Large-scale tests for leachate flow through composite liner due to geomembrane defects

Transcription

1 Large-scale tests for leachate flow through composite liner due to geomembrane defects J.-C. Chai 1, N. Miura 2 and S. Hayashi 3 1 Institute of Lowland Technology, Saga University, 1 Honjo, Saga , Japan, Telephone: , Telefax: , chai@cc.saga-u.ac.jp 2 Institute of Soft Ground Engineering Co. Ltd, Ohtakara, Saga , Japan, Telephone: , Telefax: , miuran@viola.ocn.ne.jp 3 Institute of Lowland Technology, Saga University, 1 Honjo, Saga , Japan, Telephone: , Telefax: , hayashi@ilt.saga-u.ac.jp Received 23 June 24, revised 22 January 25, accepted 6 February 24 ABSTRACT: Large-scale and relatively long-term model tests of leachate flow through a composite liner due to geomembrane defects were conducted. The model composite liner consisted of a.363 m thick soil layer and one layer of geomembrane. The diameter of the model device is about 1.2 m. The equipment used is capable of applying up to 2 kpa effective overburden pressure, p, to the model composite liner. Test and analysis results indicate that increasing the p value on the geomembrane reduces the leachate flow rate significantly. It is considered that this reduction is due mainly to the reduction of geomembrane/soil interface transmissivity, Ł. After a leachate flow test, by measuring the concentration of target source ions, it was confirmed that there was flow at the geomembrane/soil interface. Comparing the measured data with predicted values using existing equations shows that assuming a perfect contact condition at the geomembrane/soil interface is not applicable for the conditions tested. Empirical equations by Giroud and Touze-Foltz for the good contact condition can provide a reasonable prediction of the flow rate through a defect in a geomembrane of composite liner under lower p values (close to zero). Based on the test results of this study, equations by Giroud and Touze-Foltz are modified to consider the effect of the p value. Using analytical solutions by Rowe and Touze-Foltz et al., the Ł values are back-evaluated from the test results. KEYWORDS: Geosynthetics, Geomembrane liner, Defect, Experimental, Leachate flow REFERENCE: Chai, J.-C., Miura, N. & Hayashi, S. (25). Large-scale tests for leachate flow through composite liner due to geomembrane defects. Geosynthetics International, 12, No. 3, INTRODUCTION Geomembrane/soil composite liners are widely used in landfill construction. There are four lining systems used for municipal solid waste (MSW) landfills in Japan (Japanese Ministry of Health and Welfare 1998), and two of them require the use of a composite liner. However, in the field, defects in the geomembrane cannot be completely avoided (Giroud and Bonaparte 1989; Rollin et al. 22). Therefore, to design and assess the potential impact of a landfill on the surrounding environment it is necessary to be able to evaluate leachate flow rates through the composite liners due to geomembrane defects. There are several predictive equations proposed for this problem (Giroud 1997; Foose et al. 21; Touze-Foltz and Giroud 23). However, predicted values vary over a wide range. It is difficult to obtain reliable field data to assess the validity of predictive equations because of inadequate # 25 Thomas Telford Ltd knowledge of the size, shape and number of defects in the geomembrane, and unknown hydraulic conditions above and below the composite liner. Therefore carefully controlled large-scale model test data are desirable for validating the predictive methods. Only a few authors have reported large-scale model tests on leachate flow through a defect in a geomembrane (e.g. Fukuoka 1986; Jayawickrama et al. 1988). Also, the effect of effective overburden pressure, p, acting on a geomembrane on the leachate flow rate and the mechanism of leachate migration in composite liners has not been investigated experimentally. In Japan, more than 7% of MSW is incinerated, and the ash is disposed in landfills (Department of Recycling, Japanese Ministry of Environment 1999). For a 15 m thick landfill, the p value on the liner will be about 2 kpa. In this study, large-scale and relative long-term model tests on leachate flow through defects in geomembranes underlying a soil layer were 134

