بكارگيري روش المان هاي مرزي جهت تعيين توزيع فشار هيدروديناميكي در مخزن سد وزني: بررسي اثرات هندسه و رسوبات كف مخزن

Boundary Element Formulation for Computing Hydrodynamic Pressure on Concrete Gravity Dams: Influence of Reservoir Shape and Bottom Sediment Absorption

روش المان هاي مرزي به عنوان يكي از قدرتمندترين روش هاي عددي در مدل سازي پديده هاي مهندسي مطرح مي باشد در مقاله حاضر از اين روش جهت بررسي چگونگي توزيع فشار هيدروديناميك در مخزن دوبعدي سدي با هندسه دلخواه استفاده شده است. در اين راستا معادله انتشار موج فشاري، معادله حاكم بر توزيع فشار هيدروديناميكي با لحاظ اثرات تراكم پذيري آب داخل مخزن، به همراه شرايط مرزي مناسب در محيط مخزن حل گرديده است براي لحاظ اثرات جذبي ناشي از رسوبات كف مخزن از شرط مرزي مناسبي در اين مرز استفاده شده است. روش به كار گرفته شده مبتني بر يك روش نيمه تحليلي به صورت تركيبي از روش المان هاي مرزي و انتگرال هاي ويژه مي باشد به طوري كه حل پايه به گونه اي انتخاب گرديده كه مستقل از فركانس بوده و شرط مرزي در سطح آزاد مخرن را ارضاء نمايد. نتايج به دست آمده گوياي كارآيي روش پيشنهادي در برآورد فشارهيدروديناميك در مخزن سد وزني با شكل دلخواه مخزن مي باشد. همچنين نتايج به دست آمده نشان دهنده اثرات كاهشي رسوبات كف مخزن بر توزيع فشار هيدروديناميكي مخزن است.

Dynamic response of dams interacting both with reservoir and foundation is a complex problem in time domain. To study the effects of reservoir and foundation on the response of dams under two-dimensional (2D) conditions, several numerical methods have been developed in the past few decades such as finite element method and the boundary element method. The boundary element method has been successfully applied to the dam dynamics (Humar and Jablonski (1988); Kucukarslan, (2004)) Fig. 1. Concrete gravity dam-reservoir domain and boundary element formulation parameters 2. Methodology In this study, a new method for determination of hydrodynamic pressure on dams with different shape of reservoir under earthquake vibration is presented. The method is based on a combination of boundary Farhoud Kalateh / J. Civ. Env. Eng. 48 (2018) elements and particular integrals. In the boundary element method the fundamental solution is selected independent of frequency and also satisfy the boundary condition in the free surface of the reservoir. Using this method and selecting the suitable boundary conditions leads to an integral equation which can be evaluated on the boundaries of the reservoir for modeling the phenomenon of wave radiation from the upstream boundary of the reservoir and wave refraction from the bottom of the reservoir. For numerical solution of the integral equation the weighted residual method has been used and based a series of equilibrium dynamic equations will result which can be solved by standard methods. In Fig. 1. depicted the computational domain of gravity dam-reservoir system and reservoir boundaries. 3. Results and discussion The results of the analysis are compared with those obtained based on analytical solution presented by Tsai (Tsai, et al. 1992) that observed good agreement between. The effect of reservoir sediment absorption and reservoir slop on hydrodynamic pressure time history near bottom of dam are computed for a dam-reservoir system that showed in Fig. 2. (a), as shown in Fig. 2. (b), the slop of reservoir bottom has significant effect on hydrodynamic pressure distribution and as shown in Fig. 2. (c), with increases the absorption ratio of the reservoir sediment, hydrodynamic pressure decrease. Obtained results verify the ability and accuracy of developed boundary element method in the simulation of hydrodynamic distribution in the dam-reservoir systems. Fig. 2. a) gravity dam –reservoir dimension and boundary elements, b) Time history of hydrodynamic pressure near bottom of dam for different slop of reservoir bottom. c) Time history of hydrodynamic pressure near bottom of dam for different reservoir sediment absorption ratio 4. Conclusions This study considers the new boundary element formulation of gravity dam –reservoir system subjected to earthquake. The results of the analysis are compared with those obtained from analytical solution. Obtained results show that above mentioned method for computing of hydrodynamic pressure has enough accuracy and workability. The comparison shows good agreement between two results. The effects of reservoir sediment absorption and reservoir bottom slop are also discussed. The results show that the geometry of reservoir bottom and the absorption effects of the reservoir sediment have major effects on the hydrodynamic pressure and the seismic behavior of gravity dam and should be considered in the dynamic analysis of gravity dam-reservoir systems.