Newmark's chart in foundation engineering is used to determine :

Explanation:

Newmark's  Chart:

Newmark developed a graphical method to find out the vertical stress at any point under a uniformly loaded area of any shape with the help of an influence chart.

• The chart consists of a number of concentric  circles and radiating lines
• As a result, the influence of each area unit is the same at the centre of the circle.
• It means each area unit causes equal vertical stress at the centre of the diagram.
• It is based on Boussinesq's equation but is more accurate.
  

Stress below any point is calculated as: \({{\rm{\sigma }}_{\rm{z}}}{\rm{\;}} = {\rm{\;}}\dfrac{1}{{{\rm{m}} \times {\rm{n}}}} \times {\rm{q}} \times {\rm{N\;}}\)

where,

m = No. of concentric circles, n = No. of Radial lines, q = Intensity of load, and N = Equivalent number of areas covered by plan area.

The product \(\left( {\dfrac{1}{{m \times n}}} \right)\) is called the influence factor.

 Important Points

Vertical stress increment at any depth (z) at a radial distance (r) as per Boussines’q theory is:

\({\rm{\Delta }}{\sigma _z} = {K_B}\dfrac{Q}{{{z^2}}}\)

Where,

KB = Boussinesq’s influence factor

\({K_B} = \dfrac{3}{{2\pi }}{\left[ {\dfrac{1}{{1 + {{\left( {\frac{r}{z}} \right)}^2}}}} \right]^{\frac{5}{2}}}\)