2 Large-scale tests for leachate flow through composite liner due to geomembrane defects 135 conducted, and the effect of the p value on the flow rate and the mechanism of leachate migration are investigated. Based on the test results, the validity of the existing predictive equations is studied, and some modifications are proposed. 2. MATERIALS TESTED AND MODEL TEST SET-UP Considering workability, decomposed granite (in Japan it is called Masado) and andesite rock flour passing a 2 mm sieve were selected to form the soil layers of the model composite liners. The particle size distributions of the soils are given in Figure 1. Compaction tests (JIS A 121) (Japanese Geotechnical Society 2) yielded optimum water contents of about 13% and 11.6%, and maximum dry unit weight of 19. and 2. kn/m 3 for the decomposed granite and rock flour respectively. The compaction curves are shown in Figure 2. For the model tests, compaction water contents were 2% wet of the optimum values. The compaction was made by a light rammer with a self-weight of about.5 kn and striking force of 7.5 to 1. kn. The initial dry unit weights of the compacted soil Percent finer by weight (%) Decomposed granite Rock flour in the model were about 17.6 kn/m 3 for the decomposed granite and about 19. kn/m 3 for the rock flour. The permeability of the soils was measured by fallinghead tests (JIS A 1218) (Japanese Geotechnical Society 2). The results are given in Figures 3 and 4 for the decomposed granite and rock flour respectively. During the large-scale model tests, the density of the soil will change owing to the change in the p value. The Taylor (1948) equation is used to consider the permeability variation due to the change in density: k ¼ k 1 e e ð Þ=:C k (1) where k is the initial permeability, e is the initial void ratio, k is the current permeability, e is the current void ratio, and C k is a constant (C k ¼.5e ; Tavenas et al. 1986). In Figures 3 and 4 the solid line shows the values calculated by Equation 1. For the rock flour, to fit the measured rate of flow of the large-scale model test by using the adopted predictive equations, the values of permeability need to be almost one-tenth of the test result. The values used are given in Figure 4 as a dashed line. The reason is not clear yet. However, after the test, the compacted decomposed granite did not show any obvious Permeability (m/s) Test data Calculated Decomposed granite Diameter (mm) Figure 1. Particle size distribution curves Dry unit weight (kn/m 3 ) Dry unit weight, ã d (kn/m 3 ) Decomposed granite Rock flour Figure 3. Permeability variation of decomposed granite Permeability (m/s) Test data Calculated Calculated (Back-fitted from measured leachate flow rate) Rock flour Water content, w (%) Figure 2. Compaction curves Dry unit weight (kn/m 3 ) Figure 4. Permeability variation of rock flour

3 136 Chai et al. change, but for the compacted rock flour layer it seemed that some kind of cementation effect occurred, and the material became very hard. Owing to the availability of material, two types of geomembrane were used. One is a 1.5 mm thick highdensity polyethylene (HDPE) and the other is a 1.5 mm thick metallocene catalysts polyethylene (MCPE). However, this study was not intended to investigate the effect of geomembrane material. The leachate used was salt water with a salt concentration of 1 g/1. Leachate head above the geomembrane was kept equal to.5 m throughout the tests. The test set-up is illustrated in Figure 5, and the actual device is shown in Figure 6. The model consists mainly of two steel cylinders with an inner diameter of 1173 mm and a system to apply air pressure. The heights of the cylinders are 363 mm and 1 mm respectively, and the thickness of the cylinder wall is about 2 mm. The test procedures are as follows: 1. Place three layers of nonwoven geotextile (3 g/ m 2 ) at the bottom of the model as drainage layers. Put leachate Monitoring tube Effluent Porous loading plate Geomembrane Salted water Soil 1173 mm Compressed air Piston Defect Figure 5. Illustration of model test set-up Sand Geotextile Figure 6. Photograph of model test device Open to air 1 mm 363 mm Then put soil into the lower part of the model and compact the soil in three layers to the desired degree of compaction. 2. Level the surface of the soil carefully and place a geomembrane with a defect in the proper position on top of the soil layer. 3. Set up the upper part of the model by putting a fine sand layer about 2 mm thick on the top of the geomembrane: this transfers the applied load uniformly over the geomembrane, and also serves as a drainage layer. Place O rings between the geomembrane and the model cylinders to prevent leakage. 4. Set up the loading frame (a porous loading plate and a permeable inner load transfer system), and put the leachate into the upper cylinder. 5. Set up the piston and air pressure system and apply the desired effective overburden pressure, p, on the geomembrane. Fix three O rings on the piston to achieve a better air-proof seal around the circumference of the piston. 6. Maintain the level of the leachate in the model, and measure the flow rate from the effluent. 