DHARMSTABILITY OF EARTH SLOPES 351
9.7 A 40-degree clay slope has a height of 5 m. Assuming a toe circle failure starting 1 m from the
edge of the slope (at the top), calculate the shear strength required for the soil for a factor of
safety of 1.5.
[Hind: Assume γ = 19.6 kN/m^3. Also since the existence of the hard layer is not mentioned, take
Taylor’s N as 0.1817] (S.V.U.—B.E., (R.R.)—Nov., 1969)
9.8 The unit weight of a soil of a 30° slope is 17.5 kN/m^3. The shear parameters c and φ for the soil
are 10 kN/m^2 and 20° respectively. Given that the height of the slope is 12 m and the stability
number obtained from the charts for the given slope and angle of internal friction is 0.025,
compute the factor of safety. (S.V.U.—B.Tech. (Part-time)—May, 1983)
9.9 What is the maximum depth to which a trench of vertical sides can be excavated in a clay stra-
tum with c = 50 kN/m^2 and γ = 16 kN/m^3? Assume the clay to be saturated.
(S.V.U.—B.E., (N.R.)—Sep., 1967)
9.10 A cutting is to be made in a soil with a slope of 30° to the horizontal and a depth of 15 m. The
properties of the soil are: c = 25 kN/m^2 , φ = 15°, and γ = 19.1° kN/m^3. Determine the factor of
safety of the slope against slip, assuming friction and cohesion to be mobilised to the same
proportion of their ultimate values.
9.11 An earth dam of height 20 m is constructed of soil of which the properties are: γ = 20 kN/m^2 ,
c =^ 45 kN/m^2 , and φ = 20°. The side slopes are inclined at 30° to the horizontal. Find the factor of
safety immediately after drawdown.
9.12 A cutting of depth 10.5 m is to be made in a soil for which the density is 18 kN/m^3 and cohesion
is 39 kN/m^2. There is a hard stratum under the clay at 12.5 m below the original ground surface.
Assuming φ = 0° and allowing for a factor of safety of 1.5, find the slope of the cutting.