# Consolidation Settlement Analysis

In one dimensional consolidation, the change in the height(

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

**V/V**………….(

**1**).

Consolidation Settlement (Settlement Analysis) |

Now, at an initial condition, void ratio**(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(

**Δ****V**) = V – V**՛**Or,

**Δ****V =****Vs(1+e****0) –****Vs(1+e****)**Or,

**Δ****V = Vs(e0-e)**Or,

**Δ****V = Vs.****Δe****Where****[****Δe****=****(e0-e)]****Now,**

**Δ****V/V =****Vs.****Δe****/****V**Or,

**Δ****V/V =****Vs.****Δe****/****Vs(1+e****0)**Or,

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

Compression Index(Cc) =

**Δe****/ Log****10****(p/p****0****)**Or,

**Δe****=****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

**ΔH/H = Δ****V/V**Or,

**ΔH = (Δ****V/V).H**Or,

**ΔH = {Δ****e/****(1+e****0)}.H**Or,

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

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

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