Geotechnical Engineering

(Jeff_L) #1
DHARM

STRESS DISTRIBUTION IN SOIL 359

10.2.3 Stress Isobar or Pressure Bulb Concept
An ‘isobar’ is a stress contour or a line which connects all points below the ground surface at
which the vertical pressure is the same. In fact, an isobar is a spatial curved surface and
resembles a bulb in shape; this is because the vertical pressure at all points in a horizontal
plane at equal radial distances from the load is the same. Thus, the stress isobar is also called
the ‘bulb of pressure’ or simply the ‘pressure bulb’. The vertical pressure at each point on the
pressure bulb is the same.


Pressure at points inside the bulb are greater than that at a point on the surface of the
bulb; and pressures at points outside the bulb are smaller than that value. Any number of
pressure bulbs may be drawn for any applied load, since each one corresponds to an arbitrarily
chosen value of stress. A system of isobars indicates the decrease in stress intensity from the
inner to the outer ones and reminds one of an ‘Onion bulb’. Hence the term ‘pressure bulb’. An
isobar diagram, consisting of a system of isobars appears somewhat as shown in Fig. 10.5:


Q

Isobars

Fig. 10.5 Isobar diagram (A system of pressure bulbs for
a point load—Boussinesq’s)
The procedure for plotting an isobar is as follows:
Let it be required to plot an isobar for which σz = 0.1 Q per unit area (10% isobar):
Form Eq. 10.9,

KB =

σzz
Q

Qz
Q

. ... z


(^22012)
== 01
Assuming various values for z, the corresponding KB-values are computed; for these
values of KB, the corresponding r/z-values are obtained; and, for the assumed values of z, r-
values are got.
It is obvious that, for the same value of r on any side of the z-axis, or line of action of the
point load, the value of σz is the same; hence the isobar is symmetrical with respect to this axis.
When r = 0, KB = 0.4775; the isobar crosses the line of action of the load at a depth of:
z = KB/..
.
01 0 4775.
01
==4 775 = 2.185 units.

Free download pdf