Technical Paper by JP Giroud, KL Soderman and K. Badu-Tweneboah

Technical Paper by J.P. Giroud, K.L. Soderman and 

K. Badu-Tweneboah 

OPTIMAL CONFIGURATION OF A DOUBLE 

LINER SYSTEM INCLUDING A GEOMEMBRANE 

LINER AND A COMPOSITE LINER 

ABSTRACT: A number of landfills are designed with a double liner system that includes 

a geomembrane liner and a composite liner. The design engineer must select which of these 

two liners should be the primary liner. A comparative study is presented in this paper to help 

determine which configuration is preferable. The comparative study consists of comparing 

the rate of leachate migration through two double liner systems having the following inverse 

configurations: (i) a double liner system where the primary liner is a geomembrane liner and 

the secondary liner is a composite liner; and (ii) a double liner system where the primary liner 

is a composite liner and the secondary liner is a geomembrane liner. The composite liner considered 

in the study consists of a geomembrane on a geosynthetic clay liner (GCL). The comparison 

between the two liner systems is based only on advective flow through geomembrane 

defects (i.e. defects in the geomembrane liner as well as defects in the geomembrane 

component of the composite liner). Other factors that may have an impact on the selection 

of a liner configuration, such as diffusive flux and construction issues, are not considered in 

the comparison. The study shows that, from the viewpoint of minimizing the advective flow 

of leachate through geomembrane defects, it is preferable to use the configuration where the 

primary liner is a composite liner. 

KEYWORDS: Double liner, Composite liner, Landfill, Leachate migration, Theoretical 

analysis. 

AUTHORS: J.P. Giroud, Senior Principal, K.L. Soderman, Project Engineer, and K. 

Badu-Tweneboah, Senior Project Engineer, GeoSyntec Consultants, 621 N.W. 53rd Street, 

Suite 650, Boca Raton, Florida 33487, USA, Telephone: 1/561-995-0900, Telefax: 

1/561-995-0925, E-mail: jpgiroud@geosyntec.com, kriss@geosyntec.com, and 

kwasib@geosyntec.com, respectively. 

PUBLICATION: Geosynthetics International is published by the Industrial Fabrics 

Association International, 345 Cedar St., Suite 800, St. Paul, Minnesota 55101-1088, USA, 

Telephone: 1/612-222-2508, Telefax: 1/612-222-8215. Geosynthetics International is 

registered under ISSN 1072-6349. 

DATES: Original manuscript submitted 28 April 1997 and accepted 16 July 1997. 

Discussion open until 1 March 1998. 

REFERENCE: Giroud, J.P., Soderman, K.L. and Badu-Tweneboah, K., 1997, “Optimal 

Configuration of a Double Liner System Including a Geomembrane Liner and a Composite 

Liner”, Geosynthetics International, Vol. 4, Nos. 3-4, pp. 373-389. 

GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NOS. 3-4 

373

GIROUD et al. D Optimal Configuration of a Double Liner System 

1 INTRODUCTION 

In many landfills and other waste containment systems where a double liner system 

is used, the primary liner is a geomembrane and the secondary liner is a composite liner 

that consists of a geomembrane on a layer of compacted clay (Figure 1a). The inverse 

configuration where the geomembrane-compacted clay composite liner is the primary 

liner and the geomembrane used alone is the secondary liner (Figure 1b) is rarely considered 

because: (i) compaction of the clay could damage the geomembrane used as the 

secondary liner (and the geonet, if one is used in the secondary leachate collection layer); 

and (ii) regulations often prescribe the first configuration. 

Geosynthetic clay liners (GCLs) are increasingly used instead of compacted clay in 

composite liners. GCLs are usually installed with light equipment that should not damage 

the underlying geosynthetics. Therefore, when a GCL is used, both configurations 

can be considered: (i) the geomembrane alone as the primary liner and the geomembrane-GCL 

composite liner as the secondary liner (Figure 1c); and (ii) the inverse configuration 

(Figure 1d). A comparison between these two configurations is presented in 

this paper. 

It is realized that several criteria and approaches can be used to compare liner systems. 

However, only leachate migration due to advective flow of leachate through geomembrane 

defects is considered herein. The considered defects are defects in the geomembrane 

used alone as well as defects in the geomembrane component of the 

composite liner. 

The purpose of the comparison presented herein is to provide information that may 

be used as part of the process for selecting the optimal configuration for a double liner 

system. 

2 METHODOLOGY 

2.1 Approach 

The two double liner systems considered in the study are shown in Figure 2. For each 

of the two liner systems, the rate of leachate migration through the secondary liner is 

calculated according to the following four steps: 

S A given average head of leachate on top of the primary liner is considered. 

S The rate of leachate migration through the primary liner due to advective flow 

through defects in the primary liner geomembrane is calculated. 

S The average head of leachate on top of the secondary liner due to leachate that has 

migrated through the primary liner is calculated. 

S The rate of leachate migration through the secondary liner due to advective flow 

through defects in the secondary liner geomembrane is calculated. 

The rate of leachate migration through the secondary liner thus calculated is the rate 

of leachate migration into the ground. 

