General Aspects of Size Effect and Brittleness in Concrete Structures
In the preceding chapter, it became obvious that the strength of geometrically similar specimens of a quasibrittle material ■ – particularly concrete— can be written in the general form
where ft is the tensile strength, D a characteristic stmctural dimension, and t a characteristic material size; we explicitly indicate that the function depends on geometry, which is equivalent to say that the dependence on D/t is different for different structural types and loading.
The material characteristic size t (as well as the function ф itself) is different for the various existing models. However, as shown in the previous chapter, all the models can be set to give very similar size effect predictions over the practical experimental range; thus, there is a strong correlation between the fracture parameters of the various models for a given material.
In principle, the foregoing equation can be computed for every geometry and material model. In practice, computations can be very complex except for some simple cases. Thus, simplified expressions are convenient to extrapolate the experimental results. The simplest of these expressions is Bazant’s size effect law expounded in Chapters 1 and б — Eqs. (1.4.10) or (6.1.5). As discussed in the previous chapter, this law can be generalized to give mote precise descriptions over a broader range of sizes and a broader range of geometries. However, the extended size effect laws, including those derived from cohesive models, require information that is usually lacking for the classical tests on which the formulas for the codes were based. Therefore, in this chapter, wc mostly use the simplest (Bazant’s) law in comparing the experimental trends and the theoretical size effect. The correlations in the previous chapter can then be used to shift. to other models.
In this section, we first discuss the conditions under which Bazant’s size effect law is expected to give a good description of the size effect; we then analyze the existing proposals to characterize the structural brittleness through a brittleness number. We conclude the section by examining the general methodology proposed by Bazant to generate size effect corrections to ultimate loads in codes, including the effect of reinforcement.
Figure 10.1.1 (a) Load-deflection curves for a relatively ductile structure (full line), and for a brittle structure that fails at first cracking (dashed line), (b) A brittle structure failing at crack initiation, the crack at maximum load still being microscopic.