Fracture and size effect analysis in concrete using 3-D G/XFEM and a CZM-LEFM correlation model: Validation with experiments

The existence of process zones at crack tips in quasi-brittle materials is responsible for the structural size-dependent fracture strength. Hence, accurate prediction tools should not only be capable of predicting the fracture propagation and its load–displacement attributes, but should render themselves capable of the size effect analysis as well. This paper applies a robust 3-D generalized/eXtended finite element method (G/XFEM) algorithm to fracture propagation in concrete and validates its capability to capture the size effect behavior based on the cohesive zone model (CZM). Equipped with the capability of mesh adaptivity, the framework utilized in discretizing the resulting system of equations allows the adoption of independent representation for the background solid mesh and the fracture surfaces without the need for conformity between the two. The fracture simulations on a series of geometrically similar concrete beams under three-point bending have shown very good agreement with available experimental results in terms of both load–displacement (peak load and post-peak) characteristics and size effect behavior. The study also models the experimental problems using Linear Elastic Fracture Mechanics (LEFM) to investigate the structure's size threshold below which the applicability of LEFM diminishes. The effect of beam geometry and concrete material properties on the LEFM accuracy is assessed by calculating the deviations between LEFM and bilinear cohesive model solutions. The simulation results show that power functions best describe the effect of beam's depth and tensile strength, and linear functions best fit the effect of elastic modulus and fracture toughness. Subsequently, the study presents and validates an empirical correlation model that modifies the LEFM solution to predict similar ultimate strength as the CZM in addition to capturing the concrete size effect law successfully.