Evaluation of dam stability under various temperature conditions; case study: Karaj reservoir dam

Variation of temperature in concrete dams has a direct effect on the thermo-elasticity properties and creep phenomenon of concrete. These variations also, the stress and strains from them should be evaluated as initial loading used in the stability analysis of the dam. In this study, ABAQUS three-dimensional finite element model used to determine the thermal response of a dam under the effect of air temperature variations, solar radiation and water behind of the dam. So, a structural meshing with tetrahedral element block was used that each element had 20 nodes with 6 degrees of freedom in which there was the ability to analyze the stress and displacement.
In this research, the air temperature in the format of average daily air temperature was introduced closely as a boundary condition in ABAQUS model. The water temperature is other boundary conditions that were estimated based on the method proposed by Bofang to predict the water temperature at different depths. Also, in this model, the water level as the average daily water level was applied. The amount of displacement and moment of rotation at the level of dam foundation, both essential as boundary conditions, were used as fixed support and equal to zero. The attenuation model of the concrete was considered using the concrete damage plasticity (CDP) criteria with the coefficient of 3%. The modeling of dam foundation was performed according to a ratio of bedrock modulus of elasticity to the modulus of elasticity of concrete dam and using cubic model. The acoustic element was used to reservoir modeling. This element is the best choice in the modeling of water behind of dam. In this study, the considered hypotheses in the analyzing the dam models were as follow: A) Analysis carried out in a time domain, in which the time range of solving problem would be considered from zero to the alternation time. In dynamic analysis (earthquake), the real-time would be entered into the equation's solution. But in the statical analysis, the alternation time would be considered virtual time, and depending on the amount, the time of performing the program could be lower or higher. The software needs this virtual time to solve the equations step by step in different time periods. Generally, to solve a non-linear statically complex problem such as the provided model, it is recommended to analyze these problems by explicit analyzer and it is suggested to consider the entire time of the analysis longer than the alternation time or natural frequency corresponds to the first figure of the vibration mode of problem. Since time or the necessary frequency period for analyzing arc dam commonly is between to 10 to 30 seconds in dynamical analysis; therefore, this time was considered from zero to 20 seconds in the present study. B) Constituent material of the dam was linear, homogenous and viscoelastic.
The results showed that by thermal modeling, the final displacement direction was toward the reservoir while without thermal analysis and only by hydrostatic force modeling, the hydrostatic pressure tended to displace the dam in the opposite direction. This indicated the effect of thermal changes on the dam body that not only removed the effect of hydrostatic force but also it displaced the body toward the upstream reservoir. Also, the maximum displacement occurred during the warmest month of July and toward the reservoir. Therefore, due to high solar radiation, the slope of the heat changes in areas near the dam’s crest and the downstream areas exposed to sunlight were at high level. The dam body displacements toward the downstream in hot months were more than cold months. This was due to the simultaneous displacements caused by the thermal and hydrostatic loads in cold months. The results of analyzing finite element in different 12 months showed that upstream tensile stress was at low level and as a result, the possibility of cracking due to the static loads is excluded in this area. Based on the average level of the reservoir in 2009, it could be expected that as the water level decrease under the minimum level of the safety operation, the stress level would move from pressure to tensile state and increase the level of the main stresses in the dam body. So the effect of temperature on the creating critical states was assessed more than the effect of the water pressure.
The results obtained from model parameters such as displacement of dam crest, depth of cracked areas and analyzing temperature variation between different points indicated the high ability of this method for evaluation of the stability of the dam. The analysis showed that the maximum temperature and temperature gradient happen in the shallow area of the downstream level. Also, the temperature difference between different points of the downstream level and the same level point was considerable because of the effects of solar radiation. This could reveal that a lack of attention to operation of dam would lead to the occurrence of instability and cracks in whole arc dam body. The result of the proposed model showed that developed methodology had suitable accuracy in prediction of dam thermal behavior under the environmental actions.