Role of slope reliability analysis
in landslide risk management
R. Chowdhury Ć P. Flentje
Abstract Progress in the use of qualitative and préférence au « facteur de sécurité dans des pro-
quantitative methods of landslide risk assessment is cédures globales de gestion du risque de glissement
briefly reviewed. The use of a hazard-consequence de terrain.
matrix approach is highlighted and attention is then
restricted to aspects of hazard assessment in which Keywords Reliability index Ć Factor of safety Ć
formal reliability concepts can be used. Widely ac- Hazard Ć Risk management Ć Landslides Ć
cepted geotechnical and geological models must Probabilistic models
form the basis of credible hazard assessments under
different environmental conditions. However, con- Mots clés Indice de fiabilité Ć Facteur de
ventional deterministic methods of geotechnical sécurité Ć Aléa Ć Gestion des risques Ć Glissements
analysis need to be supplemented by studies within a de terrain Ć ModÅles probabilistes
probabilistic framework which takes into consider-
ation parameter variability and other uncertainties.
Suggestions are made for using the reliability
index in preference to the factor of safety
Introduction
in comprehensive procedures for landslide risk
management.
Risk management of sloping areas in relation to the po-
tential for and occurrence of landsliding requires the
Résumé Les progrÅs dans l utilisation de méthodes
consideration of a number of factors and scenarios. Con-
qualitatives et quantitatives pour l évaluation du
siderable knowledge and experience is required in order to
risque de glissement de terrain sont briÅvement
identify the potential for the occurrence of different types
présentés. L utilisation d une approche par matrice
of landslide events and the basic failure mechanisms as-
aléa-conséquences est soulignée, puis l attention est
sociated with each of them. Considerable skill is required
focalisée sur certains aspects relatifs Ä… l évaluation
to assess the scale, spatial distribution and temporal fre-
de l aléa pour lesquels des concepts de fiabilité
quency of different landslide types, their travel distances
peuvent Ä™tre utilisés. Les modÅles géologiques et
and consequences. An understanding of fundamental
géotechniques reconnus doivent former la base des
causes of slope instability is, of course, vital and, in that
méthodes d évaluation de l aléa pour toutes sortes de
regard, it is also necessary to differentiate between natural
contextes environnementaux. Cependant, les méth-
slopes, excavations and embankments. There are many
odes déterministes conventionnelles d études
situations involving urbanised hill slopes in which the
géotechniques doivent Ä™tre complétées par des
long-term effects of human interventions have been poorly
approches probabilistes prenant en compte la vari-
understood. The assessment and management of any fu-
abilité des paramÅtres de calcul. Des suggestions
ture risk of instability requires a thorough understanding
sont faites pour utiliser « l indice de fiabilité de
of (1) the role of natural processes over time and (2) the
short-term and long-term effects of deforestation, exca-
vation, embankment construction and other types of slope
modification or disturbance.
Many landslides are triggered as a consequence of natural
Received: 24 October 2001 / Accepted: 1 June 2002
Published online: 27 September 2002 events such as rainstorms and earthquakes. Careful at-
ª Springer-Verlag 2002
tention must be given to the role and potential of these
triggering agents in initiating new slope movements or
reactivating existing landslide masses. The size and de-
R. Chowdhury (&) Ć P. Flentje
structiveness of any landslide may be related to the in-
Civil Engineering Discipline, Faculty of Engineering,
tensity, duration and timing of the specific triggering
University of Wollongong,
agent. Even if catastrophic failure does not occur after
Wollongong, New South Wales 2522, Australia
e-mail: robin_chowdhury@uow.edu.au such an event, significant slope deformations may occur
DOI 10.1007/s10064-002-0166-1 Bull Eng Geol Env (2003) 62:41 46 41
R. Chowdhury Ć P. Flentje
which constitute or lead to unsatisfactory performance recognising the important role of geotechnical models as
or failure . There are also instances in which landslides well as their limitations. Before discussing the use of
have occurred with a significant delay after a triggering probabilistic approaches and reliability analysis, the paper
agent such as an earthquake. A more general consequence considers the use of hazard and risk assessment methods
of a triggering agent may be to induce or accelerate pro- for slopes and landslides. However, it is important to note
cesses of progressive failure within a slope. that while the use of a probabilistic framework can be a
Even with knowledge and experience, many factors need to significant improvement over the use of conventional
be considered and a number of steps taken to develop approaches (deterministic framework), the role may be
strategies for slope safety and landslide risk management. limited to handling only some of the main uncertainties.
