Newmark's influence chart and its use

Newmark's influence chart is a diagram made of concentric circles divided by radial lines into a number of small areas (elements), each of which causes the same vertical stress at the centre point at a given depth $z$ when loaded with a uniform pressure. It is based on Boussinesq's equation for a uniformly loaded circular area.

        \  |  /
      ---(   O   )---   circles: R/z = 0.27, 0.40,
        /  |  \          0.52, 0.64, 0.77, 0.92, 1.11,
                         1.39, 1.91, ∞  (influence 0.1 each)

The chart has 10 circles (stress ratio 0 to 1 in steps of 0.1) and 20 radial lines. Each element then has an influence value $I = \dfrac{1}{10\times20} = 0.005$.

Use

To find the vertical stress increase $\Delta\sigma_z$ at any point below a loaded area of irregular shape (any plan shape):

$$\Delta\sigma_z = I \times N \times q$$

where $N$ is the number of elements covered by the plan of the loaded area (drawn to a scale such that the length OQ equals the depth $z$ and the point is placed at the centre of the chart), and $q$ is the uniform load intensity.