Effect of the vertical earthquake component on permanent seismic displacement of soil slopes based on the nonlinear Mohr–Coulomb failure criterion

In the present study, a model is developed to calculate the upper bound of the seismic displacement of a slope based on the sliding rigid block model. In this model, it is assumed that the geotechnical materials satisfy the nonlinear Mohr–Coulomb (M–C) failure criterion, and the instantaneous shear strength parameters are introduced by the “external tangent method”. A sequential quadratic program, based on the nonlinear iteration procedure, is also employed to obtain the optimal solution for the objective function. Using the upper bound method and the Newmark sliding rigid block model, the effect of the vertical earthquake component on the permanent displacement of slopes is studied under the following two conditions: (1) It is assumed that the vertical acceleration is in phase with the horizontal acceleration; (2) Actual vertical ground motion records are used (i.e., the vertical and horizontal accelerations are mutually independent). The results show that the nonlinear parameter m significantly affects the permanent displacement of slopes, and that the effect of the vertical earthquake component on permanent displacement cannot be ignored. The impact of the vertical earthquake component on slope stability will be overestimated if the vertical acceleration is in phase with the horizontal acceleration.

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