Sobol' sensitivity analysis of a 1D stochastic elasto-plastic seismic wave propagation

A novel numerical framework for the Sobol' sensitivity analysis of 1D stochastic elasto-plastic wave propagation is proposed and evaluated. The forward propagation of uncertain input motions through uncertain elasto-plastic soils and structures is often conducted using the finite element method (FEM) together with the Monte Carlo simulation. However, it is computationally much more efficient to use the stochastic elasto-plastic FEM (SEPFEM) instead. Hence the developed framework is based on the SEPFEM. The backward propagation of uncertainties, that is, the determination of relative influences of individual uncertain input motions and uncertain material properties on the resulting uncertain seismic wave propagation, is known as the global sensitivity analysis. A global sensitivity analysis, namely, the Sobol' sensitivity analysis, is included in the proposed framework. Uncertain input, bedrock motions are obtained using the ground motion prediction equations of Fourier amplitude spectra and Fourier phase derivative, and they are modeled as a non-stationary random process. Stochastic elasto-plastic soil properties are represented as heterogeneous random fields. The random process and the random fields are discretized in the probabilistic space using an orthogonal Hermite polynomial chaos (PC) basis. The probabilistic system response is obtained efficiently using the Galerkin stochastic FEM. The Sobol' sensitivity analysis is conducted for the PC-represented uncertain system response. The benefits of the presented framework to the site-specific probabilistic seismic hazard analysis are discussed. The novel approach enables to take into account the uncertainty in both, seismic load and elasto-plastic material parameters, and to assess their individual influences on the overall uncertainty in the resulting wave field accurately and efficiently. The presented framework has been implemented into Real-ESSI Simulator and, here, it is evaluated and demonstrated to be very useful for the seismic site response analysis.