A displacement-softening contact model for discrete element modeling of quasi-brittle materials

A displacement-softening contact model is proposed to simulate the failure behaviors of quasi-brittle materials using the discrete element method (DEM) based on spherical particles. The contact model is modified from the parallel bond option in the DEM code PFC2D/3D. By adjusting the softening coefficient, which defines the ratio between the unloading and loading contact stiffnesses in the normal component, the softening contact model can not only yield realistic compressive over tensile strength ratios as high as about 30, but also capture the highly nonlinear failure envelope at the low confining stress range, typical for rocks. Formulation of the contact model is first introduced. Uniaxial compression, direct tension and confined compression/extension tests are then performed in both 2D and 3D to illustrate the effects of the softening coefficient on the micro- and macro-scale failure mechanisms, the stress-strain behaviors and the compressive over tensile strength ratio. Calibration of the mechanical properties is conducted to identify the set of micro-scale parameters for two widely modeled rocks, Lac du Bonnet granite and Berea sandstone. Excellent agreement is achieved between the numerical simulations and the experiments in terms of the uniaxial strengths and the failure envelopes.