Hydrodynamic Pressure Evaluation of Reservoir Subjected to Ground Excitation Based on SBFEM

Abstract

Dynamic responses of dam-reservoir systems subjected to ground motions are often a major concern in the design. To ensure that dams are adequately designed for, the hydrodynamic pressure distribution along the dam-reservoir interface must be determined for assessment of safety. Due to the fact that analytical methods are not readily available for dam-reservoir systems with arbitrary geometry shape, numerical methods are often used to analyze responses of dam-reservoir systems. In numerical methods, dams are often discretized into solid finite elements through Finite Element Method (FEM), while the reservoir is either directly modeled by Boundary Element Method (BEM) or is divided into two parts: a near field with arbitrary geometry shape and a far field with a uniform cross section. The near field is discretized into acoustic fluid finite elements by using FEM or boundary elements by BEM, while the far field is modeled by BEM or a Transmitting Boundary Condition (TBC). Based on these numerical methods, several coupling procedures were developed. A FEM-BEM coupling procedure was used to implement the linear and non-linear analysis of dam-reservoir interaction problems (Tsai & Lee, 1987; Czygan & Von Estorff, 2002), respectively, in which the dam was modeled by FEM, while the reservoir was modeled by BEM. A BEM-TBC coupling method was adopted to solve dam-water-foundation interaction problems and dam-reservoir-sediment-foundation interaction problems (Dominguez & Maeso, 1993; Dominguez et al., 1997). The dam and the near field of the reservoir were discretized by using BEM, while the far field of the reservoir was represented by a TBC. As a traditional numerical method, BEM has been popular in simulating unbounded medium, but it needs a fundamental solution and includes a singular integral, which affect its application. In order to avoid deriving a fundamental solution required in BEM, the TBC attracted some researchers’ interests. A Sommerfeld-type TBC was used to represent the far field (Kucukarslan et al., 2005), while a Sharan-type TBC was proposed for infinite fluid (Sharan, 1987). The Sommerfeld-type and Sharan-type TBCs are readily implemented in FEM due to their conciseness, but a sufficiently large near field is required to model accurately the damping effect of semi-infinite reservoir. Except for the aforementioned TBCs, an exact TBC (Tsai & Lee, 1991), a novel TBC (Maity &