a substantial increase in the yield stress, followed by an increase in the plastic viscosity.

Figure 1.24 Intersecting flow curves for two mixes which give conflicting results with single-point tests. be obtained by using two tests on the same mix that we discussed at the end of Section 1.2.2. Figure 1.24 shows flow curves of two mixes which intercept within the range of equivalent shear rates of two single-point tests — for example, obtained with mixes with varying water content and superplasticizer dosage. Test 1, with a low equivalent shear

Figure 1.22 Slump and yield stress results for a wide range of mixes.

Figure 1.23 Slump and plastic viscosity results for a range of mixes (Ferraris and de Larrard, 1998).

Table 1.4 Results of quality control tests on successive loads of the same concrete mix iiaiseeiaiimial: ‘iehcemanias Tests on successive truckloads of nominally the same concrete gave the results shown in Table 1.4 (the g and / values were obtained with the two-point workability test, and have not been converted to t, and LW). The mix contained Portland cement and a superplasticizer. The specified slump was 75 mm, and so on arrival at site loads 2 and 4 could have been rejected on the basis of the slump value. However, there were two possible reasons for the excessive slump — too much water or too much superplasticizer. Examination of the g and h values shows that for mix 2, both g and / are much lower than those of the satisfactory mixes 1, 3, 4 and 5; however, with mix 6, g is lower but h is

VAULCTHELY USClUl Lt PlOUUCIITA TAGS WHICH Call DO sdlislaClOllly HallGiea alld Pldeed, Figure 1.25 shows the regions of the yield stress/plastic viscosity diagram for fou ypes of concrete. In ‘normal’ concrete, in which the workability is controlled mainly b water content, the yield stress and plastic viscosity will vary together, as already discussec ‘lowing concrete, produced by adding superplasticizer to a normal mix (with perhaps ligher fines content to ensure stability), has a yield stress lower than that of norm< -oncrete, and hence a high slump, but a relatively high viscosity for stability. High trength concrete mixes, which have a high paste content commonly containing microsilic: an be viscous and sticky, making them difficult to handle despite including superplasticize1 o produce a high slump/low yield stress. Self-compacting concrete, which needs to flo\ inder self-weight through and around closely spaced reinforcement without segregatin yr entrapping air is perhaps the best example of a rheologically controlled mix (Okamuri 1996). The yield stress must be very low to assist flow, but the viscosity must be hig nough to ensure stability, but not so high for flow to be prohibitively slow. All thes ypes of concrete are discussed in more detail elsewhere in these volumes.

Figure 1.26 Typical slump loss behaviour of mixes without admixtures (Previte, 1977).

Figure 1.28 Segregation and bleed in freshly placed concrete Fresh concrete is a mixture of solid particles with specific gravities ranging from about 2.6 (most aggregates) to 3.15 (Portland cement). After the concrete has been placed, the particles tend to settle and the water to rise (Figure 1.28). This can lead to segregation, in which the larger aggregate particles fall to the lower parts of the pour, and/or bleeding, in which water or water-rich grout rises to the surface of the concrete to produce laitance, a weak surface layer, or becomes trapped under the aggregate particles thus enhancing interface transition zone effects. These processes are hindered by the interlocking of the particles and for the smaller particles, the surface forces of attraction. It follows that the major causes of segregation and bleed are poorly graded aggregates and excessive water contents. Bleed also decreases with increasing fineness of the cement, cement content of

Figure 1.29 Variation of concrete strength in a column after full compaction (Hoshino, 1989). Bleed can be measured in two ways:

Table 2.1 Typical times for appearance of defects (from Concrete Society Technical Report 54)

Figure 2.1 Examples of intrinsic cracks in hypothetical structure (from Concrete Society, 1992). The Concrete Society (1992) provides information on the most common forms of mtrinsic’ cracks in concrete. Figure 2.1 (taken from the Technical Report) illustrates 1ost of the types of crack that are likely to be experienced in the lifetime of a concrete fructure. The following sections are chiefly concerned with early-age movements but also discuss the longer-term effects of drying shrinkage.

Figure 2.2 Formation of plastic settlement crack (initial and final state). depth (Turton, 1981). The wind speed (rate of evaporation) and mix proportions (tendency to bleed) would be expected to affect the severity of the cracking. The number of cracks is influenced by the occurrence of the restraint. However, the reinforcement diameter and concrete workability have little influence.

The most common restraint in slabs is from the reinforcement. The cracks occur on the top surface and usually follow the line of the uppermost bars, giving a series of parallel cracks; there may also be shorter cracks at right angles over the bars running in the opposite direction. Cracks are typically 1 mm wide and usually run from the surface to the bars (see Figures 2.3 and 2.4). The settlement may also result in visible undulations on the concrete surface, with the high points over the top reinforcing bars.

Figure 2.6 Cracks at change of section in mushroom head column. SN: tae SE Ee ee: ee RN Ss MER Renee See RN ee ee nae ee The concrete can also be supported by the formwork face. This causes restraint to the concrete between connected members and is especially evident where changes in section cause differential settlement, the concrete in the deeper section settling more than the shallower section resulting in a crack. This is noticeable in the transition between a flared column head (mushroom) and the plain column, and in trough and waffle slabs where more settlement takes place in the web than the comparatively thin flange (see Figures 2.6 and 2.7). The cracks may pass through the flange and appear similar to shrinkage cracks. It can also occur at other locations, such as under spacer blocks. Cracks at mushroom heads of columns are generally horizontal. They are also typically 1 mm wide and can cross the full section.

Figure 2.7 Cracks at change of section in trough and waffle slabs.

Figure 2.8 Process of plastic shrinkage cracking (initiation and final state).

Figure 2.9 Plan of diagonal cracking. Plastic shrinkage cracks tend to be up to 3 mm wide, and vary in length from 50 mm up to 3 m. They are generally 20-50 mm deep rapidly tapering down within the concrete. In some circumstances they may extend through the full depth of a member. The pattern of cracks generally appear at an approximate angle of 45° to the direction of casting and run parallel to one another (see Figure 2.9). The distance between cracks is variable but could be 1 to 2m. Cracks may also form randomly as a large map pattern (see Figure 2.10). These different patterns may be influenced by the direction in which finishing operations have been carried out or by physical features such as deep tamping marks. A notable characteristic of plastic shrinkage cracks is that they do not normally extend to the edge of a slab as this is able to shrink without restraint. These cracks can form in both unreinforced and reinforced concrete.

