10th Asian Regional Conference of IAEG (2015)

Evaluation of Hazardous Area of Falling Rocks Using Digital Elevation Model
Takuya URAKOSHI(1)*, Atsushi HASEGAWA(1), Yoko SEKIGUCHI(2)and Yasuhisa AKIYAMA(2)(1) Railway Technical Research Institute, Japan, *E-mail:urakoshi@rtri.or.jp(2) KOKUSAI KOGYO CO., LTD., Japan
Abstract
We have developed a method to extract hazardous area of rockfall, using digital
elevation model; DEM. Our proposed method consists of three components: an estimationof the distribution of rock-outcrops, a search of pathways of falling rocks from theestimated rock-outcrops, and an evaluation of the reach probability of falling rocks. The
rock-outcrops distribution is estimated from topographic characteristics calculated using theDEM, as reported in a previous paper. The pathways of falling rocks are searched on the
DEM with assumption that falling rocks move to the direction of the maximum downward
gradient. The reach probability of the falling rocks is evaluated using an existing rockfall
simulation. The rock-outcrops distribution, the pathways and the reach probability are
shown on a geographical information system as a rockfall hazard map. This hazard map ishelpful for screening of rock-outcrops to investigate and for planning of measures against arockfall disaster.
Keywords: hazard map, rockfall, pathway search, reach probability, DEM
1.

Introduction
Estimation of the distributionof the rock-outcrops

Travel distances and travel paths of falling rocks
are ones of the most important factors for considering
the hazard and risk (Bridearu and Roberts, 2015). A
reach probability that is the probability of reaching ofa falling rock to some interest site is desirable
information to plan measures against a rockfall
disaster. Especially for lineal long structures, e.g.
railways and road, that are accompanied with manyslopes, the reach probability would be helpful to findthe section where the hazard of the rockfall is higher
in the extensive area.
Many methods to estimate rockfall hazard andrisk have been proposed. Some methods are
qualitative (e.g. Abbruzzese et al., 2009) and others
are quantitative (e.g. Agliardi et al., 2009; Copons etal., 2009). Mavrouli et al. (2014) conducted acomprehensive review about it. These methods
consider mechanisms of rockfall at rock-outcrops,
post failure movements of falling rocks. Worthiness
exposed for the falling rocks is additionallyconsidered to evaluate risks. However, there is no
method, where an estimation of a distribution ofrock-outcrops and evaluation of the reach probability
from the rock-outcrops are integrated.
Our proposed method consists of threecomponents as shown in Fig.1: an estimation of the

Search of the pathway of fallingrock from each rock-outcrop
Evaluation of the reachprobability to the railway

Rockfall hazard map
Figure 1. The process of the proposed method toevaluate hazardous area of rockfall
distribution of rock-outcrops, search of pathway offalling rock from each rock-outcrop, and evaluationof the reach probability using rockfall simulation on
two dimensional sections along the pathways. We
have already developed a method of the estimation of
the distribution of rock-outcrops according to indicescalculated using DEM. This part was reported by
Hasegawa and Ohta (2015).
In this research, firstly, we develop a method of
the pathway search using DEM. Secondly, we apply
an existing rockfall simulation to evaluate the reachprobability on two dimensional section along every
pathway. Finally, we map the reach probabilities

110th Asian Regional Conference of IAEG (2015)

c < 0 m-1

using a geographical information system; GIS.
2.

Method. These conditions are derived from the results of thestatistical analysis (Hasegawa and Ohta, 2015). The
condition shown as Eqn.(3) is corresponding tocommon slope angles of rock-outcrops. The condition
shown as Eqn.(4) means that the ground surface isconvex at a rock-outcrop.

2.1 Studied area and high resolution DEM
The studied area is a hill up to around 250m inelevation, where sedimentary rocks of the Late
Cretaceous are distributed. Rock-outcrops areobserved on slopes of the hill, and railway, road andhouses exist along the base of the hill. In this study,
we treat the railway as a target of disaster mitigation.
We created a high resolution DEM with 1m meshfrom three dimensional data obtained by airborne
LiDAR at Dec. 2010.

