A key step in the formulation and solution of the soil-structure interaction (SSI) problem is the calculation of the displacements of the soil without the presence of a structure, also known as free-field displacements. The free-field displacements are used as basis for the formulation of the compliance matrix or soil flexibility matrix. A new approach to calculate the soil flexibility matrix is presented and implemented as an option in SC-SASSI which uses Green’s functions formulation for ring and disk loads to calculate free field displacements in the soil. This approach represents an improvement in the accuracy of the free field displacements, and also allows the simulation of soil-pile-structure interaction problems.

The new Green’s function approach uses analytical (exact) solutions in the horizontal direction and discrete (approximate) solutions in the vertical direction, inside and outside of the loaded circle. This is in contrast to the traditional approach in SASSI which calculates the free field displacements in the soil based on a cylindrical core that uses a finite element (FE) approximation inside of the cylindrical core (discrete solution in horizontal and vertical direction) and transmitting boundaries (TB) outside of the cylindrical core (analytical solution in the horizontal direction and discrete solution in the vertical direction). The Green’s functions formulation calculates displacements in the soil using Hankel Functions, Bessel Functions, as well as the eigenvalues and eigenvectors solution to the one-dimensional site response (wave propagation) problem.

This study demonstrates and compares the calculation of free field displacements due to forced vibration loads. First, the results of free field displacements using Green’s functions’ approach with SC-SASSI are presented and verified. Next, a comparison is presented for free-field displacements using different approaches: (1) Green’s functions approach with SC-SASSI; (2) Finite Element-Transmitting Boundary approach with SC-SASSI; and (3) Results from DOE SASSI V&V Report. The results from different approaches are compared and evaluated, and the relative influence of key parameters is assessed.