Abstract
Soil-structure-interaction (SSI) analyses are essential to evaluate the seismic performance of important structures before finalizing their structural design. SSI under seismic condition involves much more complex interaction with soil compared to the dynamic loads having source on the structure. Seismic SSI analysis requires due consideration of site-specific and structure-specific properties to estimate the actual ground motion (scattered motion) experienced at the base of the structure, and subsequently the effects of the scattered motion on the structure. Most challenging aspect of seismic SSI analysis is to implement transmitting boundaries that absorb the artificial reflections of stress waves at the truncated interface of the finite and infinite domains, while allowing the seismic waves to enter the finite domain. In this paper, the time domain implementation of seismic analysis of a soil-structure system is presented using classical discrete models of structure and interactive force boundary conditions for soil. These models represent typical SSI systems- a single Degree of Freedom (DOF) of a spherical cavity with mass attached to its wall, a two DOF system consisting of a mass attached by a nonlinear spring to a semi-infinite rod on elastic foundation, and a three DOF system with additional DOFs for modelling the structural stiffness and damping. The convolution integral representing the force boundary condition on the truncated interface, is evaluated interactively using UAMP user-subroutine in ABAQUS and applied as concentrated forces at the interface (truncated interface) nodes of the bounded domain or generalized-structure domain. The verification problems presented in the paper show the satisfactory performance of the developed MATLAB code and ABAQUS implementation with FORTRAN user-subroutines. The classical phenomena associated with the dynamic soil-structure systems are discussed through the present work.
Highlights
The accuracy, and the usefulness, of a dynamic Soil-Structure Interaction (SSI) analysis depend on the ability to model the boundary at the truncated interface of the finite geometry and the semi-infinite geometries
The frequency dependence of the stiffness of the unbounded domain along with the stress waves and their multiple reflections makes the modelling of this domain the most challenging part
That method which can integrate with the well-developed state-of-the-art finite element (FE) solvers like ABAQUS will be of special significance
Summary
The accuracy, and the usefulness, of a dynamic Soil-Structure Interaction (SSI) analysis depend on the ability to model the boundary at the truncated interface of the finite geometry (bounded domain) and the semi-infinite geometries (unbounded domain). The soil-structure interaction force vector {Rb(t)} is obtained from convolution integral of unit displacement impulse response (or dynamic stiffness matrix in time domain) [Sbb(t)] of the truncated unbounded domain, and the relative motion at the interface({ubt (τ)} − {ubg(τ)}), as in Eq (2). Where the soil-structure interaction force Rb(t) is obtained from convolution integral of Unit displacement impulse response (or dynamic stiffness coefficient in time domain) Sbb(t) and the relative motion of the base ({ubt (τ)} − {ubg(τ)}), as in Eq (2).
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