Question

From the consolidation test data using the ‘Height of solids’ method, the coefficient of volume change can be calculated by _____________

(a) \(m_v=-\frac{∆H_o}{H_o}\frac{1}{∆σ’}\)

(b) \(m_v=\frac{∆H}{H_o}   \frac{1}{∆σ’}\)

(c) \(m_v=-\frac{∆H}{H_o}   \frac{1}{∆σ’}\)

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

The question was posed to me in my homework.

I would like to ask this question from Calculation of Voids Ratio and Coefficient of Volume Change topic in portion One Dimensional Consolidation of Geotechnical Engineering I

Answer 1

Right choice is (c) \(m_v=-\frac{∆H}{H_o}   \frac{1}{∆σ’}\)

To elaborate: Since we know the relation of change in voids ratio with the pressure increment is given by the relation,

\(\frac{∆e}{1+e_0}=\frac{∆H}{H_0},\) and coefficient of volume change is given by \(m_v=-\frac{∆e}{1+e_o}\frac{1}{∆σ’}.\)

Therefore, from the two equations, we get,

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