Example Questions Related to Soil Phase Diagram

1) One cubic metre of wet soil weighs 19.80 kN. If the specific gravity of soil particles is 2.70 and water content is 11%, find the void ratio, dry density and degree of saturation.

Solution

Bulk unit weight, = 19.80 kN/m³

Water content, w = 11%

                                    = 0.11

Specific gravity of soil particles G = 2.70

                         

Unit weight of water, γw = 9.81 kN/m³

                       

            Void ratio, e = 0.485

 Degree of Saturation, S = 61.24 %

2) Determine the Water content, Dry density, Bulk density, Void ratio and Degree of saturation from the following data.

Sample size 3.81 cm dia. × 7.62 cm ht.

Wet weight = 1.668 N

Oven-dry weight = 1.400 N

Specific gravity = 2.7

Wet weight, W = 1.668 N

Oven-dry weight, Wd = 1.400 N

Solution

   

Specific gravity of solids, G = 2.70

3) A soil has bulk density of 20.1 kN/m³ and water content of 15%. Calculate the water content if the soil partially dries to a density of 19.4 kN/m³ and the void ratio remains unchanged.

Solution

Bulk unit weight, γ = 20.1 kN/m³

Water content, w = 15%

If the void ratio remains unchanged while drying takes place, the dry unit weight also remains unchanged since G and γw do not change.

New value of γ = 19.4 kN/m³

           

Hence the water content after partial drying = 10.86%

4) The porosity of a soil sample is 35% and the specific gravity of its particles is 2.7. Calculate its void ratio, dry density, saturated density and submerged density.

Solution

Porosity, n = 35%

         

Specific gravity of soil particles = 2.7

       

           

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Important Relationships Based on Soil Phase Diagram

A number of useful relationships may be derived based on the foregoing definitions and the soil-phase diagram.

1) Relationships Involving Porosity, Void Ratio, Degree of Saturation, Water Content, Percent Air Voids and Air Content

This may provide a practical approach to the determination of n.

This may provide a practical approach to the determination of e.

                                 

From the above equation, we can derive

These interrelationships between n and e facilitate computation of one if the other is known.

              

By multiplying both of these equations

By definition,

                      

By multiplying the equation of S and e

This equation is valid even if both w and S are expressed as percentages.

For saturated condition,

S = 1.

We know that,

But

2) Relationships Involving Unit Weights, Grain Specific Gravity, Void Ratio and Degree of Saturation

But

                 

              w G = S e

This is a general equation from which the unit weights corresponding to the saturated and dry states of soil may be got by substituting S = 1 and S = 0 respectively.

The submerged unit weight γ′ may be written as

                   

On solving

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Composition of Soil – Three Phase Diagram

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.

Fig. 1 (a) Actual Soil Mass (b) Representation of Soil Mass by Phase Diagram

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.

Fig. 2 (a) Saturated Soil (b) Dry Soil Represented as Two-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.

Fig. 3 Soil-Phase Diagram

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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Structure of Soil

The structure of a soil may be defined as the manner of arrangement and state of aggregation of soil grains. In a broader sense, consideration of mineralogical composition, electrical properties, orientation and shape of soil grains, nature and properties of soil water and the interaction of soil water and soil grains, also may be included in the study of soil structure, which is typical for transported or sediments soil. The engineering behaviour of soil is influenced by soil structure to varying degrees. Structural composition of sediment soil influences, many of their important engineering properties such as permeability, compressibility and shear strength. Hence, a study of the structure of soil is important. The following types of structure are commonly considered.

1) Single Grained Structure

Single grained structure is characteristic of coarse grained soils, with a particle size greater than 0.02 mm. Gravitational forces predominate the surface forces and hence grain to grain contact results. The deposition may occur in a loose state, with large voids or in a sense state, with less of voids. When such soils settle out of suspension in water, the particles settle independently of each other. The major force causing their deposition is gravitational and the surface forces are too small to produce any effect. There will be particle-to-particle contact in the deposit. The void ratio attained depends on the relative size of grains.

Fig. 1 Single-grained Structure

2) Honeycomb Structure

This structure can occur only in fine-grained soils, especially in silt and rock flour. Due to the relatively smaller size of grains, besides gravitational forces, inter-particle surface forces also play an important role in the process of settling down. When particles approach the lower region of suspension they will be attracted by particles already deposited as well as the neighbouring particles leading to formation of arches. Miniature arches are formed, which bridge over relatively large void spaces. This results in the formation of a honey-comb structure, each cell of a honey-comb being made up of numerous individual soil grains. The structure has a large void space and may carry high loads without a significant volume change. The structure can be broken down by external disturbances.

Fig. 2 Honey-comb Structure

3) Flocculent Structure

This structure is characteristic of fine-grained soils such as clays. In the case of flocculated structure, there will be edge-to-edge and edge-to-face contact between particles. The concentration of dissolved minerals in water leads to formation of flocculated structure with very high void ratio as in the case of marine deposits. Mutual repulsion of the particles may be eliminated by means of an appropriate chemical; this will result in grains coming closer together to form a ‘floc’. Formation of flocs is ‘flocculation’. But the flocs tend to settle in a honeycomb structure, in which in place of each grain, a floc occurs. Thus, grains grouping around void spaces larger than the grain-size are flocs and flocs grouping around void spaces larger than even the flocs result in the formation of a ‘flocculent’ structure.

Fig. 3 Flocculent Structure

Very fine particles or particles of colloidal size (< 0.001 mm) may be in a flocculated or dispersed state. This type of structure is common in fresh water deposits. In the case of dispersed or oriented structure, the particles will have face to face contact. This type for formation is due to net electrical forces between adjacent soil particles at the time of deposition being repulsive in nature. The flaky particles are oriented edge-to-edge or edge-to-face with respect to one another in the case of a flocculated structure. Flaky particles of clay minerals tend to from a card house structure, when flocculated. When inter-particle repulsive forces are brought back into play either by remoulding or by the transportation process, a more parallel arrangement or reorientation of the particles occurs. This means more face-to-face contacts occur for the flaky particles when these are in a dispersed state. In practice, mixed structures occur, especially in typical marine soils.

Fig. 4 Card House Structure

Fig. 5 Dispersed Structure

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