Library / Terramechanics and off-road mobility / TER-32
Terramechanics and off-road mobility
Void ratio from particle and dry bulk densities
Pore volume divided by solid volume, from the particle density ρs of the solids and the dry bulk density ρd in the same units.
- Ref
- TER-32
- Rev
- v1
- Field
- Terramechanics and off-road mobility
- Result
- e
The void ratio is the pore volume per unit volume of solids, e = Vv/Vs. Writing the dry density as ρd = ρs·Vs/V with V = Vs(1 + e) gives e = ρs/ρd − 1. The particle density is typically 2.60 to 2.75 Mg/m³ for mineral soils, and an assumed value that does not match the soil shifts e directly.
Pore volume divided by solid volume, from the particle density ρs of the solids and the dry bulk density ρd in the same units. It needs 0 < ρd ≤ ρs, and the particle density must represent the tested material.
Calculator
- Porosity, e/(1 + e)0.3939
- Solid volume fraction, 1/(1 + e)0.6061
- Bulk density at full saturation, (ρs + 1000 e)/(1 + e)1,994 kg/m³
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 void ratio is 0.65, a porosity of 39.4 %, so the soil is 60.6 % solid by volume.
- The sweep shows the strong dependence on dry density: the void ratio rises steeply as the soil gets looser, which is where wheels sink and lose grip.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| ρd Dry bulk density | 600 to 2,640 kg/m³ | 0 | 3.4 | 3.4 | +10% | −23.1 % |
| ρs Particle density of the solids | 2,640 to 3,200 kg/m³ | 0.65 | 1 | 0.35 | +10% | +25.4 % |
Sweep of Dry bulk density
| Dry bulk density (kg/m³) | Void ratio |
|---|---|
| 600 | 3.4 |
| 855 | 2.088 |
| 1,110 | 1.378 |
| 1,365 | 0.9341 |
| 1,620 | 0.6296 |
| 1,875 | 0.408 |
| 2,130 | 0.2394 |
| 2,385 | 0.1069 |
| 2,640 | 0 |
Sweep one variable
Variables and how each one contributes
Void ratio
What the equation gives you. Everything else feeds it.
Particle density of the solids
The particle density of the soil solids, in kg/m³. A higher particle density at the same dry density means more solid mass per unit solid volume, so more void ratio. Raising it by 10 % (to 2,904) moves the result by +25.4 %, from 0.65 to 0.815.
Dry bulk density
The dry bulk density, in kg/m³. A denser soil has less void space, so the void ratio falls steeply. Raising it by 10 % (to 1,760) moves the result by −23.1 %, from 0.65 to 0.5.
Worked example with the values above
- Ratio: ρs/ρd = 2,640 / 1,600 = 1.65.
- Subtract 1 for the pore volume per unit solid volume.
- e = 1.65 − 1 = 0.65.
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