Table 2.3 Suggested limiting temperature changes to avoid cracking (from BS 8110) Information on estimating the temperature rise may be found in Harrison (1993). In extreme cases, such as with very large sections or with a high ambient temperature, it may be necessary to consider cooling the fresh concrete (see CIRIA Publication C577, 2002).

Table 2.2 Values of restraint (taken from BS 8110)

Figure 2.12 Drying shrinkage cracks on wall. Vertical lines indicate the position of reinforcement. References

The arrows indicate the region of concrete influencing the deterioration mechanisms in question. The rate of evaporation of water from the surface, taking into account the combined influences of the ambient temperature and relative humidity, the concrete temperature, and the wind velocity can be estimated from Figure 3.2 taken from ACI 308 (1992). This

Figure 3.2 The effect of concrete and air temperatures, relative humidity, and wind velocity on the rate of evaporation of surface moisture from concrete (ACI 308, 1992). standard requires that curing measures are taken if the predicted rate of evaporation exceeds 1.0 kg/m7/h, to prevent plastic shrinkage cracking, but also recommends that such measures may be needed if the rate exceeds 0.5 kg/m7/h.

Table 3.1 BS 8110: 1997 curing recommendations

Table 3.2 UK Department of Transport specification (1986) for curing

Table 3.3 The influence of practical on-site curing on durability-related performance criteria (after CIRIA, 1997) The long-term relative humidity profile in concrete is independent of curing. To be effective, curing must prevent the relative humidity in the concrete from falling below 95 per cent.

Notes: ' 102 mm cubes. ? 244 x 102 mm prisms Table 4.1 Compressive strength with and without lateral restraint by the machine platens (data from Hughes and Bahramian, 1967) Conditions where the machine platens provide no lateral restraint can be achieved by a number of techniques, e.g. loading via two layers of plastic film which have between them a thin layer of grease. These loading conditions give even lower strengths (Table 4.1) and the specimens fail with tensile cracks parallel to the direction of loading (Figure 4.1).

Figure 4.2 shows a comparison of different methods under uniaxial compression. Research by Spooner and Dougill (1975) revealed that the failure of concrete was progressive. During loading microcracking occurs. When the load is released and re- applied, the modulus of elasticity has reduced if cracking has taken place and no further damage occurs until the peak load attained previously is reached. From this point onwards further microcracking occurs. It was noted that the envelope drawn around curves for the cyclic loading fell within the envelope obtained from a specimen subject to monotonically increasing strain, i.e. a single load cycle (Figure 4.3). This research tended to disprove previous theories that postulated that concrete behaved in a linear-elastic way up to some discontinuity stress level (about one third the ultimate load). However, it should be noted that in the Spooner and Dougill model, the amount of damage (microcracking) that occurs when the loading is restricted to about one third the ultimate load is very small. Therefore loading to about half the ultimate load provides a safe basis for design for most structures. At higher levels of loading, many loading cycles will tend to increase the amount of microcracking and eventually may result in failure by fatigue.

surrounded by a water-filled space. The higher the initial water content, the further will be the average spacing between the cement grains. Provided the concrete is not allowed to dry out, the cement grains will continue to hydrate with time and fill the space between the cement grains with a mixture of hydrates and pores. The further the initial spacing between the cement grains, i.e. the higher the water/cement ratio, the more pores per unit volume and the weaker the resulting concrete. Where the initial water/cement ratio is high, the resulting pore structure within the hydrates is interconnected and the resulting concrete has low strength, high penetrability and low durability. These Awan es wee) Acacweteesswe Chase eta aR ere As

Figure 4.5 Early strength gain of PPFAC concretes at 20°C (Harrison and Spooner, 1986). Figure 4.4 Typical envelope of strength for PC-42.5 concretes (Harrison, 1995).

Figure 4.6 Early strength gain of ggbs concretes at 20°C (Harrison and Spooner, 1986).

Figure 4.7 Long-term development in relation to cement content (Concrete Society, 1991).

Figure 4.8 Strength development of standard cubes with and without pfa (Concrete Society, 1991).

Figure 4.9 Strength gain at 20°C of high and medium workability CEM |-42.5 concretes (Harrison, 1995).

Figure 4.10 Cube strength as a function of cement type and content (Buenfeld and Okundi, 1998). 4.1.5 Temperature and temperature history Low temperatures decrease the early strength development whilst high temperatures increase the early strength development (Figure 4.12). The temperature at casting has an effect on 28-day strength. A few hours at a low/high temperature prior to standard curing increases/decreases the 28-day strength. Pitcher (1976) showed that only short periods were needed at high temperatures to have a detrimental effect on 28-day cube strength (Figure 4.13). He also found that the effect of low temperature was less pronounced.

Figure 4.11 Effect of cement content on the concrete strength versus water/cement relationship (Popovics, 1990). gain in strength (Figure 4.14). The effect on concrete containing a pozzolanic material is slightly different. At 28 days the in-situ strength is enhanced relative to standard specimens due to the acceleration of the pozzolanic reaction. At about 3 months the strength development

Figure 4.13 Effect of time at 35°C on 28-day strength (Pitcher, 1976).

Figure 4.16 Influence of moist curing on concrete with a w/c ratio of 0.50 (Price, 1953).

Table 4.3 Methods of assessing formwork striking times (strength of concrete)

Minimum striking times (days) for slab and beam soffits with an uninsulated top surface ARAN DEES SSPE SORTER Se ee ee The concrete placing temperature is at least the mean air temperature. Higher placing temperatures are not significant. The table applies to any concrete that satisfies the criteria given in section 4.1.7.

Figure 4.18 Maturity meter (Wexham Development Ltd).

Figure 4.21 Principle of the break-off test. Figure 4.20 Windsor Probe.

