## Abstract

Groundwater is one of the most important water sources but it is often not far away from pollution. One source of pollution is leakage from polluted streams such as open drains. The effect of open drains on groundwater quality has become an essential issue. This study aims to use different lining materials to minimize the seepage from open drains to protect groundwater. MODFLOW is used to investigate flow and contaminant transport and to evaluate efficiency of different lining materials. A hypothetical case study is used to assess different lining materials such as clay, bentonite, geomembranes and concrete. The results showed that decreasing the conductivities of lining materials reduced the extension of the contaminate. The extension of contaminants was reduced by 43, 89.6, 91.4 and 93% compared with the base case when drains were lined by clay, bentonite, geomembranes and concrete, respectively. Also, cost analysis of lining materials was done to detect the best lining material. Lining using geomembranes reduced contaminant extension at low cost compared with concrete, which reduced contaminant extension at double the cost. This reveals that the geomembranes represent the preferred material to protect groundwater from drain seepage due to its high durability and low cost compared with concrete.

## INTRODUCTION

Drainage systems consist of two main types: subsurface drainage and surface open drains. Surface open drains are open channels that may be lined by grass, concrete, earth or stone. They are usually used to transport agricultural drainage water, residential and industrial wastes. Groundwater is an important natural source that may be directly affected by seepage from open drains. Groundwater is very sensitive to anthropogenic activities such as industrial activities, wastewater drains and leakage from sewage systems. However, agricultural activities showed a low contribution (Arnous & El-Rayes 2013). Deep confined groundwater has low content of heavy metals contaminates from local sources of pollution, while shallow depths have the highest content of nitrate and salinity (Ahmed et al. 2011).

Groundwater contamination has been studied by a number or researchers due to its importance. Ghasemlounia & Herfeh (2017) investigated water quality using a geographic information system (GIS) in Ardabil, Iran for 76 sample wells. The results showed that in the wet season only 6.58% were good quality, 22.37% were considered of unsuitable quality and 71.05% were of medium quality, while in the dry season these values reached 4, 32 and 64% for the three cases, respectively, using 50 wells. Kyere et al. (2018) investigated the level of heavy metals in soils from Agbogbloshie Recycling Site in Ghana using 132 soil samples. The results showed that the concentrations of cadmium (Cd), chromium (Cr) and nickel (Ni) were lower than the permissible levels of the Dutch and Canadian soil standards, while the concentrations of copper (Cu), lead (Pb) and zinc (Zn) were between 100% and 500% higher than the standard permissible levels.

A number of earlier studies have started to consider the impact of open drains on groundwater quality and quantity. Ali et al. (2004) studied the impact of deep open drains on groundwater levels at farm and sub-catchment level. The results showed that water levels changed between 1.5 and 2.5 m of the ground surface for drained areas, while in undrained areas levels changed between 0 and 1 m. The impact of irrigation loss and canal seepage on groundwater interactions in the lower valley of the Cachapoal River, Chile was assessed by Arumí et al. (2009). The results revealed that groundwater recharged by 22% from irrigation loss and 52% from canal seepage; also the study recommended that the hydrological system and agricultural production will be affected by changing the canal lining and irrigation system. Gomaah et al. (2016) used stable isotopes and hydrogeochemistry to evaluate groundwater in a Quaternary aquifer and its sources and geochemical evolution in the zone between Ismailia and Elkassara canal, Egypt. The results showed three sources of recharge: current Nile water including heavy isotopes, old Nile water which is more developed and depleted in heavy isotopes, and recharge from the underlying Miocene aquifer due to excessive pumping.

Tahershamsi et al. (2018) simulated groundwater flow using MODFLOW and the geostatistical method in the Ardebil plain in Iran. The result showed a small normal root-mean-square (NRMS) error of 2% using the mathematical model to confirm the accuracy of the calibrated model. Also, the statistical results indicated that the mathematical model accuracy is higher than the geostatistical method. Hosseini & Saremi (2018) tested 17 samples from the Malayer plain aquifer area of southern Hamedan Province, Iran using the modified DRASTIC and GODS models. In this aquifer 30 physicochemical parameters were studied to assess the groundwater vulnerability to different pollution sources. The results showed that the DRASTIC model is better than GODS in determining the groundwater vulnerability to pollution.

