1. Purpose: To provide a multi-scale theoretical and computational model of variably saturated granular/porous media that will improve our ability to perform engineering-scale analyses. Product/Results: Theoretical and computational modeling frameworks for air/water/particle systems. New constitutive relations for macroscopic models of porous media. Payoff: Understanding how the microscopic properties of variably saturated media relate to the engineering scale properties will lead to improved ability to detect subsurface features, to build reliable structures, and to predict transport in soils. Schedule & Cost Total $738K MILESTONES Prior FY08 FY09 FY10 Years Army ($K) Other Initial Plan/Prep Particle-Scale Theory Particle-Scale Simulator Three-phase Theory Three-phase Simulator Multiscale Theory Multiscale Simulator Particle-Scale Distribution of Soil Moisture in Porous Materials Status: Basic 6.1 $738K Total Army Program 227 261 250

2. What is the Problem? – We don’t understand the macroscopic structural, hydraulic, thermal, electromagnetic, and chemical properties of variably saturated soils. These properties affect our ability to detect subsurface targets and features, build structures, and predict chemical species transport in soils. What are the barriers to solving the problem? – Accurately measuring thermodynamic conjugate variables in physical experiments under dynamic conditions, as required for formulation of fundamentally sound constitutive relationships, is not possible. Quantities such as phase pressures, surface tension, fluid phase distribution, fluid phase kinetic and potential energies cannot be independently measured at the pore scale. Collaboration across ERDC, commercial firms and/or academia – High Fidelity Vessel Effects Project (CHL), Level-set methods GEOTACS/IMTPS (GSL), Macroscale models DAAC (MSRC) 3D viz and data formats Kitware, Inc. (Albany) - 3D viz and sotware development Y. Bazilevs (UC-San Diego), Multiscale numerical methods G. Carey and C. Dawson (UT-Austin), Finite element analysis J. Chrispell (Tulane), Immersed interface methods D. DiCarlo and M. Prodanovic (UT-Austin), Pore-scale models S. Gasda and C. Miller (UNC-Chapel Hill), Macroscale models P. Imhoff (Delaware), Macroscale models L. Jenkins (Clemson), Numerical methods C. Willson (LSU), Particle scale measurements What is innovative about this work? The use of particle-scale continuum fluid mechanics simulations that explicitly model the separate phases and the fluid-water and fluid-solid interfaces. The coupling of those models to discrete element models of granular materials to facilitate multi-scale numerical modeling of these systems. What is your publication plan? FY07 - Mini-symposium on near surface air/water flow at U.S. National Congress on Computational Mechanics (July). FY08 - Computer Methods in Applied Mechanics and Engineering (in review). FY09 - Journal of Computational Physics (In preparation), Advances in Water Resources (in preparation). Particle-Scale Distribution of Soil Moisture in Porous Materials How will you overcome these barriers? – Apply state-of- the-art computational methods to rigorous continuum thermo-mechanical models of the interaction of air and water phases in granular materials; collaborate with experimentalists and numerical analysis specialists from academia. What are the results of this research and what is its value? – A multiscale theoretical and computational modeling capability for variably saturated granular materials. The ability to calculate macroscopic properties from particle-scale measurements and/or use simulations to supplement experimental methods in complex three- dimensional settings where direct observation of all physical quantities is not possible; a computational multiscale framework that can be used to carry out fundamentally sound engineering analyses.