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A highway on a slope failed due to extensive seasonal rain and the failure surface is approximated with

surface ABC. Ignore the thickness of the Highway DAE from all calculations.

a) Calculate the factor of safety against slope stability for the current geometry using Spencer Method.

b) You are tasked to repair to repair the slope using crushed limestone buttress only. Assume the crushed

limestone has a friction angle of 42 degree, no cohesion, and a dry unit weight of 130 pcf. Improve

the factor of safety for the slope using crushed limestone buttress with no additional reinforcement

(i.e., no nails, anchors, walls, etc.) to rebuild the highway (i.e., slope will start at point D). Your design

is limited by the end of right of way at coordinate (0,0). You have the choice to cut some of the current

slope soil as long as you use it part of the current slope (no hauling away any cut soil). Let us assume

that cutting and compacting slope soil cost is equivalent to brining and placing an equivalent volume

of crushed limestone. Develop the most economical design for a safe slope. Of course, the factor of

safety (FS) is a function of volume of limestone and the volume of cut soil (if any); therefore, your

answer should be presented as FS = xx for a volume of limestone = yy, volume of cut soil = zz (if

any). You may choose to develop a chart that displays the relationship between FS and volume of

fill/cut materials. The minimum factor of safety is 1.15 based on spencer method. This problem will

be graded based on the most economical solution (highest FS with the minimum volume of crushed

limestone).

ton go 74ड्य jopu3

((0120)

(0,0)

C(80,20)

D

25

All dimensions are in ft

B

15¹

+

Co

ж бод

3oft

40 ft

N

3

X=115 lb/ft

C=900 lb/f

$=10°

No effect of water table

(210,0)