Formula for void ratio | Degree of unsaturation calculator

image_pdf
image_print

Here, you are going to learn how to calculate the moister content, void ratio, and degree of saturation of the soil by using the formula for void ratio, degree of saturation, etc.

Before we can calculate the above value we must have to know the meaning of each term related to the soil like void ratio, water content, specific unit weight, etc. Let us start from phase diagram of water and it’s a relationship.

The solid soil particles, containing voids space between them is known as soil mass.

The void is the space between particles filled either with air or water.

Formula for void ratio
Formula for void ratio

For two-phase, the void space should be filled with one of the component either air or water. If the void space is filled with air then the soil is called dry.   If the void space is filled with water then the soil is called saturated.

But if there are both air and water present in void space of soil then it is called the three-phase system of soil.  

Hence, the diagrammatic representation of the different phases in soil mass is called the phase diagram.

The three constituents of soil mass are blended together forming a complex material as shown below.    

The total weight (Wt)  of the soil mass equal to the sum of the weight of solid particle (Ws), the weight of water (WW), the weight of gas (air) (Wg).  

i.e., Wt= Ww + Ws + Wg  

The total weight (Vt)  of the soil mass equal to the sum of the weight of solid particle (Vs), the weight of water (VW), the weight of gas (air) (Vg).  

i.e Vt = Vv + Vs      

= Va + Vw + Vs + Vg (Where Vv is volume of void).  

Volumetric Relationships

i) Void ratio  

The ratio of the volume of voids to the volume of solids is known as a void ratio. It is denoted by (e).

The formula for void ratio

i.e, e = Vv/Vs (The void ratio is expressed in decimal.)  

ii) Porosity (η)

The ratio of the volume of voids to the total volume of soil mass is known as porosity. It is denoted by (η) (Neeta).  

i.e, η = Vv/V (Porosity is expressed as a percentage and should not exceed 100%.)    

iii) Degree of Saturation (S)    

The ratio of the volume of water to the volume of the void is known as the degree of saturation. It is denoted by (S).  

i.e, S = Vw/Vv

(It is generally expressed as a percentage. Its value is equal to zero when the soil is absolutely dry & 100 % when the soil is fully saturated.)      

v) Air Content (ac)  

The ratio of the volume of air to the volume of voids is known as air content. It is denoted by (Ac)

i.e, Ac = Va/Ve,  

(Air Content is usually expressed as a percentage. At the saturated condition of soil air Content and percentage of air, voids are zero. (kVa=0)    

vi) Water content (w)  

The ratio of the mass of water to the mass of solids is known as water content. It is denoted by (w).  

i.e, w = Mw/Ms It is also known as moisture content (m);

it is also expressed as a percentage but used as a decimal computation.  

vii)Density of solids     

The ratio of the mass of solids to the volume of solids is known as the density of solid.

i.e, ρ(s)= Ms/Vs  

viii)Bulk unit weight

The total weight per unit total volume is known as bulk unit weight.   i.e, Y =W/V  

ix) Dry unit weight (Yd)  

The weight of soil solids per unit total volume is known as dry unit weight. i.e, Yd= Ws/V  

x) Saturated unit weight  

The bulk unit weight when the soil is fully saturated is known as saturated unit weight. The ratio of the weight of saturated solid soi to the unit total volume is called saturated unit weight.l  

i.e, Ysat=Wsat/V  

xi) Submerged unit weight (Y’)  

The submerged weight per unit of the total volume is known as submerged unit weight.  

i.e, (Y’) = Wsub/V 

xii) Unit weight of soil solids (Ys)  

The ratio of the weight of solids to the total volume of solids is known as the unit weight of soil solids.

i.e, Ys= Ws/Vs  

Also Read,

Different types of concrete mix ratio

Different Size of Aggregate for Concrete 

Types of Retaining Wall

What is Specific gravity?

  The specific gravity of solid particles is defined as the ratio of the mass of a given volume of solids to the mass of an equal volume of water at 4 C°.  

i.e, G =ps/pw  

The specific gravity of solids varies from 2.65 to 2.80  for most natural soils.
Now you have to learn some relations between these terms to solve any problem. The relations are given below:-

Now, we are going to solve a question that will make your concept clear in the calculations.  

Numericals to Calculate Moisture content void ratio

Q) A clay sample containing its natural moisture content weighs 0.33 N. The specific gravity of the solid of this soil is 2.70. after oven drying the soil sample weighs 0. 2025 N.

The volume of the moist sample before the oven drying found by the displacement of mercury is 24. 30 cm cube. Determine the moisture content void ratio and degree of saturation of the soil.

Solution:-

Given That,

Volume of Soil mass (V) = 24.30 cm cube.

Weight of Soil Mass (W) = 0.333 N

Weight of dry soil mass = (Wd) = 0.2025 N

Specific gravity (G) = 2.70

Water content = (the ratio of the mass of water) to (the mass of solids)

After that, we calculate the void ratio.

1) Moister Content

(w) = (Ww/Wd)

= ( (W-Wd)/Wd)

= ((0.333-0.2025)/0.2025)

= 0.644

= 64.4%

ii) Void Ratio

From the formula of Void Ratio,
e = (G*Yw/Yd)- 1

e = (((2.7*9.81)/8.33) – 1

e = 2.81

Also,

We have,

Yd = (Wd/V )

Yd = (0.2025/24.30)

Yd = 0.00833 N/ cm Cube.

Yd = 8330 N/ meter cube.

iii) Degree of Saturation

We have formula to get the value of the degree of saturation.

Sr x e = w x G

Sr = (w*G)/e

Sr = (0.644 * 2.7)/2.18

Sr = 0.797

Once you have done more and more practice you can able to use formula at once i.e which formula should be used where without trial process.

So, be confident. Practice more.

I hope friends, you liked my written article on “Formula for void ratio” and remains helpful.  

Please comment below if you have any questions regarding the Formula for void ratio. I will try to answer as soon as possible.

 

Any Confusion? Comment here !!!

error: Content is protected !!