Question

The coefficient of volume change with respect to thickness is given by ______

(a) \(m_v= H\frac{1}{∆σ’}  \)

(b) \(m_v= \frac{-∆H}{H_0}  \)

(c) \(m_v= \frac{-∆H}{H_0}\frac{1}{e}\)

(d) \(m_v= \frac{-∆H}{H_0}\frac{1}{∆σ’}  \)

I had been asked this question by my school teacher while I was bunking the class.

This question is from Consolidation Process in portion One Dimensional Consolidation of Geotechnical Engineering I

Answer 1

Correct option is (d) \(m_v= \frac{-∆H}{H_0}\frac{1}{∆σ’}  \)

Best explanation: When the soil is laterally confined, there is decrease in volume due to the decrease in the thickness of the sample.

∴ \(m_v= \frac{-∆e}{1+e_o} \frac{1}{∆σ’} =\frac{-∆H}{H_0}\frac{1}{∆σ’} \)

Hence \(m_v= \frac{-∆H}{H_0}\frac{1}{∆σ’}  \).