The toppling failure of anti-dip rock slopes is significantly affected by crack propagation from non-persistent cross-joints (NPCJs). In this study, a strength-based localized maximum stress (SLMS) criterion is adopted to model the toppling failure process caused by crack propagation in anti-dip rock slopes containing a set of NPCJs via the finite element method. The crack initiation sequence from NPCJs and the toppling evolution of anti-dip slopes under different stratum dips and slope angles, as well as the influences of stratum dips and slope angles on toppling evolution, are investigated. Variations in the displacements during the toppling of the slope and the influence of toppling on the displacements are analyzed. Additionally, variations in the magnitude and distribution area of interlayer friction between rock layers during the toppling evolution process and the effects of toppling on the evolution of interlayer friction are examined. The results indicate that the toppling process of the anti-dip slope containing NPCJs involves three stages: crack initiation and propagation from the NPCJs, the development of interlayer tensile and shear cracks, and toppling failure of the rock layers. The stability of anti-dip slopes containing NPCJs is greatly affected by the stratum dip and slope angle. The horizontal displacements and interlayer crack aperture increase nonlinearly with the development of toppling evolution, and the magnitude of the increase gradually increases. Moreover, the magnitude and distribution area of interlayer friction vary with the development of toppling evolution. The maximum interlayer friction gradually increases, but the distribution area of friction decreases.

中文翻译：

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通过基于强度的断裂方法研究含有非持久性交叉节理的反倾岩边坡的倾倒破坏

反倾岩边坡的倾倒破坏受到非持久性交叉节理（NPCJ）裂纹扩展的显着影响。在本研究中，采用基于强度的局部最大应力（SLMS）准则，通过有限元方法模拟包含一组 NPCJ 的反倾岩石边坡中裂纹扩展引起的倾倒破坏过程。研究了不同地层倾角和坡角下NPCJ裂缝萌生序列和反倾边坡的倾倒演化过程，以及地层倾角和坡角对倾倒演化的影响。分析了边坡倾倒过程中位移的变化情况以及倾倒对位移的影响。此外，还考察了倾覆演化过程中岩层间层间摩擦力大小和分布区域的变化以及倾覆对层间摩擦演化的影响。结果表明，含有NPCJ的反倾边坡的倾倒过程经历了3个阶段：裂纹从NPCJs起生和扩展、层间拉裂和剪切裂缝的发展以及岩层的倾倒破坏。含有NPCJ的反倾边坡的稳定性受地层倾角和坡角的影响较大。随着倾倒演化的发展，水平位移和层间裂缝孔径呈非线性增加，且增加幅度逐渐增大。而且，层间摩擦力的大小和分布区域随着倾覆演化的发展而变化。最大层间摩擦力逐渐增大，但摩擦力分布面积减小。