Spring-Supported Newmark Model Calculating Earthquake-Induced Slope Displacement

In a conventional Newmark slope model, a soil block is assumed to slide along a rigid plane in a perfectly plastic mode when an input motion exceeds yield acceleration. In reality, a small deformation may well be expected to occur immediately before sliding due to shear deformation in a thin layer underneath the sliding block. In this research, a spring-supported Newmark model (SSNM) has been developed by adding a linear spring for the presliding yield displacement $u_0$ to the slider of the conventional Newmark model (CNM), demonstrating the reproducibility of key behavior of slope sliding in model tests. Dynamic responses of slopes to harmonic and earthquake motions have been calculated to find that in the SSNM the acceleration for slide initiation tends to overshoot the yield acceleration of the CNM by a larger margin due to a tiny yield displacement $u_0$ of millimeters. The overshoot is also found to become larger with increasing input frequency, which has also been observed in model shaking table tests. According to example calculations on a typical slope with realistic design parameters shaken by recorded strong earthquake motions, the number of slide repetitions and the associated cumulative slope displacements are calculated much smaller than in the CNM due to the overshooting of yield acceleration. Thus, the newly developed SSNM can be more realistic than the conventional method in evaluating seismic slope behavior by providing a small yield deformation $u_0$ as a specific slope-dependent parameter.