Modeling Multi-Scale Damage in Transversely Isotropic Rocks: A Micro–Macro Model Based on Wing-Crack Propagation
摘要
The macroscopic mechanical behavior of transversely isotropic rocks is primarily governed by the differential response and competitive interaction between two types of highly oriented internal microstructures (e.g., foliation planes and random matrix defects) under external loading. To characterize this multi-scale damage process, a new micro–macro damage constitutive model for transversely isotropic rocks is established based on wing-crack propagation theory. This model represents the foliation planes as meso-scale wing cracks with a preferred spatial orientation and the initial matrix defects as micro-scale wing cracks with random orientations, thereby providing a unified framework to describe the distribution, propagation, and interaction of these two crack sets. Crack interactions in the model are quantified through the introduction of crack space influence functions and fracture factor degradation functions. Using an incremental constitutive formulation and a return mapping algorithm, the model successfully reproduces the complete macroscopic stress–strain response of transversely isotropic rocks, including the compaction, elastoplastic hardening, peak, and post-peak softening stages. The model is validated with experimental data under various conditions and compared with existing models, demonstrating its improved capability in capturing strength and deformation anisotropy. Furthermore, the evolution of wing-crack lengths and crack opening displacements at both scales reveals that the model not only accurately describes macroscopic anisotropic behavior but also clearly elucidates the competitive propagation mechanisms between meso- and micro-scale cracks across different deformation stages. This provides a new perspective for understanding the progressive failure of transversely isotropic rocks.