Date of Award
Doctor of Philosophy (PhD)
Civil and Environmental Engineering
William E. Kelly
A Monte Carlo technique is utilized to incorporate the uncertainty in media characteristics to the solution of a groundwater flow problem. This technique involves the repetitive solution of a significant number of equiprobable representations of the soil medium. Probability and statistics are utilized to model the soil parameters and study the significance of the output.
An existing computer code was adapted and significantly modified to allow characterization of the media's hydraulic conductivity (permeability) as autocorrelated and statistically homogeneous. A first order nearest neighbor model was selected to affect the autocorrelation of this parameter within the finite difference mesh. The statistical homogeneity considers that the distribution of hydraulic conductivity values within the mesh comes from a log normal probability density function. The selection of hydraulic conductivity value at any mode of the mesh is stochastic within the framework of the autocorrelation and statistical homogeneity of the mesh aggregate.
The computer code takes the stochastically generated hydraulic conductivity field and the boundary conditions and utilizing an iterative alternating direct implicit solution determines the hydraulic head values at each mode and flow rate through the medium. An array of these results are produced for each of the equiprobable representations of the soil medium.
Mass transport through the region is simulated as a combination of advection and a stochastic simulation of microscopic or particle scale dispersion. A water particle is released from a preselected location along the upgradient boundary. The particle moves toward the downgradient boundary under the influence of advective forces caused by the differences in hydraulic head and the stochastic simulation of microscopic dispersion. This simulation of microscopic dispersion displaces the particle parallel to and perpendicular to the advective transport direction based on laboratory scale dispersivities. The computer code establishes arrays for the particle location at a predetermined time after start as well as the location along the downgradient boundary and total travel time upon completion of transit of the region.
Uniform flow results in most of the regions considered although some alternate configurations were considered. An effective hydraulic conductivity is calculated on the basis of flow rate. After application of a shape factor this value was found to be slightly less but closest to the geometric mean of the hydraulic conductivity distribution thus confirming earlier work. An alternative effective hydraulic conductivity calculated on the basis of travel time was also determined. This value was generally less than the other effective hydraulic conductivity value but again after application of a shape factor the value was best estimated by the geometric mean. These results suggest that the mean flow rate and mean travel time may be estimated by the use of the shape factor from a flow net solution or the method of fragments and the geometric means of the hydraulic conductivity.
The results of the simulations indicate that macroscopic or field scale longitudinal and lateral dispersion is significantly affected by the standard deviation of the hydraulic conductivity distribution. Region size, hydraulic gradient and time interval were found to cause lesser effects.
The techniques utilized provide a means to develop confidence in the output. The effects of the variations in parameters become evident from a review of the results of the equiprobable results. Confidence limits may even be developed in the output where the characteristics of known probability density functions may be utilized. Example problems are presented where confidence limits on the estimates of travel time are developed for the conditions considered.
Aldinger, Paul Bruce, "Groundwater Flow Simulation by a Stochastic Representation of Soil" (1983). Open Access Dissertations. Paper 546.