A multi-objective optimal parameter design procedure for slide bridge bearings under seismic excitation based on a deterministic-stochastic modeling approach

In the process of seismic performance-based design of bridges with slide bearings, there exist intrinsic tradeoffs between minimization of bearing displacement and that of the pier response in selecting bearing parameters for strong earthquake events. However, difficulty in determining the optimal parameters of the bearings that satisfy the two objectives arises, in conjunction with considerable computational resource requirement for nonlinear time-history analysis. In order to find the solutions of the multi-objective optimization problem that reduce the computational cost, a procedure that utilizes the stochastic structural response of equivalent linear systems is proposed. To obtain the performance indices, seismic load is modeled as a stationary random process, whose characteristics are determined for the standard design ground motions specified by the Japanese design code, and the nonlinear behavior of the slide bearings is modeled as equivalent-linear elements using the stochastic linearization technique. As the result, a set of optimal parameter candidates is obtained as the Pareto-front solutions in the multi-objective function space. As the next step, the search of the optimal parameters is conducted by performing nonlinear time-history analysis only for the Pareto-front solution parameter sets to save the computational requirement. As a numerical example, the proposed method is applied to bridges with two types of slide bearings: the uplifting sliding shoe (UPSS) consisting of multiple sliding surfaces, and functionally discrete bearings (FDB) in which friction bearings and elastomeric bearings set in parallel are combined. It is demonstrated that the seismic performance of the bridge for the case of the design parameters obtained by the proposed procedure is almost equivalent to the one with the optimal parameters found by the conventional exhaustive search approach.