SEISMIC DAM-RESERVOIR INTERACTION OF CONCRETE GRAVITY DAMS Bakenaz A. Zedan Associate Professor, Irrigation and Hydraulic Engineering Department, Faculty of Engineering, Tanta University, Tanta, Egypt Ref. E-mail: [email protected] Problem Statement Governing Equation& Boundary Conditions Finite Element Modeling Fluid-Structure Interaction Formulation ell-known Helmholtz equation governing the pressure p reads Material Properties Dam body : Elasticity modulus of concrete 22.75 GPa; Poison’s ratio of concrete 0.20; Mass density of concrete 2480 kg m -3 , Uniaxial compressive strength of concrete 30 MPa, Uniaxial tensile strength of concrete 3.0 MPa, Biaxial compressive strength of concrete 36 MPa, Cohesion factor of concrete 3.0 MPa, Angle of internal friction of concrete 45 o . Water body : Mass density of water 1000 kg m -3 , Water Speed of pressure wave 1440 m s -1 ; Wave reflection coefficient 0.90. Model Dimensions in meters of a sample gravity dam (refer to Figure 1): H B = 100; H C =20; L B = 75; L C =15; LF = 200; H F =95 El-Centro earthquake Record CONCLUSIONS Dam-Reservoir interaction on the linear responses of a selected concrete gravity dam to ground motion excitation is investigated in this study. The deformations of the dam concrete remain in the elastic range for the assumed stress-strain relationship. Various responses are extracted using the conducted finite element model utilizing ANSYS code. All of the results demonstrate that the following conclusions: 1.Considering dam-reservoir interaction in analysis affect significantly the seismic response of the gravity dam at its heel where maximum responses prevail while at toe of the dam no significant effect appears. 2.The time history of horizontal crest displacement as well as vertical stress component at dam heel assign significant effect for the coupled fluid-structure system. 3.The time history of hydrodynamic pressure exerting on the upstream face of the dam is maximum during the first five seconds of the earthquake excitation with peak values at 2.16 second. 4.The time history of hydrodynamic pressure exerting on the upstream face of the dam is significantly affected by reservoir depth. 5.Numerical results show that the coupled dam-reservoir interaction effect of gravity dams play an important role in accurately estimating the gravity dam response. 6.ANSYS code is an appropriate software for simulating coupled fluid-structure systems. Figure14: Maximum hydrodynamic pressures exerting on upstream dam face. Figure 10: Time history of hydrodynamic pressure at reservoir depth=50ms Dynamic Analysis of Dam-Reservoir System Figure 7: Time history of stresses at dam heel Figure 6: Time history of stress components at dam toe Figure 5: Time history of stress components at dam heel Figure 4: Time history of crest displacement
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SEISMIC DAM-RESERVOIR INTERACTION OF CONCRETE GRAVITY DAMSBakenaz A. Zedan
Associate Professor, Irrigation and Hydraulic Engineering Department, Faculty of Engineering, Tanta University, Tanta, Egypt
Ref. E-mail: [email protected]
Problem Statement
Governing Equation& Boundary Conditions
Finite Element Modeling
Fluid-Structure Interaction Formulation
The well-known Helmholtz equation governing the pressure p reads
Material PropertiesDam body: Elasticity modulus of concrete 22.75 GPa; Poison’s ratio of concrete 0.20; Mass density of concrete 2480 kg m-3, Uniaxial compressive strength of concrete 30 MPa, Uniaxial tensile strength of concrete 3.0 MPa, Biaxial compressive strength of concrete 36 MPa, Cohesion factor of concrete 3.0 MPa, Angle of internal friction of concrete 45o.
Water body: Mass density of water 1000 kg m-3, Water Speed of pressure wave 1440 m s-1; Wave reflection coefficient 0.90. Model Dimensions in meters of a sample gravity dam (refer to Figure 1):
HB= 100; HC=20; LB= 75; LC=15; LF = 200; HF=95
El-Centro earthquake Record
CONCLUSIONSDam-Reservoir interaction on the linear responses of a selected concrete gravity dam to ground motion excitation is investigated in this study. The deformations of the dam concrete remain in the elastic range for the assumed stress-strain relationship. Various responses are extracted using the conducted finite element model utilizing ANSYS code. All of the results demonstrate that the following conclusions:1.Considering dam-reservoir interaction in analysis affect significantly the seismic response of the gravity dam at its heel where maximum responses prevail while at toe of the dam no significant effect appears.2.The time history of horizontal crest displacement as well as vertical stress component at dam heel assign significant effect for the coupled fluid-structure system.3.The time history of hydrodynamic pressure exerting on the upstream face of the dam is maximum during the first five seconds of the earthquake excitation with peak values at 2.16 second. 4.The time history of hydrodynamic pressure exerting on the upstream face of the dam is significantly affected by reservoir depth.5.Numerical results show that the coupled dam-reservoir interaction effect of gravity dams play an important role in accurately estimating the gravity dam response.6.ANSYS code is an appropriate software for simulating coupled fluid-structure systems.
Figure14: Maximum hydrodynamic pressures exerting on upstream dam face.
Figure 10: Time history of hydrodynamic pressure at reservoir depth=50ms
Dynamic Analysis of Dam-Reservoir System
Figure 7: Time history of stresses at dam heelFigure 6: Time history of stress components at dam toe
Figure 5: Time history of stress components at dam heelFigure 4: Time history of crest displacement
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