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GIROUD et al. D Leachate Flow in Leakage Collection Layers Due to Geomembrane Defects (a) t t o < L L < X < L + o t L – o < x < L 2sinβ or 2sinβ 2sinβ t o /(2 sinβ) L x X (b) t o 2sinβ > L t o 2sinβ < X < L + or 0 instead of ≤ and ≥). Notes: The dot represents the horizontal projection of the location of the primary liner defect and L is the horizontal projection of the length of the leakage collection layer. The limit case for x = L can exist for any value of t o /(2L sinβ); it is illustrated in Figure 7. to L 2sinb £ and t o L £ X £ L + 2sinb (57) the condition expressed by Equation 57 being equivalent to: 236 GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NOS. 3-4
GIROUD et al. D Leachate Flow in Leakage Collection Layers Due to Geomembrane Defects to L - £ x £ L 2sinb (58) S Set 2 (Figure 8b): to L 2sinb ≥ (59) and to to £ X £ L + 2 sinb 2 sinb (60) the condition expressed by Equation 60 being equivalent to: 0 ≤ x ≤ L (61) 4.3.2 Maximum Surface Area of the Wetted Zone For a given leachate collection layer whose length along the slope has a horizontal projection L, the maximum value of the surface area of the wetted zone, A wmax , occurs when the defect in the primary liner is at the high end of the leakage collection layer slope (Figure 7), i.e. when x = L (Equation 38). In this case, the parabola is truncated (Figure 7) and the equation for the surface area of the wetted zone is obtained by combining Equations 38 and 55, hence: A wmax F 2 to = H G I L K J F + 3 sin b NM HG 2 32 L 1 2 sin b 1 t o / I O - KJ QP The same equation would have been obtained by combining Equations 24, 38 and 54. (A table and a graph for calculating A wmax will be provided in Section 4.4.3.) 4.3.3 Summary of the Cases Regarding the geometry of the wetted zone, there are two major cases depending on whether the parabola is complete (Figures 1, 2 and 6) or truncated. When the parabola is truncated, there are two cases, as illustrated in Figure 8, with a limit case illustrated in Figure 7. Therefore, there is a total of four cases, one case of a complete parabola and three cases of truncated parabolas. (These cases will be considered again in Section 5.1.1.) 4.3.4 Actual and Projected Surface Areas It should be remembered that, as indicated at the beginning of Section 4.1.1, the projection of the wetted zone on a horizontal plane is considered in the analysis, which is (62) GEOSYNTHETICS INTERNATIONAL S 1997, VOL. 4, NOS. 3-4 237
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