Rebound hammer This test measures surface hardness. It is fully described in a European Standard EN 12504-2 Testing concrete in structures — Part 2: Determination of rebound number. It is a useful test for assessing the uniformity of an element and for selecting points for more detailed investigation, e.g. coring. It can be used to estimate strength if it is calibrated for the concrete being tested. ACI 228 (1995) states that the repeatability, expressed as < coefficient of variation, is about 10 per cent. At low concrete strengths these tests are not very sensitive and they are not recommended as a means of determining formwork striking times.

Figure 4.24 Strength gain for a specific PC-42.5 concrete. The relationship between strength and maturity is not unique for all concretes of 4 constant 28-day strength and therefore it has to be determined experimentally for the particular concrete being used. This is most easily achieved by crushing cubes which have been stored in water at 20°C at 1, 2, 3, 7 and 28 days to obtain the strength development curve for the specific concrete mix (Figure 4.24). Then, if the formwork striking times criterion requires, say, 10 N/mm? from the cubes of equal maturity to the structure, this equates to a maturity of at least 1.4 days at 20°C (Figure 4.24). 4.2.3 Maturity laws

Table 4.5 Comparison of k-values for Portland cement 42.5 and 52.5 concretes, obtained from the Arrhenius and Sadgrove equations _ Given the very wide range of types and classes of cements, combinations, addition: and admixtures, it is important that an appropriate or safe maturity law is selected. A maturity function where k = 0/20 is considered to be a safe relationship in the strength range for formwork striking with any normal cement (including those with ggbs) anc therefore, in the absence of data, this function could be used. This function implies tha there is no strength development at O°C and that the rate of strength gain is a lineal function between 0°C and 20°C. This function cannot be used at temperatures below 0°C as one would get a negative value, i.e. a reduction in the strength already achieved. This or some other selected maturity law can be checked experimentally by curins

Example 1 A hand calculation of maturity using the Sadgrove equation 4.2.4 Calculations of maturity

Figure 4.25 Check on the application of the Sadgrove equation.

Table 5.1 Problems resulting from hot weather at various stages in the concrete production process Higher water demand

Figure 5.1 Effect of temperature on slump (after ACI 305).

Figure 5.3 Effect of ambient temperature, relative humidity, concrete temperature and wind speed on rate of evaporation of surface moisture (after ACI 305).

Figure 5.4 Variation of 1-day strength and 28-day strength with curing temperature (after ACI 305) 5.2.2 Control measures

Figure 5.5 Effect of using chilled mixing water on reduction of initial concrete temperature. Values shown are reductions from temperature which would be obtained when using water at the temperatures shown on the curves (after ACI 305).

Figure 5.6 Effect of substitution of ice for mixing water at various temperatures on initial temperature o' concrete (after ACI 305). Figure 5.6 illustrates the possible reductions in concrete temperature which can be

Table 5.2 Summary of measures to reduce the adverse effects of hot weather The measures which can be taken at all stages to reduce to adverse effects of hot weather are summarized in Table 5.2. i I a aa I The freshly placed concrete should also be shaded from the direct rays of the sun and curing should be applied at the earliest opportunity after finishing. Good curing is extremely important in hot climates as the conditions often favour rapid loss of moisture from the surface. One method that is often used for slabs in the Middle East is to cover the surface with a sheet of polythene as soon after finishing as possible. The polythene in turn is covered with wet hessian to reduce temperature build-up. As soon as the concrete has set the layers are reversed. It is not unusual for wet curing to continue for at least 7 days under hot arid conditions. MRR wrrnnedtie8rn «ty i ae a a: | i i i i a: ee: a ae a is

Table 5.3 Problems resulting from cold weather at various stages in the life of concrete greater durability and is less subject to thermal cracking than similar concrete placed at higher temperatures.

Table 5.4 Summary of measures to reduce the adverse effects of cold weather As noted above, protection should remain in place until the concrete has reached a strength of 5 N/mm”. This can be checked by taking additional cubes and storing them alongside the member. Table 6.1 in BS 8110 Part 1 gives minimum periods of curing and protection for different types of cement, different ambient conditions and different average surface temperatures of concrete. Table E.1 in ENV 13670 gives minimum curing periods for different temperatures and also takes account of cements with different rates of concrete strength development. This is by specifying different curing periods depending on the ratio between strength at 2 days and strength at 28 days.

Table 6.1 Categories of theories and models for the behaviour of composite materials Category 1

Figure 6.1 Relationship between radius of crack tip and stress at crack tip using Inglis’s solution.

Assuming concrete to be a two-phase material (matrix and aggregate) then its stiffness (elastic modulus E,) can be calculated using models in which the matrix phase (E,,) and aggregate phase (E,) are arranged in various configurations and proportions. All models described below assume that all phases are elastic and the simplest are the Dantu upper and lower bound models (Dantu, 1958) which give the highest and lowest values for E,. The upper bound model, in which both phases experience the same strain is shown in Figure 6.2(a). For this arrangement, and assuming zero Poisson’s ratio for the constituents, then E, = (EmVm + E,V,) where V, and V, are the volume fractions of the matrix and ageregate respectively.

Figure 6.3 Relationships between elastic modulus of concrete and volume fraction of aggregate for various models assuming £, = 12.5 and £, = 50 kN/mm2. The Hirsch—Dougill model combined the upper and lower bound models as shown in Figure 6.2(c). Assuming zero Poisson’s ratio for the constituents, for a volume proportion of lower bound model of x then I/E, = x[1/(VnEm + VaE.)] + U - )[Vn/Em + V2/E,]. However, both the lower bound and Hirsch/Dougill models predict E, = 0 for E, = 0 which is clearly incorrect. To overcome this problem Counto (1964) proposed the model in Figure 6.2(d). For this model 1/E, = (1 — V V,/Em+ I{[(. — V V,)/V ValEm + Ey}. Assuming for a paste with a water/cement ratio of 0.45 that E, = 12.5 kN/mm/? and E, = 50 kN/mm’ the relationships between E, and V, for the various models are shown in Figure 6.3.

—_ ee These are based on the use of combinations of elements modelling stiffness (elastic springs), plasticity (yield stress) and viscosity (damper). For example, the combination of elements shown in Figure 6.4 will give the stress/strain relationship shown but only if the relevant constants for the various elements are assumed (Teeni and Staples, 1969).