7. After termination of the test, sample the soil at designated locations and measure the concentration of the target source ion in the porewater. 3. TEST RESULTS In total, three tests were conducted. Test conditions, materials used and test period are summarized in Table 1. For Test 1, after the termination of the test, the salt concentration distribution in the soil layer was measured to investigate the mechanism of leachate migration in the composite liner. For Test 2 and Test 3, only the flow rate was measured. Although the tests were conducted in an air-conditioned room, during the test periods a temperature variation of about 1 deg C was measured. Owing to the temperature variation and other influencing factors, it is difficult to obtain an absolute steady state. In the following discussion, the steady flow rate means a relatively steady or a quasi steady state only. Also, for the cases using a decomposed granite soil layer, the permeability of the soil layer is in the order of 1 8 m/s, and higher than the value (1 9 m/s) required for the soil liner. Therefore the flow rate presented below cannot be directly used for design of a geomembrane/soil layer composite liner Results of Test 1 (including a circular defect) For Test 1, first an effective overburden pressure, p, of 5 kpa was applied to the geomembrane. After about 2 weeks the flow became steady, and the flow rate was measured for about 1 month. Then, to investigate the effect of the p value on the leachate flow rate, p was reduced to 1 kpa. After the flow steadied, the measurement was continued for another month. For Test 1 the flow rate before the flow became steady was not recorded properly, and only the steady flow rates, Q, are presented in Figure 7. It can be seen that a decrease of p on the geomembrane increased Q significantly. Q corresponding

4 Large-scale tests for leachate flow through composite liner due to geomembrane defects 137 Table 1. Test conditions Test no. Soil layer Geomembrane Defects Overburden pressure (kpa) Test period Soil Initial dry unit weight (kn/m 3 ) Test 1 Decomposed granite 18. HDPE Circle Radius ¼ 5mm 5!1 4 months (August to November 21) Test 2 Decomposed granite 17.6 HDPE Seam 1mm 3 3 mm 5!2!1!5! 1 months (May 22 to March 23) Test 3 Rock flour 19. MCPE Seam 1mm 3 3 mm (5) (a)!!5!1!2!1!5 9 months (May 23 to January 24) (a) Initially 5 kpa overburden pressure was applied for a few days to obtain a better contact between soil layer and geomembrane, but the rate of flow was not measured Leachate flow rate, Q ( m 3 /s) Test data Forchheimer (193) Giroud (1997) Proposed Overburden pressure, p (kpa) Figure 8. Locations of soil sampling Figure 7. Measured and predicted flow rates (Test 1) Defect to p ¼ 5 kpa is about 55% of that for p ¼ 1 kpa. The possible reasons considered are reduction of the geomembrane/soil interface transmissivity, Ł, and densification of the soil layer under pressure. The analysis revealed that the reduction of the Ł value is most likely the main reason, and the details will be presented in Section 3.3. After termination of Test 1, the soil was divided into four layers 9 mm thick. In each layer 17 samples were taken from different locations, as illustrated in Figure 8. The salt concentrations in the porewater of the samples were measured by using an ion meter. The solution was prepared by mixing 15 g soil sample with 15 g distilled water. After mixing for about 5 min the sample was left for 24 h, and then the concentrations of Na þ and Cl ions in the top clear solution were measured. Also, the water content of the soil sample before mixing with distilled water was measured. So, the salt concentration of the porewater of the soil sample can be calculated. The salt concentration distribution on a cross-section through the center of the model (Test 1) is given in Figure 9. Generally, the simultaneous downward as well as lateral flow pattern can be observed. This is a direct indication that there was flow at the geomembrane/soil interface Figure 9 also indicates that the concentration directly under the defect is relatively lower. The reason for this is not clear, but possibly it is due to the scatter of data or some mistakes in preparing the source solution. The plane view of the concentration of the surface layer is given in Figure 1. The measured flow pattern is not an ideal axisymmetric pattern, but it is close to axisymmetric. Note that the samples were from the top 9 mm thick layer, but there was no special attention paid to obtaining the sample at exactly the same depth g/l Salt content in porewater Figure 9. Contours of salt concentration (source concentration 1 g/1)

