# Soil phase relationships

Let’s start with the basics, phase relationships, which is the first thing to learn in soil mechanics…

Any given soil volume contains solid particles, water, and, if it is not fully saturated, air too. Phase relationships define the volume and weight relations in soil for solids, water, and air.

These relationships are fundamental to know about a soil and they affect soil properties. For example they are used to calculate the earth quantities or degree of compaction for any work that involves excavation or filling of soil, they are used to determine how saturated is soil which in turn affects strength calculations.

Now lets give a little bit more detail about these most important properties:

• Air is taken into consideration for only it’s volume. It’s density and therefore mass and therefore weight is neglected and taken as zero, but it’s volume is not taken as zero, if there is air in the soil (if the soil is not fully saturated).
• Density of a material is one of it’s fundamental property. It is shown by small Greek letter “rho”, and written as “ρ”. Solid particles have a certain density, which we will talk about below, and water has another value of density.
• Unit weight of a material is often confused by density but they are different things. Unit weight shown by Greek letter gamma, “γ”, is found by multiplying density, by gravity. So, γ = ρ.g
• Mass of a material (M) is found by multiplying it’s density with it’s volume , so, M = ρ.V
• Mass and volume of solids, water and air are as shown in the figure above. Air mass is neglected. So total mass, Mt= Ms+Mw.
• Weight is not the same as mass. Mass is the quantity of material, which is measured in units such as pounds or kilograms. Weight however, is a force, which is obtained by multiplying mass by gravity of earth (as we are on earth, so on the moon, the mass would be the same but weight would be different).

So W = M.g, where g is gravity.

Since we know M = ρ.V

Then W =  ρ.V.g

But we also know γ = ρ.g

So we can write W = γ.V

So it means, for both water and solid particles, we can multiply their respective volumes by their respective unit weights and find their weight. For example weight of water = Ww= γw.Vw

• Moisture Content (m): Weight of Water / Weight of Solids x 100 (ratio of weight of water to weight of solid particles in a soil sample, expressed as percentage). In short, m = Ww/Ws
• Degree of saturation (S): It is the ratio of water volume to total void volume. In other words, how much of void volume is filled with water. S = Vw/Vv
• Void Ratio (e): It is the volume of voids, divided by volume of solids, so, Vv/Vs. This is a useful parameter that can be used in many further calculations in soil mechanics. For example, during soil compaction, or for critical state soil mechanics, which we will define later.
• Porosity (n): It is similar to void ratio except this time we divide voids volume by total volume. so n=Vv/Vt = e/(1+e)
• γdry is the dry unit weight of soil, after all of the water has been removed from it, by drying the soil. γsaturated is the fully saturated unit weight of the soil, where all pores in the soil are completely filled with water, so in this state S = 1.
• Specific Gravity of Solid Particles of Soil (Gs): It is the ratio of weight of solid particles to weight of water for an equal volume solid and water. Since it is ratio of same kind of quantities, Gs has no units. It is just a numerical ratio.

So,

Gs =Wsolid / Wwater

and since we said “for equal volume”, volumes cancel out and,

Gs = γsolid / γwater

Since γ = ρ.g, divide both by gravity, g, and we obtain

Gs = ρ solid / ρ water

So in other words, specific gravity is the ratio of density of solid particles to density of water. For SI units, density of water is unity, which is 1. So, for SI units, Gs becomes equal to ρ of that soil. But just numerically. Gs has no units, as you can see from above. But density has units of mass/volume, such as grams / cm3.

So Gs is for solid particles only. It is not to be confused with density of the whole soil, which also includes pores within that soil. So when we talk about specific gravity, we talk about how many times more those particles weigh in comparison to same volume of water. For example, specific gravity of 2.7 means, the solid particles of that soil, weigh 2.7 times more than water that occupies the same volume of the solid particle. Most soils have specific gravity that ranges between 2.6 to 2.8. But note that this concept is good for fine grained soils only. When dealing with coarse grained soils, it is better not to use this, but to use apparent specific gravity or the density of the bulk soil volume, because coarse grained particles contain pores, which makes the concept of specific gravity as described here meaningless. You will read what is fine grained and what is coarse grained soil in the coming sections. Specific gravity is very useful in phase relationship calculations.

By simple algebraic manipulations of the quantities we listed here, we can derive the relationships below, writing here just for info, which we will not use anywhere again in this book and please do not be confused by them:

S.e = w.Gs

In the next post of this series, we discuss “Soil Classification”

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