Effects of foundation rocking and uplifting on displacement amplification factor

Prediction of displacement demand to assess seismic performance of structures is a necessary step where nonlinear static procedures are followed. While such predictions have been well established in literature for fixed-base structures, fewer bodies of researches have been carried out on the effect of rocking and uplifting of shallow foundations supported by soil, on such prediction. This paper aimed to investigate the effect of soil structure interaction on displacement amplification factor C1 using the beam on nonlinear Winkler foundation concept. A practical range of natural period, force reduction factors, and wide range of anticipated behavior from rocking, uplifting and hinging are considered and using thousands nonlinear time history analysis, displacement amplification factors are evaluated. The results indicate that the suggested equations in current rehabilitation documents underestimate displacement demands in the presence of foundation rocking and uplift. Finally, using regression analyses, new equations are proposed to estimate mean values of C₁.