5 138 Chai et al Unit: g/l Figure 1. Contours of salt concentration of 9 mm thick surface layer 3.2. Results of Test 2 (including a defect seam) The flow rate measurement started with a p value of 5 kpa. Subsequently the test was continued under p ¼ 2 kpa, and then p was reduced to 1, 5 and kpa. The measured relationships of flow rate Q against time t are given in Figures 11a d. Initially, it took about 1 days for the flow to become steady under p ¼ 5 kpa (Figure 11a). When p increased to 2 kpa, it took about 4 days for the flow to become steady (Figure 11b), and this was considered to be due to the consolidation of the soil layer. When p was reduced to 1 kpa, the flow rate was not measured for about 1 week. When measurement renewed, after about 1 days (about 17 days in total) the flow rate became apparently steady. However, after about 3 days, the flow rate reduced rapidly. The reason for the reduction is not clear, but it was most possibly due to clogging of the defect seam or the geotextile at the bottom of the model. The test was then continued under p ¼ 5 and kpa. For the relationship between flow rate Q and time t for an applied pressure of kpa, the flow rate was initially reduced, possibly owing to the rebound effect of the soil layer. Because of the one-week measurement gap, this phenomenon was not recorded for p reduced from 2 to 1 kpa. Using the values of steady flow rates, the relationship of flow rate Q against effective overburden pressure p is shown in Figure 12. The flow rate reduction with increased p is clearly shown. For the data before the rapid reduction of flow rate under p ¼ 1 kpa, the flow rates under 1 and 2 kpa are, respectively, about 2% and 3% of that under 5 kpa Results of Test 3 (including a defect seam) Test 3 was conducted using the rock flour as the soil layer and a 1.5 mm thick MCPE geomembrane. To obtain a fair contact between the geomembrane and the soil layer, the same pressure as for Test 1 and Test 2 (i.e. p ¼ 5 kpa) was applied initially. However, p ¼ 5 kpa was maintained for a only few days; then p was reduced to and the flow Leachate flow rate, Q ( m 3 /s) Leachate flow rate, Q ( m 3 /s) (a) (c) Leachate flow rate, Q ( m 3 /s) Leachate flow rate, Q ( m 3 /s) (b) (d) Figure 11. Flow rate against time (Test 2): (a) p 5 kpa (loading); (b) p 2 kpa (loading); (c) p 1 kpa (unloading); (d) p kpa (unloading)

6 Large-scale tests for leachate flow through composite liner due to geomembrane defects 139 Leachate flow rate, Q ( m 3 /s) Test data Test data Giroud (1997) 1 Touze-Foltz & Giroud (23) Proposed Forchheimer (193) 1 Foose et al. (21) Overburden pressure, p (kpa) Figure 12. Flow rate against overburden pressure (Test 2) rate was measured. As listed in Table 1, p was increased to 5, 1 and 2 kpa and then returned to 1 and 5 kpa, and the flow rate was measured for each p value. Figure 13a d gives the measured relationship of flow rate Q against time t for p increased from to 2 kpa. For the p ¼ kpa case, the flow rate was gradually increased to a steady value, and with the increase of p the flow rate was reduced to a steady value. The relationship of steady flow rate against p is shown in Figure 14. As for Test 1 and Test 2, the flow rate was reduced significantly with the increase of p. From Test 2, the flow rate difference between loading and unloading cannot be discussed effectively because of the dramatic flow rate change under p ¼ 1 kpa. For Test 3, there was no dramatic change of the flow rate under any p value. For p ¼ 5 and 1 kpa conditions, both during loading and unloading, the flow rates were measured. It can be seen that the flow rate under unloading conditions is less than that under loading conditions. For p ¼ 5 kpa, the flow rate for unloading is about 25% of the value for loading. For a well-compacted soil layer and under the stress range tested, the loading/ unloading cycle may not cause much change of density and therefore of the permeability of the soil layer. This implies that the reduction of the flow rate might be caused mainly by the reduction of the interface transmissivity, Ł. It is hypothetically considered that, under higher p, the contact condition between the geomembrane and the underlying soil will be improved (reducing the interface thickness and therefore the transmissivity), and this improvement is partially permanent: that is, even with the reduction of p, Ł will not increase to the value it had before the higher p value was applied. 4. PREDICTING FLOW RATE 4.1. General consideration Several equations have been proposed to predict the leachate flow rate through a composite liner due to geomembrane defects (e.g. Foose et al. 21; Touze-Foltz and Giroud 23). They can be divided into two groups according to the assumed contact conditions between the Leachate flow rate, Q ( m 3 /s) (a) Leachate flow rate, Q ( m 3 /s) (b) Leachate flow rate, Q ( m 3 /s) (c) Leachate flow rate, Q ( m 3 /s) (d) Figure 13. Flow rate against time (Test 3): (a) p kpa; (b) p 5 kpa; (c) p 1 kpa; (d) p 2 kpa

