Question

A vertical cut is to be made in a saturated clay with c = 18 kN/m² , ɸ = 0° and γ = 16 kN/m³ . What is the theoretical depth to which the clay can be excavated without side collapse?
1. 0.89 m
2. 2.5 m
3. 4.5 m
4. 9 m

Answer 1

Correct Answer - Option 3 : 4.5 m

Concept:

Maximum height of vertical cut is given by:

\({{\rm{H}}_{\rm{c}}} = \frac{{4{\rm{\;}}{{\rm{c}}_{\rm{u}}}}}{{{\rm{\gamma \;}}\sqrt {{\rm{ka}}} }}\)

γ = γsat

For pure clay ɸ = 0°

\({{\rm{k}}_a} = \frac{{1 - {\rm{sin\;}}\phi }}{{1 + {\rm{sin\;}}\phi }}\)

Calculation

Given,

 c = 18 kN/m2 , ɸ = 0° and γ = 16 kN/m3

\({k_a} = \frac{{1 - \sin 0^\circ }}{{1 + \sin 0^\circ }} = 1\)

∴ \(Z = \frac{{4C}}{{\gamma \sqrt {{K_a}} }} = \frac{{4 \times 18}}{{16\times \sqrt 1 }} = 4.5\;m\)