Page 127 - Numerical Analysis and Modelling in Geomechanics

108 C.W.W.NG AND Q.SHI
this parametric study. The rainfall events considered correspond to 1 in 10-year
return period storms. In addition to water permeability, rainfall intensity and
duration are treated as variables for the parametric studies. For the slope stability
analysis, results from the parametric study are used as input groundwater
conditions for limit equilibrium calculations. The factor of safety is obtained
using Bishop’s simplified method, with modified Mohr-Coulomb failure
criterion to allow for shear strength variation due to the presence of matrix
suction. The transient seepage analyses (assuming a non-deforming soil) and
slope stability calculations (assuming rigid perfectly plastic soil behaviour) were
treated in a completely uncoupled manner.
The objectives of this study are, firstly, to illustrate and clarify the nature of
the pore pressure distribution in a typical unsaturated slope; secondly, to
demonstrate the sensitivity of transient flow systems to various initial hydraulic
boundary conditions, rainfall intensities and duration, and in situ soil
permeabilities; and finally to show and report the sensitivity of the factor of
safety to these variables.

Theory of water flow in unsaturated soils

Water flow through unsaturated soils is governed by the same physical law–
Darcy’s law–as fluid flow through saturated soils. The major difference between
water flow in saturated and unsaturated soils is that the coefficient of
permeability (hydraulic conductivity), which is conventionally assumed to be a
constant in saturated soils, is a function of degree of saturation or matrix suction
in the unsaturated soils. The pore water pressure generally has a negative gauge
value in the unsaturated region, whereas the pore water pressure is positive in the
saturated zone. Despite the differences, the formulation of the partial differential
flow equation is similar in the two cases.
The governing differential equation (Lam et al. [12]) for water flow through a
two-dimensional unsaturated soil element is as follows:

(4.5)

where h is total hydraulic head, k and k are the hydraulic conductivity in the x-
y
x
direction and y-direction respectively, Q is the applied boundary flux, θ is the
W
volumetric water content. The equation illustrates that the sum of the rates of
change of flows in the x-direction and y-direction plus an external applied flux is
equal to the rate of change of the volumetric water content with respect to time.
The amount of water stored within the soil depends on the matrix suction and
the moisture retention characteristics of the soil structure (see Figure 4.2). The
slope of the curve represents the retention characteristics of a soil, i.e., it
represents the rate of water taken or released by the soil as a result of a change in