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Iranian Journal of Science & Technology, Transaction B,Vol. 28, No. B5Printed in The Islamic Republic of Iran, 2004

Shiraz University

ADVECTIVE-DIFFUSIVE AND HYDRAULIC TRAP MODELING

IN TWO AND THREE LAYER SOIL SYSTEMS*

K. BADV** AND A. A. MAHOOTI

Dept. of Civil Engineering, Urmia University, I. R. of IranEmail: [email protected]

Abstract Downward and upward (hydraulic trap) advective-diffusive transport of chloride was

modeled in two and three layer soil laboratory systems with Darcy velocities ranging from 310-9

m/s to 5.710-8

m/s. Two layer soil models simulated a compacted clayey layer over a sandy layer,

underlying a landfill. Three layer soil models simulated an unsaturated secondary leachate collection

system in a landfill with overlying and underlying saturated compacted silty liners. The effect of the

hydarulic trap in minimizing diffusive downward chloride movement was investigated in both

models. The agreement between the experimental results and theoretical predictions suggests that

existing solute transport theory can adequately predict chloride migration through two saturatedlayers of clay over sand and also three layer soil systems consisting of two saturated silt layers with

an unsaturated sand drainage layer in between. The comparison of the downward and upward

advective-diffusive transport in two and three layer soil models, having two different Darcy

velocities and soil density, showed that the upward flow (hydraulic trap) could reduce the

concentrations in the underlying receptor reservoirs in both models. The rate of the Darcy velocity

(or soil density) played a controlling role in chloride movement in both systems.

KeywordsLaboratory models, two and three layer soil, hydraulic trap, advection, diffusion

1. INTRODUCTION

The majority of laboratory studies on contaminant migration through soil have focused on the transport behavior

of migrating species in a single soil layer of either fine-grained soil such as clay or silt [1-9] or granular soil such

as sand [10, 8, 11]. The results of laboratory modeling on advective-diffusive transport through two layer

saturated/unsaturated soil systems have also been reported [8, 11-13]. In some practical applications involving

soil liners at waste disposal sites, there is a clayey layer underlain by a saturated or nearly saturated granular

material. Depending on the potensiometric surface in the underlying aquifer, there may be downward flow

(advection and diffusion at the same direction) or upward flow (the natural hydraulic trap, upward advection

against downward diffusion) through the soil layers [3].

Some modern landfills are built using multilayered barrier systems consisting of primary and secondary

clayey liners with a secondary leachate collection and removal system (SLCS) in between. This layer is

expected to remain unsaturated. Contaminants migrating through the overlying liner would pass through this

unsaturated coarse-grained layer. If the potensiometric surface in the underlying aquifer is lower than the

leachate mound in the SLCS, there may be downward advective-diffusive transport from the contaminant

source through the primary liner, the unsaturated SLCS, the secondary liner, and into the aquifer. On the

contrary, if the potensiometric surface in the underlying aquifer is higher than the leachate mound in the

SLCS, there will be downward advective-diffusive transport from the contaminant source through the

primary liner and into the unsaturated SLCS, but there will be upward advection (natural hydraulic trap) and

downward diffusion through the secondary liner. This might have an effect in reducing the contaminant

migration from the SLCS into the underlying aquifer.

Received by the editors July 27, 2003 and in final revised form May 24, 2004Corresponding author

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K. Badv / A. A. Mahooti

Iranian Journal of Science & Technology, Volume 28, Number B5 October 2004

560

The objectives of this investigation were twofold. (1) The effect of a natural hydraulic trap on reducing

chloride migration through two layer soil (clay over sand) was examined. Two different soil density and Darcy

velocities were used in the tests to observe the effect of flow rate. By comparing the predicted and observed

concentration profiles, an assessment was made of how well existing theory predicted chloride migration

through two-layered soil systems with downward and upward flow. The downward and upward Darcy velocities

examined in these tests were from 0.117 m/yr to 1.825 m/yr, and thus exceed Darcy velocities commonlyencountered through compacted clay soil liners in engineered landfill sites [14, 15]. This range of Darcy velocity

may occur in un-engineered landfill sites with underlying low density natural soil deposits. (2) The effect of a

natural hydraulic trap on reducing chloride migration through a three layer soil system (silt over un-saturated

coarse sand, over silt) was examined by downward and upward flow tests. During the downward flow test,

there was flow from the source through the primary silt layer, unsaturated coarse sand (as SLCS), and secondary

silt layer into the receptor. During the upward flow test, there was downward flow from the source through the

primary silt layer into the unsaturated coarse sand, and there was upward flow from the receptor through the

secondary silt layer into the unsaturated coarse sand (the hydraulic trap configuration from the receptor up to the

SLCS). The silt sample was used instead of clay to accelerate flow through the system.

