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8 pages, 219 KiB

Open AccessEditorial

Modeling of Flow and Transport in Saturated and Unsaturated Porous Media

by Anis Younes, Marwan Fahs and Philippe Ackerer

Water 2021, 13(8), 1088; https://doi.org/10.3390/w13081088 - 15 Apr 2021

Cited by 7 | Viewed by 2728

Abstract

Modeling fluid flow and transport processes in porous media is a relevant topic for a wide range of applications. In water resources problems, this topic presents specific challenges related to the multiphysical processes, large time and space scales, heterogeneity and anisotropy of natural [...] Read more.

Modeling fluid flow and transport processes in porous media is a relevant topic for a wide range of applications. In water resources problems, this topic presents specific challenges related to the multiphysical processes, large time and space scales, heterogeneity and anisotropy of natural porous media, and complex mathematical models characterized by coupled nonlinear equations. This Special Issue aims at collecting papers presenting new developments in the field of flow and transport in porous media. The 25 published papers deal with different aspects of physical processes and applications such as unsaturated and saturated flow, flow in fractured porous media, landslide, reactive transport, seawater intrusion, and transport within hyporheic zones. Based on their objectives, we classified these papers into four categories: (i) improved numerical methods for flow and mass transport simulation, (ii) looking for reliable models and parameters, (iii) laboratory scale experiments and simulations, and (iv) modeling and simulations for improved process understanding. Current trends on modeling fluid flow and transport processes in porous media are discussed in the conclusion. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

Research

Jump to: Editorial, Review, Other

26 pages, 9638 KiB

Open AccessArticle

Analysis of Seepage Characteristics of a Foundation Pit with Horizontal Waterproof Curtain in Highly Permeable Strata

by Chenghua Shi, Xiaohe Sun, Shengli Liu, Chengyong Cao, Linghui Liu and Mingfeng Lei

Water 2021, 13(9), 1303; https://doi.org/10.3390/w13091303 - 6 May 2021

Cited by 6 | Viewed by 4596

Abstract

At present, jet-grouted horizontal waterproof curtain reinforcement has become an essential method for deep foundation pit groundwater control. However, there is still a lack of an effective theoretical calculation method for horizontal waterproof curtain reinforcement, and there is little research on the seepage [...] Read more.

At present, jet-grouted horizontal waterproof curtain reinforcement has become an essential method for deep foundation pit groundwater control. However, there is still a lack of an effective theoretical calculation method for horizontal waterproof curtain reinforcement, and there is little research on the seepage laws of foundation pits under different horizontal waterproof curtain conditions. Based on Darcy’s seepage theory, theoretical analysis models of deep foundation pit seepage were established considering the effect of a horizontal curtain in a highly permeable formation. Through the established models, the calculation method of the water inflow and the water pressure under the condition of a horizontal curtain was derived. Then through indoor tests, the reliability of the theoretical calculation method was verified. Furthermore, the established theoretical calculation method is used to analyze the influence of various factors on the water inflow and the water pressure, such as the ratio of hydraulic conductivity of the horizontal curtain to surrounding soil, thickness, and reinforcement position of the horizontal curtain. It is found that the hydraulic conductivity ratio has the most significant influence on the seepage characteristics of the foundation pit. Finally, the design method was applied to an example of the horizontal waterproof curtain of the foundation pit, which is located at Juyuanzhou Station in Fuzhou (China). The water inflow per unit area is 0.36 m³/d in the foundation pit, and this implies that the design method of the horizontal waterproof curtain applied for the excavation case is good and meets the requirements of design and safety. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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14 pages, 3178 KiB

Open AccessFeature PaperArticle

Numerical Evaluation of Fractional Vertical Soil Water Flow Equations

by Ali Ercan and M. Levent Kavvas

Water 2021, 13(4), 511; https://doi.org/10.3390/w13040511 - 16 Feb 2021

Cited by 2 | Viewed by 2447

Abstract

Significant deviations from standard Boltzmann scaling, which corresponds to normal or Fickian diffusion, have been observed in the literature for water movement in porous media. However, as demonstrated by various researchers, the widely used conventional Richards equation cannot mimic anomalous diffusion and ignores [...] Read more.

Significant deviations from standard Boltzmann scaling, which corresponds to normal or Fickian diffusion, have been observed in the literature for water movement in porous media. However, as demonstrated by various researchers, the widely used conventional Richards equation cannot mimic anomalous diffusion and ignores the features of natural soils which are heterogeneous. Within this framework, governing equations of transient water flow in porous media in fractional time and multi-dimensional fractional soil space in anisotropic media were recently introduced by the authors by coupling Brooks–Corey constitutive relationships with the fractional continuity and motion equations. In this study, instead of utilizing Brooks–Corey relationships, empirical expressions, obtained by least square fits through hydraulic measurements, were utilized to show the suitability of the proposed fractional approach with other constitutive hydraulic relations in the literature. Next, a finite difference numerical method was proposed to solve the fractional governing equations. The applicability of the proposed fractional governing equations was investigated numerically in comparison to their conventional counterparts. In practice, cumulative infiltration values are observed to deviate from conventional infiltration approximation, or the wetting front through time may not be consistent with the traditional estimates of Richards equation. In such cases, fractional governing equations may be a better alternative for mimicking the physical process as they can capture sub-, super-, and normal-diffusive soil water flow processes during infiltration. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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26 pages, 1698 KiB

Open AccessArticle

Jacobian Free Methods for Coupling Transport with Chemistry in Heterogenous Porous Media

by Laila Amir and Michel Kern

Water 2021, 13(3), 370; https://doi.org/10.3390/w13030370 - 31 Jan 2021

Cited by 3 | Viewed by 2995

Abstract

Reactive transport plays an important role in various subsurface applications, including carbon dioxide sequestration, nuclear waste storage, biogeochemistry and the simulation of hydro–thermal reservoirs. The model couples a set of partial differential equations, describing the transport of chemical species, to nonlinear algebraic or [...] Read more.

