A Hybrid SSI Analysis Method for Embedded and Partially Bonded Rigid Foundations

CLASSI and SASSI are two sub-structuring approaches to analyze the phenomena of soil-structure interaction (SSI) with extensive applications in the nuclear power industry. Many similarities exist in the two methods; both approaches treat the SSI problem as a linear problem (soil and structure are modeled as behaving linearly), solve the problem in the frequency domain, and treat complex free-field wave propagation mechanisms, including incoherence of ground motion. SASSI has distinct advantages in modeling embedded foundations of irregular shapes, including foundation flexibility. Standard versions of CLASSI treat the foundation of the structures as behaving rigidly with respect to earthquake motions and the calculation of overall response. Structures are modeled in CLASSI using their fixed-base eigen-system. This permits very detailed structure models of 100,000s of degrees of freedom represented by 1000s of fixed-base modes to be incorporated directly into the SSI analysis. Other advantages of CLASSI are the ability to interrogate sub-structure elements of the problem efficiently, and the ability to cost-effectively perform probabilistic response analyses of soil-structure systems. The limitation of CLASSI is its inability to treat embedded foundations of complex geometry and its assumption of rigid foundation behavior.

A Hybrid approach has been developed which combines the advantages of SASSI in the development of impedance and scattering functions for flexible embedded foundations, with the response analysis advantages of CLASSI by enforcing rigid-body constraints to the SASSI foundation model. This is performed by the computer program RIGID, which has been validated and verified against published results. This paper summarizes the general CLASSI approach to the SSI problem followed by a description of an extension of the Hybrid approach in the program RIGID2017 to include embedded foundations that are partially bonded to the soil. This extension is accomplished by performing a condensation of the complex-valued frequency-dependent dynamic stiffness matrix from SASSI to eliminate the degrees of freedom that are not part of the foundation that is bonded to the soil followed by the application of rigid-body constraints to the bonded degrees of freedom. This extension of RIGID is verified against published results, examples of which are included in this paper.

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