# What is the Coefficient of Consolidation, Compressibility and Volume change With Their Equation

3rd May 2019

## Coefficient of Consolidation

The term coefficient of consolidation($C_{v}$) is used to indicate the combined effects of the permeability and compressibility of soil on the rate of volume change.

It is the ratio of the coefficient of permeability(K) to the product of the coefficient of volume compressibility($m_{v}$) and unit weight of water( $\gamma _{w}$).

### Equation of The Coefficient of Consolidation

•  $C_{v} = \frac{K}{m_{v}.\gamma _{w}}$

The unit of coefficient of consolidation( $C_{v}$ ) is cm²/Sec.

## Coefficient of Compressibility or Coefficient of Compression(av)

Coefficient of Compressibility is defined as the decrease in void ratio per unit increase in pressure.

### Equation of The Coefficient of Compressibility

•   $a_{v}$ = -Δe/Δp (negative sign indicate the decrease in void ratio with an increase in pressure).

It is a measure of compression of the soil mass. The unit of Coefficient of Compressibility($a_{v}$) is cm²/gm.

## Coefficient of Volume Change or Coefficient of Volume Compressibility

The term coefficient of volume change or the coefficient of volume compressibility($m_{v}$) is defined as the change in volume of a soil mass per unit of initial volume due to an increase in pressure.

### Equation of The Coefficient of Volume Change

• Mathematically, $m_{v} = \frac{a_{v}}{(1+e_{0})}$)

where $e_{0}$ is the initial void ratio.