Nonlinear Seismic Analysis of Concrete Gravity Dams Using Extended Finite Element method and Plastic Damage Model

The present paper investigates and compares the crack propagation in concrete gravity dams using two models of linear fracture mechanics and plasticity damage concrete. The first model is based on linear concrete behavior using the extended finite element method without considering the effect of strain softening on the crack tip while the second model is based on the nonlinear concrete behavior and the strain softening in tension with damage parameter. According to two different algorithms and based on two models, several benchmark examples are reviewed and the results compared with those reported in the literature. Then, path of the crack growth in Koyna gravity dam due to a seismic excitation of Koyna earthquake in 1962 has been performed by considering the dam-reservoir interaction. The results show that due to low compressive stresses during analysis of concrete gravity dams, consideration of compressive nonlinear behavior has no effect on crack initiation and almost is the same for two models. However because of crack opening and closing with tapping the crack faces together in extended finite element model, the compressive stress will be more than the allowable stress of concrete. Crack initiation at downstream and upstream face occurred at angle of 90 and zero degrees respectively, which in both models, the numerical results are in agreement with the experimental model. The crack in the extended finite element model grows faster such that the crest block of dam in this model is separated from the dam body, earlier than the concrete plastic damage model. Also the values of dam crest displacement and hydrodynamic pressure in the reservoir in extended finite element model with linear elastic fracture mechanic are more than the other model, which can be attributed to the linear and nonlinear behavior of concrete in extended finite element and concrete plastic damage model respectively. In the extended finite element model, due to using linear fracture mechanic, the maximum principal stress in the cracked elements reaches the values greater than the maximum tensile strength, but in the concrete plastic damage model as soon as the stress reaches a tension limit value, elements are damaged and the stress is reduced. In both models, the crack located at the slope change area, propagates with the downward slope from downstream dam face and connects to the crack at upstream face which is growth horizontally. Because of laboratory sample dimension and boundary condition of dam-reservoir compared with actual manner, neither of two crack profiles covered the experimental model, accurately. But it is shown that the crack profiles in the extended finite element model are more consistent with experimental results. Finally, the results show that the crack profile are slightly different in the two models because of quasi brittle behavior of the dam concrete, which can be attributed to the small fracture process zone of the crack tip in comparison with the dimension of the concrete gravity dams such that by removing strain softness part, the error in the amount of additional computation can be neglected.