In modeling multilayered systems, all conventional techniques (e.g., finite element, finite layer, etc.; see

[16]) assume that the migration can be simulated by adopting appropriate layer properties and invoking

continuity conditions at the layer boundaries. This has been verified by laboratory modeling on two layer

saturated/unsaturated soils [8, 11-13]. The theoretical model used to analyze the results [17] was selected

because of its ability to easily simulate the conditions of the conducted tests.

2. SOIL PROPERTIES AND PREPARATION

Four soil types were used in the experiments. The clay and silt samples were obtained from the Urmia City

landfill site. The soil mechanical tests were conducted and the samples were identified as clay with low

plasticity (CL) and silt with low plasticity (ML). The samples were air dried, pulverized, and passed through

a No. 4 sieve (

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Advective-diffusive and hydraulic trap modeling in

October 2004 Iranian Journal of Science & Technology, Volume 28, Number B5

561

with inlet and outlet valves and a septum sampling port, (3) the bottom and top aluminum plates, (4) four

stainless steel rods, (5) a pipette and its discharge tube attached to the receptor reservoir (downward flow

tests), or (6) a constant head water column attached to the receptor reservoir (upward flow tests), and (7) a

magnetic stirrer. The upper Teflon tube contained the compacted clay soil (first soil layer) at the bottom, and

the remaining upper space contained the source reservoir and a free space above the reservoir. The lower

Teflon tube contained the medium sand (second soil layer). The boundary between two tubes and betweenthe lower Teflon tube and the receptor reservoir were sealed by O rings. A magnetic bar was located

inside the receptor reservoir and stirred the solution by means of a magnetic stirrer. The upper source

reservoir was stirred manually during the tests. A glass cap was placed on top of the upper aluminum plate

to prevent evaporation of the solution.

I. Advective-diffusive downward flow tests: Figure 1 shows the schematic of the test equipment for two-

layer soil tests with the advective-diffusive downward flow (advection and diffusion at the same downward

direction). The air dried clay sample was mixed with tap water to a 2-4 weight percent wet of optimum

water content to obtain a minimum hydraulic conductivity after standard compaction [19]. The wet sample

was then compacted inside the tube using the standard proctor method [20] to the height of about 7-cm.

Some wet samples were saved for chloride background concentration measurements.

Fig. 1. Schematic of the test equipment in two-layer soil downward flow tests

The Teflon receptor reservoir was placed on top of the magnetic stirrer, a magnetic bar was placed

inside the reservoir, a stainless steel porous disk was placed in the chamber inside the reservoir, and the

lower Teflon tube was placed on top of the reservoir (on top of the porous disk). Dry medium sand was

placed and compacted inside the tube to a height of about 10-cm. The pipette and its discharging tube was

attached to the outlet valve in the reservoir. The level of the pipette was adjusted to the bottom level of the

sand. The sand sample was saturated by attaching a distilled water tank to the inlet valve in the bottom

reservoir and allowing water to flow upward through the sample for about 24 hours. During saturation, a

temporary fine mesh and a steel perforated plate was placed on top of the sand and a small load was applied

to prevent any sand particle movement during the saturation process. At the termination of the saturation

process, the outlet valve attached to the pipette was opened and water was allowed to flow through thepipette to fill the pipette and to wash any air bubbles out of the pipette. The discharging tube attached to the

pipette was also filled with distilled water. The inlet and outlet valves were then closed. The upper Teflon

tube containing the compacted clay sample was placed on top of the lower Teflon tube. Care was taken to

ensure a good contact between the lower saturated sand and the upper clay samples. The top aluminum plate

and the steel rods were placed and the test cell was tightened. A sodium chloride solution with a known

chloride concentration was poured on top of the clay sample inside the free space above the clay sample (the

source reservoir), to a height of about 4.8-cm. A sodium chloride sample solution was taken from the source

reservoir and the extracted solution was replaced with the same volume of distilled water to keep the

solution height constant inside the source reservoir. This first extracted sodium chloride solution was then

analyzed for chloride concentration to determine the source solution concentration (Co) at the beginning of

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the test. A solution sample was also extracted from the receptor reservoir through the septum port. During

sampling, the outlet valve was opened to allow distilled water inside the pipette to flow inside the reservoir

and to replace the extracted solution. This configuration is essential to prevent movement of the sand pore

water during sampling from the receptor reservoir.

