CIVL2410 Chap.1 Soil as a three phase material
Soil as a three phase material
Soil is a particulate assembly rather than a solid: mineral grains in contact, with the space between them holding water, air or both. This chapter turns that picture into numbers.
It sets up the phase block, defines the three ways of describing how loosely the grains are packed, adds the two ways of describing how much water sits in the voids, and combines them into the four unit weights that every stress calculation in Module 3 begins from. Short assessment items on this material are the most reliable early marks in the unit.
What this chapter covers
- 01
The phase block: reading volume, mass and weight off one diagram
- 02
Void ratio, porosity and solid fraction, and why only one of them is unbounded
- 03
Converting between the packing ratios without inverting a denominator
- 04
Relative density, and where the loosest and densest states come from
- 05
Degree of saturation as a volume ratio against moisture content as a mass ratio
- 06
The bridge relation eS = mc Gs, and what it does for a saturated soil
- 07
Weight, density and unit weight, and the unit weight of water at 9.81 kN per cubic metre
- 08
Specific gravity of solids, usually near 2.65
- 09
Bulk, dry, saturated and submerged unit weight as one relation with three settings
- 10
Which unit weight a stress calculation actually wants, above and below the water table
Laboratory masses in, unit weights out
- +1Saturated means the degree of saturation is 1, so the bridge relation gives the void ratio directly: e = mc Gs = 0.38 x 2.70 = 1.026.
- +1Dry unit weight counts only the grains: 2.70 x 9.81 / (1 + 1.026) = 13.07 kN/m3.
- +1Saturated unit weight adds the water filling the voids: (2.70 + 1.026) x 9.81 / 2.026 = 18.04 kN/m3.
- +1Submerged unit weight subtracts buoyancy: 18.04 - 9.81 = 8.23 kN/m3.
- +1Check by an independent route: saturated should equal dry times (1 + mc), that is 1.38 x 13.07 = 18.04 kN/m3, which agrees.
Key terms
- Void ratio
- Volume of voids divided by volume of solids. The solid volume does not change under load, so a change in void ratio is a clean measure of compression, and unlike porosity it has no ceiling.
- Porosity
- Volume of voids divided by total volume, so it is a proper fraction between 0 and 1. It converts to void ratio through e = n divided by one minus n.
- Specific gravity of solids
- The density of the mineral grains divided by the density of water. For most soils it is close to 2.65, and it is what links a measured mass to a volume of solids.
- Submerged unit weight
- Saturated unit weight minus the unit weight of water. It already has buoyancy taken out, so it produces effective stress directly and must never be used to compute a total stress.
Soil as a three phase material FAQ
Why is void ratio used instead of porosity?
Because the quantity it divides by does not move. Both describe how loosely a soil is packed, but porosity divides by the total volume, which shrinks as the soil compresses, so its denominator changes at the same time as its numerator. Void ratio divides by the volume of solids, and that is fixed for a given specimen however hard it is loaded.
A change in void ratio therefore measures compression cleanly, which is why the compression curve, the settlement relation and the critical state are all written in terms of it.
Which unit weight do I use below the water table?
For a total stress, the saturated value, because total stress counts the weight of the water in the voids as well as the grains. For an effective stress you may either subtract the pore pressure afterwards or use the submerged value as a shortcut, but never both, since the submerged value already has the pore water taken out and applying it twice removes the water pressure twice.
Exam move
Learn the phase block as a picture rather than as four formulas, then practise reading ratios off it until the denominators are automatic. The single habit that pays here is writing the void volume on its own line before computing anything, because every answer in the topic is a fraction involving it.
For the laboratory direction, memorise one relation only, that void ratio times saturation equals moisture content times specific gravity, and derive the rest from it. Finish every calculation by bracketing the answer against the range a real soil occupies, and check any unit weight by a second route, since the two routes share no arithmetic and agreement is real evidence.
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