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_>tt <br />12 <br />11 <br />10 <br />n <br />ii` 8 <br />5 <br />a <br />1' 1. .1 ti'I' 11' k: l! 1 1 1. 1 11 It 1 1' ~I . 1' II . .~ <br />3 <br />t41° Sll° 70° GO° 50° a0° 311° 211° 10° ll° <br />~ .'; <br /> u <br /> n <br /> ~o ~~ <br /> r <br />a ri <br />a <br /> r <br /> n ,~ <br /> <br /> <br />I b <br /> <br /> <br /> <br />' p \,=5 .52 <br /> o S3° <br />I <br />3. ti <br />A <br />Fit;. a:_I. tilahility number s. 41ar Tci zaghi <br />:Ind Perk (I`1a~7.i <br />Cun'rs arc constructed relating A', W J fur various values of ~, as shown in <br />Fi_". S._' 3. <br />A very tonnnon cast ul nonhonwetnrity is that of a very slifT material <br />IocateJ at a depth n,,H below the top of the slope (Fig, g.?~). This poses a <br />restriction on the failure surlare, as it cannot penetrate [he still ntarerial. In <br />this connection wr should define the diH~trenl types of failure surface. They <br />arc the toe circle, which passes through rhr for [Fig. 3?5(11)]; the slope circle, <br />Ivhich intenrcts Ihz slope of some point about the toe [Fig. 6.25(6)]; and the <br />midpoim tide u•husr center lies on a vrrtiral line that passes through the <br />midpoint of the slope [Fig. 6_'S(c)j. Calculations show that for all values of m <br />greater than ?deg, tht critical circles are all toe circles. If the value of ¢ is <br />tibsr to or equal to 0, the position of tht critical tirclr and the stability <br />nuiithrr is in0urnced by the distance to the stiff bottom. Thr stability numbers <br />:Intf the types of (ailurrs as tlrtermineJ b}' theoretical analysis are shown in <br />Fi~_'~ ti. ti. For all slopes with angle d larger than ~3 deg, failure occurs abng <br />yF<~. a.u xl.ure e~~.l l.r.l. <br />I <br />r, <br />r <br />r <br />/ <br />fl ~ <br />n,lll I / Y <br />Tue circle <br />(n) <br />:I;.i <br />11 <br />i <br />r <br />r <br />51npc Cin4r <br />i6} <br />the toe circle. Ifd is Irss than 53 deg, rhr tvpt o!'failure drprntls nn the Jrpth <br />factor n,,. Failure may occur along Ihr slops circle or midpoint cirtlr as wall <br />ai tltr tot circle. Failure ocean along the Illld 1101It1 CIrCIC ss'hr^ II,I C..\l'rl'tl$ 1 <br />\1'e nut+• introduce a alightl}' dilTucnt approach. InstraJ of asking wh.tt <br />is the drnsiq or loail at failure, as is Joni in the bearing-tapacit}~ probltm. <br />we osk how close is a given slope to lailurt, the proprltirs of the ntarerial <br />being known. It is egtllValCnl to a comparison of tht shear su~rss on tht <br />potential failure surl~lce antler the given conditions to the shear stresses at <br />falllll'L', K'hICIt I$ equal tU tIIC strength Of tltr material. Thr ratio of the shear <br />steength to the shear stress under given conditions, is callrtl the jtcmr o! <br />suje(n F„ or <br />r <br />I[ can also be considered as the ratio of the load at failure to the en'en Toad. <br />To evaluate the factor of safety for a given slope, we first determine the <br />parameters r, H, anti y al failure. This can be obtained from Figs. 5.2.1 ur <br />8.26 in the form of the stability number rV, for the given slope angle p and <br />angle of friction ¢. For the given Hand c', we can calcuhtte by Eq. (5.:9) <br />what y should be in order to yield this particular srabilit}' number. This is <br />the value that would result in failure of the slope with the given values of c, <br />~, H, and p. The factor of sa(rty is dtrn the ratio of the y required (or failure <br />to the given y. <br />III^IIOIIII ClrClc <br />([) <br />I+i Q. 5.25. l\ pes of Liiure ~url;lce. <br />