Civil Engineering - Soil Mechanics and Foundation Engineering - Discussion

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!

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.

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.

The value of water density is given to find the right value of degree of saturation,
As we have found void ratio = 0.6.

We have ,
e * s = w * g,
=> S = (.15 * 2.56)/0.6,
=> S = 64%. Where w = (1.84/1.6)-1.

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.

If we have to take the density of water as 1 gm/cc then why 1.84 g/cc is given in question?

In order to get the right answer ignore the value given in question.

Just remember that whatever value of water density is given we have to neglect it, density of water is fixed at 1g/cc.

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.

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

Taking value of water density as 1.84 g/cc, answer comes to be 0.67.

Is not this the right answer?