A novel micromechanics-enhanced phase-field model for frictional damage and fracture of quasi-brittle geomaterials

Abstract

Cracking in quasi-brittle geomaterials is a complex mechanical phenomenon, driven by various dissipation mechanisms across multiple length scales. While some recent promising works have employed the phase-field method to model the damage and fracture of geomaterials, several open questions still remain. In particular, capturing frictional sliding along the lips of microcracks, incorporating lower scale physics, and calibrating the length scale parameter, are some examples. The present paper addresses these essential problems. By leveraging homogenization-based damage-friction coupling formulations for microcracked solids, the linkage is built between the macroscopic phase-field damage variable and the microcrack density parameter. The phase-field is thus treated not only as an indicator for the location of cracks but also accounts for the density of microcracks. A unified Helmholtz free energy function is then constructed as a sum of the bulk energy ( including elastic strain energy and plastic free energy) and the crack surface energy. Furthermore, a new set of degradation functions for the plastic free energy are provided, and a calibration procedure for the length scale parameter is proposed by reflecting a more realistic description of fracture process zone. In addition, an accelerated staggered iteration algorithm is developed to solve the strongly coupled problem more efficiently. Four numerical examples concerning a system of macroscopic cracks are investigated to illustrate the predictive capability of the proposed model in simulating tensile fracture, fault slippage and shear bands.