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.

准脆性地质材料中的开裂是一种复杂的机械现象，由跨多个长度尺度的各种耗散机制驱动。虽然最近一些有前景的工作已经采用相场方法来模拟岩土材料的损坏和断裂，但仍有几个悬而未决的问题。特别是，捕捉沿微裂纹边缘的摩擦滑动，结合低尺度物理，校准长度尺度参数，是一些例子。本论文解决了这些基本问题。通过利用基于均匀化的微裂纹固体损伤摩擦耦合公式，在宏观相场损伤变量和微裂纹密度参数。因此，相场不仅被视为裂纹位置的指标，而且还解释了微裂纹的密度。然后将统一的亥姆霍兹自由能函数构造为体能（包括弹性应变能和塑性自由能）和裂纹表面能的总和。此外，还提供了一组新的塑性自由能退化函数，并通过反映更真实的断裂过程区描述提出了长度尺度参数的校准程序。此外，加速交错迭代算法开发是为了更有效地解决强耦合问题。研究了关于宏观裂缝系统的四个数值例子，以说明所提出的模型在模拟拉伸断裂、断层滑动和剪切带方面的预测能力。