Effective/total stress in soil
Vertical normal stress σ_{z} is defined as:
where: | σ_{z} | - | vertical normal total stress |
γ_{ef} | - | submerged unit weight of soil | |
z | - | depth bellow the ground surface | |
γ_{w} | - | unit weight of water |
This expression in its generalized form describes so called concept of effective stress:
where: | σ | - | total stress (overall) |
σ_{ef} | - | effective stress (active) | |
u | - | neutral stress (pore water pressure) |
Total, effective and neutral stress in the soil
Effective stress concept is valid only for the normal stress _{ }σ, since the shear stress τ is
not transferred by the water so that it is effective. The total stress
is determined using the basic tools of theoretical mechanics, the
effective stress is then determined as a difference between the total
stress and neutral (pore) pressure (i.e. always by calculation, it can
never be measured). Pore pressures are determined using laboratory or
in-situ testing or by calculation. To decide whether to use the total or
effective stresses is no simple. The following table may provide some
general recommendations valid for majority of cases. We should realize
that the total stress depends on the way the soil is loaded by its self
weight and external effects. As for the pore pressure we assume that for
flowing pore water the pore equals to hydrodynamic pressure and to
hydrostatic pressure otherwise. For partial saturated soils with higher
degree of it is necessary to account for the fact that the pore pressure
evolves both in water and air bubbles.
Assume conditions | Drained layer | Undrained layer |
short – term | effective stress | total stress |
long – term | effective stress | effective stress |
In layered subsoil with different unit weight of soils in individual
horizontal layers the vertical total stress is determined as a sum of
weight of all layers above the investigated point and the pore pressure:
where: | σ_{z} | - | vertical normal total stress |
γ | - | unit weight of soil | |
- unit weight of soil in natural state for soils above the GWT and dry layers | |||
- unit weight of soil below water in other cases | |||
d | - | depth of the ground water table below the ground surface | |
z | - | depth bellow the ground surface | |
γ_{w} | - | unit weight of water |