Optimal Structural Control Considering Soil-Structure Interaction Effects

Accurate representation of soil-structure interaction (SSI) effects is a crucial part of the dynamic analyses of structures in seismic zones where it is generally recognized that the dynamic response of soils can drastically alter the response of structures subjected to earthquake excitations. The research presented in this dissertation discusses two topics, both related to the study of soil-structure interaction effects.

The first part of this study presents a finite element (FE) methodology for modeling nonlinear SSI effects and applies the model to the problem of machine foundation vibrations. 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-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 in different vibrational modes for circular, square, rectangular, and strip foundations, using two and three-dimensional FE modeling. It is shown that 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. Furthermore, nonlinear soil effects are found to be dominant over a wide range of excitation frequencies for foundations vibrating in torsional and horizontal modes, whereas the corresponding effects are significant over a much narrower range of excitation frequencies for the vertical and rocking modes.

In the second part of this study, a methodology is developed to include SSI effects in the optimal control algorithms. The major difficulty in including soil-structure interaction in optimal structural control comes from the fact that the accurate analysis of an SSI system is usually formulated in the frequency domain due to the frequency dependent foundation impedances, whereas conventional optimal control problem is performed in the time domain. This difficulty is eliminated in the proposed methodology by utilizing an equivalent fixed-base structural model to represent the actual SSI system.

The control effectiveness of considering soil-structure interaction is investigated for both the SDOF and MDOF structural models. For the general MDOF structural models and real earthquake excitations, it is found that the control algorithm considering SSI effects is more effective than the corresponding control algorithm assuming a fixed-base system model. In addition, the advantage of applying this methodology is observed to be more prominent in the cases where the SSI effects are more significant.