SOIL AND GROUNDWATER - Introduction to Soft Soil Geotechnique: Content, Context and Application - page 49

4 SOIL AND GROUNDWATER

A VERTICAL SOIL STRESS

Terzaghi's effective stress principle
Intergranular soil forces at micro scale are averaged over the soil bulk surface
and referred to as intergranular normal stress

" .
Saint-Venant's principle permits to state that an individual grain completely
surrounded by a uniform water pressure u carries everywhere inside the same
pressure u . Hence, on any cross section through a granular fabric (arrangement of
grains) the pore pressure u is present in the pores and in the grains, i.e. uniform
over a bulk surface. This allows to add the intergranular stress

" and intergranular shear stress

" and the pore

pressure u into a total normal stress " + u . Since the pore water does not

convey shear stress, the total shear stress becomes

=

" .
If the pore water partly surrounds the grains, i.e. if the intergranular contact
areas are large (deep sand formations) or in unsaturated soil, the normal pressure
inside the grains generated by the pore fluid will be less than u .
Soil deformations are related to rearrangements and compression of the granular
fabric. It is convenient to have a stress that directly relates to deformations.
Terzaghi (after Fillunger) defined such stress, the effective stress

=

' . When the
grains are relatively incompressible 13 the deformations will not involve changes at
the granular contacts (indenting) and then

" . However, when grains
compression is involved, as a consequence the pore water becomes involved, and

' =

' " . In any bulk cross section in the soil the total normal stress becomes

= ' u with 0 < < 1 (4.1a)

For deep soil layers, is related to the Biot coefficient, and for unsaturated flow

is related to the pF value. In saturated soils with relatively incompressible grains
and relatively small intergranular contact areas

= 1, and Terzaghi's effective

stress principle holds

= ' u (4.1b)

Formula (4.1b) allows to separate granular deformation and pore water flow in a
simple way, in terms of partial stresses, i.e. the effective stress ' and pore pressure

u , in more dimensions. Pore pressures are affected by and may induce groundwater
flow. Effective stress changes induce soil deformation (rearrangements of the
granular fabric), which changes the porosity and affects the pore pressure. This
interconnected system is the core of soil mechanics, i.e. equilibrium and
deformation behaviour.

13 Order of magnitudes of compressibility factors in m 2 /N: water 0.5x10 9 , sand grain
(silicate) ~10 11 , granite ~10 13 , water with small air bubbles ~10 6 , granular fabric (sand,
clay) ~10 6 .