Upper Bound Method For Limit Analysis Of 3D Loess Slope Stability

Slope stability is one of the hotspot issues in geotechnical engineering.Actual slope engineering,the shape of slope failure surface has certain three-dimensional(3D)characteristics,while the two-dimensional(2D)plane-strain analysis method ignores the 3D effect,resulting in the actual slope stability assessment is conservative.Loess is widely distributed in China,and a large number of loess slopes are produced naturally or artificially.The instability process of loess slope is complex and there are many influencing factors.Therefore,it is necessary to carry out 3D loess slope stability research.Based on the upper bound theorem of limit analysis,this paper studies the stability of 3D loess slope with cracked structural plane.Programming random search method to optimize the upper limit solution of loess slope stability.On the basis of verifying the effectiveness and feasibility of the algorithm,the 3D stability under the condition of considering the structure of loess and the nonlinear failure criterion applicable to loess is further studied,and a new method and theoretical basis are proposed to solve the problem of slope stability in loess areas.The main achievements of this research are listed as follows:(1)Summary the 3D admissible rotational failure mechanism.Based on the upper bound theorem of limit analysis,the 3D critical height expression of cracked loess slope under different failure mechanisms(face failure,base failure and toe failure)is derived by introducing the crack surface in loess slope.Programming optimization program to obtain upper bound solution of critical height.Compared with the existing results,the validity and feasibility of the program are proved.Through a large number of data analysis,the influence of crack depth,soil parameters and slope constraint width on slope stability and critical sliding surface is studied.The 3D slope stability diagram of cracked loess is plotted,to quickly evaluate the slope safety factor in practical engineering and provide reference for the design of actual slope engineering.(2)Based on the 3D admissible rotational failure mechanism.The structural parameter mu is introduced to study the 3D stability of structural loess slope under different failure modes,and the expression of critical height of structural loess 3D slope is derived.The influence of structural parameter mu on the stability of loess slope is discussed by using MATLAB programming optimization calculation,which provides a theoretical basis for solving the design problems of structural loess slope engineering.(3)Based on a nonlinear failure criterion suitable for loess areas and the idea of tangent method,the strength parameters ct and φt under nonlinear failure are introduced to derive the stability number of 3D homogeneous loess slope.Compared with the results of existing literature,the accuracy of the derived results is verified.The rule between slope stability and influencing factors of loess slope with 3D spatial characteristics is studied,which provides a new train of thought for 3D loess slope analysis.