Mechanism of Failure in Concrete Loaded in Compression
Concrete is a mixture of cement paste and aggregate, each of which has an essentially lin- ear and brittle stress–strain relationship in compression. Brittle materials tend to develop tensile fractures perpendicular to the direction of the largest tensile strain. Thus, when con- crete is subjected to uniaxial compressive loading, cracks tend to develop parallel to the maximum compressive stress. In a cylinder test, the friction between the heads of the test- ing machine and the ends of the cylinder prevents lateral expansion of the ends of the cylinder and in doing so restrains the vertical cracking in those regions. This strengthens conical regions at each end of the cylinder. The vertical cracks that occur at midheight of the cylinder do not enter these conical regions and the failure surface appears to consist of two cones.
Although concrete is made up of essentially elastic, brittle materials, its stress–strain curve is nonlinear and appears to be somewhat ductile. This can be explained by the grad- ual development of microcrackingwithin the concrete and the resulting redistribution of stress from element to element in the concrete [3-1]. Microcracks are internal cracks to in length. Microcracks that occur along the interface between paste and aggregate are calledbond cracks; those that cross the mortar between pieces of aggregate are known as mortar cracks.
There are four major stages in the development of microcracking and failure in concrete subjected to uniaxial compressive loading:
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1. Shrinkage of the paste occurs during hydration, and this volume change of the concrete is restrained by the aggregate. The resulting tensile stresses lead to no-load bond cracks, before the concrete is loaded. These cracks have little effect on the concrete at low loads, and the stress–strain curve remains linear up to 30 percent of the compressive strength of the concrete, as shown by the solid line in Fig.3-1.
2. When concrete is subjected to stresses greater than 30 to 40 percent of its compressive strength, the stresses on the inclined surfaces of the aggregate particles will exceed the tensile and shear strengths of the paste–aggregate interfaces, and new cracks, known as bond cracks, will develop. These cracks are stable; they propagate only if the load is increased. Once such a crack has formed, however, any additional load that would have been transferred across the cracked interface is redistributed to the remain- ing unbroken interfaces and to the mortar. This redistribution of load causes a gradual bending of the stress–strain curve for stresses above 40 percent of the short-time strength. The loss of bond leads to a wedging action, causing transverse tensions above and below the aggregates.
3. As the load is increased beyond 50 or 60 percent of ultimate, localized mortar cracksdevelop between bond cracks. These cracks develop parallel to the compressive loading and are due to the transverse tensile strains. During this stage, there is stable crack propagation; cracking increases with increasing load but does not increase under constant load. The onset of this stage of loading is called the discontinuity limit[3-2].
4. At 75 to 80 percent of the ultimate load, the number of mortar cracks begins to increase, and a continuous pattern of microcracks begins to form. As a result, there are fewer undamaged portions to carry the load, and the stress versus longitudinal-strain curve becomes even more markedly nonlinear. The onset of this stage of cracking is called the critical stress[3-3].
If the lateral strains, are plotted against the longitudinal compressive stress, the dashed curve in Fig. 3-1 results. The lateral strains are tensile and initially increase, as is expected from the poisson’s effect. As microcracking becomes more extensive, these cracks contribute to the apparent lateral strains. As the load exceeds 75 to 80 percent of the ultimate
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Fig. 3-1
Stress–strain curves for concrete loaded in uniaxial compression. (From [3-2].)
compressive strength, the cracks and lateral strains increase rapidly, and the volumetric strain (relative increase in volume), begins to increase, as shown by the broken line in Fig. 3-1.
The critical stress is significant for several reasons. The ensuing increase in volume causes an outward pressure on ties, spirals, or other confining reinforcement, and these in turn act to restrain the lateral expansion of the concrete, thus delaying its disintegration.
Equally important is the fact that the structure of the concrete tends to become unstable at loads greater than the critical load. Under stresses greater than about 75 percent of the short-time strength, the strains increase more and more rapidly until failure occurs.
Figure3-2ashows the strain–time response of concrete loaded rapidly to various fractions of its short-time strength, with this load being sustained for a long period of time or until failure occurred. As shown in Fig. 3-2b, concrete subjected to a sustained axial load greater than the critical load will eventually fail under that load. The critical stress is be- tween 0.75 and
Under cyclic compressive loads, axially loaded concrete has a shake-downlimit approximately equal to the point of onset of significant mortar cracking at the critical stress. Cyclic axial stresses higher than the critical stress will eventually cause failure.
As mortar cracking extends through the concrete, less and less of the structure remains. Eventually, the load-carrying capacity of the uncracked portions of the concrete reaches a maximum value referred to as the compressive strength(Fig. 3-1). Further strain- ing is accompanied by a drop in the stress that the concrete can resist, as shown by the dotted portion of the line for in Fig. 3-1.
When concrete is subjected to compression with a strain gradient, as would occur in the compression zone of a beam, the effect of the unstable crack propagation stage shown in Fig. 3-1 is reduced because, as mortar cracking softens the highly strained concrete, the load is transferred to the stiffer, more stable concrete at points of lower strain nearer the neutral axis. In addition, continued straining and the associated mortar cracking of the highly stressed regions is prevented by the stable state of strain in the concrete closer to the neutral axis. As a result, the stable-crack-propagation stage extends almost up to the ultimate strength of the concrete.
Tests [3-5] suggest that there is no significant difference between the stress–strain curves of concrete loaded with or without a strain gradient up to the point of maximum stress. The presence of a strain gradient does appear to increase the maximum strains that can be attained in the member, however.
The dashed line in Fig. 3-2crepresents the gain in short-time compressive strength with time. The dipping solid lines are the failure limit line from Fig. 3-2b plotted against a log time scale. These lines indicate that there is a permanent reduction in strength due to sustained high loads. For concrete loaded at a young age, the minimum strength is reached after a few hours. If the concrete does not fail at this time, it can sustain the load indefi- nitely. For concrete loaded at an advanced age, the decrease in strength due to sustained high loads may not be recovered.
TheCEB–FIP Model Code 1990[3-6] gives equations for both the dashed curve and the solid curves in Fig. 3-2c. The dashed curve (short-time compressive strength with time) can also be represented by Eq. (3-5), presented later in this chapter.
Under uniaxial tensile loadings, small localized cracks are initiated at tensile–strain concentrations and these relieve these strain concentrations. This initial stage of loading results in an essentially linear stress–strain curve during the stage of stable crack initiation.
Following a very brief interval of stable crack propagation, unstable crack propagation and fracture occur. The direction of cracking is perpendicular to the principal tensile stress and strain.
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Fig. 3-2
Effect of sustained loads on the behavior of concrete in uniaxial compression.
(From [3-4].)