Upward seepage stress variation diagram

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

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

 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.