<p>To address the challenge of calculating the flexural toppling fracture depth of antidip layered slopes under seismic loading, this study proposes a mechanical analysis model based on the stress exceedance principle. A force system for the rock plate is established using the cantilever beam theory. In this model, we comprehensively consider the coupling of the rock gravity stress, interlayer sliding resistance, and seismic dynamics. Then, an analytical solution is derived for the fracture depth of the rock plate due to flexural toppling. The accuracy of the proposed model is validated through DEM simulations (discrete element method) and engineering case studies, which also reveal the mechanism of seismic-induced toppling failure in slopes. To examine the stress assumptions in the analytical model, FEM simulations (finite element method) are conducted to obtain interlayer stresses, which are then compared with the results from the analytical formula. The comparison shows that numerical methods yield more precise predictions of the fracture depth at the slope toe. In addition, parameter sensitivity analysis indicates that the toppling instability of antidip slopes mainly occurs when the interlayer dip angle exceeds 60°. For antidip slopes with slope angles greater than 65°, failure tends to manifest as shallow toppling or collapse. The fracture depth shows high sensitivity to the rock layer thickness. Thus, techniques such as anchor bolting that effectively bond multiple rock layers into a single unit can greatly enhance slope stability.</p>

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Analytical Model for the Toppling Fracture Depth of Antidip Layered Rock Slopes Under Seismic Loading

  • Yang Wang,
  • Fei Ye,
  • Leilei Jin,
  • Ning Sun,
  • Shuang Yao,
  • Wenxi Fu

摘要

To address the challenge of calculating the flexural toppling fracture depth of antidip layered slopes under seismic loading, this study proposes a mechanical analysis model based on the stress exceedance principle. A force system for the rock plate is established using the cantilever beam theory. In this model, we comprehensively consider the coupling of the rock gravity stress, interlayer sliding resistance, and seismic dynamics. Then, an analytical solution is derived for the fracture depth of the rock plate due to flexural toppling. The accuracy of the proposed model is validated through DEM simulations (discrete element method) and engineering case studies, which also reveal the mechanism of seismic-induced toppling failure in slopes. To examine the stress assumptions in the analytical model, FEM simulations (finite element method) are conducted to obtain interlayer stresses, which are then compared with the results from the analytical formula. The comparison shows that numerical methods yield more precise predictions of the fracture depth at the slope toe. In addition, parameter sensitivity analysis indicates that the toppling instability of antidip slopes mainly occurs when the interlayer dip angle exceeds 60°. For antidip slopes with slope angles greater than 65°, failure tends to manifest as shallow toppling or collapse. The fracture depth shows high sensitivity to the rock layer thickness. Thus, techniques such as anchor bolting that effectively bond multiple rock layers into a single unit can greatly enhance slope stability.