Preliminary study of seismic permanent displacement of 3D slope

An approach for evaluating the seismic permanent displacement of 3D slope is presented, which extends the famous Newmark's method to three dimensions. For a certain potential sliding mass, its yield acceleration and average seismic acceleration-time history are obtained from the 3D limit equilibrium theory and numerical analysis, relatively. Then, the seismic permanent displacement is estimated by integrating twice with respect to time over the parts of an average acceleration-time history that exceed the yield acceleration. A case study indicates that the presented method is reasonable. However, by using the traditional 2D method, the yield acceleration and peak of average acceleration are lower and seismic permanent displacement is higher; and the error decreases gradually with the increase of the length of sliding mass.