Award Abstract # 0838224
The Hydrology of Desiccation and Cracking with Application to Desertification

NSF Org: EAR
Division Of Earth Sciences
Recipient: PURDUE UNIVERSITY
Initial Amendment Date: April 23, 2009
Latest Amendment Date: April 6, 2011
Award Number: 0838224
Award Instrument: Continuing Grant
Program Manager: Thomas Torgersen
EAR
 Division Of Earth Sciences
GEO
 Directorate for Geosciences
Start Date: May 1, 2009
End Date: September 30, 2013 (Estimated)
Total Intended Award Amount: $345,520.00
Total Awarded Amount to Date: $358,020.00
Funds Obligated to Date: FY 2009 = $111,134.00
FY 2010 = $127,549.00

FY 2011 = $119,337.00
History of Investigator:
  • John Cushman (Principal Investigator)
Recipient Sponsored Research Office: Purdue University
2550 NORTHWESTERN AVE # 1100
WEST LAFAYETTE
IN  US  47906-1332
(765)494-1055
Sponsor Congressional District: 04
Primary Place of Performance: Purdue University
2550 NORTHWESTERN AVE # 1100
WEST LAFAYETTE
IN  US  47906-1332
Primary Place of Performance
Congressional District:
04
Unique Entity Identifier (UEI): YRXVL4JYCEF5
Parent UEI: YRXVL4JYCEF5
NSF Program(s): Hydrologic Sciences
Primary Program Source: 01000910DB NSF RESEARCH & RELATED ACTIVIT
01001011DB NSF RESEARCH & RELATED ACTIVIT

01001112DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s): 0000, 9251, OTHR
Program Element Code(s): 157900
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.050

ABSTRACT

The Hydrology of Desiccation and Cracking with Application to Desertification
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.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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(Showing: 1 - 10 of 14)
Cushman, J. H., D. O?Malley and M. Park "Anomalous Diffusion, Renormalization Groups, Scaling Laws and Classification: A Reflection on Recent Efforts" Advances in Water Resources , v.62 , 2013 , p.207
Cushman, J. H., M. Park,and D Oâ??Malley "A Stochastic Model for Diffusion in Confined Nano-films Near a Strain Induced Critical Point." Advances in Water Resources , 2011 10.1016/j.advwatres.2011.01.005
Cushman, J.H., M. Park, M. Moroni, N. Kleinfelter-Domelle* and D. Oâ??Malley "A Universal Field Equation for Dispersive Processes in Geophysics." Stoch. Env. Res. and Risk Assesment , v.25 , 2011 , p.1
Cushman, JH; O'Malley, D; Park, M "Anomalous diffusion as modeled by a nonstationary extension of Brownian motion" PHYSICAL REVIEW E , v.79 , 2009 View record at Web of Science 10.1103/PhysRevE.79.03210
Kleinfelter-Domelle*, N. and J. H. Cushman (2012) The Role of Connectivity in the Theory of Saturated/Unsaturated Flow in Swelling Porous Media. Water Res. Research. (48): W001543, 1-16 "The Role of Connectivity in the Theory of Saturated/Unsaturated Flow in Swelling Porous Media" Water Res. Research , v.48 , 2012
Oâ??Malley, D., J. H. Cushman, and G. Johnson "Scaling Laws for Fractional Brownian Motion with a Power-law Clock." J Stat. Mech: Theory and Experiment , 2011 10.1088/1742-5468/2011/00/L00000.
O?Malley, D. and J. H.Cushman "A Geostatistical Tool for Stochastic Processes with Nonstationary Increments" Water Resources Research , v.49 , 2013 , p.4525
O?Malley, D. and J. H. Cushman "Random Renormalization Group Operators Applied to Stochastic Dynamics" J Statistical Physics , v.149 , 2012 , p.943
O?Malley, D. and J. H. Cushman "Two Scale Renormalization Group Classification of Diffusive Processes." Phys. Rev. E , v.86 , 2012 , p.011126
O'Malley, Daniel; Cushman, John H. "A Renormalization Group Classification of Nonstationary and/or Infinite Second Moment Diffusive Processes" JOURNAL OF STATISTICAL PHYSICS , v.146 , 2012 , p.989-1000
O'Malley, Daniel; Cushman, John H. "Random Renormalization Group Operators Applied to Stochastic Dynamics" JOURNAL OF STATISTICAL PHYSICS , v.149 , 2012 , p.943-950
(Showing: 1 - 10 of 14)

PROJECT OUTCOMES REPORT

Disclaimer

This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.

 



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.



 


Last Modified: 12/03/2013
Modified by: John H Cushman

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