These steps include a study of existing observational and
experimental data, analysis of past performance, carrying
out subsurface investigations, conducting laboratory or
Landslide risk assessment
field tests for the evaluation of geotechnical parameters
and performing slope analyses using appropriate geo-
approaches
technical models. Observation and monitoring is often
carried out to ascertain information on slope deformations
Evaluating slope stability at a specific site in conventional
and changes in pore water pressures. Such systems also
geotechnical terms is not sufficient for the evaluation of
assist in validating the results of analyses and in updating
hazard and risk of landsliding. In recent years, attention
them on the basis of new or more accurate information. It
has therefore been given to systematic approaches within a
is obvious that the cost of all the above steps may not be
risk assessment framework. Qualitative risk assessment
justified for many projects or for individual slopes within
may be carried out by experienced professionals on the
the project area. Indeed, many assessments are carried out
basis of available information and site inspections. Risk
on a qualitative basis and many management decisions are
may be characterised in several categories such as very
thus based on experience and judgement. However, as far
high , high , medium , low and very low . Semi-
as possible, geotechnical engineers try to support such
quantitative approaches may also be used. For example,
judgements and decisions with valid methods of analysis
each of a number of factors influencing stability may be
and assessment, which can be carried out within the cost
considered explicitly. These may include slope angle, slope
constraints of a particular project.
height, seepage/pore water pressure, previous history of
instability. A range of scores and settings for each factor
may be used to assess the extent to which that factor is
favourable or unfavourable to (1) the occurrence of
Uncertainties
instability and (2) the occurrence of loss or damage
consequential to failure.
In most cases of slope analysis, uncertainty is associated
A hazard-consequence matrix approach can be used. Risk
with (1) geotechnical parameters, (2) geotechnical models
is regarded as the product of hazard and consequence.
and (3) the frequency, intensity and duration of triggering
Therefore, a set of hazard categories is combined with a set
agents. The range and importance of different uncertain-
of categories of consequences. Hazard may thus be eval-
ties depend on the size and importance of the project as
uated separately from consequence based on one or more
well as on the scope and quality of the geotechnical in-
site inspections. From the matrix of the two sets of cate-
vestigation and testing. One major source of uncertainty
gories, several risk categories are then defined, again in
concerns the spatial variability of geotechnical parameters.
qualitative terms. The consequence assessment may be
Even a comprehensive geotechnical investigation cannot
made separately for (1) loss of life and (2) economic loss.
guarantee identifying all the uncertainties except at pro-
Accordingly, there will be two risk assessment matrices,
hibitive cost. Another source of uncertainty is the temporal
although there is a single matrix of hazard assessment.
variability of important parameters such as pore water
Quantitative risk assessment requires the identification
pressure within a slope at different locations or depths and
and quantitative evaluation of the factors contributing to
especially along a potential slip surface. To these uncer-
risk and has recently been discussed at length (AGS 2000;
tainties are added the effects of systemic uncertainties
Ho et al. 2000). Thus in order to calculate the annual
which are a consequence of the limited number of ground
probability of loss of life Pll one must evaluate the
investigation boreholes, a limited number of shear strength
following (Morgan et al. 1992):
and other geotechnical tests and the fact that no method of
measurement is perfect. Modelling uncertainties may re- P1=P(H) the annual probability of a hazard occurring;
late to minor geological details and to assumptions in- P2=P(S/H) the conditional probability of spatial impact
herent in concepts such as limit equilibrium. Neglecting considering travel distance, etc. (e.g. land-
the process of progressive failure in simulating slope per- slide impacting a building);
formance also introduces an important uncertainty. P3=P(T/S) the conditional probability of temporal im-
With the above background, one can appreciate the pact (probability of building being occupied
enormous difficulties in accurately predicting the perfor- by people at the time of impact);
mance of slopes. The best one can hope for is to make P4=V(L/T) the vulnerability of individual given landslide
systematic assessments of hazard, risk and reliability, impact (e.g. probability of loss of life).