7 14 Chai et al. Leachate flow rate, Q ( m 3 /s) Test data (loading) Test data (unloading) Giroud (1997) 1 Touze-Foltz & Giroud (23) Proposed Forchheimer (193) 1 Foose et al. (21) Overburden pressure, p (kpa) Figure 14. Flow rate against overburden pressure (Test 3) Vertical strain (%) Unloading 4.2. Circular defects Loading Pressure, p (kpa) Figure 16. Relationship between pressure and vertical strain for compacted rock flour geomembrane and the underlying soil, namely perfect contact and imperfect contact. The main difference between perfect and imperfect contact conditions is that the former assume that there is no flow at the geomembrane/ soil interface, whereas the latter assume that there is. As discussed previously, the variation of flow rate can be caused by the change of the interface transmissivity, Ł, and the permeability, k L, of the soil layer. To evaluate the validity of predictive equations for flow rate through a composite liner due to geomembrane defects, the change of k L due to the change of p needs to be considered. The relationships for the vertical strain of the soil layer against p are shown in Figures 15 and 16 for the decomposed granite and rock flour respectively. The deformation was measured before the termination of Test 2 and Test 3, with the condition that each value of p was maintained for 1 day. It is considered that this kind of test provides a first approximation to the variation of the vertical deformation under each p value. With the data in Figures 15 and 16, the corresponding changes of void ratio e were calculated, and therefore the change of k L was evaluated by Equation 1 and used in predictive equations. Vertical strain (%) Unloading Loading Perfect contact condition For a circular defect, a simple predictive equation for perfect contact condition was proposed by Forchheimer (193) as follows: Q ¼ 4r k L h w (2) where Q is the flow rate, r is the radius of a circular defect, k L is the permeability of the underlying soil layer, and h w is the head on the geomembrane. Foose et al. (21) discussed other more complicated predictive equations for a circular defect with perfect contact condition Imperfect contact condition The imperfect contact condition can be further divided into good and poor contact conditions (Giroud and Bonaparte 1989). Assuming there is flow at the geomembrane/soil interface, and a head distribution at the interface as shown in Figure 17, Giroud (1997) proposed an empirical equation as follows: " # :95 Q ¼ 1:12C q 1 þ :1 h w H L r :2 k:74 L h :9 w (3) where C q is a constant,.21 for good contact and 1.15 for poor contact; and H L is the thickness of the underlying soil layer. Equation 3 should be used only with the units Geomembrane Head distribution 2r Soil liner R h w Pressure, p (kpa) Figure 15. Relationship between pressure and vertical strain for compacted decomposed granite Figure 17. Assumed head distribution pattern around a circular defect

8 Large-scale tests for leachate flow through composite liner due to geomembrane defects 141 specified (m for h w, H L, r, and m/s for k L ). Other parameters are as defined previously. For Test 1 (a circular defect), the values predicted by Equations 2 and 3 are also included in Figure 7. It will be discussed in Section 4.5 that Test 1 might be affected by the boundary conditions of the model. In this case, conceptually using Equation 3 may overpredict the flow rate of Test 1. Accepting this limitation, there are two points that can be observed from Figure 7. The first is that the perfect contact condition (Equation 2) is inapplicable to the test condition, and the second is that Equation 3 with a good contact condition yields a fair prediction of the test data under p ¼ 1 kpa. However, it does not consider the effect of the value of p, and overpredicted the flow rate under p ¼ 5 kpa. Touze-Foltz and Giroud (23) classified the imperfect contact conditions into excellent, good and poor based on the type of underlying soil layer and the quality of the geomembrane layout (whether there are wrinkles). The results from this study indicate that the contact condition is also influenced by the effective overburden pressure, p, on the geomembrane Defect seams As for a circular defect, there are predictive equations for a defect seam with perfect contact and imperfect contact conditions Perfect contact condition There are theoretical equations for the problems analogous