DHARM
SHEARING STRENGTH OF SOILS 299
Similarly the other normal stresses and shear stresses are obtained by dividing by the
area of the box and are as follows in kN/m^2 :
Normal stress, σ 80 160 240
Peak shear stress, τmax 80 160 240
Ultimate shear stress, τf 46.4 92.8 139.2
Since more than one set of values are available, graphical method is better:
240
180
120
60
0
60 120 180 240
Normal stress, kN/m^2
Shear stress, kN/m
(^2) Peak
Ultimate
f
f
peak
ultimate
(dense state) : 45°
(loose state) : 30°
by measurement with a protractor
Fig. 8.46 Failure envelopes (Ex. 8.2)
Example 8.3: Calculate the potential shear strength on a horizontal plane at a depth of 3 m
below the surface in a formation of cohesionless soil when the water table is at a depth of 3.5
m. The degree of saturation may be taken as 0.5 on the average. Void ratio = 0.50; grain
specific gravity = 2.70; angle of internal friction = 30°. What will be the modified value of shear
strength if the water table reaches the ground surface? (S.V.U—B.E., (R.R.)—Feb, 1976)
Effective unit weight γ′ =
()
()
G
e
−
- 1
1
. γw
≈
(. )
(.)
270 1
105
−
+
× 10 = 11.33 kN/m^3
Unit weight, γ, at 50% saturation
= (.)
()
GSe
e
+
1 +
. γw =
(.. .)
(.)
270 05 05
105
+×
+
× 10 = 19.667 kN/m^3
(a) When the water table is at 3.5 m below the surface:
Normal stress at 3 m depth, σ = 19.67 × 3 = 59 kN/m^2
Shear strength, s = σ tan φ for a sand
= 59 tan 30° = 34 kN/m^2 (nearly).
(b) When water table reaches the ground surface:
Effective Normal stress at 3 m depth
σ = γ′. h = 11.33 × 3 = 34 kN/m^2