Phase-field modelling of mixed-mode fracture and coalescence in fissured rocks

IF 5.6 2区工程技术 Q1 ENGINEERING, MECHANICAL

Theoretical and Applied Fracture Mechanics Pub Date : 2026-04-01 Epub Date: 2026-01-17 DOI:10.1016/j.tafmec.2026.105468

Sheng Shi , Yu Zhang , Fengjin Zhu , Anxin Meng

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Abstract

The fracture behaviour of quasi-brittle rocks plays a decisive role in the safety and stability of rock mass engineering. The phase-field method offers significant advantages in modelling complex crack propagation. In this study, by introducing a parametric energy degradation function and a geometric crack function, a phase-field damage model is developed to accurately describe the processes of crack initiation, propagation, and coalescence in rocks. In terms of numerical implementation, a staggered iterative algorithm is employed to solve the coupled governing equations of the displacement and phase fields. The model systematically simulates the fracture process of rock specimens containing pre-existing cracks at various inclinations under uniaxial compression, successfully reproducing full-mode fracture behaviours ranging from pure Mode I to pure Mode II, as well as various typical coalescence patterns such as wing cracks and bridge cracks. Furthermore, by analysing the dynamic evolution of the maximum principal stress and the maximum shear stress, the mechanical mechanisms driving crack initiation, propagation, and coalescence under tensile–shear coupled stress fields are elucidated.

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裂隙岩石混合模式裂缝与聚并的相场模拟

准脆性岩石的断裂行为对岩体工程的安全稳定起着决定性的作用。相场法在模拟复杂裂纹扩展方面具有显著的优势。本文通过引入参数能量退化函数和几何裂纹函数，建立了相场损伤模型，以准确描述岩石中裂纹的萌生、扩展和合并过程。在数值实现方面，采用交错迭代算法求解位移场和相场的耦合控制方程。该模型系统地模拟了单轴压缩下含不同倾角裂缝的岩石试件的断裂过程，成功再现了纯ⅰ型到纯ⅱ型全模断裂行为，以及翼裂、桥裂等多种典型聚结模式。通过对最大主应力和最大剪应力的动态演化分析，阐明了拉剪耦合应力场作用下裂纹萌生、扩展和合并的力学机制。

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来源期刊

Theoretical and Applied Fracture Mechanics 工程技术-工程：机械

CiteScore

8.40

自引率

18.90%

发文量

435

审稿时长

37 days

期刊介绍： Theoretical and Applied Fracture Mechanics'' aims & scopes have been re-designed to cover both the theoretical, applied, and numerical aspects associated with those cracking related phenomena taking place, at a micro-, meso-, and macroscopic level, in materials/components/structures of any kind. The journal aims to cover the cracking/mechanical behaviour of materials/components/structures in those situations involving both time-independent and time-dependent system of external forces/moments (such as, for instance, quasi-static, impulsive, impact, blasting, creep, contact, and fatigue loading). Since, under the above circumstances, the mechanical behaviour of cracked materials/components/structures is also affected by the environmental conditions, the journal would consider also those theoretical/experimental research works investigating the effect of external variables such as, for instance, the effect of corrosive environments as well as of high/low-temperature.