It is preferable to discuss leachate head calculation prior to discussing leachate migration 

calculations due to numerous references to leachate head in leachate migration cal- 

374 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NOS. 3-4


(a) 

P-L 

(b) 

P-L 

S-L 

S-L 

(c) 

P-L 

(d) 

P-L 

S-L 

S-L 

Materials 

Geomembrane 

Geosynthetic clay liner 

(GCL) 

Compacted clay 

Granular material 

Geonet (could be 

used instead of 

the granular material) 

Functions 

P - L : Primary liner 

S - L : Secondary liner 

P - LCL : Primary leachate collection layer 

S - LCL : Secondary leachate collection layer 

Composite liners 

Geomembrane - clay 

Geomembrane - GCL 

Figure 1. Double liner systems. 

Note: The small space between the GCL and the overlying geomembrane is shown only for clarity. In 

reality, a geomembrane and a GCL,which are associated toform a composite liner,should be in close contact. 

Filters are not shown for the sake of simplicity. 

culations. Accordingly, the method used to determine the average head of leachate on 

top of the secondary liner is described in Section 2.2, and the methods used to calculate 

leachate migration through liners are described in Section 2.3. 

2.2 Method for Calculating the Average Head of Leachate on Top of the 

Secondary Liner 

2.2.1 Influence of the Approach Used for Leachate Migration Evaluation on the 

Selection of a Relevant Leachate Head on the Secondary Liner 

As indicated in Section 2.1, a given value of the average head of leachate on top of 

the primary liner is considered. In contrast, the average head of leachate on top of the 


375


(a) 

Gravel primary leachate 

collection layer 

Geomembrane primary liner 

Geonet secondary 

leachate collection layer 

Geomembrane - GCL composite 

secondary liner 

Permeable subgrade 

(b) 

Gravel primary leachate 

collection layer 

Geomembrane - GCL composite 

primary liner 

Geonet secondary 

leachate collection layer 

Geomembrane secondary liner 

Permeable subgrade 

Figure 2. The two double liner systems used in the comparative study: (a) double liner 

system where the primary liner is a geomembrane liner and the secondary liner is a 

composite liner; (b) double liner system where the primary liner is a composite liner and 

the secondary liner is a geomembrane liner. 

Note: The terminology “geomembrane primary liner” means that the primary liner consists of a 

geomembrane used alone. The terminology “primary liner geomembrane” (used in the text) refers to the 

geomembrane of the primary liner whether it is used alone or in association with a GCL to form a composite 

liner. Filters are not shown for the sake of simplicity. 

secondary liner must be calculated based on the rate of leachate migration through the 

primary liner. 

Leachate migration through the primary liner occurs through a relatively small number 

of defects in the primary liner geomembrane. As a result, leachate flow in the secondary 

leachate collection layer takes place only in certain zones called “wetted” zones, 

i.e. zones of the secondary leachate collection layer and the secondary liner that are in 

contact with leachate that has migrated through the primary liner. If there are only a few 

defects, there is a wetted zone for each defect, but if the frequency of geomembrane 

defects in the primary liner is high, some of the wetted zones may overlap. The ratio 



between the combined surface area of the wetted zones and the total surface area of the 

liner is called the “wetted fraction” (Giroud et al. 1997a). 

The relevant average head of leachate on top of the secondary liner depends on the 

approach used for calculating the rate of leachate migration through the secondary liner. 

There are two possible approaches for calculating the rate of leachate migration through 

the secondary liner: 

S The first approach, which is the most rigorous, consists of: (i) calculating the combined 

surface area of the wetted zones due to leachate migrating through all of the 

defects in the primary liner; (ii) calculating the wetted fraction; (iii) calculating the 

average leachate head on top of the secondary liner in the wetted zones; (iv) calculating 

the rate of leachate migration through a defect in the secondary liner geomembrane, 

assuming the defect is in a wetted zone; and (v) multiplying the rate of leachate 

migration thus obtained by the wetted fraction and by the frequency of geomembrane 

defects in the secondary liner. 

S The second approach, which is only approximate, consists of: (i) assuming that all 

of the leachate migrating through the primary liner results in a uniform rate of liquid 

impingement over the entire surface area of the secondary leachate collection layer; 

(ii) calculating the average leachate head on top of the entire surface area of the secondary 

liner; (iii) calculating the rate of leachate migration through a defect in the 

secondary liner geomembrane; and (iv) multiplying the rate of leachate migration 

thus obtained by the frequency of geomembrane defects in the secondary liner. The 

second approach is similar to the first approach with a wetted fraction equal to one. 

The first approach, which is described in detail by Giroud et al. (1997a), is extremely 

tedious. The second approach is used herein. It is shown in the paper by Giroud et al. 

(1997a, at the end of Section 5.2.5 and in Section 6.1 after Example 6) that both approaches 

give rates of leachate migration of the same order of magnitude, and that the 

second approach is conservative, i.e. gives a head of leachate on top of the secondary 

liner that is greater than the head of leachate obtained with the first approach. 

