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

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GIROUD et al. D Optimal Configuration of a Double Liner System 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). 380 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NOS. 3-4
GIROUD et al. D Optimal Configuration of a Double Liner System 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 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NOS. 3-4 381
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