Estimation of the Seismic Bearing Capacity of Shallow Strip Footings Based on a Pseudodynamic Approach

Abstract

The bearing capacity of a shallow strip footing is investigated by a pseudodynamic method under earthquake conditions. A nonsymmetrical multiblock mechanism is herein adopted to describe the uplift failure of the foundations based on the kinematic theorem of limit analysis. This nonsymmetrical mechanism comprises a series of rigid triangular blocks that translate into the failure area. The seismic load, varying with time and space, is represented by a pseudodynamic method that considers the dynamic properties of earthquake waves. A slice method is proposed to adapt the variation in inertial force with time and depth for the convenience of calculating the earthquake-induced work rate. Then, equating the external work rate and the internal dissipation rate, the rigorous upper-bound solution of the seismic bearing capacity factors, which will be optimized by the sequential quadratic programming (SQP) in the MATLAB toolbox for searching for the optimal value, is explicitly derived. Comparisons between the present solution and previous works are made to validate the rationality and accuracy of the proposed methodology. A specific parametric analysis is conducted to reveal the influence of dynamic parameters on the bearing capacity of the strip footing. Numerical results are provided graphically as well as in the tabular form for reference in footing design.