Seismic Analysis Of Arch Dam With The Effects Of Contraction Joints And Dam-Foundation Interaction

The purpose of this paper is to provide a practical numerical method to simulate the seismic response of the arch dam with the consideration of effects of contraction joints and dam-foundation interaction. Therefore, the studies on frictional contact problems, structure-foundation dynamic interaction analysis in time domain and the time integration algorithms are carried out by large amount of numerical tests. Finally, some approaches which can be satisfied with the need of practical engineering in the aspects of accuracy, efficient, convergence property and stability are presented. The contents of the paper include the following three aspects.1. Firstly, the study on the applications of the Non-smooth Equations method (simply denoted by NEQ) in three-dimensional frictional contact problems has been carried out in order to simulate the response of the arch dam with contraction joints under static and seismic loads. The effects of contraction joints on the response of the arch dam belong to the contact nonlinear problems. There are two solution methods to the contact problem, one is the "trial-error" iteration method and the other is Mathematical Programming which has rigorous mathematical theoretical foundation and in which the convergence analysis can be performed. NEQ which is proposed on the base of fast development of the theory of Non-smooth analysis has the property of high accuracy, high efficient and good convergence. In this paper, two kind of NEQ are introduced, one is proposed by Chen Wanji et al. and the other is B-differential Equation proposed by Christensen. And a new solution method to the B-differential Equation method in which the contact flexibility matrix is not computed any more is presented. The generations of the NEQ to dynamic elastic contact problems and the static elastoplastic contact problems is studied. In the solution of dynamic elastic contact problems, the conservation of momentum and kinetic energy at the time of impact are taken into consideration to obtain a reasonable results, and the implicit Newmark time integration algorithm is used. Some numerical examples demonstrate the valid of algorithms.2. Secondly, in order to consider the effect of dam-foundation dynamic interaction, the artificial boundary condition (ABC) expressed by Multi Transmitting Formula (MTF) of the second order is implemented on the external boundary of the system of dam-foundation to simulate the energy of scattered wave dissipates to infinite. Numerical instability will occur when the ABCs are introduced in the numericalintegration. Through the numerical tests, it is found that Prediction-Correction explicit integration algorithm can be used to integrate the dynamic differential equations with MTF stably and accurately. For the implicit Newmark method is used in the simulation of dynamic contact among the contraction joints and explicit integrator algorithm in the analysis of dam-foundation interaction, so the Implicit-Explicit integration algorithm by Hughes which couple these two algorithm, implicit Newmark and explicit Prediction-Correction algorithm is adopted to analyze effects of the contraction joints and dam-foundation dynamic interaction on seismic response of the arch dam.3. Finally, the dynamic analysis method mentioned in 2 is used to analyze the seismic responses of Xi Luo Du and Xiao Wan arch dams. The effects of space and locations of the joints on the stress distribution and magnitude of the dam body and the joint opening are discussed. The results by the method proposed in this paper provide reference to the aseismic safety assessment of high arch dam.