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Effective stress with up/down seepage

Short answer

Downward flow increases effective stress at depth by i γ_w H, making soil denser and stronger. Upward flow reduces effective stress by i γ_w H, reaching zero at the critical hydraulic gradient (γ'/γ_w), causing quick condition and loss of strength.

Explain the variation of effective stress due to the flow of water through the soil mass in downward and upward directions.

For a soil layer of thickness HH with water depth hwh_w above it, if there is no flow, σ′=γ′H\sigma' = \gamma' H at the bottom. Flow changes the pore pressure and hence σ′\sigma'. Let hh be the head loss through the soil.

Downward flow

Water flows down, so the head at the bottom is less than hydrostatic: u=γw(hw+H−h)u = \gamma_w (h_w + H - h).

σ′=γ′H+γwh=γ′H+iγwH\sigma' = \gamma'H + \gamma_w h = \gamma' H + i\gamma_w H

The effective stress increases (seepage force acts down, in the direction of gravity). Soil becomes denser and stronger.

Upward flow

Water flows up, so the head at the bottom exceeds hydrostatic: u=γw(hw+H+h)u = \gamma_w (h_w + H + h).

σ′=γ′H−γwh=γ′H−iγwH\sigma' = \gamma' H - \gamma_w h = \gamma' H - i\gamma_w H

The effective stress decreases. It becomes zero when i=ic=γ′/γwi = i_c = \gamma'/\gamma_w (quick condition), and the soil loses its strength.

Flowσ′\sigma' at depth HH
No flowγ′H\gamma' H
Downwardγ′H+iγwH\gamma' H + i\gamma_w H (increase)
Upwardγ′H−iγwH\gamma' H - i\gamma_w H (decrease)

✓ Answer checked by Claude Opus 5.5 (high effort)

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