to leachate through a composite liner having defect seams with a perfect contact condition (Foose et al. 21). However, the equations include either infinite series or elliptic integrals, and are not convenient for practical use. Foose et al. (21) proposed an empirical equation for a defect seam with perfect contact conditions as follows: 1 Q l ¼ :52 :76 logðw= H L Þ k Lh w (4) where Q l is the leachate rate per unit length of a seam, and w is the width of a seam. Other parameters are as defined previously Imperfect contact condition Giroud et al. (1992) proposed an equation for defect seams with an imperfect interface contact condition. The equation was revised by Touze-Foltz and Giroud (23) as follows: " # :59 Q l ¼ C l 1 þ :52 h w H L w :4 h :45 w k:87 L (5) where C l is a constant, equal to.65 for the good contact and 1.64 for the poor contact. In the case where the length of a seam is finite and the effect of the ends cannot be ignored, as illustrated in Figure 18, the effect of two ends can be approximately evaluated as a circular defect with a radius of w/2 (Giroud et al. 1992). Tests 2 and 3 were analyzed using Equations 2 and 4 for the perfect contact conditions and Equations 3 and 5 for the good contact conditions respectively. Touze-Foltz Defect seam B 2 w Figure 18. Assumed analysis model for a rectangular defect and Giroud (23) stated that Equation 5 is applicable for the permeability of a soil layer within 1 1 to 1 8 m/s conditions. For the decomposed granite soil layer, the permeability was in the order of 1 8 m/s but higher than 1 8 m/s. The use of Equation 5 may result in some error. However, other analytical equations require the value of the interface transmissivity between the geomembrane and the soil layer, and this value was not measured. The results are also included in Figures 12 and 14. They indicate that, under lower p values (close to zero), the Giroud (1997) and Touze-Foltz and Giroud (23) equations provide a reasonable prediction. With the increase of p, the flow rate tends to approach the predicted value with the perfect contact condition. Another interesting point revealed by the analysis is that, for the conditions of the tests, plane flow through a 29 mm long and 1 mm wide seam contributes only 7 28% of the total flow rate. In other words, the flow through the ends is more important. Analytical solutions by Touze-Foltz et al. (1999) show that, for a given diameter or width of a defect, the wetted width of a seam defect is larger than the wetted area (Giroud and Bonaparte 1989) of a circular defect. The above observation is made based on the analysis results using the appropriate equations that consider this difference. Conversely, using Equations 2 and 4, for the perfect contact condition, the plane flow of a 29 mm long and 1 mm wide seam (excluding end effects) is about six times that of a circular hole with a diameter of 1 mm. This is because, under good contact conditions, the radius of the wetted area due to a circular hole is larger than 29 mm, and the leachate can flow more easily for a radial flow than for a plane flow Modification of Giroud (1997) and Touze-Foltz and Giroud (23) equations Based on the test data of this study and the comparison made above, the Giroud (1997) and Touze-Foltz and Giroud (23) equations for circular and seam defects respectively are modified to consider the effect of the value of p on the flow rate. It is assumed that the Giroud (1997) and Touze-Foltz and Giroud (23) equations are suitable for the condition p ¼. To consider the effect of the value of p on the flow rate, it is proposed to multiply by the following dimensionless correction factor, C p : 1 C p ¼ ð1 þ p= p a Þ 2:5 (6) where p a is atmospheric pressure. Conceptually, C p does not include the effect of the p-induced permeability B w

9 142 Chai et al. change of the soil layer, and it only considers the effect of p on the geomembrane/soil interface transmissivity. The values predicted by the proposed equations are also indicated in Figures 7, 12 and 14, and they are closer to the test data, especially for loading conditions. However, the difference between the test results and the predicted values is still large. For example, for Test 2, under p ¼ 5 kpa the predicted value is about 6% of the test result, and under p ¼ 2 kpa the predicted value is about 2.7 times the test result. Also, Equation 6 is proposed based on the test results of this study alone, and further investigation is required on the effect of the effective overburden pressure on the interface transmissivity Back-evaluating the values of interface transmissivity Ł For a circular defect, Rowe (1998) derived an analytical solution based on a model, as