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