Reactive transport plays an important role in various subsurface applications, including carbon dioxide sequestration, nuclear waste storage, biogeochemistry and the simulation of hydro–thermal reservoirs. The model couples a set of partial differential equations, describing the transport of chemical species, to nonlinear algebraic or differential equations, describing the chemical reactions. Solution methods for the resulting large nonlinear system can be either fully coupled or can iterate between transport and chemistry. This paper extends previous work by the authors where an approach based on the Newton–Krylov method applied to a reduced system has been developed. The main feature of the approach is to solve the nonlinear system in a fully coupled manner while keeping transport and chemistry modules separate. Here we extend the method in two directions. First, we take into account mineral precipitation and dissolution reactions by using an interior point Newton method, so as to avoid the usual combinatorial approach. Second, we study two-dimensional heterogeneous geometries. We show how the method can make use of an existing transport solver, used as a black box. We detail the methods and algorithms for the individual modules, and for the coupling step. We show the performance of the method on synthetic examples. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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21 pages, 4855 KiB

Open AccessArticle

Spatial and Temporal Evolution of Leaching Zones within Potash Seams Reproduced by Reactive Transport Simulations

by Svenja Steding, Thomas Kempka, Axel Zirkler and Michael Kühn

Water 2021, 13(2), 168; https://doi.org/10.3390/w13020168 - 13 Jan 2021

Cited by 7 | Viewed by 2130

Abstract

Leaching zones within potash seams generally represent a significant risk to subsurface mining operations and the construction of technical caverns in salt rocks, but their temporal and spatial formation has been investigated only rudimentarily to date. To the knowledge of the authors, current [...] Read more.

Leaching zones within potash seams generally represent a significant risk to subsurface mining operations and the construction of technical caverns in salt rocks, but their temporal and spatial formation has been investigated only rudimentarily to date. To the knowledge of the authors, current reactive transport simulation implementations are not capable to address hydraulic-chemical interactions within potash salt. For this reason, a reactive transport model has been developed and complemented by an innovative approach to calculate the interchange of minerals and solution at the water-rock interface. Using this model, a scenario analysis was carried out based on a carnallite-bearing potash seam. The results show that the evolution of leaching zones depends on the mineral composition and dissolution rate of the original salt rock, and that the formation can be classified by the dimensionless parameters of Péclet (Pe) and Damköhler (Da). For Pe > 2 and Da > 1, a funnel-shaped leaching zone is formed, otherwise the dissolution front is planar. Additionally, Da > 1 results in the formation of a sylvinitic zone and a flow barrier. Most scenarios represent hybrid forms of these cases. The simulated shapes and mineralogies are confirmed by literature data and can be used to assess the hazard potential. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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18 pages, 3278 KiB

Open AccessArticle

A Fully Implicit Finite Volume Scheme for a Seawater Intrusion Problem in Coastal Aquifers

by Abdelkrim Aharmouch, Brahim Amaziane, Mustapha El Ossmani and Khadija Talali

Water 2020, 12(6), 1639; https://doi.org/10.3390/w12061639 - 8 Jun 2020

Cited by 3 | Viewed by 3017

Abstract

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural [...] Read more.

We present a numerical framework for efficiently simulating seawater flow in coastal aquifers using a finite volume method. The mathematical model consists of coupled and nonlinear partial differential equations. Difficulties arise from the nonlinear structure of the system and the complexity of natural fields, which results in complex aquifer geometries and heterogeneity in the hydraulic parameters. When numerically solving such a model, due to the mentioned feature, attempts to explicitly perform the time integration result in an excessively restricted stability condition on time step. An implicit method, which calculates the flow dynamics at each time step, is needed to overcome the stability problem of the time integration and mass conservation. A fully implicit finite volume scheme is developed to discretize the coupled system that allows the use of much longer time steps than explicit schemes. We have developed and implemented this scheme in a new module in the context of the open source platform DuMu

^{X}

. The accuracy and effectiveness of this new module are demonstrated through numerical investigation for simulating the displacement of the sharp interface between saltwater and freshwater in groundwater flow. Lastly, numerical results of a realistic test case are presented to prove the efficiency and the performance of the method. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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21 pages, 8691 KiB

Open AccessArticle

B-Spline Method of Lines for Simulation of Contaminant Transport in Groundwater

by Ersin Bahar and Gurhan Gurarslan

Water 2020, 12(6), 1607; https://doi.org/10.3390/w12061607 - 4 Jun 2020

Cited by 4 | Viewed by 2468

Abstract

In this study, we propose a new numerical method, which can be effectively applied to the advection-dispersion equation, based on B-spline functions and method of lines approach. In the proposed approach, spatial derivatives are calculated using quintic B-spline functions. Thanks to the method [...] Read more.

In this study, we propose a new numerical method, which can be effectively applied to the advection-dispersion equation, based on B-spline functions and method of lines approach. In the proposed approach, spatial derivatives are calculated using quintic B-spline functions. Thanks to the method of lines approach, the partial differential equation governing the contaminant transport in groundwater is converted into time-dependent ordinary differential equations. After this transformation, the time-integration of this system is realized by using an adaptive Runge–Kutta formula. In order to test the accuracy of the proposed method, four numerical examples were solved and the obtained results compared with various analytical and numerical solutions given in the literature. It is proven that the proposed method is faster and more reliable than other methods referenced herein and is a good alternative for simulation of contaminant transport problems as a result of these comparisons. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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16 pages, 3454 KiB

Open AccessFeature PaperArticle

Simulation of Water and Salt Dynamics in the Soil Profile in the Semi-Arid Region of Tunisia—Evaluation of the Irrigation Method for a Tomato Crop

by Sabri Kanzari, Issam Daghari, Jiří Šimůnek, Anis Younes, Riadh Ilahy, Sana Ben Mariem, Mourad Rezig, Béchir Ben Nouna, Hassouna Bahrouni and Mohamed Ali Ben Abdallah

Water 2020, 12(6), 1594; https://doi.org/10.3390/w12061594 - 3 Jun 2020

Cited by 12 | Viewed by 2992

Abstract

In Tunisia, water used for irrigation is often saline, increasing the risk of salinization for soils and crops. In this study, an experiment was conducted on a tomato crop cultivated on a silty-clay soil irrigated with three different water qualities: 0, 3.5, and [...] Read more.

