Calculation method for seismic permanent displacement of cantilever retaining walls considering different movement modes

The seismic permanent displacement of cantilever retaining walls are affected by the potential slip failure characteristics of the backfill above the heel plate. In this paper, solutions of the permanent displacement are derived based on the quasi-static approach, upper bound limit analysis and Newmark sliding block model. The proposed method involves three possible wall displacement modes comprising overall rotation with log-spiral curve, horizontal translation along the wall base and rotation around the wall toe. A worked example indicates that the seismic permanent displacement obtained by the first two modes are similar and much higher than the third. Thus, the first two modes are more crucial for engineering project design. Compared with existing empirical formulas, relative error of the proposed method is below 30%. Besides, the proposed result is 7% less than that by Ambraseys-Menu's method with probability confidence level of 0.7. For the overall rotation mode of the wall-slope system under a specified horizontal seismic action, sensitivity analysis of ten main parameters' influence on the horizontal yield acceleration is conducted and the order of these sensitivities is recommended.