Dynamic analysis of concrete gravity dam-reservoir systems by approximate wavenumber approach

Purpose 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. Design/methodology/approach 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). Findings 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. Originality/value 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.