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Subsequently, the response of idealized Morrow Point arch dam is studied due to stream, vertical and cross-stream ground motions for reservoir bottom/sidewalls conditions of both fully reflective and absorptive. For each combination, different orders of Hagstrom–Warburton (HW) condition are evaluated from accuracy point of view by comparing them against exact solutions. It should be emphasized that normalized length of reservoir near-field region is taken as a very low value of L/H = 0.2 during this process which makes it a very challenging test for any kind of truncation boundary condition.

In present study, dynamic analysis of concrete arch dam-reservoir systems is formulated by FE-(FE-TE) approach [i.e. finite element-(finite element-truncation element)]. In this technique, dam and reservoir are discretized by solid and fluid finite elements. Moreover, the HW high-order condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model. The formulation is initially explained in details.

The trend in gaining accuracy with increase in order of HW condition were basically the same for all three types of excitations under both full reflective and absorptive reservoir bottom/sidewalls conditions. The only exception was for cross-stream excitation response which was showing less accurate results near the first major peak for moderate orders of HW (e.g. O3-2) in comparison to what was observed for responses due to symmetric excitations (stream and vertical). This is mainly attributed to the selection of evanescent-type parameters of HW condition which is based on the first symmetric mode of reservoir. However, it is noted that error diminishes even for cross-stream excitation as order increases. High orders of HW condition, such as O5-5 considered herein, generate highly accurate responses for all three possible excitations under both types of full reflective and absorptive reservoir bottom/sidewalls conditions. It is such that responses are hardly distinguishable from corresponding exact responses. This reveals that proposed FE-(FE-TE) analysis technique based on HW condition is quite successful, and one may fully rely on that for accurate and efficient analysis of concrete arch dam-reservoir systems.

Dynamic analysis of concrete arch dam-reservoir system is formulated by new method. HW high-order condition is applied for a very low and challenging reservoir length. Different orders are evaluated against exact solution with excellent agreement. Generalized matrices of truncation element are derived for FEM programmers. The method is discussed for all types of excitation and reservoir base conditions.

The response of the Pine Flat dam–water–foundation rock system is studied by a new described approach (i.e. FE-(FE-TE)-FE). 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 the FE-(FE-HE)-FE approach (referred to as exact method which employs a rigorous fluid hyper-element). Subsequently, the transient analysis is carried out. In that part, it is only possible to compare the results for low and high normalized reservoir length cases. Therefore, the sensitivity of results is controlled due to normalized reservoir length values.

In the present study, dynamic analysis of a typical concrete gravity dam–water–foundation rock system is formulated by the FE-(FE-TE)-FE approach. In this technique, dam and foundation rock are discretized by plane solid finite elements while, water domain near-field region is discretized by plane fluid finite elements. Moreover, the H-W (i.e. Hagstrom–Warburton) high-order condition is imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model.

High orders of H-W condition, such as O5-5 considered herein, generate highly accurate responses for both possible excitations under both types of full reflective and absorptive reservoir bottom conditions. It is such that transfer functions are hardly distinguishable from corresponding exact responses obtained through the FE-(FE-HE)-FE approach in time harmonic analyses. This is controlled for both low and high normalized reservoir length cases (L/H = 1 and 3). Moreover, it can be claimed that transient analysis leads practically to exact results (in numerical sense) when one is employing high order H-W truncation element. In other words, the results are not sensitive to reservoir normalized length under these circumstances.

Dynamic analysis of concrete gravity dam–water–foundation rock systems is formulated by a new method. The salient aspect of the technique is that it utilizes H-W high-order condition at the truncation boundary. The method is discussed for all types of excitation and reservoir bottom conditions.

The response of an idealized triangular concrete gravity dam is studied due to horizontal and vertical ground motions for both fully reflective and absorptive reservoir bottom conditions. For each combination, in this paper different orders of Givoli-Neta (G-N) high-order truncation condition are aimed to be evaluated from accuracy point of view by comparing the results against corresponding exact solutions which relies on utilizing a two-dimensional fluid hyper-element.

In present study, the dynamic analysis of concrete gravity dam-reservoir systems is formulated by Finite Element (FE)-(FE-TE) approach. In this technique, dam and reservoir are discretized by plane solid and fluid finite elements. Moreover, the G-N high-order condition imposed at the reservoir truncation boundary. This task is formulated by employing a truncation element at that boundary. It is emphasized that reservoir far-field is excluded from the discretized model.

It was observed that trend in gaining accuracy with increase in the order of G-N condition were basically the same for both horizontal and vertical ground motions under full reflective reservoir bottom condition. Moreover, convergence rate increases for absorptive reservoir bottom condition cases in comparison with fully reflective cases. It is also noticed that in certain cases, the responses are hardly distinguishable from corresponding exact responses. This reveals that proposed FE-(FE-TE) analysis technique based on G-N condition is quite successful, and one may fully rely on that for accurate and efficient analysis of concrete gravity dam-reservoir systems.

Dynamic analysis of concrete gravity dam-reservoir systems are formulated by a new method. The salient aspect of the technique is that it utilizes G-N high-order condition at the truncation boundary. This is achieved by developing a special truncation element which its generalized matrices are derived for Finite Element Method (FEM) programmers. The method is discussed for all types of excitation and reservoir bottom conditions. It must be emphasized that although time harmonic analysis is considered in the present study, the main part of formulation is explained in the context of time domain. Therefore, the approach can easily be extended for transient type of analysis.

Recently, the original Wavenumber approach was introduced for dynamic analysis of dam-reservoir systems in frequency domain in the context of pure finite element programming. But its main disadvantages are that it cannot be implemented in time domain. The purpose of this paper is to propose an approximation to the original approach which enables one to carry out this effective method in time domain as well as in frequency domain. Based on the present investigation, it is proven that the Approximate Wavenumber approach has inherent characteristics, which allows it to be envisaged as an effective technique for calculating the response of concrete gravity dam-reservoir systems in time domain.

The method is described initially. Subsequently, the response of an idealized triangular dam-reservoir system is obtained by the proposed approach as well as by applying two other well-known absorbing conditions which are widely utilized in practice. The results are also controlled against the corresponding exact responses. It should be emphasized that all results presented herein are obtained by the FE-FE method under different absorbing conditions applied on the truncation boundary. These include two well-known absorbing conditions referred to as Sommerfeld and Sharan as well as the proposed approach of the present study (i.e. Approximate Wavenumber condition).

It is concluded that the maximum error for the Approximate Wavenumber approach is in the range of 10 percent at the major peaks of the response. This occurs mainly for the very low reservoir lengths under full reflective reservoir base condition and vertical excitation. This is a remarkable result for any kind of robust truncation boundary simulation that one may expect. The fundamental frequency of the system is captured correctly for the Approximate Wavenumber approach, even in cases of low reservoir length.

Based on this investigation, it is proven that the Approximate Wavenumber approach has inherent characteristics, which allows it to be envisaged as an effective technique for calculating the response of concrete gravity dam-reservoir systems in time domain. It is concluded that the maximum error for the Approximate Wavenumber approach is in the range of 10 percent at the major peaks of the response. This occurs mainly for the very low reservoir lengths under full reflective reservoir base condition and vertical excitation. This is a remarkable result for any kind of robust truncation boundary simulation that one may expect.