Analytical Calculation And Analysis Of Stability For Homogenous Soil Slopes And Optimization Program Complied By MATLAB

The problem of slope stability analysis has always been a concern of geotechnical engineering.The disasters caused by slope instability are not uncommon,So It is very important to evaluate the slope stability effectively and quickly.In this paper,two kinds of seismic slope stability analysis algorithm are proposed based on the quasi-static method,one is to divide the soils into kinds of vertical slices,and another one is to divide the soils into horizontal slices and oblique slices.By introducing the vertical central angle,the analytical expressions of the safety factor with respect to the vertical center angle are established,and the optimization program is compiled by MATLAB software.In this paper,the main contents are as follows:By introducing the vertical central angle,the analytical expressions of the safety factor deduced by the method of vertical slice and the method of combination of horizontal slices and oblique slices with respect to the vertical center angle are established based on the Mohr-Coulomb criterion.At the same time,the slope stability problem is transformed into the multi-dimensional nonlinear constrained optimization problem,and the optimization program is compiled by MATLAB software.The correctness of the analytical algorithm and the optimization program is verified by the numerical examples.The variation law of the yield horizontal acceleration coefficient Kh.max with the dimensionless parameters ?c,the slope angle ? and the internal friction angle(p are analyzed.The effects of scale factor ?,horizontal seismic acceleration coefficient kh on safety factor and potential sliding surface are analyzed,and the effects of seismic amplification on the stability analysis are analyzed.It is found that the amplification effect should be considered when kh is comparatively large(K_h>0.10).Based on the analytical expressions of safety factor and dimensionless parameters,some tables are designed to estimate the safety factor and its corresponding critical slip surface for homogeneous soil slopes.Based on the center point method,the analytical expression of safety factor deduced by the method of combination of horizontal slices and oblique slices is applied to calculates slope reliability,when c and?are normal distribution.The influence of coefficient of variation ?,slope inclination ? and internal friction angle?on the reliability index ? and failure probability Pf are analyzed.It is found that it is unreasonable to evaluate the slope stability based on the condition F_s =1 when the coefficient of variation ? is comparatively large(?>0.10).