Seepage from canals and reservoirs is considered an important source of groundwater pollution. A number of approaches can be used to reduce that seepage and reduce the transmission of pollutants to groundwater by lining the canal with different materials. Some studies investigated natural materials with low permeability such as clay and bentonite and industrial materials such as geomembranes, geosynthetic clay liners and concrete mixtures to reduce the leakage from drains to groundwater. Figure 1 shows different types of lining materials used for canal lining. Lambert & Touze-Foltz (2000) presented a study to determine the geomembrane permeability. The study results indicated that geomembrane permeability is less than 10−6 m/d. Li et al. (2017) investigated factors affecting the control of groundwater contamination in the vadose zone. The results proved that contamination can easily extend into groundwater and the vadose zone that becomes more vulnerable under high values of hydraulic conductivity.

Figure 1

(a) Clay, (b) concrete and (c) geomembranes used in canal lining (Source:http://www.geosyn.co.uk/product/geomembranes).

Figure 1

(a) Clay, (b) concrete and (c) geomembranes used in canal lining (Source:http://www.geosyn.co.uk/product/geomembranes).

Stark & Hynes (2009) studied the effect of using geomembranes for canal lining on seepage. The results showed that seepage from the canal was reduced by 90% using the geomembrane lining. Also, covering the geomembranes by concrete increased durability but at high cost. Blanco et al. (2012) used different geomembrane types (plasticized polyvinyl chloride (PVC-P), high density polyethylene (HDPE), and ethylene-propylene-dienic monomer (EPDM) for waterproofing of reservoirs. The study indicated that these materials are suitable for waterproofing of hydraulic works and their selection depends on the function of the reservoir itself and on economic factors. The EPDM geomembrane was chosen as it showed the best resistance to static impact. Ojoawo & Adegbola (2012) indicated that the effectiveness of geomembrane material liners is ordered as smooth high density polyethylene (HDPE), smooth low density polyethylene (LDPE), textured HDPE and textured LDPE.

Meer & Benson (2007) presented a study to determine hydraulic conductivity for the geosynthetic clay liners (GCLs) exhumed from landfill. The study showed that 5.2 × 10−9 to 1.6 × 10−4 cm/s is the calculated value for the hydraulic conductivities of the geosynthetic clay liners. The results indicated that the gravimetric water content is the main factor affecting the hydraulic conductivity of the exhumed GCLs. Khair et al. (1991) studied the impact of lining irrigation canals with soil-cement tiles. The study recommended that soil-cement tiles are very effective to reduce the seepage losses through 2 mm or smaller soil aggregates and expected that the lining of irrigation canals by this material will be very important especially in the zones where irrigation water is very costly. Schneider et al. (2012) presented a study for determining hydraulic conductivity of concrete and mortar and found its values are 5.67 × 10−15cm/s for concrete and 5.87 × 10−16 cm/s for mortar.

Based on the literature, a number of studies have been conducted to reduce the seepage from canals and reservoirs using different materials. Natural materials with low permeability such as clay and bentonite, and industrial materials such as geomembranes, geosynthetic clay liners and concrete mixtures have been used to reduce the leakage to groundwater. Seepage from contaminated open drains has become one of the most important sources of groundwater pollution. A limited number of studies have been carried out to reduce the seepage from open drains to protect groundwater. This study aims to assess factors affecting the extension of contaminants from polluted open drains into groundwater and how to protect groundwater from contamination using different lining materials. The numerical model MODFLOW is developed in this study to assess the effect of using different lining materials on extension of contaminants into groundwater aquifers. Cost analysis of these materials is presented to help in the selection of the best material.

## MATERIALS AND METHODS

A flow chart of the methodology used in this study is presented in Figure 2. The methodology includes a number of steps: review of the previous studies, identify the problem, collect the required data, develop and calibrate the numerical model, study different scenarios of pumping rates and different lining materials for groundwater protection.

Figure 2

Flow chart of the methodology.

Figure 2

Flow chart of the methodology.

