An Exact Solution to the Local Fractional Richards' Equation for Unsaturated Soils and Porous Fabrics

2013 ◽  
Vol 843 ◽  
pp. 97-101
Author(s):  
Zheng Biao Li ◽  
Yin Shan Yun ◽  
Hong Ying Luo
Keyword(s):  
Exact Solution ◽  
Porous Media ◽  
Water Content ◽  
Unsaturated Soils ◽  
Fractal Dimensions ◽  
Volumetric Water Content ◽  
Richards Equation ◽  
Fractional Complex Transform ◽  
Porous Soil

A local fractional Richards equation is derived by considering the soil as fractal porous media, and an exact solution is obtained by a generalized Boltzmann transform and the fractional complex transform. The new theory predicts that the volumetric water content depends on the ratio (distance)2a /(time), where a is the value of fractal dimensions of the porous soil, and its value is recommended for various soils.

scholarly journals Assessment of water penetration problem in unsaturated soils

2009 ◽  
Vol 6 (3) ◽  
pp. 3811-3833 ◽  
Author(s):  
A. Barari ◽  
M. Omidvar ◽  
A. R. Ghotbi ◽  
D. D. Ganji
Keyword(s):  
Porous Media ◽  
Unsaturated Soils ◽  
Homotopy Perturbation Method ◽  
Unsaturated Flow ◽  
Variational Iteration Method ◽  
Environmental Engineering ◽  
Richards Equation ◽  
Proper Solution ◽  
Water Penetration ◽  
Homotopy Perturbation

Abstract. Unsaturated flow of soils in unsaturated soils is an important problem in geotechnical and geo-environmental engineering. Richards' equation is often used to model this phenomenon in porous media. Obtaining proper solution to this equation therefore provides better means to studying the infiltration into unsaturated soils. Available methods for the solution of Richards' equation mostly fall in the category of numerical methods, often having restrictions for practical cases. In this research, two analytical methods known as Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) have been successfully utilized for solving Richards' equation. Results obtained from the two methods mentioned show a remarkably high precision in the obtained solution, compared with the existing exact solutions available.

scholarly journals Physical processes affecting microbial habitats and activity in unsaturated agricultural soils

2002 ◽  
Author(s):  
Dani Or ◽  
Shmulik Friedman ◽  
Jeanette Norton
Keyword(s):  
Porous Media ◽  
Water Content ◽  
Bacterial Growth ◽  
Unsaturated Soils ◽  
Microbial Growth ◽  
Agricultural Soils ◽  
Short Term ◽  
Modeling Tools ◽  
Substrate Diffusion ◽  
Growth Experiments

experimental methods for quantifying effects of water content and other dynamic environmental factors on bacterial growth in partially-saturated soils. Towards this end we reviewed critically the relevant scientific literature and performed theoretical and experimental studies of bacterial growth and activity in modeled, idealized and real unsaturated soils. The natural wetting-drying cycles common to agricultural soils affect water content and liquid organization resulting in fragmentation of aquatic habitats and limit hydraulic connections. Consequently, substrate diffusion pathways to soil microbial communities become limiting and reduce nutrient fluxes, microbial growth, and mobility. Key elements that govern the extent and manifestation of such ubiquitous interactions include characteristics of diffusion pathways and pore space, the timing, duration, and extent of environmental perturbations, the nature of microbiological adjustments (short-term and longterm), and spatial distribution and properties of EPS clusters (microcolonies). Of these key elements we have chosen to focus on a manageable subset namely on modeling microbial growth and coexistence on simple rough surfaces, and experiments on bacterial growth in variably saturated sand samples and columns. Our extensive review paper providing a definitive “snap-shot” of present scientific understanding of microbial behavior in unsaturated soils revealed a lack of modeling tools that are essential for enhanced predictability of microbial processes in soils. We therefore embarked on two pronged approach of development of simple microbial growth models based on diffusion-reaction principles to incorporate key controls for microbial activity in soils such as diffusion coefficients and temporal variations in soil water content (and related substrate diffusion rates), and development of new methodologies in support of experiments on microbial growth in simple and observable porous media under controlled water status conditions. Experimental efforts led to a series of microbial growth experiments in granular media under variable saturation and ambient conditions, and introduction of atomic force microscopy (AFM) and confocal scanning laser microscopy (CSLM) to study cell size, morphology and multi-cell arrangement at a high resolution from growth experiments in various porous media. The modeling efforts elucidated important links between unsaturated conditions and microbial coexistence which is believed to support the unparallel diversity found in soils. We examined the role of spatial and temporal variation in hydration conditions (such as exist in agricultural soils) on local growth rates and on interactions between two competing microbial species. Interestingly, the complexity of soil spaces and aquatic niches are necessary for supporting a rich microbial diversity and the wide array of microbial functions in unsaturated soils. This project supported collaboration between soil physicists and soil microbiologist that is absolutely essential for making progress in both disciplines. It provided a few basic tools (models, parameterization) for guiding future experiments and for gathering key information necessary for prediction of biological processes in agricultural soils. The project sparked a series of ongoing studies (at DTU and EPFL and in the ARO) into effects of soil hydration dynamics on microbial survival strategy under short term and prolonged desiccation (important for general scientific and agricultural applications).