illustrated in Figure 19: Q ¼ ðk L r 2 þ 2 1 þ h w ht 2 (7) h t H L where h t is the total head drop across the composite liner, and 1 and 2 are expressions involving Bessel functions, with variables of the radius of a circular defect, r, the thickness of the soil layer, H L, the permeability of the soil layer, k L, the head on the geomembrane, h w, and the Geomembrane Soil liner Circular defect 2r Figure 19. Concept of flow through a defect Longer arrows indicate greater flux transmissivity, Ł, at the geomembrane/soil interface (see Rowe 1998 for detail). The solution was modified by Touze-Foltz et al. (1999) to consider the zero flow rate condition at boundary with a radius of R c. If the predicted radius of the wetted area using the solution by Rowe (1998) is larger than the radius of the model, the Touze- Foltz et al. (1999) modified equation is adopted. Touze-Foltz et al. (1999) proposed an analytical equation for two-dimensional defects: h w þ H L Q l ¼ k L w þ 2 H L Æ tanh cosh 1 h w þ H L H L (8) rffiffiffiffiffiffiffiffiffi k L Æ ¼ (9) ŁH L Equation 8 was used to calculate the flow rate of a seam defect (excluding the end effects). To use Equations 7 and 8, the value of Ł must be pre-specified. Conversely, using a known value of flow rate, the value of Ł can be backevaluated. Combining Equations 7 and 8, values of Ł can be evaluated from the test data for a seam defect. Back-evaluated values of Ł and the radii, R, of wetted area at the geomembrane/soil interface are listed in Table 2. Note that the permeabilities listed in Table 2 were calculated by Equation 1. It can be seen that, with increase of p, the reduction of the back-evaluated value of Ł is much more than the reduction of the permeability (k L )of the soil layers. For example, for Test 2, the value of k L for p ¼ 2 kpa is about 7% of that for p ¼ 5 kpa, but the value of Ł for 2 kpa is only about 1% of that for 5 kpa. Therefore it is considered that the flow rate reductions with p value as presented in Figures 7, 12 and 14 are due mainly to the reduction in values of Ł. Rowe (1998) used the flow rate from Equation 3 to backcalculate the value of Ł for good contact conditions: for k L ¼ 1 9 m/s, Ł ¼ m 2 /s and for k L ¼ 1 8 m/s, Ł ¼ m 2 /s were obtained. These values are comparable to the values in Table 2 (loading condition). However, Rowe (1998) related Ł only to the permeability Table 2. Back-evaluated values of Ł and R Test no. Overburden pressure, p (kpa) Permeability (calculated), k L (m/s) Measured quasi-steady flow rate (1 6 3m 3 /s) Transmissivity Ł (m 2 /s) Radius of wetted area R (m) Test 1 1 (unloading) (b) 5 (loading) (b) Test 2 5 (loading) (b) 2 (loading) (unloading) (unloading) (a) (unloading) (a) (unloading) (a) Test (b) 5 (loading) (b) 1 (loading) (loading) (unloading) (unloading) (a) After rapid reduction of the flow rate. (b) Flow rate was affected by the boundary condition.

10 Large-scale tests for leachate flow through composite liner due to geomembrane defects 143 of the soil layer, but this study indicates that the value of Ł is also influenced by the effective overburden pressure, p. After comparing the numerical results with the predictions using the Rowe (1998) equation for circular defects, Foose et al. (21) stated that when Ł, m 2 /s, the Rowe (1998) equation will underestimate the flow rate because of assumed unidimensional streamlines (Figure 19). The back-evaluated Ł values in Table 2 are much larger than m 2 /s, and therefore using the Rowe (1998) equations for back-calculation may not cause much error. In Table 2, the cases with a radius of wetted area of.6 m mean that the test was affected by the boundary of the model. 5. CONCLUSION Large-scale and relatively long-term model tests of leachate flow through a composite liner due to defects in geomembrane were conducted. The effect of the effective overburden pressure (p) on the leachate flow rate and the mechanism of leachate migration were investigated. Based on the test and analysis results, the following conclusions can be drawn. 1. Increasing the p value on the geomembrane reduces the leachate flow rate significantly. Analysis indicates that the reduction is due mainly to the reduction of the geomembrane/soil interface transmissivity, Ł. 2. The assumption of a perfect geomembrane/soil contact condition is not applicable for the conditions tested. For the conditions considered, it is reasoned that there was interface flow between the geomembrane and the underlying soil layer. After the leachate flow test, by measuring the concentration of target source ion, it is confirmed that there was flow at the geomembrane/soil interface. 