基于相场数值流形法的裂隙岩体断裂失稳机理研究

Fractures in rock masses are generally in a mixed-mode state (tension-shear or compression-shear). In rock material, critical energy release rate for mode I fracture is significantly lower than that for mode II fracture. A phase field numerical manifold method is proposed in this project, to simulate the initiation, propagation, branching and coalesce of mixed-mode fractures. Based on the classical numerical manifold method, a multi-field physical cover function including phase field is constructed. A diffuse fracture propagation model with two strain energy release rates is developed in the framework of the phase field numerical manifold method, considering the fact that mode II fracture strain energy release rate can be orders of magnitude higher than that of mode I fracture. Fracture initiation positions, propagation directions, and steps are solved implicitly with nonlinear iteration algorithm, which significantly reduces errors resulted from unreasonable assumptions and people’s intervention. To track the topology and the opening of the diffuse fracture, a transition scheme from diffuse fracture model to sharp cohesive fracture model based on equivalent energy dissipation principle is proposed together with an efficient diffuse fracture tracking algorithm and a cohesive fracture model. An analysis program with parallel computing extensible to engineering application is developed, based on which, failure mechanisms of fractured rock massed are analyzed.

岩体中的裂纹通常处于复合应力状态（拉剪、压剪）下，其I型裂纹临界应变能释放率远小于II型裂纹临界应变能释放率。本项目提出“相场数值流形法”，用于岩体中复合应力状态下裂纹萌生、分叉扩展、贯通等裂纹动态扩展模拟。该方法基于经典数值流形方法，构造包含相变量在内的多场物理覆盖函数。考虑岩体中I型裂纹、II型裂纹应变能释放率相差悬殊的特性，建立岩体相场数值流形法双应变能释放率弥散裂纹扩展模型。该模型实现裂纹萌生位置、扩展路径的非线性隐式求解，显著降低裂纹扩展过程中不合理假设以及人为干预所产生的误差。基于能量耗散守恒原理，建立弥散裂纹跟踪算法和黏聚型弥散裂纹模型，提出岩体弥散-离散裂纹模型转换理论，获得弥散裂纹拓扑形状及开度。开发可延伸至工程应用的并行计算分析程序，开展裂隙岩体断裂失稳机理研究。

岩体在漫长的自然风化和构造地质作用下，其内外边界都具有复杂的几何特征。此外，由断层节理控制的岩体变形具有典型的连续-非连续特性。.本项目基于流形元理论，主要研究荷载作用下复杂裂隙岩体连续-非连续变形3D数值计算方法。考虑岩体复杂几何特征为CAD建模以及高质量（如六面体网格）协调网格划分等带来的困难和巨大的工作量，发展可直接采用可自动获取的点云模型、规则网格的流形元自动化前处理方法。.经过三年期的项目探索，我们发展了直接基于图像模型、采用规则网格的流形元三维计算方法，并通过一系列具有解析解或参考解的算例验证了方法的正确性和收敛性。将这一方法应用到实际复杂岩体工程分析中，直接采用这些复杂岩体的点云（图像）模型，实现了复杂裂隙岩体连续-非连续变形的自动化计算，并进一步分析了其连续-非连续三维变形机理。.本项目的实施，对复杂裂隙岩体连续-非连续三维自动化计算，考虑岩体三维特性科学评价其稳定性以及支护措施，具有重要意义。