A modified Newmark block method for determining the seismic displacement of a slope reinforced by prestressed anchors

The seismic permanent displacement is an essential aspect to evaluate the seismic stability of slope. The conventional Newmark block method commonly adopts a constant yield acceleration to determine the seismic permanent displacement of slope. In order to reflect a more realistic behavior of seismic displacement, the dynamic kinetic failure mechanism and the instant displacement model of slope reinforced by prestressed anchors in infinitesimal time are established. The time-dependent formula for dynamic yield acceleration is deduced based on upper bound method. A modified method is proposed to determine the seismic permanent displacement within the framework of Newmark block theory. The results are compared with the existing work with regard to the yield acceleration and seismic permanent displacement. Three typical seismic ground motions are performed to study the responses of the anchor force, the dynamic yield acceleration and the seismic permanent displacement. Results show that the anchor force, the dynamic yield acceleration and the seismic displacement all increase continuously during the excitation of seismic ground motion. The anchor causes the yield acceleration to increase, and the seismic permanent displacement to decrease significantly. The conventional method adopting a constant yield acceleration greatly overestimates the seismic permanent displacement.