42 Bull Eng Geol Env (2003) 62:41 46
Role of slope reliability analysis in landslide risk management
Accordingly, one may define probability of loss of life: engineers have developed a range of methods over several
decades. However, the profession has not yet adopted the
PllźP1 P2 P3 P4 ð1Þ
probabilistic approach widely or with much enthusiasm.
Moreover, the application of the methods and techniques
Similarly, the probability of damage or loss to property
to landslide risk assessment has lagged behind other ap-
may be defined as Ppl where
plications. Therefore, a recent paper reiterating the merits
PplźP1 P2 P5 ð2Þ
of a reliability approach is most welcome (Duncan 2000).
In that paper, it is argued that probabilistic approaches
in which P1 and P2 have the same definition as above and
can be justified in geotechnical engineering even where
P5=V(P/S) is the vulnerability of property to spatial impact
there is a lack of detailed data concerning geotechnical
(e.g. proportion of the value of property that is lost).
parameters, their variabilities and uncertainties. Guidance
The value of property loss or property risk may be
is provided for assessing the standard deviation or coef-
expressed as
ficient of variation of important geotechnical parameters.
Those involved with landslide hazard and risk assessment
PLźPV Ppl ð3Þ
should follow this excellent example concerning the use of
in which PV is the value of the element at risk or
formal analysis in conjunction with informed judgement.
property in its undamaged or original state.
From the above, it is obvious that the assessment of
hazard is a very important part of landslide risk as-
sessment. It represents the frequency of landslide occur-
Reliability index and probability
rence which includes the probability of failure of a slope
of failure
and this may be a first-time failure or a reactivation of an
existing or fossil landslide.
The assessment of reliability and probability of failure for
The accurate and reliable assessment of probability of
a slope should be considered as complementary to the
failure or landsliding and, more generally, the frequency
usual deterministic analyses. Thus it is acceptable to retain
of landsliding is not an easy task. In the paper cited
basic geotechnical models developed after consideration of
earlier (AGS 2000) there is an appendix entitled fre-
potential failure mechanisms and scenarios based on
quency analysis a review of the methods available to
triggering agents. Moreover, special probabilistic models
estimate the probability of landsliding . Without pro-
may also be considered for developing innovative ap-
viding details of procedures or comprehensive examples,
proaches which offer insights that are not available from
the following approaches are mentioned as possible
conventional geotechnical models. However, consideration
alternatives:
of these special models is outside the scope of this paper.
1. Consideration of historic record of landsliding.
Due to space limitations attention will not be focused here
2. Empirical approaches for ranking potential for insta- on the modelling of progressive failure or on the use of
bility of different slopes.
Bayesian and other approaches for updating reliability or
3. Relationship of landslide frequency to geomorphology
on the use of system reliability approaches.
and geology.
Assuming the factor of safety F of a slope to be a random
4. Relationship of rainfall (duration, intensity and fre- variable with an expected or mean value F and a standard
F
quency) to landsliding.
deviation rF, the reliability index may be defined simply
5. Direct assessment based on judgement.
as:
6. Modelling a dominant parameter such as the pore water
F
F 1
pressure.
bź ð4Þ
rF
7. Application of formal probabilistic methods.
The probability of failure pf is defined as:
Some of these approaches can prove unreliable and are not
repeatable. For example, historical data may be lacking or
pfźPF 1Š ð5Þ
½
incomplete or inaccurate. Empirical methods may work
for specific areas from which the original data were taken
It is important to note here that failure may or may not
but may be misleading for other areas. The use of sub- mean catastrophic failure . This has been emphasised by
jective judgement or expert opinion, although feasible, still
Duncan (2000) who provided an example of a retaining
requires, for its validation, an alternative approach within
wall which may suffer limited sliding without collapse
a formal probabilistic framework. Consideration of geo- under certain conditions. Thus, in general, pf may be re-
morphology and geology will provide a sound basis for
garded as the probability of unsatisfactory performance .
understanding the frequency of major processes but may
The situation with regard to slopes is far more complex
not be sufficient for evaluating frequency within an engi- than for a retaining wall. There may be different modes of
neering time-scale.