2.2.2 Equation for Calculating the Average Head of Leachate on Top of the Secondary 

Liner 

Based on the fact that the second of the two approaches described in Section 2.2.1 

is selected, the average head of leachate on the secondary liner is calculated assuming 

that the rate of leachate impingement is uniform over the entire surface area of the secondary 

leachate collection layer. Accordingly, the following equation (Giroud and 

Houlihan 1995) is used to calculate the average leachate head on top of the secondary 

liner: 

h 

2 

qi 

L q1 

L l L tanb 

= = = 

2 k tanb 

2 k tanb 

2 

2 

where: h 2 = average leachate head on top of the secondary liner; q i = uniform rate of 

leachate impingement onto the considered leachate collection layer (i.e., in this case, 

the secondary leachate collection layer), which, in this case, is equal to the unit rate of 

leachate migration through the primary liner, q 1 (defined in Section 2.3.3); L = horizon- 

2 

(1) 


377


tal projection of the length of the liner system in the direction of the slope; k 2 = hydraulic 

conductivity of the secondary leachate collection layer material; β = slope angle of the 

liner system; and λ is a dimensionless parameter defined by: 

qi 

q1 

l = = 

2 2 

(2) 

k tan b k tan b 

2 

As indicated by Giroud and Houlihan (1995), Equation 1 is valid only if λ is small 

(e.g. λ < 0.01). This condition is always satisfied in the study presented in this paper. 

2.3 Methods for Calculating the Rate of Leachate Migration Through Liners 

2.3.1 Leachate Migration Mechanism 

As indicated in Section 1, the only mechanism of leachate migration through a liner 

(whether it is a geomembrane used alone or a composite liner) that is considered in this 

study is advective flow through defects in the geomembrane. The defects are defects 

in the geomembrane used alone as well as defects in the geomembrane component of 

the composite liner. 

2.3.2 Assumption 

For the leachate migration rate calculations, it is assumed that the leachate head on 

top of the considered liner is uniform over the entire surface area of the liner. Therefore, 

the rate of leachate migration through a geomembrane defect is independent of the geomembrane 

defect location in the considered liner. 

The uniform leachate head is equal to the given average head for the primary liners 

(see Section 2.1), and is equal to the average head calculated using Equation 1 for the 

secondary liners (see Section 2.2.2). 

2.3.3 Unit Rate of Leachate Migration Through a Liner 

Since it is assumed in Section 2.3.2 that the leachate head is uniform over the entire 

surface area of both the primary and secondary liners, the same methodology for leachate 

migration calculation applies to both liners. The methodology consists of: (i) calculating 

the rate of leachate migration, Q, through a geomembrane defect; and (ii) multiplying 

the rate of leachate migration through a defect by the geomembrane defect 

frequency, F, to obtain the unit rate ofleachate migration, q, through the considered liner: 

q = F Q 

(3) 

where the geomembrane defect frequency, F, is expressed as the number of defects per 

unit area (e.g. five defects per hectare, i.e. F =5× 10 -4 m -2 ). As a result, if Q is expressed 

in m 3 /s, q is expressed in m/s. Herein, the same geomembrane defect frequency, F, will 

be used for both the primary and secondary liners of a given double liner system, and 

the following notations will be used for the rate of leachate migration through a defect 

and the unit rate of leachate migration through a liner: Q 1 and q 1 for the primary liner, 

and Q 2 and q 2 for the secondary liner. 

2 



Essentially, Equation 3 shows that the unit rate of leachate migration through a liner 

is derived from the rate of leachate migration through a geomembrane defect. The 

method used to calculate the rate of leachate migration through a geomembrane defect, 

Q, depends on the type of liner: a geomembrane liner, or a composite liner. These two 

cases are addressed in Sections 2.3.4 and 2.3.5, respectively. 

2.3.4 Rate of Leachate Migration Through a Defect in a Geomembrane Liner 

Traditionally, the rate of leachate migration through a geomembrane liner defect has 

been calculated using Bernoulli’s equation for free flow through an orifice: 

Q = 06 . a 2 g h 

(4) 

where: a = defect surface area; g = acceleration due to gravity; and h = leachate head 

on top of the liner. 

Giroud et al. (1997b) show that Equation 4 may give leachate migration rate values 

that are grossly exaggerated if the leachate head is relatively small and/or if the hydraulic 

conductivity of the leachate collection layer material overlying the liner is relatively 

small. In such cases, the following relationship exists (Giroud et al. 1997b): 

h 

R 

S| 

T| 

a qi 

Q Q 

= + ln - 1 + 

2 k p 2 k p a q 

L 

N 

M 

F 

HG 

i 

I 

KJ 

O 

Q 

P 

F 

HG 

1 Q 

2 

4 g 06 . a 

I K J 

U 

V| 

W| 

/ 

4 12 

where: k = hydraulic conductivity of the leachate collection layer overlying the geomembrane; 

and q i = uniform rate of leachate impingement onto the leachate collection 

layer overlying the geomembrane. 

Equation 5 cannot be solved for Q; therefore, iterations are necessary to determine 

Q when h, a, k,andq i are known. Equation 5 is more general than Equation 4 and it tends 

toward Equation 4 for high values of h and k, as indicated by Giroud et al. (1997b). Herein, 

due to the values selected for the parameters (see Section 3.1), Equation 4 is applicable 

to the geomembrane primary liner. Therefore, in the study presented in this paper, 

it is not necessary to know the rate of leachate impingement onto the primary leachate 

collection layer (a parameter that is included in Equation 5, but not in Equation 4). This 

greatly simplifies the comparative study presented in Section 4. 

