Predicting self-healing ratio of GCL with a damage hole

Geotextiles and Geomembranes xxx (2016) 1e9

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Predicting self-healing ratio of GCL with a damage hole Jin-Chun Chai a, *, Kartika Sari a, Shui-long Shen b, **, Yuanqiang Cai c a

Graduate School of Science and Engineering, Saga University, Japan Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China c College of Civil Engineering and Architecture, Wenzhou University, Wenzhou University Town, Zhejiang, China b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 8 July 2015 Received in revised form 29 March 2016 Accepted 15 May 2016 Available online xxx

Self-healing ratio of geosynthetic clay liner (GCL) with a damage hole has been investigated and a prediction method has been proposed. Laboratory leakage rate/self-healing capacity tests of GCLs with a damage hole were conducted and the test results indicate that the amount of bentonite entered the damage hole and its water content are a function of the type of liquid used, diameter of the damage hole and overburden pressure on the GCL sample. The proposed prediction method uses basic physical properties of a GCL, and the liquid limit of the bentonite in the GCL with the corresponding liquid. Good agreement has been obtained between the predicted and laboratory measured self-healing ratio (healed area divided by the total damage area). It is suggested that the method can be used to evaluate the suitability of a GCL to a particular site. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Geosynthetic clay liner Self-healing capacity Bentonite Free swelling index

1. Introduction Geosynthetic clay liner (GCL) has been widely used as a liner for preventing leachate migration in landfill construction (e.g., Bouazza, 2002; Rowe, 2005; Guyonnet et al., 2009; Koerner, 2012; Rowe, 2013) and other containment facilities (Lupo and Morrison, 2007; Rowe et al., 2007; Bouazza and Gates, 2014). This is because of its low permeability and high self-healing capacity. In a field construction, due to machinery operation on the site, angular stones and other sharp objects exist on the site, and not well constructed connections between panels of GCL or other liner materials, there may be defects in the liner system in the field (Fox et al., 1998; Buckley et al., 2010). Also, for GCLs placed in the field, before covering it by soils or wastes, daily temperature variation can cause erosion/migration of bentonite in the GCLs and form spots without bentonite (Rowe and Orsini, 2003; Rowe et al., 2014; Take et al., 2015). Bentonite, a part of GCL, has a high expansion capacity when hydrated. Therefore for a GCL liner, even if some defects exist, due to the expansion of the bentonite when it meets liquid certain defects can be self-healed. This is one of the advantage of GCL over

* Corresponding author. ** Corresponding author. Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China. E-mail addresses: [email protected] (J.-C. Chai), [email protected] (S.-l. Shen), [email protected] (Y. Cai).

other liquid proof liners. While the amount of volumetric expansion of bentonite is strongly influenced by the type of liquid to hydrate the GCL and overburden pressure applied on the GCL. There are several publications about self-healing capacities of GCLs (Takahashi and Kondo, 1999; Mazzieri and Pasqualini, 2000; Egloffstein, 2001; Babu et al., 2001; Sari and Chai, 2013), but there is no method proposed for predicting the self-healing capacity of a GCL. In engineering practice this kind of prediction method is needed because the designers need to judge for a given condition, the amount of self-healing capacity of a GCL can be expected, which may alter the design. In this paper, based on the results of a series of laboratory tests on the leakage rate/self-healing capacity of GCL samples with a damage hole, a method for predicting the self-healing capacity of GCL has been proposed. Basic considerations and prediction method are presented first, followed by the comparison of the predicted and the measured self-healing ratios of the GCLs tested. Finally, the usefulness of the proposed method is discussed. 2. Methodology For a given GCL with a known size of damage, properties of the leachate and overburden pressure (p0 ), it is considered that if (a) the amount (mass) of bentonite (mb) entered the damage hole; (b) water content (w) of the bentonite in the damage hole; and (c) the thickness (t) of the hydrated GCL can be predicted, the self-healing

http://dx.doi.org/10.1016/j.geotexmem.2016.05.010 0266-1144/© 2016 Elsevier Ltd. All rights reserved.

