Geotechnical Engineering

DHARM

356 GEOTECHNICAL ENGINEERING

0.5

0.4775

0.4

0.3

0.2

0.1

0

123

Influence coefficient, K

B 0.329

0.221

0.139

0.084

0.051

0.0320.020

0.0130.0090.0060.0040.00290.00210.0015

r/z
Fig. 10.2 Influence coefficients for vertical stress due to
concentrated load (After Boussinesq, 1885)
Poisson’s ratio υ, for the soil enters the equations for σx, σy, σr, and σt. For elastic mate-
rials v ranges from 0 to 0.5. (For cork, υ is nearly zero and for clay soil it is nearly the maxi-
mum of 0.5). For a material for which υ approaches 0.5, the volume change is negligible on
loading; then it is said to be practically incompressible. Poisson’s ratio for a soil is a highly
tenuous property and one which is very difficult to determine. However, it has been found that
it is closer to the upper limit of 0.5 than it is zero.

If the value of 0.5 is taken for ν for soil, the equations for σx, σy, σr and σt get simplified

as follows:

σx =

3

2

2

5

Qxz

π R

. ...(Eq. 10.12 (a))

σy =

3

2

2

5

Qyz

π R

. ...(Eq. 10.12 (b))

σr =

3

2

2

2

Qrz

π R

. ...(Eq. 10.12 (c))

σt = 0 ...(Eq. 10.12 (d))

10.2.2 Pressure Distribution

It is possible to calculate the following pressure distributions by Eq. 10.2 (d) of Boussinesq and

present them graphically:

(i) Vertical stress distribution on a horizontal plane, at a depth z below the ground

surface.

(ii) Vertical stress distribution along a vertical line, at a distance r from the line of

action of the single concentrated load.