Geotechnical Engineering

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