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Notations A A1 Cc Cs D D0 e0 e0 G k m0 mb

area of a damage hole healed area of a damage hole compression index swelling index diameter of the damage hole a constant (¼ 50 mm) initial void ratio elementary electric charge (¼1.602  1019 C) specific gravity of the bentonite particles Boltzmann's constant (¼1.38  1023 J/K) a constant (mass) mass of the bentonite entered the damage hole on a GCL molar concentration of ions in pore fluid over burden pressure a reference pressure atmospheric pressure specific surface area thickness of a GCL absolute temperature in Kelvin

n p0 p0 0 pa S t T

ratio (a ¼ A1/A; A1 is the area healed by the bentonite, and A is the total area of a damage hole) can be calculated as:




a ¼ min 1; b

v1 v0

v1 ¼ ð1 þ wGÞ

v0 ¼

pD2 4

 (1)

mb Grw

(2)

t

(3)

where v1 ¼ the volume of the hydrated bentonite entered the damage hole, v0 ¼ the volume of the damage hole, b ¼ a lager than 1 multiple, G ¼ specific gravity of the bentonite particles, rw ¼ density of water, and D ¼ diameter of the damage hole. As illustrated in Fig. 1(a), the ratio of v1/v0 represents an idea case that the hydrated bentonite filled the whole thickness of a part of the hole. While in a realistic case (Fig. 1(b)), the thickness of the bentonite in part of the hole may be less than the total thickness of the hydrated GCL. In practice, it is generally considered that the part of the hole with bentonite coverage is “healed”, i.e. the healing ratio is defined as a ratio of area but not volume, and therefore in Eq. (1), b > 1.

GCL

Damage hole D

GCL

Damage hole D

Bentonite

(a) Idea case

Bentonite

( b ) R e a li s ti c c a s e

Fig. 1. Illustration of healed areas.

tb tb0 tbi tg v0 v1 w wl wl0 wp

a b dt rw n ε

k

initial thickness of bentonite layer in a GCL a reference thickness (¼ 4 mm) initial thickness of bentonite in a GCL thickness of GM in case of GM-GCL, and the thickness of geotextile in case of GT-GCL volume of the damage hole on a GCL volume of the hydrated bentonite entered the damage hole on a GCL water content liquid limit liquid limit of bentonite using distilled water plasticity limit self-healing ratio a larger than unit dimensionless multiple a reduction in thickness due to bentonite entered into the voids of geotextile density of water valence of cation dielectric constant of pore fluid double layer parameter (1/k ¼ thickness of the double layer)

Then, the key issue is how to predict the values of mb, w and t. Based on the laboratory test results reported by Sari and Chai (2013) and Chai et al. (2013), the main factors influencing these three quantities are (1) type of liquid; (2) overburden pressure (p0 ); and (3) the size of a damage hole. Further it has been shown that the effect of type of liquid can be quantified by liquid limit (wl) and/ or free swelling index (FSI) of the bentonite with a corresponding liquid. Referring to these findings, procedures adopted for establishing prediction method are: (1) conducting leakage rate/selfhealing capacity test using GCL samples with a damage hole, and after the test, measuring the amount of bentonite entered the hole, its water content and the healed area of the damage hole (A1); (2) based on the test results, proposing methods for predicting the values of mb, w and t using basic parameters of the bentonite and the liquid considered; and (3) using the measured values of a, backfitting a suitable value of b.

3. Materials used and their physical properties 3.1. GCLs A geomembrane (GMB) supported GM-GCL and a geotextile (GTX) encased GT-GCL were used for leakage rate/self-healing capacity tests. The same Naþ type bentonite mined from Wyoming, USA was used in both the GM-GCL and the GT-GCL. The GM-GCL tested consisted of a 4 mm-thick (under zero confining pressure) layer of granular bentonite that was glued onto a 0.5 mm thick high density polyethyelene geomembrane (HDPE). The GT-GCL tested consisted of granular bentonite powder encased in geotextiles (nonwoven as “cover” and geotextiles with a slit film woven layer as “carrier”). These geotextiles were connected by thermally treated needle-punched fibers at pitches of 3 mm  4.5 mm. The thicknesses of the GT-GCL as well as the geotextile alone (by removing the bentonite inside) were measured using samples of 200 mm  200 mm, and the results are given in Table 1. Under air dry condition, the weights of the GM-GCL and GT-GCL were about 53 and 49 N/m2, respectively, and the water content of the bentonite in the GCLs was about 10% (Sari and Chai, 2013).

