Question

According to Rankine’s formula, the minimum depth of foundation (h) computed with gross bearing capacity (p), density of soil (γ) and angle repose (ϕ) is:

1. \(h = \frac{p}{\gamma }{\left[ {\frac{{1 - \sin \phi }}{{1 + \tan \phi }}} \right]^2}\)
2. \(h = \frac{\gamma}{p }{\left[ {\frac{{1 - \sin \phi }}{{1+ \sin \phi }}} \right]^2}\)
3. \(h = \frac{p}{\gamma }{\left[ {\frac{{1 - \sin \phi }}{{1 + \sin \phi }}} \right]^2}\)
4. \(h = \frac{p}{\gamma }{\left[ {\frac{{1 + \sin \phi }}{{1 - \sin \phi }}} \right]^2}\)

Answer 1

Correct Answer - Option 3 : \(h = \frac{p}{\gamma }{\left[ {\frac{{1 - \sin \phi }}{{1 + \sin \phi }}} \right]^2}\)

Concept: 

Rankine’s formula provides guidance on the minimum depth of foundation based on the bearing capacity of the soil.

\( p={\gamma } {h}\left( {\frac{{1 +\sin \varphi }}{{1 - \sin \varphi }}} \right)^2\)

Therefore, the depth of the foundation can be expressed as

\(h = \frac{p}{\gamma }\left( {\frac{{1 - \sin \phi }}{{1 + \sin \phi }}} \right)^2\)

Where

h = minimum depth of foundation,

p = ultimate bearing capacity of the soil, γ = density of soil,

ϕ = angle of repose or internal friction of soil.