Seismic Bearing Capacity of Shallow Embedded Foundations on a Sloping Ground Surface

By using the lower-bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization, bearing-capacity factors, $N_c$ and $N_{\gamma q}$, with an inclusion of pseudostatic horizontal seismic body forces, have been determined for a shallow embedded horizontal strip footing placed on sloping ground surface. The variation of $N_c$ and $N_{\gamma q}$ with changes in slope angle ($\beta$) for different values of seismic acceleration coefficient ($k_h$) has been obtained. The analysis reveals that irrespective of ground inclination and the embedment depth of the footing, the factors $N_c$ and $N_{\gamma q}$ decrease quite considerably with an increase in $k_h$. As compared with $N_c$, the factor $N_{\gamma q}$ is affected more extensively with changes in $k_h$ and $\beta$. Unlike most of the results reported in literature for the seismic case, the present computational results take into account the shear resistance of soil mass above the footing level. An increase in the depth of the embedment leads to an increase in the magnitudes of both $N_c$ and $N_{\gamma q}$.