From the foregoing discussion, it appears that, in this study, Equation 5 needs to be 

used only for the secondary liner. Alternatively, the following equation, obtained by 

combining Equations 2 and 5, can be used for the secondary liner: 

b g b g b g 

1= 2 p A 1+ C ln C- 1 + B C 06 . 

2 4 

where A, B, andC are dimensionless parameters defined as follows (Giroud et al. 

1997b): 

ak2 

tan 2 b 

A = 

(7) 

2 

q L 

1 

(5) 

(6) 


379


B = 

q 

k tanb 

g L 

1 2 

(8) 

C = 

Q2 

aq 

1 

(9) 

Equation 6, like Equation 5, must be solved iteratively. However, Equation 6 is slightly 

more convenient than Equation 5 due to the use of dimensionless parameters and the 

availability of a graphical solution given in Figure 13 of the paper by Giroud et al. 

(1997b). In the comparative study presented in Section 3, the rate of leachate migration 

through the geomembrane secondary liner is calculated by solving Equation 6 iteratively 

for C and, then, using the following equation derived from Equation 9: 

Q 

= C a q 

2 1 

(10) 

The value of Q 2 thus obtained is then checked using Equation 5 with q i = q 1 , k = k 2 

and Q = Q 2 . 

2.3.5 Rate of Leachate Migration Through a Geomembrane Defect in a Composite 

Liner 

The rate of leachate migration through a composite liner, due to one defect in the geomembrane 

component of the composite liner, is calculated using the following equation 

(Giroud 1997): 

Q 

L F 

= 021 . 1+ 01 . 

H G 

NM 

h 

t 

s 

I 

KJ 

095 . 

O 

QP 

a h k 

01 . 09 . 074 . 

s 

where: t s = thickness of the soil component of the composite liner; and k s = hydraulic 

conductivity of the soil component of the composite liner. 

Equation 11 is the latest development of the work on the evaluation of leachate migration 

through composite liners initiated by Giroud and Bonaparte (1989) and continued 

by Giroud et al. (1989, 1992). 

(11) 

3 COMPARATIVE STUDY 

3.1 Presentation of the Comparative Study 

The two double liner systems that are used in the comparative study are shown in Figure 

2. Values of the relevant parameters are as follows: 

S The primary leachate collection layer material is gravel with a hydraulic conductivity, 

k 1 , greater than 0.1 m/s and a thickness sufficient to contain the maximum considered 

leachate head (0.1 m). 



S The secondary leachate collection layer material is a geonet with a hydraulic conductivity 

k 2 = 0.1 m/s and a thickness of 5 mm. 

S Two values of the average leachate head on top of the primary liner (i.e. in the primary 

leachate collection layer) are considered: h 1 =0.01mandh 1 =0.1m. 

S Two types of geomembrane defects are considered: (i) diameter, d =0.5mm(a = 

(1/16) π × 10 -6 m 2 ) with a frequency of 25 defects per hectare (F =2.5× 10 -3 m -2 ); 

and (ii) diameter, d =2mm(a = π × 10 -6 m 2 ) with a frequency of 2.5 defects per hectare 

(F =2.5× 10 -4 m -2 ). In a given double liner system, the sizes and frequencies of 

defects in the two geomembranes are assumed to be the same; however, the defects 

are located at random. 

S The GCL, which is the soil component of the composite liner, has the following characteristics: 

thickness, t s = 7 mm; and hydraulic conductivity, k s =1× 10 -11 m/s. These 

characteristics are consistent with the GCL characteristics used by Giroud et al. 

(1997c). In particular, the hydraulic conductivity is typical of the hydraulic conductivity 

of a hydrated GCL permeated by water or a leachate that does not contain chemicals 

likely to increase bentonite hydraulic conductivity. 

S The considered liner system area is square, 50 m × 50 m in plan dimensions, with a 

2% slope in one direction (i.e. L = 50 m and tanβ = 0.02). 

Four cases are thus defined (two values of the average head and two types of defects). 

3.2 Detailed Calculations for One Case 

3.2.1 Values of the Parameters 

Detailed calculations are presented in Section 3.2 for one of the four cases defined 

in Section 3.1 in order to illustrate the methodology. The case considered in Section 3.2 

is characterized by a leachate head on top of the primary liner h 1 = 0.01 m, a defect diameter 

d = 2 mm (i.e. a defect area a = π × 10 -6 m 2 ), and a defect frequency of 2.5 defects 

per hectare (i.e. F =2.5× 10 -4 m -2 ). The values of the other parameters are as defined 

in Section 3.1. 

In the case considered in Section 3.2, as in any of the three other cases, two liner systems 

are considered: (i) a double liner system where the primary liner is a geomembrane 

liner (Figure 2a); and (ii) a double liner system where the primary liner is a composite 

liner (Figure 2b). For each of the two liner systems considered, the four steps identified 

in Section 2.1 are performed. 

3.2.2 Calculations for the Double Liner System Where the Primary Liner is a 

Geomembrane 

Average Head of Leachate on Top of the Primary Liner. The value assumed for the 

average head of leachate on top of the primary liner is h 1 =0.01m. 

