Predicting rainfall-induced slope
instability
Civ. Engrs
Geotech. Engng,
1998, 211—214
A. B. Fourie
Proc. Instn
M. G. Anderson, J. Hartshorne, D. M.
Uoyd and A. Othman, Department of
Geography, University of Bristol and
Perunding ZNA, Consulting Engineers,
Kuala Lumpur
This paper addresses an issue of slope stability
analysis that has widespread relevance in tropical areas and is also the subject of major
theoretical analysis.32 It outlines a method for
estimating the time taken to saturate soil to a
specified depth based upon the standard Green
and Ampt infiltration model. This
determination is coupled to an infinite slope
stability model in order to assess the
significance of soil-suction reduction
contributing to slope instability. A
further assumption relates to the exclusion of
runoff from the analysis.
39. The wetting band concept was first
introduced by Lumb 33 in 1975 in relation to an
investigation of slope failures in Hong Kong.
Whilst this broad concept marked an advance
in that it provides the initial methodology for a
consideration of suction, there remains a conundrum. Soil water conditions in the unsaturated phase can be the subject of rapid change
in response to precipitation events. To fully
capture the dynamic negative pore water pressure changes that then contribute to potential
instability requires a methodology that models
the dynamics of soil water. In 1982 the
Proc. lnstn
Civ. Engrs.
Geotech. Engng,
1996, 119, Oct.,
211—218
Paper 10768
211
Geotechnical Control Office, Hong Kong
undertook such an investigation and
Anderson34 developed a finite difference soil
water model for this specific purpose which
was coupled to an infinite slope stability
model.35
40. The soil water finite difference model
uses the Millington—Quirk (M—Q) method
for unsaturated hydraulic conductivity
estimation.36 The M—Q method can be
parameterized by field-derived suction-
moisture curves or from pre-existing extensive
databases such as that developed by the
USDA.37
41.The concept of coupling a hillslope
finite difference model for soil water, capable
of modelling the full dynamics of the pore
pressure environment (negative, positive,
perched water tables, runoff and evaporation)
was thereby established and the full model
reported by Anderson and Lloyd in 199138.
Fig. 9. CHASM for
Windows: (a) view crosssection; and (b)
vegetation pre-processor
dialogue box
212
This combined hydrology and slope stability
model (CHASMTM) relaxes many of the
assumptions required in the method proposed
by Fourie. For example, the Fourie paper
reuses the classical wetting front approach and
so requires assumptions to be made concerning
the maintained suction levels immediately
above the wetting front (see para 9). CHASMtype models, in utilizing full finite difference
formulations, require no such assumptions.
CHASM allows for circular sup search by
selected stability analysis methods every
second of the dynamic simulation of pore
pressure conditions in response to precipitation
events. Fig. 8 from Collinson et al.39 shows the
model structure and Fig. 9 the configuration
for an element of the Windows version of
CHASM. Vegetation effects can be
incorporated because the hydrological equations incorporate runoff, evaporation and vegetation thatch effects. An illustrative discretization of the model was presented by Anderson
and Lloyd and is shown in Fig. 10. In that it
encompasses a full two-dimensional finite difference soil water model for hillslope
hydrology coupled to circular slip search
stability analysis, it is much more
representative of the processes relevant to
suction-induced slope stability than the method
proposed by Fourie. An example of model
output of CHASM is shown in Fig. 11. This
shows the dynamic predictions of factor of
safety in response to the finite difference
modelled hillslope hydrology. The irregular
response in the CHASM dynamic analysis is
due to shifts in the selected slip surface in
response to rapid temporal predicted changes
in pore water pressures.40
42. Fredlund41 has paralleled this style of
development with a finite element solution for
slope pore pressure determination in the
SLOPE/W and SEEP/W models available
through GEOSLOPE. Both CHASM and the
GEOSLOPE models offer full dynamic representation of the slope pore pressures and are
thus of much higher resolution both spatially
and in terms of process representation than
Green—Ampt type approaches with infinite
slope stability models.
43. Clearly CHASM and GEOSLOPE
models, in that the precipitation input is
modelled on a specified model (finite
difference and finite element time steps),
specifically include duration, intensity and
recurrence interval. Thus, these models allow
the critical link to be made using design
rainfall events for stability analysis. CHASM
has provided slope design charts based upon
numerical simulations of this type.42’43 Slope
construction and design can thus be related to
design life criteria. Thus whilst we agree with
the general style of the conclusions provided
by Fourie, our view is that there is already
significant published evidence to show that
higher resolution modelling of soil water
conditions (than Green—Ampt/infinite slope
models as discussed by Fourie can deliver
engineering solutions and insights to the very
important questions relating to the
relationships between negative pore pressures
and slope stability.
116
Author’s reply
Anderson et al. draw attention to the possibility
of using a proprietary computer code
(CHASM), developed by the authors, to more
realistically simulate the problem of rainfallinduced instability.
