Effect of effective overburden pressure on geomembrane/soil interface transmissivity

Transcription

1 Geosynthetics International, 28, 15, No. 1 Effect of effective overburden pressure on geomembrane/soil interface transmissivity J.-C. Chai 1, S. Hayashi 2 and N. Khalili 3 1 Department of Civil Engineering, Saga University, 1 Honjo, Saga , Japan, Telephone: , Telefax: , chai@cc.saga-u.ac.jp 2 Institute of Lowland Technology, Saga University, 1 Honjo, Saga , Japan, Telephone: , Telefax: , hayashi@ilt.saga-u.ac.jp 3 School of Civil and Environmental Engineering, The University of New South Wales, UNSW Sydney, NSW 252, Australia, Telephone: , Telefax: , n.khalili@unsw.edu.au Received 3 September 26, revised 16 October 27, accepted 16 October 27 ABSTRACT: Fluid flow through a defect in the geomembrane of a composite geomembrane/soil liner (flow rate tests) and interface transmissivity tests between a geomembrane and a soil layer were conducted. The results are compared, and the effect of overburden pressure p9 on the geomembrane/soil interface transmissivity Ł and interface thickness t in is investigated. For flow rate tests, the values of Ł are back-calculated using the Rowe and Touze-Foltz et al. solutions. With known values of Ł, t in is calculated using Newton s viscosity law for fluid flow between two parallel plates. For the conditions considered, it is shown that Ł and t in reduce significantly with increasing p9. Comparisons are made between the calculated values of Ł and t in and those reported in the literature. It is shown that ignoring the effect of p9 on Ł and t in can lead to gross overestimation of these parameters. KEYWORDS: Geosynthetics, Geomembrane, Interface transmissivity, Laboratory model test REFERENCE: Chai, J.-C., Hayashi, S. & Khalili, N. (28). Effect of effective overburden pressure on geomembrane/soil interface transmissivity. Geosynthetics International, 15, No. 1, [doi: 1.168/gein ] 1. INTRODUCTION Composite geomembrane/soil liners are widely used in landfill construction. The dominant modes of fluid movement through these liners are flow through defects of the geomembrane, and Darcian flow through the compacted clay layer. In the field, defects in geomembranes cannot be avoided, and thus their impact on the flow through composite geomembrane/soil liners must be taken into account (Giroud and Bonaparte 1989; Rollin et al. 22; Needham et al. 24). In recent years, several approaches have been proposed for the determination of flow through defective geomembrane/soil liners (e.g. Rowe 1998; Touze-Foltz et al. 1999). The typical assumption made is that flow through a defect in a geomembrane simultaneously flows radially between the geomembrane and the soil (i.e. the interface flow) and in the downward direction through the compacted soil layer. The parameters influencing the interface flow are: the interface transmissivity, Ł; the radius of the defect, r, in the case of a circular defect; the contact condition between the geomembrane and the soil layer (normally included in the value of Ł); the permeability, k L, # 28 Thomas Telford Ltd and the thickness of the underlying soil layer, H L ; the hydraulic head above the geomembrane, h w ; and the effective overburden pressure, p9. Wrinkles of the geomembrane formed during field installation have a significant influence on the interface flow (Rowe, 25; Take et al. 27), but this is not the subject of this study. There have been many investigations into the effect of interface contact condition and k L on the value of Ł (e.g. Jayawickrama et al. 1988; Harpur et al. 1993; Giroud 1997; Rowe 1998), but very little work has been conducted investigating the effect of p9 on Ł. Chai et al. (25) for the first time reported test results on the effect of p9 on the flow rate of a geomembrane/soil layer composite liner with geomembrane defects. They conducted large-scale flow rate tests using decomposed granite and rock flour as soil layers, and showed that the flow rate reduced significantly with increasing p9. Barroso et al. (26) conducted a similar series of laboratory tests on flow through a geomembrane and geosynthetic clay liner (GCL) with a defect in the geomembrane, but concluded that, when using non-prehydrated GCL, the effect of p9 on the flow rate was insignificant. 31