Rate of Leachate Migration Through the Geomembrane Primary Liner. The methodology 

for calculating the rate of leachate migration through a geomembrane liner defect 

is described in Section 2.3.4. Equation 5 (i.e. the general equation) should be used unless 


381


conditions are met for the simpler, but less general, Equation 4 (Bernoulli’s equation) to 

be applicable. According to Figure 6 of the paper by Giroud et al. (1997b), Equation 4 

is applicable fora defect with a diameter of2 mm and a leachate head on top of the primary 

liner of 0.01 m if the hydraulic conductivity of the leachate collection layer overlying 

the geomembrane liner is greater than 1 × 10 -1 m/s. According to Section 3.1, this condition 

is met. (It has also been checked that Equation 4 is applicable to the geomembrane 

primary liner in the three other cases considered in the comparative study.) Consequently, 

Equation 4 can be used as follows to calculate the rate of leachate migration through 

a defect in the geomembrane primary liner due to a leachate head of 0.01 m: 

Q 1 

= ¥ - 6 

(.)( 0 6 10 ) ()(. 2 9 81)(. 0 01) = 8. 

349 ¥ 10 

- 7 3 

p m /s 

The unit rate of leachate migration through the geomembrane primary liner is then 

calculated using Equation 3 as follows: 

q 1 

= ( 2. 5 ¥ 10 ) (8. 349 ¥ 10 ) = 2. 

087 ¥ 10 

- 4 - 7 -10 

m/s 

Average Head of Leachate on Top of the Secondary Liner. The methodology for calculating 

the average head of leachate is described in Section 2.2. The average head of 

leachate on top of the secondary liner due to the above calculated unit rate of leachate 

migration through the primary liner is calculated using Equation 1 as follows: 

-10 

( 2087 . ¥ 10 ) (50) 

h 2 

= 

= 2609 . ¥ 10 

( 2) ( 01 . ) ( 002 . ) 

- 6 m 

Rate of Leachate Migration Through the Composite Secondary Liner. The methodology 

for calculating the rate of leachate migration through a composite liner due to a geomembrane 

defect is described in Section 2.3.5. The rate of leachate migration through 

the secondary liner resulting from the above calculated head is calculated using Equation 

11 as follows: 

L 

NM 

Q 2 

= 021 . 1+ 

01 . 

= 4. 

044 ¥ 10 

F 

HG 

-15 

2. 

609 ¥ 10 

-3 

7 ¥ 10 

3 

m /s 

-6 

I 

KJ 

095 . 

O 

QP 

- - - 

( p ¥ 10 ) ( 2. 609 ¥ 10 ) ( 1 ¥ 10 ) 

6 01 . 6 0. 9 11 0. 

74 

The unit rate of leachate migration through the composite secondary liner is then calculated 

using Equation 3 as follows: 

q 2 

= ( 2. 5 ¥ 10 ) ( 4. 044 ¥ 10 ) = 1011 . ¥ 10 

- 4 - 15 -18 

m/s 



3.2.3 Calculations for the Double Liner System Where the Primary Liner is a 

Composite Liner 

Average Head of Leachate on Top of the Primary Liner. The value assumed for the 

average head of leachate on top of the primary liner is h 1 =0.01m. 

Rate of Leachate Migration Through the Composite Primary Liner. The methodology 

for calculating the rate of leachate migration through a composite liner due to a geomembrane 

defect is described in Section 2.3.5. The rate of leachate migration through 

the primary liner resulting from a head of 0.01 m is calculated using Equation 11 as follows: 

L 

NM 

Q 1 

= 021 . 1+ 

01 . 

F 

HG 

001 . 

7 ¥ 10 

-3 

I 

KJ 

095 . 

O 

QP 

-6 0. 1 0. 9 -11 0. 

74 -12 

3 

( p ¥ 10 ) ( 0. 01) ( 1 ¥ 10 ) = 7. 

744 ¥ 10 m /s 

The unit rate of leachate migration through the composite primary liner is then calculated 

using Equation 3 as follows: 

q 1 

= ( 2. 5 ¥ 10 ) ( 7. 744 ¥ 10 ) = 1936 . ¥ 10 

- 4 - 12 -15 

m/s 

Average Head of Leachate on Top of the Secondary Liner. The methodology for calculating 

the average head of leachate is described in Section 2.2. The average head of 

leachate on top of the secondary liner due to the above calculated unit rate of leachate 

migration through the primary liner is calculated using Equation 1 as follows: 

-15 

(. 1936 ¥ 10 )(50) 

h 2 

= 

= 2420 . ¥ 10 

( 2) ( 01 . ) ( 002 . ) 

- 11 m 

Rate of Leachate Migration Through the Geomembrane Secondary Liner. Themethodology 

for calculating the rate of leachate migration through a geomembrane liner defect 

is described in Section 2.3.4. As shown by the graphical solutions published by Giroud 

et al. (1997b), Equation 4 is not applicable for very small heads such as the above 

calculated head. Therefore, Equation 5 (or Equation 6, which is equivalent) must be 

used. Both Equations 5 and 6 must be solved by iterations. Due to the use of dimensionless 

parameters, Equation 6 is slightly more convenient than Equation 5. Therefore, 

Equation 6 will be used. The result will then be checked using Equation 5. 

The dimensionless parameter A is calculated using Equation 7 as follows: 

-6 2 

( p ¥ 10 ) ( 01 . ) ( 0. 02) 

A = 

= 259636 . 