Figure 6.6 Typical relationships between stress and strain for concrete under uniaxial compression. Stress—strain relationships for a typical concrete subjected to short-term monotonic uniaxial compressive loading to ultimate and beyond are shown in Figure 6.6. To allow the measurement of post-ultimate behaviour the load application was controlled to produce a constant rate of axial deformation (see below). Axial and lateral strains were measured using electrical resistance strain gauges (ERSG) and the overall axial deformation of the

Figure 6.5 Initiation and propagation from a single crack in a brittle material.

Figure 6.7 Comparison between stress-strain relationships for steel and concrete (not to scale). pidlenl GElouliaaullon, Although the axial and lateral relationships appear reasonably linear up to about 40- 60 per cent of ultimate strength, they are not strictly linear. Thus, unlike steel (see Figure 6.7), concrete has no readily identifiable elastic limit and, for simplicity, engineers resort to tangent and secant ‘elastic’ moduli (EZ values, defined in the next section) for design purposes. Up to a stress of about 60 per cent of ultimate the lateral tensile strain (in a direction orthogonal to the applied compressive stress) is a near-constant proportion of the axial compressive strain. The constant of proportionality is termed Poisson’s ratio (v) and has a value of between 0.15 and 0.20 depending on the mix and its constituents. Above this stress the tensile strain increases at a much faster rate than the compressive strain and v increases to above 0.5 (the value for rubber). Since the material is discontinuous at these stress levels the concept of Poisson’s ratio is not valid. To add to this complexity, the deformations are not reversible (i.e. are inelastic) and are time-dependent.

Figure 6.8 Diagram of stress-strain relationship for concrete under uniaxial compression.

Rate of loading The measured strength increases with an increase in the rate of stressing (McHenry and Shideler, 1951) or straining (Bischoff and Perry, 1991) (Figure 6.9). This shows that at higher strain rates strength increases significantly to values approaching 2.5 x short-term static strength (equivalent to a strain rate of approximately 10~>), probably due to a limiting rate of crack propagation. Lower strain rates result in strengths approaching 0.8 x static strength since cracks have more time to propagate and the mechanisms o! creep predominate (see Chapter 7). This behaviour relates closely to that observed wher concrete specimens are loaded in uniaxial compression to various proportions of ultimate and then the load is maintained (Rusch, 1960). Creep strains occur with time and by connecting the strain values occurring after similar periods of time for different appliec stress levels a family of isochronous curves is obtained as shown in Figure 6.10. Repeated loading Studies have shown that concrete fatigue strength is significantly influenced by a large number of variables including stress range, rate of loading, load history, stress reversal, rest period, stress gradient, material properties, etc. It has been suggested that concrete has no definite fatigue limit (i.e. the stress below which it will not fail under repeated load). However, a fatigue life of 10’ cycles, adequate for most engineering purposes, can be achieved if the maximum stress is between 50 per cent and 60 per cent of the static strength (Murdock, 1900) (Figure 6.11). The data in Figure 6.11 relates to load repeatedly applied from zero to the maximum

Figure 6.11 Diagram showing variation of load cycles to failure with maximum stress for repeated load applied from zero to maximum stress. Figure 6.10 Isochronous relationships between deformation and stress under constant loac (after Rusch, 1960).

Load control Standard static tests on plain concrete usually require load to be appliec in such a manner as to induce a defined and constant rate of increase of stress within the specimen. This normally results in sudden ‘brittle’ failure and offers no possibility o: investigating the post-ultimate portion of the stress—strain relationship. If it is required tc measure both the pre- and post-ultimate behaviour then the testing machine must be ‘stiff? (see Chapter 2 of Volume 4 (Testing and Quality)) and capable of applying < controlled rate of strain within, or deformation on, the specimen. Such control could be exercised by using a screw-jack arrangement but for the normal hydraulically basec systems it generally requires continuous measurement of strain or deformation which car be used to electronically control the loading rate to maintain the rate of strain or deformation The loading system must be able to rapidly reduce the stress on the specimen if required Figure 6.13 shows the typical type of stress—strain relationships for stress- and strain. controlled tests. BRionre 6 12 aecnmes that the nIitimate ctreee and ctrain remaine the came far hoth tyne<

Figure 6.13 assumes that the ultimate stress and strain remains the same for both types of test but this has yet to be demonstrated.

conditions in specimens essentially independent of any specimen/testing machine interaction. It is often not realized that the actual state of stress induced in specimens and the resulting deformational and ultimate strength behaviour depend to a large extent on such characteristics as the longitudinal and lateral stiffness of the testing machine, the influence of machine platens and packings, the shape of the specimen and the method of applying load to the specimen. This applies particularly to test specimens loaded by mechanical means through rigid platens or grips and Chapter 2 of Volume 4 deals with such problems. Concrete specimens for testing in compression are usually loaded uniaxially through steel machine platens. However, since (a) the value of v/E for steel is less than that for concrete and (b) there is friction at the platen/specimen interface the resulting restraint induces a complex and indefinable three-dimensional state of triaxial compressive stress near the ends of the specimen. The influence of this restraint gradually decreases with distance from the ends of a specimen until at a distance approximately equal to the specimen width, a central zone exists which is subjected to the desired state of uniaxial compression. Many attempts have been made to overcome these effects by the introduction of various materials at the specimen/platen interface but if the material is too soft it squeezes out under pressure since its v/E value is greater than that of concrete. This induces lateral tensile stresses which can cause a tensile mode of failure even though the specimen is loaded in compression. Tests carried out on nominal 100 x 100 mm prisms (Newman and Lachance, 1964) (Figure 6.14) show the effect on measured strength of rigid and soft interface materials. These effects will be discussed in more detail in section 6.2.2, but for the moment it can simply be stated that they can be minimized by matching the v/E value of the platens

to that of the material being tested and/or eliminating friction at the platen/specimen interface. However, this matching must be maintained throughout the entire test which is impossible. The simplest, and probably the most effective, method is to use a specimen with a height/width ratio large enough to produce a definable and desired state of stress within the central zone of the specimen but not too large to cause buckling. Figure 6.14 indicates that a height/width ratio of about 2.5 is suitable for uniaxial compressive tests. The relationships for 150 mm diameter cylinders of concrete of various strengths (of 150 dia. x 300 mm cylinders) (Murdock and Kesler, 1957) are shown in Figure 6.15 which indicates that the variation in measured strength increases with decreasing concrete strength. In addition, irregularities on the loaded surfaces of the loading platens and specimen can influence the induced stress state and these are discussed in Chapter 4. Even the heterogeneous nature of mortars and concretes can produce non-uniform compressive stress distribution near the ends of the specimen.

