Soil is a complex physical system. A mass of soil includes accumulated solid particles or soil grains and the void spaces that exist between the particles. The void spaces may be partially or completely filled with water or some other liquid. Void spaces not occupied by water or any other liquid are filled with air or some other gas. ‘Phase’ means any homogeneous part of the system different from other parts of the system and separated from them by abrupt transition. In other words, each physically or chemically different, homogeneous and mechanically separable part of a system constitutes a distinct phase. A system consisting of more than one phase is said to be heterogeneous.
Since the volume occupied by a soil mass may generally be expected to include material in all the three states of matter - solid, liquid and gas. Soil is referred to as a “three-phase system”. A soil mass as it exists in nature is a more or less random accumulation of soil particles, water and air-filled spaces as shown in Fig. 1 (a). For purposes of analysis it is convenient to represent this soil mass by a block diagram, called ‘Phase-diagram’, as shown in Fig. 1 (b). It may be noted that the separation of solids from voids can only be imagined. The phase-diagram provides a convenient means of developing the weight-volume relationship for a soil.
When the soil voids are completely filled with water, the gaseous phase being absent, it is said to be ‘fully saturated’ or merely ‘saturated’. When there is no water at all in the voids, the voids will be full of air, the liquid phase being absent; the soil is said to be dry. (It may be noted that the dry condition is rare in nature and may be achieved in the laboratory through oven drying). In both these cases, the soil system reduces to a ‘two-phase’ one as shown in Fig. 2 (a) and (b). These are merely special cases of the three-phase system.
Basic Terminology – Weight Volume Relationship
The general three-phase diagram for soil will help in understanding the terminology and also in the development of more useful relationships between the various quantities. Conventionally, the volumes of the phases are represented on the left side of the phase diagram, while weights are represented on the right side as shown in Fig. 3.
Va = Volume of air Wa = Weight of air (negligible or zero)
Vw = Volume of water Ww = Weight of water
Vv = Volume of voids Wv = Weight of material occupying void space
Vs = Volume of solids Ws = Weight of solids
V = Total volume of soil mass W = Total weight of solid mass
Wv = Ww
1) Porosity (n)
Porosity of a soil mass is the ratio of the volume of voids to the total volume of the soil mass. It is denoted by the letter symbol ‘n’ and is commonly expressed as a percentage. Porosity is also known as percentage voids.
Here Vv = Va + Vw
V = Va + Vw + Vs
2) Void Ratio (e)
Void ratio of a soil mass is defined as the ratio of the volume of voids to the volume of solids in the soil mass. It is denoted by the letter symbol ‘e’ and is generally expressed as a decimal fraction.
Both porosity and void ratio are measures of the denseness (or looseness) of soils. As the soil becomes more and more dense, their values decrease. The term porosity is more commonly used in other disciplines such as agricultural engineering. In soil engineering, the term void ratio is more popular. It is more convenient to use void ratio than porosity. When the volume of a soil mass changes, only the numerator (i.e. Vv) in the void ratio changes and the denominator (i.e. Vs) remains constant. However, if the term porosity is used, both the numeration and the denominator change and it will become inconvenient.
3) Degree of Saturation (S)
Degree of saturation of a soil mass is defined as the ratio of the volume of water in the voids to the volume of voids. It is designated by the letter symbol ‘S’ and is commonly expressed as a percentage.
For a fully saturated soil mass, Vw = Vv
Therefore, for a saturated soil mass S = 100%.
For a dry soil mass, Vw is zero.
Therefore, for a perfectly dry soil sample S is zero.
In both these conditions, the soil is considered to be a two-phase system. The degree of saturation is between zero and 100%, the soil mass being said to be ‘partially saturated’ and is the most common condition in nature.
4) Percent Air Voids (na)
Percent air voids of a soil mass is defined as the ratio of the volume of air voids to the total volume of the soil mass. It is denoted by the letter symbol ‘na’ and is commonly expressed in percentage.
