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Vegetation on railway or highway slopes can improve slope stability through the generation of soil pore water suctions by plant transpiration and mechanical soil reinforcement by the roots. To incorporate the enhanced shearing resistance and stiffness of root-reinforced soils in stability calculations, it is necessary to understand and quantify its effectiveness. This requires integrated and sophisticated experimental and multi-scale modelling approaches to develop an understanding of the processes at different length scales, from individual root–soil interaction through to full soil-profile or slope scale. One of the challenges with multi-scale models is ensuring that they sufficiently closely represent real behaviour. This requires calibration against detailed high-quality and data-rich experiments. This study presents a novel experimental methodology, which combines in situ direct shear loading of a willow root-reinforced soil with X-ray computed tomography to capture the three-dimensional chronology of soil and root deformation within the shear zone. Digital volume correlation (DVC) analysis was applied to the computed tomography dataset to obtain full-field three-dimensional displacement and strain information. This paper demonstrates the feasibility and discusses the challenges associated with DVC experiments on root-reinforced soils. [ABSTRACT FROM AUTHOR]

Most water and nutrients essential for plant growth travel across a thin zone of soil at the interface between roots and soil, termed the rhizosphere. Chemicals exuded by plant roots can alter the fluid properties, such as viscosity, of the water phase, potentially with impacts on plant productivity and stress tolerance. In this paper, we study the effects of plant exudates on the macroscale properties of water movement in soil. Our starting point is a microscale description of two fluid flow and exudate diffusion in a periodic geometry composed from a regular repetition of a unit cell. Using multiscale homogenization theory, we derive a coupled set of equations that describe the movement of air and water, and the diffusion of plant exudates on the macroscale. These equations are parametrized by a set of cell problems that capture the flow behaviour. The mathematical steps are validated by comparing the resulting homogenized equations to the original pore scale equations, and we show that the difference between the two models is ~7% for eight cells. The resulting equations provide a computationally efficient method to study plant- soil interactions. This will increase our ability to predict how contrasting root exudation patterns may influence crop uptake of water and nutrients. [ABSTRACT FROM AUTHOR]

We show how a combination of X-ray computed tomography (X-CT) and image-based modelling can be used to calculate the effect of moisture content and compaction on the macroscopic structural properties of soil. Our method is based on the equations derived in Daly & Roose (2018 Proc. R. Soc. A 474, 20170141. (doi:10.1098/rspa.2017.0141)), which we have extended so they can be directly applied to the segmented images obtained from X-CT. We assume that the soils are composed of air-filled pore space, solid mineral grains and a mixed phase composed of both clay particles and water. We considered three different initial soil treatments, composed of two different compaction levels and two differentmoisture contents. We found that the effective properties of the soils were unaffected by compaction over the range tested in this paper. However, changing the moisture content significantly altered the hydraulic and mechanical properties of the soils. A key strength of this method is that it enables the optimization or even design of soils composed from different constituents, with specific mechanical and hydraulic properties. [ABSTRACT FROM AUTHOR]

The parameters in Richards' equation are usually calculated from experimentally measured values of the soil--water characteristic curve and saturated hydraulic conductivity. The complex pore structures that often occur in porous media complicate such parametrization due to hysteresis between wetting and drying and the effects of tortuosity. Rather than estimate the parameters in Richards' equation from these indirect measurements, image-based modelling is used to investigate the relationship between the pore structure and the parameters. A threedimensional, X-ray computed tomography image stack of a soil sample with voxel resolution of 6 µm has been used to create a computational mesh. The Cahn--Hilliard--Stokes equations for two-fluid flow, in this case water and air, were applied to this mesh and solved using the finite-element method in COMSOL MULTIPHYSICS. The upscaled parameters in Richards' equation are then obtained via homogenization. The effect on the soil--water retention curve due to three different contact angles, 0°, 20° and 60°, was also investigated. The results show that the pore structure affects the properties of the flow on the large scale, and different contact angles can change the parameters for Richards' equation. [ABSTRACT FROM AUTHOR]

The macroscopic behaviour of air and water in porous media is often approximated using Richards' equation for the fluid saturation and pressure. This equation is parametrized by the hydraulic conductivity and water release curve. In this paper, we use homogenization to derive a general model for saturation and pressure in porous media based on an underlying periodic porous structure. Under an appropriate set of assumptions, i.e. constant gas pressure, this model is shown to reduce to the simpler form of Richards' equation. The starting point for this derivation is the Cahn- Hilliard phase field equation coupled with Stokes equations for fluid flow. This approach allows us, for the first time, to rigorously derive the water release curve and hydraulic conductivities through a series of cell problems. The method captures the hysteresis in the water release curve and ties the macroscopic properties of the porous media with the underlying geometrical and material properties. [ABSTRACT FROM AUTHOR]

Flow in both saturated and non-saturated vuggy porous media, i.e. soil, is inherently multiscale. The complex microporous structure of the soil aggregates and the wider vugs provides a multitude of flow pathways and has received significant attention from the X-ray computed tomography (CT) community with a constant drive to image at higher resolution. Using multiscale homogenization, we derive averaged equations to study the effects of the microscale structure on the macroscopic flow. The averaged model captures the underlying geometry through a series of cell problems and is verified through direct comparison to numerical simulations of the full structure. These methods offer significant reductions in computation time and allow us to perform three-dimensional calculations with complex geometries on a desktop PC. The results show that the surface roughness of the aggregate has a significantly greater effect on the flow than the microstructure within the aggregate. Hence, this is the region in which the resolution of X-ray CT for image-based modelling has the greatest impact. [ABSTRACT FROM AUTHOR]