During the test, samples from the source and receptor reservoirs were taken regularly and were then

analyzed for chloride concentration to plot the observed chloride concentration versus time graphs for thesource and receptor reservoirs. At the test termination, final solution samples from the source and receptor

reservoirs were taken. The source reservoir solution was drained and the test cell was disassembled. The

clay soil sample from the upper Teflon tube was extruded from the tube and sliced into 5 sublayers of

approximately equal thickness. A pneumatic soil pore water squeeze apparatus was used to obtain

contaminated pore water from the sliced soil samples and the chloride concentrations were measured. The

medium sand sample was extruded from the Teflon tube, sliced for equal thickness, weighed for water

content determination, and placed in the oven. The chloride concentrations of the sliced samples were then

determined using the wash method [8].

Three tests were performed with different densities of clay samples and different test Darcy velocities,

but equal downward hydraulic gradients of 1.34. These tests will be referred to as Tests DAD1, DAD2, and

DAD3 with test durations of 5, 23, and 20.8 days, respectively. Table 2 shows the tests geometrical,

physical, and chemical data along with the data for upward flow tests to be described later.All tests were

performed at 23 2oC.

Table 2. Two-layer soil tests geometrical, physical, and chemical properties, a) properties of the clay

layers, b) properties of the medium sand layers, c) tests other characteristics

II. Advective-diffusive upward flow tests: Figure 2 shows the schematic of the test equipment for two-

layer soil tests with the advective-diffusive upward flow (upward advection against downward diffusion-the

hydraulic trap configuration). The test setup is similar to what is described above for the downward flow

tests except that an upward flow was applied. To creat upward flow, instead of pipette and its discharging

tube as used for the downward flow tests, a constant head water column was attached to the outlet valve in

the receptor reservoir, as shown in Fig. 2. The water level in the column was maintained constant and higher

than the level of the sodium chloride solution in the source reservoir during the tests. This configuration

(a)

Properties Test

DAD1

Test

DAD2

Test

DAD3

Test

UAD1

Test

UAD2

Soil depth (cm) 7 7 7 7 7

Average water content (%) 16.3 14.5 22.2 14.5 18.5

Average volumetric water content (cm3/cm

3) 0.32 0.29 0.38 0.29 0.34

Dry density (gr/cm3

) 1.85 1.92 1.68 1.92 1.79[Cl

-] Background concentration (mg/l) 180 180 180 180 180

[Cl-] Effective diffusion coefficient (De10

10m

2/s) 11.3

9.77 13.42 9.77 12.04

(b)

Soil depth (cm) 10 10 10 10 10

Average water content (%) 21.8 22 22 22 22

Average volumetric water content (cm3/cm

3) 0.37 0.37 0.37 0.37 0.37

Dry Density (gr/cm3) 1.67 1.65 1.65 1.65 1.65

[Cl-] Background concentration (mg/l) 15 15 15 15 15

[Cl-] Effective diffusion coefficient (De1010 m2/s) 13.6 13.9 13.9 13.9 13.9

(c)

Source solution height (cm) 4.8 4.8 4.8 4.8 4.8

Source solution concentration (mg/l) 3150 3300 2000 3010 2050

Test hydraulic gradient 1.34 1.34 1.34 1.34 1.34

Test Darcy velocity (va109 m/s) +3.7* +7.4* +57* -5.2* -74*

Test duration (days) 23 20.8 5 21 5

*Positive sign implies downward flow and negative sign implies upward flow

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created an upward flow from the receptor reservoir through the soil layers and into the source reservoir (the

hydraulic trap configuration). To maintain a constant head in the source reservoir, excess infiltrated water to

the reservoir was regularly drained. This configuration created a constant upward hydraulic gradient during

the tests. Two tests were performed which will be referred to as Tests UAD1 and UAD2 with equal upward

hydraulic gradients of 1.34 and with test durations of 21 and 5 days, respectively. The methodology at the

test termination and observed data collection were as described for downward flow tests. Tests forgeometrical, physical, and chemical data are listed in Table 2. These tests were performed at 23 2

oC.

Fig. 2. Schematic of the test equipment in two-layer soil upward flow

tests (the hydraulic trap configuration)

b) Three-layer soil models

Figures 3 and 4 show the schematic of the test equipment for three-layer soil tests with the advective-

diffusive downward and upward flow, respectively. By comparing Fig.1 with Fig. 3, and Fig. 2 with Fig. 4,

it could be verified that the three layer downward and upward flow models are very much similar to two

layer downward and upward flow models, respectively, except that there is a coarse sand drainage layer in

between the upper and lower silt layers (as described earlier, silt was used instead of clay to accelerate flow

in these experiments). A plexiglass ring with an 8.9 cm inside diameter and an 3.8 cm height was used to

create a compartment for the drainage layer. Two ports in opposite directions were installed in the tube. The

left port was installed 0.8 cm from the top of the tube and was used as air-inlet port to maintain atmospheric

pressure inside the upper unsaturated portion of the coarse sand drainage layer. The right port was installed

1-cm from the bottom of the tube and was used as a septum port for sampling from the lower saturated

portion of the coarse sand drainage layer during the tests.

