 |
| STRENGTH OF CONCRETE |
The strength of concrete originates from the strength of the hardened cement paste, which, in turn, originates from the hydration products The major portion of these hydration products is in the form of a rigid gel, called cement gel Although there is no adequate theory yet as to the source of the strength of the cement gel itself, it is reasonable to assume that the bonds of the gel particles to each other, to the aggregate particles, and to other bodies in the concrete are responsible for the strength (Popovics 1998) There are several significant different ways to measure the strength of concrete, such as compressive strength, tensile strength, shear strength, tensional strength, impact strength, etc. The two standard types of concrete strength of the most interest in research and structural design are compressive strength and tensile strength, as measured by the splitting tensile strength test. Another method for measuring tensile strength is the pressure tension test, which has not yet been standardized
Compressive strength is typically considered to be the most important mechanical property of concrete. In most structural applications, concrete is employed primarily to resist compressive stresses. In those rare cases where other stresses (flexural, etc.) are of primary importance, the compressive strength is still frequently used as the measure of resistance because it is the most convenient to measure. For the same reason, compressive strength is generally used as a measure of the overall quality of a concrete, even when strength itself may be relatively unimportant
The compressive strength of
concrete or mortar is usually determined by submitting a specimen of constant
cross section to a uniformly applied axial compression load, which is increased
until failure occurs. The resulting strength is expressed as the ultimate compression
load per cross-sectional area, usually in pounds per square inch (psi) or pascals
(Pa). Testing of the compressive strength of concrete started about 100 years
ago. Two types of compression test specimens are used: cubes and cylinders.
Cubes are used in
Cylinders are the standard specimens
in the
 |
Figure 10-1. Normal stress
distribution near ends of specimens when tested in a machine.
(a) with hard platens; (b) with
soft platens (Neville 1996)
|
Because friction exists between
the steel loading platens of the testing machine and the concrete specimen, a
rather more complex system of stresses is induced due to the tangential forces
being developed between them. The platen restrains the lateral expansion of the
concrete in the portions of the specimen near its ends: the degree of restraint
exercised depends on the friction actually developed. It is also this
tangential force that changes the mode of the concrete specimen’s fracture.
With friction acting, under normal test conditions, an element within the
specimen is subjected to a shearing stress as well as to compression. The
magnitude of the shearing stress decreases, and the lateral expansion increases
with an increase in distance from the platen. As a result of such restraint, a
specimen tested to failure exhibits a relatively undamaged cone or pyramid of
height approximately equal to 1 2 d 3 (where d is the lateral dimension of the specimen). Sketches of typical fracture modes can be seen in
the figure 10-2
 |
Figure 10-2. Sketches of
typical fracture modes
|
The typical failure of a concrete specimen in a uniaxial compression test takes place in the middle of the height because the restricting effect of the fractional forces is at a minimum there.
The more slender the specimen, the lower the compressive strength measured because the effect of the frictional forces in the middle section becomes smaller. However, once the specimen is slender enough, a further increase in the slenderness, up to the point where the stability starts controlling the failure, does not cause further significant reduction in the measured strength.
If the end friction is reduced, for instance by applying appropriate layers between the loading surfaces, this not only reduces the measured value of the compressive strength but also reduces the variation in strength caused by variations in slenderness of the specimen. This effect is especially spectacular when Teflon layers are applied, due to the low surface friction of this material.
The magnitude of the cube strength-cylinder strength ratio is not a constant; it can depend on the type of concrete or aggregate
The failure mechanism of the specimen is also affected by the design of the machine, especially by the energy stored in it. With a very rigid machine, the high deformation of the specimen under loads approaching the ultimate load is not followed by the movement of the machine head, so that the rate at which the load is applied decreases and a higher strength is recorded. On the other hand, in a less rigid machine, the load follows more nearly the load-deformation curve for the specimen and, when cracking commences, the energy stored by the machine is released rapidly. This leads to failure under a lower load than would occur in a more rigid machine, often accompanied by a violent explosion. Under this condition, tests have to be stopped at the point of the largest load and the decreasing load-deformation curve after that point can not be obtained. The exact behavior depends on the detailed characteristics of the machine. Other than longitudinal stiffness, the machine’s lateral stiffness also becomes relevant. Proper and regular calibration of testing machines is essential for a successful test with valid results.
