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#### Paper Information

Journal:   JOURNAL OF FACULTY OF ENGINEERING (UNIVERSITY OF TEHRAN)   JANUARY 2008 , Volume 41 , Number 6 (108); Page(s) 683 To 697.

Paper:

# MODEL ANALYSIS OF CONCRETE ARCH DAMS IN TIME DOMAIN INCLUDING DAM-RESERVOIR INTERACTION

Author(s):

*

Abstract:

Modal approach is one of the usual methods utilized in dynamic analysis of structures due its computational time efficiency. This paper presents the general application of this approach for analyzing dams. Dam body and water domain are discretized by finite elements. Material of the dam body is assumed to be isotropic and homogeneous with linear viscoelastic behavior. The foundation is assumed to be rigid. However, the effects of wave absorption in sediments are included. Water in the reservoir is considered as an irrotational, inviscid and compressible fluid. Furthermore, Sommerfeld boundary condition is imposed for the upstream boundary of the reservoir. Pressure and nodal displacements degrees of freedom are used for the water in the reservoir and dam body, respectively. It is noteworthy that these selection of degrees of freedom leads to a coupled equation of the dam - reservoir system with unsymmetric mass and stiffness matrices. Therefore, an unsymmetric eigenproblem should be solved to obtain the mode shapes of the system, which requires a complicated computer programming. Decoupled modal approach is used as an alternative to avoid this problem. In this method, a symmetric eigenproblem is solved which is obtained by eliminating the unsymmetric terms of the initial eigenproblem. Thus, a series of mode shapes are calculated that can be used for the analysis of the coupled system. By increasing the number of mode shapes utilized, results of this approach converges to the exact response of the system. Moreover, unsymmetric eigenproblem is also studied for comparison purposes. As mentioned above, this unsymmetric eigenproblem is difficult to solve and a special technique is utilized for calculating mode shapes of system. Results of the coupled modal approach are compared with the decoupled method and it is observed that the former technique gives good results with relatively low number of modes. Moreover, a direct method referred to as the pseudo-symmetric method is also utilized for comparison purposes. Based on the above techniques, a special computer program is prepared in FORTRAN. This program can analyze 2D and 3D models of dam – reservoir systems with first and second order finite elements.

Keyword(s): ARCH DAM, COUPLED MODAL APPROACH, DAM, DECOUPLED MODAL APPROACH, DYNAMIC ANALYSIS, RESERVOIR INTERACTION

References:
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