Fig. 3. Schematic of the test equipment in three-layer soil downward flow tests

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Fig. 4. Schematic of the test equipment in three-layer soil upward flow tests(the hydraulic trap configuration through the lower silt layer)

Installation of the silt and coarse sand samples in the apparatus for the upward and downward flow tests

was identical. The silt samples were compacted inside the lower and upper Teflon tubes the same way as

described earlier for the clay samples in two layer soil tests. After installation of the lower Teflon tube

containing the compacted lower silt layer, a thin geotextile sheet was placed on top of the silt and the

Plexiglas ring was installed. The coarse sand layer was placed and compacted inside the ring. Another thin

geotextile sheet was placed on top of the coarse sand and the upper Teflon tube containing the upper

compacted silt layer was placed on top of the Plexiglas ring. There were O rings in both sides of the

Plexiglas ring to prevent any leakage at the interfaces between the ring and the upper and lower Teflon

tubes. The upper aluminum plate and the rods were installed and the test cell was tightened. To create a

small hydraulic gradient across the lower silt layer, distilled water was injected inside the coarse sand layer.

This was done through the septum port until about 1 cm of the coarse sand layer became saturated and the

flow was initiated through the lower silt. The source sodium chloride solution was poured on top of the

upper silt layer and the test was started.

I. Advective-diffusive downward flow test:The conducted test will be referred to as Test D3LAD with a

test duration of 30 days. A pipette and its discharging tube was attached to the outlet valve in the source

reservoir to replace extracted sodium chloride solution by the same volume of distilled water during the test.

When the test started, sodium and chloride ions migrated downward through the upper silt layer by

advection and diffusion. The infiltrated solution through the upper silt layer passed the upper unsaturated

coarse sand layer and was collected at the bottom saturated portion of the coarse sand layer. The solution

mound in this layer, on top of the lower silt layer, created a hydraulic gradient through the lower silt layer

and caused downward advective-diffusive migration through this layer and into the receptor reservoir. The

infiltrated solution into the receptor reservoir was then exfiltrated through the pipette and was collected in a

container as shown in Fig. 3. The infiltrated and also sampled solutions from the source reservoir was

regularly replaced by the same volume of distilled water during the test. The Darcy velocity through the

upper silt layer was calculated based on the volume of solution infiltrated through this layer. To maintain a

constant solution mound inside the coarse sand drainage layer, extra solution was extracted by a syringe

through the septum port above the lower silt layer. The collected solutions were then analyzed for chloride

concentration to plot the observed concentration change with time in the drainage layer. The Darcy velocity

through the lower silt layer was calculated based on the infiltrated solution through the pipette. The collected

solutions infiltrating from the pipette were also analyzed for chloride concentrations to plot the observed

chloride concentration change with time in the receptor reservoir. The sampled solutions from the source

reservoir were also analyzed for chloride concentrations to plot the observed chloride concentration change

with time in the source reservoir. During the test, the sum of the volumes of the extracted solution from the

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coarse sand drainage layer and the exfiltrated solution from the pipette, was equal to the volume of the

infiltrated solution from the source reservoir (without taking into account the volume of solutions extracted

from the source reservoir and the drainage layer for concentration measurement). The procedure for chloride

concentration measurement versus depth in the silt layers at the end of the test was as described for the clay

layer in the two layer soil tests. For the coarse sand drainage layer, the upper unsaturated portion of the

layer inside the ring was collected by a spoon, and its chloride concentration measured using the washmethod described earlier for the medium sand layer in two layer tests. For the lower saturated portion of the

layer, enough pore water was extracted by a syringe and analyzed for chloride concentration. The observed

chloride concentrations in the upper silt layer, upper unsaturated portion and lower saturated portion of the

coarse sand layer and lower silt layer, were plotted against soils depth which will be discussed later.

Geometrical, physical, and chemical test data are listed in Table 3. The test was performed at 23 2oC.

