Question

The relation between mv and av is __________

(a) \(m_v=\frac{a_v}{e_0} \)

(b) \(m_v=\frac{a_v}{1+∆σ’} \)

(c) \(m_v=\frac{a_v}{1+e_0} \)

(d) \(m_v=\frac{1}{e_0}\frac{a_v}{1+e_0}  \)

I have been asked this question in my homework.

The origin of the question is Consolidation Process topic in division One Dimensional Consolidation of Geotechnical Engineering I

Answer 1

Correct choice is (c) \(m_v=\frac{a_v}{1+e_0} \)

For explanation I would say: The coefficient of volume change mv is given by,

\(m_v= \frac{-∆e}{1+e_o} \frac{1}{∆σ’}\)  now substituting \(a_v=\frac{-∆e}{∆σ’},\)

we get  \(m_v=\frac{a_v}{1+e_0}. \)