| The response behavior of seismically excited frame structures with active control and boundless soil is investigated. The mathematical models based on the existence or absence of the structure-soil interaction (SSI) and/or control are presented. In the SSI consideration, the frequency-dependent property of unbounded nonhomogeneous soil and foundation embedment are applied. The optimal closed-loop control laws are established based on the generalized performance index. In the control system considering the SSI effects, foundation translation and rocking are included in the control rule. The algorithms are implemented in the time domain.;The studies indicate the strong influence of the foundation embedment and depth of soil layer on soil rocking coefficients and consequently on structural responses. In a certain structure, the additional modes as a result of the foundation's degrees of freedom dominate and hence result in a distinct structural response behavior. For example, the rocking mode is important in a massive and/or high-rise structure while the translation mode dominates in a low-rise structure. In a massive low-rise structure such as a nuclear reactor, the combination of these two dominant modes leads to large structural responses. In the studied control system including the SSI effects, the reduction of structural responses is a result of the decrease in foundation rocking instead of relative floor translation as done where the structure is fixed at its base. Furthermore, the effect of control force in strengthening the system's stiffness and damping is reduced in the case of the structure that founded on soft soil. |