Table 3. Three-layer soil tests D3LAD and U3LAD geometrical, physical, and chemical properties

*Positive sign implies downward flow and negative sign implies upward flow

II. Advective-diffusive upward flow test: The conducted test will be referred to as Test U3LAD with the

test duration of 26 days. As shown in Fig. 4, the test setup is similar to what has been described above forTest D3LAD except that a constant head water column was attached to the outlet valve in the receptor

reservoir to create an upward hydraulic gradient through the lower silt layer (the hydraulic trap configuration

from the receptor reservoir up to the coarse sand drainage layer). There was a downward flow through the

upper silt layer as described for Test D3LAD. The infiltrated solutions through the upper and lower silt

layers were collected in the coarse sand drainage layer and regularly drained through the septum port to

maintain a constant solution mound on top of the lower silt layer. Selected samples from the drained

solutions were analyzed for chloride concentration to plot the observed concentration change with time in

the drainage layer. The source and receptor reservoir solutions were also monitored for chloride

concentration change with time as described for Test D3LAD. The methodology at test termination and

chloride concentration measurement at soil depth were as described for Test D3LAD. Geometrical, physical,

and chemical test data are listed in Table 3. The test was performed at 23 2oC.

Test D3LAD Test U3LAD

Properties Upper

andlower

silt

Unsaturated

coarse sand

Saturated

coarsesand

Upper

andlower

silt

Unsaturated

coarse sand

Saturated

coarse sand

Soil depth (cm) 7 1.5 2.3 7 1.5 2.3

Average water content(%) 18.8 5.3 26 18.8 5.3 26

Average volumetric water

content (cm3/cm

3) 0.34 0.084 0.42 0.34 0.084 0.42

Dry density (gr/cm3) 1.81 1.61 1.61 1.81 1.61 1.61

[Cl-] Background

concentration (mg/l) 90 20 20 90 20 20

[Cl-] Effective diffusion

coefficient (1010

m2/s) 6.38 2.3 11.6 6.38 2.3 11.6

Source solution height

(cm) 5 5

Source solution

concentration (mg/l) 1950 2000Upper silt hydraulicgradient 1.7 1.7

Lower silt hydraulic

gradient 1.2 1.2

Upper silt Darcy velocity

( 109m/s) +7.4

*+5.6

*

Lower silt Darcy velocity(10

9m/s) +3.0

*-3.0

*

Test duration da s 30 26

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4. THEORETICAL MODELING

The transport of contaminants through saturated soils can be described by the advection-diffusion equation

[2, 8, 15, 21-23], which can be written for a one dimensional condition as:

z

cv-

z

cD=

t

c)K+(

2

2

d

(1)

where c is the contaminant concentration at a depth z at time t; is the soil volumetric water content (=n, the

soil porosity for saturated soil); v is the average linearized ground water velocity (seepage velocity); is the dry

bulk density of the soil, Kd is the distribution coefficient, nv=va is the Darcy velocity, and D is referred to as the

coefficient of hydrodynamic dispersion.

The coefficient of hydrodynamic dispersion D is commonly defined as the sum of the coefficient of

mechanical dispersion, Dmd, and effective diffusion coefficient in the porous medium, De, viz

emd DD=D + (2)

It is known that the effective diffusion coefficient, De, varies with the volumetric water content [6, 7]. Many

researchers attribute the decrease in the rate of diffusion as the water content decreases, to the increasedtortuosity of the pathway for diffusion. It has been reported that there is a linear (or approximately linear)

relationship between the effective diffusion coefficientDe, and the volumetric water content of the soil, [8, 11].

The relationship reads as follows:

D=D e(ref)ref

e

(3)

where De is the effective diffusion coefficient in the soil at a volumetric water content , ref is the volumetric

water content at full saturation (i.e. total porosity), and De(ref) is the effective diffusion coefficient in soil at full

saturation.

For modeling the multilayered system (such as two or three layer systems used in this study), and for one-

dimensional steady flow conditions, the Darcy velocity must satisfy continuity of flow [12] and this implies that:

)1()1()1()()()( +++ == iiiaiiia vvv=v (4)

for any layer pair i, i+1. Furthermore, conservation of mass and continuity of concentration require that for

any layer boundary at some depth, zi, the mass flux and concentration are continuous, hence

ii zziazzia z

cDcv=

cDcv =+=

|1| )()( (5)

and

)()( 1 iiii zzc=zzc == + (6)

The analysis of the tests involves solving these equations, which are subject to appropriate boundary

conditions. The boundary condition imposed by the source reservoir whose concentration cs(t) reduces with time

due to the movement of chloride into the soil and also sampling, [16, 24] can be modelled by:

d)(cH

q-df

H

1-c=(t)c s

0

t

f

cs0

t

fos (7)

where co is the initial concentration in the reservoir, Hf is the height of fluid in the source reservoir, qc is the

volume of fluid per unit area per unit time removed from the reservoir for chemical analysis during the test and

replaced by distilled water, and fs is the contaminant flux into the soil and is given by

z

cD-vc=fs

(8)

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567

where all the terms are as previously described.

