## Consolidation Settlement Analysis

In one dimensional consolidation, the change in the height(

**Î”****H**) (i.e settlement) per unit of original height(**H**) equals to the change in volume(**Î”****V**) per unit of the original volume(**V**).**Î”H/H = Î”**

**V/V**.............(

**1**).

Consolidation Settlement (Settlement Analysis) |

**(e**

**0) = Vv/Vs**Or

**V**

**v= e0.Vs**

Where

But,

Or,

Or,

At compressed condition, void ratio

Where

Now, V

Where V

Therefore, change in volume(

Or,

Or,

Or,

Or,

Or,

Compression Index(Cc) =

Or,

Where p0 is the initial pressure and p is the pressure at the compressed condition.

Now, from equation (1), (2), and (3) we get

Or,

Or,

Or,

###

**V****v**and**V****s****are the volume of voids and volume of soil solids respectively.**But,

**V = V****v + Vs**Or,

**V = e****0.Vs+ Vs**Or,

**V = Vs(1+e****0)**At compressed condition, void ratio

**(e) =****V՛v/Vs**Where

**V****՛****v**is the volume of voides at compressed condition.Now, V

**՛**=**Vs(1+e****)**Where V

**՛**and e are the volume of soil sample and void ratio respectively at the compressed condition.Therefore, change in volume(

**Î”****V**) = V - V**՛**Or,

**Î”****V =****Vs(1+e****0) -****Vs(1+e****)**Or,

**Î”****V = Vs(e0-e)**Or,

**Î”****V = Vs.****Î”e****Where****[****Î”e****=****(e0-e)]****Now,**

**Î”****V/V =****Vs.****Î”e****/****V**Or,

**Î”****V/V =****Vs.****Î”e****/****Vs(1+e****0)**Or,

**Î”****V/V =****Î”e****/****(1+e****0) ...............(2).****From compression curve of e versus Log p we get**

Compression Index(Cc) =

**Î”e****/ Log****10****(p/p****0****)**Or,

**Î”e****=****Cc****.****Log****10****(p/p****0****)****..................(3).**Where p0 is the initial pressure and p is the pressure at the compressed condition.

Now, from equation (1), (2), and (3) we get

**Î”H/H = Î”****V/V**Or,

**Î”H = (Î”****V/V).H**Or,

**Î”H = {Î”****e/****(1+e****0)}.H**Or,

**Î”H = {****Cc****.****Log****10****(****p****/p****0****)****/****(1+e****0)}.H**###
**The Equation of The **Consolidation **Settlement**

**Î”H = {****Cc****.****Log****10****(p/p****0****)****/****(1+e****0)}.H**

*Read Also:*
## No comments:

## Post a Comment