Earthquake response of arch dams to nonuniform canyon motion, 1988

A numerical procedure is developed for the earthquake response analysis of concrete arch dams to nonuniform accelerations and displacements of the canyon walls. The isoparametric finite elements are applied for modeling of the dam. Interaction between the dam and foundation can be accounted for by taking a portion of the foundation rock discretized by finite elements. Influence of the reservoir during the dam response is approximated by the added-mass of the incompressible water according to the generalized Wetsergaard formula. The nonuniform, free-field canyon motion is obtained by solving the two-dimensional wave equation via Bessel and Hankel function expansions. The boundary conditions are satisfied exactly on the flat surfaces outside the canyon walls and approximately, ie., at the finite number of points along the canyon walls. The motions of canyon during an earthquake are analyzed for the plane, body SH-, P-, and SV-waves as well as for the surface Rayleigh waves. For defined nonuniform motion of the canyon walls the response of the dam is computed in the time domain.; The response of the idealized arch dam Type 5 is investigated in detail and possible effects caused by the wave propagation across the canyon are shown. The results demonstrate that the motion of the canyon and consequently the response of the dam are highly dependent on the kind and on the angle arrival of the earthquake waves. The dynamic stresses in the dam can be much larger and with different distribution than the corresponding stresses caused by the uniform canyon motions. The quasi-static stresses induced by the nonuniform canyon displacement can be very significant and in many cases larger than the stresses caused by the inertial forces during the dynamic response of the dam. These stresses are distributed in the zones of the dam abutments indicating that the dam supports can be seriously damaged during the largest nonuniform displacements of the canyon walls.