Lesson 3: Using the curve
Unsaturated Soil Mechanics · Course 2 · about 90 minutes, plus the assessmentYou will learn
Why the curve matters for water flow
You can now read a soil-water curve. In this lesson you will use one: to understand how easily water moves through an unsaturated soil, to compare curves from different sources fairly, and to support a real choice between two soils.
- Explain why permeability falls sharply as a soil desaturates, and compare permeabilities using ratios and orders of magnitude.
- Check whether two curves can be compared, and use them to support a proportionate engineering recommendation.
The idea, in plain words
Water can only flow where water is
In a saturated soil, water flows through every pore. As the soil dries past its air-entry value, air fills the largest pores first. Water is left in smaller pores and thin films, so the paths for flow become fewer, narrower and more tortuous. The hydraulic conductivity (permeability) therefore falls as suction rises, and it can fall by several orders of magnitude.
The relationship between permeability and suction is called the permeability function. Measuring it directly is slow and expensive, so it is often estimated from the SWCC and the saturated permeability, using methods such as those of van Genuchten (1980) or Fredlund, Xing and Huang (1994).
A surprising result
When saturated, the sand is far more permeable than the clay. But the sand drains at low suction, so beyond a few tens of kPa it can become less permeable than the clay, which is still nearly saturated. This is why a layer of coarse material under a fine soil can act as a capillary barrier: water is held in the fine layer above rather than draining into the dry coarse layer below.
Working with numbers
Ratios and orders of magnitude
Permeability changes are easiest to discuss as ratios. One order of magnitude is a factor of 10.
Worked example
A silty clay has a saturated permeability ksat = 5 × 10−8 m/s. At a suction of 300 kPa its estimated permeability is 5 × 10−11 m/s.
Step 1: Ratio
Step 2: Interpret
The permeability has fallen by a factor of 1000: three orders of magnitude. Water entering this soil when it is dry moves far more slowly than a saturated permeability test would suggest, at least until the soil wets up.
This is one reason why rain does not soak through a dry soil instantly, and why wetting fronts move gradually, as you saw in Course 1.
Like with like
Before you compare two curves
Curves for different soils often come from different laboratories, methods and reports. Before saying one soil “holds more water” or “has a higher air-entry value”, check that the curves can be compared.
| Check | Why it matters |
|---|---|
| Same vertical axis (w, θ or Sr) | A soil can look wetter in w and drier in Sr if the void ratios differ |
| Same path (drying or wetting) | Hysteresis can shift a curve by a large amount |
| Similar sample preparation and density | Density and structure change the AEV and the slope |
| Matric or total suction | At high suction the difference may be large in saline soils |
| Range actually measured | A curve drawn beyond the measured points is an extrapolation |
| Method and equilibrium criterion | Short equilibration can shift points |
Putting curves on the same axis
Converting before comparing
Worked example
At 100 kPa suction, Soil A has w = 0.22, Gs = 2.70, e = 0.80. Soil B is reported as Sr = 0.70 at the same suction. Which is closer to saturated?
Step 1: Convert Soil A to degree of saturation
Step 2: Compare
Soil A (Sr = 0.74) is slightly closer to saturated than Soil B (0.70) at 100 kPa. Whether that small difference matters depends on the scatter in the data and on whether both curves were measured on the same path.
Small differences, big claims
Two curves a few per cent apart may be within the scatter of the tests. Do not build a design decision on a difference the data cannot resolve.
Reporting what the curve can support
Say what the evidence shows, and no more
A curve on its own can support statements about how much water a soil holds at a given suction, and roughly when it starts to desaturate. It cannot by itself tell you the field water content next year, the permeability, the strength or the volume change. Those need more data or further analysis.
Use the same four elements as in Course 1:
- Observation: what the curve shows, on which axis and path.
- Interpretation: what that may mean for the problem.
- Limitation: what is not known, such as wetting behaviour or field density.
- Recommendation: a proportionate next step.
Worked case
Which soil should form the cover?
