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In this example, we verified the level 2 seismic performance of the dam reservoir pier, and examined the retrofit plan. Based on the results from the nonlinear push-over analysis by the finite element model and earthquake response analysis, we estimated the behavior and damages of the structure after the rebar yielding, and then calculated the required reinforcement amount.
【Diagram 1】shows the evaluation of the dam pier. Evaluation was done using the three-dimensional FEM model. For the rebar, we used the truss element, and applied the material with bilinear characteristics to rebar’s axial direction. The rebar shares the node with the three-dimensional solid element of concrete. We evaluated the expression of adhesion between rebar and concrete by the tension stiffening after a cracking occurred in the concrete model. As shown in the 【Diagram 2】, we applied the nonlinear characteristics of ADINA to the concrete part, and performed the push-over calculation until concrete crushed under compression. Also, we performed the concrete nonlinear earthquake response analysis using the input earthquake ground motions.
Based on the analysis results shown in 【Diagram 3】～【Diagram 5】, we proposed and examined the retrofit method. We performed a nonlinear finite element analysis on the retrofit plan, and from the analysis results, we confirmed the plasticity condition of the reinforcing steel plate at the end point.
We can perform the retrofit design and design improvement by utilizing the breakdown phenomenon captured by this examination.
In this example, we examined the earthquake response taking into consideration the interaction between the dam water and levee in a concrete gravity dam at the time of an earthquake occurrence.
We modeled the levee using the two-dimensional plane solid element to take into consideration the concrete material nonlinear. We modeled the water using the potential fluid element. As for the attenuation, we considered that it occurs in proportion to the initial stiffness, with a 10% attenuation constant of the first natural frequency.