NONLINEAR RESPONSE OF VERTICALLY OSCILLATING RIGID FOUNDATIONS

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.