Slope creep behavior: observations and...

ORIGINAL ARTICLE

Slope creep behavior: observations and simulations

Kuang-Tsung Chang • Louis Ge • Hsi-Hung Lin

Received: 21 December 2013 / Accepted: 7 June 2014 / Published online: 20 June 2014

� Springer-Verlag Berlin Heidelberg 2014

Abstract Rock slopes undergoing long–term effects of

weathering and gravity may gradually deform or creep

downslope leading to geological structures such as bend-

ing, bucking, fracturing, or even progressive failure. This

study uses geomechanics-based numerical modeling to

qualitatively explain the cause and evolution of slope creep

behavior. Constitutive models used include the creep,

Mohr–Coulomb, and anisotropic models. The last two

models are used with the strength reduction in calculation.

First, the results of field investigation around a landslide

site occurring in slate are present. The causes and modes of

creep structures observed on slopes and underground are

studied. Second, the study investigates the influences of

slope topography and anisotropy orientations on slope

creep behavior. Finally, progressive failure of slopes with

different shapes is examined. The simulated results show

that the bending type of structures develops near slope

surfaces, and the buckling type of structures is associated

with the deformation or slides of a slope. The creep pattern

varies with the orientation and position of an original

planar structure. The shear zone involves a joint or fracture

along which displacement has taken place. Moreover,

creep behavior is more significant on slopes with greater

height and inclination as well as on steeper portions

whether on concave or convex slopes. In addition, with the

same topographic conditions, consequent slopes with

coinciding cleavage and obsequent slopes with steep

cleavage result in greater creep behavior. Without the

effects of anisotropic cleavage, concave and straight slopes

develop failure surfaces from the crowns downwards,

whereas convex slopes develop failure surfaces from the

toes upwards.

Keywords Slope � Creep � Numerical modeling �Progressive failure � Slate

Introduction

Slope creep is the behavior describing slow downward

movements of slopes due to long term influence of gravity.

The movements may be very slow without surface geo-

morphic evidences or can result in abnormal curvature of

trees, tilt of poles, or subsidence of structures and roads.

Creep–related structures in rocks, which may take geo-

logical time to form, have been observed underground and

on outcrops. Varnes (1978) related bedrock flow to creep,

and Goodman (1993) pointed out that creep involves

movement or failure modes of sliding and toppling.

Surface displacements of creeping slopes can be inves-

tigated using extensometer, GPS, geodetic networks, aerial

photographs, LiDAR, InSAR, etc. (Wangensteen et al.

2006). Willenberg et al. (2008) examined the deformation

patterns of a slope with comprehensive investigation and

monitoring data over numerous years. Using cosmogenic

dating of deformation structures, El Bedoui et al. (2009)

estimated the surface displacement rates of a rock slope as

4–30 mm/year in the past 10,000 years and as 80 mm/year

of higher rate in recent 50 years. Because creep is a time–

K.-T. Chang (&)

Department of Soil and Water Conservation, National Chung

Hsing University, Taichung 402, Taiwan

e-mail: [email protected]

L. Ge � H.-H. Lin

Department of Civil Engineering, National Taiwan University,

Taipei 106, Taiwan

H.-H. Lin

Central Geological Survey, MOEA, Taipei, Taiwan

123

Environ Earth Sci (2015) 73:275–287

DOI 10.1007/s12665-014-3423-2

dependent behavior with slide velocity increasing before

total collapse, the characteristics of creep velocity is typi-

cally used for the time prediction of total collapse (Muf-

undirwa et al. 2010; Federico et al. 2012).

In soil and rock mechanics, creep refers to continuing

deformation of a material under constant effective stress

(Mitchell and Soga 2005; Goodman 1989). A slope may

have experienced numerous episodes of sliding or defor-

mation over decades whether induced by raining or earth-

quake, which changes effective stress states in the slope.

However, geologists and geomorphologists commonly

describe it as a creep slope as it keeps deforming without

total collapse during a period of time, ignoring the changes

of effective stress that cause the movements. For example,

Martin (2000) considered slow quasi-continuous slope

movements as creep processes for a time scale of decades.

From a macroscopic viewpoint, creep behavior implies

strength reduction of rock mass (Goodman 1993; Shin et al.

