Library / Terramechanics and off-road mobility / TER-33
Terramechanics and off-road mobility
Degree of saturation from phase relationships
Fraction of the pore space filled with water, from the gravimetric water content w, the specific gravity of the solids Gs and the void ratio e.
- Ref
- TER-33
- Rev
- v1
- Field
- Terramechanics and off-road mobility
- Result
- Sr
The degree of saturation is the fraction of the pore volume that holds water, Sr = Vw/Vv. From the phase relationships, w·Gs = e·Sr, so Sr = wGs/e. The result should lie between 0 and 1; a value above 1 shows inconsistent measurements, such as an underestimated void ratio or an overestimated specific gravity or water content.
Fraction of the pore space filled with water, from the gravimetric water content w, the specific gravity of the solids Gs and the void ratio e. For ordinary two-fluid pore space it lies between 0 and 1; values outside indicate inconsistent measurements.
Calculator
- Saturation in percent66.25 %
- Water content at full saturation, e/Gs0.2264
- Water volume per unit solid volume, w Gs0.3975
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The soil is 66.3 % saturated; it would be saturated at a water content of 22.6 %, so the data are consistent.
- Strength drops sharply with saturation in most soils, so vehicle mobility tests are usually reported with Sr alongside the water content.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| w Water content (fraction of dry mass) | 0 to 1 kg/kg | 0 | 4.417 | 4.417 | +10% | +10 % |
| e Void ratio | 0.2 to 2 | 0.1987 | 1.987 | 1.789 | +10% | −9.09 % |
| Gs Specific gravity of the solids | 2.4 to 3 | 0.6 | 0.75 | 0.15 | +10% | +10 % |
Sweep of Water content (fraction of dry mass)
| Water content (fraction of dry mass) (kg/kg) | Degree of saturation |
|---|---|
| 0 | 0 |
| 0.125 | 0.5521 |
| 0.25 | 1.104 |
| 0.375 | 1.656 |
| 0.5 | 2.208 |
| 0.625 | 2.76 |
| 0.75 | 3.313 |
| 0.875 | 3.865 |
| 1 | 4.417 |
Sweep one variable
Variables and how each one contributes
Degree of saturation
What the equation gives you. Everything else feeds it.
Water content (fraction of dry mass)
The water content, as a fraction of dry mass. Raises the saturation in direct proportion. Raising it by 10 % (to 0.165) moves the result by +10 %, from 0.6625 to 0.7288.
Specific gravity of the solids
The specific gravity of the solids. Raises the saturation in direct proportion, because heavier solids hold more water mass per unit volume. Raising it by 10 % (to 2.915) moves the result by +10 %, from 0.6625 to 0.7288.
Void ratio
The void ratio. A larger pore space dilutes the water, so the saturation falls in inverse proportion. Raising it by 10 % (to 0.66) moves the result by −9.09 %, from 0.6625 to 0.6023.
Worked example with the values above
- Product: w Gs = 0.15 × 2.65 = 0.3975.
- Divide by the void ratio: 0.3975 / 0.6.
- Sr = 0.6625.
Assumptions and limits
- Representative, intact specimens of known mass or volume, with the same units for all masses and densities.
- Solid particles of a single particle density, and fully drained, non-swelling soil.
Common mistakes
- Including the container mass in the masses.
- Entering water content in percent where a fraction is needed.
- Using a particle density that does not represent the soil, which shifts the void ratio and the saturation.
Statistics and uncertainty
Soil index quantities depend on sampling and handling: water content is typically repeatable to 1 % to 2 % of the value, and void ratio to about 0.02, but sampling disturbance or a non-representative specimen can dominate the error.
Where it is used
- Recording the state of a test bed before a plate, shear or wheel test.
- Checking soil data for consistency before fitting strength models.
Maths you need
- Phase diagram: solids, water and air volumes and masses
- Water content: mass of water over mass of dry solids
- Particle density: mass of solids per unit volume of solids