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600

Table 1 Thicknesses of GT-GCL used. 0

Overburden pressure, p (kPa)

GT-GCL, t (mm) GT alone, tg (mm)

0

50

100

0 (after unload)

8.12 2.81

5.74 1.46

5.15 0.80

7.42 2.81

3

Assuming the density of the HDPE GMB in GM-GCL is 950 kg/m , the weight per unit area of 4.65 N/m2 can be estimated. And then the weight per unit area of bentonite in GM-GCL will be about 48.35 N/m2. For the GT-GCL, the weight per unit area of the geotextiles is about 4.6 N/m2, and the weight per unit area of the bentonite will be about 44.4 N/m2. All GM-GCL samples and all GTGCL samples were cut from the corresponding same roll respectively.

Liquid limit, wl (%)

Material

3

L2 L1

500 400 300 200

L3 L4

100 0 0

10 20 30 Free swelling index, FSI (ml/2g)

40

Fig. 2. Relationship between free swelling index (FSI) and liquid limit (wl).

3.2. Bentonite and its physical properties Based on the information given by the manufacturer, the main chemical compositions of the bentonite were SiO2 (66.32%) and Al2O3 (21.16%). The cation exchange capacity (B) measured by atomic absorption spectrophotometry is 77 meq/100 g (77 cmol/ kg). Four (4) types of liquid used were: (1) a drinkable tap water; (2) 1% NaCl solution; (3) 10% ethanol solution; and (4) 1.1% (0.1 mol/l) CaCl2 solution. For each liquid, the liquid limit (wl), plasticity limit (wp), free swelling index (FSI) of the bentonite, and PH value and electric conductivity (EC) of the liquid phase from the bentonitewater mixture with a solid/liquid ratio of 1:10 were measured and the results are summarized in Table 2. The FSI tests were conducted according to ASTM D 5890-11 (2011). Fig. 2 plots the relationship between wl and FSI. Although there are certain scatters, there is a clear generally trend that wl and FSI are almost linearly related. 3.3. Relationship between thickness of electrical double layer and wl In studying the swelling properties of a bentonite, the theory of diffusive electric double layer (DDL) (Bolt, 1956; Olphen, 1963; Mitchell, 1993) is often used. The relationship between the thickness of DDL and wl is investigated to provide a theoretical base for selecting a physical parameter to be used for predicting self-healing capacity of GCLs. According to the theory of DDL, the double layer parameter, k (1/k ¼ thickness of the double layer) can be calculated as follows:

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ðe0 Þ2 n2 n k¼ εkT

(4)

ε ¼ dielectric constant of pore fluid (for water, ¼ 7.083  1010 C2J1M1, and for ethanol, ¼ 2.15  1010 C2J1M1), k ¼ Boltzmann's constant (¼1.38  1023 J/K), and T ¼ absolute temperature in Kelvin. Although the concentration of cations in the drinkable tap water is not measured, Naþ in the liquid phase of the water-bentonite mixture with a solid/liquid ratio of 1:10 was measured as 590 mg/l. Referring to this value, it is assumed that Naþ of 590 mg/l (0.026 mol/l) was existed in all four types of the liquid tested. The dielectric constant for the tap water, the NaCl and CaCl2 solutions is the same as for pure water and for the ethanol solution, a weighted average value of pure water and ethanol is adopted. Values of total molar concentration of cations estimated by weighted average valance method (Sridharan and Jayadeva, 1982) and dielectric constant are listed in Table 3. Using Eq. (4), the calculated values of 1/k are listed in Table 3 also. The relationships between values of 1/k and wl is plotted in Fig. 3. Generally, close to linear relationships can be observed. The results in Fig. 3 indicate that wl can be used as an index to represent the effect of the type of liquid on the swelling behavior of a bentonite. 4. Consolidation and leakage rate/self-healing capacity tests 4.1. Consolidation test Since the initial water content of the bentonite in the GCL was about 10%, normally, during the process of hydration, the bentonite will swell. Therefore, the swelling index (Cs) is an important parameter for predicting the thickness of hydrated GCL. To investigate the compression and swelling indexes of the bentonite, odometer tests using hydrated bentonite by the four (4) types of the liquid (Table 2) were conducted. The test procedures are as followings.