The tensile strength of
concrete plays a fundamental role in the fracture mechanism of hardened
concrete. The actual strength of hydrated cement paste, or of similar brittle materials
such as stone, is very much lower than the theoretical strength estimated on
the basis of molecular cohesion, and calculated from the surface energy of a
solid assumed to be as high as 10.5 GPa. It is an accepted view that fracture
in concrete occurs through cracking. This means that concrete fracture is essentially
a tensile failure regardless of whether the fracture is induced by compression
(or other loading mechanisms), freezing, internal expansion, or by other
factors. This theory can be explained by the presence of flaws as postulated by
We have known that the strength of concrete at a given age and cured in water at a prescribed temperature is assumed to depend primarily on two factors: the water to cement ratio (W/C) and the degree of compaction. In addition to these major factors, there are many other factors that can, and do, influence the strength of concrete to a varying extent. Some of them are
The concrete making
procedure, such as batching, mixing, delivering, placing, and consolidating the
fresh concrete
Effectiveness and duration of curing
When concrete is fully compacted, its strength is taken to be inversely proportional to its water/cement ratio. This relationship was established by Duff Abrams in 1919 and described by the equation:
Where c f is the compressive strength of
the concrete, w/c is the water to cement ratio of the mixture
(originally taken by volume), an K1 and
However, the range of validity for the water/cement ratio equation is limited due to practical reasons. At very low values of water/cement ratio, the curve deviates from the expected values since full compaction is no longer possible. The actual position of the point of departure depends on the means of compaction available
The general form of the strength versus water/cement ratio curve is shown in Figure 10.3
 |
Figure 10.3 The relationship between strength and
water/cement ratio of concrete
(Neville 1996)
|
The water/cement ratio also determines the porosity of the hardened cement paste at any stage of hydration, which will directly affect the volume of voids in concrete. In fact, there is a minimum water/cement ratio for the hydration products to form because there is insufficient space at low water/cement ratios. For complete hydration, the water/cement ratio should not be below 0.42 (by weight). Water/cement ratio is a convenient concept because it means a single variable can be used to estimate many concrete properties, including strength. The relationship between water/cement ratio and concrete strength is only approximate because it can be affected by secondary factors. Fortunately, the approximation is acceptable in most practical cases.
The influence of water/cement ratio on strength does not truly constitute a law because the water cement ratio rule does not include many qualifications necessary for its validity. In particular, strength at any water/cement ratio depends on such factors as; the degree of hydration of the cement and its chemical and physical properties; the temperature at which hydration takes place; the air content of the concrete, the change in the effective water/cement ratio, and the formation of cracks due to bleeding. The cement content of the mix and the properties of the aggregate-cement paste interface are also relevant (Neville 1996).
 |
Figure 10.4. Compressive
strength as a function of temperature at the time of testing
(Mindess et al. 2002)
|
It has been recognized from the
beginning of concrete production that the ambient temperature, especially the
curing temperature, has a major effect on the properties of concrete, including
strength. A rise in curing temperature speeds up the chemical reactions of
hydration and thus beneficially affects the early strength of concrete without
any ill effects on later strength. But increasing temperature during placing
and setting may adversely affect the strength from about 7 days onwards because
a rapid initial hydration appears to form products of a poorer physical
structure, probably more porous, so that a proportion of the pores will always
remain unfilled. A high gel/space ratio will lead to a lower strength, compared
with a less porous product.
A possible explanation for the inverse correlation between early strength and ultimate strength is that certain strength-affecting properties of the hydration products are modified by a change in the rate of hardening, and the cause of the rate change is secondary at most (Popovics 1998). It was also suggested that the rapid initial rate of hydration at higher temperatures retards the subsequent hydration and produces a nonuniform distribution of the products of hydration within the paste. At the high initial rate of hydration, there is insufficient time available for a uniform precipitation in the interstitial spaces. As a result, a high concentration of the products of hydration is built up in the vicinity of the hydration particles, and this retards subsequent hydration and adversely affects long-term strength (Neville 1996). Figure 10.5 shows the relationship between compressive strength and curing time at different curing temperatures
 |
Figure 10-5. Relation between
compressive strength and curing time of neat cement paste
at different curing
temperatures (Neville 1996)
|
A curing temperature below the
freezing point at early ages is also a problem, as it reduces concrete
strength. When concrete is frozen immediately after being placed, the compressive
strength may decrease 30 to 40%. In practice, there is a temperature during the
early life of the concrete that may be considered optimum with regard to
strength at later ages, or more strictly, at comparable degrees of hydration.
This temperature is somewhat influenced by cement type (Klieger 1958). This
optimum curing temperature was 13oC for Type I cement and 4.5oC for Type III for strengths after 28 days for Klieger’s concrete.
In general, the best curing temperature for most concretes is the ‘normal’
temperature, between about 15oC through 40oC (Popovics 1998).