3. The Giroud (1997) and Touze-Foltz and Giroud (23) empirical equations for a good contact condition can provide a reasonable prediction of the flow rate for p values close to zero. Based on the results of this study, a modification of the Giroud (1997) and Touze-Foltz and Giroud (23) equations is proposed to consider the effect of the value of p. However, further research on the effect of the value of p on the interface contact condition is needed. 4. Using the Rowe (1998) and Touze-Foltz et al. (1999) solutions, the geomembrane/soil interface transmissivities, Ł, are back-evaluated from the test data, and were found to be comparable with other reported values. ACKNOWLEDGMENTS The authors are indebted to J. Small at the University of Sydney for his thorough review of the paper. The financial support for this study has been provided by the Japanese Grant-in-Aid for Scientific Research program with a grant number of The large-scale model tests were conducted by A. Matsumoto and S. Matsumoto, graduate students at Saga University, Japan. NOTATIONS Basic SI units are shown in parentheses. C k C l C p C q constant (Equation 1) (dimensionless) constant (Equation 5) (dimensionless) constant (Equation 6) (dimensionless) constant (Equation 3) (dimensionless) e void ratio (dimensionless) e initial void ratio (dimensionless) H L thickness of soil layer (m) h w head on geomembrane (m) h t total head drop across composite liner (m) k permeability (m/s) k initial permeability (m/s) k L permeability of soil layer (m/s) p effective overburden pressure (N/m 2 ) p a atmospheric pressure (N/m 2 ) Q flow rate (m 3 /s) Q l flow rate per unit length of a seam (m 3 /s) R radius of wetted area (m) r radius of circular defect (m) t time (s) w width of seam (m) 1 expression involving Bessel functions (Equation 7) (m 2 ) 2 expression involving Bessel functions (Equation 7) (m 2 ) Ł interface transmissivity (m 2 /s) REFERENCES Department of Recycling, Japanese Ministry of Environment (1999). Report on Amount of Municipal Solid Waste and Deposal (Record of Year 1999). Tokyo: Japanese Ministry of Environment (in Japanese). Foose, G. J., Benson, C. H. & Edil, T. B. (21). Predicting leachate through composite landfill liners. Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 127, No. 6, Forchheimer, P. (193). Hydraulik, 3rd edn. Leipzig/Berlin: B. G. Teubner ed., 596 pp. Fukuoka, M. (1986) Large scale permeability tests for geomembranesubgrade system. Proceedings of the 3rd International Conference on Geotextiles, Vienna, 3, Giroud, J. P. (1997). Equations for calculating the rate of liquid migration through composite liners due to geomembrane defects. Geosynthetics International, 4, No. 3 4, Giroud, J. P. & Bonaparte, R. (1989). Leakage through liners constructed with geomembranes. Part II: Composite liners. Geotextiles and Geomembranes, 8, No. 2, Giroud, J. P., Badu-Tweneboah, K. & Bonaparte, R. (1992). Rate of leakage through a composite liner due to geomembrane defects. Geotextiles and Geomembranes, 11, Japanese Geotechnical Society (2). Soil Testing, Methods and Explanations. Tokyo: Japanese Geotechnical Society (in Japanese). Japanese Ministry of Health and Welfare (1998). Technical Standard for Landfill Design of Municipal Solid Waste and Industrial Waste. Order No. 2. Tokyo: Japanese Ministry of Health and Welfare (in Japanese).

11 144 Chai et al. Jayawickrama, P. W., Brown, K. W., Thomas, J. C. & Lytton, R. L. (1988). Leakage rates through flaws in membrane liners. Journal of Environmental Engineering, ASCE, 114, No. 6, Rollin, A., Marcotte, J. M. & Caquel, F. (22). Lessons learned from geo-electrical leaks surveys. Proceedings of the International Conference on Geosynthetics, Nice, Vol. 2, pp Rowe, R. K. (1998). Geosynthetics and the minimization of contaminant migration through barrier systems beneath solid waste. Proceedings of the 6th International Conference on Geosynthetics, Atlanta, 1, Tavenas, F., Tremblay, M., Larouche, G. & Leroueil, S. (1986). In situ measurement of permeability in soft clays. Proceedings of the ASCE Special Conference on Use of In-situ Tests in Geotechnical Engineering, Blacksburg, pp Taylor, D. W. (1948). Fundamentals of Soil Mechanics. New York: John Wiley & Sons. Touze-Foltz, N. & Giroud, J. P. (23). Empirical equations for calculating the rate of liquid flow through composite liners due to geomembrane defects. Geosynthetics International, 1, No. 6, Touze-Foltz, N., Rowe, R. K. & Duquennoi, C. (1999). Liquid flow through composite liners due to geomembrane defects: analytical solutions for axisymmetric and two-dimensional problems. Geosynthetics International, 6, No. 6, The Editors welcome discussion in all papers published in Geosynthetics International. Please your contribution to by 15 December 25.