-15 2 

( 1936 . ¥ 10 ) (50) 

The dimensionless parameter B is calculated using Equation 8 as follows: 


383


B = 

-15 

(. 1936 ¥ 10 )( 01 .)( 0. 02) 

( 981 . ) (50) 

= 7. 

8940 ¥ 10 

-21 

The graphical solution presented in Figure 13 of the paper by Giroud et al. (1997b) 

confirms that Equation 4 is not applicable to this case, and shows that the value of the 

dimensionless parameter C that corresponds to the above values of A and B is approximately 

1.3. Using 1.3 as a starting value for iterations with Equation 6 gives, after several 

iterations: 

C = 13675 . 

Then, the rate of leachate migration through a defect of the geomembrane secondary 

liner is calculated using Equation 10 as follows: 

Q 2 

= ¥ - 6 

¥ - 15 

(. 13675)( 10 )(. 1936 10 ) = 8. 

3173 ¥ 10 

- 21 3 

p m /s 

The unit rate of leachate migration through the geomembrane secondary liner is then 

calculated using Equation 3 as follows: 

q 2 

= ( 2. 5 ¥ 10 ) (8. 3173 ¥ 10 ) = 2. 

079 ¥ 10 

- 4 - 21 -24 

m/s 

Equation 5 is then used as follows to check that the above calculated value of Q 2 is 

consistent with the value of h 2 calculated in the preceding step: 

h 2 

= 

R 

S 

T| 

-6 -15 -21 -21 

( p ¥ 10 ) ( 1936 . ¥ 10 ) 83173 . ¥ 10 83173 . ¥ 10 

+ 

ln 

- 1 

-6 -15 

( 2) ( 01 . ) ( p) 

( 2) ( 01 . ) ( p) 

( p ¥ 10 ) ( 1936 . 10 ) 

1 

+ 

( 4) ( 981 . ) 

2 

L 

NM 

-21 

83173 . ¥ 10 

-6 

(.)( 06 p ¥ 10 ) 

O 

QP U V | 

4 

W| 

12 / 

L 

NM 

= 2420 . ¥ 10 

- 11 m 

This value of h 2 is identical to the value calculated in the preceding step, which indicates 

that the value of Q 2 calculated above is correct. 

Finally, it is interesting to repeat the last step using Bernoulli’s equation (Equation 

4), which was the method typically used to calculate the rate of leachate migration 

through a defect in a geomembrane liner prior to the development of Equation 5 (or 

Equation 6, which is equivalent) by Giroud et al. (1997b). In the case considered herein, 

Equation 4 can be used as follows: 

Q 2 

= ¥ - 6 

¥ - 11 

(.)( 0 6 10 ) ()(. 2 9 81)(. 2 420 10 ) = 41073 . ¥ 10 

- 11 3 

p m /s 

hence, using Equation 3: 

q 2 

= ( 2. 5 ¥ 10 ) ( 41073 . ¥ 10 ) = 1027 . ¥ 10 

- 4 - 11 -14 

m/s 

It appears that the value of q 2 calculated using Bernoulli’s equation (i.e. 1.027 × 10 -14 

m/s) is much greater than the value calculated using Equation 5 (i.e. 2.079 × 10 -24 m/s). 

O 

QP 



Furthermore, the use of Bernoulli’s equation gives an absurd result: a value of the unit 

rate of leachate migration through the secondary liner (q 2 = 1.027 × 10 -14 m/s) that is 

greater than the unit rate of leachate migration through the primary liner (q 1 = 1.936 × 

10 -15 m/s). Therefore, great caution should be exercised when Bernoulli’s equation is 

used to predict or analyze the performance of a geomembrane liner: there are many 

cases where absurd results can be obtained. There are also cases where Bernoulli’s 

equation is applicable, such as the second step of Section 3.2.2. Detailed guidance is 

provided in the paper by Giroud et al. (1997b) for determining in which cases Bernoulli’s 

equation is applicable. 

3.3 Results of the Comparative Study 

The results of the comparative study conducted for the four cases defined in Section 

3.1 are presented in Table 1. The results are presented in two columns (Columns A and 

B), so the results for the case where the primary liner is a geomembrane liner (Column 

A, Figure 2a) can be readily compared to the results for the case where the primary liner 

Table 1. Results of the comparative study presented in Section 3.1. 

Defect diameter and 

frequency 

Quantity 

(unit) 

(Column A) 

Geomembrane primary liner 

Composite secondary liner 

(Figure 2a) 

(Column B) 

Composite primary liner 

Geomembrane secondary liner 

(Figure 2b) 

