Category: consolidation

# The Utility of Consolidation Data

## The Utility of Consolidation Data

The consolidation data is used for the following purpose:

1. Safe engineering design of structures.
2. Forecasting of the probable settlement of a structure.
3. Solving of various problems connected with the settlement of structures due to consolidation.

# 9 Assumption in Terzaghi Theory of Consolidation

## Terzaghi Theory of Consolidation

The theoretical concept of consolidation process was developed by Terzaghi. In order to compute the amount of consolidation( or settlement) after any given time t, Terzaghi derived the following basic equation is a free surface. δu/δt = cv (δu/δz) Where, cv = Coefficient of consolidation.

The above differential equation of consolidation describes the distribution of the hydrostatic excess pressure(u) with time(t) along with depth(z).

### The Assumption in the Terzaghi Theory of Consolidation

In the development of the Terzaghi theory of consolidation, the following 9 assumptions are made:

1. The soil is fully saturated.

2. The soil is homogeneous.

3. The time lag consolidation is entirely due to the low permeability of the soil.

4. Soil particles and water are incompressible.

5. Darcy’s law is strictly valid.

6. Coefficient of permeability is constant during consolidation.

7. The soil is restrained against lateral deformation.

8. Excess pore water drains out only in the vertical direction.

9. The boundary is a free surface.

Assumption of Bernoulli’s Theorem

What is Coefficient of Consolidation, Compressibility & Volume change With Their Equation

# Consolidation Settlement Analysis – Soil

## Consolidation Settlement Analysis

In one dimensional consolidation, the change in the height(ΔH) (i.e settlement) per unit of original height(H) equals to the change in volume(ΔV) per unit of the original volume(V).
ΔH/H = ΔV/V ………….(1).

 Consolidation Settlement (Settlement Analysis)

Now, at an initial condition, void ratio(e0) = Vv/Vs Or Vv= e0.Vs

Where Vv and Vs are the volume of voids and volume of soil solids respectively.
But, V = Vv + Vs
Or, V = e0.Vs+ Vs
Or, V = Vs(1+e0)

At compressed condition, void ratio(e) = v/Vs
Where V՛v is the volume of voids 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(ΔV) = V – V՛
Or, ΔV = Vs(1+e0) – Vs(1+e)
Or, ΔV = Vs(e0-e)
Or, ΔV = Vs.Δe Where [Δe (e0-e)]
Now, ΔV/V = Vs.Δe/V
Or, ΔV/V = Vs.Δe/Vs(1+e0)
Or, ΔV/V = Δe/(1+e0) ……………(2).

From compression curve of e versus Log p we get
Compression Index(Cc) = Δe/ Log10 (p/p0)
Or, Δe = CLog10 (p/p0) ………………(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 = ΔV/V
Or, ΔH = (ΔV/V).H
Or, ΔH = {Δe/(1+e0)}.H
Or, ΔH = {CLog10 (p/p0)/(1+e0)}.H

### The Equation of The Consolidation Settlement

• ΔH = {CLog10 (p/p0)/(1+e0)}.H

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

## 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.

What is Degree Of Compaction, Optimum Moisture Content & Compacting Effort -Soil

What is Porosity, Void Ratio, Water or Moisture Content, And Degree of Saturation of Soil

Define Specific Gravity,  Bulk Specific Gravity, Air Content and Percentage Air Voids-Soil

# What is Consolidation and Consolidation Factors?

## What is Consolidation?

Consolidation can be defined as the compression resulting from a long-term static load and the consequent escape of pore water from the saturated soil mass.

According to Terzaghi, every process involving a decrease in the water content of a saturated soil mass due to the replacement of water by air is called a consolidation process.

### Factors

Consolidation occurs due to one or more of the following factors:

a) Due to external static loads from structures.
b) Due to the self-weight of the soil such as recently placed fills.
c) Due to the lowering of the groundwater table.
d) Due to desiccation.