Page 129 - Numerical Analysis and Modelling in Geomechanics
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110 C.W.W.NG AND Q.SHI
Figure 4.3 Water permeability vs pore water pressure.
coefficient of volume change, m . For transient seepage analysis, it can be
v
assumed that the total stress in the soil mass and the pore air pressure remain
constant. This means that (σ–u ) does not have any effect on the change in
a
volumetric water content. In addition, no hysteresis is assumed between drying
and wetting paths in the water retention curve (as shown in Figure 4.2). Then, a
change in volumetric water content can be related to a change in pore water
pressure by:
(4.7)
Substituting equation (4.7) into (4.5), leads to the following governing
differential equation for water flow in unsaturated soils:
(4.8)
where m w is equal to the slope of the water retention curve (see Figure 4.2),
which can readily be determined by experiments (Fredlund and Rahardjo [7]). If
the water permeability is homogenous and isotropic, i.e. k =k =k, and Q=0,
y
x
equation (4.8) can be reduced to the following equation:
