Important Relationships Between Properties Of Soil



There are few important relationships between properties of soil that will help us solve many soil mechanics related problems.

 

Lets start with

Porosity and Void Ratio :

We define void ratio as volume of voids to the volume of solids

image : void-ratio

 

and porosity as volume of voids to the total volume of soil mass.

image : porosity

image : phase-diagram

Using 3 phase diagram of soil, in the void ratio equation we can write Vs, which is volume of solids, as total volume minus volume of voids.

image : volume-of-solids

 

Then divide both numerator and denominator with total volume of soil mass capital V.

image : void-ratio-porosity

 

now we can see the porosity in the equation.

image : void-ratio-porosity

 

Hence the relationship between void ratio and porosity is established.

image : void-ratio-porosity

 

Which can also be written as this.

image : void-ratio-porosity

 

 

Now lets develop relationship between void ratio, water content, specific gravity and degree of saturation

We write void ratio as volume of voids to the volume of solids

image : void-ratio

 

lets multiply and divide this equation with volume of water and rearrange a little

image : void-ratio

 

Now we can write volume of water as weight of water to the unit weight of water, and similarly volume of solids as weight of solids to the unit weight of solids.

image : void-ratio

 

After slight rearrangement we can write the unit weight of solids as specific gravity of solids multiply with unit weight of water

image : void-ratio-unit-weight-specific-gravity

 

Again after re-arranging the equation we can see that volume of water divided by volume of voids is degree of saturation and weight of water divided by weight of solids is water content.

image : void-ratio-unit-weight-specific-gravity

 

So after rewriting the equation we found the relationship as

image : void-ratio-unit-weight-specific-gravity

image : void-ratio-unit-weight-specific-gravity

 

 

Now we will establish an important relationship between unit weight, specific gravity, void ratio, water content and unit weight of water.

We know bulk unit weight gamma T is written as total weight of soil sample to its volume.

image : bulk-unit-weight

 

Total weight of any soil is actually weight of solids and weight of water present in it and its volume combines volume of solids and volume of voids.

image : bulk-unit-weight

 

Take out W s in numerator and Vs in denominator.

image : bulk-unit-weight

 

Now here we notice that water content and void ratio in the equation.

image : bulk-unit-weight-water-content-void-ratio

 

also Ws divided by Vs in the equation is unit weight of solids which we write as specific gravity times unit weight of water.

image : bulk-unit-weight-water-content-void-ratio

 

So by substituting these, we get this.

image : bulk-unit-weight-water-content-void-ratio

 

And now here we know

Gsw = Se

So we can write water content w in the equation as this

image : water-content

 

and after substituting we get a new relationship to be remembered.

image : bulk-unit-weight-water-content-void-ratio

 

Using this relationship we can also see that…

When soil is dry, bulk unit weight becomes dry unit weight and degree of saturation of soil becomes zero as no water is present in it. Then equation will become something like this:

image : dry-unit-weight-relationship

Using this equation we can find the dry unit weight of soil if other parameters are known.

 

On the other hand, when soil is fully saturated then degree of saturation will become one and equation will look like this.

image : saturated-unit-weight-relationship

 

Now as we know submerged unit weight of a soil, gamma dash, is equal to gamma sat minus gamma w

ϒ' = ϒsat - ϒw

 

now using previously established equation we can write gamma sat as this

image : submerged-unit-weight-relationship

 

and by simplifying it, we get a new relationship.

image : submerged-unit-weight-relationship

 

 

Lets establish one more relationship between bulk unit weight, dry unit weight and water content

bulk unit weight gamma T is total weight divided by its volume.

image : bulk-unit-weight

 

And total weight can be written as weight of solids plus weight of water.

image : bulk-unit-weight

 

We can take out weight of solids from the numerator and we can see in the equation dry unit weight and water content.

image : bulk-unit-weight-dry-unit-weight

 

Which forms the following relationship.

image : bulk-unit-weight-dry-unit-weight

 

We can establish many such relationships but these are most important and frequently used equations in soil mechanics problems





Tags : relationship

Published on :2019-08-04




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