10th Asian Regional Conference of IAEG (2015)

Probability of Failure based on Morphometric Characteristic of Slopein Padang Pariaman, West Sumatera, Indonesia
Luthfan Harisan JIHADI(1), Zufialdi ZAKARIA (1), Faisal HELMI(1), Fikri Noor AZY (1),Arif Rahmansyah DARANA(1), and Sumaryono SUMARYONO(2)(1) Faculty of Geology, University of Padjadjaran, Indonesia(2) PVMBG, Indonesia
E-mail:luthfan.2005@gmail.com
Abstract
Infrastructure is needed to provide human’s civilization. In the process of building an
infrastructure, risk planning is needed in order to prevent disaster. Therefore, probability
method is needed in order to retrieve the probability of slope failure, the studied natural
phenomenon, as the morphometric used in order to simplify the process. Slope failure, inthe context of natural slope, is very influenced by geological condition of the slope.
Morphometric is a method that used in order to provide interpretation based onmorphological condition of studied area. Probability method that commonly used inprobability of failure analysis is Monte Carlo. The data then is used to create randomvariables for Monte Carlo calculation. By using factor of stability (FS) ≥1 as a threshold ofsafe slope or FS≤1 as a threshold of failure, the results from all of the tests are divided into
two: the results that fulfill the requirement of safe slope and the results that fulfill therequirement of failure. Ratio between the results that fulfill the requirement of failure withtest frequency becomes the probability of failure. Regions are divided by slope inclination,
based on morphometric process. These regions have their own probability of failure (PF)range, which the lowest number is 0% and the highest number is 23.61%. According to thesimulations, the PF range is always increased in wet condition. Furthermore, the PF fromthe result should be appropriate with the design criterion and aspect of natural situation
based on literature for acceptable PF. If not, further analysis has to be done.
Keywords: Failure probability, morphometric analysis, Monte Carlo simulation
1.

Introduction

phenomenon, as the morphometric used in order tosimplify the process. While the orthodox failure
analysis usually has a very detailed study area scale,this probability method can be applied into a wide
area as long as the area said is in a same population.
If we can apply this probabilistic method to a widearea, lots of time and expenses will be saved. And by
all means, this study about probability of failure
based on morphometric is only a small step to further
risk assessment.

As human become more civilized, their demandof needs is actually increased. Infrastructure indeed,is one of the needs that can support human’scivilization. In the process of building an
infrastructure, risk planning is needed in order toprevent disaster. The disaster in the context is anatural phenomenon that causes loss of life orproperty damage. In this study, we treat thephenomenon of slope failure and by knowing
probability of failure, risk categories can be assessed.
We have to accept that there will always be an
uncertainty in the acquired data and even more ofuncertainty if the study area is very big. The
uncertainty of data cannot be solved by averaging
their number as we know that averaging bias iscannot be accepted in any scientific analysis, thesolution is probability method where the output is thechance of phenomenon to occur. Therefore,probability method is needed in order to retrieve theprobability of slope failure, the studied natural

2. General
2.1 Slope Failure
Slope failure, in the context of natural slope, isvery influenced by geological condition of the slope.
If it causes loss of life or property damage, it can becategorized as geological hazard. As the failure may
occur when the slope cannot hold the mass of its own,
the causes of failure can be categorized into two i.e.:internal factor and external factor. Internal factor is its

110th Asian Regional Conference of IAEG (2015)

In this study, where slope failure is thephenomenon, we use factor of stability (FS) as thethreshold. Assumed that slope failure is occurs when
the R (equation 1) of slope is lower than the D(equation 2). Therefore the threshold of failure is,FS ≤ 1(4)
While the threshold of safe slope is,
FS ≥1
(5)
Then by using the threshold, probability of failure(PF) is given by,
PF = (N-M)/N(6)Where (N-M) is the results of test that did not
fulfill the threshold of safe slope, instead they fulfill
threshold of failure. M, is the results that fulfill thethreshold of safe slope and N is the total frequency oftests. Therefore, the PF will be given as percentage.
The frequency of test (N), however, is assumed
to have correlation with standard deviation (d), error(α), and PF. The following shows the mathematicalformula of N given by Gibson (2011):

own technical characteristic of consisting material,
while external factor is every other thing that not
coming from the slope itself such as artificial load. In
this study, these factors are termed as parameters. As
the geological condition affect the failure, the type offailure is depends on it. Mathematically, a very
simplified formula of factor of stability (FS) given by
Wyllie et al. (1981) calculates ratio between driving
force (D) and resisting force (R):FS = R/D(1)Where, R and D could be affected by cohesion (c),internal friction angle (ϕ), weight of slope mass (W),water pore pressure (μ), length of sliding plane (L),and slope angle (α). Therefore, R and D can bewritten as:
R = c x L + (W.cosα-μ)D = W.sinαtanϕ (2)(3)

