A New Sensitivity and Reliability Analysis Framework for Structural and Geotechnical Systems

Abstract eng:
This paper presents recent advances in response sensitivity, probabilistic response and reliability analyses of structural and geotechnical systems. These developments are integrated into general-purpose nonlinear finite element (FE) software frameworks and provide the structural engineers with analytical and computational tools to propagate uncertainties through advanced large-scale nonlinear simulations and obtain probabilistic estimates of the predicted system response performance. The Direct Differentiation Method (DDM) for accurate and efficient computation of FE response sensitivities is extended and applied to large-scale nonlinear Soil-Foundation-Structure-Interaction (SFSI) systems. Extensions include numerical algorithms for response sensitivity analysis of FE models with multi-point constraints, force-based and three-field mixed elements, as well as various nonlinear material constitutive models, including a pressure independent multi-yield-surface J2 plasticity material model used to simulate the clay soil nonlinear behavior. Response sensitivity analysis results are shown for structural and SFSI systems. Examples of probabilistic response as well as time-invariant and time-variant reliability analyses are provided. Importance sampling and orthogonal plane sampling techniques are adopted and implemented into the considered FE software frameworks for accurate computation of failure probabilities. A new visualization technique, the Multidimensional Visualization in the Principal Planes (MVPP), is developed to visualize limit state surfaces in a neighborhood of the design points, giving insight into inaccuracy of the First-Order Reliability Method (FORM) for highly nonlinear systems. Based on the MVPP technique results, a novel hybrid method, the Design Point - Response Surface Simulation (DP-RS-Sim) method is developed for both time-invariant and time-variant reliability analysis. Application examples are provided to show that the DP-RS-Sim method can provide failure probability estimates more accurate than FORM at a small increment of the computational cost.

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