2 32 Chai et al. Generally, there are two methods of evaluating values of Ł: back-calculating from the result of flow rate tests, i.e. fluid flow through a composite geomembrane/soil liner with a defect in the geomembrane (e.g. Rowe 1998); and direct measurement by the geomembrane/soil layer interface transmissivity test (e.g. Harpur et al. 1993). The flow rate test simulates a situation closer to the field condition, but the theoretical solutions (e.g. Rowe 1998) used for the back-calculation normally assume unidirectional flow in the soil layer, which does not strictly represent the test condition. Also, the laboratory model test may be affected by the scale of the model. The transmissivity test provides a direct measurement of the value of Ł, but the test cannot eliminate possible fluid flow to the edge of the interface through the soil layer. In the literature, there is no report of direct comparison of Ł values obtained by these two methods. In this paper, the effect of p9 on the interface transmissivity, Ł, and the interface thickness, t in, of the geomembrane/soil interface is investigated through additional experimental test data. The results from several flow rate tests on two composite geomembrane/soil liners with geomembrane defects and interface transmissivity tests between a geomembrane and a soil layer are presented, and the values of Ł are calculated and compared. Combined with the results of Chai et al. (25), the effect of p9 and k on Ł and t in is discussed. 2. FLOW RATE TESTS 2.1. Equipment and materials The flow rate tests were conducted using a rigid-wall permeameter, designed and manufactured during the course of this investigation. The device consisted of: (1) a transparent cylinder made of acrylic resin with an inner diameter of 15 mm (wall thickness of 5 mm) and height of 4 mm; (2) upper and lower pedestals made of stainless steel; (3) a piston made of stainless steel; and (4) a bellofram fixed to the top of the upper pedestal for applying overburden pressure, p9. The piston was perforated with 3 mm diameter holes at 2 mm pitch to allow for drainage. Sealing between the cylinder and the piston was achieved by a 4 mm diameter O ring lubricated with silicone grease and fixed around the piston. On the lower pedestal, between the piston and the geomembrane, a 5 mm thick ceramic porous stone was placed to ensure uniform distribution of fluid pressure on the geomembrane. A schematic and a photograph of the device are shown in Figure 1. The geomembrane used in the experiments was 1.5 mm thick metallocene catalysts polyethylene (MCPE) sheet. Two types of soils were used: a decomposed granite, and an Ariake clay. The particle size distributions of the soils are shown in Figure 2. The Ariake clay had a liquid limit of 116.6% and plastic limit of 57.5%, and consisted primarily of smectite clay mineral (Ohtsubo et al. 1995). For the decomposed granite, compaction tests (JIS A 121) (Japanese Geotechnical Society, 2) yielded an optimum water content of about 13% and a maximum dry unit weight of 19. kn/m 3. For the Ariake clay, the test sample was made by consolidation. The relationships between the void ratio e and permeability k for both soils are given in Figure 3. The permeability values for the decomposed granite were measured by falling-head tests, and those for the Ariake clay were back-calculated from laboratory consolidation test results. The variation of permeability with void ratio e generally followed the correlation proposed by Taylor (1948), k ¼ k 1 e e ð Þ=C k (1) Bellofram cylinder Compressed air Dial gauge Solution inlet Piston O ring Geomembrane (Glued here) Clay Porous stone 4 mm Solution Clay Piston and porous stone Geomembrane 15 mm Effluent collection (a) (b) Figure 1. Test device: (a) schematic; (b) photograph Geosynthetics International, 28, 15, No. 1

3 Effect of effective overburden pressure on geomembrane/soil interface transmissivity 33 Percent finer by weight (%) Clay Decomposed Granite Diameter (mm) Figure 2. Particle size distributions of the soils Hydraulic conductivity, k (m/s) Decomposed granite Test data Calculated Taylor s (1948) equation Clay Void ratio, e Figure 3. Relationship between dry unit weight and permeability of decomposed granite 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 ¼.4e to.5e ; Tavenas et al. 1986). In this study, C k ¼.5e for the decomposed granite and.4e for the Ariake clay were found to be suitable. In Figure 3, the term calculated refers to permeability values predicted by Equation Sample preparation and test procedure To make identical specimens for testing, the test soils were statically compacted or consolidated inside the permeameter to a target dry density and a target thickness. For the decomposed granite, prior to compaction, the soil was carefully wetted to the optimum water content and then placed in a sealed plastic bag and allowed to cure for a minimum of 48 h. The soil was compacted to a dry unit weight of 17.7 kn/m 3 (about 93% of maximum dry unit weight obtained by Japanese standard JIS A 121). Then the surface of the soil sample was levelled and the sample was subjected to a compression pressure of 5 kpa for a period of one week. In the case of the Ariake clay, the sample was prepared in a paste close to its liquid limit, and was then consolidated under an axial pressure of 5 kpa. Although the procedure used for preparing the Ariake clay specimen was not identical to the field condition, it was considered acceptable given that the Geosynthetics International, 28, 15, No. 1 main purpose of the study