2.2 Morphometric Analysis
Morphometric is a method that used in order toprovide interpretation based on morphologicalcondition of studied area. As the geometry of slope is
one of the factors that affect the slope stability,
morphometric analysis is taken as an approach tosimplify the process. Taken as grid or contour, every
point has its own elevation. Based on the elevationand contour interval, slope inclination can be
determined by using a very simple tangentialequation.

N=(7)The equation can also be written as,
α=d(8)As refer to Gibson (2011), standard deviation
assumed based on a certain confidence level. Thefollowing table (Table 1) is the correlated standard
deviation and confidence level. By using error
number (α), PF range can be acquired as follow:
PF’= PF – (PF. α)(9)PF’= PF + (PF. α)(10)

2.3 Monte Carlo Simulation
Probability method that commonly used inprobability of failure analysis is Monte Carlo. Referto Gibson (2011); the method is very simple
compared to other elegant and complicated methodsof probabilistic, yet powerful enough to provide
proper analysis. The basic concept of Monte Carlo isto predict occurrence of a phenomenon whichassumed by a threshold. The calculation formula ofMonte Carlo depends on the threshold and theparameters that affect it, while the accuracy depends
on frequency of test. The parameters are used tocreate random variables for test, where each test has
random variable that differs with the other. Given
10000 of tests, the random variable that needed are
10000 sets.

Table 1 Standard deviation based on confidence
level, Gibson (2011)
Confidence Level (%)

Standard Deviation (d)

80

1.28

85

1.44

90
95

1.64
1.96

99

2.57

2.4 Acceptance Level of PF
Based on Read & Stacey (2010), a few
recommendations exist in the literature for acceptable
PF for design; one of them is Kirsten (1983) cited in2

10th Asian Regional Conference of IAEG (2015)

Table 2 PF design acceptance guidelines Kirsten (1983) in Read & Stacey (2010)
Design criteria
Aspects of natural situation
PF(%)

Minimum
surveillance
requiredFrequency of slope
failures

Frequency ofunstable
movements
Abundant evidenceof creeping valley
sides

Serviceable life

Public liability

None

Public accessforbidden

Serves no purpose

Slope failures
generally evident

20-50

Very very
short-term

Public access
forcibly
prevented

Continuous
monitoring withintensive
sophisticatedinstruments

Significant numberof unstable slopes

Clear evidence of
creeping valley
sides

10-20

Very
short-term

Public accessactively
prevented

Continuous
monitoring withsophisticatedinstruments

Significant
instability evident

Some evidence ofslow creeping
valley sides

Short-term

Public accessprevented

Continuous
monitoring withsimple instruments

Odd unstable slope
evident

Some evidence ofvery slow creeping
valley sides

Medium-term

Public accessdiscouraged

Conscious
superficial
monitoring

No ready evidenceof unstable slopes

Extremely slow
creeping valleysides

0.5-1.5

Long-term

Public accessallowedIncidental
superficial
monitoring

No unstable slopes
evident

No unstable
movements
evidence<0.5

Very long-term

Public access free

No monitoring
required

Stable slopes

No movement

50-1005-10

1.5-5of failure. Ratio between the results that fulfill therequirement of failure with test frequency becomesthe probability of failure. The test will be done in twoconditions which are wet condition and dry condition,
each condition is assumed in an extreme condition.
Therefore, the final output is PF ranges for eachregion in wet and dry condition, and then this PF
ranges will be categorized based on theirrecommended acceptance level.

Read & Stacey (2010), as follows (Table 2):
3.