where n ¼ valence of cation, e0 ¼ elementary electric charge (¼1.602  1019 C), n ¼ molar concentration of ions in pore fluid (mole/m3 multiplied by Avogadro's number NA ¼ 6.023  1023),

(1) Making bentonite slurry. The bentonite slurry with a water content of about 1.1 times of its liquid limit was made by

Table 2 Some chemical-physical and mechanical properties. Symbol

Fluid type

PH

EC (mS/cm)

Liquid limit, wl (%)

Plastic limit, wp (%)

FSI (ml/2 g)

Compression index Cc

Swelling index Cs

L1 L2 L3 L4 L5

Tap water 10% ethanol solution 1% NaCl solution 1.1% CaCl2 solution Distilled water

7.02 7.46 7.24 7.60

105 85 17,600 199

537 560 235 165

45.8 67.4 46.3

30.0 30.0 16.5 9.0 30

5.22 6.18 1.95 1.66

1.41 1.09 0.32 0.25

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Table 3 Some properties of the fluids and calculated thickness of DDL. Parameters

Liquid

n (mole/l)

n

10

2 1

1

ε (10 C J m 1/k (Angstrom)

L2

L3

L4

Tap water

10% ethanol solution

1% NaCl solution

1.1% CaCl2 solution

0.026a 1 7.083 18.9

0.026 1 6.59 18.2

0.197 1 7.083 6.9

0.126 1.79b 7.083 4.8

15

30 Void ratio, e

Double layer thickness, 1/k (Angstrom)

Assume 590 mg/l of Naþ (0.026 mol/l) in the bentonite and the tap water mixture. Weighted average of Naþ (0.026 mol/l) and Ca2þ (0.1 mol/l)

25 20

L1 L2

15

5 0

0

L4

Tap water Ethanol solution

10

5

0 1

10 L3

10 100 1000 10000 Consolidation pressure, p' (kPa) (a) Tap water and ethanol solution

200

400

600

15

800

Liquid limit, w l (%) Fig. 3. Relationship between the thickness of defuse double layer and wl.

adding the amount of corresponding liquid into the bentonite and keeping the mixture in a container wrapped by a plastic sheet and cured for one week. (2) Pre-consolidation. The slurry was put into a consolidation container of 60 mm in diameter and 60 mm in height (20 mm consolidation ring plus 40 mm height of a collar) with an initial thickness of about 35 mm, and consolidated under 10 kPa pressure for 3 days. Next, 20 mm thick specimen was cut from the pre-consolidated sample for further consolidation test. (3) The incremental loading consolidation tests were conducted according to ASTM D2435/D2435M-11 (2011). The test results are given in Fig. 4(a) and (b) for using the tap water and ethanol solution, and the NaCl and CaCl2 solutions respectively. The resulting values of compression and swelling indexes, Cc and Cs, are listed in Table 2 also. 4.2. Leakage rate/self-healing capacity test Leakage rate/self-healing capacity tests were conducted using both a constant head and a falling head devices to providing a cross check of the reliability of the test results and increasing the cases tested. The GCL samples used had a diameter of 150 mm and each

Void ratio, e

a b

)

L1

10

NaCl solution CaCl2 solution

5

0 1

10 100 1000 10000 Consolidation pressure, p' (kPa) (b) NaCl and CaCl2 solutions Fig. 4. e-log(p0 ) relationships of odometer test result.

