Simple discrete models for dynamic structure-soil-structure interaction analysis

Abstract

Simple models are presented for dynamic analyses of Structure-Soil-Structure Interaction (SSSI). Structures built on rigid, circular surface foundations resting on a homogeneous, elastic soil half-space are considered. The proposed models consist of discrete mass and spring elements that represent inertial, stiffness, and damping characteristics of an SSSI system. Frequency-dependent springs are developed to simulate Foundation-Soil Interaction (FSI) and Cross-Interaction (CI) between adjacent foundations, both being affected by the number and arrangement of neighbouring foundations. The stated springs are developed using a novel approach that approximates the through-the-soil interaction between adjacent footings using existing solutions to soil-structure interaction (SSI) analyses. Static stiffness matrices are obtained by means of compliance matrices using well known analytical solutions of surface displacement field to a ‘single-disk’ problem and a suggested displacement averaging rule. Dynamic stiffness matrices are created by applying modification factors to their static counterparts. To this end, a practical expression for dynamic modification factors that relate static and dynamic amplitudes of surface displacement field is provided. Equations of motion are formulated and solved in both time and frequency domains, taking into account time-lagging effects on input motion at separate foundations due to their vibration and wave passage. Validation results against more advanced numerical models prove the effectiveness of the proposed models. Finally, the limitations and potential improvements on the models are discussed.