Methodology
First, we assume that soil in the study area isresidual soil of weathered former rock. Based on thatassumption, we can simplify soil’s technicalcharacteristic based on its lithological source.
Morphometric process is taken in order to provide
slopes geometric data, and then region are divided
based on its morphometric properties. Soil samples
are taken in some points in order to retrieve
geotechnical data, which are cohesion and friction
angle. The data then is used to create randomvariables for Monte Carlo calculation. By using FS≥1
as a threshold of safe slope or FS≤1 as a threshold of
failure, the results from all of the tests are divided
into two: the results that fulfill the requirement ofsafe slope and the results that fulfill the requirement

4

Result and Discussion
The study area consists of pumiceous tuff, mixed
layer, and paleosol. Commonly, grain sizes varyfrom silt to silt with low plasticity. The properties ofparameters and assumed slope geometry that will be
used to create random variables are taken, peakcohesion and peak friction angle are taken by using
direct shear test (Table 3).
The regions are divided based on its slope3

10th Asian Regional Conference of IAEG (2015)

inclination (Figure 1). Each Monte Carlo test is doneby using equation (1) to (3), where the mentioned
thresholds are (4) and (5) in 10000 number of test.
Assumed that the tests have 95% of confidence level,
the given standard deviation for results is 1.96. The
error can be retrieved by using equation (8). The
result (Table 4) can be retrieved by using equation (6),(9), and (10). Therefore, by using literature for PF by
Kirsten (1983) in Read & Stacey (2010), each region
can be assessed based on its design criterion andaspects of natural situation (Table 5).

References
Gibson W (2011) Probabilistic Methods for Slope
Analysis and Design, Australian Geomechanics
Vol 46, No 3 2011, pp. 1-4
Kirsten HAD (1983) Significance of the probabilityof failure in slope engineering. The Civil
Engineer in South Africa vol. 25, p. 17
Read J & Stacey P (2010) Guidelines for Open Pit
Slope Design, Collingwood: Csiro Publishing, pp.
223-226
Wyllie DC & Mah CW (1981) Rock SlopeEngineering: Civil and Mining 4th Edition, New
York: Taylor & Francis Group, p. 132

5Conclusion
Regions are divided by slope inclination, basedon morphometric process. These regions have theirown PF range, which the lowest number is 0% andthe highest number is 23.61%. According to thesimulations, the PF range is always increased in wetcondition. Furthermore, the PF from the result should
be appropriate with the design criterion and aspect ofnatural situation based on literature for acceptable PF.
If not, further analysis has to be done.

Table 3 Parameter used to create random variables
Parameter

MinMaxAverageStandard
deviation

Peak cohesion(kg/m)

4000

340000121833.3

110945.78

Peak friction angle
(o)

23.91

39.42

31.91

5.85

Density (kg/m3)

1172

17681395

261.69Mass area (m )

42.55

54.48

48.52

8.44

Length of sliding
plane (m)

86.80

88.34

87.57

1.09

Slope height (m)

57

76.50

66.75

12.79

2Table 4 Results of Monte Carlo testRegion

Inclination(%)

PF dry (%)

PF wet (%)

10-20%

1.16%-1.63%

2

2-150%

2.46%-3.11%

3415-7070-1001.6%-2.2%
10.39%-11.62%

11.78%-13.07%
21.96%-23.61%

4

10th Asian Regional Conference of IAEG (2015)

Table 5 PF guidelines for study area
Design criteria
RegionAspects of natural situation

Serviceable life

Public liability

Minimum surveillance
requiredFrequency of slope
failures

Frequency of unstable
movements

1

Very long-term
up to medium
Term

Public accessfree up todiscouraged

No monitoring required
up to conscious
superficial monitoring

Stable slopes up to
no ready evidenceof unstable slopes

No movement up to
extremely slow
creeping valley sides

2

Very long-term
up to medium
Term

Public accessfree up to
discouraged

No monitoring required
up to conscious
superficial monitoring

Stable slopes up to
no ready evidenceof unstable slopes

No movement up to
extremely slow
creeping valley sides

Long-term up
to very shortterm

Public accessallowed up to
actively
prevented

Incidental superficial
monitoring up tocontinuous monitoringwith sophisticatedinstruments

No unstable slopes
evident up tosignificant
instability evident

No unstable movements
evidence up to someevidence of slow
creeping valley sides

Very very
short-term

Public access
forcibly
prevented

Continuous monitoringwith intensive
sophisticatedinstruments

Significant numberof unstable slopes

Clear evidence of
creeping valley sides

34

Figure 1 Map of the regions in study area5