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Sec. 5.3 Liquid Containment (Pond) Liners 4629 oa = the average horizontal sness in anchor traxtch = Koav, Qd = 'Y H., y = the unit weight of backfill soil, H.r. - the average depth of anchor trench (requires an estimaw), Ko - 1 — sin 4, 10 - the angle of shearing resistance of backfill soil, and dAT - the (unknown) depth of anchor trench. I Note that this situation results in one equation with two unknowns,thus a choice of Lw or dAT is necessary to calculate the other. As with the previous situation the factor of safety is placed on the gco=mbcane fora T, which is used as an allowable value,i.e.,%w.- An example illustrates the procedure. Ex mpk: Repeat the previous problem of a 30 mil CPE geotnembnm of allowable stress 350 lb./in.2 on an 3(N)to I M side slope. 'There is a 12-in.cover soil placed over the geornembrane weigh- ing 100 lb./ft.3(also the snit weight of the backfill soil). the friction angle between the liner and soil is 20 deg. and the soil itself is 30 deg. Determine the required length of runout for A 12-in.-deep anchor trench and for a zero-depth anchor trench to check the previous.prob- lem. Solation: Using the pmviousJy developed design oquatlons baud on Fq=5.28: i T&u. =Fu+FL + 2FAT o.b.(t) -0+q tan b(LRo) + 2(Koov,..)tan 6 VAO =.. /p 030 —0+ (1.0)(100) tan 20'(LR.) (350 x l44) ` � f - �� \ 12 J + 2(0.5)(2.0 x I00)tan 2(r(dAT) 126 — 36.4 40+ 72.8 dAr which for dA-r= 1.0 ft-,Lgo - 1.5 ft.,and for dAr C 0 ft.,Lao- 3.5 ft.(which chocks the previous answer reasonably well). Exanipic Developa set of des carves .� design using the previous problem but now using various 6axneaa- brant allowable stresses of 700, 525 and 3301bAn.2. t' Solation: As before, but wow with a.ao„being the variable: 4 (aa. x 144) (0'120 - 36.4 L O + 72.8 dAT - :n- 0.36®d,,. - 36.4 L*o+ 72.$dAT which when plonod produces the following set of crams. Nott that as a.n.,,,tne"*=the required LAo and dAr valwea also increase WWMMXWy. ' t 11