Civil Engineering - Soil Mechanics and Foundation Engineering - Discussion

As we take the given value of water density then the answer will come porosity(n) =0.66 by giving confusion of water density the answer will come wrong, for correct answer yo can take water density =1g/cc.

Yd=((G*Yw)/(1+e)),
Yd= 0.6,

n = e / 1+e = 0.375.

Dry density = (Gs*water density)/1+e.
Water density = 1 g/cm^3.
1.6 = (2.56*1)/1+e,
e = 0.6,
n = e/1+e,
n = 0.375.

Given,
Dry density = 1.69g/cc
Density of water=1.84g/cc
Specific Gravity of solids=2.56
The porosity of the Soil sample =?

We know that,
Dry density = (specific gravity * density of water )/(1+e).
1.6 = (2.56*1.84)/(1+e).
=>1.6=4.7104/(1+e).
=> (4.7104-1.6) = 1.6e.
=> e= 3.1104/1.6
so e = 1.944
Now,
n= e/(1+e).
or, n= 1.944/(1+1.944).
n = 0.66 .

As per the given problem, the Porosity of the given solid is 0.66.
But, 0.66 isn't available in the option.

Now try out this way ;
Usually, we take the density of water as 1g/cc or 1000kg/m^3
Let's input density of water is equal to 1 g/cc then,
Dry density = (specific gravity *density of water )/(1+e)
1.6=(2.56*1)/(1+e)
=> 1.6=2.56/(1+e)
=>, 2.56-1.6=1.6e
=> 0.96=1.6e
e= 0.96/1.6.
It gives the value of void ratio e= 0.6.
and we can easily find out the value of the porosity of solids by using this relation;
n = e/(1+e)
n = 0.6/(1+0.6)
n = 0.6/1.6
n = 0.375.

And 0.375 is available in the option so it is the correct answer. Option A is answer!

Agree @Abhik,

The answer will be 0.66.

Here,
Dry density, Yd=1.6g/cc.
Specific Gravity, G=2.56.
[Consider, water density, Yw as 1g/cc].
Porosity, n= e/1+e.
Void ratio, e= (GYw/Yd) -1=((2.5*1) /1.6)-1=0.6.
Then, porosity, n= e/1+e=0.6/(1+0.6) =0.375.

How you got .375? Please explain.

If we take water density 1.84 then porosity will be 0.66.

Here, e is the void ratio. What is the actual formula to finding out the value of porosity? Please tell me.

Dry density of soil is = 1.6g/cc.
Specific gravity of soil = 2.56.
Density of water take it as = 1g/cc.

Then use the relation between dry density and void ratio,

i.e,dry density of soil = (specific gravity*density of water)/(1+void ratio).

Here you got void ratio value then use the relation between porosity and void ratio.

Then you will get answer as 0.375.

By using the density of water the answer is 0.66.