### Case study

A hypothetical case study is used to evaluate the impact of open drains lining using different materials on groundwater contamination by investigating contaminate extension (XT) from the pollution source. The study area of 4,000 m2 is used with length (Lx) 2,020 m divided into 101 columns, width (Ly) 2,000 m divided into 100 rows and depth of the domain was selected to be large enough to avoid the effect of bottom and side boundaries (d = 100 m) and divided into 10 layers as presented in Figure 3. Figure 4 shows the 3-D domain for the current case study and Figure 5 shows the vertical cross-section of the case study.

Figure 3

(a) Plane and (b) elevation view of the hypothetical case domain.

Figure 3

(a) Plane and (b) elevation view of the hypothetical case domain.

Figure 4

3-D domain of the case study.

Figure 4

3-D domain of the case study.

Figure 5

Vertical cross-section of the case study.

Figure 5

Vertical cross-section of the case study.

The polluted drain was installed in the center of the area as a major source of pollution with a constant concentration of 2,000 mg/l. Two rivers were assigned on both sides of the domain and parallel to the drain. The two rivers represent the source of recharge with a distance of 1,000 m from the drain. The abstraction was assigned using six wells with a discharge of 90 m3/h for each well. The wells are installed in two rows at the middle between the rivers and drain as shown in Figures 4 and 5.

### Numerical model

A 3-D VISUAL MODFLOW is used to investigate the effect of polluted open drains on groundwater quality and assess the effect of lining on contaminant extension. This version of the numerical model is used to simulate groundwater flow and solute transport for steady state and transit flow. The groundwater flow equation used in MODFLOW (McDonald & Harbaugh 1988) and the contaminants transport in groundwater (Javandel et al. 1984) are presented in detail in Abd-Elhamid et al. (2018).

#### Model boundary conditions and hydraulic parameters

The boundary conditions for the case study are described in Figure 5. The river package is used to describe the two rivers on the left and right sides with gradually constant head stage range from −0.50 to −0.8 m and river bed bottom range from −3 to −3.3 m. The drain package is used to describe the open drain with elevation stage ranging from −2.5 to −2.8 m. A constant concentration of 2,000 mg/L has been assigned in the drain. Also, the annual recharge is 365 mm/year and the abstraction is 60 m3/h from each well with total abstraction of 360 m3/h. The aquifer is assumed to be homogeneous with horizontal and vertical hydraulic conductivities of 50 and 5 m/day, respectively, specific storage (Ss) is 27 × 10−7 while the specific yield (Sy) and total porosity (ntotal) are 0.20 and 20%, respectively, to represent the graded sand and gravel soil type (El-Arabi 2007).

#### Model calibration

For model calibration, the results for head are compared with calculated heads at certain points in the study area. Equation (1) is used to calculate the head between the drain and the river. This equation is based on Darcy's law and can be written as follows (Abd-Elhamid et al. 2018):
(1)
where: h, h0, and hL are the water elevation between the drain and the river, the elevation of the drain, and the elevation of the river, respectively; N is groundwater vertical recharge (LT−1); K is hydraulic conductivity (LT−1); and X is distance from the drain on the west along the aquifer (L).

Figure 6 shows different parameters of the numerical equation. The head between the drain and the river is calculated using Equation (1) at different points. The calculated heads are assigned to the model at nine observation wells. Figure 7 shows the calibration results as a comparison between the head calculated by the model versus the head calculated by Equation (1). Good agreement is observed between numerical model results and calculated head.

Figure 6

Parameters of numerical equation.

Figure 6

Parameters of numerical equation.

Figure 7

Figure 7

#### Model results

The numerical model MODFLOW is applied to the current case study with the above boundary conditions to assess the extension of contaminant in the aquifer. Figure 8 shows the extension of contaminate (XT) into the aquifer which is considered the base case. For the current abstraction rate (60 m3/h), the equi-concentration line 100 mg/l extended to 100 m in the aquifer measured from the drain center. Abd-Elhamid et al. (2018) studied the effect of well depth, location and abstraction rate on extension of contaminate (XT); their study found that increasing abstraction rate caused the highest extension of contaminants from the drain into the aquifer. In this study MODFLOW is used to assess the impact of increasing abstraction rate Q on the extension of contaminate (XT) using different abstraction rates of 60, 90, 120, and 150 m3/h. The results are shown in Figure 9. The contamination extension (XT) for equi-concentration line 100 mg/l reached 100, 290, 408 and 510 measured from the drain center, respectively. Figure 10 shows the relation between contaminant extension and abstraction rate. The result showed that increasing abstraction rate increased extension of contaminates, which matches the results of Abd-Elhamid et al. (2018). The second case with abstraction rate of 90 m3/h is used as the base case where extension of contaminant (XT) reached 290 m.

