Modified Pseudo-Dynamic Bearing Capacity of Shallow Foundations Subjected to Inclined-Eccentric Combined Loading

Abstract

Shallow foundations are commonly subjected to simultaneous inclined and eccentric combined loadings exerted by the overlying superstructure and geo-environmental sources. The performance of such footings in seismic-prone areas is a topic of great interest in geotechnical engineering practice. 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 action of vertical-horizontal-moment combined loading. 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 second-order cone programming (SOCP) is adopted for efficient optimization purposes so as to model the actual nonlinear form of the universal Mohr-Coulomb yield function. In addition, the equilibrium equations associated with the combined loading are incorporated into the lower bound formulations. The seismic condition is simulated by the well-established modified pseudo-dynamic 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. The employed formulations are rigorously validated against a majority of high-quality studies in the literature in the static combined loading condition. The results of the seismic bearing capacity are presented in the forms of spectral responses and failure envelopes for the eccentric and inclined loadings. Accordingly, the influences of non-dimensional frequency, induced seismic acceleration and material damping on the ultimate bearing capacity of eccentrically and obliquely loaded strip footings are thoroughly examined and discussed. The results show that the most critical responses of the shallow foundation are captured in the resonance condition of earthquake excitation. As the seismic intensity decreases and the damping ratio increases, the spectral vertical, horizontal and moment bearing capacities of surface footings become smoother. In addition, 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.