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GIROUD et al. D Leachate Flow in Leakage Collection Layers Due to Geomembrane Defects Knowing (or assuming) the leachate head, h o , on top of the secondary liner vertically beneath the primary liner defect, one may derive the virtual leachate thickness, t o ,using Equation 4. Then, knowing t o , t LCL and k, one may use Equation 16 to calculate the rate of leachate flow through a defect that the leakage collection layer can convey. The following equation can be derived from Equation 16: t o F HG tLCL = + 2 Q kt 1 2 LCL I KJ (17) The following equation can be derived from Equations 13 and 16: F Q tLCL = to 1− 1− 2 kt HG o I KJ (18) Equation 18 is valid only if the following condition is met: 2 Q ≤ k t o (19) It should be noted that if t LCL = t o , i.e. if the leakage collection layer is filled with leachate at only one point, i.e. at the location of the primary liner defect, Equation 16 is equivalent to Equation 9. 3.3 Parametric Study Using the equations presented in Sections 3.1 and 3.2 it is possible to compare the flow capacity of different leakage collection layers in case of a defect in the primary liner. In Table 1, three different leakage collection layers are compared: S a geonet with a thickness of 5 mm and a hydraulic transmissivity resulting in a hydraulic conductivity (obtained by dividing the hydraulic transmissivity by the thickness) of 1 × 10 -1 m/s; S a gravel layer with a thickness of 300 mm and a hydraulic conductivity of 1 × 10 -1 m/s; and S a sand layer with a thickness of 300 mm and a hydraulic conductivity of 1 × 10 -3 m/s. The first two leakage collection layers have the same hydraulic conductivity and the last two have the same thickness. In the case of the geonet, the virtual leachate thickness, t o , considered in Table 1 is greater than, or equal to, the thickness of the leachate collection layer, t LCL ; therefore, in all cases considered in Table 1, the geonet is filled with leachate over a certain area around the defect (this area being zero for t o = 5 mm). In the case of the gravel and sand layers, the leachate thicknesses considered in Table 1 are less than, or equal to, the thickness of the leakage collection layer; therefore, in all cases considered in Table 1, the gravel and sand layer are not filled (or just filled) with leachate, and for these two materials the leachate thicknesses, t o ,showninTable 1 are actual (not virtual) thicknesses. 226 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NOS. 3-4
GIROUD et al. D Leachate Flow in Leakage Collection Layers Due to Geomembrane Defects Table 1. Rate of leachate flow in three different leachate collection layers resulting from a defect in the primary liner. Leachate thickness (actual or virtual) Geonet t LCL =5mm k =1× 10 -1 m/s Leakage collection layer material Gravel t LCL = 300 mm k =1× 10 -1 m/s Sand t LCL = 300 mm k =1× 10 -3 m/s t o Q Q Q (m) (mm) (m 3 /s) (lpd) (m 3 /s) (lpd) (m 3 /s) (lpd) 0.005 5 2.5 × 10 -6 216 2.5 × 10 -6 216 2.5 × 10 -8 2.16 0.01 10 7.5 × 10 -6 648 1.0 × 10 -5 864 1.0 × 10 -7 8.64 0.05 50 4.75 × 10 -5 4,104 2.5 × 10 -4 21,600 2.5 × 10 -6 216 0.1 100 9.75 × 10 -5 8,424 1.0 × 10 -3 86,400 1.0 × 10 -5 864 0.3 300 2.975 × 10 -4 25,704 9.0 × 10 -3 777,600 9.0 × 10 -5 7,776 Notes: The leachate thickness, t o , can be derived from the leachate head on top of the secondary liner using Equation 4. The leachate thickness, t o , isthe actual leachate thickness if t o < t LCL and a virtual leachate thickness if t o > t LCL . The tabulated values of the rate of leachate flow, Q, were calculated using Equation 9 when t o < t LCL and Equation 16 when t o > t LCL . Units: 1 m 3 /s = 86,400,000 liters per day (lpd). It appears from Table 1, that for a given value of t o , i.e. a given value of the head of leachate on top of the secondary liner, h o (see Equation 4), the gravel and the geonet can convey significantly more leachate than the sand. It is interesting to compare the flow rates of Table 1 with rates of leachate migration through defects of geomembranes used alone (i.e. not part of a composite liner) calculated using Bernoulli’s equation, which is expressed as follows: 2 2 Q= 06 . a 2gh = 06 . p( d / 4) 2gh ≈ ( 2/ 3) d gh prim prim prim (20) where: a = defect area; d = defect diameter; g = acceleration due to gravity; and h prim = head of leachate on top of the primary liner. Table 2 gives rates of leachate migration through geomembrane defects calculated using Equation 20. It appears that, with the leachate heads that typically exist on the primary liners of actively operating landfills (i.e. landfills that are receiving waste), and provided that the geomembrane is used alone (i.e. is not part of a composite liner): S a small geomembrane defect (e.g. 1 to 2 mm diameter), which may occasionally be undetected during construction, results in a rate of leakage on the order of 100 liters per day (lpd); S a geomembrane defect (e.g. 3 to 5 mm diameter), which may occasionally occur during construction phases where defect detection may not be possible (e.g. placement of granular leachate collection material on geomembrane), results in a rate of leakage on the order of 1000 lpd (1 m 3 /day); and S a large geomembrane defect (e.g. 10 mm diameter or more), which may occur under special circumstances, results in a rate of leakage of 10,000 lpd (10 m 3 /day) or more. GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NOS. 3-4 227
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