Figure 8

Vertical cross-section for contaminant extension (XT) at the base case.

Figure 8

Vertical cross-section for contaminant extension (XT) at the base case.

Figure 9

Extension of contaminates (XT) at different abstraction rates: (a) 60 m3/h, (b) 90 m3/h, (c) 120 m3/h, and (d) 150 m3/h.

Figure 9

Extension of contaminates (XT) at different abstraction rates: (a) 60 m3/h, (b) 90 m3/h, (c) 120 m3/h, and (d) 150 m3/h.

Figure 10

Relation between abstraction rates and contaminates extension (XT).

Figure 10

Relation between abstraction rates and contaminates extension (XT).

## PROTECTION OF GROUNDWATER USING DIFFERENT LINING MATERIALS

MODFLOW is used to assess the protection of groundwater from leakage of polluted drains using different materials for an abstraction rate of 90 m3/h. Different lining materials are used to investigate the effect of each material on the extension of contaminate (XT) into the aquifer. These materials are selected based on hydraulic conductivity (K). Low hydraulic conductivity values are used because this has a clear effect on solute transport. Table 1 presents the hydraulic conductivity for the lining materials used. Four materials of low hydraulic conductivity have been selected for lining the drain: clay, bentonite, concrete and geomembrane. The results of these cases are shown in Figure 11.

Table 1

Hydraulic conductivity for different lining materials

ScenariosMaterialHydraulic conductivity (K) (m/d)
Base case Graded sand with clay lenses 50
Scenario 1 Clay 0.25
Scenario 2 Bentonite 0.033
Scenario 3 Geomembrane 0.0001
Scenario 4 Concrete 4 × 10−9
ScenariosMaterialHydraulic conductivity (K) (m/d)
Base case Graded sand with clay lenses 50
Scenario 1 Clay 0.25
Scenario 2 Bentonite 0.033
Scenario 3 Geomembrane 0.0001
Scenario 4 Concrete 4 × 10−9
Figure 11

Effect of different lining materials on the contaminant extension (XT): (a) clay, (b) bentonite, (c) geomembrane, and (d) concrete.

Figure 11

Effect of different lining materials on the contaminant extension (XT): (a) clay, (b) bentonite, (c) geomembrane, and (d) concrete.

Abd-Elhamid et al. (2018) showed that groundwater contamination was highly affected by the pumping schemes. However, the current study aims to protect the groundwater aquifer from contamination using different lining materials. The lining materials were selected based on hydraulic effect, availability, durability and cost. Four materials have been selected: clay, bentonite, geomembrane and concrete. The hydraulic conductivity for the clay is 0.25 m per day (m/d) (El-Arabi 2007). The hydraulic conductivity for the sand-bentonite mixture with a ratio of 20% bentonite to 80% sand is 0.033 m/d (Ojoawo & Adegbola 2012). The geomembrane permeability is less than 10−6 m/d (Lambert & Touze-Foltz 2000), and the hydraulic conductivity of concrete and mortar was 4 × 10−9 m/d and 4 × 10−10 m/d, respectively (Schneider et al. 2012).

### Drain lining with clay

In the first case, the clay material is used for lining the polluted open drain due to its low hydraulic conductivity of 0.25 m/d compared with the base case with conductivity of 50 m/d. The results showed a large decrease in the extension of contaminant (XT) into the aquifer for equi-concentration line 100 mg/l, which decreased to 165 m compared with the base case of 290 m without lining at an abstraction rate of 90 m3/s. Figure 11(a) shows the effect of using clay for drain lining on the contaminant extension (XT). The results of this case indicated that the extension of contaminant (XT) into the aquifer has decreased by 43% from 290 to 195 m due to the use of clay lining.

