The various relations can be grouped into Volume relations ,Weight relations and Inter-relations

 The various relations can be grouped into:

 Volume relations

 Weight relations

 Inter-relations

Volume Relations:

As the amounts of both water and air are variable, the volume of solids is taken as the reference quantity. Thus,

several relational volumetric quantities may be defined. The following are the basic volume relations:

1. Void ratio (e) is the ratio of the volume of voids (Vv) to the volume of soil solids (Vs), and is expressed as a decimal. e = Vv/Vs

2. Porosity (n) is the ratio of the volume of voids to the total volume of soil (V ), and is expressed as a percentage. n = (Vv/V)x100

Void ratio and porosity are inter-related to each other as follows:

e = (n/1-n) and n = (e/1+e)

3. The volume of water (Vw) in a soil can vary between zero (i.e. a dry soil) and the volume of voids. This can be S = (Vw/Vv) x 100

expressed as the degree of saturation (S) in percentage.

For a dry soil, S = 0%, and for a fully saturated soil, S = 100%.

4. Air content (ac) is the ratio of the volume of air (Va) to the volume of voids. ac = (Va/Vv)

5. Percentage air voids (na) is the ratio of the volume of air to the total volume. na= (Va/V) x 100 = n x ac

Weight Relations:

Density is a measure of the quantity of mass in a unit volume of material. Unit weight is a measure of the weight of a unit volume of material. Both can be used interchangeably. The units of density are ton/m³, kg/m³ or g/cm³. The following are the basic weight relations:

1. The ratio of the mass of water present to the mass of solid particles is called the water content (w), or sometimes the moisture content. w = (Ww/Ws)

Its value is 0% for dry soil and its magnitude can exceed 100%.

2. The mass of solid particles is usually expressed in terms of their particle unit weight Ɣs or specific gravity (Gs) Ɣs = (Ws/Vs) = GsƔw

of the soil grain solids.

where  Ɣw = Unit weight of water

For most inorganic soils, the value of Gs lies between 2.60 and 2.80. The presence of organic material reduces the value of Gs.

3. Dry unit weight is a measure of the amount of solid particles per unit volume. Ɣd = Wd/V

4. Bulk unit weight (Ɣz or Ɣ) is a measure of the amount of solid particles plus water per unit volume. Ɣz = Ɣ = (Ws+Ww)/(Vs+Vv)

5. Saturated unit weight (Ɣsat )is equal to the bulk density when the total voids are filled up with water.

6. Buoyant unit weight (Ɣ')or submerged unit weight is the effective mass per unit volume when the soil is submerged below standing water or below the groundwater table. Ɣ' = Ɣsat - Ɣw

Inter-Relations:

It is important to quantify the state of a soil immediately after receiving in the laboratory and prior to commencing other tests. The water content and unit weight are particularly important, since they may change during transportation and storage. Some physical state properties are calculated following the practical measurement of others. For example, dry unit weight can be determined from bulk unit weight and water content. The following are some inter-relations:

Example 1: A soil has void ratio = 0.72, moisture content = 12% and Gs= 2.72. Determine

its

(a) Dry unit weight

(b) Moist unit weight, and the

(c) Amount of water to be added per m3 to make it saturated. Use: Ɣw = 9.81 kN//m3

Water to be added per m3 to make the soil saturated

= Ɣsat - Ɣ = 19.62 – 17.38 = 2.24 kN

Example 2: The dry density of a sand with porosity of 0.387 is 1600 kg/m3. Find the void

ratio of the soil and the specific gravity of the soil solids. [Take Ɣw = 1000 kg/m3   ]

n = 0.387

Ɣd= 1600 kg/m3

Solution: