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C, <br />Sec. 5.6 Solid -Material (Landfill) Liners 535 <br />Solution: The necessary information for solving the design equation is <br />(a) For out -of -plane tension testing, the yield -stress of HDPE (from Table 5.5c) is <br />conservatively estimated as 20,000 kPa. <br />(b) The mobilization distance for HDPE at 50 x 12.5 = 625 kPa (from Fig. 5.10) is <br />approximately 80 mm. <br />(c) The friction angle (from Table 5.7) for HDPE against Ottawa sand (Su) is 18°. <br />(d) The friction angle for HDPE against a geonet (separate test results) (SL) is 10°. <br />(e) These values give the required geomembrane thickness. <br />_ (625)(0.080)[tan 18 + tan 101 <br />t (20,000)[cos 20 — (sin 20)(tan 10)] <br />_ 25.1 <br />17600 <br />= 0.00143 in <br />t = 1.43 mm <br />Thus the regulated values of 1.5 mm in the U.S. or 2.0 mm in German regulations <br />would control in this situation. <br />5.6.7 Puncture Protection <br />There are many circumstances where geomembranes are placed on or beneath soils <br />containing relatively large-sized stones, for example poorly prepared soil subgrades <br />with stones protruding from the surface or resting on the surface, soil subgrades over <br />which geomembranes (particularly textured) have been dragged dislodging near -sur- <br />face stones, and cases where crushed -stone drainage layers are to be placed above the <br />geomembrane. All of these situations, particularly the last (which is unavoidable since <br />it is a design situation), could use a protective geotextile to avoid puncturing the geo- <br />membrane. Note that if the soil subgrade is a CCL, a geotextile cannot be used and the <br />isolated stones must be physically removed. For the drainage layer case, which is com- <br />mon to all landfills, a nonwoven needle -punched geotextile can provide significant <br />puncture protection (recall Figure 5.8). The issue of required mass per unit area of the <br />geotextile becomes critical. <br />In a series of papers, Wilson-Fahmy, Narejo, and Koerner [71, 72, 73] have pre- <br />sented a design method that focuses on the protection of 1.5 mm thick HDPE geo- <br />membranes. The method uses the conventional factor of safety equation. <br />where <br />FS = Pallow <br />Pact <br />(5.32) <br />FS = factor of safety (against geomembrane puncture), <br />Pact = actual pressure due to the landfill contents (or surface impoundment), and <br />