Question

Assume initial void ratio = e_o, final void ratio = e, initial pressure = p_o and final pressure = p. then, what is the value of coefficient of compressibility (a_v)?

1.  a_v = (e – eo)/(p – po)
2. a_v = (eo – e)/(p – po)
3. a_v = (eo – e)/(p0 – p)
4. a_v = (eo + e)/(p + po)

Answer 1

Correct Answer - Option 2 : a_v = (eo – e)/(p – po)

Explanation:

Coefficient of compressibility, av = (eo – e)/(p – po)

Where,

Initial void ratio = eo, final void ratio = e, initial pressure = po and final pressure = p

Parameter	Formula
Coefficient of compressibility (av)	av = Δe/Δσ Δe = Change in void ratio and Δσ = change in effec­tive stress
Coefficient of volume compressibility (mv)	\({{\rm{m}}_{\rm{v}}} = \frac{{{\rm{\Delta V}}}}{{\rm{V}}} \times \frac{1}{{{\rm{\Delta \sigma }}}}\) or \(\frac{{{\rm{\Delta V}}}}{{\rm{V}}} = {\rm{Strain}}\) \(\Rightarrow {{\bf{m}}_{\bf{v}}} = \frac{{{\bf{Strain}}}}{{{\bf{Stress}}}}\) ΔV = Change in Volume, V = Original Volume
Compression Index (C)	\({\rm{C}} = \frac{{{\rm{\Delta e}}}}{{{\rm{log}}\left( {\frac{{{{\rm{\sigma }}_2}}}{{{{\rm{\sigma }}_1}}}} \right)}}\) σ1 = Initial effective stress; σ2 = Final Effective stress