Nonlinear Shear Wave Propagation in Strain Stiffening and Strain Softening Soil

Linear or equivalent linear wave propagation models, such as SHAKE, assume that the shear wave velocity is constant, hence the wave form is not distorted during propagation. If the tangent shear modulus is not constant, then perturbations in stress travel at different speed depending on the tangent modulus at that point and time. In cyclic loading, the shear stress-strain curve can be concave down, which we call strain-softening (near failure, for example) or concave up, which we call strain-stiffening (if there are negative pore pressures being generated due to dilatancy). In strain stiffening soil, the peak of a stress wave travels faster than the front, the wave front sharpens, and there is a possibility to form a shock wave. If the soil is strain softening, the peak travels slower than the front and the wave front elongates to form a dispersed wave. In this study, we describe evidence of nonlinear wave propagation including formation of shock waves that has been observed using a vertical array of accelerometers in centrifuge model tests and in real earthquake data. Implications of non-linear wave propagation in strain-stiffening and strain-softening soil are discussed. We also look at the reflection phenomena of nonlinear waves at rigid and free boundaries. One result is that for a soil that is undergoing cyclic mobility (negative pore pressure development during loading, and positive pore pressure development during unloading), the wave sharpens as it approaches the ground surface and the reflected wave is almost negligible.