Seismic bearing capacity of shallow foundations subjected to inclined and eccentric loading using modified pseudo-dynamic method

In this paper, a comprehensive parametric study is conducted to evaluate the seismic bearing capacity of shallow strip foundations overlying dry and cohesionless granular soil under the actions of inclined and eccentric loadings. For this purpose, a systematic combination of the lower-bound theorems of the limit analysis, the finite element method, and the nonlinear programming is implemented. The seismic loading condition is simulated by the well-established modified pseudo-dynamic (MPD) approach by accounting for the significant influence of phase difference as well as the primary and shear waves propagation through applying non-uniform inertia forces along the vertical and horizontal directions, respectively. Unlike the pseudo-static approach, in the so-called modified pseudo-dynamic loading, a more realistic dynamic nature of the seismic excitation is taken into account using various soil dynamic properties and spectral parameters of the problem under study. In this way, a more viable response of the shallow foundation subjected to seismic loading could be captured by simulating a visco-elastic material through the well-defined Kelvin-Voigt model. The modified pseudo-dynamic (MPD) method considers the influences of shear and primary wave velocities, amplification of earthquake loading, and period of lateral shaking. The current MPD approach is capable of considering the local site effects and damping characteristics of the soil deposit underneath shallow footing by adopting a non-uniform and nonlinear acceleration field inside the soil medium. The results of the seismic bearing capacity are presented in the forms of spectral responses and failure envelopes for the eccentric and inclined loadings. The results show that the failure envelopes of the shallow foundation subjected to either inclined or eccentric loading significantly shrink with the increase in the earthquake accelerations and decrease in the material damping of the underlying soil mass. The amount of changes in the size of failure envelopes in the normalized V-H and V-M spaces due to the variation of seismic intensity and material damping depends directly on the non-dimensional frequency of the earthquake excitation.