5. Conclusion
The paper presents a new framework to integrate the nonlinear model of soil foundation system with frequency dependent properties of soil in dynamic loading application. The nonlinearity of the soil and foundation system is captured with a computationally efficient macro element by Chatzigogos [17] while the frequency dependent behavior of soil-foundation system is captured with a recursive parameter model in Nakamura [20,21]. The proposed framework, however, is very general such that any other nonlinear element or frequency-dependent model can be integrated.
The results from the proposed framework have shown good agreement with FE model at low amplitude excitation with a broad range of frequencies. Also, the model can capture the nonlinear behavior of soil foundation system with uplift of the foundation at high amplitude excitation with low frequency. However, the accuracy of the model decreases when both the excitation frequency and magnitude are high. Thus, there exist still limitation in capturing a full inelastic frequency dependent behavior of soil foundation system. This limitation might be one of the shortcomings of the proposed framework in application to structures with significant higher mode effects.
It is also worthwhile to mention that while the framework was implemented for shallow foundations, the framework can be applied to embedded or deep foundations as long as reliable inelastic model and dynamic impedance functions are available. In addition, depending on the characteristics of the analyzed structure, the impact of the nonlinearity or frequency-dependency of soil-foundation system is expected to be different. Thus, it is equally important to have good understanding on structural characteristics when determining the modelling approach for soil-foundation system.
