Efficient nonlinear seismic analysis of arch dams: User's manual for SCADA, Smeared Crack Arch Dam Analysis

Abstract

Linear earthquake analysis of a concrete arch dam, conducted either in the evaluation of an existing dam or in the design of a new one, typically shows large tensile stresses when the ground motion employed represents strong shaking. This result has spurred development of nonlinear analysis capabilities that attempt to model the opening and closing of contraction joints as well as cracks that are produced. Two recent computer programs (1a and lb, 2) both treat joints and cracks as zero-width zones of nonlinear springs connecting adjacent finite elements, but differ in detail. ADAP-88 (la and lb) uses a multi-element discretization of solid elements through the thickness of the dam so as to be able to represent states of partial contact in the joints and cracks. Standard joint elements are used in the joint and crack planes. The program of reference 2 uses a single shell element discretization in the thickness direction with specially calibrated nonlinear rotational and axial springs to represent states of partial contact. The disadvantage of ADAP-88 is the relatively high computational effort required, while disadvantages of the formulation of reference 2 are some loss of accuracy and an inability to be generalized to include sliding in the joints and cracks. However, while sliding is straightforward conceptionally when using the standard joint elements such as employed in ADAP-88, including friction may lead to severe convergence difficulties. At present, nonlinear analysis methods have not gained acceptance in the dam engineering community. Reliance is still based on the inadequate linear methods and ad hoc procedures to assess the high tensile stresses that are computed. Part of the problem is the difficulty of validating the nonlinear analysis capabilities. Some progress is being made, however, by different researchers taking different approaches of nonlinear analysis and then comparing results. In this spirit and also with the goal of developing a practical nonlinear analysis technique that attempts to reach a compromise between computational effort and model complexity, while still giving useful results, this simplified nonlinear earthquake analysis procedure for concrete arch dams is offered together with fully documented computer program. The procedure is based on the "smeared" approach to model joints and cracks whereby the contact nonlinearities are incorporated through conditions placed on the stresses at the integration points of the (shell) finite elements of the dam. This approach sacrifices some accuracy for computational efficiency. The faster computation comes about by a reduction in the number of degrees of freedom and an improvement in convergence even to the point of being able to handle frictional sliding. A typical computer run for an earthquake analysis of an arch dam to strong ground motion takes about one hour on a DEC 3000 Model 400 computer with a 100 MEPS processor. This efficiency allows parameter studies to be undertaken which are an essential part of any evaluation process. As with the linear analysis methods, engineering judgment is still a necessary and important element. However, it is hoped that the gap between mathematical model and real-world situation is reduced enough with the offered program so that the engineer can now be confident in spanning between them.

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