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Forecasting landslide hazard by the 3D discreteelement method: A case study of the unstable

slope in the Lushan hot spring district, central

Taiwan

ARTICLE in ENGINEERING GEOLOGY · DECEMBER 2014

Impact Factor: 1.74 · DOI: 10.1016/j.enggeo.2014.09.007

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Forecasting landslide hazard by the 3D discrete element method: A casestudy of the unstable slope in the Lushan hot spring district,central Taiwan

Chiao-Yin Lu a,b,d, Chao-Lung Tang a, Yu-Chang Chan b,⁎, Jyr-Ching Hu a, Chung-Chi Chi c

a Department of Geosciences, National Taiwan University, Taipei, Taiwanb Institute of Earth Sciences, Academia Sinica, Taipei, Taiwanc Central Geological Survey, Ministry of Economic Affairs, Taipei, Taiwand National Science and Technology Center for Disaster Reduction, Taipei, Taiwan

a b s t r a c ta r t i c l e i n f o

Article history:

Received 20 March 2014

Received in revised form 27 August 2014

Accepted 16 September 2014

Available online 28 September 2014

Keywords:

Landslide hazard

Numerical modeling

Particle ow code 3D

Lushan

Taiwan

Catastrophic landslides and related phenomena are commonly facilitated by the subtropical climate with fre-

quent typhoons and recurrent earthquakes in Taiwan's mountainous areas. One area susceptible to potentially

catastrophic landslides is located at Lushan in central Taiwan, which is famous for its hot springs and tourism.

The northern slope above the hot spring district slips gradually and frequently due to heavy rainfall. For safety

reasons, the slip-affected areahas beenunder constant boreholemonitoring by government agencies, and a con-

troversial public debate has arisen overpermanent evacuation of the hotspring district. In thisstudy, we attempt

to simulate possible scenarios of catastrophic slope failure using slip geometries derived from the monitoring

data, and assess potential landslide impact areas by a discrete element method using the PFC3D code. In the

worst case scenario, the Lushan hot spring district is predicted to be destroyed by debris in 20 s. Besides, the

planned regional emergency refuge is rapidly jeopardized by ooding resulted from landslide-dammed lakes.

This study addresses catastrophic slope failure under heavy rainfall conditions given a range of friction coef -

cients and varied continuity of the failure surfaces. It is noted that the PFC3D code has limitations in modeling

all complex mechanisms of landslide, particularly in modeling loss of material shear strength due to increases

in pore pressure. Nevertheless, the numerical simulation results by the 3D discrete element method providescenario-based runout paths, particlevelocities andlandslide-affectedareas,which are useful information forde-

cision support and future landslide hazard assessment.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Extremely rapid landslides, such as debris and rock avalanches, are

the most obvious and major geological hazards in mountainous areas.

They have caused extensive infrastructure damage and threatened

human lives through the centuries (Eisbacher and Clague, 1984;

Turner and Schuster, 1996; Dai et al., 2002; Nadim et al., 2006; Keefer

and Larsen, 2007; Highland and Bobrowsky, 2008). According to the

World Disaster Report (IFRC, 2011), there were more than 200 land-

slides and about ten thousand people killed by landslides during the

last ten years (2001–2010) around the world. Taiwan has a subtropical

climate and an annual average of four typhoons. Active orogeny due to

the collision between the Eurasian and Philippine Sea plates has also

produced both mountainous terrain and frequent earthquakes (e.g.

Dadson et al., 2003). Taiwan is therefore one of the landslide-hazard

hotspots of the world (Nadim et al., 2006).

Large earthquakes and torrential rainfall are considered to be the

main agents generating catastrophic landslides (e.g., Keefer, 1984,

2000; Terlien, 1998; Crozier, 1999; Van Asch et al., 1999; Lin et al.,

2004; Jibson, 2007; Crosta and Frattini, 2008). The basic physics of trig-

gering and initiation of landslides such as gravity, strength of material,

external forces due to seismic shaking and pore-water pressure have

been well investigated for decades (Erismann, 1979; Campbell, 1989;

Iverson, 2000; Legros, 2002; Guzzetti et al., 2007; Wasowski et al.,

2011). However, more progress in forecasting andunderstanding of cat-

astrophic landslides is needed to reduce casualties and property losses.

Catastrophic failures can involve slopes in metamorphic rocks with

well-developed foliation, following long-term mass rock creep that

tends to change the orientation of foliation (Chigira, 1992). Mass rock

creep or the so-called deep-seated gravitational slope deformations

can evolve from continuous and very slow displacements to catastroph-

ic and rapid movement (Chigira, 1992, 2009; Dramis and Sorriso-Valvo,

1994; Kilburna and Petley, 2003; Petley et al., 2005). The deformation

Engineering Geology 183 (2014) 14–30

⁎ Corresponding author at: Institute of Earth Sciences, Academia Sinica, No.128, Sec. 2,

Academia Road, Taipei 115, Taiwan. Tel.: +886 2 27839910x411; fax: +886 2 27839871.

E-mail address: [email protected] (Y.-C. Chan).

http://dx.doi.org/10.1016/j.enggeo.2014.09.007

0013-7952/© 2014 Elsevier B.V. All rights reserved.

Contents lists available at ScienceDirect

Engineering Geology

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e n g g e o

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and fragmentation of the rock mass through the creep process may fur-

ther lead to the occurrence of landslides (Giraud et al.,1990). Therefore,

the phenomenon of mass rock creep offers a clue to forecasting poten-

tial sites of catastrophic landslides.

