Numerical modeling the full spectrum of failure envelope of quasi-brittle materials

Quasi-brittle materials, such as rock and concrete, exhibit various failure modes depending on the loading configurations, material properties, and stress states. Numerical modeling of such a complicated phenomenon can be challenging and requires a careful consideration of the micro-mechanics. Though many numerical models, either continuum based or discontinuum based, have shown satisfying results when simulating the failure mode under a given stress state, the full spectrum of the failure envelope is rarely considered. For example, quasi-brittle rocks simulated using the discrete element method (DEM) with an elastic-brittle contact law match the compressive strength well while the tensile strength is over estimated. In this study, a novel displacement-softening contact model is implemented in the Particle Flow Code 3D (PFC3D) to simulate realistic failure modes of quasi-brittle materials while capturing the whole range of the failure envelope. Both direct and indirect strength testing configurations are considered. The numerical model is first calibrated using the uniaxial compression and Brazilian test, then the experimental results from three-point bending tests with different notch geometries are used to validate the model. Formulation of the softening contact model and the effect of the micro-scale softening parameter on the macro-scale behaviors are also discussed. Simulation results suggest that the numerical model can successfully capture both mode I and mix-mode fractures of the gypsum samples fabricated using a ProJet CJP 360 3D printer while matching the whole range of the failure envelope characterized by the Hoek-Brown failure criterion. The simulated fracture initiation and evolution processes also match the experimental observations.