The strength of concrete appears to be a good index, whether direct or inverse, of most of the other properties of practical significance. In general, stronger concretes are stiffer, more nearly water-tight, and more resistant to weathering and certain destructive agencies. On the other hand, stronger concretes usually exhibit higher drying shrinkage and lower extensibility, hence are more liable to cracking. These relationships, together with the fact that strength tests are relatively simple to make, form the basis for the common use of strength in specifying and controlling quality and in evaluating the effects of variable factors such as materials, proportions, manufacturing equipments, methods, and curing conditions.
Definition of strength with regard to concrete (unless otherwise stated) is unit force (stress) required to cause rupture. Rupture may be caused by applied tensile stress (failure in cohesion), by applied shear stress (sliding), or by compressive (crushing) stress. However, a brittle material such as concrete is much weaker in tension and in shear than in compression, and failures of concrete specimens under compressive load are essentially shear failures on oblique planes. Since the resistance to failure is due to both cohesion and internal friction, the angle of rupture is not 45° (plane of maximum shear stress) but is a function of the internal friction angle φ; the angle α which the plane of failure makes with the axis of loading is equal to 45 - φ/2. The internal friction angle for concrete is approximately 20°. The nature of failure is illustrated in FIG 6.1.
FIG. 6.1. Representation of failure of concrete under compressive load.
FACTORS AFFECTING STRENGTH
Strength of concrete has three components: (1) Strength of the cement paste, (2) Strength of the aggregate, and (3) Bond between the paste and the aggregate. Generally speaking, the first item is primarily related with the porosity; the second item is not a big problem as long as the aggregate is sound; and the third one is related mainly with the particle shape and the maximum size of the aggregate.
Strength of Paste as Related to Concrete Strength:
Powers' gel/space ratio law states that the "strength of Portland Cement mortars is directly proportional to the increase in (gel/space ratio) regardless of age, original W/C ratio, or type of cement. The gel/space ratio, X, is the ratio of solid hydration products volume to the space available for these products. In other words, the gel/space ratio is a representation of the capillary porosity of the paste in terms of its measurable parameters. It is given as follows:
It has been found that the relationship between compressive strength (σc) and the gel/space ratio can be written as σc = AXn where, A is a constant representing the strength of the gel at X =1.0
n is a constant having values in the range of 2.6 to 3.0 depending on the characteristics of cement.
This relationship can be written as σc=235 X3 kgf/cm2 for portland cement concretes.
Summarizing, for a given cement, strength of the paste depends on (1) cement content (C), (2) water content (Wo), (3) age (α), and (4) air content (Ao).
Water-Cement Ratio:
Even though the strength of concrete is dependent largely on the capillary porosity or gel/space ratio, the quantities are not easy to measure or predict. Therefore, they are not suitable for practical purposes.
Fortunately, however, capillary porosity of a properly compacted concrete at any degree of hydration is determined by the W/C ratio. Therefore, in practice, the strength of a properly compacted concrete can be assured by specifying the W/C ratio. The relationship between W/C ratio and compressive strength is given in FIG. 6.2.
FIG. 6.2. Relationship between compressive strength and W/C ratio.
Time:
Gain of strength with time is basically related with the increase in gel/space ratio due to the increase of α value. However the rate of strength gain is also dependent on (1) characteristics of the cement, (2) curing conditions, and W/C ratio of the mix. Generally speaking, coarser cement particles (∼25μm) contribute to late strength (>28 days) and finer cement particles (∼5μm) contribute to early strength (<7 days="" font="" gain="" high-w="" low-w="" mixes.="" mixes="" more="" rapidly="" ratio="" strength="" than="">
In practice, it is common to obtain 7-day as well as 28-day compressive strength tests. Thus, it becomes possible to extrapolate the 28-day strength from 7-day (or other) strengths. Of course, this depends on the type of the cement and curing temperature, but as a general rule, the ratio of 28-day to 7-day strength lies between 1.3 and 1.7.
Age 1-d 3-d 7-d 28-d 3-m 6-m 12-m
Strength Ratio 0.15 0.45 0.67 1.0 1.16 1.20 1.24
Maturity:
The hydration of cement is greatly affected by both the time and the temperature of hydration, so the gain in strength of concrete is also largely controlled by these two factors. There had been a considerable amount of research on how to express strength as a function of time and temperature. Out of these studies came the concept of maturity which is defined as some function of the product of curing time t and curing temperature T.
The maturity function that best correlates with the strength of concrete is the "Nurse-Saul Expression":
maturity (°C • days) = Σ at (T+10)
where at is the time of curing in days and T is the temperature in °C.
There are certain limitations to the use of maturity for predicting concrete strengths:
1. Maturity functions do not take into consideration the effect of humidity conditions.
2. Proposed functions can not be applied to mass concrete, because the rate of heat loss from such concrete is much less than that from normal members. In other words, only the ambient heat is considered but the effect of heat of hydration is ignored.
3. Maturity functions are not applicable to very low maturities.
4. Type of cement, W/C ratio, etc. are not considered in these functions.
5. Accelerated curing may lead to contradictory results.
Nevertheless, in spite of these limitations, the maturity concept may be useful when trying to establish the strength of concrete in a structure at some previous time. This may be done by measuring the core strengths at some time and then using the maturity functions to estimate the strength at some earlier time. Also, the maturity concept can be used to estimate the appropriate time for form removal when concreting at lower-than-normal temperatures.
Maximum Size of Aggregate:
In practice maximum size of aggregate is limited by member dimensions and minimum reinforcement bar spacing. Below these structural limitations, various maximum sizes can be used. For smaller aggregate sizes, bonding surface between the aggregate and the paste is larger, therefore the interfacial bond is stronger. However, in this case, water requirement for a specified workability becomes higher and paste gets weaker. On the other hand, larger aggregate particles provide more restraint on volume changes in the paste and thus may induce additional stresses in the paste, which tend to weaken the concrete. This effect is offset, however, by the reduced water content necessary to achieve a given workability. In general, there is an optimum maximum aggregate size to give highest strength.
Rate of Loading:
Slow or rapid rates of loading may give misleading strength results. Therefore, standards always specify ranges for loading rates. For compressive strength testing this rate is ~ 2 kgf/cm2/sec. Loads applied slower than standard rates cause creep and reduce the apparent strength.
6.3. COMPRESSIVE STRENGTH
Compressive strength is the most significant strength for concrete since the concrete members are primarily designed for compressive loads. Furthermore, some reliable correlations exist between the compressive strength and other strengths and properties of practical significance.
Certain characteristics of the testing machine may affect the compressive strength of concrete. Testing machines may be classified as "hard" (very rigid machines) and "soft" (less rigid machines). In very soft machines, the energy stored in the machine is released as the specimen begins to fail; this additional energy will cause greater crack propagation and failure at lower loads than with very rigid machines, which cannot release their energies as easily.
Different types of platens can lead to different results, too. The effects of using "hard " and "soft" platens are illustrated in Fig.6.3. The difference in the properties of the steel platen of the test machine and those of the concrete specimen will lead to certain discrepancies at the "ends" of the specimen. In other words, concrete near the steel platen will be in lateral compression. This is called the "end effect". It diminishes at a certain distance from the ends. When the length of the specimen is ≥1.7 times its diameter, the effect of the distorted region is eliminated. This is the reason why length-to-diameter ratio (l/d) of 2 is used. The mathematical explanation of the “end effect” is described below.
Fig. 6.3 Specimen deformation and normal stress distribution for (a) hard and (b) soft platens
εxs : lateral strain in steel
εxc : lateral strain in concrete
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