In Tunisia, water used for irrigation is often saline, increasing the risk of salinization for soils and crops. In this study, an experiment was conducted on a tomato crop cultivated on a silty-clay soil irrigated with three different water qualities: 0, 3.5, and 7 dS·m⁻¹. Experimental data were then used to calibrate and validate the Hydrus-1D model, which simulates water flow and salt transfer in soils. The successfully-calibrated and validated model was then used to study the combined effects of the soil osmotic and soil matrix potentials on root water uptake. The values of the root mean square error (RMSE), the coefficient of determination (CD), the modeling efficiency (EF), and the coefficient of residual mass (CRM) were close to their optimal values for both soil water content and soil electrical conductivity profiles, indicating the reliability of the model to reproduce water and salt dynamics. Relative yields (Y_r), indirectly estimated using actual and potential root water uptake (transpiration), indicated that the multiplicative stress response model (using the S-shape model) satisfactorily simulates measured yields and reproduces the effects of irrigation with saline waters on crop yields. An alternative scenario using a reduction of water requirements by 50% was investigated to assess an irrigation method with considerable water savings. As the results show that relative yields, Y_r, were only slightly reduced, the crop water requirements estimated by CROPWAT 8.0 must have been overestimated. The variation of the soil salinity in the root zone highlighted a high salinization risk in the short-term when water of 7 dS·m⁻¹ is used for irrigation. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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15 pages, 3846 KiB

Open AccessArticle

Influence of Streambed Heterogeneity on Hyporheic Flow and Sorptive Solute Transport

by Yuanhong Liu, Corey D. Wallace, Yaoquan Zhou, Reza Ershadnia, Faranak Behzadi, Dipankar Dwivedi, Lianqing Xue and Mohamad Reza Soltanian

Water 2020, 12(6), 1547; https://doi.org/10.3390/w12061547 - 28 May 2020

Cited by 21 | Viewed by 3329

Abstract

The subsurface region where river water and groundwater actively mix (the hyporheic zone) plays an important role in conservative and reactive solute transport along rivers. Deposits of high-conductivity (K) sediments along rivers can strongly control hyporheic processes by channeling flow along [...] Read more.

The subsurface region where river water and groundwater actively mix (the hyporheic zone) plays an important role in conservative and reactive solute transport along rivers. Deposits of high-conductivity (K) sediments along rivers can strongly control hyporheic processes by channeling flow along preferential flow paths wherever they intersect the channel boundary. Our goal is to understand how sediment heterogeneity influences conservative and sorptive solute transport within hyporheic zones containing high- and low-K sediment facies types. The sedimentary architecture of high-K facies is modeled using commonly observed characteristics (e.g., volume proportion and mean length), and their spatial connectivity is quantified to evaluate its effect on hyporheic mixing dynamics. Numerical simulations incorporate physical and chemical heterogeneity by representing spatial variability in both K and in the sediment sorption distribution coefficient (

K_{d}

). Sediment heterogeneity significantly enhances hyporheic exchange and skews solute breakthrough behavior, while in homogeneous sediments, interfacial flux and solute transport are instead controlled by geomorphology and local-scale riverbed topographies. The hyporheic zone is compressed in sediments with high sorptive capacity, which limits solute interactions to only a small portion of the sedimentary architecture and thus increases retention. Our results have practical implications for groundwater quality, including remediation strategies for contaminants of emerging concern. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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17 pages, 2513 KiB

Open AccessArticle

Porous Medium Typology Influence on the Scaling Laws of Confined Aquifer Characteristic Parameters

by Carmine Fallico, Agostino Lauria and Francesco Aristodemo

Water 2020, 12(4), 1166; https://doi.org/10.3390/w12041166 - 19 Apr 2020

Cited by 3 | Viewed by 2312

Abstract

An accurate measurement campaign, carried out on a confined porous aquifer, expressly reproduced in laboratory, allowed the determining of hydraulic conductivity values by performing a series of slug tests. This was done for four porous medium configurations with different granulometric compositions. At the [...] Read more.

An accurate measurement campaign, carried out on a confined porous aquifer, expressly reproduced in laboratory, allowed the determining of hydraulic conductivity values by performing a series of slug tests. This was done for four porous medium configurations with different granulometric compositions. At the scale considered, intermediate between those of the laboratory and the field, the scalar behaviors of the hydraulic conductivity and the effective porosity was verified, determining the respective scaling laws. Moreover, assuming the effective porosity as scale parameter, the scaling laws of the hydraulic conductivity were determined for the different injection volumes of the slug test, determining a new relationship, valid for coarse-grained porous media. The results obtained allow the influence that the differences among the characteristics of the porous media considered exerted on the scaling laws obtained to be highlighted. Finally, a comparison was made with the results obtained in a previous investigation carried out at the field scale. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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11 pages, 5310 KiB

Open AccessArticle

Transmissibility Upscaling on Unstructured Grids for Highly Heterogeneous Reservoirs

by Dominique Guérillot and Jérémie Bruyelle

Water 2019, 11(12), 2647; https://doi.org/10.3390/w11122647 - 15 Dec 2019

Cited by 5 | Viewed by 3996

Abstract

One critical point of modeling of flow in porous media is the capacity to consider parameters that are highly variable in space. It is then very challenging to simulate numerically fluid flow on such heterogeneous porous media. The continuous increase in computing power [...] Read more.