deformation and multiple failure modes within a single
It is therefore important to try to use formal reliability
slope. However, in some situations there may be no overall
approaches within a probabilistic framework. Indeed
failure. If the potential for overall failure exists there may
geotechnical researchers and progressive geotechnical
be alternative failure mechanisms, some of which are
Bull Eng Geol Env (2003) 62:41 46 43
R. Chowdhury Ć P. Flentje
unpredictable. Even if the failure mechanism is predictable 2000, a thorough review of quantitative risk assessment
and overall movement along a slip surface does occur, its was made by Ho et al. (2000) who included references to
extent may be so limited as not to constitute catastrophic formal probability assessment approaches. It is interesting
failure. that the static performance of slopes in an example of
From the above remarks, it is obvious that considerable earthquake-triggered landsliding was distinguished on the
emphasis has to be placed on correct interpretation of basis of a 10, 20 or 40% margin of safety. This implies
calculated failure probabilities, having due regard to the considering F values of 1.1, 1.2 and 1.4 without any
location and type of slope and the manner in which it mention of the standard deviation or the coefficient of
performs when the safety margin reduces to zero. There is variation of F. Assuming zero standard deviation would
also a need to develop a different definition for the imply infinite reliability under static conditions and that
probability of catastrophic failure as distinct from certainly was not the intention of the authors.
unsatisfactory performance in appropriate circum- Table 1 shows that, with a relatively small value for the
stances. standard deviation rF=0.1, the reliability indices vary by a
Assuming F to have a normal probability distribution, factor of as much as four and the nominal failure proba-
widely published tables of cumulative probabilities based bilities by five orders of magnitude. This is certainly not
on the standard normal variate may be used to calculate revealed from factors of safety varying from 1.1 to 1.4. A
probability of failure pf directly from reliability index b. more reasonable assumption of the variability of F may be
Calculations may also be made based on the assumption of to consider a coefficient of variation of 10%. Table 2 again
an alternative probability distribution for F. In particular, shows the huge variation in (1) reliability index and (2)
a lognormal reliability index may be defined (Duncan probability of failure.
2000) as These calculations are based on a normal probability
distribution for F. Calculations were also made assuming a
F
F
lognormal probability distribution. In that case the reli-
pffiffiffiffiffiffiffiffi
ln
1þv2
ability indices increased relative to those for normal
bLNźpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð6Þ
distribution assumptions and probabilities of failure
l1þv2Þ
decreased for the higher values of F. This example shows
F
in which v represents the coefficient of variation of F, i.e.
that the implication of assumed or adopted safety margin
values or factor of safety values may not be clear unless
rF
vź ð7Þ
one steps out of the deterministic framework and con-
F
F
siders the variability and the associated probability values.
The probability of failure based on a lognormal distribu-
To take this example further, if the average factors of
tion for F may then be determined using standard normal
safety were indeed 1.1, 1.2 and 1.4 for three different slopes
tables and the above lognormal reliability index.
and the intention was that the reliability of these slopes be
in the same proportion, one can calculate the implied
coefficients of variation. These would have to be 8.26, 13.88
and 20.41% respectively, i.e.
Application to slope stability
bź1:1;Fź1:1;vFź8:26%
F
and potential landslides
bź1:2;Fź1:2;vFź13:66%
F
As stated earlier, it is important for landslide risk assess-
ment to calculate the hazard first. The hazard is a
probability that includes both the occurrence of failure
Table 1
and the frequency of such occurrence. These two aspects
Reliability index and probability of failure values for slope (constant
are intimately interrelated and there are no guidelines of rF)
how formal probability calculations can be combined to
F
F rF b Pf
evaluate hazard on a formal basis. This aspect requires
careful attention. One approach is to consider the formal 1.1 0.1 1 15.86·10 2
1.2 0.1 2 2.27·10 2
probability value as an indication of susceptibility to
1.4 0.1 4 3.30·10-5
failure, conditional upon the assumed values of key pa-
rameters. This value is then multiplied by conditional
probabilities of these parameters which are chosen to re-
flect the frequency of the triggering event or agent. A
Table 2
relatively simple example of this approach for a landslide
Reliability index and probability of failure values for slope (constant
vF)
was given by Chowdhury and Flentje (1999).
