**8. References**

106 Hydrodynamics – Natural Water Bodies

Fig. 15. Displacement at top of gravity dam subjected to El Centro horizontal acceleration

Aiming for dam-reservoir system problems subjected to horizontal ground motions, this chapter presented the SBFEM formulations in the frequency and time domain and its corresponding FEM-SBFEM coupling formulations to evaluate the hydrodynamic pressure of the reservoir through dividing the reservoir into a near field and far field, where the dam and the near field were modeled by FEM and the far field was discretized by the SBFEM. The SBFEM uses the dynamic stiffness matrix and the dynamic mass matrix to describe the dynamic characteristics of the far field in the frequency and time domain, respectively. The merits of the SBFEM in representing the semi-infinite reservoir were illustrated through comparisons against benchmark solutions. Numerical results showed that its accuracy and efficiency of the FEM-SBFEM formulation to obtain the harmonic and transient analysis of a dam-reservoir system. Of note, the SBFEM is a semi-analytical method. Its solution in the radial direction is analytical so that only a near field with a small volume is required. Compared to the sub-structure method, its formulations are in a simpler mathematical form

This research is supported by the National Natural Science Foundation of China (No. 10902060) and China Postdoctoral Science Foundation (201003123), for which the author is

**6. Conclusion** 

**7. Acknowledgments** 

grateful.

and can be coupled with FEM easily and seamlessly.


**Part 2** 

**Tidal and Wave Dynamics:** 

**Seas and Oceans** 

