Gabor M. Karadi

Effect of Non-Darcian Flow on Time Rate of Consolidation

Abstract The effect of non-Darcian flow on the consolidation behavior of clay soils is studied, and its role in the extrapolation of laboratory test results to field problems is evaluated. This is accomplished by postulating a reasonably general four-parameter velocity-gradient relationship which, by proper choice of parameters, is capable of characterizing much of the published experimental data; then, this relationship is combined with the standard assumptions of classical consolidation theory to develop a nonlinear parabolic partial differential equation, which is solved by use of a finite difference technique. The stability and convergence criteria for related linear and quasi-linear equations are empirically extended to the associated nonlinear equations, and a comparison is made between various explicit and implicit finite difference schemes, with the result that a sufficiently accurate and more economical numerical solution is obtained by use of an explicit scheme. Typical solutions for various specific cases confirm and offer an explanation for the well-known phenomenon wherein the time rate of consolidation is found to decrease as the load increment decreases; also, the thickness of the consolidating layer is shown to affect the dimensionless time rate of consolidation. These conditions indicate that laboratory consolidation test results can be applied to a field situation only if appropriate stress and thickness corrections are made.

Hydrodynamic dispersion in a single rock joint

This paper deals with the hydrodynamic dispersion of a contaminant in a single rock joint; the effects of molecular diffusion due to a concentration gradient are considered to be negligible relative to the hydrodynamic effects, and the surfaces of the rock joint are assumed to be geochemically stable. Both laminar and turbulent flow are treated, and the constitutive properties of the contaminant are assumed to be the same as those of the parent fluid. Within this framework and with a knowledge of the boundary condition at the origin, the time‐dependent average concentration at any point within the joint can be found by using either (a) a Taylor series expansion or a polynomial approximation for this boundary condition, or (b) an incremental approach based on the principle of superposition. Experimental data are given to substantiate the acceptability of the assumptions employed.

Effect of non-darcian behavior on the characteristics of transient flow

Abstract A modified form of the boundary value problem describing the one-dimensional transient flow in clay soils is formulated to include a non-Darcian flow law with a threshold gradient. The solution is obtained by matrix techniques, and calculated results are compared with results obtained from conventional one-dimensional theory.

Unsteady seepage flow between fully-penetrating trenches

Abstract The problem of unsteady seepage flow, including either evaporation or infiltration, in the domain between two fully-penetrating trenches is considered. The method of solution is based on matrix mathematics and has the advantages of being able to handle complicated boundary and initial conditions and to consider step by step the nonlinearity of the governing differential equation. Typical results are presented for a variety of boundary and initial conditions, and results calculated by this technique for one particular set of boundary and initial conditions are shown to exhibit better agreement with experimental data than do results calculated by linearizing the governing field equation.

Flow toward periodic tile drains

Abstract The method of conformal mapping is applied to the analysis of transient flow toward parallel periodic drains in a semi-infinite aquifer taking into consideration the non-linear boundary conditions on the free surface. The mapping function is expressed as a power series in time and the seepage domain is mapped onto a domain of an auxiliary complex variable. Mapping is performed in such a manner that the free surface will always remain the real axis. Calculations are carried out for different ratios of drain depth to drain spacing using various drain diameter to depth ratios.