When upward flow is concerned (hydraulic trap), a negative sign is used for the Darcy velocity in Eq. (8)

(i.e.,c

D-vc=fs

).

For the advection-diffusion tests with a fluid receptor, the concentration in the receptor at time t can be

described by

d)(ch

q-]d

h

)(f[=(t)c Ro

tbRo

tR (9)

where fR() is the flux entering the receptor at time and is given by Eq. (8) (i.e.,z

cD-vc=fR

)( ), h is the

thickness of the receptor, and qb is the volume of fluid per unit cross sectional area of the soil per unit time

removed from the receptor for chemical analysis during the test. When upward advection is against downward

diffusion (hydraulic trap) between the receptor and the coarse sand drainage layer, a negative sign is used for the

Darcy velocity in the equation (i.e.,c

D-vc=fR

)( ).

For modeling the multilayered system where there were different volumetric water contents for any

sublayer within a given layer (such as unsaturated coarse sand sublayer above the saturated coarse sand

sublayer, in Tests D3LAD and U3LAD), Eq. (1) was used for each sublayer, together with the appropriatevalue of and D (or De, since no dispersion was observed in the experiments). Continuity between sublayers

is defined by Eqs. (4-6). The initial concentration distribution in the soil layers was explicitly modeled.

A solution to Eq. (1) has been given by Rowe and Booker [24, 17] and has been implemented in a

computer program POLLUTE (Rowe and Booker [25, 17]). This program is used in this study to predict the

observed data from the laboratory models discussed earlier.

5. EXPERIMENTAL AND MODELING RESULTS

The effective diffusion coefficient of chloride in the upper unsaturated portion of the coarse sand drainage

layer was estimated based on the volumetric water content of the unsaturated portion using Eq. (3). The

chloride concentrations in the pore water of clay, medium sand, silt, saturated and unsaturated coarse sand,

were normalized relative to the initial source solution concentrations in each test and plotted against soil

depths. Also the chloride concentrations in the source and receptor reservoirs and drainage layer (three layer

tests) were normalized relative to the initial source solution concentrations in each test and plotted against

the elapsed time.

a) Results for two-layer soil models

The results obtained from advective-diffusive downward flow Tests DAD1, DAD2, and DAD3 are

summarized in Table 2 and the observed and predicted (theoretical modeling) results in the source and

receptor reservoirs, and in the soils depth are plotted in Figs. 5a, 5c, and 5b, respectively. Similarly, the

results for upward flow Tests UAD1 and UAD2 are summarized in Table 2 and plotted in Figs. 6a, 6c, and

6b. The water content distribution in the clay and medium sand layers were measured at the end of the testsand were almost uniform in both the clay and medium sand layers in all tests. The water content and the

volumetric water content of the clay and medium sand sublayers were calculated and averaged for the entire

soil profiles as summarized in Table 2 for all tests.

It is evident from the results that the effective diffusion coefficients obtained from the diffusion tests on

single isolated layers, along with the tests observed from geometrical, physical, and chemical data which

were used in the theoretical model, POLLUTE, could reasonably predict the observed behavior of the

experimental models. Due to a uniform water content profile in the soils, a single value of the volumetric

water content and effective diffusion coefficients were used for clay and medium sand layers in modeling

with POLLUTE. These data, along with the other data, resulted in theoretical curves, which reasonably fit

the observed data.

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Fig. 5. Observed and modeled profiles of two-layer soil Tests DAD1, DAD2, and DAD3 with downward flow:

a) Relative chloride concentrations in source reservoirs versus time, b) Relative chloride concentrations

versus soil depths, and c) Relative chloride concentrations in receptor reservoirs versus time

The Darcy velocities in downward flow Tests DAD1, DAD2, and DAD3 were in the increasing order,

respectively (Table 2). As shown in Fig. 5b, the higher Darcy velocity caused faster downward movement of

the chloride ion by advection, in Test DAD3 compared to Test DAD2, and in turns, compared to Test

DAD1. This effect could also be verified by comparing the relative chloride concentrations in the source

reservoirs of the tests (Fig. 5c). In Test DAD3 with a Darcy velocity 15.6 times greater than that in Test

DAD1, and much shorter test duration (5 days in Test DAD3 compared to 23 days in Test DAD1), the final

observed relative chloride concentration in the source reservoir was about 0.4, compared to about 0.65 in

Test DAD1 at the end of the tests.