5) Air Content (ac)
Air content of a soil mass is defined as the ratio of the volume of air voids to the total volume of voids. It is designated by the letter symbol ‘ac’ and is commonly expressed as a percentage.
6) Water Content/Moisture Content (w)
Water content or Moisture content of a soil mass is defined as the ratio of the weight of water to the weight of solids (dry weight) of the soil mass. It is denoted by the letter symbol 'w' and is commonly expressed as a percentage.
7) Bulk Unit Weight/Mass Unit Weight (𝛾)
Bulk unit weight or Mass unit weight of a soil mass is defined as the weight per unit volume of the soil mass. It is denoted by the letter symbol 'γ'. Hence,
Here, W = Ww + Ws
and V = Va + Vw + Vs
The term ‘density’ is used for ‘unit weight’ in soil mechanics, although density means the mass per unit volume and not weight.
8) Unit Weight of Solids (γs)
Unit weight of solids is the weight of soil solids per unit volume of solids alone. It is also sometimes called the ‘absolute unit weight’ of a soil. It is denoted by the letter symbol 'γs'.
9) Unit Weight of Water (γw)
Unit weight of water is the weight per unit volume of water. It is denoted by the letter symbol 'γw'.
It should be noted that the unit weight of water varies in a small range with temperature. It has a convenient value at 4°C, which is the standard temperature for this purpose. γo is the symbol used to denote the unit weight of water at 4°C. The value of γo is 1g/cm3 or 1000 kg/m3 or 9.81 kN/m3.
10) Saturated Unit Weight (γsat)
The saturated unit weight is defined as the bulk unit weight of the soil mass in the saturated condition. This is denoted by the letter symbol γsat.
11) Submerged Unit Weight/Buoyant Unit Weight (γ′)
The submerged unit weight or buoyant unit weight of a soil is its unit weight in the submerged condition. In other words, it is the submerged weight of soil solids (Ws)sub per unit of total volume, V of the soil. It is denoted by the letter symbol γ′.
(Ws)sub is equal to the weight of solids in air minus the weight of water displaced by the solids. Hence
(Ws)sub = Ws – (Vs . γw)
Since the soil is submerged, the voids must be full of water.
The total volume V must be equal to (Vs + Vw) . (Ws)sub may now be written as,
(Ws)sub = W – Ww – Vs . γw
= W – Vw . γw – Vs . γw
= W – γw (Vw + Vs)
= W – V . γw
Dividing throughout by V, the total volume,
Or
γ′ = γsat – γw
It may be noted that a submerged soil is invariably saturated, while a saturated soil need not be submerged. This equation may be written as a direct consequence of Archimedes’ Principle which states that the apparent loss of weight of a substance when weighed in water is equal to the weight of water displaced by it. Thus,
γ ′ = γsat – γw
12) Dry Unit Weight (γd)
The dry unit weight is defined as the weight of soil solids per unit of total volume, the former is obtained by drying the soil, while the latter would be got prior to drying. The dry unit weight is denoted by the letter symbol 'γd' and is given by
13) Mass Specific Gravity (Gm)
The mass specific gravity of a soil may be defined as the ratio of mass or bulk unit weight of soil to the unit weight of water at the standard temperature (4°C). This is denoted by the letter symbol Gm and is given by
This is also referred to as ‘bulk specific gravity’ or ‘apparent specific gravity’.
14) Specific Gravity of Solids (G)
The specific gravity of soil solids is defined as the ratio of the unit weight of solids (absolute unit weight of soil) to the unit weight of water at the standard temperature (4°C). This is denoted by the letter symbol G and is given by
This is also known as ‘Absolute specific gravity’ and ‘Grain Specific Gravity’.
15) Specific Gravity of Water (Gw)
Specific gravity of water is defined as the ratio of the unit weight of water to the unit weight of water at the standard temperature (4°C). It is denoted by the letter symbol, Gw and is given by
Since the variation of the unit weight of water with temperature is small, this value is very nearly unity and in practice is taken as such.
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