One critical point of modeling of flow in porous media is the capacity to consider parameters that are highly variable in space. It is then very challenging to simulate numerically fluid flow on such heterogeneous porous media. The continuous increase in computing power makes it possible to integrate smaller and smaller heterogeneities into geological models of up to tens of millions of cells. On such meshes, despite computer performance, multi-phase flow equations cannot be solved in an acceptable time for hydrogeologists and reservoir engineers, especially when the modeling considers several components in each fluid and when taking into account rock-fluid interactions. Taking average reservoir properties is a common approach to reducing mesh size. During the last decades, many authors studied the upscaling topic. Two different ways have been investigated to upscale the absolute permeability: (1) an average of the permeability for each cell, which is then used for standard transmissibility calculation, or (2) computing directly the upscaled transmissibility values using the high-resolution permeability values. This paper is related to the second approach. The proposed method uses the half-block approach and combines the finite volume principles with algebraic methods to provide an upper and a lower bound of the upscaled transmissibility values. An application on an extracted map of the SPE10 model shows that this approach is more accurate and faster than the classical transmissibility upscaling method based on flow simulation. This approach keeps the contrast of transmissibility values observed at the high-resolution geological scale and improves the accuracy of field-scale flow simulation for highly heterogeneous reservoirs. Moreover, the upper and lower bounds delivered by the algebraic method allow checking the quality of the upscaling and the gridding. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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24 pages, 7242 KiB

Open AccessArticle

A Spacetime Meshless Method for Modeling Subsurface Flow with a Transient Moving Boundary

by Cheng-Yu Ku, Chih-Yu Liu, Jing-En Xiao, Weichung Yeih and Chia-Ming Fan

Water 2019, 11(12), 2595; https://doi.org/10.3390/w11122595 - 9 Dec 2019

Cited by 8 | Viewed by 2821

Abstract

In this paper, a spacetime meshless method utilizing Trefftz functions for modeling subsurface flow problems with a transient moving boundary is proposed. The subsurface flow problem with a transient moving boundary is governed by the two-dimensional diffusion equation, where the position of the [...] Read more.

In this paper, a spacetime meshless method utilizing Trefftz functions for modeling subsurface flow problems with a transient moving boundary is proposed. The subsurface flow problem with a transient moving boundary is governed by the two-dimensional diffusion equation, where the position of the moving boundary is previously unknown. We solve the subsurface flow problems based on the Trefftz method, in which the Trefftz basis functions are obtained from the general solutions using the separation of variables. The solutions of the governing equation are then approximated numerically by the superposition theorem using the basis functions, which match the data at the spacetime boundary collocation points. Because the proposed basis functions fully satisfy the diffusion equation, arbitrary nodes are collocated only on the spacetime boundaries for the discretization of the domain. The iterative scheme has to be used for solving the moving boundaries because the transient moving boundary problems exhibit nonlinear characteristics. Numerical examples, including harmonic and non-harmonic boundary conditions, are carried out to validate the method. Results illustrate that our method may acquire field solutions with high accuracy. It is also found that the method is advantageous for solving inverse problems as well. Finally, comparing with those obtained from the method of fundamental solutions, we may obtain the accurate location of the nonlinear moving boundary for transient problems using the spacetime meshless method with the iterative scheme. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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20 pages, 1443 KiB

Open AccessArticle

Permeability Coefficient of Low Permeable Soils as a Single-Variable Function of Soil Parameter

by Tomasz Kozlowski and Agata Ludynia

Water 2019, 11(12), 2500; https://doi.org/10.3390/w11122500 - 27 Nov 2019

Cited by 12 | Viewed by 4943

Abstract

Based on the results of experimental studies concerning the filtration coefficient, the Darcianity of the observed flows for eight cohesive soils at four hydraulic gradients was analyzed. It is observed that linear dependence of flow velocity on hydraulic gradient is an approximation only, [...] Read more.

Based on the results of experimental studies concerning the filtration coefficient, the Darcianity of the observed flows for eight cohesive soils at four hydraulic gradients was analyzed. It is observed that linear dependence of flow velocity on hydraulic gradient is an approximation only, and it is the worse the more cohesive a given soil is. Despite this, Darcy’s law can be a correct approximation of the empirical relationship between hydraulic gradient and the flow velocity, also in very cohesive soils. A statistical analysis was carried out to identify correlation between soil properties and permeability coefficient. For each soil, 109 parameters were analyzed, among others applying mercury intrusion porosimetry, scanning electron microscopy, dynamic image analysis, and laser diffraction. Ultimately, three single-variable models best fitted to the experimental data were found, using the plasticity index I_P as the independent variable, the average pore diameter D_P, and the convexity of silt fraction particles. All model parameters are statistically significant at p < 0.05. Comparison with reference multi-variable models showed that the best fit for experimental data is observed by the model with the plasticity index, while the results suggest low usability of single-variable models with structural parameters. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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22 pages, 6930 KiB

Open AccessFeature PaperArticle

Laboratory Experiments of Drainage, Imbibition and Infiltration under Artificial Rainfall Characterized by Image Analysis Method and Numerical Simulations

by Benjamin Belfort, Sylvain Weill, Marwan Fahs and François Lehmann

Water 2019, 11(11), 2232; https://doi.org/10.3390/w11112232 - 25 Oct 2019

Cited by 6 | Viewed by 3284

Abstract

Two laboratory experiments consisting of drainage/imbibition and rainfall were carried out to study flow in variably saturated porous media and to test the ability of a new measurement method. 2D maps of water content are obtained through a non-invasive image analysis method based [...] Read more.

