Lesson 2: The soil-water characteristic curve
Unsaturated Soil Mechanics · Course 2 · about 90 minutesYou will learn
One curve, many names
Plot how much water a soil holds against the suction it is under, and you get the soil-water characteristic curve (SWCC), also called the soil-water retention curve. It is the most important single description of an unsaturated soil, because so much else (permeability, strength, volume change) is linked to it.
- Convert between gravimetric water content, volumetric water content and degree of saturation, and read the air-entry value and residual conditions from a curve.
- Explain why drying and wetting give different curves, and why density and structure change the curve.
This lesson uses the phase relationships from Soil Mechanics Fundamentals, Lesson 6. Have a calculator ready.
Read the axes first
Three ways to say “how much water”
The horizontal axis is suction, almost always on a logarithmic scale because it spans from below 1 kPa to around 1 000 000 kPa. The vertical axis can be any of three quantities, and published curves use all of them:
| Quantity | Definition | Notes |
|---|---|---|
| Gravimetric water content, w | mass of water ÷ mass of solids | Easiest to measure (weigh, oven-dry, weigh) |
| Volumetric water content, θ | volume of water ÷ total volume | Used in flow and infiltration analysis |
| Degree of saturation, Sr | volume of water ÷ volume of voids | Shows how full the pores are, from 0 to 1 |
The three are linked through the void ratio e and the specific gravity Gs:
Worked example
A specimen has w = 0.20, Gs = 2.70 and e = 0.65. Find Sr and θ.
Step 1: Degree of saturation
Step 2: Porosity
Step 3: Volumetric water content
Check
ρd = Gs ρw ÷ (1 + e) = 2.70 ÷ 1.65 = 1.64 Mg/m³, so θ = 0.20 × 1.64 = 0.33.
The same state is w = 20%, θ = 0.33 and Sr = 0.83. Three numbers, one soil.
If the soil changes volume, the curves disagree
For a soil that shrinks as it dries, e falls with suction. A curve in w can then look very different from the same data plotted as Sr. Converting needs the void ratio at each point, not one value for the whole test.
The shape
Three regions on a drying curve
- Boundary effect region. The pores stay essentially full. Suction rises, but little water leaves.
- Air-entry value (AEV). The suction at which air starts to enter the largest pores. Beyond it, the soil desaturates.
- Transition region. Water drains from progressively smaller pores. A small change in suction gives a large change in water content.
- Residual region. The remaining water is held in small pores and as films on the grains. It takes very large suction increases to remove more.
A number from the curve
Reading the air-entry value
The change from boundary effect to transition is gradual, so the AEV is found by construction. Draw a horizontal line at the saturated value, and a tangent through the steep part of the curve. Where they meet is the AEV. A second tangent through the flatter, residual part gives the residual point in the same way.
Worked example
On a plot of Sr against log suction, the steep part of the curve passes through (100 kPa, 0.80) and (1000 kPa, 0.40). Find the AEV.
Step 1: Slope per log cycle
From 100 to 1000 kPa is one log cycle, and Sr falls by 0.40. So the tangent falls 0.40 per log cycle.
Step 2: How far back to full saturation?
From Sr = 0.80 up to 1.0 is a rise of 0.20, which is 0.20 ÷ 0.40 = 0.5 log cycle.
Step 3: Convert back to suction
AEV ≈ 32 kPa. Below this the soil stays essentially saturated, even though it is under suction.
Typical orders of magnitude. Clean sands have air-entry values of only a few kPa, silts of tens of kPa, and clays of hundreds of kPa or more. These are only rough guides: density and structure move them a long way, as you will see on the next page.
Hysteresis
Drying and wetting give different curves
At the same suction, a soil that is wetting usually holds less water than one that is drying. This is hysteresis. The main reasons:
- The ink-bottle effect. A large pore connected through narrow throats drains only when the suction is high enough to empty the throat, but refills only when the suction falls low enough to fill the large pore.
- Contact angle. Water advancing over a grain surface meets it at a different angle from water retreating.
- Trapped air. On wetting, pockets of air are cut off, so the soil rarely returns to full saturation.
Between the main drying and wetting curves, a soil that reverses direction part-way follows a scanning curve. In the ground, rain followed by dry spells keeps the soil moving along scanning curves.
Not a fixed property
Density and structure change the curve
The SWCC describes the pores, so anything that changes the pores changes the curve.
Density
Compacting a soil more densely makes the pores smaller. The air-entry value rises and the soil holds more water at a given suction (in terms of Sr).
