Geotechnical Engineering

DHARM

BEARING CAPACITY 589

Terzaghi’s factors for φ = 0° are : Nc = 5.7, Nq = 1, and Nγ = 0.

qu = 100 kN/m^2

∴ c =

1

2

qu = 50 kN/m^2

qult = 1.3 cNc = 1.3 × 50 × 5.7 = 370 kN/m^2

∴ qult = 370 kN/m^2.

Example 14.8: Determine the ultimate bearing capacity of a square footing of 1.5 m size, at a
depth of 1.5 m, in a pure clay with an unconfined strength of 150 kN/m^2. φ = 0° and γ = 17 kN/m^3.

(S.V.U.—Four-year B. Tech.,—Sept., 1983)

Square footing b = 1.5 m = 150 cm Df = 1.5 m = 150 cm

Pure clay φ = 0°, qu = 150 kN/m^2 , γ = 17 kN/m^3

c =

qu

2

= 75 kN/m^2

Terzaghi’s factors for φ = 0° are Nc = 5.7, Nq = 1, and Nγ = 0.

∴ qult = 1.3 c Nc + γDf Nq + 0.4 γb Nγ = 1.3 cNc + γDfNq, in this case

qult = 1.3 × 75 × 5.7 +

17 1 50

1000

×.
× 1 = 580 kN/m^2
∴ qult = 580 kN/m^2.
Example 14.9: A square footing, 1.8 m × 1.8 m, is placed over loose sand of density 16 kN/m^3
and at a depth of 0.8 m. The angle of shearing resistance is 30°. Nc = 30.14, Nq = 18.4, and
Nγ = 15.1. Determine the total load that can be carried by the footing.
(S.V.U.—Four-year B.Tech.,—Apr., 1983)
Square footing b = 1.8 m
γ = 16 kN/m^3 , c = 0,φ = 30°, Df = 0.8 m
Nc = 30.14,Nq = 18.4, Nγ = 15.1
qult = 1.3 cNc + 0.4γ b Nγ + γ DfNq = 0.4 γ b Nγ + γDf Nq, in this case
∴ qult = 0.4 × 16 × 1.8 × 15.1 + 16 × 0.8 × 18.4 = 174 + 236 = 410 kN/m^2
The ultimate load that can be carried by the footing
= qult × Area = 410 × 1.8 × 1.8 kN = 1328.4 kN.

Example 14.10: Compute the safe bearing capacity of a square footing 1.5 m × 1.5 m, located at
a depth of 1 m below the ground level in a soil of average density 20 kN/m^3. φ = 20°, Nc = 17.7,
Nq = 7.4, and Nγ = 5.0. Assume a suitable factor of safety and that the water table is very deep.
Also compute the reduction in safe bearing capacity of the footing if the water table rises to the
ground level. (S.V.U.—B.Tech., (Part-time)—Sept., 1983)
b = 1.5 m Square footing Df = 1 m
γ = 20 kN/m^3 φ = 20° Nc = 17.7, Nq = 7.4, and Nγ = 5.0
Assume c = 0 and η = 3
qult = 1.3 c Nc + 0.4 γ b Nγ + γDf Nq = 0.4 γ b Nγ + γ Df Nq, in this case.
= 0.4 × 20 × 1.5 × 5.0 + 20 × 1 × 7.4 = 60 + 148 = 208 kN/m^2
qnet ult = qult – γ Df = 208 – 20 × 1 = 188 kN/m^2