A 3-D Limit Analysis Method For Slope Stability Considering The Non-Associated Flow Rule

The associated flow rule is the theoretical basis of the 3D slope stability analysis upper bound method. One of the consequences of the associated flow rule is that the plastic dilation velocity (strain rate) of rock and soil mass is perpendicular to the yield surface. This assumption is not always coincidental to the tests, so it may overestimate the dilatation property of the rock and soil mass. The disagreement of the dilatation property and the associated flow rule results in the fact that the 3D slope stability upper bound method may overestimate the limit load of the slope (or the factor of safety), and the velocity field can not converge due to the big dilatation angle during the calculations. Therefore, introducing the non-associated flow rule in the 3D slope stability limit analysis is the ultimate approach to solving the problem, so that the rock and soil mass can dilate according to its physical admission conditions.A 3D slope stability limit analysis method based on the non-associated flow rule is proposed in the paper. This method allows that the rock and soil mass follow one angle less than or equal to the internal friction angle when dilating, so it can get over the limitation of the associated flow rule. In order to solve the problem that the energy dissipation is related to the perpendicular force that can't be known in advance, the proposed approach is that, by constructing a virtual velocity field, the unknown internal force on the velocity discontinuity surface will disappear through virtual work principle. Then the energy dissipation can be easily calculated and the problem will be converted to solving a non-linear equation only including one unknown F. So the factor of safety can be calculated by iteration through numerical calculation. The 3D slope stability limit analysis method based on the non-associated flow rule can avoid the limitation that the velocity field may not converge because of the big friction angle in the 3D slope stability upper method. A series of examples have showed that the result using this method is equivalent to the generalized solution of wedge stability in solving the wedge stability problems. Furthermore, the method can also get feasible result in solving other 3D slope stability problems that the slip surface is arbitrary.This paper applies the mixed optimization strategy to seeking the critical slip surface and critical slip pattern of 3D slope stability. A series of examples haveshowed that the mixed optimization methods such as the simulated annealing - genetic algorithm; simplex-simulated annealing method; can get satisfactory results in solving the problems. The mixed optimization method is a very powerful tool in searching for the global minimum factor of safety.Furthermore; This paper discusses the visualization method of 3D slope stability. The terrain before and after sliding is rebuilt by combining the bilinear interpolation and the random fractal; and the stratum surface is simulated by the scattered - data spatial curved surface rebuilding technique. So the 3D slope Visualization model can be built.