Soil as a Three-Phase Material

Steel is one material with one set of properties. Soil is three phases at once: solids (the mineral skeleton), water, and air. The grains themselves are strong and essentially incompressible, so almost nothing interesting happens inside them.

Compress a soil sample and the grains do not squash — the voids get smaller. Every characteristic behaviour of soil follows from that, which is why the index properties are all ratios describing the void space.

The sample is imagined separated into three layers, with volumes down one side and weights down the other. Air is taken as weightless. It is a bookkeeping device rather than a picture, and every index property is a ratio read off it.

Void ratio divides by V_s rather than by the total precisely because V_s does not change when the soil compresses. A change in e therefore describes the compression directly, with nothing else moving — which is why the consolidation curve is plotted as e against log p.

Submerged unit weight is roughly half the saturated value, because buoyancy removes the weight of the displaced water. A layer below the water table therefore contributes about half the effective stress it would above one, and using the wrong unit weight is a common and consequential error.

Load a saturated soil suddenly. Water is nearly incompressible and cannot escape instantly, so it takes almost all of the new load as excess pore water pressure.

Terzaghi's principle: σ = σ′ + u. Total stress divides between the effective stress carried by grain-to-grain contact and the pore water pressure carried by the water.

Only σ′ produces strength or settlement, because water has no shear strength at all. Any part of the load the water is carrying is doing nothing whatsoever to hold the soil together.

• Raise the water table and u rises while σ is unchanged, so σ′ falls and the soil weakens — with no new load applied at all.
• This is the mechanism behind most rainfall-triggered landslides.
• It is also quicksand: upward seepage can raise u until σ′ reaches zero, and a soil with no effective stress has no strength.

1. 1t = 0. Excess pore pressure is high, σ′ is low. No settlement yet, and the soil is at its weakest.
2. 2Water drains. u falls, σ′ rises, and the soil both settles and gains strength.
3. 3Long term. u returns to hydrostatic, σ′ carries the whole load, and primary settlement is complete.
4. 4Secondary compression continues slowly afterwards, as the soil skeleton creeps.

The rate is governed by permeability, and clay's permeability is smaller than sand's by a factor of around a million. Sand consolidates in minutes; clay takes decades, which is why a building can still be settling twenty years after it was finished.

So a design has two cases to check. The undrained short-term case, immediately after loading, is often the critical one for stability; the drained long-term case is critical for settlement. Which governs depends on the soil and on how fast the load is applied.

They are routinely confused, and they are genuinely different processes on the same phase diagram. Compaction has an optimum moisture content: too dry and the grains cannot slide past each other, too wet and water occupies the space you were trying to expel.

• Classification — grain size and Atterberg limits predict behaviour from the solids and their interaction with water.
• Compaction — expel air, raise dry density, at the right moisture content.
• Permeability and seepage — how fast water moves through the voids, and the pressure it exerts on the way.
• Consolidation — voids shrinking as water is squeezed out over time.
• Shear strength — τ = c′ + σ′·tan φ′, using effective stress, which is this topic restated.