The upper and lower-bound solutions of slope safety factor based on rigorous limit equilibrium method

Subjects: Mechanics >> Solid Mechanics submitted time 2023-06-21 Cooperative journals: 《应用力学学报》

许佳君 朱大勇 姚华彦 段海澎

Abstract：
The rigorous limit equilibrium method satisfies all of the equilibrium conditions,commonly with high accuracy.However,such a solution may represent neither the lower solution,nor the upper one,as the forces acting upon the interslice surfaces with some assumptions cannot ensure non-violation of failure criterion and full mobilization of those shear strengths,the results of which,to some degree,are dependent upon the assumptions made about the relationships between the interslice forces.In the paper,with the value of the factor of safety initially assumed,the normal stresses acting on the slip surface are taken as the unknowns and the coefficient of horizontal seismic forces as the objective function,the equation of the objective function is established according to the horizontal force equilibrium for the whole body of sliding mass.Then,the inequality constraint conditions are established according to the equilibrium condition of local sliding body and the failure criteria for both interslice surfaces and the slip surfaces,and the equality constraint condition is further established according to the vertical force and moment equilibrium conditions for the whole body of sliding mass.The equation of objective function as well as these constraint conditions thus constitutes a standard linear programming program; the maximum and minimal values of the coefficient of horizontal seismic forces,causing the sliding mass into rigorous limit equilibrium condition,can be precisely determined by using the simplex method.The final upper- and lower bound solutions for values of the factor of safety associated the prescribed coefficient of horizontal seismic force can be obtained by adopting an iterative procedure.The results of example study show that the difference between the upper and lower bounds of the factor of safety is within the range of 5% of the average value.Since the interslice forces on the all the interslice surfaces do not violate the failure criterion and,the shear strength of which is,to the largest extent,mobilized.Therefore,the results of present method are reasonable and theoretically rigorous.

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