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Top1. Introduction
The dam-foundation rock interaction effects may influence the dynamic response of gravity dams significantly under certain conditions. The main effects of the interaction between the dam and flexible foundation rock are to increase the fundamental resonant period and the effective damping of the system. Depending upon the distribution of the energy of input excitation among different frequencies, the increase in resonant period may result in an increase or a decrease in the response. But the increase in effective damping always results in a decrease in the response, which mostly dominates. Also, the soil-structure interaction decreases the contribution of the higher vibration modes, because the radiation and material damping in the foundation rock region reduces the amplitudes of the higher resonant peaks more than the amplitude of the fundamental resonant peak. Thus the net effect of dam-foundation rock interaction is to reduce the maximum principal stresses in the dam.
Two commonly used techniques for considering the soil structure interaction effects are the substructure and FEM approaches. In the substructure approach, the dam is analyzed as a separate super-structure with the interaction forces defined in terms of a foundation stiffness matrix and the base node displacements (Vaish and Chopra, 1973; 1974). Later studies defined the foundation stiffness matrix by considering the foundation as elastic half-space (Chopra et al., 1976; Dasgupta and Chopra, 1977; 1979), thus modeling accurately the radiation damping in the foundation. Before the results on foundation stiffness matrix were available, the most common approach, which is still prevalent, was to analyze the dam along with a limited portion of the foundation as a single system by finite element idealization (Chopra and Perumalswami, 1969; Wilson, 1969; Seed et al., 1975).
A major difficulty with the FEM approach is that the amount of energy radiated depends upon the size of foundation considered. For smaller size of the foundation, the waves radiated into the foundation are reflected back, resulting in increased stresses in the dam body. Another, equally important difficulty is the mechanism of applying the input ground acceleration to the FEM model. If the free-field ground motion is applied as it is at the base of the foundation, it gets amplified resulting in unrealistically high stresses in the dam. Application of the free-field motion at the base nodes of the dam is also unable to consider the spatial variation of the motion, resulting in erroneous response. A more realistic way of using the FEM approach would therefore be to consider a sufficiently large portion of the foundation block and apply the ground excitation expected to occur at the base of the foundation. Estimation of earthquake acceleration time history at depth from a given time history at the free ground surface is known as deconvolution, which is difficult to perform accurately and the errors increase with increase in the depth of the foundation block. A commonly used practice to avoid deconvolution is to consider only the stiffness and material damping of the foundation rock and neglect its mass (ICOLD, 1987; USACE, 2003). But, this fails to simulate the energy dissipation characteristics due to radiation damping.
In this paper, detailed investigations are carried out for the response of an idealized triangular dam section resting on a homogeneous foundation by varying the extent of the foundation block and the impedance contrast between the dam and the foundation rock, under excitation by several different free-field ground acceleration time histories with varying characteristics. The analysis is performed for empty reservoir condition, as the objective is to study the dam-foundation rock interaction effects alone. As the hydrodynamic forces will simply act as additional excitation on the dam, this is not expected to affect the generality of the conclusions made. Also, inclusion of hydrodynamic forces would make it difficult to separate out the effects of the dam-foundation rock interaction, intended to be studied. The results obtained have been used to identify the conditions under which the FEM approach is compatible with the substructure approach.