Geotechnical Engineering

DHARM

STRESS DISTRIBUTION IN SOIL 379

Example 10.2: A load 1000 kN acts as a point load at the surface of a soil mass. Estimate the

stress at a point 3 m below and 4 m away from the point of action of the load by Boussinesq’s

formula. Compare the value with the result from Westergaard’s theory.

(S.V.U.—B.E., (N.R.)—Sept., 1967)

Boussinesq’s theory:

σz =

Q

zrz^2252

32

1

. (/ )
[(/)]/

π

+

Here r = 4 m, z = 3 m and Q = 1000 kN

∴σz =

1000

33

32

× 143 +^252

. (/ )
[(/)]/

π

= 4.125 kN/m^2

Westergaard’s Theory:

σz =

Q

zrz^2232

1

12

. (/ )
[(/)]/

π

+

∴σz =

1000

33

1

× 1243 +^232

. (/ )
[(/)]/

π

= 3.637 kN/m^2.

Example 10.3: A raft of size 4 m × 4 m carries a uniform load of 200 kN/m^2. Using the point
load approximation with four equivalent point loads, calculate the stress increment at a point
in the soil which is 4 m below the centre of the loaded area.
(S.V.U.—B.E. (N.R.)—March-April, 1966)
Depth below the centre Q of the loaded area (raft) = 4m. Dividing the loaded area into
four equal squares of 2 m size, as shown in Fig. 10.22, the load from each small square may be
taken to act through its centre.

Thus, the point loads at A, B, C and D are each:

200 × 4 = 800 kN

The radial distance r to 0 for each of the loads is 2 m,

∴ r/z =

2

4

1

22

=

2m 2m

2m

2m

A B

D C

O

Ö2m

Fig. 10.22 Loaded area (Ex. 10.3)