Concrete beams under three-point bending : size effect prediction of tensile strength and fracture process zone

Abstract

This thesis aims to predict tensile strength in concrete beams subjected to three-point bending loading and having different dimensions. Experimental concrete beams series were modeled on Cast3m software in 2D, and both deterministic and stochastic finite element methods were used to predict energetic size effect on tensile strength. Determenistic FE models of 3-point bending beams are modeled using Mazars damge model. The use of the non local approach is studied, along with the effect of the choice of internal length. Due to energetic size effect, the choice of input tensile strength is investigated. Two choices are considered: splitting tensile strength measured on cylindrical specimens and structural tensile strength calculated using analytical WL2 approach. Moving to stochastic FE method, in order to determine the random field that highly affects concrete mechanical properties, random fields on both tensile strength and Young’s modulus and the correlation between them are studied. Additionally, a sensitivity analysis of the autocorrelation length selection is carried out. In deterministic FE model, analytical WL2 method using non-local approach allows the redistribution of stresses, hence avoiding the failure of the structure. Hence, using ft estimated by analytical WL2 approach is enough to account for size effect. While in stochastic FE model, the variability on ft is the suitable solution for running SFE simulations and enough to account for size effect. What makes stochastic FE method significant is its ability to use tensile strength as random field to model size effect.