### Drain lining with bentonite

For the second case, mixed bentonite is used for drain lining with low hydraulic conductivity of 0.033 m/d. A sand-bentonite mixture is used with a ratio of 20% bentonite to 80% sand. Figure 11(b) shows the effect of using a sand-bentonite mixture on contaminant extension. The contamination has decreased with this type of lining and helped to prevent the spread of contamination into the aquifer. The extension of contaminant (XT) into the aquifer for equi-concentration line 100 mg/l decreased from 290 m at base case to 30 m after lining the polluted drain using bentonite. The extension of contaminant (XT) into the aquifer has decreased by 89.6% when bentonite is used for lining.

### Drain lining with geomembranes

In the third case manufactured geomembrane sheets are used for drain lining with low hydraulic conductivity of 0.0001 m/d. Figure 11(c) shows the contamination extension into the aquifer was decreased using the geomembrane for lining. The extension of contaminant (XT) into the aquifer for equi-concentration line 100 mg/l decreased from 290 m at base case to 25 m with the geomembrane lining. The extension of contaminant (XT) into the aquifer has decreased by 91.4% when geomembrane is used for lining.

### Drain lining with concrete

The fourth case represents lining of the drain using concrete with hydraulic conductivity of 4 × 10−9 m/d. Figure 11(d) shows a sharp decrease in the extension into the aquifer after the concrete lining was used. The extension of contaminant (XT) for equi-concentration line 100 mg/l was 20 m. The extension of contaminant (XT) into the aquifer has decreased by 93% when concrete lining is used.

Figure 12 shows the relation between the hydraulic conductivity of lining materials and extension of contaminate (XT) into the aquifer. The figure indicated that decreasing hydraulic conductivity of the materials used for lining led to a decrease in the extension of the contaminant. The results showed that using lining reduced the extension of contaminants by 43%, 89.6%, 91.4% and 93% for clay, bentonite, geomembrane and concrete, respectively.

Figure 12

Comparison between contaminate extension (XT) for different lining materials.

Figure 12

Comparison between contaminate extension (XT) for different lining materials.

Cost analysis is discussed in the next section to distinguish the best material that can be used for lining. The mass balance for each material used for lining is calculated using the numerical model. The salt mass for the base case reached 1,128.40 kg, but for the other lining materials reached 876.30, 205.10, 41.50 and 39.40 kg for clay, bentonite, geomembranes and concrete, respectively. Figure 13 shows the relation between the lining materials and transport mass balance (kg). The results showed that the contamination extension decreased with decreasing conductivity of lining material.

Figure 13

Comparison between salt mass balance for different lining materials.

Figure 13

Comparison between salt mass balance for different lining materials.

## COST ANALYSIS OF MATERIALS USED FOR LINING

This section presents a cost-effectiveness study for using different lining materials (clay, bentonite, geomembranes and concrete) based on the cost of lining for the drain cross-section. The numerical model results showed that the effectiveness of materials used for lining to protect groundwater from contamination can be ordered as concrete, geomembranes, bentonite and clay. Also, from previous studies the cost of geomembrane was found to be between $0.50 and$5 m−2 depending on its properties and life time; the cost of concrete is $13/m2 for 25 cm thickness, bentonite costs$6/m2 and clay $3/m2. The open drain cross-section has a wetted perimeter of 43.40 m and the lining cost of this section was$130.20, $260.60,$217 and $564.20 m−2 for clay, bentonite, geomembranes and concrete, respectively. A summary of the results for different lining materials is presented in Table 2. The cost was estimated based on the Egyptian market prices. Table 2 Results of different lining materials MaterialContaminant extension (XT) (m)Salt mass balance (kg)Cost$/m2
Base case 290 1,128.40 –
Clay 165 876.30 130.20
Bentonite 30 205.10 260.60
Geomembranes 25 41.50 217
Concrete 20 39.40 564.20
MaterialContaminant extension (XT) (m)Salt mass balance (kg)Cost \$/m2
Base case 290 1,128.40 –
Clay 165 876.30 130.20
Bentonite 30 205.10 260.60
Geomembranes 25 41.50 217
Concrete 20 39.40 564.20

Figure 14 shows the comparison between the costs of different lining materials. From the figure it can be observed that clay had the lowest cost of lining followed by geomembranes, bentonite and concrete with the highest cost. However, clay was low cost but reduced the extension of contaminant by 44% only. From this comparison geomembrane is considered the best material for lining as it reduced the extension of contaminant by 91% with a lower cost than concrete, which reduced the extension of contaminant by 93% but at double the cost of geomembranes.