2005). For constitutive modeling of rock creep behavior,

some researchers defined strength degradation as a function

of time (Fakhimi and Fairhurst 1994; Aydan et al. 1996;

Malan 1999).

Slope creep phenomena and structures have been sum-

marized in Turner and Schuster (1996). The mechanical

behavior was studied through laboratory experiments on

rocks (Shin et al. 2005; Fabre and Pellet 2006). Dubey and

Gairola (2008) studied the influence of rock salt anisotropy

on creep behavior and mentioned that the influence

decreases in high stress levels. Furthermore, constitutive

models were developed to describe creep stress–strain

relationships (Desai et al. 1995; Shao et al. 2003). Many of

slope instability were attributed to creep behavior of rock

mass, which was incorporated in the analyses and modeling

of slope behavior (Grøneng et al. 2010; Fernandez-Merodo

et al. 2012).

Creep behavior of a rock as in laboratory experiments is

attributed to damage and strength degradation of rock. In

microscopic viewpoint, it is associated with the formation

and propagation of fractures. At the slope scale, the term

progressive failure is used to describe a slope that involves

multi-temporal movements and takes a period of time to

collapse. The gradual formation of a failure surface

involves progressive development of persistent disconti-

nuities in rock mass (Petley et al. 2005; Fischer et al.

2010). Eberhardt et al. (2005) simulated progressive

development of a failure surface in a slope with progressive

strength degradation corresponding to different degrees of

weathering. Pellegrino and Prestininzi (2007) investigated

a deep-seated deformed slope and emphasized the influ-

ence of weathering on its creep behavior. For a short time

scale or engineering context, the progressive development

of a failure surface results from the strain softening

behavior of materials. For a long time scale, progressive

development of a failure surface may be attributed to

weathering of rocks resulting in progressive strength

reduction.

Creep behavior and progressive failure describe differ-

ent aspects of slope failure processes. In the long term, both

macroscopically involve strength degradation of rocks.

Many geological structures observed in the field are asso-

ciated with creep behavior of rock mass. Creep structures

can form over very large time scales including the geo-

logical time scale and as such cannot be replicated in the

field or laboratory under normal gravity conditions.

Numerical and physical modeling provides tools capable of

explaining the creep geological structures that formed in a

long time scale. This study looks at the processes and

mechanisms of slope creep behavior in a sense of a long

time scale using the finite element numerical modeling. In

the first part, the results of field investigation around a

landslide site occurring in slate are presented, and the

causes and modes of creep structures observed on slopes

and underground are studied. The numerical modeling with

creep stress–strain behavior and strength reduction is

shown to be able to simulate the creep structures observed

in the field. The second part of the paper investigates the

influences of slope topography and anisotropy orientations

on slope creep behavior. Finally, progressive failure of

slopes with different shapes is examined.

Creep structures observed in the field

Slates are extensively distributed in the west portion of the

central ridge of Taiwan. The properties and orientations of

slaty cleavage are related to slope deformation. The studied

landslide, which is located in central Taiwan slid whenever

heavy rainfall occurred in recent decades. The unstable

mass is around 800 m long and 500 m wide and elevations

from 1,100 to 1,500 m (Fig. 1). The bedrock involved in

the rock slope creep is slate that belongs to the Miocene

Lushan Formation. The unstable slope is above a village

and gives rise to safety concern. The government is pro-

cessing the relocation of the village. Surface investigation

shows that the strikes of cleavage range from N10� to

40�E, which are not parallel to the strike of the slope face,

and the dips of the cleavage from 40� to 70� toward east.

The representative attitude is expressed as N30�E/57�SE.

The geologic section along the slide direction is shown in

Fig. 2. According to the results of geophysics refraction

exploration and borehole logs (Soil and Water Conserva-

tion Bureau of Taiwan 2006), the slope is defined as

composed of 20 m thick weathered slate near the surface

and fresh slate at bottom. The weathered slate is further

276 Environ Earth Sci (2015) 73:275–287

123

divided into highly weathered slate at upper part and

moderately weathered slate at lower part.

This study does not focus on its slide mechanism.