was to investigate the effect of overburden pressure and the soil type on the interface transmissivity. Therefore the Ł values obtained for the Ariake clay and the geomembrane interface may not be directly used for a field design. The geomembrane sample used in the experiments was 15 mm in diameter, glued to the base of the piston to ensure no radial flow occurred between the piston and the geomembrane (see Figure 1). The defect made in the geomembrane was circular, with a nominal diameter of 1 mm, and located at the centre of the geomembrane. The glue condition was checked by applying about.5 m water head between the piston and the geomembrane and stopping water flow through the hole by pressing a fingertip over it. If there was leakage between the piston and the geomembrane, the geomembrane was re-glued. Following the sample set-up, flow rate tests were conducted by lowering the piston to position, applying the target overburden pressure, and subjecting the sample to a predetermined hydraulic head, which was maintained constant during the test. The flow rates were measured using a graduated glass with a capacity of 1 5 m 3. The mouth of the glass was covered by a plastic sheet to eliminate evaporation. For a given overburden pressure, the measurements were continued until the flow rate reached a quasi-steady state. After that the piston, together with the geomembrane, was disassembled and washed to make sure the flow system was not clogged. Then the test was set up again and continued with a new overburden pressure. Three series of tests (designated Tests 1 to 3) were conducted, with the test conditions listed in Table 1. Test 1 was conducted using the decomposed granite, and Tests 2 and 3 were conducted using the Ariake clay Test results Decomposed granite The test results for decomposed granite (Test 1), in terms of measured flow rate Q against elapsed time for different p9 values, and measured quasi-steady flow rate Q qs, against p9, are given in Figs 4 and 5, respectively. As indicated in Table 1, the sample for Test 1 was prepared under an overburden pressure of 5 kpa, and the flow rate tests were conducted at overburden pressures of 4, 3, 2, 1 and kpa, and then increasing p9 to 5 kpa again. During the reduction of the overburden pressure from 5 kpa to kpa there was a certain rebound of the soil layer along the unloading path, which was estimated to be less than.2% of the thickness of the sample. This was considered to have a negligible effect on the permeability of the test soil. However, since the absolute flow rate was very small, the elastic deformation/rebound resulted from the changing of p9 did affect the flow rates. Reducing the overburden pressure will induce certain rebounding of the sample, and the rebounding will absorb a certain amount of water and affect the flow rate. Also, reducing the overburden pressure will increase the interface transmissivity, and it takes time for the flow rate to become quasisteady. The increase in the overburden pressure from to

4 34 Chai et al. Table 1. Test conditions Test no. Soil type Diameter of geomembrane defect (mm) Thickness of soil layer H L (mm) Hydraulic head above geomembrane h w (mm) Overburden pressure p9 (kpa) Test 1 Decomposed granite (5) 4!3!2!1!!5 Test 2 Ariake clay 1 67!67!62!59! (5)!5!1!15!2 Test 3 Ariake clay 1 62!57!54! (5)!1!15! Flow rate, Q (1 m /s) Flow rate, Q (1 m /s) (a) (b) Flow rate, Q (1 m /s) Flow rate, Q (1 m /s) (c) (d) 1. Flow rate, Q (1 m /s) Flow rate, Q (1 m /s) (e) (f) Figure 4. Flow rates elapsed time curves of Test 1: (a) ó kpa; (b) ó 1 kpa; (c) ó 2 kpa; (d) ó 3 kpa; (e) ó 4 kpa; (f) ó 5 kpa 5 kpa conversely resulted in reducing the flow rate with time (Figure 4f). As shown in Figure 5, there is a strong dependence of quasi-steady Q qs on p9. Atp9 ¼ 5 kpa, the value of Q qs is about 37% of its corresponding value at p9 ¼ Ariake clay Test results for the Ariake clay (Tests 2 and 3), in terms of the measured flow rates Q against elapsed time t for different values of p9 are given in Figure 6. The test conditions are given in Table 1. For all cases considered, Geosynthetics International, 28, 15, No. 1

5 Effect of effective overburden pressure on geomembrane/soil interface transmissivity Flow rate, Q qs (1 m /s) Overburden pressure, p (kpa) Figure 5. Flow rate overburden pressure plot of Test 1 except p9 ¼, the value of p9 increased from a lower value to a higher target value. As p9 increased, due to the effect of consolidation, there was an initial increase in the rate of flow. This trend continued until the end of primary consolidation (approximately two days) before the flow rates started to decrease towards a quasi-steady value (Figs 6b to 6e). For p9 ¼ (where p9 was reduced from 5 kpa to ), Test 3 showed a gradual increase of the flow rate as in Test 1, but Test 2 did not, and the reason for this is not clear. It is noted that in Figs 6b and 6c for Test 3, the quasisteady