---
title: "Effective stress with up/down seepage"
subject: "Soil Mechanics"
chapter: 6
key: "semester_4/soil_mechanics:effective-stress-upward-downward-flow"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/effective-stress-upward-downward-flow
site: BCT Engineering
---

# Effective stress with up/down seepage

Soil Mechanics · Chapter 6: Principle of Effective Stress, Capillarity and Permeability

- Asked in: 2075 Baisakh, 2 marks
- Video: [Effective stress, Total stress and Pore water pressure in Soil Mechanics || Example solved](https://www.youtube.com/watch?v=5r3McEtuyXU) — Civil Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/effective-stress-upward-downward-flow
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-6

## Question

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

## 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.

## Answer

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

#### Downward flow

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

$$
\sigma' = \gamma'H + \gamma_w h = \gamma' H + i\gamma_w H
$$

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: $u = \gamma_w (h_w + H + h)$.

$$
\sigma' = \gamma' H - \gamma_w h = \gamma' H - i\gamma_w H
$$

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

| Flow | $\sigma'$ at depth $H$ |
|---|---|
| No flow | $\gamma' H$ |
| Downward | $\gamma' H + i\gamma_w H$ (increase) |
| Upward | $\gamma' H - i\gamma_w H$ (decrease) |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. With no flow, the effective stress at the bottom of a submerged layer of thickness H is:
   A. gamma_sat H
   B. gamma' H
   C. gamma_w H
   D. gamma' H + gamma_w H
   Answer: B. Submerged unit weight acts: sigma' = gamma' H. (Key point: No-flow reference)

2. For downward flow with head loss h, the effective stress at depth H is:
   A. gamma' H - i gamma_w H
   B. gamma' H
   C. gamma' H + i gamma_w H
   D. gamma_sat H - gamma_w h
   Answer: C. Pore pressure falls below hydrostatic, so sigma' increases by gamma_w h = i gamma_w H. (Key point: Downward flow)

3. For upward flow, the effective stress:
   A. Increases by i gamma_w H
   B. Decreases by i gamma_w H and becomes zero at i = gamma'/gamma_w
   C. Is unchanged
   D. Becomes zero at i = 0
   Answer: B. sigma' = gamma' H - i gamma_w H, zero at the critical gradient (quick condition). (Key point: Upward flow)

## Related in Soil Mechanics

- [Upward seepage stress variation diagram](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aupward-seepage-stress-diagram) — Soil Mechanics, chapter 7
- [Capillarity; water table effect on stress](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Acapillarity-water-table-effective-stress) — Soil Mechanics, chapter 6
- [Seepage in anisotropic soil](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aseepage-anisotropic-soil-derivation) — Soil Mechanics, chapter 7
- [Sea level fluctuation, effective stress](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Asea-water-level-effective-stress) — Soil Mechanics, chapter 6
- [Clay over sand, effective stress at depths](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aclay-sand-profile-effective-stress-depths) — Soil Mechanics, chapter 6
- [Role of effective stress in shear strength](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Arole-effective-stress-shear-strength) — Soil Mechanics, chapter 6

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