# Design of concrete mixes for minimum brittleness

Abstract

Abstract Designers of concrete mixes are often faced with competing requirements such as high strength and high ductility and have to rely on empirical and heuristic approaches. In the present study, this is overcome by incorporating the characteristic length 1ch and the brittleness number B into the design criteria and using well-established, mostly nonempirical, formulae relating the effective properties (elastic modulus, tensile strength, and fracture energy) to the microstructural parameters (water/cement ratio, aggregate size, and volume fractions of coarse and fine aggregates). Nonlinear mathematical optimization problems, equivalent to the design criteria, are formulated and solved with a view to: (1) maximizing 1ch for a prescribed minimum direct tensile strength f′t; (2) maximizing lch and f′t simultaneously for a prescribed compressive strength f′c; (3) minimizing B for a prescribed f′c.