The coefficient of the volume change mv is given by ______.

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SSC JE Civil 10 Oct 2023 Shift 1 Official Paper-I

\( \mathrm{m}_{\mathrm{v}}=\frac{1}{\Delta \sigma^{\prime}} \)
\( \mathrm{m}_{\mathrm{v}}=\frac{-\Delta \mathrm{e}}{1-\mathrm{e}_{\mathrm{o}}} \frac{1}{\Delta \sigma} \)
\( \mathrm{m}_{\mathrm{v}}=\frac{-\Delta \mathrm{e}}{1+\mathrm{e}_{\mathrm{o}}} \frac{1}{\Delta \sigma^{\prime}} \)
\( \mathrm{m}_{\mathrm{v}}=\frac{-\Delta \mathrm{e}}{1-\mathrm{e}_{\mathrm{o}}}\)

Answer 1

Explanation:

Coefficient of volume change (mv) is given by:

We know,

→ \({{\rm{m}}_{\rm{v}}} = \frac{{{{\rm{a}}_{\rm{v}}}}}{{1 + {{\rm{e}}_{\rm{o}}}}}\) Where av = Δe/Δσ

\({m_v} = \frac{{ - \left( {\frac{{{\rm{Δ }}e}}{{{\rm{Δ }}\bar \sigma }}} \right)}}{{1 + {e_o}}}\)

Δe = Change in void ratio of the soil

eo = initial void ratio

Additional Informationa) Coefficient of consolidation(Cv)

\(C_v = {k \over m_v \gamma_w}\)

Where k = coefficient of permeability of the soil,

mv = Coefficient of volume change

b) Coefficient of compressibility:

The ratio of decrease in voids ratio of soil to the increase in effective stress is called as coefficient of compressibility.

\( {{{\rm{a}}_{\rm{v}}}} = \frac{{{\rm{\Delta e}}}}{{{\rm{\Delta \bar \sigma }}}}\)

Where Δe = change in void ratio,

Δσ̅ = change in pressure