Two laboratory experiments consisting of drainage/imbibition and rainfall were carried out to study flow in variably saturated porous media and to test the ability of a new measurement method. 2D maps of water content are obtained through a non-invasive image analysis method based on photographs. This method requires classical image analysis steps, i.e., normalization, filtering, background subtraction, scaling and calibration. The procedure was applied and validated for a large experimental tank of internal dimensions 180 cm long, 120 cm wide and 4 cm deep that had been homogenously packed with monodisperse quartz sand. The calibration curve relating water content and reflected light intensities was established during the main monitoring phase of each experiment, making this procedure very advantageous. Direct measurements carried out during the water flow experiments correspond to water content, pressure head, temperature, and cumulative outflow. Additionally, a great advantage of the proposed method is that it does not require any tracer or dye to be injected into the flow tank. The accuracy and other benefits of our approach were also assessed using numerical simulations with state-of-the-art computational code that solves Richards’ equation. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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19 pages, 10063 KiB

Open AccessArticle

Dewatering Characteristics and Inflow Prediction of Deep Foundation Pits with Partial Penetrating Curtains in Sand and Gravel Strata

by Linghui Liu, Mingfeng Lei, Chengyong Cao and Chenghua Shi

Water 2019, 11(10), 2182; https://doi.org/10.3390/w11102182 - 19 Oct 2019

Cited by 17 | Viewed by 4924

Abstract

The dewatering of deep foundation pits excavated in highly permeable geology usually requires waterproofing technologies to relieve groundwater flow. However, no effective prediction formula is yet available for determining water inflow in the presence of partial penetrating curtains. In this study, a dewatering [...] Read more.

The dewatering of deep foundation pits excavated in highly permeable geology usually requires waterproofing technologies to relieve groundwater flow. However, no effective prediction formula is yet available for determining water inflow in the presence of partial penetrating curtains. In this study, a dewatering project with partial penetrating curtains is analyzed via a finite difference method to show evident three-dimensional (3D) seepage characteristics. The standard curve and distortion functions are established under the assumption of an equivalent well by quantifying the blocking effects; thus, the empirical inflow prediction formulas for steady flow are further developed. Moreover, a dewatering design method based on the prediction formulas is proposed and applied to the field dewatering project in sand and gravel strata. Measured results show that dewatering efficiency is considerably enhanced by 3D flow, forming appropriate pressure distributions for dewatering construction. The uplift pressure below the pit bottom is controlled within a 25% safety margin to verify the reliability of the design method. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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31 pages, 8215 KiB

Open AccessFeature PaperArticle

A Modeling Platform for Landslide Stability: A Hydrological Approach

by Mohsen Emadi-Tafti and Behzad Ataie-Ashtiani

Water 2019, 11(10), 2146; https://doi.org/10.3390/w11102146 - 15 Oct 2019

Cited by 17 | Viewed by 12725

Abstract

Landslide events are among natural hazards with many fatalities and financial losses. Studies demonstrate that natural factors such as rainfall and human activities such as deforestation are important causes of triggering a landslide. In this study, an integrated two-dimensional slope stability model, SSHV-2D, [...] Read more.

Landslide events are among natural hazards with many fatalities and financial losses. Studies demonstrate that natural factors such as rainfall and human activities such as deforestation are important causes of triggering a landslide. In this study, an integrated two-dimensional slope stability model, SSHV-2D, is developed that considers various aspects of hydrological effects and vegetation impacts on the stability of slopes. The rainfall infiltration and water uptake of roots change the water content of the unsaturated zone. The temporal and spatial distribution of water content is estimated in the hydrological unit of the developed model. The vegetation unit of the model considers interception loss due to the existence of canopies and trunks, soil reinforcement effect by roots, root water uptake, the impact of root on hydraulic conductivity, and the influence of vegetation weight on slope stability. Benchmark problems with and without vegetation are solved for the model verification. The analyses demonstrate that the consideration of matric suction in the unsaturated zone can increase the safety factor more than 90%. It is also observed that the existence of trees with high density on a slope can increase the factor of safety about 50% and prevent shallow landslides. The present model is a platform for further development of more comprehensive and elaborative slope stability models. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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16 pages, 3508 KiB

Open AccessArticle

Bayesian Simultaneous Estimation of Unsaturated Flow and Solute Transport Parameters from a Laboratory Infiltration Experiment

by Anis Younes, Jabran Zaouali, Sabri Kanzari, Francois Lehmann and Marwan Fahs

Water 2019, 11(8), 1660; https://doi.org/10.3390/w11081660 - 11 Aug 2019

Cited by 4 | Viewed by 3278

Abstract

Numerical modeling has become an irreplaceable tool for the investigation of water flow and solute transport in the unsaturated zone. The use of this tool for real situations is often faced with lack of knowledge of hydraulic and soil transport parameters. In this [...] Read more.

Numerical modeling has become an irreplaceable tool for the investigation of water flow and solute transport in the unsaturated zone. The use of this tool for real situations is often faced with lack of knowledge of hydraulic and soil transport parameters. In this study, advanced experimental and numerical techniques are developed for an accurate estimation of the soil parameters. A laboratory unsaturated flow and solute transport experiment is conducted on a large undisturbed soil column of around 40 cm length. Bromide, used as a nonreactive contaminant, is injected at the surface of the undisturbed soil, followed by a leaching phase. The pressure measurements at different locations along the soil column as well as the outflow bromide concentration are collected during the experiment and used for the statistical calibration of flow and solute transport. The Richards equation, combined with constitutive relations for water content and permeability, is used to describe unsaturated flow. Both linear and non-equilibrium mobile–immobile transport models are investigated for the solute transport. All hydraulic and mass transport parameters are inferred using a one-step Bayesian estimation with the Markov chain Monte Carlo sampler. The results prove that the pressure and concentration measurements are able to identify almost all hydraulic and mass transport parameters. The mobile–immobile transport model better reproduces the infiltration experiment. It produces narrower uncertainty intervals for soil parameters and predictive output concentrations. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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17 pages, 3615 KiB

Open AccessArticle

Smoothing of Slug Tests for Laboratory Scale Aquifer Assessment—A Comparison among Different Porous Media

by Francesco Aristodemo, Agostino Lauria, Giuseppe Tripepi, Maria Fernanda Rivera-Velasquéz and Carmine Fallico

Water 2019, 11(8), 1569; https://doi.org/10.3390/w11081569 - 29 Jul 2019

Cited by 5 | Viewed by 3305

Abstract

A filtering analysis of hydraulic head data deduced from slug tests injected in a confined aquifer with different porous media is proposed. Experimental laboratory tests were conducted in a large-scale physical model developed at the University of Calabria. The hydraulic head data were [...] Read more.