2.3 Searching of pathways of falling rocks
The pathways of falling rocks are analyzed withthe assumption that a falling rock moves in the
direction of maximum downward gradient; DMDG.
The gradient g is defined as

2.2 Estimation of the distribution of rock-outcrops
We adopt the method reported in Hasegawa andOhta (2015) to estimate the distribution ofrock-outcrops. Hasegawa and Ohta (2015) revealed
that a slope angle and a curvature of ground surface
calculated using DEM were discriminative indiceswhether rock-outcrop existed or not, based on a
statistical analysis between characteristics of groundsurface and distributions of rock-outcrops confirmedby field investigation.
The summary of the estimation method is asfollows.

g

z no  z i, j dgz nd  z i, j 

The orthogonalneighbor of cells of
the cell (i, j)z(i,j+1)1(1)z(i-1,j)andz (i  1, j )  z (i  1, j )  2 z (i, j )d2z (i, j  1)  z (i, j  1)  2 z (i, j )d2z(i,j)

z(i+1,j)dz(i,j-1)y

The diagonalneighbor cells of
the cell (i, j)dx

Figure 2. Numbering of DEM cells.
Z(i,j) is the elevation of the cell (i, j)(2), where z(i,j) is the elevation of the cell (i, j) of theDEM, i and j are cell numbers along x-axis and y-axis,
and d is the width of the cell as shown in Fig.2. The
curvature c is spatially-smoothed.
(2) Estimation of the distribution of rock-outcrops
A cell is classified as the rock-outcrop cell if thecharacteristics of the cell satisfy the both conditions,s > 50 deg.

(6)

2d

, where zno is the elevation of an orthogonal neighborcell of the cell (i, j) where a falling rock exists, andznd is that of a diagonal neighbor cell (Fig.2). The
arrow A shown in Fig.3 represents the DMDG.
If two or more DMDG-s are analyzed from one
cell, for example the arrows B and C shown in Fig.3,
we save all DMDG-s as possible direction of pathway.
Hence, more than one pathway may be obtained from2 2
 z (i, j  1)  z (i, j  1)  

 
2d

 

c

(5)

and

(1) Calculation of slope angle and curvature
Slope angle s and curvature c of ground surface
are defined as
 z (i  1, j )  z (i  1, j )  2
s  Arctan 

2d



(4)

101

101

101

101

101

101

100

100

95

96

100

98

97

98

96

100

95

98

99

97

A

B

C

An estimatedrock-outcrop cell
A depression cellD

Figure 3. An example of the pathway searchusing DEM.
Values in each cell are elevations (m). A detail
explanation of the arrows A, B, C and D is on the
text.

(3)

and

2

10th Asian Regional Conference of IAEG (2015)

Table 1. Set values for the rockfall simulation
Property

Area or target

Set value
average

Friction coefficient
Reflection coefficient in vertical direction
On pathway
Reflection coefficient in horizontal direction
Critical velocity for changing of the motion of thefalling rock from rolling and slipping to jumping
Falling rock
Simulation settings

0.48 [1]standard deviation

0.06 [1]average

0.58 [1]standard deviation

0.26 [1]average

0.77 [1]standard deviation

0.17 [1]average

8.5 m/s [1]standard deviation

2.5 m/s [1]Diameter

1m

Mass

170 kgNumber of trials on each pathway

100 times

Time step in the simulation

0.05 s[1]: Values for gravelly talus, obtained by a case study (Japan Road Association, 2002)
an estimated rock-outcrop cell. In the case shown in
Fig.3, two pathways are obtained.
If a falling rock trap in depressions of DEM, i.e. if
the elevations of the surrounding eight cells arehigher than that of the cell where the rock exists, we
assume the rock moves in the direction of minimum
upward gradient; DMUG, only if the gradient is lessthan 10 deg. because falling rocks may leap ridges ofground surface in practical cases. The arrow D shownin Fig.3 is an example of the DMUG.

Trajectories(A)
Elevation(m)
30
Ground surface
0
5
10
15
100
Reach
probability
(%)
0
0
10
5
15
Distance from a rock-outcrops (m)(B)

2.4 Evaluation of reach probability
To evaluate the reach probability, we conduct anexisting rockfall simulation (Yoshida et al., 1991), towhich the Monte Carlo method is applied. This
simulation analyzes the movement of a falling rockon a two-dimensional vertical cross-section, andoutputs the trajectory of the falling rock in each trialof the Monte Carlo simulation. The friction
coefficient and the reflection coefficient between thefalling rock and ground surface, and the criticalvelocity for changing of the motion of the falling rockfrom rolling and slipping to jumping, areautomatically set for each trial as the occurrence
probabilities of these parameters obey the normal
probability distributions.
We project the searched pathway of falling rockonto the two-dimensional vertical cross-section of therockfall simulation although the pathway is generally
skewed. The parameters required for the simulation
are set as shown in Table.1.
From the trajectories of falling rocks in all trials,
reach probability p from the l-th rock-outcrop via them-th pathway to point x is evaluated byp lm ( x) N reached 100
N trial40

Figure 4. Example of the evaluation of reachprobability using the Monte Carlo type rockfall
simulation.
(A): Trajectories of falling rocks calculated intrials of the rockfall simulation. (B): The reachprobability evaluated from the trajectories.

