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<p>The Numerical Manifold Method (NMM) introduces two independent cover systems—mathematical and physical—allowing discontinuities associated with crack propagation to be represented in a natural manner. To clarify the instability pattern and crack evolution of stratified rock slopes under top loading, this study implements a quadrilateral NMM framework incorporating the LT criterion, formulated from the Mohr–Coulomb strength theory, together with a damage factor. The LT criterion is used to determine the onset and propagation of cracks, while the damage factor serves to distinguish crack types. The proposed framework is first examined through a Brazilian splitting test, which confirms its capability to resolve crack development in a transparent and physically consistent way. It is then applied to systematically investigate the failure pattern and crack propagation characteristics of stratified slopes containing cracks of different inclinations or randomly distributed bedding cracks under overload conditions. The results show that, as crack inclination increases, the failure pattern of top-loaded stratified slopes shifts from shallow bedding-parallel shear failure to deep sliding–tensile composite failure. For slopes with randomly distributed bedding cracks, progressive failure follows a sequence of dispersed crack initiation, coalescence, penetration, and subsequent layered sliding–splitting. The proposed method captures the complex discontinuous failure process with high fidelity, demonstrating its effectiveness for stability analysis of stratified slopes with inherent cracks. The findings provide a theoretical basis for hazard assessment and protective design of top-loaded stratified rock slopes.</p>

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Investigation of progressive failure and instability in stratified rock slopes based on the NMM

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月6日

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  • Dawen Tan,
  • Tao Wan,
  • Chunyao Hou,
  • Heng Cheng,
  • Hongyi Zhang,
  • Jingjie Tian

摘要

The Numerical Manifold Method (NMM) introduces two independent cover systems—mathematical and physical—allowing discontinuities associated with crack propagation to be represented in a natural manner. To clarify the instability pattern and crack evolution of stratified rock slopes under top loading, this study implements a quadrilateral NMM framework incorporating the LT criterion, formulated from the Mohr–Coulomb strength theory, together with a damage factor. The LT criterion is used to determine the onset and propagation of cracks, while the damage factor serves to distinguish crack types. The proposed framework is first examined through a Brazilian splitting test, which confirms its capability to resolve crack development in a transparent and physically consistent way. It is then applied to systematically investigate the failure pattern and crack propagation characteristics of stratified slopes containing cracks of different inclinations or randomly distributed bedding cracks under overload conditions. The results show that, as crack inclination increases, the failure pattern of top-loaded stratified slopes shifts from shallow bedding-parallel shear failure to deep sliding–tensile composite failure. For slopes with randomly distributed bedding cracks, progressive failure follows a sequence of dispersed crack initiation, coalescence, penetration, and subsequent layered sliding–splitting. The proposed method captures the complex discontinuous failure process with high fidelity, demonstrating its effectiveness for stability analysis of stratified slopes with inherent cracks. The findings provide a theoretical basis for hazard assessment and protective design of top-loaded stratified rock slopes.