Framework for Finite Element Response Sensitivity and Reliability Analyses of Structural and Geotechnical Systems

This paper presents recent developments in response sensitivity, probabilistic response and reliability analyses of structural and geotechnical systems. These developments are integrated within general-purpose software frameworks for non-linear finite element response analysis and provide the structural engineers with analytical tools to propagate uncertainties through advanced large-scale non-linear simulations to obtain probabilistic estimates of the predicted system response performance. Necessary extensions of the Direct Differentiation Method (DDM) for accurate and efficient computation of finite element response sensitivities are presented. Examples of such response sensitivity computations are shown for structural and Soil-Foundation-StructureInteraction (SFSI) systems. Uncertainty propagation is illustrated through examples of probabilistic response (First-Order Second-Moment approximation), time-invariant (Firstand Second-Order Reliability Method) and time-variant (mean outcrossing rate computation) reliability analyses. These examples are based on two types of analysis, namely pushover analysis and time history analysis, which are used extensively in earthquake engineering.