state may not have been reached. These tests had to be terminated as the flow rate was too small to be measured accurately. Although the thickness of the Ariake clay sample was much less than that of the decomposed granite (Table 1), owing to its lower permeability, the flow rates recorded were about 1/1th of the values for the decomposed granite. Sometimes the amount of outflow was merely a few drops per day. Barroso et al. (26) reported similar problems, and they measured the amount of inflow into the system from a Marriott bottle (a burette system able to apply a constant head) instead of measuring the outflow. Another factor is the deformation of the soil.8.8 Flow rate, Q (1 ml/s) Flow rate, Q (1 ml/s) (a) (b) 3 Flow rate, Q (1 ml/s) Flow rate, Q (1 ml/s) (c) (d).8 Test 2 Test 3 Flow rate, Q (1 ml/s) (e) 4 5 Figure 6. Flow rates elapsed time curves of Tests 2 and 3: (a) ó kpa; (b) ó 5 kpa; (c) ó 1 kpa; (d) ó 15 kpa; (e) ó 2 kpa Geosynthetics International, 28, 15, No. 1

6 36 Chai et al. layer during the tests. In general, in all tests, the consolidation process was complete within 2 days. However, owing to the variation of air pressure in the tank of the air compressor during the test, there was a certain fluctuation of the pressure, which was within 3 kpa. Owing to creep and the variation of p9 (3 kpa), sometimes the daily change of soil layer thickness of about.1 mm was observed after 1 week s elapsed time. If this is converted to the amount of water absorbed in or squeezed out, an equivalent flow rate of about m 3 /s can be obtained. Therefore, for a measured flow rate of this order, the value can be viewed only as an order, but not an absolute magnitude. The relationships of quasi-steady Q qs against p9 for Tests 2 and 3 are given in Figure 7. Again, the Q qs values show a tendency to reduce with increasing p9, as in Test 1. (a) Burette 3. INTERFACE TRANSMISSIVITY TESTS 3.1. Equipment and materials In addition to the flow rate tests, a series of direct interface transmissivity tests were conducted. A schematic description and a photograph of the transmissivity test device utilised are shown in Figs 8a and 8b, respectively. The main body of the device is made of copper, and consists of lower and upper parts. The lower part consists of a container with 15 mm inner diameter and 5 mm wall thickness. A ceramic porous stone, 5 mm in diameter and 3 mm thick, is located at the centre of the bottom of the container to provide drainage for consolidation tests. On the top edge of the container a ceramic porous stone ring, 2 mm thick, is placed to provide drainage for transmissivity tests. The upper part of the device is a loading plate, 15 mm in diameter, with a ceramic porous stone, 12 mm in diameter, located at the centre and in turn connected to a burette. The cross-sectional area of the burette is m 2. A geomembrane sample, 15 mm in diameter with a hole in the centre, was glued to the loading plate. The overburden pressure up to 2 kpa was applied by using the vertical loading system of standard consolidation test equipment. To conduct the consolidation.5 Porous stone ring Outlet Geomembrane Porous stone Overburden pressure ( 2 kpa) 15 mm Defect Clay layer Figure 8. Transmissivity test device: (a) picture of main body; (b) schematic (b) tests a collar with an inner diameter of 15 mm and a height of 25 mm was set on the top of the lower part to form a consolidation cell. The geomembrane used in the experiments was 1.5 mm thick MCPE sheet, the same as that used in the flow rate tests. The soil used in the experiments was the Ariake clay, the properties of which were described in Section Flow rate, Q qs (1 m /s) Test 2 Test Overburden pressure, p (kpa) Figure 7. Overburden pressure against quasi-steady state flow rate of Tests 2 and 3 Geosynthetics International, 28, 15, No Sample preparation and test procedure The soil layer can be made by compaction or consolidation. In this study the Ariake clay was used and the soil layer was made by consolidation. First, Ariake clay about 2 mm thick and with a water content close to its liquid limit was placed in the cell, and consolidated under the desired pressure for 2 days. Then the sample was unloaded to remove the collar, and excess soil was cut away to form a soil layer 5 mm thick in the container. The surface was levelled by both a wire saw and a straight metal cutter. The geomembrane sample had a diameter of 15 mm, and a hole 2.9 mm in diameter was made in the centre of the sample. Then the geomembrane was glued to the upper

