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Leakage Rate Through Geomembrane Liner - Design Calculator
This calculator computes the rate of leakage through defects in a geomembrane underlain by a very permeable medium. A geonet sandwiched between two geomembranes in a double liner system is one application of this calculator. The rate of leakage through a geomembrane liner due to geomembrane permeability is negligible compared to the rate of leakage through defects in the geomembrane. Hence, only leakage through defects will be considered. As proposed by Giroud (1984), Bernoulli's equation (shown and used below) for free flow through an orifice can be used to evaluate the rate of leakage through a defect in a geomembrane underlain by a very permeable medium. This free flow condition occurs when the underlain porous medium has a average opening size that is greater than the diameter of the geomembrane defect. This free flow condition is valid if the hydraulic conductivity of the underlain media (gravel, geonet, eg.) in contact with the geomembrane is greater than 10-1 to 1 m/s if a = 0.1 cm2 (10-5 m2) and greater than 1 to 10 m/s if a = 1 cm2 (10-4 m2). A typical geonet/geocomposite has a hydraulic conductivity of 10-1 to 1 m/s, therefore, this leakage rate calculation is valid for geonet, only when the defect size in the geomembrane is less than or equal to 0.1 cm2.
| Q | Leakage rate (m3/s) |
| A | Considered geomembrane surface area (m2) |
| n | Number of defects in the geomembrane area |
| a | Area of a single defect (m2) |
| g | Acceleration of gravity (m/s2) |
| h | Hydraulic head on top of the geomembrane (m) |
Note that Bernoulli's equation often overestimates the leakage rate, especially in landfills, even absurd leakage rates are possible, e.g. the calculated rate through a defect in a geomembrane may be greater than the impingement rate above the geomembrane. Giroud et al. (1997) has extended this equation to include impeded flow. Design equations in this case are more complex and requires iteration for calculating the leakage rate. Design charts are available in the above referenced paper.
Studies by Giroud and Bonaparte (1989) have shown that for geomembrane liners installed, with strict construction quality assurance, could have one to two defects per acre (4000 m2) with a typical defect diameter of 2 mm (i.e., a defect area of 3.14 * 10-6 m2 ).
Typical for liner performance evaluation one defect per acre (4000 m2) is considered with a defect area of 0.1 cm2 (equivalent to defect diameter of 3.5 mm), for a conservative design a defect area of 1 cm2 (equivalent defect diameter of 11 mm) can be considered (Giroud et al., 1994)
J.P. Giroud, "Impermeability: The Myth and a Rational Approach", Proceedings of the International Conference on Geomembranes, Denver, USA, 1:157-162, 1984.
J.P. Giroud and R. Bonaparte, "Leakage Through Liners Constructed with Geomembranes, Part I: Geomembrane Liners", Geotextiles and Geomembranes, 8, 1: 27-67, 1989.
J.P. Giroud, K. Badu-Tweneboah & K.L. Soderman, "Evaluation of Landfill Liners" , Fifth International Conference on Geotextiles, Geomembranes and Related Products, Singapore, 5-9 September 1994.
J.P. Giroud, M.V. Khire, and K.L. Soderman, " Liquid Migration Through Defects in a Geomembrane Overlain and Underlain by Permeable Media" ,Geosynthetics International, Vol. 4, Nos. 3-4, pp.293-321, 1997.
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