Yield design based numerical analysis of three-dimensional reinforced concrete

The present contribution aims at evaluating the load bearing capacity of massive reinforced concrete structures using a finite element implementation of the lower bound static approach and the upper bound kinematic approach. The concrete is modelled using the three-dimensional Rankine criterion while rebars are modelled using a homogenization procedure by modelling the strength of each individual reinforcement with its surrounding concrete volume as an isotropic continuum accounting for the axial strength of the reinforcing inclusion. Both static and kinematic approaches are written as optimization problems which are solved using Semi-Definite Programming (SDP) techniques. The whole design method will be illustrated on the typical example of evaluating the ultimate bearing capacity of a reinforced concrete bridge pile cap, leading to a fairly narrow bracketing of the exact failure load of this kind of structure.