Governing Equations:
The settlement of the corner of a rectangular base of dimensions B x L on the surface of an elastic
half-space can be computed from an equation from the Theory of Elasticity as follows
(Note: This App has been modified to assess the settlement below the centre of loaded area)
\[
\Delta H = q_o B \cdot \frac{1 - \nu^2}{E_s} \left( I_1 + \frac{1 - 2\nu}{1 - \nu} I_2 \right) I_F
\]
where
\[
I_1 = \frac{1}{\pi} \left[
M \ln \left( \frac{(1 + \sqrt{M^2 + 1}) \sqrt{M^2 + N^2}}{M (1 + \sqrt{M^2 + N^2 + 1})} \right) +
\ln \left( \frac{(M + \sqrt{M^2 + 1}) \sqrt{1 + N^2}}{M + \sqrt{M^2 + N^2 + 1}} \right)
\right]
\]
\[
I_2 = \frac{N}{2\pi} \tan^{-1} \left( \frac{M}{N \sqrt{M^2 + N^2 + 1}} \right)
\quad \text{(}\tan^{-1} \text{ in radians)}
\]
\[
M = \frac{L}{B}
\]
\[
N = \frac{H}{B}
\]
Figure 1 - IF variation with D/B, L/B and Poisson's ratio based on Fox (1948)
References: Timoshenko and Goodier (1951)
