Seismic Active Earth Pressure of Granular Soils Considering Inhomogeneous Wave Velocities under Harmonic Excitation

Complete analytical solutions were developed for horizontal and vertical seismic accelerations considering wave velocities varying with depth as a generalized power-law function. This was done by enforcing the traction-free ground surface and the base’s displacement compatibility condition. The resultant horizontal and vertical accelerations were used to compute the seismic active thrust on a rigid retaining wall supporting dry granular soils. The seismic stability problem was solved using a conservative statically admissible stress limit analysis coupled with the finite element procedure, and the greatest lower bound was found using robust second-order cone programming. The active earth pressure coefficient was obtained in the time and frequency domains and found to be affected by the combined effect of shear and primary waves. The influence of the horizontal acceleration coefficient was not generic but dependent on the level of proximity of the selected frequency to the corresponding fundamental frequency. The present study also proposed simple mathematical functions to define the slip surface using a rigorous curve-fitting procedure from the numerical data based on the strong duality of the collapse load theorems and advanced primal-dual interior-point algorithms for optimization. The validity of slip surfaces has been ascertained by comparing them with the trend of the shear strain rate and experimental results. The slip surface was found to be planar or nonplanar, depending on the level of wave velocity heterogeneity, horizontal acceleration coefficient, and the relative difference between the selected and corresponding fundamental frequency.