Abstract
An analytical three-dimensional slope reliability evaluation framework was developed in this work independent of use of numerical simulations. The slope stability analysis was necessarily carried out by utilizing an extended three-dimensional Morgenstern–Price method, which was characterized by analytical formulations and competitive computational efficiency. Incorporation of the presented stability analysis method into response surface methodology led to an effective slope reliability evaluation framework. The applicability and superiority of this framework was examined and validated using a real complicated landslide case reported in practice, and a hypothetical slope example widely adopted in the literature. The impact of correlation coefficients and probability distribution patterns on the slope reliability assessment results was further addressed to derive additional benefits of this framework.
Highlights
The stability analysis on a two-dimensional (2D) cross-section of a real slope has been stated to be capable of giving reasonable and acceptable stability evaluation of threedimensional (3D) slopes or excavations in terms of the factor of safety [1,2]
The end effect of slope geometry and probability effect of soil properties were gradually taken into account by performing 3D stability analysis and reliability analysis, with efforts to remove different hypotheses in the formulation of corresponding techniques [3,4]
This paper presents the formulation of the 3D Morgenstern–Price Method (3DMPM), and examines its accuracy and effectiveness on a practical landslide case with complex geometry, and a hypothetical spherical slope example with external evaluation results, both
Summary
The stability analysis on a two-dimensional (2D) cross-section of a real slope has been stated to be capable of giving reasonable and acceptable stability evaluation of threedimensional (3D) slopes or excavations in terms of the factor of safety [1,2]. Based on the limit equilibrium principle, the rigorous formulation for 3D slope stability analysis requires static force equilibrium and moment equilibrium on both the single column and the whole sliding mass in all directions. It includes a certain static condition of intercolumn faces and a limit state of the slip surface with specific failure criterion. The values of F3s, λ and ρj can be solved by combining Equations (21), (25) and (26) or Equations (27)–(30) and (35)
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