scholarly journals Evaluating the maximum shear modulus (G0) for different bender-soil coupling loads

2020 ◽  
Vol 195 ◽  
pp. 03007
Author(s):  
Caio de Mattos Azevedo de Paula ◽  
Thiago de Souza Carnavale
Keyword(s):  
Shear Modulus ◽  
Water Content ◽  
Unsaturated Soils ◽  
Granite Gneiss ◽  
Soil Samples ◽  
Volumetric Water Content ◽  
Current Paper ◽  
Bender Elements ◽  
Cylindrical Samples

The current paper aims to test the effects of vertical loads on the maximum shear modulus (G0). The tests were undertaken with unsaturated soils in unconfined conditions. As a material, was used a set of granite-gneiss soil samples collected in the Quinta do Paraiso Campus, at the Centro Universitário Serra dos Órgãos (UNIFESO), Teresópolis – Brazil. To perform it, cylindrical samples were submitted to bender elements under four vertical loads (200 g, 400 g, 500 g, and 600 g). Further, the readings were done with the same amplitude and frequency values. The results revealed a decrease in the shear wave’s velocity reducing the volumetric water content. Besides, the shear modulus increased with the vertical loads’ addition.

Soil Properties and Water Movement

1999 ◽  
Author(s):  
J.-Y. Parlance ◽  
T. S. Steenhuis
Keyword(s):  
Water Content ◽  
Soil Water ◽  
Hydraulic Properties ◽  
Volumetric Water Content ◽  
Richards Equation ◽  
Field Scale ◽  
Soil Hydraulic Parameters ◽  
Soil Hydraulic ◽  
Definition Of

For all spatial scales, from pore through local and field, to a watershed, interaction of the land surface with the atmosphere will be one of the crucial topics in hydrology and environmental sciences over the forthcoming years. The recent lack of water in many parts of the world shows that there is an urgent need to assess our knowledge on the soil moisture dynamics. The difficulty of parameterization of soil hydrological processes lies not only in the nonlinearity of the unsaturated flow equation but also in the mismatch between the scales of measurements and the scale of model predictions. Most standard measurements of soil physical parameters provide information only at the local scale and highlight the underlying variability in soil hydrological characteristics. The efficiency of soil characteristic parameterization for the field scale depends on the clear definition of the functional relationships and parameters to be measured, and on the development of possible methods for the determination of soil characteristics with a realistic use time and effort. The soil’s hydraulic properties that affect the flow behavior can be expressed by a soil water retention curve that describes the relation between volumetric water content, θ(L3L3), and soil water pressure, h(L), plus the relation between volumetric water content and hydraulic conductivity, K(L/T). In the next section, the determination of soil hydraulic parameters is first discussed for local and field scale. Then, we show how the pore-scale processes can be linked to soil hydraulic properties. These properties are then used in some of the modern methods that use integral and superposition solutions of Richards’ equation for infiltration and water flow problems for both stable and preferential types of flows. Finally, some practical aspects for watersheds are discussed to highlight the difficulties encountered when large-scale predictions are needed.

scholarly journals Numerical analysis of Richards' problem for water penetration in unsaturated soils

2009 ◽  
Vol 6 (5) ◽  
pp. 6359-6385 ◽  
Author(s):  
A. Barari ◽  
M. Omidvar ◽  
A. R. Ghotbi ◽  
D. D. Ganji
Keyword(s):  
Porous Media ◽  
Numerical Analysis ◽  
Unsaturated Soils ◽  
Homotopy Perturbation Method ◽  
Unsaturated Flow ◽  
Variational Iteration Method ◽  
Environmental Engineering ◽  
Richards Equation ◽  
Water Penetration ◽  
Homotopy Perturbation