Several studies have improved our understanding of the effects of

topography and geological structureson landslide occurrence and prob-

ability (e.g., Chigira et al., 2003; Sidle and Ochiai, 2006; Lee et al., 2008;

Wasowski et al., 2011). The most frequently used empirical method for

the runout analysis is derived from the correlations between landslidevolume and the angle of reach (Heim, 1932; Scheidegger, 1973;

Nicoletti and Sorriso-Valvo, 1991; Corominas, 1996; Legros, 2002).

The relationship between landslide volume and deposition area has

also been discussed (Hungr, 1990; Inverson et al., 1998). In addition to

empirical methods, numerical methods can simulate the runout behav-

ior of landslide debris through the time-stepping algorithms that have

been developed over the past decade (McDougall et al., 2012). The nu-

merical methods for modeling landslides mainly include the continuum

method and the discrete element method (DEM).

The continuum method models the runout of landslides by analyz-

ing the ow of uids in channels. Savage and Hutter (1989) developed

the continuum model from depth-averaged (shallow ow) equations

to simulate the ow of dry sand. Hungr (1995) used DAN2D (dynamic

analysis 2D), which is a meshless Lagrangian model, to take different

uid rheology into consideration. DAN3D, a 3D extension of the existing

2D model,was later used to simulate the1855–1856 RubbleCreek land-

slide in British Columbia by McDougall (2006). A similar approach,

RASH3D, a xed-mesh Eulerian model, has also been developed and ap-

plied (Pirulli, 2005).

In the discrete element method (DEM), a group of individual parti-

cles interact with each other by sliding, falling and rolling on the ground

surface, to simulate the cracks and the subsequent large-scale displace-

ment of a catastrophic landslide. Itasca Consulting Group, Inc. (Cundall

and Strack, 1979) developed the Particle Flow Code (PFC) model

based on the DEM. In the PFC model, particles can be bonded together

or separated during the simulation process (Poisel and Roth, 2004).

There have been several studies that simulate real landslide cases by

using the PFC (Poisel and Preh, 2008; Chang and Taboada, 2009; Tang

et al., 2009, 2013; Lo et al., 2011). Because large displaced fracturescan be simulated by the discrete element method, the method is appro-

priate for modeling the kinematic processes of landslide events.

However, from the viewpoint of landslide hazard assessment, not

only the potential landslide source but also the runout path and the

landslide-affected area are crucial targets for investigation. Through

simulating landslide scenarios, it will help in better assessing landslide

hazards and eventually decreasing casualties and property losses.

While numerical modeling has often been used to analyze past events

(Crosta et al., 2003; Stead et al., 2006; Posiel et al., 2008; Chang and

Taboada, 2009; Crosta et al., 2009; Kuo et al., 2009; Tang et al., 2009 ),

few attempts have been carried out to forecast scenarios of potential

catastrophic slope failures, possibly due to limited spatial and temporal

eld observational data (Crosta et al., 2006; Poisel et al., 2009).

With the aforementioned motivation, we applied the programPFC3D (Particle Flow Code 3D) to simulate the potentially catastrophic

slope failure of an unstable rock mass and its impact in the Lushan hot

spring district, where eld observational data have been accumulated

for the past decade. The northern slope of the district was among the

few potential landslide areas in Taiwan that show strong evidence of

mass rock creep by monitoring data. Abundant data have been collected

which indicate that the slope slid several to tens of centimeters

during recent torrential rainfall events (Soil and Water Conservation

Bureau, 2006, 2008; Central Geological Survey, 2011). Because of the

noticeable creep events, a controversial public debate has arisen

concerning whether or not the Lushan hot spring district should be

evacuated permanently for safety reasons. The present work intends

to model and forecast detailed 3D landslide occurrence, specically,

the landslide transportation and deposition in the famous resort

area. Although the 3D discrete element method has limitations in

modeling landslides, the work demonstrates that it can provide useful

insights for mapping areas susceptible to potentially catastrophic

slope failures.

2. Characteristics of the Lushan hot spring district

2.1. Geographical and geological setting

The Lushan hot spring district is located at Jin-Yin Village, Ren-Ai

Township, Nan-Tou County at the western side of the central mountain

range of Taiwan, and is famous for itshot spring tourism (Figure 1). The

Tai-14 highway, N87 highway, and the village roadways are used by the

residents and tourists traveling between the Lushan district and western

Taiwan. Thedrainage system of the study area belongs to the Jhuo-Shuei

River, and the Lushan district is located at the conuence of the Ta-Lou-

Wan and Ma-Hai-Pu rivers. Most hotel buildings in Lushan are distribut-

ed along or near the Ta-Lou-Wan River reach, where the northern valley

slope often slides following torrential rainfall events.

The Lushan Formation, the major unit in the study area, is mainly

composed of Miocene slate and sandy slate (Figure 2). Based on previ-

ous investigations (Soil and Water Conservation Bureau, 2006, 2008;

Central GeologicalSurvey, 2011), theslope is composed of surface collu-

vium with complex subsurface geology and ground water conditions.

The elevation of the slope susceptible to failure varies from 1085 to

1495 m with an average gradient of about 22o.

2.2. Recorded failures at the Lushan district

During pouring rain or typhoon seasons, the torrential rainfall fre-

quently destroyed the roads, split the retaining walls, and caused struc-

ture tilting and subsidence at the northern valley slope of the Lushan

hot spring district. The 25 creep monitoring systems (mainly borehole

inclinometers) installed by SWCB(Soiland WaterConservation Bureau)

and CGS (Central Geological Survey) (Figure 3), recorded the slip phe-

nomena at different depths during the 2005–2011 period. The mea-

sured surface displacements were about 10 cm during typhoon Matsa

in August 2005, more than 50 cm during the torrential rainfall in June2006 and 25 cm during typhoon Sinlarku in September 2008.

