Question

The change of volume per unit time is __________

(a) \(\frac{∂∆V}{∂z}=-V_0 ∆σ’\)

(b) \(\frac{∂∆V}{∂z}=-a_v V_0 ∆σ’\)

(c) \(\frac{∂∆V}{∂z}=-m_v  \frac{∂∆σ’}{∂t}\)

(d) \(\frac{∂∆V}{∂z}=-m_v dxdydz \frac{∂∆σ’}{∂t}\)

The question was asked in unit test.

My doubt stems from Terzaghi’s Theory of One Dimensional Consolidation in portion One Dimensional Consolidation of Geotechnical Engineering I

Answer 1

The correct answer is (d) \(\frac{∂∆V}{∂z}=-m_v dxdydz \frac{∂∆σ’}{∂t}\)

Best explanation: Since the decrease in volume is given by the equation,

∆v=-mv V0 ∆σ’ where V0=dxdydz,

differentiating the equation, we get,

\(\frac{∂∆V}{∂z}=-m_v dxdydz \frac{∂∆σ’}{∂t}\) where, mv is the coefficient of volume change.