Question

Rankine’s formula for finding the minimum depth of foundation for loose soil is
1. \(d= \frac{q}{\gamma }{\left( {\frac{{1 + \sin \phi }}{{1 - \sin \phi }}} \right)}\)
2. \(d= \frac{q}{\gamma }{\left( {\frac{{1 - \sin \phi }}{{1 + \sin \phi }}} \right)^2}\)
3. \(d= \frac{q}{\gamma }{\left( {\frac{{1 - \sin \phi }}{{1 + \sin \phi }}} \right)}\)
4. \(d= \frac{q}{\gamma }{\left( {\frac{{1 + \sin \phi }}{{1 - \sin \phi }}} \right)^2}\)

Answer 1

Correct Answer - Option 2 : \(d= \frac{q}{\gamma }{\left( {\frac{{1 - \sin \phi }}{{1 + \sin \phi }}} \right)^2}\)

Concept: 

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

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

Therefore, the depth of the foundation can be expressed as

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

Where d = minimum depth of foundation,

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

ϕ = angle of repose or internal friction of soil.