As an emerging numerical calculation method, the numerical manifold method (NMM) has incomparable advantage in solving continuous and discontinuous deformation problems in a unified framework. In this study, an improved numerical manifold method was deployed to solve the crack propagation and coalescence problem with cracking friction effect in fractured rock mass. Firstly, based on the basic theory of NMM, the structural surface roughness JRC coefficient was introduced into the friction matrix, and the numerical manifold matrix derivation of the friction matrix is embedded into the original software package, which enhanced the NMM calculation program module. A new method of numerical manifold displacement method for solving crack propagation problem is proposed. The calculation formula of stress intensity factor in crack propagation process are given, and the program module used to simulate crack propagation process was developed. Furthermore, two case study was introduced to verify the reliability and applicability of the calculation package. Through comparison of the experiment result with the numerical solution of a rectangle flawed red sandstone specimen with prefabricated hole and fissure, it could be certified that the improved method can acquired the accuracy to an extent, and also enhanced the effectiveness of the proposed method for fracture propagation and coalescence behavior under complex geometry.

作为新兴的数值计算方法，数值流形方法（NMM）在统一框架中解决连续和不连续变形问题具有无与伦比的优势。在这项研究中，采用了一种改进的数值流形方法来解决裂隙岩体中具有裂纹摩擦效应的裂纹扩展和合并问题。首先，基于NMM的基本理论，将结构表面粗糙度JRC系数引入摩擦矩阵，并将摩擦矩阵的数值流形矩阵推导嵌入到原始软件包中，从而增强了NMM计算程序模块。提出了一种求解裂纹扩展问题的数值流形位移法。给出了裂纹扩展过程中应力强度因子的计算公式，并开发了用于模拟裂纹扩展过程的程序模块。此外，引入了两个案例研究来验证计算包的可靠性和适用性。通过将实验结果与带有预制孔和裂缝的矩形缺陷红砂岩标本的数值解进行比较，可以证明改进的方法可以在一定程度上获得精度，并且可以提高所提出的断裂方法的有效性。在复杂几何形状下的传播和合并行为。介绍了两个案例研究，以验证计算包的可靠性和适用性。通过将实验结果与带有预制孔和裂缝的矩形缺陷红砂岩标本的数值解进行比较，可以证明改进的方法可以在一定程度上获得精度，并且可以提高所提出的断裂方法的有效性。在复杂几何形状下的传播和合并行为。介绍了两个案例研究，以验证计算包的可靠性和适用性。通过将实验结果与带有预制孔和裂缝的矩形缺陷红砂岩标本的数值解进行比较，可以证明改进的方法可以在一定程度上获得精度，并且可以提高所提出的断裂方法的有效性。在复杂几何形状下的传播和合并行为。