Abstract. Unsaturated flow of soils in unsaturated soils is an important problem in geotechnical and geo-environmental engineering. Richards' equation is often used to model this phenomenon in porous media. Obtaining appropriate solution to this equation therefore provides better means to studying the infiltration into unsaturated soils. Available methods for the solution of Richards' equation mostly fall in the category of numerical methods, often having restrictions for practical cases. In this research, two analytical methods known as Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM) have been successfully utilized for solving Richards' equation. Results obtained from the two methods mentioned show a remarkably high precision in the obtained solution, compared with the existing exact solutions available.

scholarly journals Soil–Water Retention Curves Derived as a Function of Soil Dry Density

GeoHazards ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 3-19 ◽  
Author(s):  
Yulong Chen
Keyword(s):  
Water Content ◽  
Soil Water ◽  
Unsaturated Soils ◽  
Water Retention ◽  
Matric Suction ◽  
Soil Samples ◽  
Volumetric Water Content ◽  
Proton Nuclear Magnetic Resonance ◽  
Dry Density ◽  
Soil Water Retention

The soil–water retention curves (SWRC) of soil plays a key role in unsaturated soil mechanics, which is a relatively new field of study having wide applications particularly in geotechnical and geo-environmental engineering. SWRCs were used to evaluate the ability of unsaturated soils to attract water with various water contents and matric suctions. Drying and wetting SWRCs for a sandy soil with different dry densities were studied in a laboratory. Proton nuclear magnetic resonance, image processing technology, and mercury intrusion porosimetry were used to characterize the microscopic mechanisms of pore size distribution in the soil. Soil–water retention in the soil samples was strongly dependent on the dry density. With zero matric suction, soil samples with a higher dry density had a lower initial volumetric water content. Volumetric water content changed at a slower rate when values of matric suction increased in soils with a higher dry density. Soil samples had residual matric suction and a larger air-entry value with a smaller slope of the SWRC when they had a higher density. Dry density change is mainly responsible for the large pores. The number of large pores decreased as dry density increased. As the dry density increased, the area of macropores occupying the largest portion decreased, while the area of mesopores and micropores increased. Minipores accounted for the smallest proportion of total area and they were nearly constant. The proportion of large diameter pores decreased relative to pores with small diameters in the tested soils. The total pore volume was lower for soil specimens that had larger dry densities, as compared to relatively loose specimens. There was hysteresis between the drying and wetting curves for all soil samples. Hysteresis decreased as the dry density of the soil increased. The different liquid–solid contact angle was the main factor causing hysteresis of SWRC.

scholarly journals Sensitivity Analysis and Validation for Numerical Simulation of Water Infiltration into Unsaturated Soil

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Eng Giap Goh ◽  
Kosuke Noborio
Keyword(s):  
Sensitivity Analysis ◽  
Water Content ◽  
Unsaturated Soil ◽  
Isothermal Condition ◽  
Sensitivity Coefficient ◽  
Volumetric Water Content ◽  
Water Infiltration ◽  
Richards Equation ◽  
Time Step ◽  
Time Step Size

A FORTRAN code for liquid water flow in unsaturated soil under the isothermal condition was developed to simulate water infiltration into Yolo light clay. The governing equation, that is, Richards’ equation, was approximated by the finite-difference method. A normalized sensitivity coefficient was used in the sensitivity analysis of Richards’ equation. Normalized sensitivity coefficient was calculated using one-at-a-time (OAT) method and elementary effects (EE) method based on hydraulic functions for matric suction and hydraulic conductivity. Results from EE method provided additional insight into model input parameters, such as input parameter linearity and oscillating sign effect. Boundary volumetric water content (θL (upper bound)) and saturated volumetric water content (θs) were consistently found to be the most sensitive parameters corresponding to positive and negative relations, as given by the hydraulic functions. In addition, although initial volumetric water content (θL (initial cond)) and time-step size (Δt), respectively, possessed a great amount of sensitivity coefficient and uncertainty value, they did not exhibit significant influence on model output as demonstrated by spatial discretization size (Δz). The input multiplication of parameters sensitivity coefficient and uncertainty value was found to affect the outcome of model simulation, in which parameter with the highest value was found to be Δz.

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