A filtering analysis of hydraulic head data deduced from slug tests injected in a confined aquifer with different porous media is proposed. Experimental laboratory tests were conducted in a large-scale physical model developed at the University of Calabria. The hydraulic head data were deduced from the records of a pressure sensor arranged in the injection well and subjected to a processing operation to filter the high-frequency noise. The involved smoothing techniques are the Fourier transform and two types of wavelet transform. The performances of the filtered hydraulic heads were examined for different slug volumes and four model layouts in terms of optimal fitting of the Cooper’s analytical solution. The hydraulic head variations in the confined aquifer were analyzed using wavelet transform in order to discover their energy contributions and frequency oscillations. Finally, the raw and smoothed hydraulic heads were adopted to calculate the hydraulic conductivity of the aquifer. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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25 pages, 3891 KiB

Open AccessFeature PaperArticle

A Comparative Study of Water and Bromide Transport in a Bare Loam Soil Using Lysimeters and Field Plots

by Arnaud Isch, Denis Montenach, Frederic Hammel, Philippe Ackerer and Yves Coquet

Water 2019, 11(6), 1199; https://doi.org/10.3390/w11061199 - 8 Jun 2019

Cited by 13 | Viewed by 3548

Abstract

The purpose of this methodological study was to test whether similar soil hydraulic and solute transport properties could be estimated from field plots and lysimeter measurements. The transport of water and bromide (as an inert conservative solute tracer) in three bare field plots [...] Read more.

The purpose of this methodological study was to test whether similar soil hydraulic and solute transport properties could be estimated from field plots and lysimeter measurements. The transport of water and bromide (as an inert conservative solute tracer) in three bare field plots and in six bare soil lysimeters were compared. Daily readings of matric head and volumetric water content in the lysimeters showed a profile that was increasingly humid with depth. The hydrodynamic parameters optimized with HYDRUS-1D provided an accurate description of the experimental data for both the field plots and the lysimeters. However, bromide transport in the lysimeters was influenced by preferential transport, which required the use of the mobile/immobile water (MIM) model to suitably describe the experimental data. Water and solute transport observed in the field plots was not accurately described when using parameters optimized with lysimeter data (cross-simulation), and vice versa. The soil’s return to atmospheric pressure at the bottom of the lysimeter and differences in tillage practices between the two set-ups had a strong impact on soil water dynamics. The preferential flow of bromide observed in the lysimeters prevented an accurate simulation of solute transport in field plots using the mean optimized parameters on lysimeters and vice versa. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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15 pages, 5462 KiB

Open AccessArticle

A Unified Equation to Predict the Permeability of Rough Fractures via Lattice Boltzmann Simulation

by Peijie Yin, Can Zhao, Jianjun Ma and Linchong Huang

Water 2019, 11(5), 1081; https://doi.org/10.3390/w11051081 - 24 May 2019

Cited by 16 | Viewed by 3243

Abstract

In this paper, the fluid flow through rough fractures was investigated via numerical simulation based on the lattice Boltzmann method (LBM). The accuracy of LBM was validated through the numerical simulation of the parallel plate model and the verification of the mass conservation [...] Read more.

In this paper, the fluid flow through rough fractures was investigated via numerical simulation based on the lattice Boltzmann method (LBM). The accuracy of LBM was validated through the numerical simulation of the parallel plate model and the verification of the mass conservation of fluid flow through rough fracture. After that, the effect of roughness on fluid flow was numerically conducted, in which, the geometry of fractures was characterized by the joint roughness coefficient (JRC), fractal dimension (D) and standard deviation (σ). It was found that the JRC cannot reflect the realistic influence of roughness on the permeability of single fracture, in which, an increase in permeability with increasing JRC has been observed at the range of 8~12 and 14~16. The reason behind this was revealed through the calculation of the root mean square of the first derivative of profile (Z₂), and an equation has been proposed to estimate the permeability based on the aperture and Z₂ of the fracture. The numerical simulations were further conducted on fluid flow though synthetic fractures with a wide range of D and σ. In order to unify the parameter that characterizes the roughness, Z₂ was obtained for each synthetic fracture, and the corresponding relationship between permeability, aperture and Z₂ was analyzed. Meanwhile, it was found that the fluid flow behaves differently with different ranges of Z₂ and the critical point was found to be Z₂ = 0.5. Based on extensive study, it was concluded that Z₂ is a generic parameter characterizing the roughness, and the proposed equation could be used to predict the permeability for fluid flow in fracture. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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21 pages, 5195 KiB

Open AccessArticle

Assess Effectiveness of Salt Removal by a Subsurface Drainage with Bundled Crop Straws in Coastal Saline Soil Using HYDRUS-3D

by Peirong Lu, Zhanyu Zhang, Zhuping Sheng, Mingyi Huang and Zemin Zhang

Water 2019, 11(5), 943; https://doi.org/10.3390/w11050943 - 5 May 2019

Cited by 13 | Viewed by 3212

Abstract

The low permeability of soil and high investment of salt management pose great challenges for implementation of land reclamation in coastal areas. In this study, a temporary soil leaching system was tested in which bundled maize straw (straw drainage module, SDM) was operated [...] Read more.

