EVALUATING RADIATION DAMPING OF SHALLOW FOUNDATIONS ON NONLINEAR SOIL MEDIUM FOR SOIL-STRUCTURE INTERACTION ANALYSIS OF BRIDGES

The paper evaluates the radiation damping associated with shallow foundations sitting on linear or nonlinear soil medium. The study is motivated by the need to develop a macroscopic foundation model that can realistically capture the nonlinear behavior and energy dissipation mechanism of shallow foundations. Such model is essential to simulate the complex behavior of bridges sitting on flexible foundations due to soilstructure 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 study revealed responses’ strong dependency on amplitude and frequency of the motion. It also found that the radiation damping of nonlinear soil medium is significantly lower than the elastic soil counterpart, which in turn affects the bridge response. Introduction Recent earthquakes in major urban areas have underscored the need to better understand the responses of bridges to seismic actions. The responses of bridges are affected by not only the nonlinear dynamic behavior of individual components (i.e. superstructure, foundations and surrounding soil) but also the complex interaction among them, i.e. the soil-structure interaction effects. In particular, the changing stiffness and energy dissipation either by means of hysteretic damping or radiation damping are the most important characteristics of soil-structure interaction. In this study, the radiation damping and its effects are evaluated for bridges sitting on shallow foundations. Although various models are available to account for radiation damping of shallow foundations on elastic soil medium (Veletsos and Verbic 1974; Luco and Westmann 1972; Hryniewicz 1981; Gazetas 1991 and Veletsos et al. 1997 among others), there are essentially no previous studies on evaluating the radiation damping of shallow foundations on nonlinear soil medium. In this study, finite element method is adopted to compute the dynamic response of an infinitely long strip foundation resting on an elastic and inelastic half-space. Numerical results from finite element method are compared with theoretical solution of strip foundation resting on elastic half-space so as to provide guidance on choosing appropriate domain scale, mesh size and boundaries for subsequent nonlinear analysis. Closed-form formulas are developed to describe the linear frequency-dependent dynamic stiffness. The study utilizes realistic nonlinear constitutive models to exhibit yielding and kinematic hardening behavior of soil. An extensive parametric study has been conducted to reveal the amplitude and frequency dependent response of strip foundation. In particular, the radiation damping is evaluated when there is yielding in soil medium. Dynamic Stiffness of Rigid Strip Foundation on Elastic Soil Half-space Consider an infinitely-long rigid strip foundation sitting on elastic half-space, as shown in Figure 1. Its dynamic stiffness can be obtained analytically. Muskhelishvili (1963) first conducted the static analysis and revealed the zero stiffness of strip foundation in either vertical or horizontal direction. Luco and Westmann (1972) later derived theoretic dynamic compliance of rigid strip foundation bonded to an elastic soil half-space using the theory of singular integral equations. An exact solution was presented for incompressible soil (Poisson’s ratios ν=0.5) while approximate solutions were obtained for soil of Poisson’s ratio ν=0, 1/4, and 1/3. Hryniewicz (1981) obtained the dynamic stiffness of rigid strip foundation on an elastic half-space of Poisson’s ratio ν=0.25. Under a harmonic motion, the reacting forces are related to displacements by the general form shown in Eq. (1): ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + + = ⎭ ⎬ ⎫ ⎩ ⎨ ⎧ ) ( ) ( i 0 0 i ) ( ) ( 22 22 11 11 t U t U d c d c G t P t P