ABSTRACT
In 1925, Terzaghi suggested the principles of effective stress for a saturated soil, according to which the total vertical stress σ at a point O (Figure 5.1) can be given as
σ σ= ′ + u (5.1)
where
σ γ γ= +h h1 2 sat (5.2)
σ′ is the effective stress
u h= =pore w ater pressure 2 wγ (5.3)
γw is the unit weight of water
Combining Equations 5.1 through 5.3 gives
σ σ γ γ γ γ γ′ = − = + − = + ′u h h h h h( )1 2 sat 2 w 1 2 (5.4)
where γ′ is the effective unit weight of soil = γ γsat w− . In general, if the normal total stresses at a point in a soil mass are σ1, σ2,
and σ3 (Figure 5.2), the effective stresses can be given as follows:
D irection1: ′ = −σ σ1 1 u
D irection 2: ′ = −σ σ2 2 u
D irection 3: ′ = −σ σ3 3 u
where ′σ1, ′σ2, and ′σ3 are the effective stresses
u is the pore water pressure, h ′γw
A knowledge of the increase of pore water pressure in soils due to various loading conditions without drainage is important in both theoretical and applied soil mechanics. If a load is applied very slowly on a soil such that sufficient time is allowed for pore water to drain out, there will be practically no increase of pore water pressure. However, when a soil is subjected to rapid loading and if the coefficient of permeability is small (e.g., as in the case of clay), there will be insufficient time for drainage of pore water. This will lead to an increase of the excess
Figure 5.1 Definition of effective stress.
