Page 143 - Numerical Analysis and Modelling in Geomechanics

124 C.W.W.NG AND Q.SHI
boundary conditions, rainfall infiltration and duration, they also found that soils
with a permeability greater than a certain limiting value will not become
saturated.
In fact, two extreme cases can be considered, i.e. k tending to infinity and k
tending to zero. In the former extreme, there will be no infiltration of water into a
slope during rainfall, hence no increase in pore water pressure and no drop in the
factor of safety. At the latter case, water will infiltrate the slope but will
immediately drain away through the boundaries, so that again there is no
increase in pore water pressures and no drop in the factor of safety. However, at
intermediate permeability values, water will infiltrate the slope to a certain
degree and will not entirely drain away, hence giving rise to an increase of pore
water pressures and a reduction in the factor of safety. This implies that a critical
saturated water permeability exists which corresponds to the minimum factor of
safety.
To investigate the sensitivity of the factor of safety to saturated water
permeability in Hong Kong soils, a typical range of saturated soil permeabilities
have been adopted (see Table 4.1). The range of saturated soil permeabilities is
taken with reference to the measured limits in colluvium and CDG, ranging from
−7
−3
1.0× 10 to 1.0×10 m/sec (GCO [22]). Since only a limited but practical range
of saturated soil permeabilities have been selected, there is no guarantee that the
critical saturated water permeability will fall within the selected range.
Initially homogeneous isotropic flow is considered, i.e., the saturated water
permeability in the x-direction (k ) and in the y-direction (k ) are assumed to be
y
x
equal. Examining the governing groundwater flow equation (4.8), it can be
deduced that in a model of fixed geometry and rainfall intensity, the response to
infiltration is a function of the ratios k/m and Q/k.
w
Figures 4.11a and b show the pore water pressure distributions with depth,
−6
−4
corresponding to saturated soil permeabilities of 4.8×10 m/sec and 4.8×10 m/
sec respectively. The pore water pressure distribution with depth for a saturated
−5
water permeability of 4.8×10 m/sec is shown in Figure 4.6b. For a given slope
−6
and rainfall intensity (Q) of 267 mm/day (3.1×10 m/sec), there is no significant
–4
difference between the ground pore water response for k=4.8×10 m/sec and 4.
−5
8×10 m/sec (see Figures 4.11a and 4.6b), except that the degree of saturation
(indicated by the formation of a perched water table) above the main water table
at Section C-C is higher for soils with lower permeability. This is consistent with
the findings reported by Pradel and Raad [13]. The groundwater response is
dominated by the ratio (k/m ) when the rainfall intensity is small relative to the
w
saturated water permeability, i.e., negligible Q/k. The higher the ratio of k/m ,
w
the faster the water table rises and decays.
−6
For soils with very low permeability of 4.8×10 m/sec, the main groundwater
rises significantly at Sections B-B and C-C (see Figure 4.11b) and the degree of
saturation increases further at Section A-A, comparing Figure 4.6b and
−6
Figure 4.11b. As the magnitude of saturated water permeability (4.8×10 m/sec)
is comparable with the rainfall intensity (3.1×10 −6 m/sec), the ratio Q/k is one