Variations of porosity in a sheared pressurized layer of saturated soil induced by vertical drainage of water

Abstract

We use the mixture model of soil saturated by a fluid, as developed by dell’Isola and Hutter and applied to an isothermal steady simple shear flow pressed and drained by a steady flow of water from above. The governing equations are reduced to a single second–order ordinary differential equation (ODE) for the solid–volume fraction; its coefficients depend on the fluid viscosity and the thermodynamic pressure. The coefficients of this ODE give rise to the application of perturbation techniques; the solutions constructed in this way demonstrate that when the thermodynamic pressure is ignored, the solid–volume profile varies unrealistically largely over the layer thickness. Furthermore, when the vertical fluid convective acceleration terms are incorporated, they give rise to a ‘destabilizing’ mechanism in the sense that a boundary layer over which large changes of the solid–volume fraction arise and which is located where the draining fluid enters may flip to the exit boundary, and so make effective fluidities against shear deformations large. So, depending on the amount of water flow through the layer, the horizontal shearing to prescribed shear tractions may be small or large. For ice–sheet flow situations on soft beds, the flow rates achieving this flip are of the order of a few tens of centimetres per year and are, thus, fairly realistic.