sample had a damage hole in the center with different size. The hole penetrated the whole thickness of the GCL sample. The details of the devices and test procedures have been reported by Sari and Chai (2013). Both the GM-GCL and GT-GCL were tested. For the GM-GCL all 4 types of liquid listed in Table 2 were used, while for GT-GCL, only the tap water was used. For each test, it was continued until the leakage rate was steady, and normally it took more than 3 weeks. After the leakage rate test, (a) the healed area (A1) of the damage hole, and (b) the amount of bentonite (mb) entered the hole and its water content (w) were measured. In the following section, the test

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5. Test results and prediction methods 5.1. Amount of bentonite entered the damage hole The amount of bentonite entered a damage hole is influenced by the size of the damage hole (D), overburden pressure (p0 ) and the type of liquid used. (1) Effect of D The test results using GT-GCL, the tap water and under p0 ¼ 200 kPa are shown in Fig. 5. There is a tendency of the amount of the bentonite entered the hole increased with the increase of the diameter of the hole. However, the value of mb was slightly decreased for D increased from 30 mm to 40 mm. Although the exact reason is not clear, the small difference may be within the accuracy limit of the test. (2) Effect of the type of the liquid Fig. 6 shows the results of both the GM-GCL and GT-GCL under p0 ¼ 0, and D ¼ 40 mm. It can be seen that the amount of the bentonite entered the hole is affected by the type of the liquid significantly. Generally, the liquid has a higher value of wl had more bentonite entered the hole. (3) Effect of p0 p0

It is considered that has two effects on the amount of the bentonite entered a damage hole. One is squeezing the hydrated bentonite into the hole, and another is restricting the amount of swelling of the bentonite. The former tends to increase and the later tends to reduce mb. Fig. 7 shows the test results of GM-GCL and GTGCL samples using the tap water. There is a tendency of decreasing of mb with the increase of p0 . For cases of p0 > 50 kPa, the data are scattered and further investigation may be needed.

5

D = 40 mm p' = 0 kPa

3

GM-GCL

2

GT-GCL

1 0

Tap water

Ethanol solution

CaCl2 solution

NaCl solution

Fig. 6. Effect of the type of liquid on the amount of bentonite entered the hole.

Dry weight of bentonite, mb (g)

results and prediction methods will be presented in terms of mb, w and thickness (t) of the GCL samples.

Dry weight of bentonite, mb (g)

J.-C. Chai et al. / Geotextiles and Geomembranes xxx (2016) 1e9

5 4

Tap Water D = 40 mm, GM-GCL D = 50 mm, GT-GCL

3 2 1 0 0

50 100 150 200 Overburden pressure, p' (kPa)

Fig. 7. Effect of the overburden pressure on the amount of bentonite entered the hole.

(4) Prediction method

Dry weight of bentonite, mb (g)

The test results presented above clearly show that mb is a function of D, p0 and the type of liquid. Although these three variables may influence each other, for simplicity it is assume that they are

3

GT-GCL Tap water p' = 200 kPa

independent variables. It is considered that wl can be used to evaluate the effect of the type of liquid. Firstly, it is assumed that mb is proportional to the perimeter of a damage hole (pD). Then by observing the results in Figs. 6 and 7, and by try and error it has been found that with the following power function, the test results of mb can be well simulated.



0 0:1 ! D tb wl 0:55 p mb ¼ m0 1  0:2 D0 tb0 wl0 2$pa

2

ðp0  200 kPaÞ (5)

1

0 0

10 20 30 40 50 Diameter of damage hole, D (mm)

Fig. 5. Variation of the amount of bentonite entered the hole.

60

where D0 ¼ a constant (¼ 50 mm), m0 ¼ a constant, and with the test results in Fig. 6, m0 ¼ 3.0 g has been evaluated, wl0 ¼ liquid limit of bentonite using distilled water, pa ¼ atmospheric pressure, tb ¼ initial thickness of bentonite layer in GCL, and tb0 ¼ 4 mm (a reference thickness). For GM-GCL, the value of tb can be evaluated as the thickness under zero confining pressure. While for GT-GCL, it is suggested that the thickness of the bentonite in it can be evaluated by assuming a void ratio of 1.43, which is a value estimated from the bentonite on GM-GCL tested in this study, and the thickness of the geotextiles to be measured under 100 kPa confining pressure. Considering that hydraulic bentonite may enter into the

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voids of geotextiles, the value of tb will be the sum of the thickness of the bentonite and the geotextiles, and minus a value of dt (<0.5 mm).

