The Hydrology of Desiccation and Cracking with Application to Desertification

干燥和破裂的水文学与荒漠化的应用提案#EAR-0838224约翰·H·库什曼，普渡大学摘要要了解荒漠化过程，重要的是知道氮的位置以及它是如何运输、储存和积累的。最近的研究表明，全球范围内包气带的氮库可能被低估了3%至16%，温暖沙漠中的氮库被低估了14%至71%。也有人推测，沙漠底土中硝酸盐的积累是罕见的深度湿润事件的结果，并表明底土中发现的硝酸盐数量与沙漠的年龄呈正相关。关于在沙漠土壤中发现的不寻常的硝酸盐沉积物，特别令人感兴趣的是智利的阿塔卡马沙漠。高度浓缩的硝酸盐沉积物的起源一直是许多争论的主题。这片沙漠是地球上最干燥的环境之一，年平均降雨量为1到2毫米，据估计，这种干旱已经持续了1000到1500万年。出于这个原因，它经常被用作火星环境的模型。该地区硝酸盐沉积物的持续干燥导致了多孔地层的收缩，形成了小的和大的干燥多边形。随着时间的推移，大型干燥多边形留下的裂隙被盐胶结砂、粉砂和岩石碎屑填充，形成了富含硝酸盐的沙堤。虽然现有的几个模型都适用于经历大的非弹性变形的饱和和非饱和土壤的本构模型，但可用的数学工具要么不能解释土壤在干燥过程中破裂所产生的两个时间尺度，要么不包括模拟长期化学运移所需的演变尺度。我们将开发一个通用的数学模型来描述饱和/非饱和裂解土中的流动和运移。特别是，我们将使用混合混合物理论(HMT)方法来模拟流动和块传输机制，预测裂缝的形成，并获得对经历干燥的土壤的水力和传输特性的动态描述。通过放宽一些限制性假设，如使用标准的达西？S定律来描述水相中的流动，并确定适当的自变量，从而建立严格而有意义的屈服函数来分析塑性，对这个问题的HMT方法将比以往的多相系统弹塑性行为的方法有所改进。这包括对双重时间尺度问题进行建模，其中弹性沉积物填充在干燥过程中产生的裂缝的空隙空间，以及经常导致的非局部传输通过分形断裂路径。对于后一部分，我们将使用从属的随机常微分方程式对分形裂缝中的成分速度进行建模；放大将通过广义中心极限定理来完成。如果有时间和人力，我们将把理论发现应用于智利阿塔卡马沙漠的氮沉积物。

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.