(Cell 1A) (Cell 1B) 

h 1 (m) 0.01 0.01 

q 1 (m/s) 2.09 × 10 -10 1.94 × 10 -15 

h 2 (m) 2.61 × 10 -6 2.42 × 10 -11 

d =2mm q 2 (m/s) 1.01 × 10 -18 2.08 × 10 -24 

F =2.5× 10 -4 m -2 (Cell 2A) (Cell 2B) 

h 1 (m) 0.10 0.10 

q 1 (m/s) 6.60 × 10 -10 3.04 × 10 -14 

h 2 (m) 8.25 × 10 -6 3.79 × 10 -10 

q 2 (m/s) 2.85 × 10 -18 6.36 × 10 -23 

(Cell 3A) (Cell 3B) 

h 1 (m) 0.01 0.01 

q 1 (m/s) 1.31 × 10 -10 1.47 × 10 -14 

h 2 (m) 1.63 × 10 -6 1.83 × 10 -10 

d =0.5mm q 2 (m/s) 5.02 ××10 -18 4.93 × 10 -23 

F =2.5× 10 -3 m -2 (Cell 4A) (Cell 4B) 

h 1 (m) 0.10 0.10 

q 1 (m/s) 4.13 × 10 -10 2.30 × 10 -13 

h 2 (m) 5.16 × 10 -6 2.88 × 10 -9 

q 2 (m/s) 1.42 × 10 -17 4.71 × 10 -21 

Notes: The methodology used to develop Table 1 is presented in Section 2 and detailed calculations are 

presented in Section 3.2. The most important result is q 2 , the rate of leachate migration through the secondary 

liner, i.e. the rate of leachate migration into the ground. F =2.5× 10 -4 m -2 = 2.5 defects per hectare = one defect 

per 4000 m 2 ;andF =2.5× 10 -3 m -2 = 25 defects per hectare = ten defects per 4000 m 2 . 


385


is a composite liner (Column B, Figure 2b). Each of the four pairs of cells (1A - 1B, 2A 

- 2B, 3A - 3B, and 4A - 4B) corresponds to one of the four cases defined in Section 3.1. 

The first of these four pairs of cells is related to the case presented in detail in Section 

3.2. Each of these eight cells comprises four lines: one line for the result of each of the 

four steps defined in Section 2.1. 

Comparing Columns A and B in Table 1, it appears that calculated values of the rate 

of leachate migration into the ground (i.e. the rate of leachate migration through the 

secondary liner, q 2 ) are smaller when the primary liner is a composite liner and the secondary 

liner is a geomembrane liner than with the inverse configuration. 

4 DISCUSSION AND CONCLUSIONS 

4.1 Discussion of the Results 

4.1.1 Liner System Configuration 

The purpose of this paper was to compare two configurations of double liner systems: 

(i) a double liner system where the primary liner is a geomembrane and the secondary 

liner is a composite liner; and (ii) a double liner system where the primary liner is a composite 

liner and the secondary liner is a geomembrane. In the double liner systems used 

for the comparison, the composite liner consists of a geomembrane on a GCL (Figure 

2). The comparison was performed by calculating the rate of leachate migration due to 

geomembrane defects. The results of the calculations, presented in Table 1, show that 

the rate of leachate migration into the ground is significantly less with the second configuration 

(Figure 2b) than with the first (Figure 2a). Therefore, if a design engineer has 

to choose between the two double liner systems described above, it may be recommended, 

on the basis of the comparison presented in this paper, to use the composite 

liner as the primary liner and the geomembrane liner as the secondary liner. However, 

this recommendation is mostly applicable to the case where the composite liner consists 

of a geomembrane on a GCL. If the composite primary liner consists of a geomembrane 

on a layer of compacted clay, compaction of the clay component of a primary liner may 

damage the underlying geosynthetics, i.e. the geonet secondary leachate collection system 

and the geomembrane secondary liner, which would likely cause more leachate 

migration through the secondary liner. 

It should be remembered that, as mentioned in Section 1, the comparison presented 

in this paper is based on advective flow calculations. A different ranking of the liner 

systems might have been obtained if other migration mechanisms (such as diffusion) 

had been considered. 

4.1.2 Magnitude of Leachate Migration Rate 

The calculated rates of leachate migration into the ground (q 2 in Table 1) are extremely 

small. The largest value of q 2 calculated, 1.42 × 10 -17 m/s, is equivalent to 5 × 10 -3 

liters per hectare per year, which should cause virtually no pollution. However, it should 

be remembered that mechanisms of contaminant migration other than advective flow 

have not been considered in this study. Nevertheless, it is clear that double liner sys- 



tems, even with defects in the geomembranes, can provide a high level of protection 

of the environment. 

4.2 Discussion of the Methodology 

4.2.1 Leachate Migration Mechanism 

As mentioned in Sections 1 and 4.1.1, only one leachate migration mechanism has 

been considered in this study: advective flow through geomembrane defects. It would 

be interesting to perform a similar study considering contaminant migration by diffusion 

instead of, or in addition to, advective flow. 

4.2.2 Leachate Distribution in the Secondary Leachate Collection Layer 

As indicated in Section 2.2.1, an average head of leachate over the entire surface area 

of the secondary liner has been considered (which entails only simple calculations) 

instead of the more sophisticated approach which consists of calculating the fraction 

of the secondary liner that is “wetted” by leachate, calculating the rate of leachate 

migration through the secondary liner, and prorating to account for the fact that only 

a fraction of the defects in the secondary liner are in the wetted zones. However, as indicated 

in Section 2.2, the calculated rates of leachate migration should not be significantly 

affected by the approach used. As a result, the ranking of the liner system configurations 

should not be affected by the approach used. 

