An Analytical Method For Mechanical And Stability Analysis Of Slopes

In this paper,the slope is simplified as plane strain problem.The slope is assumed to consist of homogeneous elastomer and be not subjected to other loads except gravity.The analytical gravity-induced stresses solution of slope is obtained.When the landslide occurs,the Mohr-Coulomb criterion is satisfied on the sliding surface.Based on the stress solution,the stability safety factor of the slope is defined according to the limit equilibrium theory.The most dangerous sliding surface can be obtained by using the optimization method.A slope stability analysis method that does not need to divide the landslide body into vertical slices is proposed and the main research contents are as follows:(1)The half plane with a slope is mapped onto the unit circle in ? plane by conformal transformations.Based on the mapping function proposed by Schwarz-Christoffel,the explicit expression of the mapping function,which is easy to use and has high precision,is obtained through power series approximation.Based on the complex potentials with body force,the stress boundary conditions that applicable to the problem in this paper are derived.The analytic functions are expressed as power series.Through the stress boundary condition on the ground surface,a set of linear equations with the coefficients of the power series can be directly constructed to solve the complex potential function and calculate the stress.(2)The stress results obtained by the presented analytical method are compared with the numerical solution obtained by using ANSYS software,which illustrates the correctness of the derivation and solution approach in this paper.The influence of Poisson's ratio and slope Angle on stress is analyzed and the results show:when the slope is only subjected to gravity,the smaller the Poisson's ratio is,the greater the tangential compressive stress is along the slope surface,and the greater the stress concentration near the slope foot is.In the places near the slope apex,the stress components are small and the stress contour lines are sparse,and the changes of stress value are gentle.The slope angle has great influence on the stress distribution.When the slope angle is small,the stress changes along the slope surface are relatively gentle,and the stress concentration at the bottom of the slope is not obvious.When the value of slope angle is great,the stress along the slope surface changes rapidly,and as the slope angle increases,the stress concentration at the foot of the slope increases sharply.(3)The sliding surface is described by piecewise quadratic polynomial function.When the piecewise interval is short enough,this description method can reflect arbitrary curved shape.According to the analytical stresses solution,the sliding force and sliding resistance on each point of sliding surface is calculated.And the stability safety factor is obtained.The optimization model is formed through taking the stability safety factor as the objective function and the polynomial coefficients as the design variables.The polynomial coefficients of the most dangerous sliding surface are obtained by using the mixed penalty function optimization method.(4)By using different material coefficients combinations,the safety factor results of the stability analysis method in this paper are compared with some classical analysis methods,which illustrates its reliability.The effects of Poisson's ratio and slope height on slope stability are analyzed according to the method presented in this paper.The results show:the factors of safety obtained by the method in the paper,which is based on stress analytical solution and limit equilibrium theory,are very close to the results obtained by the simplified Bishop method and the finite element strength reduction method,and are basically between the simplified Bishop method and the finite element method.The sliding surface obtained is a smooth curve concave upward,which can explain the steep cracks at the top of the slope.The results of the calculation examples show that the greater the Poisson's ratio is,the greater the safety factor of slope stability is,and the influence of Poisson's ratio is not obvious.When other parameters are the same,the slope height has a great influence on the stability safety factor,and the stability safety factor decreases rapidly with the increase of slope height.