Equivalent-Linear Dynamic Impedance Functions of Surface Foundations

An approximate linearization method using the familiar concept of G-γ and D-γ curves is presented for determining the dynamic impedance (stiffness and damping) coefficients of rigid surface footings accounting for nonlinear soil behavior. The method is based on subdivision of the soil mass under the footing into a number of horizontal layers of different shear modulus and damping ratio, compatible with the level of strain imposed by an earthquake motion or a dynamic load. In this way, the original homogeneous or inhomogeneous soil profile is replaced by a layered profile with strain-compatible properties within each layer, which do not vary in the horizontal sense. The system is solved in the frequency domain by a rigorous boundary-element formulation accounting for the radiation condition at infinity. For a given set of applied loads, characteristic strains are determined in each soil layer and the analysis is repeated in an iterative manner until convergence in material properties is achieved. Both kinematic and inertial interaction can be modeled simultaneously by the method, which thus encompasses primary and secondary material nonlinearity in a single step. The results are presented for a circular footing resting on: (1) a half space made of clay of different plasticity index and (2) a half space made of sand of different density, excited by a suite of recorded earthquake motions. Dimensionless graphs are provided for the variation of foundation stiffness and damping with frequency and excitation level in vertical, swaying, rocking, and torsional oscillations.