Physical effects between the interaction of a Maxwell fluid and a uniform marine current on the mechanical response of a poroelastic soil

In this work, an analytical solution to the soil's dynamic response induced by the interaction between a long water wave and a viscoelastic mud is obtained. The system is divided into three regions: the upper layer is water, the middle layer is a viscoelastic mud, and the lower layer is a poroelastic soil. It is assumed that there is an horizontal marine current with uniform vertical profile. The water hydrodynamics is obtained under the assumption of a potential flow. In the mud region, which thickness is of the same order of magnitude as the water depth, the simplified Cauchy governing equations are solved, where the Maxwell rheological model is adopted. Because it is considered a viscoelastic mud at the mud–soil interface, the continuity of shear and vertical stresses is assumed. Increasing the mud thickness, the vertical stresses and the vertical displacements of the soil are also increased. It should be noted that increasing the mud viscoelasticy, represented by increasing values of the Deborah number, affects only the shear stresses and the horizontal soil displacements. It is identified that currents that are found in the same direction that the wave propagation induce larger liquefaction depth than those calculated for opposite currents. The present solution can serve, as a first approximation, to identify the effects of the wave–current interaction in the presence of a viscoelastic mud on the liquefaction depth.