Reliability analysis of an inter-story isolated structure under a main-aftershock sequence based on the Laplace asymptotic method

After a strong mainshock, subsequent ground motion is the result of a sequence of multiple aftershocks, and the damage to a structure under these conditions is more severe than from a single earthquake. Most seismic studies are based on a single earthquake event. To explore the influence of a main-aftershock sequence on an isolated inter-story structure, we constructed a three-dimensional finite-element model of such a structure and subjected it to repeated main-aftershock sequences. The Laplace asymptotic method of second-order second-moment was used to calculate the reliability of the structure under the action of a single mainshock and after a main-aftershock sequence at different seismic levels. The effects of the number of aftershocks, the location of the isolation layer, and the stiffness of the isolation bearing in the structure were analyzed. The results showed that aftershocks increased the failure probability of each sub-structural part of the inter-story isolated structure. The failure probability of the lower structure had the greatest influence, which was about 3.89 times that for the mainshock alone. The probability of failure from multiple vs single aftershocks was similar, but the magnitude of the aftershock plays a major role in failure. The number of aftershocks reduced the overall reliability of an inter-story isolation structure. In the case of different isolation layer positions, the placement of the isolation layer at the top of the seventh story under an extremely rare earthquake level resulted in a reduction of 6.01%. With isolation bearings of different stiffness, the largest decrease was 7.88% when the stiffness was 50%.