Lesson 6: The phase diagram
Soil is solids, water and air · about 40 minutesYou will learn
What is a soil made of?
A handful of soil looks like one material, but it is really three: solid grains, water and air. How much of each is present controls how heavy the soil is, how strong it is and how much it will squash. In this lesson you will learn the simple drawing engineers use to keep track of the three, and the handful of ratios that describe them.
- Draw a phase diagram and explain what each part means.
- Calculate void ratio, porosity, water content and degree of saturation, and link them with S e = w Gs.
You will need a calculator. Every formula in this lesson comes straight from the phase diagram, so there is very little to memorise.
Why it matters
Grains that are not glued together
Steel and concrete are solid all the way through. Soil is not. It is a pile of separate grains, touching each other, with gaps between them called voids or pores. The grains are held in place mostly by friction where they touch, plus attraction between particles in clays.
That makes the packing of the grains, and what fills the gaps, very important. A loosely packed soil with lots of voids can squash under a building. A tightly packed one barely moves. Water in the voids, called pore water, can carry part of a load, flow out over time, or push the grains apart. Much of soil mechanics comes back to these three phases.
The idea, in plain words
The phase diagram
In real soil the grains, water and air are mixed together. To work with them, engineers imagine squeezing each phase into its own layer. This picture is the phase diagram. Volumes (V) go on the left, masses (M) on the right.
| Symbol | Meaning |
|---|---|
| Va, Vw, Vs | Volume of air, water and solids |
| Vv = Va + Vw | Volume of voids: all the space that is not solid grains |
| VT = Vs + Vv | Total volume |
| Mw, Ms, MT | Mass of water, mass of solids and total mass. Air has mass, but so little that we take it as zero. |
Not every soil has all three phases:
Dry
Voids full of air. No water phase.
Partly saturated
Voids hold some water and some air. All three phases.
Saturated
Voids completely full of water. No air phase.
Volume ratios
How much space is there between the grains?
Three ratios describe the voids. Each one compares two parts of the phase diagram.
Void ratio and porosity describe the same thing in two ways, so one can be turned into the other:
Why engineers prefer void ratio
When soil is squashed, the volume of solids stays the same and only the voids shrink. Because e is measured against the solids, it changes in a simple way as the soil compresses. That makes it the natural choice for settlement calculations later in this course.
Water in the voids
How full of water are the voids?
Worked example
Reading the ratios off a phase diagram
A sample of total volume 1.00 m³ contains 0.60 m³ of solids, 0.25 m³ of water and 0.15 m³ of air.
| Quantity | Working | Answer |
|---|---|---|
| Volume of voids | 0.25 + 0.15 | 0.40 m³ |
| Void ratio, e | 0.40 ÷ 0.60 | 0.67 |
| Porosity, n | 0.40 ÷ 1.00 | 0.40 |
| Check: n = e ÷ (1 + e) | 0.667 ÷ 1.667 | 0.40 ✓ |
| Specific volume, v | 1 + 0.667 | 1.67 |
| Degree of saturation, S | 0.25 ÷ 0.40 | 0.625 (62.5%) |
| Air content, A | 0.15 ÷ 1.00, or 0.40 × (1 − 0.625) | 0.15 (15%) |
Wherever you are
The ideas are the same everywhere, but symbols vary between textbooks and standards: S or Sr for saturation, w or m for water content, and some books use n for porosity while others give it as a percentage. Check the symbols at the start of any report or textbook you use, and define your own when you write.
Mass ratios
Water content and specific gravity
Two more quantities bring the masses into the picture.
Gs is the density of the grains alone, not of the soil, which also contains water and voids. It depends on the minerals, not on how the grains are packed. For most mineral soils it falls in a narrow band of about 2.60 to 2.80. Soils rich in organic matter are lighter, and soils containing heavy minerals such as iron ores are heavier.
The key link
S e = w Gs
One relationship ties saturation, void ratio, water content and specific gravity together. It comes straight from the phase diagram. Imagine a sample with exactly 1 unit volume of solids:
- Volume of voids = e (because e = Vv ÷ Vs and Vs = 1).
- Volume of water = S × e (because S = Vw ÷ Vv).
- Mass of solids = Gs ρw × 1.
- Mass of water = ρw × S e.
Water content is mass of water divided by mass of solids:
The trick worth remembering
Whenever you are stuck, draw a phase diagram with Vs = 1. Then Vv = e, VT = 1 + e, Ms = Gsρw and Mw = wGsρw. Almost every formula in this part of the course can be read straight off that diagram.
For a saturated soil, S = 1, so e = w Gs. That gives a quick way to find the void ratio of a saturated clay from its water content.
Worked example
How saturated is this soil?
A soil has water content 20%, specific gravity 2.70 and void ratio 0.65. Find its degree of saturation, porosity and air content.
Saturation over 100% is a warning sign
When I check laboratory results, I often recalculate S from the reported water content, density and specific gravity. If it comes out above 100%, something is wrong: usually an assumed Gs that does not suit the soil, or a density measured on a disturbed sample. It is a quick check that catches real errors.
