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Slope Stability Calculations
15ft
Vueight (VU)
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Compute #ador of safety (FS) against sli ~~
ppirig -Static Case {Refi Geotedmical and Foundation Engineering -
Design and Construction", by Rebert W. Day, 1999, page 10,28
1. FS =Resisting force /Driving force
_ [c'L + N' x Tan(phi')] / [W x sin(alpha}]
[c`L + (1Nx cos (alpha) - u x L) tan (phi')] / [VYx sin(alpha)]
where: FS = Factor of Safety against sliding (dimensioNess parameter)
c' =drained shear strength of the slide plane (c' ~ 300 psf for dense glaaal tills)
phi' _ angle ofi intemai fridian of glaaal tills ~ 35 degr~s
L =length of the slip plane surface (feet) = 40 ft
N = nonr~al force, i.e-, the force acting perper~dicx,dar to the slip surface [(N = W x cos(alpha)]
W = to#al weight of the failure wedge (i.e., W = g tirp~ ~ area of the wedge), Ibs
for a ur~t length of slope = (140 prf)(40 ft x 10 ft)2 = 28,000Ibs = 28:0 kips
u ° average pore water pressure along tine slip surface (psf) = 0 for dense glaaal tilts
alpha =slip. surface inclination (degrees) = 45 degrees
FS = [ (.30x40) + [28.0 x cos(45) - (0 x 90)]tan(35)] / [ 28.0 x sin (45) ] _ [ (12.0 + 13.9)] / 19.8 =1.3 < 2.0 NOT OKAY
2. Compute factorof safety against slipping for the Dynamic (seismic) Case, (Ref: Robert W. Day, page 10.64) '
seismic factor = .3
FS = [CL + (W x cos (~pha) - b x W x Sin (alpha) - u x L) x tan
(ph~')I / IWx ~p(ali~) b x W x cos (alpha) l
_ [:3x40 + (28.0 x cos (45) - .3 x 28.0 x sin(45) - Ox 90j tan (35)] / [28:0 x sin(45) + (0:3 x 28.0 x cos(45) ]
=;[12.0+(19.8-5.9-0)0.7D]/(19.8+5.9) =29.4/15:4=0.85 <1.6 MOT OKAY'
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