The recorded failures in the Tai-14 highway and other roadways, as

well as the distribution of damaged buildings, enable the potential slid-

ing areas to be reliably dened. According to the records of the Lushan

rain station of the Central Weather Bureau (CWB) between 1952 and

2004, the rainy season begins from April to September, with an average

annual rainfall about 2500 mm. A potential sliding area labeled as SA1

(Figure 2) in the Lushan district is about 19 hectares. Another potential

larger sliding area labeled as SA2 (Figure 2), which also encompasses

the SA1 area, is nearly 30 hectares. After several typhoon events in re-

cent years, the sliding phenomena become more notable, which led to

more installations of monitoring systems by the government agencies.

The slide phenomena raised safety concerns not only for the lives and

properties of local residents, but also for the hot spring visitors at thetoe of the unstable slope.

2.3. Failure mechanisms at the northern slope of Lushan

Rock-boring samples from the northern slope of the Lushan district

show well-developed, high-angle slaty cleavage, as well as deformation

interpreted to be indicative of creeping or sliding at different depths.

Furthermore, the inclinometer monitoring data demonstrate that

deep-seated creep deformation involves depths down to 108 meters.

According to the aforementionedeld observations, the creep phenom-

ena conform to type I deformation, i.e., buckling folds, in the classica-

tion proposed by Chigira (1992). Buckling occurs whenever a foliated

rock moves downslope on a gentler slope than the foliation, and the

sliding rock mass is constrained by the stationary rock at the foot of

15C.-Y. Lu et al. / Engineering Geology 183 (2014) 14– 30

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theslope (Chigira, 1992). At Lushanthe massrockcreep is controlled bythe geometries of the dip of joints (N49W/75S) on the eastern slope and

the slaty cleavage (N30E/57E) on the western slope. The geometries of

the joint and cleavage together form a potential sliding wedge block

(Figure 4). The sliding surface may be currently developingand extend-

ing to the downslope due to pre-existing weak planes and weathering.

Duringtorrential rainfall,the mass rockcreep is likelytriggered by seep-

age and inltration of the rainwater, which may decrease the friction of

the sliding surface.

3. Three-dimensional discrete element modeling

Several studies have simulated the kinematic behaviors and mecha-

nisms of rock slope failures using discrete element models (Poisel and

Preh, 2008; Chang and Taboada, 2009; Tang et al., 2009, 2013; Lo

et al., 2011). Three Dimensional Particle Flow Code (PFC3D) is a com-puter program that is based on the Granular Discrete Element Method

and adapted to model landslide events in three dimensions. The pro-

gram considers the effects of lateral spreading during landslide events

that two dimensional approaches cannot realistically model.

3.1. Discrete element method

PFC3D models the movement and interaction between rigid spherical

particles based on the discrete element method (DEM) developed by

Itasca Consultants Group, Inc. in 1995. The DEM was introduced by

Cundall (1971) for the analysis of rock mechanics problems. It was later

applied to granular material by Cundall and Strack (1979). The DEM per-

mitsnitedisplacements androtations of discrete particles,involves com-

plete detachment of particles, and recognizes new contacts automatically

Fig. 1. Location maps andtopography in the Lushan area, centralTaiwan. The ellipticalline in the3D perspective mapindicatesthe northern slope of theLushanhot spring district, area of

the potential landslide.

16 C.-Y. Lu et al. / Engineering Geology 183 (2014) 14– 30

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during the calculation processes (Cundall and Hart, 1992). The relation-

ship between microproperties and macroproperties in the PFC bonding

model is described in detail by Potyondy and Cundall(2004). The dynam-

ic behavior of theDEM simulationis represented by a time stepping algo-

rithm, which is an explicitnite difference method that divides time into

very small time steps. In a time step, the velocities and accelerations areassumed to be constant. From the features of the DEM with time explicit

calculations, thecracksand thelarge displacedfracturescan be simulated;

accordingly the method is particularly appropriatefor modeling kinemat-

ic processes of landslide events.

3.2. Calculation cycle

The calculation cycle performed in PFC3D is a time stepping algo-

rithm that requires repeated application of Newton's second law and

the force–displacement law (Potyondy and Cundall, 2004; Itasca,

2008). At the start of every time step, contacts are renewed from the

known ball and wall positions. Then, the force–displacement law is ap-

plied to update the contact forces based on the relative motion or over-

lap between the two entities at the contact. Next, the Newton's secondlaw is applied to update the velocity and position of each ball based

on the force and moment arising from the contact forces.

3.3. Macro-properties and micro-properties

In the PFC model, balls can be bonded together or separated during

thesimulationprocess. Parallel bonds aresetto mimic themechanical be-

havior of grains joined by cement. The total force and moment between

bonded balls are comprised of a force and moment carried by parallel

bonds as the cement behavior, as well as a force arising from ball–ball

overlap as the grain behavior. If a parallel bond is broken and not existed

at a contact, then only the grain behavior occurs during simulation.