A small closed landfill is to be covered with a soil layer that will store rainfall during wet periods and release it by evaporation and plants during dry periods, limiting the water that reaches the waste. Two local soils are available. The laboratory has supplied drying curves for both, measured on specimens compacted to the density proposed for the cover.
| Property | Soil A (silty sand) | Soil B (clayey silt) |
|---|---|---|
| Air-entry value (drying) | 8 kPa | 60 kPa |
| Volumetric water content at 10 kPa | 0.20 | 0.36 |
| Volumetric water content at 1500 kPa | 0.05 | 0.14 |
| Saturated permeability | 2 × 10−6 m/s | 5 × 10−8 m/s |
Working through it
Step 1: Check the curves can be compared
Both are drying curves, on the same axis (θ), from specimens at the proposed density. Good. Neither is a wetting curve.
Step 2: Compare the storage
A simple index is the water released between a wet state (10 kPa) and a dry state (1500 kPa). Soil A: 0.20 − 0.05 = 0.15. Soil B: 0.36 − 0.14 = 0.22. Per metre of cover, that is about 150 mm of water for Soil A and 220 mm for Soil B.
Step 3: Consider flow
Soil B’s higher AEV means it stays near saturation over a wider range, and its lower permeability slows water moving down. Soil A drains at low suction.
Step 4: Identify what is missing
- Wetting curves, since rain wets the cover
- Rainfall and evaporation records for the site
- Cracking of Soil B on drying, which could open fast flow paths
- Whether field compaction will achieve the tested density
Step 5: A proportionate recommendation
On the evidence so far, Soil B appears better suited to store and release water. Before finalising, obtain wetting curves, check Soil B for shrinkage cracking, and carry out a simple water-balance check with local climate data.
Beyond the case
The same reasoning elsewhere
The steps are the same whenever a curve supports a decision: a capillary barrier beneath a road, the choice of fill for an embankment that must shed rain, or the interpretation of laboratory curves for a research project. Check comparability, compare on the same basis, think about flow, list what is missing and recommend the next step.
Wherever you are
Store-and-release covers work best where the climate has a clear dry season that lets the soil release its stored water. In a climate that is wet all year, the soil may never dry enough, and the same calculation could point to a different design. Always pair the curve with the local climate record.
Your turn
Use the curve
Task (15 minutes)
- A clay has ksat = 3 × 10−9 m/s and k = 3 × 10−11 m/s at 500 kPa. By how many orders of magnitude has the permeability fallen?
- Soil C has w = 0.18, Gs = 2.65, e = 0.60 at 50 kPa. Soil D is reported as Sr = 0.85 at 50 kPa. Which is wetter in terms of Sr?
- Rewrite this statement using the four elements: “Soil X has the better curve, so it will keep the slope dry.”
Show the answers
1. Ratio = 10−2: two orders of magnitude (a factor of 100).
2. Soil C: Sr = 0.18 × 2.65 ÷ 0.60 = 0.80. Soil D is slightly wetter (0.85), if both were measured on the same path and the difference is larger than the scatter.
3. Observation: Soil X’s drying curve holds more water at the suctions measured. Interpretation: it may store more rainfall and release it more slowly. Limitation: no wetting curve, permeability or site climate data; “keep the slope dry” also depends on drainage and slope geometry. Recommendation: obtain wetting data and permeability, and check the slope’s water balance before deciding.
Quick check
Five quick questions
Choose an answer to see the explanation.
Key points
What to take away
- Permeability falls as a soil desaturates, often by several orders of magnitude.
- A sand can become less permeable than a clay at moderate suction. This is the basis of capillary barriers.
- Before comparing curves, check the axis, path, preparation, density, type of suction and measured range.
- Convert to the same quantity before comparing, and do not over-read small differences.
- Use observation, interpretation, limitation and recommendation to keep conclusions proportionate.
You have finished the lessons of Course 2
Test yourself with the assessment below. Course 3, Using Unsaturated Soil Data in Engineering Decisions, is coming next.
Course 2 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.
