Effective/total stress in soil

Vertical normal stress σz is defined as:

where:

σz

-

vertical normal total stress

γef

-

submerged unit weight of soil

z

-

depth bellow the ground surface

γw

-

unit weight of water

This expression in its generalized form describes so called concept of effective stress:

where:

σ

-

total stress (overall)

σef

-

effective stress (active)

u

-

neutral stress (pore water pressure)

Total, effective and neutral stress in the soilTotal, 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:

σz

-

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

γw

-

unit weight of water





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