Development of three-dimensional failure mechanisms and genetic algorithm for limit analysis of two-layer slopes
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Development of three‑dimensional failure mechanisms and genetic algorithm for limit analysis of two‑layer slopes Li Zheng1 · Lin Li1 · Jingpei Li1 Received: 7 March 2020 / Accepted: 16 June 2020 © Springer Nature B.V. 2020
Abstract This paper develops general three-dimensional kinematically rotational failure mechanisms for two-layer soil slopes, which not only considers the back slope angle but also involves the face-failure, toe-failure and base-failure mechanisms. Although the failure mechanisms are developed for two-layer soil slopes, it is easy to extend for multilayer soil slopes with the framework proposed in this study. Genetic algorithm (GA), which poses the advantages of highly computational efficiency over the traditional loop searching method, is developed to search for the upper bound of the critical height of slope. The proposed mechanisms could perfectly reduce to the failure mechanism of single-layer slopes, and the results generated from the GA algorithm are more critical than those of other available approaches, which indirectly identifies the validity of the current analysis and shows the advantage of the GA algorithm. Parametric studies, which cover a wide range of soil slope angle, back slope angle, relative layer thickness and soil strength as well as the width of restriction, are performed to investigate the transformation of the failure mechanism and the corresponding the critical height of two-layer slopes. Keywords Two-layer slope · 3D failure mechanism · Genetic algorithm · Highly computational efficiency List of symbols a Distance between the midline of the conical volume to the surface of slope BC b Width of ‘plane insert’ B Width of slope ci Cohesion of soil ( i = 1, 2) c̄ Equivalent cohesion
* Lin Li [email protected] Li Zheng [email protected] Jingpei Li [email protected] 1
Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China
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Natural Hazards
d Distance between the midline of the conical volume to the top surface of slope d∗ Distance between the midline of the conical volume to the interface of two soil layers A1 B1 2D , Rates of internal energy dissipation of cohesive-frictional soil for toeD3D D cf,T cf,T failure mechanism 2D , Rates of internal energy dissipation of purely cohesive soil for toe-failure D3D D c,T c,T mechanism , D2D Rates of internal energy dissipation of cohesive-frictional soil for faceD3D cf,F1 cf,F1 failure mechanism when H ′ ≤ H 2D , Rates of internal energy dissipation of cohesive-frictional soil for faceD3D D cf,F2 cf,F2 failure mechanism when H ′ > H , D2D Rates of internal energy dissipation of purely cohesive soil for face-failure D3D c,F1 c,F1 mechanism when H ′ ≤ H 3D 2D Dc,F2 , Dc,F2 Rates of internal energy dissipation of purely cohesive soil for face-failure mechanism when H ′ > H 3D 2D Dcf,B , Dcf,B Rates of internal energy dissipation of cohesive-frictional soil for basefailure mechanism , D2D Rates of internal energy dissipation of purely cohesiv
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