7 Effect of effective overburden pressure on geomembrane/soil interface transmissivity 37 loading plate. The glue condition was checked with a similar method as for the flow rate test. Prior to each test, the drainage system of the loading plate was de-aired by flowing water. A thin layer of water was then sprayed on top of the soil sample before setting the loading plate to expel possible air bubbles between the geomembrane and the soil. The loading plate with the geomembrane sample in position was then subjected to overburden pressure of the same value as the consolidation pressure used for preparation of the soil sample (except for the test conducted at an overburden pressure of 1 kpa). The sample was left under the load for 3 h to complete the elastic and/or consolidation deformation of the soil layer. Elastic consolidation might result in a.1 to.2 mm deformation of a 5 mm thick soil sample. Since a 2 mm thick ceramic porous stone ring was fixed on the top edge of the lower part of the container, this deformation will not result in perimeter resistance for the interface. Then the consolidation drainage valve was closed, and falling-head transmissivity tests were conducted with an initial water head of about 1.3 m. A thin layer of silicone oil was put on the top of the water surface inside the burette to prevent possible evaporation. The water level inside the burette and the corresponding time interval were measured periodically. During the transmissivity test, water flow through the soil sample was not allowed Test results A total of five transmissivity tests were conducted at overburden pressures of 1, 5, 1, 15 and 2 kpa. For the overburden pressure of 1 kpa, the soil layer was consolidated to an axial pressure of 5 kpa. The test with zero overburden pressure was not successful, as the glue between the loading plate and the geomembrane was broken at about 1.3 m head of water. Since the absolute flow rate was very small, and the temperature was variable, it was difficult to adopt a rigorous criterion for the flow rate to terminate the tests. Instead, it was adopted that the duration of each test was more than 5 days. After setting up, the first day was used to stabilise the flow system; measurement was started from the second day. The measured water-head differences and corresponding time intervals are listed in Table INTERFACE TRANSMISSIVITY 4.1. Method of calculation Flow rate tests For composite geomembrane/soil liners with a circular defect in the geomembrane, Rowe (1998) derived the following analytical solution for the flow rate Q under the assumption that the flow in the soil layer is unidirectional, as illustrated in Figure 9. Q ¼ ðk L r 2 þ 2 1 þ 2 2 2h w ht 2 (2) h t H L where h t is the total head drop across the composite liner; r is the radius of a circular defect, H L is the thickness of soil layer, k L is the permeability of the soil layer, and h w is the head on the geomembrane. 1 and 2 are expressions involving Bessel functions with variables of r, H L, k L, the transmissivity Ł at the geomembrane/soil interface, and the radius of the wetted area, R. (The wetted area is the area wetted by the geomembrane/soil interface flow.) Table 2. Results of transmissivity test with Ariake clay as soil layer p9 (kpa) h (m) h 1 (m) t (s) Ł (m 2 /s) Average Ł (m 2 /s) t in (1 6 m) The cross-sectional area of the burette is a ¼ m 2. Geosynthetics International, 28, 15, No. 1

8 38 Chai et al. Geomembrane Circular defect R of Q (Q qs in this study), a corresponding value of Ł can be back-calculated. Soil liner Detailed expressions for 1 and 2 and the method for calculating R are given in the Appendix. Let the radius of a physical model be denoted as R c.in cases where R. R c, Rowe s solution is not applicable. Touze-Foltz et al. (1999) developed a solution with zero flow rate condition at r ¼ R c, which can be used for experiments in which the radius of the physical model is less than the radius of the calculated wetted area. Touze-- Foltz et al. s (1999) solution is given as Q ¼ ðr 2 k L A Q ¼ B Q ¼ h t 2ðr ŁÆ A Q I 1 ðær Þ B Q K 1 ðær Þ H L (3a) h t K 1 ðær c Þ K 1 ðær c ÞI Ær K 1 ðær c ÞI Ær 2r Figure 9. Illustration of leachate flow path ð Þþ K ðær h t I 1 ðær c Þ ð Þþ K ðær Longer arrows indicate greater flux ÞI 1 ðær c Þ ÞI 1 ðær c Þ (3b) (3c) p in which Æ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K L =H L Ł. K, K 1, I and I 1 are the modified Bessel functions of order zero and one. In both Rowe and Touze-Foltz et al. s solutions, Ł is needed to calculate the flow rate Q. Conversely, with a known value Transmissivity tests From the transmissivity tests (Table 2), the corresponding Ł values can be directly calculated by (Harpur et al. 1993) Ł ¼ aln ð R 2=r Þln ðh =h 1 Þ (4) 2ð t where R 2 is the outer radius of specimen, a is the crosssectional area of the falling-head burette, h is the initial head difference, h 1 is the final head difference, and t is the time interval. 