DHARM

BEARING CAPACITY 599

Example 14.24: A continuous wall footing, 1 m wide, rests on sand, the water table lying at a
great depth. The corrected N-value for the sand is 10. Determine the load which the footing
can support if the factor of safety against bearing capacity failure is 3 and the settlement is not
to exceed 40 mm.
Continuous footing:
b = 1 m
Let us assume a minimum depth, Df, of 0.5 m.
Assume γ = 18 kN/m^3
For N = 10, φ = 30° (Fig. 14.18 or 14.19, after Peck, Hanson and Thornburn)
Assuming general shear failure,
for φ = 30°, Terzaghi’s factors are: Nq = 22.5 and Nγ = 19.7

∴ qnet ult =

1

2

γb Nγ + γDf (Nq – 1)

=

1

2

× 18 × 1 × 19.7 + 18 × 0.5 × 21.5 ≈ 370 kN/m^2

qnet (^) safe =
qnet ult
η

370
3
≈ 123 kN/m^2
For N = 10 and b = 1m, and for a permissible settlement of 40 mm, the allowable soil
pressure = 120 kN/m^2 (From Fig. 14.22, after Peck, Hanson and Thornburn)
∴ Allowable bearing pressure ≈ 120 kN/m^2
(i.e., shear failure governs the design).
Load which the footing can support = 120 × 1 kN/m = 120 kN/metre run.
Example 14.25: What load can a 2 m square column carry in a dense sand (γ = 20 kN/m^3 and
φ = 36°) at a depth of 1 m, if the settlement is not to exceed 30 mm? Assume a factor of safety
of 3 against shear and that the ground water table is at a great depth.
γ = 20 kN/m^3 Df = 1 m b = 2 m (Square footing) φ = 36°
For φ = 36, N = 30 (from Fig. 14.18, after Peck, Hanson and Thornburn)
For N = 30, b = 2 m permissible settlement = 40 mm,
Allowable soil pressure = 500 kN/m^2. (from Fig. 14.21 after Terzaghi and Peck)
For a permissible settlement of 30 mm,
Allowable pressure =
500 30
40
×
= 375 kN/m^2
For φ = 36°, Nq = 43 and Nγ = 46
∴ qnet ult = 0.4 γ b Nγ + γ Df (Nq – 1)
= 0.4 × 20 × 2 × 46 + 20 × 1 × 42 = 736 + 840 = 1576 kN/m^2
qsafe =
1576
3
= 525 kN/m^2
∴ Settlement governs the design, and
qallowable = 375 kN/m^2
Safe load for the column = 375 × 2 × 2 = 1500 kN.