Lesson 2: Reading the water state
Unsaturated Soil Mechanics · Course 1 · about 90 minutesYou will learn
Reading the ground profile
In Lesson 1 you saw that suction pulls soil grains together. Now you will find out where it occurs in the ground, how big it is, and how to calculate it. You will also see why the strength it gives cannot be relied on like the strength of a cemented soil.
- Place the unsaturated and capillary zones on a ground profile, and calculate matric suction from pore pressures and from simple hydrostatic and capillary models.
- Explain why suction gives only apparent cohesion, and why it changes as the soil wets and dries.
You will need a calculator. Take g = 9.81 m/s² and the unit weight of water γw = 9.81 kN/m³.
The idea, in plain words
Three zones above and below the water table
The water table (or phreatic surface) is the level at which the pore-water pressure equals atmospheric pressure. Below it, pore-water pressure is positive. Above it, the pore water is in tension, so its pressure is negative relative to the atmosphere.
- Saturated zone: below the water table. Pores are full of water at positive pressure.
- Capillary zone: just above the water table. Capillary action can keep the pores full of water, but the pressure is negative. Saturated does not mean positive pore pressure.
- Unsaturated zone: higher up. Air has entered the pores. Water content and suction vary with depth, season, vegetation and drainage.
A first number
The hydrostatic profile
If water is not flowing up or down, the pore-water pressure changes with height exactly as it does in a column of still water. At a height z above the water table:
Worked example
The water table is 4.0 m below ground. Assuming hydrostatic conditions, what is the pore-water pressure 1.0 m below ground?
Step 1: Height above the water table
z = 4.0 − 1.0 = 3.0 m
Step 2: Pore-water pressure
Answer: uw ≈ −29 kPa. You will see on the next page that this means a matric suction of about 29 kPa.
Hydrostatic is a reference, not a measurement
Real profiles are rarely in equilibrium. Evaporation and plant roots pull water out and raise suction near the surface. Rain soaks in and lowers it. A single reading describes one place at one time, not the whole site.
The key definition
Matric suction
In an unsaturated soil, the pore air and the pore water are at different pressures. The difference is the matric suction:
Near the ground surface the pore air is connected to the atmosphere, so ua ≈ 0 (gauge). The suction is then simply the size of the negative pore-water pressure.
Worked examples
(a) Near the surface
ua = 0 kPa, uw = −35 kPa. s = 0 − (−35) = 35 kPa.
(b) Pore air slightly above atmospheric
ua = 3 kPa, uw = −22 kPa. s = 3 − (−22) = 25 kPa.
(c) In the laboratory
Many laboratory tests raise the air pressure so the water pressure stays positive and is easy to measure. This is called the axis-translation technique (Hilf, 1956). With ua = 300 kPa and uw = 100 kPa, s = 300 − 100 = 200 kPa.
In every case, suction is the difference. It does not matter whether the individual pressures are positive or negative.
The minus sign that confuses everyone
When I teach this topic, the most common mistake is the sign. The pore-water pressure above the water table is negative, so students write the suction as negative too. But suction is defined as ua − uw, and when you put the numbers in, it comes out positive. A pore-water pressure of −50 kPa means a suction of +50 kPa. Always write the formula first, then substitute.
Two more terms
Total suction and osmotic suction
Matric suction comes from capillary effects and the way water is held on grain surfaces. Dissolved salts in the pore water add a second part, the osmotic suction. Together they make the total suction:
For most engineering problems, changes in matric suction control the behaviour, and that is what this pathway focuses on. Osmotic suction matters most where salt content changes, for example in saline ground or near contaminated water. Different measuring methods respond to different parts, which you will meet in Course 2.
Why fine soils hold more suction
The capillary tube model
Think of the pores as tiny tubes. Water rises up a thin tube because of surface tension, and the narrower the tube, the higher it rises and the lower the water pressure in it. For a perfectly wetting surface, the suction across a curved meniscus in a tube of radius r is:
The height water rises in that tube, the capillary rise, is hc = 2Ts ÷ (ρw g r).
| Pore radius | Suction (kPa) | Capillary rise (m) | Roughly like |
|---|---|---|---|
| 0.1 mm | 1.5 | 0.15 | Coarse sand |
| 0.01 mm | 15 | 1.5 | Fine sand or silt |
| 0.001 mm | 146 | 15 | Clayey soil |
Worked example: r = 0.01 mm
r = 0.01 mm = 1 × 10−5 m.
Ten times smaller pores give ten times the suction and ten times the rise.
The model is a simplification: real pores are irregular and connected, and clays also hold water on their particle surfaces. But it explains the main trend: the finer the soil, the higher the suction it can hold and the thicker its capillary zone.
Describing stress
Two stress variables instead of one
For a saturated soil, one quantity, the effective stress (σ − uw), controls strength and volume change. For an unsaturated soil, one quantity is not always enough. A widely used approach treats two stress-state variables separately (Fredlund and Morgenstern, 1977):
Net normal stress
σ − ua: the total stress in excess of the pore-air pressure. It works like the confining stress you already know.
Matric suction
ua − uw: the extra pull between the grains from the pore water. It changes with wetting and drying.
An older approach, due to Bishop (1959), combines the two into a single effective stress using a factor χ that depends on the degree of saturation. Both approaches are still used. Course 3 and a later strength course show how they enter design.
