The key objective of this project is to couple the Richards Equation based unsaturated flow in capillary pores of soils with flow through macropores using the Navier-Stokes Equations solved using the Lattice-Boltzmann (LB) Method for two phase (liquid and gas) flow. Because computationally efficient mechanistically-based models do not exist, groundwater recharge, or deep drainage estimates, or gas emissions from landfills are often carried out by ignoring preferential flow or by modeling it empirically. Dual permeability models simulate macropore flow by specifying separate sets of unsaturated properties to the micro and macro pores. However, the flow through macropores does not follow Darcian flow and assumes all macropores are connected as a continuum while often macropores are discrete and disconnected. The central idea behind the model to be developed in this project is that flow through macropores is similar to flow in conduits having irregular shapes and hence Navier Stokes equations are more appropriate and are numerically stable when solved using the Lattice-Boltzmann method. With the advances in digital X-ray CT imaging techniques, it is now possible to have pore structure of soils characterized relatively quickly and economically. Hence, a model that can take advantage of such high resolution pore structure data can revolutionize the way we estimate long-term liquid percolation into landfills or gas emissions from landfills. The macro pore and micro pore structure in the soil system will be digitally input to the model using X-ray Computed Tomography (CT) image data for soil samples collected from instrumented field-scale clay caps to validate the modeling approach. High-resolution water balance data has been collected over a period of three years from two field-scale clay cap test sections located at a landfill in Detroit. The conventional physically-based numerical models can capture the unsaturated flow through capillary or micropores relatively accurately. However, they cannot model flow through macropores which are formed and continuously evolve due to inadequate compaction, desiccation cracking, freeze/thaw, root penetration, and rodent activity. The model that will be developed will overcome the challenge of modeling liquid or gas flow through macropores.
A numerical model that takes advantage of recent advances in X-ray imagining of soil structure for modeling flow through soils will provide practitioners and regulators a tool to accurately predict long-term deep drainage into ground water systems of environmental significance or green-house gas emissions from landfills. A course module on migration of liquids and gases from waste sites will be prepared for an undergraduate landfill design class and a course module containing theory and lab experimentation to demonstrate preferential flow through soils will be prepared and introduced in a graduate level course. Outreach to high school students during summer training camps will carried out with hands-on demonstrations at Michigan State University.
Intellectual Merit: Commonly used numerical models to simulate percolation through earthen landfill covers are based on classical theory of water flow through saturated-unsaturated porous materials that exhibit capillarity due to the relatively small size of the pores called micropores. However, these models do not simulate flow through relatively large pores (macropores) such as cracks or cavities created by rodent burrows or plant roots. The transient liquid flow in micropores is downward or upward depending on the hydraulic gradient due to the soil capillarity and gravity, respectively. Flow through macropores is predominantly downward, similar to in a conduit. Inability to model macropore flow, in addition to micropore flow, is one of the key limitations of commonly used water balance models. Hence, models capable of simulating micropore flow as well as macropore flow are needed in order to design the earthen landfill covers. As part of this project, 2D and 3D Lattice Boltzmann Models (LBMs) simulating saturated flow through micropores and macropores were developed and validated. A laboratory method was developed to create artificial desiccation cracks in compacted clay samples. These samples were scanned using the nondestructive X-Ray Computed Tomography (CT) imaging technique to develop 3D morphology of the cracks. The binary images obtained from X-ray CT scan images were used as direct input in the LBM simulations. In order to study the effect of macropore morphology on the overall flow regime in cracked clays, several artificial macropore shapes were created in 3D domain. Even though all the simulations were performed in the same condition, the cross sectional areas are the same, the velocity distribution exhibited significant difference for different cross sections. It was observed that the macropore flow rate decreases by about 10% to 70% as compared to a circular cross section when the tortuosity is increased by 40% or when the shape of the cross section is altered. Increase in aspect ratio of sectional shape shows decrease in macropore flow rate. Tortuosity plays a significant role in macropore flow where the macropore flow rate reduces by about 70% for tortuosity of 1.41 as compared to a tortuosity of 1. From the results presented on macropore flow rate through different shapes and tortuosity, it was observed that the macropore flow rate is a function of aspect ratio of the void (macropore) constriction and tortuosity of the macropore. A simple equation was formulated using the aspect ratio and tortuosity to predict the flow rate through different shapes and tortuosity based on the flow rate of straight vertical cylinder. This equation can be implemented in water balance models in order to enhance the macropore flow module to include different shapes and tortuous macropores without much complication in programming. For an instrumented final cover test section located in Michigan, the Root Zone Water Quality Model (RZWQM) developed by USDA was able to simulate the percolation relatively accurately. This test section which was in service for almost 4 years had undergone changes in its hydraulic properties due to the formation of macropores. Site specific calibrated properties of macropores were necessary to yield relatively accurate estimates of percolation. Broader Impacts: Lattice Boltzmann simulations have been developed to illustrate the seepage underneath the dams and retaining walls in an undergraduate Soil Mechanics class (www.egr.msu.edu/~kutay/teaching.html). These simulations helped improve the students' learning of the concept of water flow and seepage within soils. As part of MSU’s College of Engineering’s Preview Day events PIs disseminated the findings of this research to High School students and their parents. The Preview Day is an "Open-House" kind event where High School students and their parents visit MSU’s different Engineering Departments before they make a decision on a career. As part of this event, PIs made 4 different presentations to different groups, which included approximately 20-40 visitors each. A web site has been set up to share (freely) one of the Lattice Boltzmann fluid flow algorithms we developed as part of this project (Link: www.egr.msu.edu/~kutay/softwares/d2q9lb-software/). A teaching module on macropore flow was developed to train professionals and graduate students. This module has been implemented in the graduate level course entitled "Properties of Soils (CE812)". An online course and webinar has been developed for professionals on Long-Term Design of Water Balance Covers using the results of this study.