PFC3D derives macro-scale material properties, such as uniaxial

compression strength (UCS), Young's modulus and Poisson's ratio,

from the interactions of micro-scale properties, which are represented

by the following micro-parameters of particles and bonds (Potyondy

and Cundall, 2004; Itasca, 2008):

E c ; kn=ksð Þ; μ f g; particle micro−properties;

λ; E c ; kn

=ks

;σ c ; τ c n o

; bond micro−

properties;

where E c and E c indicate the Young's modulus of the particle and bond,

respectively; (kn/ks) is theratio of particle normal (kn) to shear stiffness

(ks) and kn=k

s

is the ratio of bond normal kn

to shear stiffness k

s

; μ is the particle friction coef cient; λ. is the radius multiplier used to

set the parallel-bond radii (which can transmit both forces and mo-

ments between particles); and σ c and τ c are the normal and shear

strengths of bonds, respectively. The Young's modulus of the particle

and parallel bond can be approximately expressed as: E c ¼ k n4R and E c ¼

kn R1 þ R2ð Þ , where R is the radius of the particles (Potyondy and

Cundall, 2004).

Before constructing the PFC3D numerical models, we already have

the macro-parameters of physical samples from laboratory experi-

ments. However, we can only give micro-parameters of the particlesand bonds in PFC3D to mimic relevant rock behaviors. The suitable

micro-parameters are determined by a calibration procedure that has

been suggested by previous studies (Potyondy and Cundall, 2004;

Itasca, 2008). For matching given properties of physical samples, we

employed numerical tests that imitate the laboratory experiments.

The micro-parameters that characterize a synthetic sample can be ac-

quired by thenumerical triaxial andBrazilian tests in PFC3D.The behav-

iors of the synthetic and physical samples can then be compared

directly. For reproducing a given Young's modulus of a physical sample,

the normal and shear strengths of the synthetic sample are set to large

values in order to prevent bond failure and to keep its elastic behavior.

The values of E c and E c are then systematically varied to acquire

the best t Young's modulus during the numerical tests. The Poisson's

ratio of the PFC bonded material is controlled by (kn/ks). and k

n

=k

s .

Fig. 2. Geologic mapof theLushanhot spring district (modied from SWCB,2006) andthe potentiallandslideareas fornumerical modeling in thisstudy. Slate layers arelabeled as SL1~ 4;

sandy slate layers are labeled as SSL1 ~ 4. The line AA′ indicates the location of the cross section shown in Fig. 6.


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As the ratio of normal and shear stiffness increases, the Poisson's

ratio also increases. Finally, the UCS of the PFC bonded material is deter-

mined by the mean normal and shear strengths of the synthetic

samples.

The input micro-parameters of the PFC3D model are systematicallyvaried during the numerical tests until the macro-parameters of the

PFC3D model match those of the physical sample. The numerical proce-

dure of deriving the micro-parameters of the PFC3D model is shown in

Fig. 5. From repeated calculations of the numerical tests, the micro-

parameters of the PFC3D models (Table 1) can be inverted for the current

study. The comparison between the macro-parameters of the PFC model

and laboratory experiments is shown in Table 2. As indicated in the table,

the values of the PFC model are very close to those of the laboratory

experiments.

4. PFC3D simulations of potential landslides at Lushan

This study focused on simulating a slidingevent, including its runout

paths, particle velocities and landslide-affected areas for the potential

sliding area SA1, which exhibits a signicant scarp on top of

the bulgy terrain of about 19 ha (Figure 2). We also considered a larger

sliding area SA2 with an area of about 30 ha to simulate the worst case

landslide scenario at Lushan based on available slope creep

observations (Figure 2). To prevent excessive calculations and dataoverloading in numerical simulations of PFC3D and to mimic realistic

conditions, the diameters of the ball-elements were limited between

1–5 m. The volume for the sliding area SA1 was about 107 m3 and was

thus lled by 30,000 ball-elements. The volume for the larger sliding

area SA2 was about 1.3 × 107 m3 and was lled by 35,000 ball-

elements. The diameters of the ball-elements ranged from 2.75–

4.57 m and were randomly distributed within the potential landslide

volume.

4.1. Construction of PFC3D numerical models

In this study, thedepth of the basal slip plane wasextrapolated using

the records of inclinometers and Time Domain Reectometers (TDR)

from the Soil and Water Conservation Bureau (SWCB) and the Central

Fig. 3. Distribution of the borehole monitoring systems and observed deepest slip/deformation depth for individual boreholes between 2005 and 2011. Monitoring borehole data were

compiled from CGS (2011) and SWCB (2006, 2008). The pink and blue lines indicate the sliding areas SA1 and SA2, respectively. Line AA′ indicates the location of cross section shown

in Fig. 6.


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Fig. 4. Geologic structureof theunstablenorthern slope ofthe potentialLushanlandslidearea (modied SWCB,2006). Theslope creepis controlled by thegeometry of thedip joint andthe

slaty cleavage, which form a potential sliding wedge block.

Fig. 5. A ow chart of deriving the micro-parameters to construct a PFC3D model. The input micro-parameters of the PFC3D model are varied during the numerical triaxial and Brazilian

tests until the macro-parameters of the PFC3D model match the properties of the particular material.


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Geological Survey (CGS) during 2005 to 2011 (Figure 3). The geometry

of the sliding surfacewas approximated by projecting and interpolating

the deepest slip records in individual boreholes along the AA′ prole

(Figure 6). Based on this approximation, the sliding surface was dened

and then constructed as a Digital Terrain Model (DTM) of the Lushan

district for the modeling purpose.

