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)