5.2. Water content of the bentonite entered a damaged hole It is considered that the same influencing factors for mb will influence the value of w of the bentonite entered a damage hole. (1) Effect of the diameter of a hole

600

Water content, w (%)

6

Fig. 10 shows variation of the value of w with p0 . Generally, the value of w reduced with the increase of p0 , especially for p0 < 100 kPa, the reduction is obvious. It is worth to mention that the pressure on the bentonite inside a damage hole is always less than the applied average value of p0 .

Water content, w (%)

(3) Effect of p0

Firstly, it is considered that the effect of the type of liquid can be evaluated using wl of the bentonite with the corresponding liquid. Then observing the results in Figs. 8 and 10, and by try and error it has been found that the following simple power function can simulate the test results well.

D D0

Water content, w (%)

400

ðp0  200 kPaÞ

(6)

200 100 0 0

Ethanol solution

NaCl CaCl2 solution solution

GT-GCL D = 40 mm p' = 0 kPa

500 400 300 200 100 Tap water

Ethanol solution

NaCl CaCl2 solution solution

Fig. 9. Effect of the type of liquid on the water content of bentonite.

5.3. Thickness of GCL

Tap Water GM-GCL p' = 200 kPa

300

Tap Water

(b) GT-GCL

10 20 30 40 Diameter of damage hole, D (mm)

Fig. 8. Effect of D on the water content of the bentonite.

50

During the leakage rate/self-healing capacity tests, only for part of the tests, the final thicknesses of the GCL samples were measured. To obtain consistent results, the variations of the thickness of the

800

Water content, w (%)

w ¼ wl

100

0

(4) Prediction methods


0 0:05 ! p 1  0:25 2$pa

200

600

Fig. 9 shows the test results of D ¼ 40 mm and p0 ¼ 0. For both GM-GCL (Fig. 9(a)) and GT-GCL (Fig. 9(b)), the type of liquid had a significant effect on the value of w.

0:35

300

(a) GM-GCL

(2) Effect of the type of liquid




400

0

For a unit value of mb, the larger the value of D, the more space for the bentonite to swell. Fig. 8 shows the results of GM-GCL samples using the tap water under p0 ¼ 200 kPa. Generally, w increased with D.

GM-GCL D = 40 mm p' = 0 kPa

500

Tap water GM-GCL, D = 40 mm GT-GCL, D = 50 mm

600 400 200 0 0

50

100

150

200

Overburden pressure, p' (kPa) Fig. 10. Effect of overburden pressure on the water content of bentonite.

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GM-GCL with p0 were investigated using the constant head leachate rate measurement device. For a 150 mm in diameter GM-GCL sample, a full penetration hole of 40 mm was made at the center. A head difference of 320 mm above and below the GM-GCL sample was applied. Started with p0 ¼ 0, and the final pressure was 200 kPa. The duration under each pressure was 1 week. It has been confirmed that for both the GM-GCL and GT-GCL, when submerged into water, after elapsed time more than 1 week, the water content of the bentonite was almost steady. For the four (4) types of the liquid tested, the results are showed in Fig. 11. The thickness including 0.5 mm thick GMB layer. It can be observed that under 200 kPa pressure, the effect of the type of liquid became small. For most field applications, hydration in the field will induce swelling of the GCL used, and the initial condition of a GCL can be considered being in an “over consolidated” state. The thickness (t) of the hydrated GCL under a confining pressure of p0 , can be calculated by the following equation:

Thickness of GM-GCL, t (mm)

 t ¼ tg þ tbi 1 

12 10 8


0  Cs p log 0 1 þ e0 p0

(7)

Tap water Measured Calculated Ethanol solution Measured Calculated

6 4 2 0

Initial thickness 50 100 150 200 Overburden pressure, p' (kPa)

250

Thickness of GM-GCL, t (mm)

