PSI - Issue 42

H. Mazighi et al. / Procedia Structural Integrity 42 (2022) 1714–1720 H.Mazighi and M.K.Mihoubi / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Cracking of concrete is an important factor to study the safety concrete gravity dams. However, during the extreme phenomenon such as credible earthquake, potential crack may appears and adversely affect the safety of the dams Bhattacharjee and Léger, (1993). However, during the last two decades, significant researchers worked on numerical modelling of cracks, especially on dam applications to investigate the real behavior under dynamic loading Ghrib and Tinawi, (1995), Javanmardi, et al. (2005), Zhang, et al. (2013), Ghaedi, et al. (2017). In addition, researchers proposed different models to analyze the initiation and crack propagation of dams considering hydrodynamic load at upstream face. Mansouri, et al. (2011) implemented a 2D Finite Element (FE) method to investigate the seismic damage of the Koyna concrete gravity dam considering the smeared crack model to calculate the crack growth. A different crack growth with and without reservoir are provided. Zhang, et al. (2013) investigated the nonlinear fracture behavior of Koyna concrete gravity dam with effect of different initial crack under seismic loading. A Concrete Damaged Plasticity (CDP) model was applied to simulate numerically the damage. As a result, initial cracks are very important for the dynamic evaluation and crack propagation process. Hariri-ardebili and Seyed-kolbadi, (2015) developed a smeared crack model for concrete dam. They take three major types of concrete dams, i.e. gravity, buttress, and arch dams as case study for the seismic analysis. The crack profile is obtained as results, a good agreement with those observed from the experimental test. In the present study, the Koyna concrete dam was considered as a case study in order to evaluate the hydrodynamic response of the dam under two earthquakes accelerations, such as Koyna earthquake taken place in India in December 1967 and Saguenay in Canada in November 1988 to study the effect of the maximum ground acceleration and motion duration. To inspect the seismic damage, the Concrete Damage Plasticity (CDP) model is implemented.

Nomenclature M s Mass matrix Damping matrix K s Stiffness matrix ̈ Acceleration (m/s 2 ) ̇ Velocity (m/s) Displacement (m) F g C s Gravity load vector (N) Pressure load vector (N) Transformation matrix Pressure shape function N u Displacement shape function Strain tensor Elastic strain tensor Plastic strain tensor Stress tensor (Pa) Effective stress tensor (Pa) d Damage variable F p Q N p

E 0

Undamaged Young Modulus (Pa)

E ρ ψ f t P

Young Modulus (Pa) Mass density (kg/m 3 ) Dilatation angle (°)

Tensile failure stress (MPa) Hydrodynamic pressure (Pa) Water density (kg/m 3 ) Normal pool level (m)

ρ w

h

h w

Water level (m)