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180_CEG 4012 Notes Fall 2011 CEG 4012 Notes Fall 2011

180_CEG 4012 Notes Fall 2011 CEG 4012 Notes Fall 2011 - o...

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Sl6 Finite Slope with Planar Failure Surface (Cullman) o Attributed to Cullman (1875) - used vector force diagrams way back then o Assume homogenous c-\$ soil and failure plane through toe of slope (lJot'-"~o=rs"'a="n=s) o "'Reasonabl\'1jOOO lor steep slopes, eftical cuts, onea aamS' o Strong evidence for curved failure surface of flatter slopes and Cullman method underestimates FS in this case o Find plane with maximum "developed" average shear stress, td (= Cd + cr tan \$d): W s sin e H L o Weight of wedge = ~ ybh = ~ y L (~) sin(i - 8) 2 2 Sin I o sum the normal forces on the plane: W s cos 8 = N o sum the forces parallel to the plane:
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Unformatted text preview: o sum the normal forces on the plane: W s cos 8 = N o sum the forces parallel to the plane: W, sin 8 = (Cd + N tan \$d) = (Cd L + W, cos 8 tan \$d) o substitute for W,: ~ y L (~) sin(i-8) sin 8 = c,L +~ y L (~) sin(i-8) cos 8 tan \$, 2 Sin I 2 Slnl o and rearranging: c, =.!. ( ,+1.) (sin(i - 8) sin 8- sin(i - 8) cos 8 tan \$,) 2 Sin I c =.!. (_,+1_) (sin(i _ 8)(sin 8 cos \$, _ ~C-=-OS=-8=-s=-in __\$'-'-d)) d 2 sini COSlPd COSQld Cd =.!. ( ,+1) (sin(i - 8) sin(S - \$d) 2 sin I...
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