Stage I Within this stage localized cracks are initiated at the microscopic level at isolated points throughout the specimen where the tensile strain concentration is the largest. Their formation relieves the strain concentration and equilibrium is soon restored, the accompanying energy changes and irrecoverable deformation being small. This shows that these cracks are stable and, at this load stage, do not propagate. Owing to the heterophase nature of concrete, there will be a distribution of strain concentrations throughout the specimen at a given applied load. As the applied load is increased during Stage I, there will be a more or less continuous multiplication process of stable crack initiation. The various methods of investigating the fracture process have been given above but the most direct and reproducible technique to estimate the end of this stage is by measuring the change in the ratio between the axial and lateral strains for small increments of stress (incremental strain ratio) (Figure 6.16).

the volume changes occurring during loading as the sum of the measured principal strains. The data in Figure 6.6 gives the typical volume change profile shown in Figure 6.18. It has been suggested by Newman (1973) that the end of Stage II can be taken to be the stress level at which the volume is a minimum. Although there is no fundamental reason why this level should represent the end of Stage II it does appear to coincide with the level at which behaviour becomes inherently unstable under sustained (Rusch, 1960) and repeated loads (Newman, 1973a).

Figure 6.19 Strains around an array of aggregate particles embedded in a mortar matrix. Figure 6.20 indicates that crack propagation paths may occur at the aggregate—paste interface, in the cement paste or mortar matrix or in the particles of aggregate. The position of crack initiation will depend upon the relative strength of the cohesive bonds and the local state of stress.

Figure 6.20 Aggregate particles after failure in uniaxial compression.

Under uniaxial compressive states of stress evidence suggests that, first, stable cracks are initiated in the mortar matrix parallel to the direction of applied compression. As the load is increased, the cracks multiply and extend in this same direction until, in the vicinity of mineral aggregate inclusions, the fracture path divides and travels around, rather than through, the hard particles. After final disruption and failure of a specimen, this fracture mechanism produces isolated particles of aggregate adhering to which are small ‘cones’ of mortar at each end aligned in the direction of maximum principal compressive stress. Figure 6.21 shows this process diagrammatically. Under biaxial compressive states of stress, the alignment of the fracture path in both directions of principal compressive stress produces a crack pattern such that, at final disruption, the ‘cones’ of mortar on aggregate are extended to form complete ‘haloes’ around the particles.

Figure 6.23 Failure mode in uniaxial tension. Figure 6.22 Failure modes in uniaxial compression. Significance of fracture stages

stress). At higher applied stress levels (Stage II) cracks begin to propagate around the aggregate particles as the aggregate—paste bond fails. The culmination of Stage III is failure of the element by cracking parallel to the maximum principal compressive stress (Figure 6.22) or orthogonal to the maximum principal tensile stress (Figure 6.23).

Figure 6.24 Devices for applying multiaxial loads.

Typical failure envelopes obtained under uniform boundary displacement are shown in Figure 6.25. The dotted lines are for compression/tension stress states and the solid lines for compression/compression. No data are available for the tension/tension region due to the difficulty of obtaining definable stress states. Zone | type failures are evident over most of the C/T region, with Zone 2 failures near uniaxial stress. Elsewhere Zone 3 failures are produced with cracking orthogonal to the unloaded direction which is the direction of zero stress (minimum compression).

Figure 6.26 Typical stress—strain relationships for a concrete under equal biaxial compressive stress using various loading devices. As for strength envelopes the measured stress-strain relationships depend on the loading method used to achieve a given stress path. In addition, the relationships may also be affected by the deformation measuring technique employed. As an illustration of the trends observed under biaxial loading Figure 6.26 shows typical relationships under equal biaxial stress (6, = 6», 63 = 0) for a concrete.

Figure 6.27 Specimen of mortar after failure under equal biaxial compression using rigid platens. 6.2.5 Behaviour of concrete under triaxial stress

Figure 6.31 Axial—lateral strain relationships for a concrete under triaxial ‘compression’ with various confining pressures. As in the case of uniaxial and biaxial stress states an indication of the level at which cracking becomes significant can be identified by examining the relationships between the strains in the directions of maximum and minimum principal stress, since such cracking will influence the strain in the direction of the minimum compressive stress more than in the direction of the maximum compressive stress. Therefore, as the cracks extend, the ratio of the strain in the direction of minimum compressive stress to the strain in the direction of maximum compressive stress should increase numerically. A typical variation of this relationship for a concrete under triaxial ‘compression’ is shown in Figure 6.31. Only a small portion of the relationship is shown in each case up to and just

Stage II behaviour As discussed above, another clearly defined and more advanced level of the cracking process (Stage II) under stress states is that defined by the stage at which the volume change relationships attain a minimum value before dilating to failure. Figure 6.32 shows typical relationships between the volume changes and total axial stress at various confining pressures. Figure 6.32 shows a non-linear volume decrease for an increase in hydrostatic pressure followed by a further decrease in volume on application of deviator stress. Mixes of a given free water/cement ratio containing a higher volume fraction of aggregate give rise to smaller volume changes at a given level of confining pressure. Greater volume changes are given for mixes with a higher water/cement ratio. Reversals of the volume change occur at a stress approaching ultimate, the point at which the volume attains a minimum value marking the end of Stage II.

