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.