4.2 Back-calculated or directly calculated values of Ł From the flow rate test results, the back-calculated Ł values and radius R of the wetted area are listed in Table 3. For Tests 2 and 3 the variation of void ratio and therefore the permeability and the thickness of the soil layers were considered during the back-calculations. For Test 1, the variation of the thickness of the soil layer during unloading was not large enough to lead to discernible changes in the soil permeability k L, and therefore it was not considered in the calculations. For this test, the value of k L adopted was that at p9 ¼. For the transmissivity tests, the calculated values of Ł are given in Table 2. Foose et al. (21) showed that when log(k i /k L ), 4.5, in which k i denotes the permeability of the geomembrane/ soil layer interface, the assumption of unidirectional flow in the soil layer would lead to an underprediction of the flow rate. In back-analyses, to fit the measured flow rates, the Ł values will then be over-evaluated. With the information in Table 3, log(k i /k L ) ranges from 3.2 to 4.. Based on the result of a comparative study by Foose et al. (21), this would result in flow rates predicted by Rowe s solution of 82 93% of the numerical value, respectively. For the conditions adopted for the model tests, from Rowe s solution, a 7 18% increase of flow rates will lead Table 3. Back-evaluated values of Łand R Test no. Overburden pressure p9 (kpa) Permeability, k (3 1 8 m/s) Measured quasi-steady flow rate, Q ( m 3 /s) Transmissivity, Ł (m 2 /s) Radius of wetted area, R (m) Interface thickness, t in (1 6 m) Test a Test Test a Restricted by the radius of the model. Geosynthetics International, 28, 15, No. 1

9 Effect of effective overburden pressure on geomembrane/soil interface transmissivity 39 to about a 9 23% overestimation of Ł values. It will be shown later (in Figure 11) that the values of Ł obtained for the geomembrane/ariake clay interface from the transmissivity tests are, in general, lower than the backcalculated values, directly supporting this argument. Figure 1 shows the relationship between the interface transmissivity Ł and the overburden pressure p9 for decomposed granite. Also included in this figure are the back-calculated data from the test results of Chai et al. (25), which typically plot above the data obtained from this study. This is considered to be due to the better interface contact condition and fewer soil surface heterogeneities achieved in the present study. Nevertheless, both data sets clearly show a reduction in Ł with increasing p9, especially for p9,1 kpa. The Ł p9 relationship for the geomembrane/ariake clay interface is given in Figure 11. Again, generally Ł reduces with increasing p9. Note that the change of the value of Ł may not be due only to the change of p9. The consolidation condition of the soil layers may also have an effect on the interface contact condition, and therefore on the value of Ł. It can also be seen that the Ł values from the transmissivity tests are comparable but relatively lower than that back-calculated values from the flow rate test results. As noted by Harpur et al. (1993), for this kind of transmissivity test the possible radial flow within the soil layer may influence the test results; nevertheless, it is considered that the results from the transmissivity test be more reliable than those back-calculated from the flow rate tests. This is because for the transmissivity tests there was no pressure variation and less discrepancy between the theoretical assumption and the test condition. As a reference, the measured data between a geosynthetic clay liner (GCL) and a geomembrane by Harpur et al. (1993) are also included in Figure 11. Harpur et al. used five types of GCL, four with geotextile on both sides of the GCL and one without geotextile. The lowest value of Ł from Harpur et al. s tests was for bentonite/geomembrane contact, and the highest value was for geomembrane/geotextile bentonite contacts. The back-calculated values for the geomembrane/ariake clay interface plot somewhere in the middle of Harpur et al. s test data. Touze-Foltz and Barroso (26) reported some values of Ł for GCL/geomembrane interfaces for p9 ranging from 25 to 2 kpa. The values reported are comparable to those from Harpur et al. (1993), but, the relationship between Ł and p9 was not given, and therefore could not be included for comparison here. The Ł values for the geomembrane/ Ariake clay interface is about two orders of magnitude less than that of the geomembrane/decomposed granite interface. The particle size at which 5% of the soil is finer, D 5, of the Ariake clay and the decomposed granite are about.1 mm and.39 mm, respectively. Conceptually, the particle size and its distribution have a direct influence on the magnitude of the interface thickness t in, and therefore on Ł. Further study is needed to find a general relationship between the value of Ł and the particle size of the soil. Interface transmissivity, θ (m /s) Small-scale test Chai et al. (25) (loading) Chai et al. (25) (unloading) Predicted Overburden pressure, p (kpa) Figure 1. Ł p9 relationship, decomposed granite Interface transmissivity, θ (m /s) From flow rate test Transmissivity test Harpur et al. (1993) Predicted Overburden pressure, p (kpa) Figure 11. Ł p9 relationship, Ariake clay Geosynthetics International, 28, 15, No Ł p9 relationship Chai et al. (25) proposed an empirical equation for considering the effect of p9 on the flow rate Q through a geomembrane defect of a composite liner. Considering the direct correlation between Ł and Q, the following relationship may be proposed for the effect of p9 on Ł: 1 Ł ¼ Ł ð1 þ p9= p a Þ 2:5 (5) where Ł is the interface transmissivity at p9 ¼, and p a is the atmospheric pressure. Values calculated by Equation 5 are presented as solid lines in Figs 1 and 11. For p9,1 kpa, Equation 5 yields a reasonable prediction of the variation of Ł with p9. However, for p9.1 kpa, the calculated values are lower than most test data. Although the number of test data are not large enough to make a general conclusion, Figs 1 and 11 show that when p9. 1 kpa, the effect of p9 on Ł may not be significant Ł k relationship Rowe (1998) proposed an empirical relationship between Ł and the permeability k L of soil layer. For good contact conditions the equation is log Ł ¼ :7 þ 1:36 logðk L Þþ :18½logðk L ÞŠ 2 (6) For excellent contact conditions, Touze-Foltz and Giroud (23) proposed replacing the constant.7 in Equation 6 by.321. Good contact conditions mean a

10 4 Chai et al. geomembrane installed on an adequately compacted soil layer with as few wrinkles as possible, and excellent contact conditions mean a geomembrane installed on a bentonite geocomposite layer (Touze-Foltz and Giroud 23). Ł k L relationships are plotted in Figure 12. The calculated values from Equation 6 for good and excellent conditions are also included in Figure 12 as reference lines. Equation 6 was obtained based on Giroud s (1997) empirical equation for predicting flow rate through the defect of the geomembrane of a geomembrane/soil layer liner: this does not consider the effect of p9, and therefore it yields values of Ł that are larger than most of the backcalculated values from the flow rate tests as well as the values from the transmissivity tests in this study. Figure 12 clearly shows that the values of Ł depend not only on the permeability of the soil layer but also on p9 acting on the geomembrane. The Ł values from Touze-Foltz and Barroso (26) for GCL/geomembrane interfaces calculated from the test results reported by Barroso et al. (26) are also included in Figure 12 for comparison. Based on the maximum Ł value of their test data, a k GLC Ł relationship for a GCL/geomembrane interface has been proposed as (Touze-Foltz and Barroso 26): log Ł ¼ 2:2322 þ :7155 logðk GCL Þ (7) where k GCL is the permeability of the GCL. The calculated values from Equation 7 are indicated in Figure 12. It can be seen that the Ł values for the Ariake clay/ geomembrane interface are roughly of the same order of magnitude as those of the GCL/geomembrane interface, although the permeability of the Ariake clay is about two orders higher than that of the GCL tested by Barroso et al. (26). This preliminary comparison indicates that the relationship between the interface transmissivity and the permeability of soil layer may not be a unique function t in p9 relationship From Newton s viscosity law for flow between two parallel plates, the relationship between interface thickness t in and Ł is t in ¼ 12çŁ 1=3 or Ł ¼ t3 in rg (8) rg 12ç where ç is the coefficient of viscosity of water ( ¼ Pa s at 28C), r is the density of water, and g is the gravitational constant. Equation 8 indicates that Ł is a function of the thickness t in of the interface. It can be reasoned that the value of t in is influenced mainly by the soil type (i.e. particle size, particle distribution, structure, mineralogy, fabric etc.), the p9 value on the interface, and the surface topography of the geomembrane. Using Equation 8 and ç ¼ Pa s, the calculated t in values from Ł are listed in Tables 2 and 3 for the flow rate tests and the transmissivity tests, respectively. Figure 13 shows the relationship between k L and t in. The relationship between t in and k L proposed by Touze-Foltz and Giroud (23) for excellent contact conditions based on the test data from Brown et al. (1987) (see Jayawickrama et al. 1988) is also plotted as a solid line for comparison. For these data, the effective overburden applied on the geomembrane was a.15 m thick gravel layer. Considering the buoyant unit weight of the gravel, the equivalent effective overburden would have been about 1.5 kpa, which is very low p9. The t in values calculated from the data reported by Chai et al. (25) are close to the data for excellent contact conditions, but the results from this study are lower than the values for excellent contact conditions. It is considered that the smaller t in values are due mainly to the effect of p9 and the improved contact conditions achieved with the small-scale model. 