Important Relationships Based on Soil Phase Diagram

A number of useful relationships may be derived based on the foregoing definitions and the soil-phase diagram.

1) Relationships Involving Porosity, Void Ratio, Degree of Saturation, Water Content, Percent Air Voids and Air Content

This may provide a practical approach to the determination of n.

This may provide a practical approach to the determination of e.

                                 

From the above equation, we can derive

These interrelationships between n and e facilitate computation of one if the other is known.

              

By multiplying both of these equations

By definition,

                      

By multiplying the equation of S and e

This equation is valid even if both w and S are expressed as percentages.

For saturated condition,

S = 1.

We know that,

But

2) Relationships Involving Unit Weights, Grain Specific Gravity, Void Ratio and Degree of Saturation

But

                 

              w G = S e

This is a general equation from which the unit weights corresponding to the saturated and dry states of soil may be got by substituting S = 1 and S = 0 respectively.

The submerged unit weight γ′ may be written as

                   

On solving