--- title: "Upward seepage stress variation diagram" subject: "Soil Mechanics" chapter: 7 key: "semester_4/soil_mechanics:upward-seepage-stress-diagram" source: https://www.bctengineer.com/q/semester_4/soil_mechanics/upward-seepage-stress-diagram site: BCT Engineering --- # Upward seepage stress variation diagram Soil Mechanics · Chapter 7: Seepage through Soils - Asked in: 2075 Baisakh, 3 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/upward-seepage-stress-diagram - Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-7 ## Question In the figure, upward seepage is shown. The rate of water supply from the bottom is kept constant. The total loss of head during upward seepage between points B and A is h. Keeping in mind that the total stress at any point in the soil is solely determined by the weight of the soil and the water above it, draw the variation of total stress, pore water pressure and effective stress with depth. Take points A, B and C as reference. [Figure: soil column in a tank with inflow at the bottom and outflow at the top, heights H1 and H2 marked, piezometers showing head h between B and A.] ## Short answer Total stress σ increases linearly: slope γw in water, γsat in soil. Pore pressure u is hydrostatic above soil; in soil it increases with excess head h, slope γw(1+i). Effective stress σ' = σ−u is zero at top of soil, increases with slope (γ'−iγw), reaching γ'H1−γw h at base, zero at quick condition. ## Answer #### Assumed figure C = water surface, B = top of the soil, A = bottom of the soil. Depth of water above the soil $= H_2$ (C to B). Soil thickness $= H_1$ (B to A). Water flows upward through the soil with a total head loss $h$ between A and B. The saturated unit weight of soil is $\gamma_{sat}$ and $\gamma' = \gamma_{sat} - \gamma_w$. Measure depths downward from C. #### Stresses at the three points | Point | Total stress $\sigma$ | Pore pressure $u$ | Effective stress $\sigma'$ | |---|---|---|---| | C (water surface) | 0 | 0 | 0 | | B (top of soil) | $\gamma_w H_2$ | $\gamma_w H_2$ | 0 | | A (bottom of soil) | $\gamma_w H_2 + \gamma_{sat}H_1$ | $\gamma_w (H_1 + H_2 + h)$ | $\gamma' H_1 - \gamma_w h$ | Pore pressure at A is increased by $\gamma_w h$ above the hydrostatic value, since water enters at higher head. The excess head $h$ is lost uniformly through the soil (linear variation). #### Diagrams ```text depth σ u σ' C | 0 0 0 | ╲ ╲ B | γw·H2 γw·H2 0 | ╲ ╲ ╲ | ╲ ╲ ╲ (reduced A | γwH2+γsatH1 γw(H1+H2+h) γ'H1 − γw·h by seepage) ``` - Between C and B, $\sigma$ and $u$ increase together with slope $\gamma_w$ and $\sigma' = 0$. - Between B and A, $\sigma$ increases linearly with slope $\gamma_{sat}$; $u$ increases linearly with slope $\gamma_w(1 + h/H_1) = \gamma_w(1+i)$; so $\sigma'$ increases linearly with slope $\gamma' - i\gamma_w$. - When $i = h/H_1 = \gamma'/\gamma_w$, $\sigma'$ at A is zero: quick condition. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is effective stress at the top of the soil, B? A. gamma' H2 B. gamma_w H2 C. 0 D. gamma_sat H2 Answer: C. Total stress and pore pressure both equal gamma_w H2, so effective stress is zero. (Key point: Effective stress at B) 2. What is the pore pressure at A? A. gamma_w (H1 + H2) B. gamma_w (H1 + H2 + h) C. gamma_w h D. gamma_w (H1 + H2 - h) Answer: B. Upward flow adds the excess head h above hydrostatic. (Key point: Pore pressure at A) 3. Effective stress at A is: A. gamma' H1 B. gamma' H1 + gamma_w h C. gamma' H1 - gamma_w h D. gamma_sat H1 Answer: C. Upward seepage reduces effective stress by gamma_w h. (Key point: Effective stress at A) 4. When does quick condition occur? A. i = gamma'/gamma_w, effective stress at A is zero B. i = 0 C. h = H2 D. i = 2 Answer: A. At i = gamma'/gamma_w, gamma' H1 = gamma_w h. 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