(a) Tap water and ethanol solution

12 10 8

NaCl solution Measured Calculated CaCl2 solution Measured Calculated

7

where tg ¼ thickness of GMB in case of GM-GCL, and the thickness of geotextile in case of GT-GCL, tbi ¼ initial thickness of the bentonite in a GCL, e0 ¼ initial void ratio of the bentonite, and p0 0 ¼ a reference pressure. For the GM-GCL tested, assuming an initial water content of the bentonite of 10%, and the specific gravity of the bentonite of 2.7, a value of e0 of about 1.43 can be evaluated. Based on the consolidation test results, it has been judged that on swelling lines (Fig. 4), e0 ¼ 1.43 corresponding to a consolidation pressure (p0) of about 1000 kPa. Using tg ¼ 0.5 mm, tbi ¼ 4.0 mm and Cs values in Table 2, the calculated variations of GCL thickness with p0 are also included in Fig. 11. For the tap water and ethanol solution, under higher p0 , the calculated thicknesses are larger than the measured data, but for the NaCl and CaCl2 solutions, generally the calculated values are smaller than the measured data. A possible reason considered is that the cation concentrations in the sample for the odometer test and in the GCL sample for compression test were slightly different. Although the solutions added were the same, since the bentonite had an initial water content of about 10% and the amount of solutions initially added to make the odometer specimen was more than that to the GCL sample. It is possible that the resulting concentrations of cation in the pore water of the odometer samples were slightly different with that in the GCL samples. In case of NaCl and CaCl2 solutions, Naþ or Caþþ in the pore water of the odometer sample might be higher, which can reduce the thickness of diffusive double layer and result in a smaller swelling index. It is considered that further investigation is required for this issue. While at this stage, it is considered that the calculated values are acceptable for estimating the self-healing ratio of the GCLs. 5.4. Summary of the prediction method (1) Parameters needed (a) Diameter (D) of a damage hole. (b) Initial thickness (tb) and void ratio (e0) (or mass per unit area and moisture content) of the bentonite layer in a GCL. (c) Thickness of geomembrane (GM-GCL) or geotextile (GTGCL) (tg). (d) Liquid limit (wl) and swelling index (Cs) of the bentonite with the corresponding liquid; and liquid limit (wl0) with distilled water. (2) Calculation procedure (a) Mass of the bentonite entered a hole (mb) by Eq. (5). (b) Water content of the bentonite (w) entered the hole by Eq. (6). (c) Thickness of hydrated GCL (t) by Eq. (7). (d) Finally the self-healing ratio (a) by Eqs. (1)e(3). 6. Predicted and measured self-healing ratios

6

By comparing the measured and predicted self-healing ratios,

b ¼ 1.1 has been suggested (Eq. (1)). In Eq. (5), the value of wl0 is

4 2 0

Initial thickness 50 100 150 200 Overburden pressure, p' (kPa)

250

(b) NaCl and CaCl2 solutions Fig. 11. Variations of the thickness of GM-GCL with over burden pressure.

needed. Unfortunately it was not measured using the same batch of the bentonite. However, the value of FSI using distilled water was measured and it was the same as using the tap water (Table 2), and therefore, wl0 ¼ 537% is used in calculation. 6.1. GM-GCL The available measured and predicted self-healing ratios (a) are compared in terms of the effect of p0 , D of the damage hole and the type of the liquid used.

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(1) Effect of p0 . Since more test data for D ¼ 40 mm are available, they are compared with predicted values in Fig. 12. Although there are scatters, generally predictions agree reasonably well with the measured data. For using the CaCl2 solution and D ¼ 10 mm, a set of test data are available and they are compared with the predicted values in Fig. 13. In Fig. 13, it can be seen that for p0 < 100 kPa, self-healing ratios are overpredicted. The reason is that using consolidation test results, the thickness of GM-GCL with the CaCl2 solution is under-estimated (Fig. 11(b)). (2) Effect of D. A series of tests using the CaCl2 solution under p0 ¼ 200 kPa and different D were conducted and the comparison of the measured and predicted values of a is shown in Fig. 14. For D larger than about 20 mm, self-healing ratios have been under-predicted, but generally a good agreement has been obtained. (3) Effect of the type of liquid. For D ¼ 30 mm and p0 ¼ 200 kPa, the measured and predicted values of a are compared in Fig. 15. Again, generally a good agreement has been obtained.