Section A: Concepts (12 marks)
- Distinguish between matric, osmotic and total suction. State which of these is measured by contact filter paper and which by non-contact filter paper. [3 marks]
- Explain how the axis-translation technique works, including the role of the high-air-entry ceramic disc, and give one limitation of the technique. [4 marks]
- Describe the three regions of a drying soil-water characteristic curve, and define the air-entry value. [3 marks]
- Explain what is meant by hysteresis in the soil-water characteristic curve, and give one cause. [2 marks]
Section B: Calculations and interpretation (16 marks)
- A specimen has w = 0.18, Gs = 2.68 and e = 0.72. Calculate the degree of saturation, the porosity and the volumetric water content. [4 marks]
(a) In a pressure plate, the air pressure is 400 kPa and the water drains to atmosphere. What suction is applied? [1 mark]
(b) In a suction-controlled triaxial test, σ3 = 350 kPa, ua = 250 kPa and uw = 100 kPa. Calculate the matric suction and the net confining stress. [2 marks]
(c) State one condition the ceramic disc must meet for the test in (a). [1 mark]
- On a plot of Sr against log suction, the steep part of a drying curve passes through (50 kPa, 0.85) and (500 kPa, 0.45). The residual part is roughly flat at Sr = 0.15. Estimate the air-entry value and the suction at the residual point, showing the construction. [4 marks]
- A soil has ksat = 2 × 10−7 m/s. At 200 kPa suction its estimated permeability is 2 × 10−10 m/s. Calculate the ratio k ÷ ksat, state the change in orders of magnitude, and explain physically why the permeability has fallen. [4 marks]
Section C: Applied case (12 marks)
A design team plans an infiltration analysis for a cut slope in a residual soil. To save time, they propose using a published drying curve for “a similar soil” from another country. The published curve was measured on reconstituted specimens.
Write a short technical note to the design team (maximum 300 words) that:
- identifies what you would check before using the published curve [3 marks]
- explains how sample preparation, density and structure could make the curve unrepresentative [3 marks]
- explains why a drying curve may be unsuitable for an analysis of rainfall infiltration [3 marks]
- states your recommendation [1 mark]
Clear, professional communication suitable for a design team. [2 marks]
How your work is judged
| Criterion | What a strong answer shows |
|---|---|
| Technical accuracy | Correct terms, conversions, units and constructions |
| Use of evidence | Conclusions tied to what the curve and data actually show |
| Engineering judgement | Recognises drying versus wetting, density, structure and the limits of the data |
| Communication | Clear, concise and well organised, in your own words |
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References
- Fredlund, D.G., Rahardjo, H. and Fredlund, M.D. (2012) Unsaturated Soil Mechanics in Engineering Practice. Hoboken, NJ: John Wiley & Sons.
- Fredlund, D.G., Xing, A. and Huang, S. (1994) ‘Predicting the permeability function for unsaturated soils using the soil-water characteristic curve’, Canadian Geotechnical Journal, 31(4), pp. 533–546.
- Lu, N. and Likos, W.J. (2004) Unsaturated Soil Mechanics. Hoboken, NJ: John Wiley & Sons.
- Ng, C.W.W. and Menzies, B. (2007) Advanced Unsaturated Soil Mechanics and Engineering. Abingdon: Taylor & Francis.
- Stormont, J.C. and Anderson, C.E. (1999) ‘Capillary barrier effect from underlying coarser soil layer’, Journal of Geotechnical and Geoenvironmental Engineering, 125(8), pp. 641–648.
- van Genuchten, M.Th. (1980) ‘A closed-form equation for predicting the hydraulic conductivity of unsaturated soils’, Soil Science Society of America Journal, 44(5), pp. 892–898.
Further learning
- Read: Stormont and Anderson (1999) show the capillary barrier effect in laboratory tests, with clear figures.
- Read: the chapters on permeability and infiltration in Ng and Menzies (2007) or Fredlund, Rahardjo and Fredlund (2012).
- Practise: take two curves from any published paper, check them against the comparison table in this lesson, and write the four elements for what they show.