Proposal # EAR-0838224 John H Cushman, Purdue University
ABSTRACT To understand the desertification process it is important to know where nitrogen is located and how it is transported, deposited and accumulated. Recent studies have suggested that nitrogen reservoirs in the vadose zone have been potentially underestimated by 3% to 16% globally and 14% to 71% in warm deserts. It has also been conjectured that the accumulation of nitrate in the desert subsoil is the result of infrequent deep-wetting events, and it has been suggested that there is a positive correlation between the amount of nitrate found in the subsoil and the age of the desert. In regard to unusual nitrate deposits found in desert soils, of particular interest is the Atacama Desert in Chile. The origins of the highly concentrated nitrate deposits have been the subject of much debate. This desert is one of the driest environments on earth with an average annual rainfall of 1 to 2 mm per year and it is estimated that it has been this dry for 10 to 15 million years. For this reason it is often used as a model for the environment of Mars. Ongoing desiccation of the nitrate deposits in the area have caused both small and large desiccation polygons to form via shrinking of the porous formation. Over time the fractures left by the large desiccation polygons have become filled with saline-cemented sand, silt and rock debris forming nitrate rich sand dykes. While several models exist that address the constitutive modeling of both saturated and unsaturated soils undergoing large inelastic deformations, the mathematical tools available either cannot account for the two time scales that result from the fracturing of soils during desiccation, or do not include the evolving scales necessary to model long-term chemical transport. We will develop a generalized mathematical model to describe flow and transport in saturated/unsaturated cracking soils. In particular, we will use a hybrid mixture theoretic (HMT) approach to model flow and block-transport mechanisms, predict crack formation, and obtain a dynamic description of the hydraulic and transport properties of soils undergoing desiccation. The HMT approach to this problem will improve over previous approaches for elasto-plastic behavior of multi-phase systems, by relaxing some of the restrictive assumptions, such as the use of the standard Darcy?s law to describe flow in the water phase, and identification of appropriate independent variables that permit development of rigorous and meaningful yield functions for analyzing plasticity. This includes modeling the dual time-scale problem where elastic sediment fills the void space of cracks created during the drying process, and the non-local transport through the fractal fracture paths that often result. For the latter part, we will model constituent velocity in fractal fractures using subordinated stochastic ordinary differential equations; upscaling will be accomplished with generalized central limit theorems. Should time and man-power be available, we will apply the theoretical findings to the nitrogen deposits in the Atacama Desert in Chile.
Swelling porous media are ubiquitous; examples include swelling soils and clays in geophysics, detergents and diapers in consumer products, drug delivery substrates in pharmaceuticals, human disk tissue, and wood, to name a handful. These substances swell upon imbibition of water and shrink upon desiccation. Often during the desiccation process crusts form and cracks may propagate through the body. While swelling systems may be saturated over large ranges of water content, at a critical point (air entry point) they begin desaturation. The behavior of saturated and unsaturated swelling systems is quite different as drainage largely occurs through connected water passages. When the system is unsaturated isolated pockets of air (bubbles) or water (pendular water) may exist. Disconnected liquid phases coupled with a locally disconnected solid phase (cracks) cause tremendous modeling problems over and beyond the already complicated nature of predicting deformation under moisture content changes in saturated swelling bodies. Additionally, from a statistical perspective properties in swelling systems are complicated by the fact that they often change over space in a non-nice fashion (non-stationary increments) and chemical transport is anomalous ( does not behave as a classical Brownian walk). The effort represented by this grant has overcome some of these complicated issues associated with swelling systems. The issue of connectedness has been addressed, as have issues involving non-stationary increment processes and anomalous dispersion of chemicals. Specific accomplishments include development of computer code to simulate saturated drying and imbibition of swelling systems and isolation of crack nucleation points, development of geostatistical tools and software for non-stationary increment processes, and development of a framework for studying the role of connectedness in swelling systems. Two graduate students and two undergrads have been funded by tis program and two courses have been designed partially based on the work carried out in this program.