The topography and sliding surface were represented by 25,620

isosceles right triangle wall-elements, which are based on a 15 m DTM

and the monitoring data of the Lushan district. Assuming the self-

lubrication mechanism, and therefore low residual friction (Dieterich,

1979; Erismann, 1979; Campbell, 1989; Di Toro et al., 2004; Han et al.,

2007), the friction coef cient wasassigned a value of 0.05 on thesliding

surface. To improve the landslidemodeling, which usually setsthe same

friction coef cient for all wall-elements, we assigned the friction coef -

cient of wall-elements as 0.05 on the sliding surface and 0.2 on the wall-

elements of the topographic surface across the river valley. Theincrease

of the friction coef cient is attributed to the velocity decrease after the

landslide debris hits the southern slope.

The present modeling differed from most other studies that use

homogeneous materials, by dividing the sliding body into three

strata: colluvium, weathered slate and fresh slate. The thicknesses

of individual strata were based on the borehole data, resistivity

image proling and seismic refraction methods (Soil and Water

Conservation Bureau, 2006, 2008; Central Geological Survey, 2011).

The colluvium and weathered slate were set to be 15 m and 40 m

in thickness, respectively, while fresh slate was set below the weath-

ered slate. Based on eld observations of cleavages and joints, we

also dened weak planes in the models based on the strikes and

dips of cleavages and joints with random spacings between 15 mand 25 m.

The micro-parameters of the PFC3D models (Table 1) are derived

from repeated calculations of the numerical tests as previously men-

tioned. The density of the potential landslide body was set as 2670 kg/

m3. Thecorrelation between Young's modulus (E ) and UCS(Unconned

compressive strength) were identied by the formula from Rodríguez-

Sastre et al. (2008): E = 429.56(UCS)0.9122. The stiffness ratio was set

as 3 because a meaningful value of Poisson's ratio (0–0.5) will be obtain-

ed only if the stiffness ratios kn=ks and kn=k

s

range between 2 and 3

(Pande et al., 1990). To track velocity and displacement duringthe land-

slide modeling, monitoring balls were placed on the surface within the

potential sliding areas SA1 and SA2.

4.2. Simulations of a landslide event

The simulations of a landslide event for the northern slope of the

Lushan hot spring district through time are shown in Fig. 7. PFC3D

models predict that the buildings below the unstable slope would be

destroyed in 10 s and almost the whole Lushan hot spring district

would be demolished in 20 s except for a few buildings on the eastern

side. This landslide hazard prediction is similar for both simulations of

the sliding areas SA1 and SA2. Based on the results of 100 s after the

landslide initiation (Figure 8), the modeled landslide-affected area (in-

cluding the landslide source, runout-affected and debris deposition

Table 1

Micro-parameters for different types of material used in the PFC models.

Micro-parameters of PFC

model/Types of material

Colluvium Weathered

slate

Fresh

slate

Joints

Minimum radius (Rmin) (m) 2.72 2.72 2.72

Ball radius ratio (Rmax/Rmin) 1.66 1.66 1.66

Ball–ball contact modulus (Ec) (GPa) 0 .97 1.89 18 .4

Ball–ball friction coef cient 0.58 0.62 0.67 0.47

Ball stiffness ratio (kn/ks) 3 3 3

Parallel bond modulus (Ēc) (GPa) 0.97 1.89 18.4Parallel bond stiffness ratio (kn/ks) 3 3 3

Parallel bond normal strength (σ c)

(MPa)

2.76 6.24 84.6 0.1

Parallel bond shear strength (τc)

(MPa)

0.92 2.08 28.2 0.1

Table 2

Comparison between macro-parameters of PFC model and laboratory experiment.

Macro-parameters/Types of material Colluvium Weathered slate Fresh slate

Macro-parameters of PFC model Young's Modulus (GPa) 1.013 1.962 17.74

UCS (MPa) 2.59 5.36 58.19

Macro-parameters of laboratory experiments Young's Modulus (GPa) 1.017 1.985 17.63

*UCS (MPa) (Rodríguez-Sastre et al., 2008) 2.57 5.35 58.7

Fig. 6. The AA′ prole of the proposed sliding surface based on the slip depths from individual borehole monitoring data. A-13, -15, -21 and -25-1 show the borehole inclinometer data

collected by CGS. B-01, -06, -09, -11 and TDR02, 03 show the records of borehole inclinometer and Time Domain Reectometer (TDR), respectively, from SWCB. Because the colluvium

on the surface is only a few meters thick and varies in thickness, it is not drawn in the cross section for simplicity.


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areas) for the caseof SA1 isabout 38.6ha and for thecase of SA2 isabout

52.4 ha. Landslide debris will ll the valley and obstruct the drainage

near the conuence of two rivers. Two landslide-dammed lakes may

thus be formed and threaten an even larger area in the Lushan hot

spring district. The potential hazard from the landslide-dammed lakes

is discussed in detail in Section 5.

Fig. 7. Scenario simulations for the landslide event and the affected area in the Lushan hot s pring district through time. (a) Landslide scenario for the sliding area SA1, and (b) landslide

scenario for the sliding SA2. In both simulations, the Lushan hot spring district is almost entirely covered by the landslide debris and demolished in 20 s.


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4.3. Landslide runout behavior

The runout paths and velocity proles based on the monitoring balls

are identied in Figs. 9 and 10. By tracing and recording the positions of

the monitoring balls in every step, the predicted maximum runout dis-

tance is about 660 m in the landslide scenario simulation of SA1

(Figure 9), and about 927 m in the simulation of SA2 ( Figure 10). The

combination of routes and velocities indicates that some acceleration

values of the monitored balls calculated from the velocity pro

les arecaused by variations of topography. The velocities of the monitoring

balls decrease rapidly during the sliding process, but through colliding

fragments, the velocities areregained in part; this explains theuctuation

of velocity proles with time.

