A four-way enhanced numerical manifold method (NMM) is proposed in order to simulate crack propagation in rock media and progressive failure of jointed rock slopes. Specifically, the original NMM is improved in the following four aspects: (1) An “enriched local approximation” is employed to characterize singularity and discontinuity of the displacement/stress fields near the crack tip. (2) A “modified generalized Duffy transformation” is proposed to improve the accuracy of numerical integration associated with the 1/r and $1/\sqrt{r}$ singularities. (3) A “critical length cracking criterion” is introduced to determine propagation length and direction for both tensile-shear and compressive-shear cracks in rock mass. (4) A “cone-complementary-based contact formulation” is incorporated to resolve the cohesive/frictional contact phenomena between discontinuous interfaces more accurately. Some examples demonstrate the performance and application prospect of the presented NMM in stability and failure analysis of the jointed rock slopes.

为了模拟裂缝在岩石介质中的传播以及节理岩质边坡的渐进破坏，提出了一种四向增强数值流形方法（NMM）。具体而言，原始的NMM在以下四个方面进行了改进：（1）采用“丰富的局部近似”来表征裂纹尖端附近位移/应力场的奇异性和不连续性。（2）提出了“修正的广义Duffy变换”，以提高与1 / r和$\mathrm{1个}/\sqrt{\mathrm{[R}}$奇点。（3）引入“临界长度开裂准则”来确定岩体中的拉伸剪切裂缝和压缩剪切裂缝的传播长度和方向。（4）引入了“基于圆锥互补的接触配方”，以更准确地解决不连续界面之间的内聚/摩擦接触现象。一些实例证明了所提出的NMM在节理岩质边坡稳定性和破坏分析中的性能和应用前景。