Figure 14

Comparison between costs of different lining materials.

Figure 14

Comparison between costs of different lining materials.

## CONCLUSION

Groundwater is considered an important source of water in many countries. But it is highly exposed to several sources of pollution. Leakage from polluted open drains is among these sources of pollution. Investigation of contaminant extension into aquifers and protection of such aquifers is an important issue. In the current study, numerical analysis is used to investigate contamination of groundwater due to seepage from an open drain. Also, the effect of drain lining using different materials on the extension of contaminate (XT) into the aquifer is presented. The numerical model MODFLOW is applied to simulate groundwater flow and contaminant transport. Different materials with different hydraulic conductivity including clay, bentonite, geomembranes and concrete are examined. The results indicated that the extension of contaminant (XT) from open drains into the aquifer is sensitive to decreasing hydraulic conductivity of the lining material. From the comparison between different materials, concrete gave the highest reduction of contaminant extension by 93% followed by geomembranes at 91.4%, bentonite at 89.6% and clay at 43%. Considering the cost of materials, geomembrane is considered the best material for lining as it is less than 50% of the cost of concrete. This study recommends using geomembranes for lining open drains as it can prevent contaminant extension at low cost and is durable with time. Drain lining could help to protect groundwater from contamination to protect the health and life of many people. This study presented a numerical simulation of a natural phenomenon that may in the future be studied experimentally.

