Foundation Flexibility Effect on Dynamic Response of Concrete Gravity Dams under Correlated Translational and Rotational Components of Ground Motion

The kinematics of any point in a medium is ideally expressed in terms of three translational and three rotational components. Observations of earthquake events have shown that many structural failures and damage are associated to rotational components of ground motions. Newmark [1] was perhaps the first to establish a relationship between the torsional and translational components of a ground motion based on constant velocity of wave propagation assumption. Lee and Liang [2] have used wave propagation and classical elasticity theories based on constant wave velocity to develop the algorithms for generating rotational motion from the corresponding available translational motions and Hong-Nan Li et al. [3] proposed an improved approach based on frequency dependent wave velocity to generate the rotational components. Kalani Sarokolayi et al. [4] have used this method and they have verified their results using recorded rotational components. Recently the effect of rotational component on dynamic analysis of dam- reservoir system without foundation effect is considered by authors in their previous research [5]; but the effects of rotational components have not been considered in dynamic analysis of dam-reservoir-foundation systems in previous researches. The fluid- structure interaction is also an important subject to dynamic analysis of dams. The Lagrangian approach which were proposed by Hamdi [6] and completed by Wilson and Khalvati [7], have been used by many researchers such as [7-9]. In addition the reservoir bottom absorption effects in earthquake response of concrete gravity dams have been also investigated by some researchers such as Fenves and Chopra [10]. The main purpose of this research is the evaluation of dynamic response of concrete gravity dams considering three correlated translational and rotational components of ground motion and dam-reservoir-foundation interaction using finite element method. For this purpose, the rotational component of ground motion is obtained using translational components and relation of classical elasticity between rotation and wave propagation theories considering frequency dependent wave velocity. Then, these rotational and translational components are applied in finite element model and the dynamic response of system are calculated using Newmark method and Lagrangian- Lagrangian approach based on displacement unknown in both solid and fluid domains. In addition, with the change of elasticity modulus of foundation, earthquake acceleration, water elevation and absorption coefficient of reservoir bottom, the sensitivity of response with respect to these parameters are evaluated. The horizontal displacement of dam crest for dam-reservoir (D-R) and dam-reservoir-foundation (D-R-F) systems subjected to two translational components, 2C, and two translational added by their correlated rotationalcomponents, 3C, are obtained and the ratio of response due to 3C and 2C which is named as Normalized response, are presented in Table 1. The effects of absorption coefficients on Normalized response of system are also shown in Table 2 and the effects of water elevation on dam crest response subjected to 3C are shown in Fig. 2. Results showed that the effects of rotational components of ground motion on the dynamic response of concrete gravity dams can be low or high depending on their frequency range and power spectrum. In cases which the rotational effect is high, the dam response to rotational component of earthquake will be decreased with the increase of the foundation elasticity modulus and reservoir bottom absorption coefficients. In addition with the increase of water elevation, the rotational effect will increase and the response time history also will change.