The Hydrology of Desiccation and Cracking with Application to Desertification

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The Hydrology of Desiccation and Cracking with Application to Desertification Proposal # EAR-0838224 John H Cushman, Purdue University ABSTRACTTo 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.