Determining the Dynamic Settlement of the Foundation Adjacent to Slope Using Analytical Method

Based on field studies, the topographic slope effects worsen the structural damage in an earthquake. It is very vital to determine the amount of foundation settlement adjacent to the slope. In this study, a new analytical model is proposed to determine the amount of vertical settlement of the shallow foundation near the slope. In this analytical model, the inertia force due to the sliding zone mass is considered in the dynamic equilibrium equations. Moreover, it was assumed that stiffness and damping under the foundation linearly increased as the distance from the slope edge increased. In this case, the maximum stiffness and damping at a distance five times as large as the foundation width from the slope edge were considered to be the same as maximum stiffness and damping in the non-slope scenario. The foundation was loaded harmonically by changing the frequency. Comparing the results of this study with the laboratory results leads to this observation that the offered analytical model can well determine the settlement located near the slope. Furthermore, the results showed that the settlement of the foundation near the slope edge was twice as large as the settlement in the absence of a slope. Also, the settlement of the foundation became equal to that of the non-slope foundation at a distance of 4 times as large as the foundation width from the slope edge. Furthermore, with increasing slope angle and declining the foundation distance from the slope edge, due to vertical harmonic load, the foundation settlement amount increases.