Soil Mechanics / Effective stress and stress in the ground

Seepage, the seepage force and the quick condition

When water flows upward, it lightens the soil — and can float it entirely.

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Why this matters

Flowing porewater exerts a seepage force on the soil skeleton. Upward flow can reduce effective stress to zero and cause boiling or hydraulic heave in cohesionless soil. Piping is a related but distinct internal-erosion process; the critical-gradient check alone does not assess its initiation or progression.

When water seeps upward through a soil, the effective stress is reduced below its no-flow value. Physically, the water dragging upward on the grains partly carries their weight. The reduction grows with the upward hydraulic gradient $i$ (head loss per unit length). At a critical gradient the effective stress reaches zero and a cohesionless soil loses all strength — the quick condition (boiling).

Critical hydraulic gradient

i_{cr} = \dfrac{\gamma'}{\gamma_w} = \dfrac{G_s - 1}{1 + e}

What it calculates: the upward gradient at which effective stress becomes zero

$i_{cr}$: critical hydraulic gradient (dimensionless)
$\gamma'$: submerged unit weight (kN/m³)
G_s: specific gravity of solids
e: void ratio

In plain terms: For most soils γ′ ≈ γw, so i_cr is close to 1. When the upward gradient approaches 1, a sandy soil is on the verge of boiling.

Predict first

A clean sand has Gs = 2.65 and void ratio e = 0.65. Roughly what upward hydraulic gradient will bring it to the quick (boiling) condition?

Summary

Flowing water exerts a seepage force on the grains; upward seepage reduces effective stress.
At the critical gradient i_cr = γ′/γw = (Gs−1)/(1+e), effective stress reaches zero and a cohesionless soil boils.
i_cr is close to 1 for most soils.
Upward seepage into an excavation base can cause boiling, heave and piping — a real failure mechanism.