3D limit analysis of reinforced concrete with sliding along smeared cracks

Limit analysis (LA) is successfully used for investigating the bearing capacity of reinforced concrete (RC) structures. Some cautions must be taken when using this method for RC since the concrete component exhibits a softening behavior with decreasing strength and limited ductility. A commonly adopted provision consists of considering isotropic reduced values of concrete strength to be input in the analysis (empirical effectiveness factors). In this paper, an alternative and completely new approach is proposed and investigated in which concrete strength is weakened in a more targeted manner. To that purpose, the commonly used 3D truncated Mohr-Coulomb (TMC) criterion is adopted to classically describe the compressive, tensile, and shear failure of concrete. However, TMC is here in an original way enriched by additional constraints that allow to account for weakness and anisotropy induced by preferential failure patterns, assumed a priori. The limit analysis approach is then formulated for two dual analyses in the convex optimization framework, making it possible to quantify the numerical error and obtain a lower and an upper bound of the limit load. Numerical examples illustrate the agreement of the formulation with academic results and laboratory tests.