Simple approach to evaluate the influence of seismic residual displacements on post-liquefaction settlements of RC-frames

Residual permanent displacements generally characterize the status of structures at the end of severe earthquake events because of large inelastic deformations demand. When the structure is founded on soils susceptible to liquefaction phenomenon, this status could particularly influence the subsequent damages due to the occurrence of liquefaction induced vertical settlements. As a consequence, the correct prediction of the effects of earthquake induced liquefaction on the built environment must consider the residual displacements induced by the ground shaking. To this aim, the paper proposes a simplified approach to evaluate the seismic response of RC frames based on a four-steps procedure composed of a set of nonlinear static analyses reproducing a sequential process of a ground shaking followed by a liquefaction induced ground settlements. The novelty of the proposal is to carry out sequential nonlinear static analyses by preserving the status of the RC frame at the end of the seismic event in terms of residual displacements and then to directly consider their influence on the subsequent analysis simulating the occurrence of post-liquefaction vertical settlements. A parametric study has been developed by means of numerical analyses, referring to two RC frames derived from literature, in order to highlight the relevance of the seismic residual displacements on the damage induced by the subsequent vertical settlements due to soil liquefaction. The proposed simplified approach has then been validated through more sophisticated nonlinear dynamic time-history analyses. The results presented in the paper underline the efficacy of the proposed approach, the simplicity in implementing the four-steps procedure and the lower computational effort with respect to nonlinear dynamic time-history analyses.