Leaving aside, for the present, the issue of temporal
F
F vF b Pf
frequency, attention needs to be focused on the use of
1.1 0.1 0.91 18.14·10 2
reliability index and probability of failure values for the
1.2 0.1 1.67 4.74·10 2
assessment of slope safety, in preference to the conven-
1.4 0.1 2.86 2.12·10 5
tional safety factor. For example, as recently as November
44 Bull Eng Geol Env (2003) 62:41 46
Role of slope reliability analysis in landslide risk management
are considered in the following paragraphs and Table 3. A
bź1:4;Fź1:4;vFź20:41%
F
similar exercise has been done separately for embank-
It is clear how the use of a reliability approach within a
ments and excavations used along highways and railways.
probabilistic framework improves the assessment of slope
The relevant table and discussions are not included here.
performance.
Many natural slopes are only marginally stable and, in
wooded areas, relatively small failures and limited defor-
mations may occur frequently but often go unnoticed. It is
difficult to obtain accurate data on the frequency of such
Minimum or indicative values
historical failures in these areas. The potential failure
of reliability index for slopes modes and consequences must be considered in proposing
nominal values of reliability index and probability of
The concept of minimum factors of safety for different failure. For slopes that may fail frequently but with limited
geotechnical structures is widely accepted. Efforts have movement and no adverse consequences, a low minimum
been made to study and analyse the performance of (or nominal) reliability index and a high failure proba-
foundations, retaining walls, earth dams and slopes and, bility may be considered acceptable. This is reflected in the
on this basis, minimum values of F or a range of values first category considered in Table 3. Several other cases are
have been suggested for each type of facility. There are listed in the same table considering different slope types,
examples of consensus on some of these values. However, locations, failure modes and potential consequences. The
it is recognised that such suggestions can only be a guide proposed values of minimum reliability index vary from
and that much depends on individual testing, analysis and one to three with corresponding maximum probabilities of
design procedures and especially on the quality of data failure ranging from 15·10 2 to 1·10 3.
used in the analysis. This table of suggested values should not be confused with
There is now a need for nominal minimum values or in- target values of hazard or acceptable values of haz-
dicative values of reliability index for different geotech- ard . Hazard is often expressed as an annual probability of
nical structures. Attention is here restricted to slope occurrence of an event such as failure; frequency on a
reliability. Due to space limitations, only natural slopes temporal basis must therefore be included. This would
located in either forested non-urban areas or urban areas have to be considered on the basis of data concerning
Table 3
Reliability index and failure probability of natural slopes suggested values
Slope type and location Potential failure mode Potential consequences Minimum reliability Maximum failure
index probability
Wooded/forested slopes, Shallow sliding, limited No elements at risk, no 1 0.15 (15%) (15·10 2)
moderate to steep movement or just slope potential for debris
inclination, colluvium or deformation without flow formation
residual soil cover overall failure
Slopes of low to moderate Slow-moving slides, No potential for 1.5 0.05 (5%) (5·10 2)
inclination in which shallow to deep-seated, catastrophic failure
high pore water relatively flat slip without warning signs.
pressures can develop, surfaces Progressive action during
forested or cleared successive rainstorms
sloping areas may induce complete
failure over time; no
elements at risk
Relatively steep slopes Shallow sliding with Significant potential for 2 0.01 (1%) (1·10 2)
with high relief in rapid movement and debris flow formation
forested or cleared areas, potential for large during intense storms,
slopes near natural travel distances considerable travel
gullies, colluvium or distance; elements at low
residual soil cover to moderate risk of
damage
Slopes in which high Sliding with rapid Elements at moderate 2.5 0.005 (0.5%) (5·10 3)
pore pressure can movement, shallow to to high risk of damage
develop; near urbanised deep slip surfaces with or destruction from
areas relatively steep landsliding
inclination
Slopes in which high Sliding with rapid Elements at high to very 3 0.001 (0.1%) (1·10 3)
pore pressures can movement, shallow to high risk of destruction
develop; very close deep slip surfaces with from landsliding
to properties in relatively steep
urbanised areas inclination
Bull Eng Geol Env (2003) 62:41 46 45
R. Chowdhury Ć P. Flentje
historical or temporal frequencies of failure, if such data potential failure mechanisms and potential travel
are available. Alternatively, data concerning the frequency distances.
