Terzaghi's One Dimensional Consolidation Theory

Dr. Karl Terzaghi is known as the father of Soil Mechanics, he gave the theory of one dimensional consolidation. For it, he made the following assumptions:

1. Soil is completely saturated.
2. Soil & water are virtually incompressible.
3. The compression is one- dimensional.
4. Darcy's Law is valid.
5. Certain properties like, soil permeability are constant.

He followed these assumptions to give this one dimensional consolidation theory as follows:

• Water flow due to consolidation:

When the water present in the saturated soil starts to expel out of the soil sample, its velocity may decrease at the following rate.

Similarly, the rate of change of the soil sample may be taken as follows:

According to the second assumption, the water and soil are virtually incompressible, so whatever rate of change in the volume of the pore water takes place, same will happen to the soil.

It may be written as follows:

It is known as Storage Equation: 

• Applying  Darcy's Law

Velocity of the water flow is given by Darcy's law:

Note that because only flows due to consolidation are of interest, the head

h = u/Yw

• Stress Strain relationship for soil

Assume soil behaves elastically, Elastic response:

• Principle of Effective Stress:

Terzaghi combined these 3 equations to form another differential equation, as follow:

If the soil is homogeneous, then

This equation can be used to find out the pore water pressure u. As the total stress remains constant, we can neglect the last term, so we get:

The solution of the above equation gives us the value of the pore water pressure.

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