Stress Distribution Through Soil - Part 02

Newmarks charts 

The Boussinesq equation for the vertical stress given in previous equation. to develop Newmarks charts we need to re-arrange that equation. 


where,
qv = point stress (delta sigma)
q0 = vertical stress increment in foundation level

As the stress ratio qv/q0 varies from 0.1 to 0.9, the ration r/z varies as given in following table.


1)If we draw a circle with the radius of 0.766 that means,

r = 0.766
r/1 = 0.766/1

therefore r/z = r/1
z = 1

According to the chart corresponding qv/q0 value is 0.5.



when r/z = 0.766
from chart
delta sigma/q0 = 0.5

therefore,
delta sigma = 0.5 q0
delta sigma = (corresponding chart value to r/z) * (q0)

therefore delta sigma (stress increment) = 0.5 x 100 = 50 K Pa

2)If we draw a circle with the radius of 0.637,
r = 0.637
r/1 = 0.637
r/z = r/1
z = 1

therefore qv/q0 value is 0.4

therefore delta sigma (stress increment) = 0.4 x 100 = 40 K Pa
  
3)If the loading like this,
 
r = r1 - r2
r/z = r1/z1 - r2/z2 (consider 1 m depth)
r/z = 0.766 - 0.637
r/z = 0.5 - 0.4
r/z = 0.1

if z = 1m, r = 0.1

stress increment = 0.1 x q0 = 0.1 x 100 = 10 K Pa

4)If the loading like this,

r/z = r1/z1 - r2/z2
r/z = 0.766 - 0.637 (for 1m depth)
r/z = 0.5 - 0.4 = 0.1

therefore stress increment = (0.1 x 100) / 20 = 50 K Pa

Newmarks charts prepare using this method (basically last cast). concentric circles of radius 0.27, 0.40 ... 1.908 are drawn and divided into 20 equal divisions by drawing radial lines as shown in the figure.

As the stress increment between any two adjacent circles is 0.1. one small element is 0.1/20 = 0.005, which is called the 'influence value'.

 

Newmarks charts Procedure

Let's see how to find the stress using Newmarks charts,

1) Find the stress increment at point A,

  

2) In the Newmarks chart AB scale = 1 unit (2 cm - depends)

therefore, 

1 unit = 2 cm -------- 10 m

2 x 10^-2 m ---------- 10 m

1 : 500 ( scale)

Draw the plane of the building according to 1 : 500 scale and place the chart on the top of that ( or plane on top) then count the number of segments covered by the plane (m)

 

I = 0.005 (influence factor)

Using this method we can find stress at any point under the foundation.