Geotechnical Engineering

DHARM

STRESS DISTRIBUTION IN SOIL 361

Kw is Westergaard’s influence coefficient, the variation of which with (r/z) is shown in Fig. 10.6;
for comparison, the variation of KB of Eq. 10.10 is also super-imposed:

0.5

0.4

0.3

0.2

0.1

0

123

Influence coefficient

0.3183

0.2836

0.2099

0.1411

0.0925

0.0613 0.0292

0.02100.01560.01180.00910.00720.00580.00470.0038

0.0416

KB

KW

sz=—,KQ

z^2

K=B 3/2p

[1 + (r/z) ]2 5/2

K=W 1/p

[1 + 2(r/z) ]2 3/2

Value of r/z
Fig. 10.6 Influence coefficients for vertical stress due to concentrated load
(Westergaard’s and Boussinesq’s solution) (After Taylor, 1948)
For cases of point loads with r/z less than about 0.8, Westergaard’s stress values, assum-
ing v to be zero, are approximately equal to two-thirds of Boussinesq’s stress values. For r/z of
about 1.5, both solutions give identical values of stresses.

This is also reflected in the comparison of vertical stress distribution on a horizontal
plane at a specified depth from Boussinesq’s and Westergaard’s solutions, as shown in Fig. 10.7
below:

Q

21 1.5 r/z r/z 1 1.5 2

z

Boussinesq’s solution

Westergaard’s

solution

Fig. 10.7 Vertical stress distribution on a horizontal plane at specified depth—

comparison between Boussinesq’s and Westergaard’s solutions

10.3 Line Load

Let a load, uniformly distributed along a line, of intensity q′ per unit length of a straight line of
infinite extension, act on the surface of a semi-infinite elastic medium. Such a loading produces