The relationship between water/cement ratio and strength of concrete applies to one type of cement and one age only, and also assumes wet-curing conditions. On the other hand, the strength versus gel/space ratio relationship has a more general application because the amount of gel present in the cement paste at any time is itself a function of age and type of cement. The latter relation thus allows for the fact that different cements require a different length of time to produce the same quantity of gel (Neville 1996).
The relative gain in strength with time of concretes with different water/cement ratios is shown in Figure 10.6
 |
Figure 10.6 Relative gain in
strength with time of concretes with different water/cement
ratio Mindess et al. 2002
|
Air content is that portion of the pores in the fresh cement paste portion of concrete that is filled with air. The quantity of liquid-filled pores can be characterized by the water cement ratio of fresh cement paste. In general, a reduction in porosity within a solid material increases its strength, an axiom particularly applicable to concrete. This was recognized long ago, and is why adobe walls, bricks, and soils were compacted in early times. Later, Roman builders manually compacted their concrete and in the twentieth century various mechanical devices (vibrators, rollers, etc.) were developed for more efficient compaction of concrete. The strength-increasing effect of reducing the water/cement ratio is an example concerning the effect of water filled pores
The effect of porosity on the strength of hydrated cement paste has been studied widely. There is no doubt that porosity (defined as the volume of pores larger than gel pores expressed as a percentage of the overall volume of the hydrated cement paste) is a primary factor influencing the strength of the cement paste. A linear relation between strength and porosity, within the range porosities between 5 and 28 per cent, was established by Rossler and Odler (1985). The effect of pores smaller than 20 nm in diameter was found to be negligible. The relationship between the strength of mortar and porosity based on volume of pores larger than 20 nm in diameter is shown in Figure 10.7
 |
Figure 10.7. Relationship
between compressive strength of mortar and porosity calculated from the volume
of pores larger than 20 nm diameter (Neville 1996)
|
Most of experimental work on porosity of hydrated cement paste has been performed on specimens of neat cement paste or mortar, not concrete. In concrete, the pore characteristics of the hydrated cement are somewhat different because of the influence of coarse aggregate particles on the cement paste in their vicinity. It has been confirmed that the difference in porosity between concrete and neat cement paste, at the same water/cement ratio, increases with the progress of hydration and arises from the presence in concrete of some pores larger than those which can exist in neat cement paste.
Whenever the concrete property in question is controlled by the matrix portion of the concrete, one can use the air content as the effective porosity influencing the property. Such is the case, for instance, for the strength of concrete, because the pores in the aggregate particles have scarcely any effect on strength in most normal-weight concrete. However, in other cases, such as the deformability of concrete, the property may be better to use the sum of the air pores in the matrix and the pores in the aggregate particles as effective porosity (Popovics 1998). Realization of this idea should, however, be left for future research
The reasons for this behavior are not completely understood; it may have something to do with a change in the structure of the C-S-H upon drying, or it may simply represent a change in the internal friction and cohesion on a macroscopic scale; that is, moisture may have a ‘lubricating’ effect, allowing particles to slip by each other in shear more easily. The lower compressive strength of wet concrete may also be due to the development of internal pore pressure as a load is applied.
Feldman and Sereda (1970)
suggested that the Si-O bonds can break more readily to form Si-OH HO-Si bonds
in the presence of adsorbed water on the gel particles. When the concentration
of water molecules is sufficient to maintain the delivery of moisture to a
spreading crack, no further decrease in strength will occur. However, this is
disputed by Glucklich and Korin (1975), who question whether enough water can
be continuously present at the crack tip to maintain the necessary aggressive
environment. Other researchers, including Wittmann and Neville, explained this
phenomenon based on combination of the
Popovics (1986) argued that a moisture gradient over the cross-section of a prismatic concrete specimen causes a change in the measured strength. When the moisture level on the outside is lower than that on the inside of a concrete specimen, the outside layer tends to shrink because it is dryer than the core of the specimen. This shrinkage is restrained by the core of the specimen. Consequently, the core is subjected to a lateral biaxial compression, increasing its measured compressive strength in the third direction.
However, tests have shown that well-cured mortar prisms and concrete cores or cylinders, when completely dried, have a higher compressive strength than when tested wet. Since these specimens were not subjected to differential shrinkage, no such biaxial stress system would have been induced and therefore this phenomenon does not explain the increase in strength. Galloway et al. (1979) argued that the presence of water in the concrete may cause a dilation of the cement gel which results in a weakness in cohesionof the solid particles. Another hypothetical explanation has been suggested by Neville, Popovics and Wittman that the water absorbed into the gel pores leads to a transverse bursting effect in the solid matrix of the concrete and this effect increases with an increase in the external compressive load. However, this is purely a conceptual hypothesis without any theoretical model to support it (Guo and Waldron 2001).