A common misunderstanding
Apparent cohesion is not cohesion
A compacted soil specimen can stand on the bench without any confining stress. A trench in clayey sand can stand vertical for days. It is tempting to say the soil “has cohesion”. Usually it does not, at least not in the true sense.
True cohesion
Comes from real bonds between particles, such as cementation. It stays when the soil is wetted.
Apparent cohesion
Comes from suction pulling the grains together. It looks like cohesion while the soil is unsaturated, but it disappears as the soil wets.
A simple soaking test
One quick way I check which one I am dealing with is an inundation test. Compact a specimen, then soak it in water and leave it. If it is still standing after one, two, three months, true cohesion from cementation is possible. If it softens, slakes or collapses, the strength was apparent: suction was holding it together, and it was lost on wetting. The loss may take time, but it happens.
This matters in design. If a strength test is run on an unsaturated sample and the result is used as if the soil were permanently cohesive, the design will rely on strength that may vanish after heavy rain.
Looking ahead
When engineers fit a strength line to test results, they often force it through the origin. That is an assumption, made partly to remove apparent cohesion from the result. Allowed to cut the axis, the same line can instead give an indication of how much apparent cohesion the suction provides. You will meet this in the strength course later in the pathway.
Suction changes
Suction is not a constant
It is easy to treat suction as a fixed soil property. It is not. It changes every time the soil wets or dries, and it rarely changes instantly. Rain soaks in gradually, so suction falls gradually, starting near the surface and moving downwards.
Three months to wet one specimen
In my PhD testing on compacted lateritic soil, a single test could take around three months. We wetted the specimens gradually, reducing the suction in steps. As the suction fell, the soil compressed significantly, even though we added no load. That is how water works in the ground too: it infiltrates gradually and suction reduces gradually. The idea that soil is suddenly saturated rarely matches what happens in practice.
Two lessons follow for practice. First, a value of suction measured once is a snapshot: the next storm or dry spell will change it. Second, wetting does more than reduce strength. It can change the soil’s structure and cause volume change, which is why collapsible and expansive soils cause problems.
Your turn
Calculate the water state
Task (20 minutes)
- The water table is 4.0 m below ground. Assuming hydrostatic conditions and ua = 0, find the matric suction at 1.0 m and at 3.5 m below ground.
- A tensiometer at 0.5 m depth reads uw = −18 kPa after a wet week and −65 kPa after a dry week (ua = 0). What are the suctions, and what has happened in between?
- Using the capillary tube model, find the suction and capillary rise for a pore radius of 0.002 mm.
- A compacted specimen stands unsupported on the bench. Your colleague writes “c = 25 kPa (cohesive soil)”. What would you check first?
Show the answers
1. At 1.0 m: z = 3.0 m, uw = −29.4 kPa, s = 29.4 kPa. At 3.5 m: z = 0.5 m, uw = −4.9 kPa, s = 4.9 kPa. Suction is highest near the surface.
2. Wet week: s = 18 kPa. Dry week: s = 65 kPa. The soil dried, so suction increased. The same soil had very different suctions a week apart.
3. r = 2 × 10−6 m. s = 0.1456 ÷ 2 × 10−6 = 72 800 Pa = 72.8 kPa. hc = 0.1456 ÷ (9810 × 2 × 10−6) = 7.4 m.
4. Whether the strength is apparent cohesion from suction. A soaking (inundation) test, or a test on a saturated specimen, shows whether any true cohesion remains once the suction is removed.
Quick check
Five quick questions
Choose an answer to see the explanation.
Key points
What to take away
- At the water table uw = 0. Above it, pore water is in tension. The capillary zone can be saturated with negative pore-water pressure.
- Hydrostatic reference: uw = −γw z above the water table. Real profiles depart from it with rain, evaporation and roots.
- Matric suction s = ua − uw. It is positive, even though uw is negative.
- Total suction = matric + osmotic. Matric suction usually controls engineering behaviour.
- Capillary model: s = 2Ts ÷ r. Finer pores hold higher suction.
- Two stress variables: net normal stress (σ − ua) and matric suction (ua − uw).
- Suction gives apparent cohesion, not true cohesion. It is lost on wetting, and it changes gradually with every wet and dry spell.
Up next: Lesson 3
From weather to engineering problem. How a change in weather becomes cracking, movement or failure, and how to reason through it with evidence. The lesson ends with the Course 1 assessment.
References
- Bishop, A.W. (1959) ‘The principle of effective stress’, Teknisk Ukeblad, 106(39), pp. 859–863.
- Fredlund, D.G. and Morgenstern, N.R. (1977) ‘Stress state variables for unsaturated soils’, Journal of the Geotechnical Engineering Division, ASCE, 103(GT5), pp. 447–466.
- Fredlund, D.G., Rahardjo, H. and Fredlund, M.D. (2012) Unsaturated Soil Mechanics in Engineering Practice. Hoboken, NJ: John Wiley & Sons.
- Hilf, J.W. (1956) An Investigation of Pore-Water Pressure in Compacted Cohesive Soils. Technical Memorandum 654. Denver, CO: U.S. Bureau of Reclamation.
- 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.
Further learning
- Read: Lu and Likos (2004) explain surface tension and capillarity in soils clearly, with more worked examples.
- Read: Fredlund and Morgenstern (1977) is the classic paper on the two stress-state variables, and it is short and readable.
- Try it: stand a drinking straw, a narrow tube and a thin glass capillary (if you have one) in coloured water, and compare how high the water rises in each.