The effect of the upward flow (advection against diffusionthe hydraulic trap) in reducing the

downward chloride movement could be verified from the relative chloride concentrations in the receptor

reservoirs. As shown in Fig. 6c, in both tests UAD1 and UAD2, no increase in the chloride concentrations in

the receptor reservoirs was observed during the tests, and modeling results also confirm this. It could be

concluded that for the governing test conditions and Darcy velocities, upward advection (hydraulic trap) has

played a good role as a hydraulic barrier against downward diffusion of chloride ion. The decrease in the

chloride concentration in Test UAD2 was due to dilution from the background contamination (about 20

mg/l) in the receptor reservoir. Tests DAD1 against UAD1, and DAD3 against UAD2 could also be

compared for the effect of the hydraulic trap.

Relative[Cl-]

Concentration

inSourceReservoir(C/C

o)

(a)

Elapsed Time (days)

0 3 6 9 12 15 18 21 24

0.0

0.5

1.0

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

10

12

14

16

Relative [Cl- ]Concentration (C/Co)

SoilDepth(cm)

0 3 6 9 12 15 18 21 24

0.00

0.01

0.02

0.03

(b)

(c)

Background

Concentration

Elapsed Time (days)

Relative[Cl-]

Concentration

inReceptorRservoir(C/C

o)

Clay

Medium Sand

Test DAD1Test DAD2

Test DAD3

Observed Data________________

Theory

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Fig. 6. Observed and modeled profiles of two-layer soil Tests UAD1 and UAD2 with upward flow: a) Relative chloride

concentrations in source reservoirs versus elapsed time, b) Relative chlorideconcentrations versus soil

depth, and c) Relative chloride concentrations in receptor reservoirs versus elapsed time

For more verification of the effect of the hydraulic trap in Test UAD1 (v a = - 510-9 m/s) compared to

the same test configuration but in the absence of the hydraulic trap, the POLLUTE analysis was repeated

using the same input data as used in the analysis of Test UAD1, but with the positive value for Darcy

velocity (i.e., downward Darcy velocity through the soil layers, va= + 510-9

m/s). The results are plotted in

Fig. 6 (a, b, and c) as dotted lines. As shown in Figs. 6a and 6c, when the hydraulic trap is not functioning,

the rate of the chloride concentration drop in the source reservoir and increase in the receptor reservoir, with

time, is higher. There is also a significant difference in the soils predicted chloride concentration profile

when the flow is downward. This implies that the hydraulic trap could minimize downward migration of

chloride by diffusion through a two-layer soil system.

b) Results for three-layer soil models

The results obtained from three-layer soil models (Tests D3LAD and U3LAD) are summarized in Table

3 and the observed and predicted results in the source and receptor reservoirs, as well as in the soils depth,

are plotted in Figs. 7a, 7c, and 7b, respectively. The observed and predicted results in the coarse sand

drainage layers are plotted in Fig. 8. As shown in the figures, there is a good agreement between the

observed and predicted data in both tests considering only advective-diffusive transport. This implies that

mechanical dispersion was negligible. There is a pronounced drop in the observed and predicted chloride

concentration profiles in the upper unsaturated portion of the coarse sand drainage layer in both tests, as

shown in Fig. 7b. This is due to slow diffusion and increased tortuosity through the unsaturated coarse sand

Relative[C

l-]

Concentration

inSource

Reservoir(C/C

o)

(a)

Elapsed Time (days)

0 3 6 9 12 15 18 21 24

0.0

0.5

1.0

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

10

12

14

16


SoilDepth(cm)

0 3 6 9 12 15 18 21 24

0.00

0.01

0.02

0.03

(b)

(c)

Background

Conc.

Elapsed Time (days)

Relative[Cl-]

Concentration


o)

Clay

Medium Sand

Test UAD1

Test UAD2

Observed________________

Upward Flow

(UAD1 & UAD2)

Theory______________________

Downward Flow

(UAD1)

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[11]. The chloride concentration in the receptor reservoir of downward flow test D3LAD increased gradually

during the test, while in Test U3LAD with the operating hydraulic trap through the lower silt layer, the

concentration remained almost constant for almost comparable test duration.