Structure
A compacted clay can have clusters of particles with small pores inside and large pores between them. Natural soils have fabric and bonding from their history. Remoulding or reconstituting destroys this.
So a curve measured on a reconstituted specimen, or one compacted to a different density or water content, may not represent the soil in the field.
Common mistake: ignoring density and structure
The mistake I see most often is a curve borrowed from a different sample, prepared in a different way, used as if it described the soil on site. A reconstituted laboratory specimen, or one compacted at a different density, can have a very different air-entry value and slope from the natural or as-placed soil. Before using any curve, check how the sample was prepared and at what density, and compare that with the soil you are designing for.
Wherever you are
Residual tropical soils, glacial tills and loess can all have structure that a reconstituted sample will not reproduce. If you work with local soils that have a strong natural fabric, prefer undisturbed samples for the curve, or at least test both and compare.
Describing a curve in words
A disciplined order for reading any curve
- Axes: what is on the vertical axis (w, θ or Sr)? Is suction matric or total? Is the scale logarithmic?
- Path: drying, wetting or both?
- Sample: undisturbed, compacted or reconstituted? At what density?
- Shape: the AEV, the steepness of the transition and the residual conditions.
- Limits: what range was actually measured, and how many points support each part of the curve?
Only then say what the curve means for the problem in front of you.
Your turn
Convert and read
Task (25 minutes)
- A specimen has w = 0.15, Gs = 2.65 and e = 0.60. Find Sr, n and θ.
- The steep part of a drying curve (Sr against log suction) passes through (20 kPa, 0.90) and (200 kPa, 0.50). Find the air-entry value.
- For the same curve, the residual part is roughly flat at Sr = 0.10. Find the suction where the steep tangent meets it.
- A designer plans to use a drying curve to model how a slope responds to heavy rain. What would you point out?
Show the answers
1. Sr = 0.15 × 2.65 ÷ 0.60 = 0.66. n = 0.60 ÷ 1.60 = 0.375. θ = 0.66 × 0.375 = 0.25.
2. The tangent falls 0.40 per log cycle. From 0.90 to 1.0 is 0.10, or 0.25 log cycle. log s = log 20 − 0.25 = 1.301 − 0.25 = 1.051, so AEV ≈ 11 kPa.
3. From 0.50 down to 0.10 is 0.40, or 1.0 log cycle beyond 200 kPa, so the residual point is at about 2000 kPa.
4. Rain wets the soil, so the soil follows a wetting path. At the same suction a wetting soil usually holds less water than the drying curve shows. Ask for a wetting curve, or at least treat the drying curve as an approximation and test how sensitive the result is.
Quick check
Five quick questions
Choose an answer to see the explanation.
Key points
What to take away
- The SWCC links water content to suction. Suction is plotted on a log scale.
- The vertical axis may be w, θ or Sr. Use Sre = wGs and θ = Srn to convert, with the void ratio at each point.
- Regions: boundary effect, transition and residual. The AEV and residual point are found by tangent construction.
- Wetting curves usually lie below drying curves (hysteresis), and wetting rarely returns the soil to full saturation.
- Density and structure change the curve. A curve from a differently prepared sample may not represent the field soil.
Up next: Lesson 3
Using the curve. How retention controls permeability, how to compare curves fairly, and a guided case on choosing a cover soil. The lesson ends with the Course 2 assessment.
References
- Fredlund, D.G. and Xing, A. (1994) ‘Equations for the soil-water characteristic curve’, Canadian Geotechnical Journal, 31(4), pp. 521–532.
- Fredlund, D.G., Rahardjo, H. and Fredlund, M.D. (2012) Unsaturated Soil Mechanics in Engineering Practice. Hoboken, NJ: John Wiley & Sons.
- 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.
- 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.
- Vanapalli, S.K., Fredlund, D.G. and Pufahl, D.E. (1999) ‘The influence of soil structure and stress history on the soil-water characteristics of a compacted till’, Géotechnique, 49(2), pp. 143–159.
Further learning
- Read: Vanapalli, Fredlund and Pufahl (1999) show clearly how compaction water content and stress history change the curve of the same soil.
- Go further: van Genuchten (1980) and Fredlund and Xing (1994) give the equations most often fitted to measured curves. You do not need them for this course, but you will meet them in reports.
- Try it: plot any published curve you can find on log paper, and draw the tangents to estimate its air-entry value yourself.