An Efficient and Accurate Method for Gradient Computation of Nonlinear Soil-structure Interaction (ssi) Systems

In the context of nonlinear finite element (FE) method, this paper presents a computational framework for ‘exact’ response sensitivity analysis of soil-structural interaction (SSI) systems based on the direct differentiation method (DDM). The DDM requires analytically differentiating the FE algorithm for the response computation with respect to material, geometry or loading parameters, involving the differentiation of various hierarchical layers of FE response, namely: (1) structure level, (2) element level, (3) section level, and (4) material level. To achieve this analysis framework, the DDM-based response sensitivity analysis algorithm is extended to various element and material models used in Reinforced Concrete (RC) frame, as well as a multi-yield surface J2 plasticity material model used to represent cohesive soil behavior under cyclic loading conditions. Furthermore, the DDM algorithm is extended to accommodate the multi-point constraints (MPC) conditions used in FE models (e.g., Transformation method, penalty method). The framework is implemented in general purpose FE software, OpenSees, an open system for earthquake engineering simulation. A three dimensional frame-soil interaction example is used to demonstrate the implementation and usage of the DDM-based response sensitivity analysis algorithm for SSI systems subjected to two orthogonal horizontal earthquake excitations. The frame is modeled with beam-column element, fiber section and nonlinear concrete and steel materials, while the soil by multi-yield surface J2 plasticity material model. The sensitivity parameters are taken as the material parameters used to represent the elastoplastic behaviors of the various soil and structural materials. The response sensitivity results obtained by using DDM are verified by their counteparterners obtained by using forward finite difference (FFD) method. The asymptotic convergence of FFD results towards DDM results verifies the presented DDM framework. As the application, the sensitivity analysis results provide the relative importance of the various material parameters for selected global and/or local response parameters of the SSI systems.