Seismic Shear Wave Propagation Through Earth Dams

Two methods are presented to study the one-dimensional propagation of seismic shear waves through tapered cross sections of earth dams with truncated crests. The earth dam material is assumed to be unsaturated and linear viscoelastic, or nonlinear strain-softening. The shear modulus may be considered to vary with depth or to be constant throughout the dam cross section. A closed form solution which involves Hankel functions with complex arguments is developed in case the earth dam material is viscoelastic and the dam base is subject to harmonic excitations. The method is extended to cases of random seismic vibrations by employing Fourier analysis in conjunction with a least squares criterion. Response curves are obtained for viscously damped tapered dam cross sections with truncated crests, by using the analytical solution developed. The method of characteristics is also used to provide a solution to the shear wave propagation problem. The method of characteristics exhibits versatility in handling different descriptions of dynamic material response, such as “strain-softening” material behavior laws. Three examples are presented to illustrate the application of the two methods and to demonstrate the relative simplicity and flexibility of the method of characteristics.