This paper investigates the dynamic response of shallow foundations on linear and nonlinear soil medium using finite element method. The study was motivated by the need to develop macroscopic foundation models that can realistically capture the nonlinear behavior and energy dissipation mechanism of shallow foundations. An infinitely long strip foundation resting on soil half-space is analyzed in depth to evaluate the dependence of its dynamic responses on various parameters, e.g. foundation width, material properties, input motion amplitude and frequency etc. Special attentions are paid to choose appropriate domain scale, mesh size and boundary conditions so as to minimize the often observed numerical oscillations when the outgoing waves are contaminated by the reflecting waves at boundaries. Such judicious choice results in an excellent agreement between the finite element analysis and the analytical solution of strip foundation on linear soil half-space. Closed-form formulas are developed to describe the frequency-dependent linear dynamic stiffness of strip foundation along both horizontal and vertical directions. Various nonlinear constitutive models of soil, which exhibit the yielding and kinematic hardening behavior of soil, are implemented in this study to evaluate the dynamic stiffness of strip foundation sitting on nonlinear soil medium. The finite element analyses reveal the strong dependency of response on input motion amplitude, frequency and yielding of soil. A nonlinearity indicator is developed to incorporate the combined effects of initial elastic stiffness, yielding stress and excitation amplitude. The numerical analyses presented here provide improved understanding on the nonlinear behavior and energy dissipation mechanism of shallow foundations under dynamic loads.

The paper evaluates the radiation damping associated with shallow foundations sitting on linear or nonlinear soil medium. The study was motivated by the need to develop macroscopic foundation models that can realistically capture the nonlinear behaviour and energy dissipation mechanism of shallow foundations. Such model is essential to simulate the complex behaviour of structure components (e.g. shear walls, columns etc.) sitting on flexible foundations due to soil-structure interaction effects. In this study, the dynamic response of an infinitely long strip foundation resting on an elastic and inelastic half-space is investigated. The numerical analysis results presented here reveal that dynamic responses of shallow foundations strongly depend on amplitude and frequency of the input motion. In particular, the radiation damping of the system is affected by soil nonlinearity, foundation geometry and excitation frequency. The yielding of soil reduces the energy dissipation through the out going waves. As a result, the radiation damping of nonlinear soil medium is significantly lower than the elastic soil counterpart. The effects of initial elastic stiffness, yielding stress and excitation amplitude are incorporated in a nonlinearity indicator, which has shown strong correspondence to the radiation damping of the system.