Surcharge and capillary effect on stress

Effective stress is $\sigma' = \sigma - u$ (Terzaghi). Surcharge changes the total stress, while capillary action changes the pore water pressure.

Effect of surcharge

A surcharge $q$ (extra load on the ground surface, e.g. a stockpile or embankment) adds to the total stress at every depth by the same amount:

$$\sigma = q + \gamma z$$

If water is able to drain (long term, or in sand), the pore pressure $u$ is unchanged, so the effective stress increases by $q$:

$$\sigma' = q + \gamma z - u$$

In a saturated clay, immediately after loading the pore pressure takes up the extra stress ($\Delta u = q$), so $\sigma'$ does not change at first. It rises later as the water drains (consolidation).

Effect of capillary action

In the capillary zone above the water table, water is held in tension. The pore pressure is negative:

$$u = -\gamma_w z_c$$

where $z_c$ is the height above the water table. Hence

$$\sigma' = \sigma - (-\gamma_w z_c) = \sigma + \gamma_w z_c$$

so the effective stress increases. The increase is maximum at the top of the capillary rise ($\gamma_w h_c$) and is zero at the water table. This extra stress (apparent cohesion in sand) gives the soil added strength; it disappears if the soil dries or is flooded.