Self-weight subsidence of saturated soft porous media

A theory for one-dimensional self-weight subsidence of saturated soft porous media is presented. The problem is formulated in terms of volume solid fraction using the Eulerian coordinates. Two different types of constitutive relationships between the effective stress and the volume fraction of solids are considered. The governing equations and initial and boundary conditions are nondimensionalized. Self-weight subsidence behavior of unconsolidated soils is analyzed both analytically and numerically. Two sets of exact solutions corresponding to two different compressibility relationships are obtained under steady state conditions. Experimental data available in the literature are used to validate one set of exact solutions; Numerical analysis of transient settlement that allows the movement of the top boundary is presented. The validity of the numerical technique is verified by comparing with exact solutions. The model can be used to predict transient and ultimate settlement and the void ratio distribution of soft soils subsiding under their own weight

A SEMIANALYTICAL ANALYSIS OF COMPRESSIBLE ELECTROPHORETIC CAKE FORMATION

Leaks in geomembrane liners of waste landfills and liquid impoundments cause chemical contaminants to leak into the subsurface environment. A mathematical model is presented to simulate electrophoretic sealing of impoundment leaks. The model describes the formation of a compressible clay cake because of electrical and gravitational forces. The model includes mass balance equations for the solid-particles and liquid phase, modified Darcy's law in an electrical field, and Terzaghi's definition of effective stress. The formulation is presented in the Eulerian coordinates. The resulting second-order, nonlinear partial differential equation and the lower boundary condition are linearized to obtain an analytical solution for time-dependent settlement. After discretizing in time the analytical solution is applied to simulate compression of an accreting Sediment. In the; simulation of an accreting sediment, solid fluxes on either side of suspension/sediment interface are coupled using a no-jump condition. The velocity of a discrete particle in the suspension zone is assumed to be equal to the algebraic sum of electrophoretic and Stoke's settling velocities. An empirical relationship available in the literature is used to account for the effect of concentration on the velocity of solid particles in the suspension zone. The validity of the semianalytical approach is partially verified using an exact steady state solution for self-weight consolidation. The simulation results obtained for a set of material parameters are presented graphically. It is noted that the electrokinetic consolidation of sediment continues even after the completion of electrophoretic settling of all clay particles. An analysis reveals that the electrophoretic cake formation process is quite sensitive to voltage gradient and the coefficient of compressibility

Electrophoretic repair of impoundment leaks: Analysis and verification with experimental data

Sealing leaks which have developed in liquid surface impoundments with geomembrane liners may be difficult due to aged liner material. A technique utilizing electrophoresis which causes clay particles to be attracted toward leaks when an electric field is applied provides a cost-effective method for repair. This study presents an experimentally verified methodology to predict electrophoretic sealing of in-service geomembrane liners. The methodology includes a procedure to simulate axis-symmetric electrophoretic cake formation and a numerical technique to solve the electric field for voltage gradients. Path lines of solid particles are generated by superposing electrophoretic and Stokes' settling velocities. A numerical method to obtain a steady-state cake profile by conserving solids mass and an approach which uses path lines to simulate transient cake formation are described. For an initially uniform suspension, final and transient cake profiles are obtained under varying conditions. The effects of voltage difference, surface electrode size, and initial bentonite concentration on cake formation are discussed. In general, a higher Voltage difference or a wider surface electrode accelerates the cake formation process. For efficient cake formation, the surface electrode should be located close to the water surface over the leak. A comparison of theoretical predictions with previously obtained experimental data shows a reasonable agreement. The analysis presented in the study provides a relatively inexpensive and useful tool in the implentation of an in situ field operation

ANALYTICAL EXPRESSIONS TO ESTIMATE THE FREE PRODUCT RECOVERY IN OIL-CONTAMINATED AQUIFERS

Petroleum products, such as gasoline, leaked from an underground storage tank can be recovered successfully by two-pump operations. The success of the recovery effort depends on the accurate placement of the recovery well at the spill site. An effective recovery operation can minimize the remaining contamination mass in the subsurface. Therefore, a careful evaluation and determination has to be made as to where to locate the recovery well. The location of the well can be decided based on an estimation of the extent and thickness of free product on the water table. Such an estimation should be based on analysis of governing mechanisms. In this study we present analytical solutions to estimate the recovery of oil from an established oil lens. These solutions are obtained by applying the Laplace transformation to averaged linear partial differential equations governing the phenomenon. The governing equation for the free product thickness is derived by averaging the oil phase mass balance equation along the free product thickness and substituting the boundary conditions at the oil/water interface and oil surface. The analytical solutions estimate the temporal and spatial distribution of free product thickness on the water table for a number of recovery scenarios. Results are presented for the temporal and spatial variation of the free product thickness, temporal variation of the free product Volume recovered, and recovery efficiency based on the readings at the monitoring wells. Since they can be utilized without a great deal of data, analytical solutions are quite attractive as screening tools in two-pump free product recovery operations