Fig. 13. Effect of p0 on a (CaCl2 solution, D ¼ 10 mm).

6.2. GT-GCL The GT-GCL tested had less bentonite per unit area than that of the GM-GCL tested. Considering an initial condition of e0 ¼ 1.43, and the reference pressure p0 0 ¼ 1000 kPa, with the weight per unit area of 44.4 N/m2 and initial water content of 10%, an initial thickness of tbi ¼ 3.7 mm can be evaluated. As for the value of tg, referring the value in Table 1 under 100 kPa confinement, and considering that the hydrated bentonite can enter the voids of the geotextile, an effective thickness of the geotextile of tg ¼ 0.5 mm is assumed. A series of tests of different p0 using the tap water and under D ¼ 50 mm were conducted, and the measured and predicted values of a are compared in Fig. 16. In this case, the comparison is fair. The test results do not show obvious effect of p0 on a, but the prediction shows a increase with p0 . Fig. 14. Diameter of damage hole versus a value (CaCl2 solution).

6.3. Discussion The above comparison clearly indicates that although there are discrepancies, generally the proposed method is capable of predicting self-healing ratio of both GM-GCL and GT-GCL with known values of D and p0 . The proposed method is simple and only uses

basic physical properties of GCL, the liquid limit (wl) and swelling index (Cs) of the bentonite in the GCL with the corresponding liquid. It is suggested that the method can be used for estimating the possible size of a damage hole which can be self-healed in a particular site.

Fig. 12. Effect of p0 on a (D ¼ 40 mm).

Fig. 15. Measured and predicted values of a for different liquid used.

Please cite this article in press as: Chai, J.-C., et al., Predicting self-healing ratio of GCL with a damage hole, Geotextiles and Geomembranes (2016), http://dx.doi.org/10.1016/j.geotexmem.2016.05.010

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encased GT-GCL. It is suggested that the method can be used to evaluate the suitability of a GCL to a particular site. Acknowledgement This research work has been partially funded by National Natural Science Foundation of China (NSFC) with a grant No. 51578333. References

Fig. 16. Measured and predicted values of a of GT-GCL.

7. Conclusions Self-healing ratio of geosynthetic clay liners (GCLs) with a fully penetrated damage hole has been investigated by laboratory leakage rare/self-healing capacity tests, and based on the test results a method for predicting self-healing ratio (a) (healed area divided by the total damage area) has been proposed. (1) Laboratory leakage rate/self-healing capacity tests. The tests were conducted using GCL samples with a damage hole and 4 types of liquid, namely tap water, 10.0% ethanol solution, 1.0% NaCl solution and 1.1% CaCl2 solution. The test results indicate that the amount of the bentonite entered the damage hole and its water content are a function of the liquid used, diameter (D) of the damage hole and the overburden pressure (p0 ) on the GCL sample. The effect of the type of the liquid can be evaluated by the liquid limit of the bentonite with the corresponding liquid. p0 can squeeze hydrated bentonite into the hole, but it will hinder the expansion of the bentonite in the GCL. For the conditions tested, p0 reduced the amount of the bentonite entered the hole as well as its water content. (2) Proposed prediction method. For a given size of a damage hole and the value of p0 , the prediction method uses basic physical properties of a GCL, and the liquid limit of the bentonite in the GCL with corresponding liquid. Explicit empirical equations for predicting the amount of bentonite entered a damage hole, its water content and the thickness of hydrated GCL, and finally for calculating the value of a have been established. (3) Comparison between the measured and predicted values of a. Good agreement has been obtained between predicted and laboratory measured values of a for both a geomembrane (GMB) supported GM-GCL and a geotextile (GTX)

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Please cite this article in press as: Chai, J.-C., et al., Predicting self-healing ratio of GCL with a damage hole, Geotextiles and Geomembranes (2016), http://dx.doi.org/10.1016/j.geotexmem.2016.05.010