Dynamic interaction between two 3D rigid surface foundations subjected to oblique seismic waves

A three-dimensional modeling approach is proposed to examine the dynamic interaction response of two foundations subjected to obliquely incident harmonic seismic waves (P, shear vertical, and shear horizontal waves). The two foundations are positioned on the surface of a uniform viscoelastic soil layer, underlain by a substratum. The dynamic response of the rigid foundations is determined by solving the wave equations, taking the soil–foundation interaction into account. The mathematical method employed is based on integral equations in the frequency domain, utilizing Green's function formalism presented by Kausel and Peek in 1982 for a multi layered soil. The solution is obtained using the frequency domain boundary element method, with Green's functions derived through the thin layer method. By discretizing the soil–foundation interface into quadrilateral constant elements, these equations are transformed into algebraic form, simplifying the force–displacement relationship within the discretized domain into a system of linear equations. This approach was applied to assess the impact of soil–structure interaction on the seismic response of two foundations, using the interaction coefficients proposed by Dobry and Gazetas in 1988. The results are presented in terms of displacement, rotation, and torsion at the center of the two massless surface foundations.