of defined events related to triggering agents may be
considered, e.g. the return period of a rainstorm of certain
intensity and duration can be related to slope perfor-
mance. Alternatively, frequency based on the concept of Conclusions
antecedent rainfall percentage exceedance time (ARPET)
may be considered (Chowdhury and Flentje 1998; Flentje In this paper the role of slope reliability analysis is dis-
and Chowdhury 1999). Acceptable or target annual cussed in the context of hazard and risk assessment
failure probabilities would also be influenced by commu- methods. In order to progress from qualitative to quanti-
nity expectations and standards in addition to technical tative approaches, the use of formal reliability analyses is
issues and the consequences of failure. appropriate. Thus it is necessary to determine not only the
The calculated reliability index and corresponding prob- average values of safety factors or safety margins but also
ability of failure may be considered in relation to the their variance. It is also necessary to provide minimum
optimum suggested values in Table 3 or a similar table values of reliability index for slopes under different con-
generated on the basis of experience in analysis as well as ditions, considering expected failure mechanisms and the
in field observation. The judgement of experts and con- potential consequences. Such values would provide guid-
sensus amongst practising engineers would also play an ance for landslide assessment and management. As an
important part. It is only after considerable experience in example, a table of suggested values of reliability index
the use of reliability analysis that sufficient confidence can relevant to natural slopes is provided in this paper. Con-
be used in such tabulated values. siderable experience and discussion with other experts
would be required in order to justify the individual values.
Moreover, a similar exercise is also necessary for man-
made slopes (excavations, embankments) considering
different locations, failure mechanisms, potential travel
Proposed future work
distances and consequences to human life, property, in-
frastructure and economic activity.
Use of database for typical calculations of reliability
Comprehensive research concerned with hazard and risk
assessment has been undertaken at the University of
Wollongong. As part of this research, GIS-based modelling
References
and simulation is being used to map the hazard and risk
of potential landslides. A comprehensive database of
AGS (2000) Landslide risk management concepts and guidelines.
existing landslides with frequencies of occurrence has
Aust Geomech 35:49 92
been developed. Data concerning slope inclinations,
Chowdhury RN, Flentje P (1998) Effective urban landslide hazard
geomorphological features and geology have also been
assessment. In: Proc 8th Int IAEG Congr, Vancouver, Canada,
organised.
Publ 2, pp 871 877
As an aspect of this research, it may be useful to carry out Chowdhury RN, Flentje P (1999) Consideration of probability
assessments relevant to hazard and risk for landslides. In: Proc
typical reliability assessments in different zones within the
ICASP8 Conf, Dec, Sydney, Australia, pp 247 253
study area or region. Variability of some parameters can
Duncan JM (2000) Factors of safety and reliability in geotechnical
be obtained on a statistical basis. For other parameters,
engineering. J Geotech Geoenviron Eng ASCE 126(4)307 316
selecting the most likely values and coefficients of varia-
Flentje P, Chowdhury R (1999) Quantitative landslide hazard
tion may require expert input in addition to the statistical
assessment in an urban area. In: Proc 8th Australia New Zea-
analysis of available data. The results could be used to
land Conf on Geomechanics, Hobart, Tasmania, Australia,
validate assumptions concerned with nominal probabili- Publ 1, pp 115 120
Ho K, Leroi E, Roberds B (2000) Quantitative risk assessment
ties such as those in Table 3 and it would be useful to
application, myths and future directions. Keynote Paper. In:
develop more such tables for further use in hazard and
Proc Geo-Eng Conf, Nov, Melbourne, Australia, Publ 1, pp 269
risk assessment.
312
As mentioned earlier, there is a need for defining cata-
Morgan GC, Rawling GE, Sobkowicz JC (1992) Evaluating total
strophic failure as distinct from failure (F<1) which
risk to communities from large debris flows. In: Proc 1st
may simply mean unsatisfactory performance in many
Canadian Symp on Geotechnique and Natural Hazards,
situations. This aspect requires careful attention to Vancouver, Canada, pp 225 236
46 Bull Eng Geol Env (2003) 62:41 46
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