Decoupled Solution for Seismic Permanent Displacement of Earth Slopes Using Deformation-Dependent Yield Acceleration

The Newmarkian sliding block analogy has been broadly used to evaluate earthquake-induced displacements of natural and man-made earth slopes. However, several modifications have been proposed by researchers to improve the analytical basis of this analogy. In this article, an analytical procedure is proposed to study interactive effect of downward-stabilizing-movement and seismic response of sliding mass through a decoupled procedure. A generalized single degree of freedom (SDOF) system with distributed mass and stiffness is employed to obtain system response, while the sliding mass is considered as a perfect flexible chain moving along the planes with gradually gentler inclinations. The results show that effect of the proposed modification is significant for period ratios (i.e., fundamental period of system to mean period of input motion) close to one, mainly in the case of small slippage lengths. Analyses using harmonic input motion indicate that time interval between initiation and stoppage of sliding phase is lower for smaller sliding length. Accordingly, lower displacements are obtained for smaller sliding lengths. The analyses representing the effect of acceleration coefficient ratio (i.e., the ratio of yield acceleration to maximum horizontal equivalent acceleration, ACR) show that at lower values of ACR, higher contributions of downward-movement are involved in computed displacements. Whereas, as the value of ACR gets larger, this effect is minimized, i.e., the proposed method tends to imitate the conventional decoupled procedure wherein the permanent displacements tend toward zero. Further studies revealed that as period ratio increases (no larger than one) the order of period ratio contribution increases as well, resulting in smaller permanent displacements, while the effect of downward-movement decreases as period ratio becomes larger than one.