Study On Seismic Reliability Methods For Bridge Structures

Various methods for reliability and random vibration analysis of bridges subjected to earthquake excitations are investigated in this dissertation. For linear structural systems, the multiple-support response spectrum combination rule is studied. For nonlinear structural sys-tems, in the framework of structural reliability the tail-equivalent linearization method is in-vestigated, and a highly efficient algorithm for finding a sequence of design points is devel-oped. Moreover, to address challenges in high dimensional reliability analysis, two sampling methods tailored especially for high dimensional reliability problems are developed. Specifi-cally, the dissertation covers the following aspects:(1) The original multiple-support response spectrum (MSRS) as well as an extended ver-sion (Extended-MSRS) that accounts for the static contribution of truncated modes is reviewed. The concept of Load-dependent Ritz vector and its generation algorithm is introduced. Based on fundamental principles of structural dynamics, the mechanical interpretation of LDR vector is also covered. A LDR vector approach for MSRS (LDR-MSRS) analysis is developed. To determine the number of LDR vectors used in MSRS analysis, mode truncation rules for LDR-MSRS are developed. For MSRS analysis with multi-component seismic excitations, two strategies for generating the LDR vectors are introduced, namely the Combined-LDR and the Separate-LDR methods. In the Combined-LDR approach, a combined set of LDR vectors using the load patterns associated with all excitation directions is generated, and the same set of LDR vectors is employed for MSRS analysis in each direction. In the Separate-LDR ap-proach, separate sets of LDR vectors associated with the load patterns in each direction are generated and then used separately in the MSRS analysis for each direction. Finally numerical results of two bridge models illustrate the accuracy and efficiency of the original MSRS, Ex-tended MSRS and the two LDR-MSRS methods.(2) General methods for finding the design points in reliability analysis are briefly re-viewed, and a highly efficient algorithm named the ?-method for finding a sequence of design points is developed. The ?-method uses the Broyden's "good" method to solve a set of non-linear simultaneous equations to find the design points for the values of an implicitly defined threshold/reliability index that is associated with parameter ?.(3) For random vibration and seismic reliability analysis of structures subjected to multi-ple-support earthquake excitations, the tail-equivalent linearization method (TELM) is ex-tended to account for spatial variation of multiple-support seismic excitations. Using a spectral decomposition technique, a method to reduce the number of random variables in TELM analy-sis is developed. Finally the applicability of TELM to multiple-support excitation problems of bridges is demonstrated by a numerical example.(4) The properties of high-dimensional standard normal space are introduced, and the or-thogonal plane sampling (OPS) method is investigated in the context of high-dimensional structural component reliability problems. Based on a geometric interpretation of the OPS in high dimensions, a modified OPS approach is developed. Furthermore, a cross-entropy-based adaptive importance sampling technique that employs a von Mises-Fisher mixture as the sam-pling density model is developed. The proposed CE-AIS-vMFM approach is specially de-signed for high dimensional reliability analysis and it is applicable to both component and sys-tem reliability problems. The CE-AIS-vMFM generates sample points on the surface of a hy-per-sphere. Two slightly different sampling strategies of CE-AIS-vMFM are developed. In the first approach, sampling of CE-AIS-vMFM is performed on a single hyper-sphere; while in the second approach, sampling is performed on various hyper-spheres with radius drawn from a ?-distribution. Finally numerical examples demonstrate the accuracy of OPS, modified OPS and the two CE-AIS-vMFM sampling methods in high dimensional seismic reliability analysis of bridges.(5) Using TELM, OPS and MOPS, and CE-AIS-vMFM, a nonlinear random vibration and seismic reliability analysis for a prestressed concrete continuous rigid frame bridge is per-formed. In terms of the numerical results, the general properties of various analytical methods are discussed.