Deficient pore pressures in an eroding soil mass

Abstract

The pore pressure response of a semi-infinite, fully saturated soil mass of finite thickness eroded at a constant rate is examined. Using Terzaghi's classical consolidation theory, an expression is derived for the deficient pore pressure as a function of depth and time. The resulting equation is mildly nonlinear with a moving top boundary. Closed form analytical solutions are obtained for various bottom boundary conditions and are presented in nondimensional quantities. The results indicate that the development of deficient pore pressures is dependent on (i) the rate of soil removal; (ii) the swelling potential of the soil mass; (iii) the ratio of the thickness of soil layer(s) removed to its original thickness; and (iv) the nature of the bottom boundary. Substantial negative pore pressures are likely to persist in the residual mass, even close to the eroded surface, although free water is made available at the top. The plots presented in this paper will be helpful for ascertaining the erosion–swelling characteristics of a soil mass that has been or is being eroded. Examples are presented to illustrate the development and dissipation of deficient pore pressures due to swelling. Keywords: constant rate, deficient pore pressures, depth factor, dredging, erosion–swelling ratio, isochrones, Laplace transform, moving boundary, swelling.