Figure 6.33 Typical failure mode for concrete under triaxial ‘compression’ at high confining pressure dependent on the type of stress state imposed. For the cases of uniaxial and biaxial stress states the failure modes are covered above. For triaxial “compression’, where each principal stress is maintained compressive or increased in compression, under low values of confining pressure failure can be observed to occur along planes parallel to the maximum compressive stress in a similar manner to uniaxial compression. For larger values of confining pressure the failure planes become less distinct as the behaviour becomes more ductile. If a conventional hydraulic triaxial cell is used to apply loads then this behaviour gives rise to the ‘bulged’ profiles of specimens under high confining pressures allied to the considerable shortening in the axial direction (Figure 6.33).

Figure 6.35 Variation of axial stress with confining pressure at the ultimate for mortars and concrete under triaxial ‘compression’ and ‘extension’. Design criteria Data from tests on various concretes under multiaxial stress states has been analysed tc derive simple lower bound linear failure envelopes (Hobbs ef al., 1977) for compatibility with the limit state approach in BS 8110. In deriving the envelopes from variable data ii has been assumed that the intermediate principal stress (6) has no effect on failure stress The bending strength in a member is 0.67f,, and the design strength is f,,/Y%, where Ym =1.5 for ultimate. The serviceability limit state (i.e. the stress level that can be maintainec without distress under sustained or fluctuating load) is 0.7 x ultimate for 6). It is recommended that the lowest credible value of 63 throughout the life of the structure be used for design.

Figure 7.1 Magnified stress—strain curve for concrete loaded for the first time. for lightweight concrete of density (p) between 1400-2400 kg/m’. Other countries use different expressions that are based on cylinder strength, which is approximately 0.8 x cube strength for normal strength concrete. For estimating the strains at very low stresses, the dynamic modulus of elasticity is used, as determined by the method in BS 1881: Part 5: 1970. The dynamic modulus corresponds to the initial tangent modulus in Figure 7.1, and Neville (1995) quotes empirical relationships that exist between the static and dynamic moduli of elasticity.

there is chemically combined water forming a definitive part of the hydrated compounds. Between these two extremes there is gel water consisting of adsorbed water held by the surface (van Der Waals) forces of the gel particles, interlayer water (zeolitic water), which is held between the C-S—H sheets, and lattice water, which is water of crystallization not chemically combined.

There are a number of rocks in the UK that shrink on drying so they offer less restraint to the cement paste shrinkage. Igneous rocks of basalt, doleritic types, and greywacke and mudstone sedimentary rocks may increase the shrinkage of concrete substantially. BS 812: Part 120: 1989 recommends categories of use for aggregates that shrink, while BS 1881: Part 5: 1989 specifies a method of assessing shrinkage of concrete. As could be anticipated, for a constant volume of aggregate, shrinkage increases as the The lower the relative humidity the greater the shrinkage because the higher relative humidity gradient between the concrete and the environment promotes a greater loss of water. The effect is demonstrated in Figure 7.4. The same figure shows that swelling of concrete stored in water (100 per cent relative humidity) is about six times smaller than shrinkage in air at 70 per cent relative humidity.

Figure 7.4 Shrinkage as a function of time for concrete stored at different relative humidity; time is from the age of 28 days after wet curing (from Troxell et a/., 1958).

Figure 7.5 Influence of volume/surface ratio on shrinkage of concrete (from Hanson and Mattock, 1966). Se, Since drying results from evaporation of water from the surface of a concrete member, he size of the member is a factor in shrinkage. Members having a large cross-sectional rea undergo less shrinkage than those with a small cross-sectional area because it is nore difficult for water to escape from the former. The effect of size can be expressed as he volume/surface ratio (V/S) or effective thickness (= 2V/S), which represent the average irying path length, so that shrinkage decreases as the volume/surface ratio increases. The letermining parameter is the surface area exposed to drying of the member. Figure 7.5 llustrates the influence of size. There is a secondary, much smaller, influence of shape of lrying shrinkage of concrete that is normally neglected.

Shrinkage and swelling of plain concrete after periods of exposure of six months and 30 years are given in BS 8110: Part 2 (1985). Alternatively, the CEB-FIP method (1990) gives shrinkage as a function of time and is applicable to concrete containing some admixtures. The BS method is shown in Figure 7.6 and applies to concrete made with high-quality normal weight and non-shrinking aggregates, with an initial water content of 8 per cent of the original mass of concrete. For other water contents, the shrinkage of Figure 7.6 is adjusted in proportion to the actual water content. Shrinkage estimated by these methods is not very accurate (+30 per cent at best) and, for better estimates, Neville and Brooks (2001) recommend a short-term test using specimens made from the actual concrete, and then the measured shrinkage-time values extrapolated to obtain long-term shrinkage.

In normal concrete structures drying shrinkage can be as high as 600 x 10~ which is about six times as high as the failure strain in tension. Consequently, if shrinkage is restrained cracking can occur. Cracks can be induced by internal or external restraint, for example, in the surface by the inner core concrete or by reinforcement. Foundations can externally restrain concrete. The actual tensile stress developed depends on creep (see section 7.5), which is beneficial as it relieves the elastic stress induced by restraint. Figure 7.7 demonstrates the schematic pattern of crack development due to restrained shrinkage. Shrinkage also causes a loss of prestress in prestressed concrete, and increases deflections of asymmetrically reinforced concrete. In high-strength or high-performance concrete, autogenous shrinkage may be greater than drying shrinkage but the majority occurs early in the life of concrete. To avoid undesirable effects, it may be possible to delay construction operations until after most autogenous shrinkage has occurred.

Figure 7.8 General form of a strain—-time curve for a material subject to creep rupture. application OF 1o0ad. Concrete is not unique in having the ability to creep. Most engineering materials do, for example, rocks at high stresses, plastics (especially thermoplastics), steel at high temperature and even timber. Figure 7.8 shows the general form of a material undergoing creep and, at some time, it will develop tertiary creep and fail by creep rupture or static fatigue. Concrete also behaves in this way but only at stresses greater than about 0.6-0.7 of the static strength. Although concrete is often thought of being brittle in nature because of its tendency to crack under small strains, it is not strictly brittle in the sense that it can develop large strains prior to failure, which is an advantage as sudden and catastrophic failure is avoided.

