BASIC QUANTITIES AND RATIOS IN SOIL MECHANICS - POROSITY, VOID RATIO, DEGREE OF SATURATION, PERCENT AIR VOIDS, AIR CONTENT (StudyCivilEngg.com)

BASIC QUANTITIES AND RATIOS IN SOIL MECHANICS

SUBJECT : SOIL MECHANICS

A number of basic quantities or ratios defined below are useful in predicting the engineering behaviour of the soil.  The general three-phase diagram for soil is quite helpful in understanding these basic quantities or ratios, and also  in the development of more useful relationships between the various quantities. In a three-phase diagram it is  conventional to represent volumes of the phases on the left side of the phase-diagram and their weights or masses  on the right side as shown in below figures respectively. The total volume V of the soil mass is equal to the  volume of air Va plus the volume of water Vw plus the volume of solid particles or soil grains Vs, i.e.,

V = (V_a + V_w + V_s)

Also the volume of voids Vv is equal to the volume of air Va plus the volume of water Vw, i.e.,  

V_v = (V_a + V_w)

and hence

V = V_v + V_s

Similarly the total weight W of the soil mass is equal to the weight of air W_a plus the weight of water W_w plus the weight of solid particles or soil grains W_s, i.e.,

W = (W_a + W_w + W_s)

The weight Wv of the materials occupying the voids is equal to the weight of air Wa plus the weight of water Ww, i.e.,

Wv = W_a + W_w

However, the weight of air being negligible, W_a ∼ 0, and hence

Wv = W_w and the total weight of the soil mass is W = (W_w + W_s)

If instead of weight, mass is considered then the total mass M of the soil mass is equal to the mass of air Ma plus  the mass of water Mw plus the mass of solid particles or soil grains

M_s, i.e.,  M = (M_a + M_w + M_s)

Three Phase Diagram of soil showing Volume and Weight

Three Phase Diagram of soil showing Volume and Mass

The mass M_v of the materials occupying the voids is equal to the mass of air M_a plus the mass of water Mw, i.e.,  M_v = (M_a + M_w). Again the mass of air being negligible, Ma ∼ 0, and hence  M_v = M_w and the total mass of the soil mass is  M = M_w + Ms

POROSITY

What is Porosity?

Porosity of a soil mass is defined as the ratio of the volume of voids Vv to the total volume of the soil mass V. It is  denoted by symbol n. Thus 

n =  V_v/V  --- Equation 1

Porosity is commonly expressed as a percentage. Thus  

n = V_v/V × 100 --- Equation 2

It is also referred to as percentage voids

VOID RATIO

What is Void Ratio?

Void ratio of a soil mass is defined as the ratio of the volume of voids V_v to the volume of solids or solid particles Vs  in the soil mass. It is denoted by symbol e and is generally expressed as a decimal fraction. Thus, 

e =  V_v/Vs  --- Equation 3

Both porosity and void ratio are the measures of denseness (or looseness) of soils. As the soil becomes more and  more dense the values of both porosity and void ratio decrease. The term porosity is more commonly used in other fields of engineering such as agricultural engineering. In soil mechanics void ratio is used more than porosity to  characterise the natural state of soil. This is so because in void ratio the denominator Vs, the volume of solids  remains more or less constant under the application of pressure, and only the numerator V_v, the volume of voids  changes, but in the case of porosity, both the numerator V_v, the volume of voids and the denominator V, the total  volume of the soil mass change under the application of pressure.

DEGREE OF SATURATION

What is Degree of Saturation? 

Degree of saturation of a soil mass is defined as the ratio of the volume of water V_w present in the voids to the  volume of voids V_v. It is denoted by symbol S (or S_r). Thus 

S (or S_r) =  V_w/V_v ---Equation 4

Degree of saturation is commonly expressed as a percentage. Thus 

S (or S_r) =  V_w/V_v  x 100  --- Equation 5

It is also known as percent saturation. For a fully saturated soil mass V_w=V_v, and hence S (or S_r) = 1 or 100%. For a perfectly dry soil V_w = 0, and hence S (or S_r) = 0. In both these conditions the soil mass is considered to be a two-phase system. When the degree of saturation of a soil is between zero and 100%, the soil mass is said to be ‘partially’ saturated which is  the most common condition found in nature, and in this condition the soil mass is considered to be a three-phase system.

PERCENT AIR VOIDS

Percent air voids of a soil mass is defined as the ratio of the volume of air V_a present in the voids to the total volume  of the soil mass V. It is denoted by symbol na.  Thus 

na = V_a/V  --- Equation 5

Percent air voids is commonly expressed as percentage. Thus

na  = V_a/V × 100

AIR CONTENT

Air content of a soil mass is defined as the ratio of the volume of air V_a present in the voids to the total volume of  voids V_v. It is denoted by symbol a_c. Thus 

a_c =  V_a/V_v

Air content is commonly expressed as a percentage. Thus  a_c =  V_a/V_v × 100

FAQs COVERED IN THIS POST

What is Porosity?

What is Degree of Saturation?

What is Percent Air Voids?

What is Air Content?

What are the basic quantities in Soil Mechanics?
What are the basic ratios in Soil Mechanics?

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