Themaximum velocity of particles appears at 10–15s after the start of

the landslide simulation of SA1 with a predicted maximum velocity of

about 30 m/s (Figure 9). The maximum velocity of particles for the land-

slide simulationof SA2appears at about 10–20 s afterthe start of the land-

slide, and the maximum velocity of the monitoring balls reaches about

46 m/s due to the higher elevation of some monitoring balls(Figure 10). In both landslide simulations, ball-element particles almost

stopped at 40 s after the start.

4.4. Variations of the landslide velocity eld

The velocity elds along prole AA′ are indicated by a color scale for

the landslide simulations of SA1 (Figure 11a)and SA2(Figure 11b)at in-

tervals of 5 s. A higher velocity occurs at the bottom of the sliding body

around 5 s after slide initiation in both scenarios. The phenomenon is

likely resulted from the low friction of the sliding surface, which may fa-

cilitate the initiation of landslide. At around 10–15s, the lower part ofthe

sliding body is obstructed and slowed down by the southern slope for

which the higher friction coef cient (0.2) of the wall elements is

assigned. The landslide debris completely lls the valley and almost

Fig. 8. Predicted landslide-dammed lakes for the simulated landslide scenarios.

(a) Dammed lakes s11 and s12 for the landslide scenario of SA1 (b) dammed lakes s21

and s22 for the landslide scenario of SA2. The aerial photo in the lower left corner shows

the simulated deposition area of the landslide debris at 100s after the landslide initiation.

The purple circle denotes the Lushan Police Reception, which is designated as the emer-

gency refuge for the Lushan hot spring district.

Fig. 9. The lower left panel indicates the distribution of monitoring balls in sliding area

SA1. The upper panel shows the velocity and runout path of monitoring balls labeled in

numbers for the landslide scenario of SA1. And the lower right panel is the prole of themonitoring ball velocity for the landslide scenario of SA1. The highest velocity (24–

30m/s)appears at10–15s andthemonitoringballssettledownat 35–45s aftertheland-

slide initiation.The velocity of themonitoringballs also uctuates probably dueto particle

collisions during the sliding process.


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settles down after 20 s in the sliding scenario of SA1. The velocity of the

sliding body of SA2 decreases downslope and its frontal part almost

stops after 20 s.

The surface velocity elds of the landslide simulations for SA1

(Figure 12a) and SA2 (Figure 12b) are extracted from the velocity data

of surface particles at intervals of 5 s. A signicantly decreased velocity

resulting from hitting the southern slope at 10 s is observed in both

cases. At 20 s, while particles on the eastern part are almost static,some particles on western part are still moving along the Ta-Lou-Wan

River with a maximum velocity of about 35–40 m/s in the SA1 landslide

simulation. Part of the velocity eld maintains high displacement rates

(about 45–50 m/s) after 20 s in the SA2 landslide simulation. The

Lushan hot spring district is almost entirely covered and destroyed by

the landslide debris in both scenario simulations.

5. Discussion

We havesimulatedtwo probable landslide scenariosat theLushanhot

spring district, based on eld investigations and borehole slip monitoring

data. Considering the complex slope geology and the likely presence of

multiple sliding surfaces, we performed additional numerical experi-

ments with different boundary conditions and parameters. In the

following, we discuss the effects of changes in the friction coef cient of

the sliding surface, the inuence of a limited sliding surface, the impact

of the landslide-dammed lakes, and the limitations of the PFC3D software

for the landslide modeling.

5.1. Effects of friction coef cient of the sliding surface

Thefriction coef cients of thesliding surface andball–ball contacts are

the most important factors in

uencing the runout distance, sliding veloc-ity anddepositionarea in thePFC3D models. Therefore, we performed ex-

periments with varying friction coef cients of 0.1, 0.2, 0.3 and 0.4 on the

sliding surface to examine theeffecton thelandslide.With increasing fric-

tion coef cient of the sliding surface, the extent of the landslide-affected

area becomes smaller in both sliding areas SA1 and SA2 (Figure 13).

When the friction coef cient of the sliding surface is 0.4, the unstable

body basically remains intact with only some debris rolling down to the

river valley. It is suggested that the unstable body will not slide down

when the friction coef cient is larger than 0.4 for the sliding areas SA1

and SA2.

Numerous studies have shown that rainfall is one of the main agents

to trigger catastrophic landslides (Terlien, 1998; Crozier, 1999; Van Asch

et al., 1999; Iverson, 2000; Crosta and Frattini, 2008; Chigira, 2009). But

PFC3D is not yet able to simulate the decrease of shear strength resulting

from the effect of water or pore pressure. The decrease of shear strength

between the detached unstable body and thesliding surface is considered

to be incorporated by reducing the friction coef cients in this study.

5.2. Effects of a limited sliding surface

Theexistence of a sliding surfaceis an important boundary condition

for a potential landslide area (Baker, 1980; Goh, 1999; Malkawi et al.,

2001; Shuzui, 2001). According to the records of inclinometers from

CGS and SWCB, a continuous sliding surface may not have formed in

the lower slope. This inference is consistent with the decreasing down-

ward movementsin thelowerportion of theslope observed in themon-

itoring boreholes, such as that of A-18 (Figure 14a). In contrast, some

monitoring data show obvious displacements concentrated at specic

depths in the middle and upper portions of the slope, such as the mon-itoring borehole of A-22 (Figure 14b).

