The geotechnical community typically relies on recommendations made from numerical simulations. Commercial software exhibits (local) numerical instabilities in layered soils across soil interfaces. This research work investigates unsaturated moisture flow in layered soils and identifies a possible source of numerical instabilities across soil interfaces and potential improvement in numerical schemes for solving the Richards' equation. The numerical issue at soil interfaces is addressed by a (nonlinear) interface problem. A full analysis of the simplest soil hydraulic model, the Gardner model, identifies the conditions of ill-posedness of the interface problem. Numerical experiments on various (more advanced and practical) soil hydraulic models show that the interface problem can also be ill-posed under certain circumstances. Spurious numerical ponding and/or oscillations around soil interfaces are observed consequently. This work also investigates the impact of different averaging schemes for cell-centered conductivities on the propensity of ill-posedness of the interface problem and concludes that smaller averaging conductivities are more likely to trigger numerical instabilities. In addition, an agent-based stochastic soil model, with hydraulic properties defined at the finite difference cell level, results in a large number of interface problems. This research compares sequences of stochastic realizations in heterogeneous unsaturated soils with the numerical solution using homogenized soil parameters. The mean of stochastic realizations is not identical to the solution obtained from homogenized soil parameters.

A new method for generating artificial fingerprints is presented. Due to their uniqueness and durability, fingerprints are invaluable tools for identification for law enforcement and other purposes. Large databases of varied, realistic artificial fingerprints are needed to aid in the development and evaluation of automated systems for criminal or biometric identification. Further, an effective method for simulating fingerprints may provide insight into the biological processes underlying print formation. However, previous attempts at simulating prints have been unsatisfactory. We approach the problem of creating artificial prints through a pattern formation model. We demonstrate how it is possible to generate distinctive patterns that strongly resemble real fingerprints via a system of partial differential equations with a suitable domain and initial conditions.

The primary objective of this study is to understand the effect of soil cracking on foundation performance for expansive soil profiles. Two major effects of cracks were studied to assess the effect of cracks on foundation performance. First, the effect of cracks on soil volume change response was studied. Second, the effect of cracks on unsaturated flow properties and extent and degree of wetting were evaluated. Multiple oedometer-type pressure plate tests were conducted to evaluate the effect of cracks on soil properties commonly used in volume change (heave) analyses, such as swell pressure, soil water characteristic curve (SWCC), and swell potential. Additionally, the effect of cracks on saturated and unsaturated hydraulic conductivity was studied experimentally to assess the impact of cracks on properties critical to evaluation of extent and degree of wetting. Laboratory experiments were performed on both intact and cracked specimen so that the effect of cracks on behavior could be benchmarked against intact soil response. Based on laboratory observations, the SWCC of a cracked soil is bimodal. However, this bimodal behavior is only observed in the very low suction ranges. Because the bimodal nature of the SWCC of cracked clays is only distinguishable at extremely low suctions, the bimodal behavior is unlikely to have engineering significance when soils remain unsaturated. A "lumped mass" parameter approach has been studied as a practical approach for modeling of cracked soils for both fluid flow and volume change determination. Laboratory unsaturated flow experiments were simulated using a saturated-unsaturated flow finite element code, SVFlux, to back-analyze unsaturated hydraulic conductivity functions for the subject soils. These back-analyzed results were compared to the results from traditionally-applied analyses of the laboratory instantaneous profile tests on intact and cracked specimens. Based on this comparison, empirical adjustments were suggested for modeling "lumped mass" cracked soil behavior in numerical codes for fluid flow through cracked soils. Using the empirically adjusted flow parameters for unsaturated flow modeling, example analyses were performed for slab-on-grade problems to demonstrate the impact of cracks on degree and extent of wetting under unsaturated and saturated flow conditions for different surface flux boundary conditions.