Geotechnical Engineering

DHARM

590 GEOTECHNICAL ENGINEERING

qsafe =

qnet ult

η

+ γ Df =

188

3 + 20 × 1 = 83 kN/m

2

If the water table rises to the ground level,

Rγ = 0.5 = Rq

∴ qult = 0.4 γbNγ. Rγ + γDf Nq. Rq

= 0.4 × 20 × 1.5 × 5.0 × 0.5 + 20 × 1 × 7.4 × 0.5 = 30 + 74 = 104 kN/m^2

qnet ult = qult – γ′Df = 104 – 10 × 1 = 94 kN/m^2

qsafe =

qnet ult

η

+ γ′Df =

94

3

+ 10 × 1 = 41 kN/m^2

Percentage reduction in safe bearing capacity

=

42

83 × 100 ≈^50.

Example 14.11: A foundation, 2.0 m square is installed 1.2 m below the surface of a uniform
sandy gravel having a density of 19.2 kN/m^3 , above the water table and a submerged density of
10.1 kN/m^3. The strength parameters with respect to effective stress are c′ = 0 and φ′ = 30°.
Find the gross ultimate bearing capacity for the following conditions:

(i) Water table is well below the base of the foundation (i.e., the whole of the rupture
zone is above the water table);

(ii) Water table rises to the level of the base of the foundation; and

(iii) the water table rises to ground level.

(For φ = 30°, Terzaghi gives Nq = 22 and Nγ = 20)

(S.V.U.—B. Tech., (Part-time)—Sept., 1982)

Square b = 2 m Df = 1.2 m c′ = 0φ′ = 30°

γ = 19.2 kN/m^3 γ′ = 10.1 kN/m^3 Nq = 22 Nγ = 20

(i) Water table is well below the base of the foundation:

qult = 1.3 c Nc + 0.4 γ b Nγ + γDf Nq = 0.4 γ b Nγ + γDf Nq, in this case.

or qult = 0.4 × 19.2 × 2 × 20 + 19.2 × 1.2 × 22 = 814 kN/m^2

(ii) Water table rises to the level of the base of the foundation:
qult = 0.4 γ′ b Nγ + γ DfNq
= 0.4 × 10.1 × 2 × 20 + 19.2 × 1.2 × 22 = 668 kN/m^2
(iii) Water table rises to the ground level:
qult = 0.4 γ′ bNγ + γ′Df Nq
= 0.4 × 10.1 × 2 × 20 + 10.1 × 1.2 × 22 = 428 kN/m^2
Thus, as the water table rises, there is about 20% to 50% decrease in the ultimate bear-
ing capacity.
Example 14.12: The footing of a column is 2.25 m square and is founded at a depth of 1 m on
a cohesive soil of unit weight 17.5 kN/m^3. What is the safe load for this footing if cohesion = 30
kN/m^2 ; angle of internal friction is zero and factor of safety is 3. Terzaghi’s factors for φ = 0° are
Nc = 5.7, Nq = 1, and Nγ = 0. (S.V.U.—B.E., (R.R.)—Feb., 1976)