“igure 7.10 Elastic and creep recovery on removal of stress. Creep is a partly recoverable phenomenon. When a sustained load is removed after some time, there is an immediate recovery of elastic strain (generally smaller than the initial elastic strain because the modulus of elasticity has increased), followed by a gradual decrease in strain, called creep recovery (Figure 7.10). The recovery reaches its maximum value more rapidly and is much smaller than the preceding creep so the most of creep is irreversible in nature. Basic creep recovery is about 25 per cent of the preceding creep while drying creep recovery is almost zero.

The only standard test available for the general measurement of creep of any type of concrete under uniaxial compression is that of ASTM C512 (1987). However, BS EN 1355: 1997 exists for the determination of creep of test specimens taken from prefabricated components of autoclaved aerated concrete or lightweight concrete with an open structure. The ASTM C512 apparatus is quite large and expensive especially when large numbers of specimens are required. Researchers tend to use smaller, less expensive equipment such as that shown in Figure 7.11. Two concrete specimens are held in series with a calibrated steel-tube dynamometer by four tie-rods and subjected to a stress of between 0.2 and 0.3 of the strength at the age of loading. After applying the load by manually tightening the four nuts, the strain is recorded as the initial elastic strain together with the time taken to apply the load. The subsequent increase in strain, after allowing for shrinkage or swelling as determined on a separate control specimen, is recorded as creep. A disadvantage of the equipment is that, since there is no spring, there is a loss of load due to creep and so the nuts have to be re-tightened often during the early stages of creep. Strain is usually measured by a de-mountable mechanical strain gauge to approximately 10 x 10~°. Neville et al. (1983) describe alternative types of apparatus for determining creep. To minimize experimental variability, it is important to store specimens and apparatus under controlled environmental conditions of temperature and relative humidity 7.5.2 Mechanism of creep

Figure 7.12 Influence of relative humidity on creep of concrete (from Troxell et a/., 1958). OF “For drying concrete, creep is greater the lower the relative humidity of the surrounding environment, as shown in Figure 7.12. Here, concrete specimens were cured at 100 per cent relative humidity for 28 days and then subjected to load in air conditioned to a different relative humidity. Thus, even though shrinkage has been taken into account in determining creep at a relative humidity less than 100 per cent, there is still an influence of drying on creep. That influence can be less if the concrete is allowed to dry prior to application of load, but such a procedure is not recommended in practice since inadequate curing is regarded as bad practice.

The type of cement affects creep in so far as it influences the strength of concrete a the time of application of load. On the basis of equality of the stress/strength ratio Neville and Brooks (2001) state that most Portland cements lead to approximately the same creep. However, for the same initial stress/strength ratio, creep is also affected by the development of strength after application of the load, a greater strength developmeni leading to lower creep. The latter feature explains why the use of mineral admixtures ir concrete, such as fly ash, ground granulated blast furnace slag, silica fume and metakaolir generally result in lower creep. The slow pozzolanic reaction contributes to later strengtt development by producing a cement paste of lower porosity.

Table 7.1 Values of the strength ratio, Feulto/feurg, for use in equation (7.7)

Figure 7.14 Influence of age at application of load on creep of concrete relative to creep of concrete loaded at 7 days; based on L'Hermite (1959).

If there is no moisture exchange, i.e. the concrete is sealed to represent mass concrete, creep is assumed to be equivalent to that of concrete with a volume/surface ratio greater than 200 mm at 100 per cent relative humidity. As for the prediction of drying shrinkage, the accuracy of prediction is low. For more accurate long-term values especially when unknown aggregates or admixtures are contemplated, a short-term test is recommended using the actual concrete and the measured data then extrapolated by the method suggested by Neville and Brooks (2001).

Table 7.2 Coefficient of thermal expansion of 1:6 concretes made with different aggregates [Neville and Brooks (2001)]. This chapter demonstrates that the short- and long-term deformations of concrete are influenced by many factors, the approach considering each type of deformation independently of each other. This approach is not necessarily fundamentally correct but it has the merit of simplicity and is used by researchers seeking a further understanding of the causes of

The amount of moisture in concrete usually is described as moisture content w, (kg/m’) or moisture ratio u (kg/kg). The state of moisture in concrete may be expressed as the relative humidity (RH) @, since there are unique relationships between RH and the ‘adsorbed water’ in the gel and RH and the ‘capillary condensed water’ in the larger pores. Consequently, the specific surface area and the pore size distribution of a concrete will give a relationship between the total amount of physically bound water and RH. This relationship is called the ‘moisture sorption isotherm’. Examples for OPC concrete are shown in Figure 8.2. The moisture sorption isotherm

where 6(@) is the moisture-dependent moisture flow coefficient giving the total flow of moisture. Consequently, 6(@) increases significantly with RH, (cf. Figure 8.4).

Figure 8.5 RH distributions through a 0.1 m thick concrete slab with the bottom surface standing in water and the top surface in contact with dry air (data from Hedenblad, 1993). From the moisture dependency in Figure 8.4 the steady-state moisture distribution can be estimated. It is highly non-linear (cf. Figure 8.5) with a dry upper surface even if the bottom is standing in water.

‘his coefficient is frequently, and easily, determined for very dry concrete with initial onditions far away from most applications. This is simply because the test requires the nitial conditions to be controlled and since it takes a very long time to reach equilibrium, ast drying at elevated temperature is used. Such a water absorption coefficient is of little se for practical applications. Instead, tests must be carried out at initial conditions much loser to reality, i.e. equilibrium conditions not too far from saturation. An excellent, but are, example is shown in Figure 8.6. The water absorption coefficient A is of course zero at saturation. At a degree of saturation of 50%, the water absorption coefficient is less than a third of what is found from usual tests on dry specimens!

Figure 8.8 Periodic moisture penetration depth d, for concrete, with different moisture diffusivities Dy = 107"? to 10° m/s, as a function of the time period t, (Lindvall, 1999).

The response to moisture variations, given by a cosine function with amplitude Aw, and with a time period ¢,, i.e. a “wave length’ of the moisture variation, is shown in Figure 8.7. The ‘moisture penetration depth’, d,, is the depth where one third of the moisture variations remain. That depth is a function of the moisture diffusivity and the time period (Lindvall, 1999):

Figure 8.9 Moisture profiles as RH from samples after two years of exposure in sea water. Slab H4, SRPC cement with 5% silica fume, water—binder ratio 0.40 (Rodhe, 1994).

