Rock is generally regarded as a heterogeneous and anisotropic material containing massive initial defects, such as cracks, joints, and porosities. In the present work, based on the maximum tensile stress and Mohr–Coulomb criteria, the fracturing modeling algorithm implemented into the numerical manifold method (NMM) is perfected and applied to a comprehensive simulation study of the fracturing of rock specimens. Disc and semi-disc specimens containing a single pre-existing crack, along with rectangular specimens containing two parallel pre-existing cracks, are simulated, respectively, to verify the fracturing modeling algorithm in terms of crack initiation, propagation, interaction, and coalescence. On this basis, four rectangular specimens containing multiple randomly distributing cracks are also simulated and the effective mechanical response of the specimen is investigated. The simulation of disc and semi-disc indicates that the crack initiation, propagation, and final crack path are all in great agreement with the experimental results. The simulation of rectangular specimens with two parallel pre-existing cracks shows the crack interaction and coalescence of the crack pairs. The results are also in good agreement with the experimental and theoretical results. For the simulation of complicated model with multiple cracks, results indicate that the increase in the crack density leads to a dramatic decrease in the effective elastic modulus and compressive strength as the evolution of pre-existing cracks. The NMM enriched with the fracturing modeling algorithm can be applied to solve more rock fracturing problems with diverse type and large number of initial defects.

岩石通常被认为是包含大量初始缺陷的非均质和各向异性材料，如裂缝、节理和孔隙。在目前的工作中，基于最大张应力和 Mohr-Coulomb 准则，对数值流形法 (NMM) 中实施的压裂建模算法进行了完善，并将其应用于岩石试样压裂的综合模拟研究。分别模拟了包含单个预存裂纹的圆盘和半圆盘试样，以及包含两个平行预存裂纹的矩形试样，以在裂纹萌生、扩展、相互作用和聚结方面验证压裂建模算法。以这个为基础，还模拟了包含多个随机分布裂纹的四个矩形试样，并研究了试样的有效力学响应。圆盘和半圆盘的模拟表明裂纹萌生、扩展和最终裂纹路径都与实验结果非常吻合。具有两个平行的预先存在裂纹的矩形试样的模拟显示了裂纹对的裂纹相互作用和合并。结果也与实验和理论结果非常吻合。对于多裂纹复杂模型的模拟，结果表明，随着已有裂纹的演化，裂纹密度的增加导致有效弹性模量和抗压强度急剧下降。