Stochastic collocation-based nonlinear analysis of concrete bridges with uncertain parameters

Abstract

This paper focuses on the stochastic response of concrete bridges considering uncertainty in bearing and abutment stiffness. A multi-span simply supported bridge with concrete girders is selected. A 3D-dimensional model is prepared, and nonlinear response history analyses are performed. For the numerical dynamic simulation, the non-sampling stochastic method based on generalized polynomial chaos (gPC) expansion is utilised. The uncertain parameters include the vertical and shear stiffness of bearings and the lateral stiffness of abutments are presented by the truncated gPC expansions. Furthermore, the system response such as base shear, acceleration, velocity and displacement in different columns is presented by gPC expansion with unknown deterministic coefficients. The stochastic Galerkin projection is employed to calculate a set of deterministic equations. A non-intrusive solution, as a set of collocation points, determines the unknown gPC coefficients of the system response and the results are compared with Monte Carlo simulations. The key advantage of spectral discretization is the combination of the mentioned method with the spatial discretization, e.g. finite element model. This study also emphasises the accuracy in results and time efficiency of the proposed non-sampling method for uncertainty quantification of stochastic systems comparing to sampling procedure (e.g. Monte Carlo simulation).

Keywords:

• Concrete bridges
• seismic risk
• stochastic response
• polynomial chaos
• random excitation
• uncertain parameters