4.2.3 Leachate Head Magnitude 

The main consideration that may affect the validity of the calculations is the fact that 

the calculated leachate heads on top of the secondary liner are extremely small. Clearly, 

with the very small leachate heads, h 2 , shown in Table 1, capillarity and wettability may 

significantly affect leachate migration. Since the advective flow calculations presented 

herein do not take capillarity and wettability into account, they should be regarded as 

conventional calculations that are mostly useful to rank various liner configurations and 

to determine an approximate order of magnitude of the rate of leachate migration. 

4.2.4 Use of Bernoulli’s Equation 

In the comparative study performed herein, great care is taken to use Bernoulli’s 

equation (Equation 4) only when it is applicable, and to use the more general Equation 

5 when Bernoulli’s equation is not applicable. Indeed, it is shown at the end of Section 

3.2.3 that using Bernoulli’s equation when it is not applicable can lead to incorrect and 

even absurd results. This confirms the conclusions reached by Giroud et al. (1997b). 

There are, however, cases where Bernoulli’s equation is applicable. Guidance is provided 

by Giroud et al. (1997b) for determining in which cases Bernoulli’s equation is 

applicable. 


387


ACKNOWLEDGMENTS 

The analysis presented in this paper was developed for the evaluation of an actual 

double liner system, and the support of GeoSyntec Consultants is acknowledged. The 

authors are grateful to K. Holcomb, N. Pierce, and S.L. Berdy for assistance during the 

preparation of this paper. 

REFERENCES 

Giroud, J.P., 1997, “Equations for Calculating the Rate of Liquid Migration Through 

Composite Liners Due to Geomembrane Defects”, Geosynthetics International,Vol. 

4, Nos. 3-4, pp. 335-348. 

Giroud, J.P. and Bonaparte, R., 1989, “Leakage through Liners Constructed with Geomembranes, 

Part II: Composite Liners”, Geotextiles and Geomembranes,Vol.8,No. 

2, pp. 71-111. 

Giroud, J.P. and Houlihan, M.F., 1995, “Design of Leachate Collection Layers”, Proceedings 

of the Fifth International Landfill Symposium, Vol. 2, Sardinia, Italy, October 

1995, pp. 613-640. 

Giroud, J.P., Khatami, A. and Badu-Tweneboah, K., 1989, “Evaluation of the Rate of 

Leakage through Composite Liners”, Geotextiles and Geomembranes, Vol. 8, No. 4, 

pp. 337-340. 

Giroud, J.P., Badu-Tweneboah, K. and Bonaparte, R., 1992, “Rate of Leakage Through 

a Composite Liner due to Geomembrane Defects”, Geotextiles and Geomembranes, 

Vol. 11, No. 1, pp. 1-28. 

Giroud, J.P., Gross, B.A., Bonaparte, R. and McKelvey, J.A., 1997a, “Leachate Flow 

in Leakage Collection Layers Due to Defects in Geomembrane Liners”, Geosynthetics 

International, Vol. 4, Nos. 3-4, pp. 215-292. 

Giroud, J.P., Khire, M.V. and Soderman, K.L., 1997b, “Liquid Migration Through Defects 

in a Geomembrane Overlain and Underlain by Permeable Media”, Geosynthetics 

International, Vol. 4, Nos. 3-4, pp. 293-321. 

Giroud, J.P., Badu-Tweneboah, K. and Soderman, K.L., 1997c, “Comparison of Leachate 

Flow Through Compacted Clay Liners and Geosynthetic Clay Liners in Landfill 

Liner Systems”, Geosynthetics International, Vol. 4, Nos. 3-4, pp. 391-431. 

NOTATIONS 

The basic SI units are given in parentheses. 

A = parameter defined by Equation 7 (dimensionless) 

a = defect surface area (m 2 ) 

B = parameter defined by Equation 8 (dimensionless) 

C = parameter defined by Equation 9 (dimensionless) 



d = geomembrane defect diameter (m) 

F = geomembrane defect frequency (m -2 ) 

g = acceleration due to gravity (m/s 2 ) 

h = leachate head on top of the liner (m) 

h 1 = average leachate head on top of the primary liner (m) 

h 2 = average leachate head on top of the secondary liner (m) 

k = hydraulic conductivity of the leachate collection layer overlying the 

geomembrane (m/s) 

k s = hydraulic conductivity of the soil component of the composite liner (m/s) 

k 1 = hydraulic conductivity of the primary leachate collection layer material 

(m/s) 

k 2 = hydraulic conductivity of the secondary leachate collection layer 

material (m/s) 

L = horizontal projection of the length of the liner system in the direction of 

the slope (m) 

q = unit rate of leachate migration through the considered liner (m/s) 

q i = uniform rate of leachate impingement onto the considered leachate 

collection layer (m/s) 

q 1 = unit rate of leachate migration through the primary liner (m/s) 

q 2 = unit rate of leachate migration through the secondary liner, equal to the 

unit rate of leachate migration into the ground (m/s) 

Q = rate of leachate migration through a geomembrane defect (m 3 /s) 

Q 1 = rate of leachate migration through the primary liner due to a 

geomembrane defect (m 3 /s) 

Q 2 = rate of leachate migration through the secondary liner due to a 

geomembrane defect (m 3 /s) 

t s = thickness of the soil component of the composite liner (m) 

β = slope angle of the liner system (°) 

λ = parameter defined by Equation 2 (dimensionless) 


389

Technical Paper by JP Giroud, KL Soderman and K. Badu-Tweneboah

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