Geology Reference
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point, we have observed either (1) infilling of the
valley which is driven by continuing deposition
on the alluvial fan, or (2) continued valley down-
cutting and incision into the deposited alluvial
fan and remobilization of the fan sediments. In
the example in Fig. 18.1 the formation of the deep
valleys was important because it was planned to
encapsulate the waste with 2 m of environmen-
tally benign material. The design depth of mate-
rial was based on an estimated average erosion of
0.3 m found by previous studies with traditional
models (and also found by Willgoose & Riley
using SIBERIA). However, while the average
erosion of 0.3 m suggested that the encapsulation
layer of 2 m depth would not fail, the existence of
8 m valleys would clearly result in the failure of
the structure. This was the major novel finding
of Willgoose and Riley over previous work using
traditional models at the site.
The exact location of the valleys depends on
the initial roughness and drainage pattern on the
landform. Willgoose and Riley (1998a,b) found
that small changes in the exact position of flow
concentration on the initial landform changed
the exact location of the valleys. Thus small
changes in the initial landform elevations (e.g.
errors in construction, dozer tracks, mine waste
compaction, etc.) would significantly change the
location of the valleys 1000 years later. Morgan
(1994) (see also Willgoose & Gyasi-Agyei, 1995)
extended this work by doing Monte Carlo simu-
lations where he randomly varied the initial
topography with noise consistent with random
settlement of up to 1.0 m, and then statistically
analysed the resulting erosion simulations.
Morgan used a slightly different landform design
proposal from that in Willgoose and Riley because
of limitations in computer speed at the time of
the work (these days, multiple Monte Carlo sim-
ulations are easily done on a desktop computer).
Figure 18.3 shows a plot of the landform, the
average and maximum erosion depth, and a plot
of the probability of the erosion being more than
2 m (i.e. the depth of the encapsulation layer)
across all the erosion simulations. Firstly, the
maximum erosion at the transition from the flat
cap to the steep batter is about three times the
average, and this region of high erosion is concen-
trated at the slope transition as was previously
observed by Willgoose and Riley. Secondly, the
probability of failure of any point of the landform
(i.e. erosion greater than 2 m, typically caused by
a valley at that point) is uniformly distributed
around the edge of the landform. No one point at
the edge of the landform looked notably more at
risk than adjacent points. Thus while an individ-
ual erosion history for the structure might have
had a valley at a particular point, the possible
range of locations of the high-erosion valleys is
more or less uniformly distributed around the
edge of the landform. One hope was that the
Monte Carlo simulations would identify regions
where the risk of valley erosion was high and
areas where the risk was low. This would have
then allowed us to concentrate erosion protection
measures in the areas of high risk. Fig. 18.3 shows
that the right-hand and left-hand corners of the
landform have a higher risk of failure with a prob-
ability peaking near 0.8, while the top corner has
a batter where the risk of failure is almost zero.
This reduced risk is also mirrored by the distribu-
tion of the mean and maximum erosion depth.
Hancock (2005) performed a similar analysis
using a natural catchment DEM and calibrated
erosion parameters. The work of Morgan (1994),
Willgoose and Gyasi-Agyei (1995) and Hancock
(2005) provides a framework for erosion risk
assessment using LEMs.
Evans
et al
. (1995) and Evans and Loch (1996)
compared the erosion loss predictions for RUSLE
and the SIBERIA LEM when each was calibrated
to the same erosion plot data, and found that they
gave similar rates for areal average erosion. They
confirmed the compatibility of traditional and
LEM erosion loss predictions when the same data
were used for model calibration and when the
landform is not allowed to evolve during the sim-
ulations. Hancock
et al
. (2008b), at the Nabarlek
uranium mine, compared erosion predictions
using the SIBERIA LEM with those derived from
a previous study using the RUSLE (Hancock
et al
., 2006), and found good agreement in average
erosion rates when calibrated to similar materi-
als. This compatibility between traditional and