Fig. 7. Observed and modeled profiles of three-layer soil Tests D3LAD and U3LAD with downward and upward flowin lower silt layers: a) Relative chloride concentrations in source reservoirs versus elapsed time, b) Relative

chloride concentrations versus soil depths, and c) Relative chloride concentrations in

receptor reservoirs versus elapsed time

Fig. 8. Observed and modeled relative chloride concentrations versus elapsed time

in coarse sand drain layers in Tests D3LAD and U3LAD

Formoreverificationof the effect of thehydraulic trap throughthe lowersilt layer in TestU3LAD(va =-310

-9m/s) compared to the same test configuration but in the absence of the hydraulic trap, the

POLLUTE analysis was repeated using the same input data as used in the analysis of Test U3LAD, but with

positive value for Darcy velocity (i.e., va = + 310-9

m/s, downward Darcy velocity through the lower silt

layer). The results are plotted in Figs. 7b, 7c, and Fig. 8 as dotted lines. As shown in Fig. 7c, the theory

Relativ

e[Cl-]Concentration

inCoa

rseSandDrain(C/Co)

Elapsed Time (days)

0 4 8 12 16 20 24 28 32

0.0

0.5

1.0

Observed______________

Test D3LAD

Test U3LAD

Theory_______________

Tests D3LAD& U3LAD

Test U3LAD(Downward Flow)

Relative[Cl-]

Concentration

inSourceReservoir(C/C

o)

(a)

Elapsed Time (days)

0 4 8 12 16 20 24 28 32

0.0

0.5

1.0

0.0 0.2 0.4 0.6 0.8 1.00

3

6

9

12

15

18

21


SoilDepth(cm)

0 4 8 12 16 20 24 28 32

0.000

0.025

0.050

(b)

(c)

BackgroundConcentration

Elapsed Time (days)

R

elative[Cl-]

Concentration


o)

Silt

Coarse Sand Drain

Test D3LAD

Test U3LAD

Observed________________

Tests D3LAD

& U3LAD

Theory______________________

Downward Flow

(Test U3LAD)

Silt

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predicts a gradual increase of chloride concentration in the receptor reservoir with time, in the absence of the

hydraulic trap, but almost constant chloride concentration with time, with the operating hydraulic trap. This

implies that for the range of the Darcy velocities and tests boundary conditions, the hydraulic trap had an

effect in minimizing downward chloride movement from the drainage layer (simulating a SLCS in a landfill)

to the underlying receptor reservoir (simulating an aquifer).

6. SUMMARY AND CONCLUSIONS

The laboratory experiments were performed on two and three layer soil systems to model the advective-

diffusive migration of chloride with and without the hydraulic trap effect. Two-layer soil models simulated a

compacted clay layer over a medium sand layer, underlying a landfill. Three-layer soil models simulated

compacted primary and secondary silty liners with a secondary leachate collection system in between. The

following general conclusions could be made for all experiments conducted: (1) one-dimensional advective-

diffusive theory Eq. (1) implemented in the computer model POLLUTE could reasonably predict the

experimental observations in all models with downward and upward (the hydraulic trap) flow, (2) the

chloride diffusion coefficients already determined in the same single isolated soils, along with the tests

geometrical, physical and chemical test data, could reasonably predict the observed concentration data in all

tests. The following test-specific conclusions could be made:

a)Two-layer soil tests

(1) The 15.6 times higher Darcy velocity in downward flow Test DAD3 compared to Test DAD1

caused a faster downward movement of chloride by advection, so that the final observed relative chloride

concentration in the source reservoir of Test DAD3 (5 days test duration) was about 0.4 compared to about

0.65 in Test DAD1 (23 days test duration). Diffusion was partly responsible for chloride downward

migration in these tests, (2) the chloride concentrations in the underlying receptor reservoirs of upward flow

Tests UAD1 and UAD2 (with the operating hydraulic trap) did not increase during the tests. It could be

concluded that for the governing test conditions and Darcy velocities, upward advection (hydraulic trap)

played a good role as a hydraulic barrier against downward diffusion of chloride ion through clay and

medium sand layers. The hydraulic trap effect was also theoretically verified in Test UAD1 by repeating the

analysis with positive value for Darcy velocity (reversed flow).

b) Three-layer soil test

(1) Slow diffusion and increased tortuosity through the unsaturated coarse sand drainage layer in Tests

D3LAD and U3LAD caused a pronounced drop of the chloride concentration in this layer. This was in

agreement with the results of previous studies on similar soil, (2) for the 25 days of elapsed time, and the test

conditions being identical except for the direction of flow in the lower silt layer, the chloride concentration

in the receptor reservoir of Test D3LAD (downward flow) increased gradually, while in Test U3LAD

(upward flow) remained almost constant. Theory also confirmed the increase of chloride concentration in

the receptor reservoir of Test U3LAD in the absence of the hydraulic trap through the lower silt layer

compared to when the hydraulic trap was in operation (i.e., no change in the concentration).

Acknowledgments- This paper forms part of a research program in laboratory modeling in contaminant

transport through soils being conducted at the Geo-Environmental Research Laboratory at the Department of

Civil Engineering in Urmia University, Iran. The funding for this research was made possible by the award

of research grant No. 21825 to K. Badv from the Management and Programming Organization of Iran.

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