5. CONCLUSIONS Laboratory tests were conducted on fluid flow through a defect in the geomembrane of a composite geomembrane/ soil liner (flow rate tests) as well as interface transmissivity tests between a geomembrane and a soil layer. Using the results from both tests, the geomembrane/soil layer interface transmissivities Ł and interface thicknesses t in were back-calculated or directly calculated, and the results were compared. Based on the calculated Ł and t in values, the following conclusions can be drawn. Ł reduces with increasing overburden pressure p9 on the geomembrane. The effect of p9 on Ł is significant when p9, 1 kpa. Specifically, Ł is found to be a function not only of the permeability k L of the soil layer, but also of p9. Interface transmissivity, θ (m /s) From flow rate test Transmissivity test Chai et al. (25) Touze-Foltz & Barroso (26) Good contact Excellent contact GM GCL contact Thickness of interface, t (m) From flow rate test Transmissivity test Data from Chai et al. (25) Data collected by Touze-Foltz & Giroud (23) Hydraulic conductivity of soil layer, (m/s) k L Hydraulic conductivity of soil layer, (m/s) k L Figure 12. Relationship between Ł and k L Geosynthetics International, 28, 15, No. 1 Figure 13. Permeability against interface thickness

11 Effect of effective overburden pressure on geomembrane/soil interface transmissivity 41 The back-calculated Ł values of the geomembrane/ Ariake clay interface are comparable to the data in the literature for geomembrane/geosynthetic clay liner (GCL) interfaces, but the permeability of Ariake clay is about two orders of magnitude higher than that of the GCL, which indicates that the relationship between Ł and k L of the soil layer may not be a unique function. The calculated interface thicknesses t in from this study are lower than the values given by Touze-Foltz and Giroud (23) for excellent contact conditions. It is considered that the lower t in values are due mainly to the effect of p9 and the better contact conditions achieved with the small-scale model used in this study. ACKNOWLEDGEMENT This research has been partially supported by the Kajima Foundation s Research Grant (26), Japan. APPENDIX. DETAIL OF ROWE S (1998) SOLUTION The expressions for 1 and 2 are 1 ¼ Rº 1ðr, RÞK 1 ðærþþ Rº 2 ðr, RÞI 1 ðærþ Æ þ r º 1 ðr, RÞK 1 ðær Þ þ r º 2 ðr, RÞI 1 ðær Þ Æ Æ 2 ¼ Rº 1ðR, r ÞK 1 ÆR ð Þ Rº 2 ðr, r Æ ÞI 1 ðærþ (7a) þ r º 1 ðr, r ÞK 1 ðær Þþ r º 2 ðr, r ÞI 1 ðær Þ Æ (7b) º 1 ðx, Y Þ ¼ º 2 ðx, Y Þ ¼ K ðæx K ðæx I ðæy Þ ÞI ðæy Þ K ðæy K ðæyþ ÞI ðæy Þ K ðæy ÞI ðæx Þ ÞI ðæx Þ (8a) (8b) where K, K 1, I and I 1 are modified Bessel functions of order zero and one. R is the radius of wetted area; it is computed by solving ð h w H L Þ 1 ðh L Þ 2 ¼ (9) 1 ¼ ÆK 1ðÆRÞI ðærþ ÆK ðærþi 1 ðærþ (1a) K ðærþi ðærþ K ðærþi ðærþ 2 ¼ ÆK 1ðÆRÞI ðærþ ÆK ðærþi 1 ðærþ K ðærþi ðærþ K ðærþi ðærþ where Æ is defined by Æ 2 ¼ K L H L Ł and Ł is the interface transmissivity. (1b) (11) NOTATIONS Basic SI units are given in parentheses. a cross-sectional area of falling-head burette (m 2 ) e void ratio (dimensionless) e initial void ratio (dimensionless) g gravitational acceleration (m/s 2 ) h initial head difference (m) h 1 final head difference (m) H L thickness of soil layer (m) h t total head drop across composite liner (m) h w head on geomembrane (m) I, I 1 modified Bessel functions of order zero and one (dimensionless) k hydraulic conductivity (m/s) k initial permeability (m/s) K, K 1 modified Bessel functions of order zero and one (dimensionless) k GCL permeability of geosynthetic clay liner (m/s) k L hydraulic conductivity of soil layer (m/s) p9 effective overburden pressure (Pa) p a atmospheric pressure (Pa) Q flow rate (m 3 /s) Q qs quasi-steady flow rate (m 3 /s) r radius distance (m) r radius of a circular defect (m) R radius of wetted area (m) R 2 outer radius of specimen (m) R c radius of physical model in axisymmetric case (m) t time (s) t time interval (s) t in thickness of geomembrane/soil interface (m) ç coefficient of viscosity of water (N/m 2 s) Ł interface transmissivity (m 2 /s) r density of water (kg) REFERENCES Geosynthetics International, 28, 15, No. 1 Barroso, M., Touze-Foltz, N., von Maubeuge, K. & Pierson, P. (26). Laboratory investigation of flow rate through composite liners consisting of a geomembrane, a GCL and a soil liner. Geotextiles and Geomembranes, 24, No. 3, Brown, K. W., Thomas, J. C., Lytton, R. L., Jayawickrama, P. W. & Bhart, S. (1987). Quantification of Leakage Rates Through Holes in Landfill Liners. United States Environmental Protection Agency Report CR8194, Cincinnati, OH, 147 pp. 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, 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, 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, Harpur, W. A., Wilson-Fahmy, R. F. & Koerner, R. M. (1993). Evaluation of the contact between geosynthetic clay liners and geomembranes in terms of transmissivity. In: Proceedings of the GRI Seminar on

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