The two scenario simulations presented in Section 4 assumed a con-

tinuous sliding surface withinthe unstable slope.However,by assuming

that the sliding surface does not exist in the lower portion of the slope,

we performed experiments limiting the sliding surface to line BB ′

(Figure 15) which is placed in the middle of the two closest inclinome-

ters showing different deformation conditions: A-22 and A-18. An ex-

perimental ball-element lled block is made below line BB′ to express

the condition that the assumed sliding surface does not extend into

the block. In the new simulations for the sliding areas SA1 and SA2,

the friction coef cient is similarly set to be 0.05 for the sliding surface.

In both cases the landslide bodies generally remain in place for 100 s

during simulation. Therefore, the slope is considered fairly stable if the

sliding surface is absent in the lower portion of the slope.Different results are obtained by shifting the downslope limit of the

well-developed slip surface from line BB′ to CC′, and having the friction

coef cient again set to 0.05 for the sliding surface. The simulation re-

sults for 100 s (Figure 16) show the landslide bodies shear through

the toe of the slope and propagate down to the valley. This means that

if the sliding surface does develop further down the slope as a result

of weathering and slope deformation, this may eventually cause a ca-

lamity in the Lushan hot spring district.

To compare the results of the simulated deformation with the sliding

surface limited down to line BB′ (Figure 15) and the actual deformation

based on borehole monitoring records, we set the “monitoring balls”

down to 75 m with 5-m intervals at the same locations of inclinometers

A-18 and A-22 (see Figure 3). The deformation patterns based on moni-

toring balls at A-18 and A-22 areshown to be similar to the actual records

Fig. 10. The lower left panel shows the distribution of monitoring balls in the sliding area

SA2.The upper panel indicates the velocity and runout path of monitoring balls labeledin

numbers for the landslide scenario of SA2. The lower right panel shows the prole of the

monitoringball velocity forthe landslide scenario of SA2.The highestvelocity (21–46m/s)

appears at 10–20 s and the monitoring balls stopat 30–40 s after the landslide starts. Like

the landslide simulation of SA1, uctuations of the monitoring ball velocities are also

observed.


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of inclinometers (see Figure14).Thedata fromA-18 (Figure14a) demon-

strate that the deformation starts at a depth about 50–55 m, while the

modeling results for the sliding areas SA1 (Figure 14c) and SA2

(Figure 14d) show the deformation at depths of about 40 m and 60 m.

The simulated deformation from the monitoring balls at the location of

A-22 indicates a sliding surface at about 45 m depth (Figure 14e), which

is similar to the observed slip depth of about 47 m from the A-22 incli-nometer records (Figure 14b). These comparisons suggest that our

PFC3D models reasonably simulate the observed eld conditions in the

northern slope of the Lushan area.

5.3. Impact of landslide-dammed lakes

Landslide-dammed lakes are commonly formed after a river valley

slope failure, and may inundate the upstream area soon afterwards.

The natural dam may be quickly breached with a rapid release of ood

and debris ow to the downstream area, causing a catastrophic event

(Costa and Schuster, 1988; Ermini and Casagli, 2003; Dong et al., 2009,

2010; Yin etal.,2009). Based on their study of 73 landslide-dam failures,

Schuster and Costa (1986) indicated that about 50% of landslide dams

will fail within 10 days.

The results of our simulations indicate that only a few buildings on

the eastern side of the Lushan hot spring district would survive a land-

slide. One of the buildings is the Lushan Police Reception, which is also

designated as an emergency refuge by the government (see Figure 8).

The slope failure scenario simulations in Section 4 indicate that two

landslide-dammed lakes will be formed for each scenario of the sliding

areas SA1 and SA2. The information on the landslide-dammed lakescaused by a potential Lushan landslide is presented in Table 3. The mor-

phology of the rock avalanche dammed lakes is based on the deposi-

tional geometry of the experimental ball-elements. Lakes s11 and s12

are caused by the landslide event of SA1 (Figure 8a), while Lakes s21

and s22 are formed after the landslide event of SA2 (Figure 8b). In all

thescenarios, thedesignated emergencyrefuge of the Lushanhot spring

district is completely ooded suggesting that the Lushan Police Recep-

tion may not be a good choice for the emergency refuge.

5.4. Limitations of PFC3D models

Here are some limitations of the PFC3D models and perspectives for

the scenario simulations of a potentially catastrophic landslide at

Lushan. Firstly, the modeled unstable slope is a complex case possibly

Fig. 11.(a) TheAA′ prolesof thevelocityeldfor thelandslidescenario of SA1at intervals of 5 s. Thevelocity of thefrontal slide body decreases dueto theimpact with theopposite valley

(southern) slope ataround10–15 s andthe landslide bodycompletely llsthevalleyand almost stopsafter20 s.(b) The AA′ prolesof thevelocityeldfor thelandslidescenario of SA2at

intervals of 5 s. The velocity is highest at the upper slope probably due to the weak bonds between particles that represent weathered slates. The velocity of the landslide body also de-

creases downslope and the movement almost stops after 20 s.


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Fig. 12. (a) Surface velocity eld of the simulated balls at intervals of 5 s for the landslide scenario of SA1. The velocity almost drops below 10 m/s after 20 s and the valley of Lushan hot

spring district is totally covered by the landslide debris. (b) Surface velocityeld of the simulated balls atintervals of 5 s for the landslide scenario of SA2. Part of the velocityeld shows

high displacement rates after 20 s in this simulation.



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Fig. 13. Simulation results for 100 s with varying values of the friction coef cients of 0.1, 0.2, 0.3 and 0.4, to illustrate its inuence on the extent of the landslide nal deposition areas.