The model does not include possible re-alkalization by hydroxides leaching from depths larger than the depth of carbonation. It also gives a distinct carbonation front, which is not what is observed if the degree of carbonation as a function of depth is measured. This is not yet explained. Besides that, most aspects of the carbonation process are included, but the limits in applicability of such a complete model are the lack of data on climatic actions on various concrete surfaces. The environmental actions at the concrete surface, and the environmental response by the concrete, are decisive for the carbonation process. The actual climate must be translated into times of wetness and intervals of dry periods between rain showers. The water absorption from driving rain must be treated with very short time steps, since that process is very rapid and the amount of rain water is limited, which makes long-term predictions for, say, 50 years very time-consuming.

Figure 8.11 Predicted profiles of total (left) and free (right) chloride by ClinConc (Tang, 1996) the sixth year after exposure. The curves are for April (6 years), July (6.25) and October (6.5) SRPC concrete with w/c 0.40 exposed to sea water with a chloride concentration of 16 g/I (Nilsson and Tang, 1998).

Figure 8.12 Chloride profiles after 0.6 to 5 years exposure, SRPC cement with 5% silica fume, water—binder ratio 0.40 (Tang and Nilsson, 1999). Recently exposure data strongly indicated that chloride binding increases with time. also in submerged concrete (see Figure 8.12.) This is not yet experimentally confirmed ot theoretically understood.

Figure 8.13 Concentration dependent diffusion coefficient in Fick's first law (Nilsson et a/., 1996), based on data from Bigas (1994).

Figure 8.14 Predicted profiles of total chloride during a steady-state experiment with a drying left surface (Nilsson, 2000).

Figure 8.16 Curve-fitting a measured chloride profile to the erfc solution to Fick's second law.

Depending on the transport process, the significance of other parameters will vary. For some transported substances the effect of the composition of the binder will be very important, especially those where a chemical binding is involved, such as carbonation and chloride ingress. For other substances, e.g. permeation of gas and liquids, the crack system will be decisive. Homogeneity, from mixing, casting and compaction will determine the variations in the potential permeation properties of concrete. The homogeneity depends on the workability of the concrete that will influence its ability to fill the formwork and surround the reinforcement with a limited energy supply, the stability to avoid separation of water and large aggregates, the shape and narrowness of the formwork and the spacing of the reinforcement.

Figure 8.18 The non-steady state electrical migration test method NT Build 492 for rapid chloride penetration test.

Figure 9.1 Expansive corrosion products on steel in chloride contaminated concrete.

Figure 9.2 Corrosion induced by carbonation of a concrete beam which has resulted in a crack in the concrete cover following the line of the reinforcement.

Figure 9.3 Schematic diagram of the electrochemical processes occurring during corrosion.

Figure 9.4 Simplified Pourbaix diagram for iron showing the most stable products at a given pH and potential. risk of high corrosion rates is lower than if the most stable products are soluble ions. If the most stable product is the metal then corrosion is thermodynamically impossible. Also included on this diagram is the potential — pH relationship of the oxygen reduction (line b) and hydrogen evolution (line a) reactions. The oxygen reduction reaction is the most important cathodic reaction stimulating the corrosion of reinforcing steel in concrete.

Figure 9.5 Backscattered electron image of a polished cross-section of steel in concrete (Grass et al., 2001).

CLES MAEVE VEER Vil ULI Bok GERAD Bet Soa Bey Vi Seater yy Speed ALITY VEVEIIVIVN. The rate of any transport process will depend on the volume fraction, tortuosity and connectivity of the pores. This is determined by factors such as the water/cement ratio (w/c), cement content, cement fineness, cement type, use of cement replacement materials (for example ground granulated blast furnace slag (ggbs), pulverized-fuel ash (pfa) and silica fume (sf)), concrete compaction, and degree of hydration (Atkinson and Nickerson, 1984). Reducing w/c (which controls the original spacing of the cement grains) and prolonged hydration may, for example, result in the capillary pores becoming blocked by gel so that they are interconnected solely by gel pores.

Table 9.1 Acid (moles H* / kg binder) required to reduce the pH to the phenolphthalein endpoint together with values extrapolated from the titration data at pH 10

Factors associated with both the concrete and the external environment affect the rate of carbonation. The nature of the porosity and the alkaline reserves of the cement hydration products are the main factors associated with the concrete that affect carbonation. Thus, for example, a high water/cement ratio will increase the capillary porosity and the rate of carbonation (Figure 9.7). Cracks resulting from tensile stresses in the concrete will also increase the carbonation depth.

Figure 9.8 Measured natural carbonation depths over a 20-year period in 65 per cent GGBS and OPC concretes plotted as a function of the root of time (Hassanein, 1997). 9.5.2 Corrosion initiation and propagation

Figure 9.9 Steel corrosion rate as a function of chloride content and relative humidity in carbonated OPC mortar (Glass et al., 1991).

Figure 9.10 A carbonated concrete beam showing areas of corrosion.

system diffusion coefficient (D,) in equation (9.4) characterizes the velocity of ions in the yore system under the influence of a concentration gradient. The ionic flux is determined elative to the cross-sectional area of the pores carrying the ions (Glass and Buenfeld, 1998). However, as noted above, all concrete will bind some chloride thereby changing he chloride profile. If the effects of linear chloride binding are included in equations 9.2) and (9.3), the pore system diffusion coefficient will be replaced by the apparent liffusion coefficient (D,). This is widely used to model the chloride profile as shown in 4igure 9.11 (Bamforth et al., 1997). Empirical models are based on an analysis of measured data. For example, many chloride profiles follow the form given by equation (9.4) even though the underlying assumptions are incorrect. This provides an empirical basis for the use of equation (9.4) to describe the chloride profile. It is important to note that, even though the chloride profile is characteristic of a diffusion process, it is not necessary to assume that it was caused solely by diffusion (Engelund and Sorensen, 1998).

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