Your turn
Two soils to work out
Task (15 minutes)
Soil A is a saturated clay with water content 40% and Gs = 2.70. Find its void ratio and porosity.
Soil B is an oven-dry sand with void ratio 0.55. Find its porosity, degree of saturation and air content.
Soil C has e = 0.80, Gs = 2.65 and S = 50%. What is its water content?
Show the answers
Soil A. Saturated, so S = 1 and e = w Gs = 0.40 × 2.70 = 1.08. n = 1.08 ÷ 2.08 = 0.52.
Soil B. n = 0.55 ÷ 1.55 = 0.35. Dry, so S = 0, and all the voids are air: A = n = 0.35.
Soil C. w = S e ÷ Gs = 0.50 × 0.80 ÷ 2.65 = 0.151, so w ≈ 15%.
Quick check
Five quick questions
Choose an answer to see the explanation.
Key points
What to take away
- Soil has three phases: solids, water and air. The phase diagram separates them, with volumes on the left and masses on the right.
- Void ratio e = Vv ÷ Vs. Porosity n = Vv ÷ VT = e ÷ (1 + e). Specific volume v = 1 + e.
- Degree of saturation S = Vw ÷ Vv, from 0 (dry) to 1 (saturated). Air content A = n (1 − S).
- Water content w = Mw ÷ Ms. Specific gravity Gs is usually 2.60 to 2.80 for mineral soils.
- S e = w Gs. For a saturated soil, e = w Gs.
- When in doubt, draw a phase diagram with Vs = 1.
Up next: Lesson 7
What’s the difference between density and unit weight? Now that you can describe what is in a soil, you will work out how heavy it is, and how to convert between kilograms and kilonewtons without mistakes.
Assessment (optional)
Test yourself properly
Unlike the practice questions, this assessment has no answers on the page. Attempt it on your own, as if it were an exam.
Instructions
- Total: 40 marks. Suggested time: 60 minutes.
- Answer all questions. The marks for each question are shown in brackets.
- You may refer to the lesson notes, but write your answers in your own words.
- Show your working in calculations. Where a question asks you to justify or explain, marks go to your reasoning, not just the final answer.
Section A: Concepts (12 marks)
- Draw a phase diagram for a partly saturated soil. Label all the volumes and masses. [3 marks]
- Define void ratio, porosity, degree of saturation and water content. [4 marks]
- Using a phase diagram with Vs = 1, show that n = e ÷ (1 + e). [2 marks]
- Explain why the degree of saturation can never be more than 100%, but the water content can. [3 marks]
Section B: Calculations (16 marks)
A soil sample has a volume of 950 cm³ and a mass of 1805 g. After oven drying its mass is 1520 g. Gs = 2.70. Take the density of water as 1 g/cm³.
(a) Calculate the water content. [2 marks]
(b) Calculate the volume of solids and the volume of voids. [3 marks]
(c) Calculate the void ratio and the porosity. [3 marks]
(d) Calculate the degree of saturation. [2 marks]
(e) Calculate the air content. [2 marks]
(f) Check your answers with S e = w Gs. [2 marks]
- A saturated clay has a water content of 52% and Gs = 2.72. Find its void ratio and porosity. [2 marks]
Section C: Applied case (12 marks)
A laboratory sheet for a clay sample reports w = 30%, e = 0.70 and Gs = 2.65. A colleague plans to use these values in a design.
Write a short technical note to your colleague (maximum 300 words) that:
- shows, with a calculation, why these three values cannot all be correct [3 marks]
- suggests likely causes of the error [3 marks]
- works out the void ratio that would be consistent if w and Gs are correct and the sample is saturated [3 marks]
- recommends what should happen before the values are used [1 mark]
Clear, well-organised communication. [2 marks]
How your work is judged
| Criterion | What a strong answer shows |
|---|---|
| Technical accuracy | Correct terms, methods and calculations |
| Use of evidence | Conclusions backed by specific information in the question (test results, descriptions, site details) |
| Engineering judgement | Results linked to what they mean for design and construction |
| Communication | Clear, concise and well organised, in your own words |
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References
- British Standards Institution (BSI) (2014) BS EN ISO 17892-1:2014 Geotechnical investigation and testing. Laboratory testing of soil. Determination of water content. London: BSI.
- British Standards Institution (BSI) (2015) BS EN ISO 17892-3:2015 Geotechnical investigation and testing. Laboratory testing of soil. Determination of particle density. London: BSI.
- Das, B.M. and Sobhan, K. (2018) Principles of Geotechnical Engineering. 9th edn. Boston, MA: Cengage Learning.
- Knappett, J.A. and Craig, R.F. (2019) Craig’s Soil Mechanics. 9th edn. Boca Raton, FL: CRC Press.
- Powrie, W. (2014) Soil Mechanics: Concepts and Applications. 3rd edn. Boca Raton, FL: CRC Press.
Further learning
- Read: Chapter 1 of Craig’s Soil Mechanics covers phase relationships with further worked examples.
- Practise: make up your own sample (pick Vs, Vw and Va), calculate every ratio, then check them against each other with S e = w Gs and n = e ÷ (1 + e).
- See it done: look for videos of the water content (oven drying) test and the particle density (pycnometer) test.