Probabilistic Performance-Based Assessment for Critical Separation Distance of Adjacent Buildings: Theoretical Analysis

Abstract

Existing methodologies to calculate the minimum separation distance between adjacent buildings are based on the estimations of the peak relative horizontal displacement of adjacent structures that are characterized by unknown pounding probabilities. The present study proposes a probabilistic performance-based procedure for determining the critical separation distance (CSD) with a designed pounding probability for adjacent buildings under different structural properties and seismic hazard sites. In the proposed procedure, the pounding events are formulated as single-barrier, first-passage reliability problems using the performance-based seismic design theory. Using the random vibration theory, the nongeometric spectral characteristics of the relative displacement response of adjacent buildings are deduced, and the approximate analytical solutions of the seismic pounding fragility are obtained by employing analytical approximations. Based on the seismic pounding fragility of adjacent buildings, the calculation of the CSD is described as an inverse reliability problem, and the specific CSDs with a target probability of pounding during the design life of the given adjacent buildings are derived using a proposed piecewise fitting iterative search algorithm. The proposed procedure is applied to different linear elastic single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems. The accuracy and efficiency of the proposed methodology for determining CSD are verified by referencing the importance of sampling using the elementary events (ISEE) method. Furthermore, different parametric analyses are conducted based on the proposed methodology and that consider the influences of different ratios of natural periods, the floor numbers of the adjacent buildings, and the different site hazard curves on the value of the CSD to verify that the procedure to determine the CSD of the adjacent buildings, as proposed in this paper, can obtain a uniform pounding probability for adjacent structures with different structural properties and seismic hazard sites.