Question
Download Solution PDFAccording to Rankine's formula minimum depth of foundation when q = 180 kN/m2, γ = 20 kN/m3 and ϕ = 30° is -
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Rankine's formula provides guidance on the minimum depth of foundation based on the bearing capacity of the soil.
\(q_u={\gamma } {D_f}\left( {\frac{{1 +\sin \varphi }}{{1 - \sin \varphi }}} \right)^2\)
Therefore the depth of the foundation can be expressed as,
\(D_f = \frac{q_u}{\gamma }\left( {\frac{{1 - \sin ϕ }}{{1 + \sin ϕ }}} \right)^2\)
Where Df = Minimum depth of foundation, qu = Ultimate bearing capacity of the soil
Calculation:
Intensity of loading (qu) =180 kN/m2,
Unit weight = 20 kN/m3 and angle of internal friction (ϕ) = 30°
Depth of foundation = \(D_f = \frac{180}{20 }\left( {\frac{{1 - \sin 30° }}{{1 + \sin 30° }}} \right)^2\)
Depth of foundation (Df) = 1.0 m
Hence, According to Rankine's formula, the minimum depth of foundation is 1.0 m.
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