The low permeability of soil and high investment of salt management pose great challenges for implementation of land reclamation in coastal areas. In this study, a temporary soil leaching system was tested in which bundled maize straw (straw drainage module, SDM) was operated as a subsurface drainage tube and diluted seawater was used for leaching. A preliminary field experiment was conducted in coastal soil-filled lysimeters to examine the system’s feasibility and a numerical model (HYDRUS-3D) based on field measured data was designed to simulate the entire leaching process. The simulation results showed that the soil water velocity and the non-uniformity of salt distribution were apparently enhanced in the region approaching the drain outlet. The mass balance information indicated that the amount of water drained with SDM accounts for 37.9–66.0% of the total amount of leaching water, and the mass of salt removal was about 1.7 times that of the salt input from the diluted seawater. Additional simulations were conducted to explore the impacts of the design parameters, including leaching amount, the salinity of leaching water, and the number of leaching events on the desalination performance of the leaching system. Such simulations showed that the salt removal efficiency and soil desalination rate both were negatively related to the seawater mixture rate but were positively associated with the amount of leaching water. Increasing the leaching times, the salt removal efficiency was gradually decreased in all treatments, but the soil desalination rate was decreased only in the treatments leached with less diluted seawater. Our results confirmed the feasibility of the SDM leaching system in soil desalination and lay a good foundation for this system application in initial reclamation of saline coastal land. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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20 pages, 6278 KiB

Open AccessArticle

On Solving Nonlinear Moving Boundary Problems with Heterogeneity Using the Collocation Meshless Method

by Cheng-Yu Ku, Jing-En Xiao and Chih-Yu Liu

Water 2019, 11(4), 835; https://doi.org/10.3390/w11040835 - 20 Apr 2019

Cited by 8 | Viewed by 3593

Abstract

In this article, a solution to nonlinear moving boundary problems in heterogeneous geological media using the meshless method is proposed. The free surface flow is a moving boundary problem governed by Laplace equation but has nonlinear boundary conditions. We adopt the collocation Trefftz [...] Read more.

In this article, a solution to nonlinear moving boundary problems in heterogeneous geological media using the meshless method is proposed. The free surface flow is a moving boundary problem governed by Laplace equation but has nonlinear boundary conditions. We adopt the collocation Trefftz method (CTM) to approximate the solution using Trefftz base functions, satisfying the Laplace equation. An iterative scheme in conjunction with the CTM for finding the phreatic line with over–specified nonlinear moving boundary conditions is developed. To deal with flow in the layered heterogeneous soil, the domain decomposition method is used so that the hydraulic conductivity in each subdomain can be different. The method proposed in this study is verified by several numerical examples. The results indicate the advantages of the collocation meshless method such as high accuracy and that only the surface of the problem domain needs to be discretized. Moreover, it is advantageous for solving nonlinear moving boundary problems with heterogeneity with extreme contrasts in the permeability coefficient. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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15 pages, 4533 KiB

Open AccessArticle

Improved Solutions to the Linearized Boussinesq Equation with Temporally Varied Rainfall Recharge for a Sloping Aquifer

by Ming-Chang Wu and Ping-Cheng Hsieh

Water 2019, 11(4), 826; https://doi.org/10.3390/w11040826 - 19 Apr 2019

Cited by 12 | Viewed by 3413

Abstract

Sloping unconfined aquifers are commonly seen and well investigated in the literature. In this study, we propose a generalized integral transformation method to solve the linearized Boussinesq equation that governs the groundwater level in a sloping unconfined aquifer with an impermeable bottom. The [...] Read more.

Sloping unconfined aquifers are commonly seen and well investigated in the literature. In this study, we propose a generalized integral transformation method to solve the linearized Boussinesq equation that governs the groundwater level in a sloping unconfined aquifer with an impermeable bottom. The groundwater level responses of this unconfined aquifer under temporally uniform recharge or nonuniform recharge events are discussed. After comparing with a numerical solution to the nonlinear Boussinesq equation, the proposed solution appears better than that proposed in a previous study. Besides, we found that the proposed solutions reached the convergence criterion much faster than the Laplace transform solution did. Moreover, the application of the proposed solution to temporally changing rainfall recharge is also proposed to improve on the previous quasi-steady state treatment of an unsteady recharge rate. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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18 pages, 6910 KiB

Open AccessArticle

Effect of Pilot-Points Location on Model Calibration: Application to the Northern Karst Aquifer of Qatar

by Husam Musa Baalousha, Marwan Fahs, Fanilo Ramasomanana and Anis Younes

Water 2019, 11(4), 679; https://doi.org/10.3390/w11040679 - 2 Apr 2019

Cited by 14 | Viewed by 4149

Abstract

In hydrogeological modelling, two approaches are commonly used for model calibration: zonation and the pilot-points method. Zonation assumes an abrupt spatial change in parameter values, which could be unrealistic in field applications. The pilot-points method produces smoothly distributed parameters compared to the zonation [...] Read more.

In hydrogeological modelling, two approaches are commonly used for model calibration: zonation and the pilot-points method. Zonation assumes an abrupt spatial change in parameter values, which could be unrealistic in field applications. The pilot-points method produces smoothly distributed parameters compared to the zonation approach; however, the number and placement of pilot-points can be challenging. The main goal of this paper is to explore the effect of pilot-points number and locations on the calibrated parameters. A 3D groundwater flow model was built for the northern karst aquifer of Qatar. A conceptual model of this aquifer was developed based on MODFLOW software (United States Geological Survey). The model was calibrated using the parameter estimation and uncertainty analysis (PEST) package employing historical data of groundwater levels. The effect of the number and locations of pilot-points was examined by running the model using a variable numbers of points and several perturbations of locations. The calibration errors for all the runs (corresponding to different configurations of pilot-points) were maintained under a certain threshold. A statistical analysis of the calibrated parameters was then performed to evaluate how far these parameters are impacted by the pilot-point locations. Finally, an optimization method was proposed for pilot-points placement using recharge and observed piezometric maps. The results revealed that the pilot-points number, locations, and configurations have a significant effect on the calibrated parameter, especially in the high permeable regions corresponding to the karstic zones. The outcome of this study may help focus on areas of high uncertainty where more field data should be collected to improve model calibration. It also helps the placement of pilot-points for a robust calibration. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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Review