(a) Cases for the sliding area SA1 and (b) cases for the sliding area SA2.



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involving several sliding surfaces. The distribution of the borehole mon-

itoring data is uneven, which makes it dif cult to reconstruct accurately

thegeometryof major slidingsurfaces. Nevertheless, based on theavail-

able monitoring data, the constructed failure surface shown in the cross

section (Figure 6) seems a reasonable approximation. Secondly, the

ball-elementnumber is generally not suf cient to simulate every failure

mechanism in detail. The particles may be too large in diameter to sim-

ulate exactly the potential landslide-affected area and reliably represent

rock shape. The shape-dominated failure and anisotropy of mechanical

parameters in the slate belt, in particular, should be taken into account

in future studies. Thirdly, the modeled slope is subjected to periods of

heavy rainfall and water table level variations. The present work was

not able to model the inuence of pore water pressure directly on the

sliding surface and sliding mass. This is the major limitation that the

PFC model cannot simulate loss of shear strength along sliding surfaces

due to increases in pore water pressure. Instead, the decrease of shear

strength along the sliding surface mainly depends on the reduction of

the friction coef cient in the model. Therefore, estimating the critical

friction coef cient under heavy rainfall conditions is a crucial topic for

future applications of PFC3D in studies of catastrophic slope failure.

Fig. 14. The eld inclinometer records shown as depth vs. displacement during (a) Typhoon Sinlaku (A-18) and (b) Typhoon Morakot (A-22) [adapted from Lin et al., 2010]. Depth vs.

displacement patterns at borehole A-18 site resulting from the landslide simulations for the sliding areas (c) SA1 (see Fig. 14a) and (d) SA2 (see Figure 14b). (e) Depth vs. displacement

pattern at borehole A-22 site resulting from the landslide simulation for the sliding area SA2 (see Figure 14b).


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Fig. 15. Slope failure simulation resultswith a limitedsliding surfaceas indicated by thevertical dashed lineB, which is also shown as lineBB′ in theinset aerialphoto.The experimentally

lled block is used to model the condition in which the sliding surface does not continue into the block. (a) Case for the sliding area SA1 and (b) case for the sliding area SA2.

Fig. 16. Slope failure simulation resultswith a limitedsliding surfaceas indicated by thevertical dashed lineC, which is also shown as lineCC′ in theinset aerialphoto.The experimentally

lled block is explained in Fig. 15. (a) Case for the sliding area SA1 and (b) case for the sliding area SA2.


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6. Conclusions

Landslides are one of the most serious natural hazards in the moun-

tainousareas of Taiwan. For several years,the potential landslidearea at

Lushan in central Taiwan has been monitored through many borehole

inclinometers. The data provide valuable information about slip geome-

tries for predicting landslide-affected areas using a 3D discrete element

method, such as the PFC3D modeling used in this study. Our simulation

results clearly display scenario-based landslide runout paths and indi-

cate that, considering the worst case scenario, theLushanhot spring dis-

trict may be rapidly destroyed by landslide debris and ooding by two

landslide-dammed lakes. Forecasting landslide-affected areas is usually

dif cult because of many poorly constrained or even unknown input

factors. The PFC3D method is useful in modeling landslides but has lim-

itations in modeling all complex mechanisms of landslide. This study

emphasizes catastrophic slope failure under heavy rainfall conditions

given uncertain dynamics in shear strength, and does not address spe-

cic conditions (i.e., pore pressure, rainfall volume and duration) for

the catastrophic slope failure to occur. We modeled catastrophic land-

slide behaviors by the PFC3D method given a range of friction coef -

cients and varied continuity of the failure surfaces. Because the shear

strength along the sliding surface depends solely on the friction coef -

cient, estimating the critical friction coef cient will be a crucial topic

for future applications of PFC3D in landslide studies. While guidelines

on landslide mitigation require further studies, the present work pro-

vides potential runout paths, particle velocities and landslide-affected

areas, which are useful information for decision support and future

landslide hazard assessment.

Acknowledgements

We thank the Soil and Water Conservation Bureau and Central Geo-

logical Survey in Taiwan for providing the valuable slip monitoring data

for this study. We thank Profs. Ming-Lang Lin, Chyi-Tyi Lee, Jia-Jyun

Dong, Kuang-Tsung Chang, Kou-Jen Chang, as well as Mrs. Hsi-Hung

Lin and Yu-Chung Hsieh for their helpful discussions during the study.

We thank Prof. Janusz Wasowski for greatly improving an earlier ver-

sion of the manuscript. The constructive comments and suggestions

by the reviewers are very much appreciated. We would like to dedicate

this work to the memory of our co-author Dr. Chao-Lung Tang who

passedaway a fewmonthsago forhis enthusiasm andimportant contri-

bution in applying the PFC3D method for landslide simulation inTaiwan. This study is supported by the Taiwan Ministry of Science and

Technology funding Nos. 98-2745-M-001-006, 103-2116-M-001-002

and the Institute of Earth Sciences, Academia Sinica (Contribution No.

IESAS1903).

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Table 3

Geometric information of the dammed lakes for the sliding area SA1 (lakes S11 and S12)

and for SA2 (lakes S21 and S22).

Dammed

lakes/Lake information

Height of

overow (m)

Maximum

depth (m)

Area

(m2)

Volume

(m3)

Lake s11 1120 43 134,000 2,326,000

Lake s12 1142 57 105,000 2,373,000

Lake s21 1118 38 110,000 1,779,000

Lake s22 1138 52 86,000 1,881,000


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