The conventional Newmark model is widely used for the estimation of permanent deformations of slopes during earthquakes. However, the calculation procedure for permanent displacements in the Newmark model is based on a distinct and fixed slip surface. In other words, the Newmark model neglects the effects of variable critical slip surfaces during an earthquake on evaluation of permanent displacements. By combining a finite element seismic analysis and dynamic programming, this paper first indicates that the critical slip surfaces and associated minimum factors of safety of a slope during an earthquake vary with time over a wide range. Then, a modified Newmark procedure which considers the effects of variable critical slip surfaces is presented to evaluate seismic displacements of slopes. Its application to a homogeneous slope subjected to two different types of motions shows that the neglect of variation of critical slip surfaces may result in an incorrect estimation of permanent displacement of slopes during an earthquake.
The seismic stability analysis of slopes now can be carried out by using a number of techniques such as an elasto-plastic finite element computation, Newmark"s sliding block model (1965), and a pseudo-static analysis. Probably Newmark"s model is most frequently used in practice for estimating earthquake-induced permanent displacements of slopes. A number of modified versions of Newmark"s method have been developed in the past two decades (e.g. Makdisi, 1978, Kramer & Smith, 1997) to deal with more rationally seismic stability problems of slopes. In both the original and modified Newmark"s methods, slope permanent displacements are estimated along a distinct slip surface. This surface, which was usually determined as the static critical slip surface was assumed to remain at a fixed location throughout an earthquake. In other words, all these analysis methods neglect the effects of variable critical slip surfaces during earthquake shaking.
