Geotechnical Engineering

DHARM

586 GEOTECHNICAL ENGINEERING

and settlement as given by Terzaghi and Peck, by Peck, Hanson and Thornburn, and by

Teng.

Details are given in the Appendices of IS: 1904–1986 (Revised), already cited.

14 .16 Illustrative Examples

Example 14.1: Calculate the elastic settlement of a rectangular foundation, 6 m × 12 m, on a

uniform sand with E = 20,000 kN/m^2 and Poisson’s ratio, ν = 0.2. The contact pressure is 200

kN/m^2. The settlements are to be calculated at the centre, mid-point of long side, and mid-

point of short side, and at the free corner.

Also compute the allowable bearing pressure, if the maximum settlement is restricted

to 40 mm.

Side ratio of rectangle = 12/6 = 2

The elastic settlement is given by Schleicher as s = K.q. A

E

.()10

−^2

K = shape factor = 1.08, 0.79, 0.69, and 0.54 for the centre, mid-point of long side, mid-

point of short-side, and free corner respectively. (Table 14.2)

∴ Settlement at the centre

= 1.08 × 200 × 12 6

102

20 000

2

×

(.)−

,

× 1000 mm = 88 mm.

Settlement at the mid-point of long-side

= 0.79 × 200 × 72 102

20 000

(.)^2

,

− × 1000 mm = 64.4 mm

Settlement at the mid-point of short-side

= 0.69 × 200 × 72 102

20 000

(.)^2

,

− × 1000 mm = 56.2 mm

Settlement at the free corner

= 0.54 × 200 × 72

102

20 000

(.)^2

,

−

× 1000 mm = 44 mm

If the maximum settlement is restricted to 40 mm, the centre settlement should not

exceed this value.

Then the allowable bearing pressure:

q = sE

A()1−ν^2

=

40 20 000

108 72 1 02^2

×

×−

,

.(.)

≈ 90 kN/m^2.

Example 14.2: What is the minimum depth required for a foundation to transmit a pressure
60 kN/m^2 in a cohesionless soil with γ = 18 kN/m^3 and φ = 18°? What will be the bearing
capacity if a depth of 1.5 m is adopted according to Rankine’s approach?

γ = 18 kN/m^3 φ = 18° q = 60 kN/m^2.

Minimum depth of foundation, according to Rankine,

Df =

q

γ

φ

φ

1

1

2

−

+

F

HG

I

KJ

sin

sin

=

60

18

118

118

2

−°

+°

F

HG

I

KJ

sin

sin

= 0.93 m ≈ 1 m