Elastic wave propagation in embankment dams
This study investigates the stresses produced in an embankment dam as a result of excitation due to elastic plane waves. A two dimensional finite element model is used to represent an embankment and its substructure. The model uses a quadrilateral element, formed from triangles with a condensed internal node, which gives a better prediction of stress direction than a constant strain triangle. The equations of motion are assembled with lumped mass and damping matrices, and solved by direct integration using a fourth order Runge-Kutta algorithm. For time-steps in the range of stability this algorithm is shown to be accurate and easy to use. It is shown that the range of stability is considerably reduced with the inclusion of damping, and so damping was not included in the models studied. Tests show that for a finite element grid to model elastic wave propagation it is essential for there to be at least eight elements per wavelength. If this requirement is violated the predicted stresses are seriously affected, and the results of previously published studies must be judged against this condition. The model grid is designed to meet this requirement for the propagation velocity typical of dam materials and the frequencies typical of seismic events. Two models, (a) homogeneous and (b) layered, are excited by P and S waves at several angles. The consequent distortions of static stress distributions are varied, but exhibit conditions that could lead to failure by slumping or by tensional cracking close to the crest. The severity of the stresses was greater in the cases of (a) S-waves, (b) angled waves, (c) layered models. The physical processes producing the stress distributions are examined. It is concluded that the stress distributions are dependent on the angle of incidence and are not capable of explanation in terms of natural modes of vibration only.