Two-layer sand, stress diagrams (3 m, 4 m)

Given

Top layer 0 to 3 m, $\gamma = 17$ kN/m³. Bottom layer 3 to 7 m, $\gamma_{sat} = 21$ kN/m³. WT at 4 m; capillary saturation 1 m above the WT (3 m to 4 m), which lies in the bottom layer, so $\gamma = 21$ kN/m³ is used there. $\gamma_w = 9.81$ kN/m³; $u = 0$ above the capillary zone.

Stresses at key levels

Diagrams

 depth  total σ     pore u                effective σ'
 0 m    0           0                     0
 3 m    51          0 -> -9.8 (suction)   51 -> 60.8
 4 m    72          0  (WT)               72.0
 7 m    135         29.4                  105.6
 (draw each as straight lines between these points
  on a stress-vs-depth plot, depth downward)

• $\sigma$ increases linearly, with a change in slope at 3 m (17 to 21 kN/m³).
• $u$ jumps to $-9.81$ kPa (suction) at 3 m, rises linearly to zero at the WT, and increases at 9.81 kPa/m below it.
• $\sigma' = \sigma - u$; it jumps by 9.81 kPa at 3 m (from 51 to 60.81 kPa), then rises by $(21 - 9.81)\times 1 = 11.19$ kPa across the capillary zone to 72 kPa at the WT. In the capillary zone it is higher than $\sigma$.

Answer: At 7 m, $\sigma = 135$, $u = 29.43$, $\sigma' = 105.57$ kPa.