Application of mixed high order-Wavenumber approach in dynamic analysis of Pine Flat dam-reservoir system

Recently, mixed HO-WN (i.e., High order-Wavenumber) method was introduced for dynamic analysis of concrete gravity dam-reservoir systems. This is formulated by FE-(FE-TE) approach (i.e., Finite Element-(Finite Element-Truncation Element)). In this technique, dam and reservoir are discretized by plane solid and fluid finite elements. Moreover, the mixed HO-WN (i.e., High order-Wavenumber) condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It should be emphasized that three alternatives are discussed for this approach. The first two alternatives result in one additional degree of freedom at each node in comparison with usual modeling in practice which employs Sommerfeld truncation condition. While, the third alternative leads to two additional degrees of freedom. The method in each case is generally derived by combining the High-order and Wavenumber approaches. The formulation is initially reviewed which was originally proposed in a previous study. Thereafter, the response of Pine Flat dam-reservoir system is studied due to horizontal and vertical ground motions for two types of reservoir bottom conditions of full reflective and absorptive. The initial part of study is focused on the time harmonic analysis. In this part, it is possible to compare the transfer functions against corresponding responses obtained by FE-(FE-HE) (i.e., Finite Element- (Finite Element-Hyper Element)) approach (referred to as exact method). Subsequently, the transient analysis is carried out. In that part, the results in each case are compared against the corresponding results obtained by the high order H-W (i.e., Hagstrom-Warburton) condition applied on the truncation boundary. It is worthwhile to emphasize that results for high order H-W condition (e.g., O5-5) are not sensitive to L/H (i.e., normalized reservoir length) value. Therefore, they can be envisaged as exact results (in numerical sense) in time domain.