Effective Stress
One equation, and most of the subject's failures. Quicksand, liquefaction and rain-triggered landslides are all the same event seen from different angles.
Skip to the animationOnly the grain skeleton can resist shear, so the stress that governs strength, stiffness and settlement is σ′ = σ − u — and quicksand, liquefaction, rain-triggered landslides and excavation heave are all the same event: pore pressure rose and effective stress fell.
Why the split matters
Soil is a skeleton of touching grains with water in the voids. The grains resist shear because they interlock and rub; the water cannot, because a fluid at rest carries only pressure. The total load is shared, and only the grains' share produces strength.
Terzaghi's principle, 1925: σ′ = σ − u. Strength, stiffness and settlement all depend on σ′ and none of them on σ, which is why two soils under identical total load can behave completely differently.
What happens when u rises
| Condition | Mechanism | Result |
|---|---|---|
| Heavy rainfall | Water table rises | σ′ falls; a slope stable for decades fails |
| Upward seepage | Seepage force lifts the grains | σ′ → 0; sand boils — quicksand |
| Earthquake shaking | Loose sand tries to densify, water cannot escape | σ′ collapses; liquefaction |
| Rapid loading of clay | Water takes the load | σ′ unchanged initially; settlement delayed for years |
In every case the total stress was unchanged. Nothing was added or removed — the water simply took a larger share, and the soil became weaker without its loading changing at all.
Quicksand and liquefaction
When upward seepage raises pore pressure until it equals the total stress, σ′ reaches zero, the grains no longer press together, and the mixture behaves as a heavy fluid. Quicksand is ordinary sand in that state, and the critical hydraulic gradient is roughly 1 — easily reached at the base of an excavation.
Liquefaction is the same end state reached by shaking rather than seepage. Buildings tilt into the ground and buried tanks float out of it, which are the same phenomenon seen from two sides.
Drained and undrained
Whether pore water has time to escape decides which strength applies. Sand drains almost instantly and is always drained. Clay is undrained during construction and drained decades later.
Which is why a cutting in clay can be stable when dug and fail years afterwards, as pore pressures come to equilibrium and effective stress on the slip surface changes.
Why drainage is the cheapest fix
Since every one of those failure modes is pore pressure rising, relieving u addresses all of them at once — and it needs no structure, no imported material and no strengthening of the soil itself. That is why drainage is consistently the most cost-effective ground engineering there is.
The numbers you will be asked for
- Terzaghi's principle
σ′ = σ − u
- Total vertical stress
σ = Σ γ·h
sum the layers above
- Pore pressure, hydrostatic
u = γ_w · h_w
- Critical hydraulic gradient
i_crit = (G_s − 1)/(1 + e) ≈ 1
- Submerged unit weight
γ′ = γ_sat − γ_w
Watch it work
Check yourself
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One question at a time. Pick an answer to see why it is right or wrong, then move on — there is no score to keep and nothing is saved.