Comment on capillary water to effective stress
All soils are permeable materials, water being free to flow through the interconnected pores between
the solid particles. It will be shown in Chapters 3–5 that the pressure of the pore water is one of the
key parameters governing the strength and stiffness of soils. It is therefore vital that the pressure of
the pore water is known both under static conditions and when pore water flow is occurring (this is
known as seepage). The pressure of the pore water is measured relative to atmospheric pressure, and
the level at which the pressure is atmospheric (i.e. zero) is defined as the water table (WT) or the
phreatic surface. Below the water table the soil is assumed to be fully saturated, although it is likely
that, due to the presence of small volumes of entrapped air, the degree of saturation will be marginally
below 100%. The level of the water table changes according to climatic conditions, but the level can
change also as a consequence of constructional operations. A perched water table can occur locally in
an aquitard (in which water is contained by soil of low permeability, above the normal water table
level) or an aquiclude (where the surrounding material is impermeable). An example of a perched
water table is shown schematically in Figure 2.1. Artesian conditions can exist if an inclined soil layer
of high permeability is confined locally by an overlying layer of low permeability; the pressure in the
artesian
layer is governed not by the local water table level but by a higher water table level at a distant location
where the layer is unconfined. Below the water table the pore water may be static, the hydrostatic
pressure depending on the depth below the water table, or may be seeping through the soil under an
hydraulic gradient: this chapter is concerned with the second case. Bernoulli’s theorem applies to the
pore water, but seepage velocities in soils are normally so small that velocity head can be neglected.
Thus (2.1) where h is the total head, u the pore water pressure, γw the unit weight of water
(9.81kN/m3 ) and z the elevation head above a chosen datum. Above the water table, soil can remain
saturated, with the pore water being held at negative pressure by capillary tension; the smaller the
size of the pores, the higher the water can rise above the water table. The maximum negative pressure
which can be sustained by a soil can be estimated using (2.2) where Ts is the surface tension of the
pore fluid (=7×10–5 kN/m for water at 10°C), e is the voids ratio and D is the pore size. As most soils
are graded, D is often taken as that at which 10% of material passes on a particle size distribution chart
(i.e. D10). The height of the suction zone above the water table may then be estimated by zs=uc/γw.
The capillary rise tends to be irregular due to the random pore sizes occurring in a soil. The soil can be
almost completely saturated in the lower part of the capillary zone, but in general the degree of
saturation decreases with height. When water percolates through the soil from the surface towards
the water table, some of this water can be held by surface tension around the points of contact
between particles. The negative pressure of water held above the water table results in attractive
forces between the particles: this attraction is referred to as soil suction, and is a function of pore size
and water content
p.39
3.4 Response of effective stress to a change in total stress As an illustration of how effective stress
responds to a change in total stress, consider the case of a fully saturated soil subject to an increase
in total vertical stress Δσ and in which the lateral strain is zero, volume change being entirely due to
deformation of the soil in the vertical direction. This condition may be assumed in practice when there
is a change in total vertical stress over an area which is large compared with the thickness of the soil
layer in question. It is assumed initially that the pore water pressure is constant at a value governed
by a constant position of the water table. This initial value is called the static pore water pressure (us).
When the total vertical stress is increased, the solid particles immediately try to take up new positions
closer together. However, if water is incompressible and the soil is laterally confined, no such particle
rearrangement, and therefore no increase in the interparticle forces, is possible unless some of the
pore water can escape. Since it takes time for the pore water to escape by seepage, the pore water
pressure is increased above the static value immediately after the increase in total stress takes place.
The component of pore water In all cases the stresses would normally be rounded off to the nearest
whole number. The stresses are plotted against depth in Figure 3.2. From Section 2.1, the water table
is the level at which pore water pressure is atmospheric (i.e. u=0). Above the water table, water is held
under negative pressure and, even if the soil is saturated above the water table, does not contribute
to hydrostatic pressure below the water table. The only effect of the 1-m capillary rise, therefore, is
to increase the total unit weight of the sand between 2 and 3m depth from 17 to 20kN/m3 , an
increase of 3kN/m3 . Both total and effective vertical stresses below 3m depth are therefore increased
by the constant amount 3×1=3.0 kPa, pore water pressures being unchanged. Development of a
mechanical model for soil 84 pressure above the static value is known as the excess pore water
pressure (ue). This increase in pore water pressure will be equal to the increase in total vertical stress,
i.e. the increase in total vertical stress is carried initially entirely by the pore water (ue=Δσ). Note that
if the lateral strain were not zero, some degree of particle rearrangement would be possible, resulting
in an immediate increase in effective vertical stress, and the increase in pore water pressure would be
less than the increase in total vertical stress by Terzaghi’s Principle. The increase in pore water
pressure causes a hydraulic pressure gradient, resulting in transient flow of pore water (i.e. seepage,
see Chapter 2) towards a free-draining boundary of the soil layer. This flow or drainage will continue
until the pore water pressure again becomes equal to the value governed by the position of the water
table, i.e. until it returns to its static value. It is possible, however, that the position of the water table
will have changed during the time necessary for drainage to take place, so that the datum against
which excess pore water pressure is measured will have changed. In such cases, the excess pore water
pressure should be expressed with reference to the static value governed by the new water table
position. At any time during drainage, the overall pore water pressure (u) is equal to the sum of the
static and excess components, i.e. (3.4) The reduction of excess pore water pressure as drainage takes
place is described as dissipation, and when this has been completed (i.e. when ue=0 and u=us) the soil
is said to be in the drained condition. Prior to dissipation, with the excess pore water pressure at its
initial value, the soil is said to be in the undrained condition. It should be noted that the term ‘drained’
does not mean that all of the water has flowed out of the soil pores; it means that there is no stressinduced (excess) pressure in the pore water. The soil remains fully saturated throughout the process
of dissipation. As drainage of pore water takes place the solid particles become free to take up new
positions, with a resulting increase in the interparticle forces. In other words, as the excess pore water
pressure dissipates, the effective vertical stress increases, accompanied by a corresponding reduction
in volume. When dissipation of excess pore water pressure is complete, the increment of total vertical
stress will be carried entirely by the soil skeleton. The time taken for drainage to be completed
depends on the permeability of the soil. In soils of low permeability, drainage will be slow; in soils of
high permeability, drainage will be rapid. The whole process is referred to as consolidation. With
deformation taking place in one direction only (vertical as described here), consolidation is described
as one-dimensional. This process will be described in greater detail in Chapter 4. When a soil is subject
to a reduction in total normal stress the scope for volume increase is limited, because particle
rearrangement due to total stress increase is largely irreversible. As a result of increase in the
interparticle forces there will be small elastic strains (normally ignored) in the solid particles, especially
around the contact areas, and if clay mineral particles are present in the soil they may experience
bending. In addition, the adsorbed water surrounding clay mineral particles will experience
recoverable compression due to increases in interparticle forces, especially if there is face-to-face
orientation of the particles. When a decrease in total normal stress takes place in a soil there will thus
be a tendency for the soil skeleton to expand to a limited extent, especially so in soils containing an
appreciable proportion of clay mineral particles. As a result, the pore water pressure will initially be
reduced and the excess pore water pressure will be negative. The pore water pressure will gradually
increase to the static value, flow taking place into the soil, accompanied by a corresponding reduction
in effective normal stress and increase in volume. This process is known as swelling. Under seepage
(as opposed to static) conditions, the excess pore water pressure due to a change in total stress is the
value above or below the steady-state seepage pore water pressure (uss), which is determined, at the
point in question, from the appropriate flow net (see Chapter 2).