Master of Science in Civil Engineering (MSCE)


Civil and Environmental Engineering

Document Type



The research presented in this thesis focuses on analytical approximations for the time-variant first-passage failure probability (FPFP) of linear elastic models of structural systems subjected to stochastic excitations. The FPFP is defined as the probability that a response quantity of an engineering system subjected to a dynamic stochastic loading outcrosses a specified threshold within a given exposure time. The FPFP is an important and useful quantity for many structural engineering applications. The classical first-passage reliability problem is studied for linear elastic single-degree-of-freedom (SDOF) and multi-degrees-of-freedom (MDOF) systems subjected to stationary and nonstationary Gaussian excitations. The absolute and relative accuracy of several analytical approximations available in the literature (i.e., the Poisson’s (P), classical Vanmarcke’s (cVM), and modified Vanmarcke’s (mVM) approximations) are studied through an extensive parametric study for SDOF systems. In addition, a new analytical approximation for the FPFP of linear SDOF systems is developed. The new proposed approximation is verified by comparing its analytical estimates of the failure probability with the corresponding results obtained using existing analytical approximations and the importance sampling using elementary events (ISEE) method for a wide range of oscillator properties and different types of input excitations. It is found that the newly developed analytical approximation provides estimates of the time-variant FPFP of SDOF systems that are significantly more accurate than the estimates obtained using the P, cVM, and mVM approximations. Real-valued and complex-valued modal analysis with modal truncation is used to study the time-variant FPFP of MDOF subjected to stationary and nonstationary stochastic excitations. The absolute and relative accuracy of the P, cVM, and mVM approximations as well as of the newly developed approximation are studied for a select number of case studies. It is found that the newly proposed analytical approximation cannot be directly extended to the computation of the FPFP of MDOF systems, while the mVM approximation appears to be more accurate than the other existing analytical approximations.



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Committee Chair

Barbato, Michele