To determine seismic permanent displacement of a new type of assembled multi-step cantilever retaining walls

based on overall rotation-sliding failure mode of the wall-slope system with potential slip surface passing by the bottom edge of the heel plate of the lowest wall member

the seismic yield acceleration coefficient of the wall-slope system is proposed by the upper bound limit analysis and pseudo-static method. Moreover

according to Newmark’s block method

calculation formulas of seismic horizontal permanent displacement at the top of each step of the wall including two

three

and four steps are derived via angular displacement of the wall-slope system determined by quadratic integration of the rotational angular acceleration. Compared with shaking table tests and numerical simulations of the wall models with two and three steps

the horizontal permanent displacements under two-step and three-step walls calculated by the proposed analysis method are 10-40% and 10-30% larger than those by the tests

respectively. However

the theoretical results are relatively close to the numerical simulation results. Analysis results of the practical example show that the proposed method is generally more conservative than the numerical simulation method. Internal friction angle and cohesion of the backfill have greatly positive correlation with the horizontal yield acceleration of the wall-slope system

while the height of a wall member has obvious negative correlation with the horizontal yield acceleration of the wall-slope system. However

width of the bench between vertically adjacent wall members

length and thickness of bottom plate of a wall member have little effect on it. In addition

the total number of the vertically assembled walls has nonlinear and positive correlation with the horizontal yield acceleration

and the seismic horizontal permanent displacement of the system is decreasing as the filling soil particle size decreases gradually.