## REFERENCES

Abd-Elhamid
H. F.
,
Abdelaal
G. M.
,
Abd-Elaty
I.
&
Said
A. M.
2018
Evaluation of groundwater vulnerability to seepage from open drains considering different pumping schemes in unconfined aquifers
. In:
Twenty-first International Water Technology Conference, IWTC21
,
28–29 June 2018
,
Ismailia
, pp.
358
364
.
Ahmed
M. A.
,
Samie
S. G. A.
&
El-Maghrabi
H. M.
2011
Recharge and contamination sources of shallow and deep groundwater of pleistocene aquifer in El-Sadat industrial city: isotope and hydrochemical approaches
.
Environmental Earth Sciences
62
(
4
),
751
768
.
https://doi.org/10.1007/s12665-010-0563-x
.
Ali
R.
,
Hatton
T.
,
George
R. J.
,
Byrne
J.
&
Hodgson
G.
2004
Evaluation of the impacts of deep drains on groundwater levels in the wheatbelt of Western Australia
.
Australian Journal of Agricultural Research
55
,
1159
1171
.
doi:10.1071/AR04068
.
Arnous
M. O.
&
El-Rayes
A. E.
2013
An integrated GIS and hydrochemical approach to assess groundwater contamination in West Ismailia area, Egypt
.
Arabian Journal of Geosciences
6
(
8
),
2829
2842
.
doi:10.1007/s12517-012-0555-0
.
Arumí
J. L.
,
Rivera
D.
,
Holzapfel
E. A.
,
Boochs
P. W.
,
Billib
M. H. A.
&
Fernald
A.
2009
Effect of the irrigation canal network on surface and groundwater interactions in the lower valley of the Cachapoal River, Chile
.
Chilean Journal of Agricultural Research
69
(
1
),
12
20
.
doi:10.4067/S0718-58392009000100002
.
Blanco
M.
,
Castillo
F.
,
Soriano
J.
,
Noval
A. M.
,
Touze-Foltz
N.
,
L.
,
Rico
G.
&
Aguiar
E.
2012
Comparative study of three different kinds of geomembranes (PVC-P, HDPE, EPDM) used in the waterproofing of reservoirs
. In:
Paper Presented at Eurogeo 5
,
Valencia, Spain
,
2
, pp.
46
54
.
El-Arabi
M.
2007
Environmental Impact of New Settlements in Groundwater in A Region in the Nile Delta
.
MSc Thesis
,
Faculty of Engineering, Zagazig University
,
Egypt
.
Ghasemlounia
R.
&
Herfeh
N. S.
2017
Study on groundwater quality using geographic information system (GIS), case study: Ardabil, Iran
.
Civil Engineering Journal
3
(
9
),
doi:http://dx.doi.org/10.21859/cej-030914
Gomaah
M.
,
Meixner
T.
,
Korany
E. A.
,
Garamoon
H.
&
Gomaa
M. A.
2016
Identifying the sources and geochemical evolution of groundwater using stable isotopes and hydrogeochemistry in the Quaternary aquifer in the area between Ismailia and El Kassara canals, Northeastern Egypt
.
Arabian Journal of Geosciences
9
,
437
.
doi:https://doi.org/10.1007/s12517-016-2444-4
.
Hosseini
M.
&
Saremi
A.
2018
Assessment and estimating groundwater vulnerability to pollution using a modified DRASTIC and GODS models (case study: Malayer Plain of Iran)
.
Civil Engineering Journal
4
(
2
),
433
.
doi:10.28991/cej-0309103
.
Javandel
I.
,
Doughty
C.
&
Tsang
C.-F.
1984
Groundwater Transport: Handbook of Mathematical Models
.
American Geophysical Union, Water Resources Monograph
.
doi:10.1029/WM010
.
Khair
A.
,
Nalluri
C.
&
Kilkenny
W. M.
1991
Soil-cement tiles for lining irrigation canals
.
Irrigation and Drainage Systems
5
(
2
),
151
163
.
doi:https://doi.org/10.1007/BF01140519
.
Kyere
V. N.
,
Greve
K.
,
Atiemo
S. M.
,
Amoako
D.
,
Aboh
I. K.
&
Cheabu
B. S.
2018
Contamination and health risk assessment of exposure to heavy metals in soils from informal e-waste recycling site in Ghana
.
Emerging Science Journal
2
(
6
),
428
436
.
doi:10.28991/esj-2018-01162
.
Lambert
S.
&
Touze-Foltz
N.
2000
A test for measuring the permeability of geomembranes
. In:
Proceedings of Eurogeo 2, Second European Conference on Geosynthetics
.
Li
J.
,
Xi
B.
,
Cai
W.
,
Yang
Y.
,
Jia
Y.
,
Li
X.
,
Lv
Y.
,
Lv
N.
,
Huan
H.
&
Yang
J.
2017
Identification of dominating factors affecting vadose zone vulnerability by a simulation method
.
Scientific Reports
7
,
45955
.
doi:10.1038/srep45955
.
McDonald
M. G.
&
Harbaugh
A. W.
1988
A modular three-dimensional finite-difference ground-water flow model
.
Techniques of Water-Resources Investigations
06-A1. doi:10.3133/twri06A1
.
Meer
S. R.
&
Benson
C. H.
2007
Hydraulic conductivity of geosynthetic clay liners exhumed from landfill final covers
.
Journal of Geotechnical and Geoenvironmental Engineering
133
(
5
),
550
563
.
doi:10.1061/(ASCE)1090-0241(2007)133:5(550)
.
Ojoawo
S. O.
&
A. A.
2012
The system dynamics modeling method in application of geo-membranes as landfill liners
.
American International Journal of Contemporary Research
2
(
10
),
138
144
.
Schneider
S.
,
Mallants
D.
&
Jacques
D.
2012
Determining hydraulic properties of concrete and mortar by inverse modelling
.
Material Research Society Proceedings
1475
,
367
372
.
doi:10.1557/opl.2012.601
.
Stark
T. D.
&
Hynes
J. M.
2009
Geomembranes for canal lining
. In:
Paper Presented at Geosynthetics 2009
,
February 25–27, 2009
, pp.
54
64
.
Tahershamsi
A.
,
Feizi
A.
&
Molaei
S.
2018
Modeling groundwater surface by MODFLOW math code and geostatistical method
.
Civil Engineering Journal
4
(
4
),
812
.
doi:10.28991/cej-0309135
.