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17 pages, 4857 KiB

Open AccessReview

Review on Numerical Simulation of the Internal Soil Erosion Mechanisms Using the Discrete Element Method

by Xiukai Wang, Yao Tang, Bo Huang, Tiantian Hu and Daosheng Ling

Water 2021, 13(2), 169; https://doi.org/10.3390/w13020169 - 13 Jan 2021

Cited by 23 | Viewed by 5237

Abstract

Internal erosion can trigger severe engineering disasters, such as the failure of embankment dams and uneven settlement of buildings and sinkholes. This paper comprehensively reviewed the mechanisms of soil internal erosion studied by numerical simulation, which can facilitate uncovering the internal erosion mechanism [...] Read more.

Internal erosion can trigger severe engineering disasters, such as the failure of embankment dams and uneven settlement of buildings and sinkholes. This paper comprehensively reviewed the mechanisms of soil internal erosion studied by numerical simulation, which can facilitate uncovering the internal erosion mechanism by tracing the movement of particles. The initiation and development of internal erosion are jointly influenced by the geometric, mechanical, and hydraulic conditions, which determine the pore channels and force chains in soil. The geometric conditions are fundamental to erosion resistance, whereas the mechanical conditions can significantly change the soil erosion resistance, and the hydraulic conditions determine whether erosion occurs. The erosion process can be divided into particle detachment, transport, and clogging. The first is primarily affected by force chains, whereas the latter two are mostly affected by the pore channels. The stability of the soil is mainly determined by force chains and pore channels, whereas the hydraulic conditions act as external disturbances. The erosion process is accompanied by contact failure, force chain bending, kinetic energy burst of particles, and other processes due to multi-factor coupling. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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31 pages, 7957 KiB

Open AccessReview

Application of Fractional Flow Theory for Analytical Modeling of Surfactant Flooding, Polymer Flooding, and Surfactant/Polymer Flooding for Chemical Enhanced Oil Recovery

by Lei Ding, Qianhui Wu, Lei Zhang and Dominique Guérillot

Water 2020, 12(8), 2195; https://doi.org/10.3390/w12082195 - 4 Aug 2020

Cited by 30 | Viewed by 9236

Abstract

Fractional flow theory still serves as a powerful tool for validation of numerical reservoir models, understanding of the mechanisms, and interpretation of transport behavior in porous media during the Chemical-Enhanced Oil Recovery (CEOR) process. With the enrichment of CEOR mechanisms, it is important [...] Read more.

Fractional flow theory still serves as a powerful tool for validation of numerical reservoir models, understanding of the mechanisms, and interpretation of transport behavior in porous media during the Chemical-Enhanced Oil Recovery (CEOR) process. With the enrichment of CEOR mechanisms, it is important to revisit the application of fractional flow theory to CEOR at this stage. For surfactant flooding, the effects of surfactant adsorption, surfactant partition, initial oil saturation, interfacial tension, and injection slug size have been systematically investigated. In terms of polymer flooding, the effects of polymer viscosity, initial oil saturation, polymer viscoelasticity, slug size, polymer inaccessible pore volume (IPV), and polymer retention are also reviewed extensively. Finally, the fractional flow theory is applied to surfactant/polymer flooding to evaluate its effectiveness in CEOR. This paper provides insight into the CEOR mechanism and serves as an up-to-date reference for analytical modeling of the surfactant flooding, polymer flooding, and surfactant/polymer flooding CEOR process. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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Other

Jump to: Editorial, Research, Review

14 pages, 3629 KiB

Open AccessTechnical Note

Experimental Study on the Permeability Characteristic of Fused Quartz Sand and Mixed Oil as a Transparent Soil

by Bo Huang, Chang Guo, Yao Tang, Jiachen Guo and Linfeng Cao

Water 2019, 11(12), 2514; https://doi.org/10.3390/w11122514 - 28 Nov 2019

Cited by 7 | Viewed by 7053

Abstract

An accurate estimation of soil permeability is essential in geotechnical engineering. Transparent soil provides a promising experimental material to visualize pore-scale fluid flow, although the permeability characteristic of transparent soil remains unclear. As a result of the replacement of the fluid and solid [...] Read more.

An accurate estimation of soil permeability is essential in geotechnical engineering. Transparent soil provides a promising experimental material to visualize pore-scale fluid flow, although the permeability characteristic of transparent soil remains unclear. As a result of the replacement of the fluid and solid phase, the permeability coefficient of transparent soil is usually several times or even more than ten times smaller than that of natural soil with the same particle size distribution and porosity. Fused quartz sand is used as the solid phase in this proposed transparent soil, which exhibits a similar mechanical behavior but different permeability to those of natural sand. Due to its low cost and eco-friendly characteristic, a mixture of mineral oil and aliphatic hydrocarbon is proposed as the liquid phase, which can achieve the same refractive index as the fused quartz sand after calculating the material proportion. Through a series of laboratory tests, the permeability of the transparent soil is obtained; the permeability is affected by the fluid dynamic viscosity, fluid density, particle size, particle size distribution, void ratio, and pore morphology. A hierarchical approach is introduced to quantitatively evaluate the effect of the particle shape on the permeability. Based on the experimental results, a modified Kozeny–Carman model is proposed for the prediction of transparent soil permeability, which can guide the preparation of transparent soil samples in further experimental studies. Full article

(This article belongs to the Special Issue Modeling of Flow and Transport in Saturated and Unsaturated Porous Media)

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