Reliability-based design optimization of reinforced concrete structures with elastomeric isolators

Abstract

Engineering design optimization aims at designing low-cost systems and structures that fulfill certain performance objectives. In civil engineering Reliability-Based Design Optimization (RBDO) is extremely important because it enables to find optimal structure configurations while considering the effects of uncertainties, such as loading, geometry, structural parameters, modeling assumptions etc., on the building structural performance and reliability. The impact of uncertainties on system response and safety levels may escape the deterministic optimization approach. In this work we perform a multiobjective RBDO of reinforced concrete structures with elastomeric base isolators. Seismic isolation makes a superstructure less susceptible to ground motion caused by earthquakes and reduces the damages on the building. We perform both a sizing optimization of the superstructure (with the beam and column sections and reinforcements as input decision variables) and an optimization of the isolator catalog variables (elastomer rubber type, allowed displacement and dimensions). Uncertainty sources are the vertical loadings and the isolator damping coefficient. We aim at minimizing the superstructure cost as well as minimizing the top floor acceleration and displacement to reduce maintenance costs, while considering probabilistic constraints (and objectives if appropriate). The probabilistic responses are given in terms of percentiles computed with the Polynomial Chaos Expansion (PCE) method [1]. PCE statistical responses can be very accurate but its computational cost is prohibitive for a large number of uncertainties or a high polynomial order. We try to mitigate this effect with an Adaptive Sparse PCE (ASPCE) approach [2] which builds a high-order sparse polynomial with limited sample evaluations. ASPCE reduces the overall computational cost while preserving accuracy. We compare the deterministic optimization and the RBDO results for a base-isolated and a fixed-base structure subject to the same type of actions.