, where Ntrial is the number of total trials and Nreached isthe number of trials in which the falling rock reachedor passed point x. An example of the evaluation ofreach probability is shown in Fig.4. We set Ntrial as
100 times.
In this study, the pathway search and the rockfall
simulation are executed for the estimatedrock-outcrops within 100m of a railway line.

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10th Asian Regional Conference of IAEG (2015)

Figure 5. (A): Topological map using the DEM with 10m interval contours. (B) and (C): Distribution of theslope angle and the curvature calculated using the DEM. (D): Distribution of the rock-outcrops estimated.
(E): An example of the pathway. (F): The reach probability of falling rocks from the estimated rock-outcrops
within 100m from the railway.

410th Asian Regional Conference of IAEG (2015)

2.5 Mapping of the reach probability
The reach probability is mapped using ageographical information system; GIS. Additionally,
the extracted rock-outcrops and the pathways are also
mapped.
3.

Acknowledgements
The authors are grateful to Dr. T. OHTA and Dr.
T. KAWAGOE at Railway Technical ResearchInstitute for their advices on this research. The
authors also thank to anonymous reviewers for theircomments on this paper.

Results and discussions

The rock-outcrops distribution (Fig.5(D)) isestimated using the DEM (Fig.5(A)) by theconditions eqn.(3) for the slope angle (Fig.5(B)) andeqn.(4) for the curvature (Fig.5(C)). Some estimatedrock-outcrops exist on the slopes facing the railway.
The pathways from the estimated rock-outcrops
within 100m from the railway are successfully
analyzed using the DEM. Some pathways extend to
the railway (Fig.5(E)).
The reach probability is evaluated and plotted on
GIS as shown Fig.5(F). Some falling rocks will reachto the railway with 100% possibility. Others areevaluated to stop at a sand control dam on a valley orflat space.
Users can use this map as a tool to selectrock-outcrops which technician should survey earlier
in many rock-outcrops along railways. Moreover, thismap enables users to find the sections where thereach probability is high, and helps users to make adecision where they should construct measures prior
to other region.
The probability of the occurrence of rockfall,
however, is not considered on the proposed method.
It is a future issue to incorporate the occurrence
probability.
4.

References
Abbruzzese, J.M., Sauthier, C. and Labiouse, V.
(2009): Considerations on Swiss methodologies forrock fall hazard mapping based on trajectorymodeling, Nat. Hazards Earth Syst. Sci., Vol. 9, pp.
1095-1109.
Agliardi, F., Crosta, G.B and Frattini, P. (2009):
Integrating
rockfallrisk
assessment
andcountermeasure design by 3D modeling techniques,Nat. Hazards Earth Syst. Sci., Vol. 9, pp.1059-1073.
Bridearu, M-A. and Roberts, N.J. (2015): Mass
Movement in Bedrock, In: Shroder, J.F. (eds.)
Landslide hazards, risks, and disasters, pp. 43-90,
Elsevier.
Copons, R., Vilaplana, J.M. and Linares, R. (2009):
Rockfall travel distance analysis by using empiricalmodels (Sola d’ Andorra la vella, Central Pyrenees),
Nat. Hazards Earth Syst. Sci., Vol. 9, pp.2107-2118.
Yoshida, H., Ushiro, T., Masuya, H. and Fujii, T.
(1991): An Evaluation of Impulsive Design Load ofRock Sheds Taking into Account Slope Properties,
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1603-1616. (In Japanese with English abstract)
Hasegawa, A. and Ohta T. (2015): An Estimation
Method of the Distribution of Rock-Outcrops Using
DEM, Proc. Of Annual Meeting of Japanese Societyof Engineering Geology, now printing. (In Japanese)
Japan Road Association (2002): Reference Materials
to the Handbook for the Rockfall Measures, p.295.
(In Japanese)
Mavrouli O.-C., Abbruzzese, J., Corominas, J. andLabiouse, V. (2014): Review and Advances in
Methodologies for Rockfall Hazard and Risk
Assessment, In: Van Asch, T., Corominas, J.,
Greiving, S., Malet, J.-P., Sterlacchini, S. (eds.)
Mountain Risks: From Prediction to Management
and Governance, pp.179-199. Elsevier.

Conclusion

We propose a new method to evaluate the reachprobability of falling rock using DEM. This method
consists of three components: estimation of the
distribution of rock-outcrops, search of pathway offalling rock from each rock-outcrop, and evaluationof the reach probability using an existing rockfall
simulation. Using this method, we successfully
evaluate the reach probability and made a rockfall
hazard map. This hazard map will be helpful for
screening of rock-outcrops to investigate and forplanning of measures against rockfall disasters.

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