Nonlinear Response of Vertically Oscillating Rigid Foundations

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Abstract
The dynamic response of vertically excited rigid foundations on an elasto‐viscoplastic half‐space is investigated in the context of nonlinear finite element (FE) analysis. A deviatoric viscoplastic theory with a linear combination of isotropic and kinematic hardening is used to model the soil constitutive response. Large‐scale nonlinear FE computations are made feasible by the use of a composite Newton‐preconditioned conjugate gradient (PCG) iteration technique, which requires the factorization of the consistent tangent operator no more than once during the solution process. Time‐domain analyses are used to investigate the nonlinear responses of vertically oscillating circular and square foundations to harmonic loads, using two‐ and three‐dimensional FE modeling, respectively. For low‐frequency excitations, resonance is created, which amplifies the motion of the foundation at amplitudes well above those obtained at the zero‐frequency level. This behavior is in stark contrast to the linear elastic response of vertically oscillating finite‐size foundations on a homogeneous half‐space, in which the amplitude of the motion is known to decrease monotonically with increasing values of the excitation frequency. The resonance phenomenon is explained in the context of a single‐degree‐of‐freedom oscillator analog that has been used successfully by previous investigators to model prototype continuum soil‐structure interaction problems.

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