Presentation by
Shreedhar S
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An isobar is a curve joining the points of
equal intensity
In other words an isobar is a contour of equal
stresses
The isobar of a particular intensity can be
obtained by
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Let it be required to plot an isobar for which
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Assuming various values of depth(z), the
corresponding IB values are computed.
For the values of IB , the corresponding r/z
values are determined
Once the value of r/z has been determined the
radial distance r can be calculated.
An isobar is symmetrical about the load axis,
the other half can be drawn from symmetry.
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It is observed that r is zero at load point and
attains the maximum value at r/z =0.75 And
again decreases
In the same manner the isobar of intensity
0.2Q,0.3Q etc can be drawn
The zone with in which the stresses have a
significant effect on the settlement of structure
is known as pressure bulb
The area outside of the pressure bulb is
assumed as negligible stress.
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The vertical stress on horizontal plane at depth
‘z’ is given by
Z being a specified depth
For several assumed values of r, r/Z is
calculated and the influence factor IB is found
for each, the value of vertical stress is then
computed.
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The maximum stress occurs just below the load
(r=0) and it is decreases rapidly as the distance
r increases
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The vertical stress distribution on a vertical
plane at a radial distance of ‘r’ can be
obtained from
In this case a radial distance r is constant and
depth changes
The value of r/z are obtained for different
depths z
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Boussinesq’ s solution assumes that the soil
deposit is isotropic.
Actual sedimentary deposits are generally
anisotropic.
There are thin layers of sand embedded in
homogeneous clay strata.
According to Westergaard the vertical stress
at a point P at a depth z below the
concentrated load Q is given by
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This is an approximate method to find the vertical
stress at any point inside a soil mass due to
uniformly distributed load acting on an area of any
shape
In this method loaded area is divided in to a
number of smaller areas and replacing the
distributed load on a small area by an equivalent
point load acting at the centroid of the area
Q= q (a X b)
Thus the total load is converted in to number of
point load
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Q1,Q2,Q3,Q4=q (aXb)
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r1,r2,r3,r4 =radial distances of point of load
acting from point P