45. We have used the computer codes
SEEP/W and SLOPE/W to carry out a study of
the stability of a dry ash dump in South Africa
and compared these results with predictions
obtained with the simplified Green—Ampt approach.44 In the course of this work we took
care to characterize accurately the relations
between suction and moisture content and
hydraulic conductivity and moisture content
for the ash using appropriate laboratory tests
rather than a database. We also carried out
suction-controlled triaxial tests on the ash in
order to quantify the contribution of matric
suction to the shear strength of the ash.
Fredlund and Rahardjo32 suggest that for
unsaturated soils the shear strength -r varies
with suction according to
where c’ = the cohesion intercept, ’ is the
angle of internal friction, ua and uw are the
pore air and pore water pressures respectively
and b is the angle indicating the rate of
increase in shear strength relative to the matric
suction (ua - uw). Our tests on the fly ash
demonstrated that for values of suction equal
to those measured in the ash dump, the value
of b = 0.2 ’ that is the full matric suction was
not contributing to the unsaturated shear
strength of the ash.
46. A number of storms of different recurrent intervals were simulated and the change in
the factor of safety with time (both during and
after a rainfall event) was calculated. The
approximate approach was consistently more
conservative than the finite element method,
which is to be expected given the relatively
greater sophistication of the latter.
Nevertheless, it may be concluded that the
approximate Green-Ampt approach provides
an extremely useful screening tool and can be
used to carry out preliminary risk analyses
without requiring a large amount of specialized
geotechnical testing data. It also highlights
very clearly the importance of antecedent soil
moisture conditions, thus allowing changes in
landslide susceptibility to be readily estimated,
without the need for recourse to a proprietary
computer package.
47. Finally, it is our experience that no
single computer package will provide for all
the variables that may need to be studied, for
example in our study of the stability of the ash
dump, we found that analyses of shallow,
planar failure surfaces as incorporated in the
SLOPE/W package usually predicted a lower
factor of safety than did circular failure
surfaces. A package that is restricted to only
circular failure surfaces or cannot account for
the non-linear changes in soil shear strength
that occur due to changes in matric suction,
would clearly be of limited use.
References
32. FREDLUND D. G. and RAHARDJO H. Soil
mechanics for unsaturated soils. Wiley, 1993.
33. LUMB P. Slope failures in Hong Kong. Q.
Journal Engineering Geology 1975, 8, 31—65.
34. ANDERSON M. G. Prediction 0/soil suction for
slopes in Hong Kong. Geotechnical Control Office,
Engineering Development Department, Hong Kong.
G.C.O publication, 1/84 1983.
35. ANDERSON M. G. and Howrs S. Development
and application of a combined soil water—slope
stability model. Q. Journal Engineering
Geology 1985, 18, 225—236.
36. MILLINGTON R. I. and QUIRK J. P.
Permeability of porous media. Nature, 1959,
183, 387—388.
37. UNITED STATES DEPARTMENT OF
AGRICULTURE. Moisture tension data from
selected soils on experimental watersheds.
Agricultural Research Service Report ARS-41144, 1968.
38. ANDERSON M. G. and LLOYD D. M. Using a
combined slope-hydrology-stability model to
develop cut slope design charts. Proc. Instn Civ.
Engrs. 1991, 91, 705—718.
39. COLLINSON A. J. C., ANDERSON M. G. and
LLOYD D. M. The impact of vegetation on
slope stability in a humid tropical
environment—a modelling approach.
Proceedings of the Institution of Civil Engineers
Water Maritime and Energy 1995. 112, 168—
175.
40. ANDERSON M. G., COLUNSON A. J. C.,
HARTSHORNE 3., LLOYD D. M. and PARK
A. Developments in slope hydrology—stability
modelling for tropical slopes. In Advances in
Hillslope Processes (Anderson M. G. and
Brooks S. M. (eds)). Wiley, 1996. 799—821.
41. F’REDLUND D. G. Slope 11 Users Manual.
GEOSCOPE Programming limited, Calgary,
1984.
42. ANDERSON M. G., KEMP M. 3. and LLOYD
D. M. Applications of soil water finite
difference models to slope stability problems.
Proceedings of the 5th International Landslide
Symposium, Lausanne, 1988, 525—530.
43. ANDERSON M. G., A feasibility study in
mathematical modelling of slope hydrology and
stability. Civil Engineering Services
Department, Hong Kong. Final report on CE
23/90 to GCO. 1990.
44. F0URIE A. B., Rowr D. and BLIGHT G. E.
Predicting the susceptibility of tailings dam
slopes to rainfall induced instability.
Proceedings of the 4th International Conference
on Tailings and Mine Waste ‘97, Fort Collins,
USA, January 1997, 147—156.
117