Question:
If the coefficient of permeability is doubled and the coefficient of volume compressibility is simultaneously halved, the coefficient of consolidation
If the coefficient of permeability is doubled and the coefficient of volume compressibility is simultaneously halved, the coefficient of consolidation
Show Hint
Remember the consolidation relation:
\[
\boxed{
C_v=\frac{k}{m_v\gamma_w}
}
\]
Thus,
\[
C_v\propto\frac{k}{m_v}.
\]
If \(k\) doubles and \(m_v\) becomes half,
\[
C_v=4\times\text{original value}.
\]
Updated On: Jul 23, 2026
- Increase by \(2\) times
- Decrease by \(2\) times
- Increase by \(4\) times
- Decrease by \(4\) times
Show Solution
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The Correct Option is C
Solution and Explanation
Concept:
The coefficient of consolidation is given by
\[
\boxed{
C_v=\frac{k}{m_v\gamma_w}
}
\]
where
\[
k=\text{Coefficient of permeability},
\]
\[
m_v=\text{Coefficient of volume compressibility},
\]
and
\[
\gamma_w=\text{Unit weight of water}.
\]
Thus,
\[
C_v\propto\frac{k}{m_v}.
\]
Step 1: Write the proportional relationship. Initially, \[ C_v\propto\frac{k}{m_v}. \] After the changes, \[ k'=2k, \] and \[ m_v'=\frac{m_v}{2}. \]
Step 2: Calculate the new coefficient of consolidation. \[ C_v' = \frac{2k}{m_v/2} = \frac{2k\times2}{m_v} = 4\frac{k}{m_v} = 4C_v. \] Therefore, \[ \boxed{C_v'=4C_v.} \] Hence, the coefficient of consolidation increases four times. Therefore, the correct option is \[ \boxed{(C)\;\text{Increase by 4 times}.} \]
Step 1: Write the proportional relationship. Initially, \[ C_v\propto\frac{k}{m_v}. \] After the changes, \[ k'=2k, \] and \[ m_v'=\frac{m_v}{2}. \]
Step 2: Calculate the new coefficient of consolidation. \[ C_v' = \frac{2k}{m_v/2} = \frac{2k\times2}{m_v} = 4\frac{k}{m_v} = 4C_v. \] Therefore, \[ \boxed{C_v'=4C_v.} \] Hence, the coefficient of consolidation increases four times. Therefore, the correct option is \[ \boxed{(C)\;\text{Increase by 4 times}.} \]
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