Instead, the creep patterns and structures observed in the

field and in the borehole logs are shown, and then these

phenomena are explained using numerical modeling. Chi-

gira (1992) classified four types of creep structures based

on field observations (Fig. 3). Figure 4a, b are creep pat-

terns observed around the surface of the landslide and

correspond to the bending type and the buckling type in

Fig. 3, respectively. Figure 5 shows other structures

observed in the field. In addition to the creep structures

observed on slope surfaces, similar phenomena are

observed underground from drilled cores around the middle

of the landslide body (Fig. 6).

Numerical modeling

The numerical modeling performed in this project utilized

the geotechnical software Plaxis (Brinkgreve et al. 2008) to

simulate the creep structures in slopes. The mathematical

model based on continuum mechanics is solved by the

finite element method. Readers may refer to Chang et al.

(2010) for brief description for the finite element method or

to Zienkiewicz and Taylor (2000) for details. As mentioned

previously, slope creep behavior may be simulated with a

creep stress–strain relationship or with strength reduction

of rock materials. In this study, the numerical modeling

involves three constitutive models: (1) creep, (2) Mohr–

Coulomb, (3) anisotropic models. The creep model can

simulate slope creep behavior directly. The Mohr–

Fig. 1 Panoramic view of the

investigated area. The geologic

section of AA0 is shown in

Fig. 2

Fig. 2 Geologic section along

AA0 in Fig. 1. The inclination of

the cleavage is apparent dip.

The data of the borehole is

shown in Fig. 6

Environ Earth Sci (2015) 73:275–287 277

123

Coulomb model is an elastic-perfectly plastic simple

model, and the anisotropic model can reflect the aniso-

tropic behavior caused by slaty cleavage or joints. Both of

them are used together with the strength reduction

calculation.

The creep model

The creep model has five main parameters. The modified

compression index k*and modified swelling index j� define

loading and unloading volumetric behavior, respectively.

The modified creep index l*defines the time dependent

creep behavior. The cohesion C and friction angle u define

strength of a material. Experiments for rock creep behavior

are mostly on weak rocks that can yield creep behavior in

relatively short time. Little information is available

regarding the creep behavior of slate.

The mechanical behavior of the three slate layers of

various degrees of weathering is estimated with reference

to the Hoek–Brown failure criterion (Hoek et al. 2002)

and the investigation report for our study site (Soil and

Water Conservation Bureau of Taiwan 2006) (Table 1).

Herein, we consider the strength properties of highly and

moderately weathered slate as residual strength according

to Cai et al. (2007). The corresponding Mohr–Coulomb

rock mass parameters are obtained using the software

RocLab (Rocscience Inc 2013) with the consideration of

stress levels. The friction angle of the moderately

weathered slate is greater than that of the fresh slate

because the relevant stress level of the moderately

weathered slate is much less than that of the fresh slate.

Despite that, the shear strength of the moderately weath-

ered slate is certainly less than that of the fresh slate. With

Young’s modulus E taken as the deformation modulus

(Table 1) and Poisson’s ratio m taken as 0.3, bulk modulus

for the three slate layers of various weathering degrees

can be estimated as K = E/[3(1-2m)]. The modified

compression index k* is determined as

k� ¼ P

Kð1Þ

where P and K are the averaged mean stress and bulk

modulus of each slate layer. Analogous to soils, j� is taken

as one fifth of k* (Brinkgreve et al. 2008). With the

assumed modified creep index l*, the parameters for the

creep model is determined in Table 2. The numerical

experiments on the highly and moderately weathered rocks

show typical creep behavior in a conventional triaxial

stress condition (Fig. 7). The rock specimens are initially

subjected to confinement of 50 kPa. Then, the axial stress

is increased to 350 kPa and yields instantaneous elastic

Fig. 3 Four types of creep patterns proposed by Chigira (1992)

Fig. 4 Creep structures observed in the field. a The bending type and

b Buckling type


123

Fig. 5 Geological structures observed in the field. a The kink fold

shows twist of the cleavage. b The large fracture speculated to form

with the coalescence of slaty cleavage and joints. c The shear zone

formed under slope deformation. d The fracture or shear zone might

be weathered and eroded out and formed the opening

Fig. 6 Borehole logs and creep

structures: the location of the

borehole is shown in Fig. 2.

a Orientations of the cleavage

and degrees of fracturing vary

along drilled cores.

b Speculated corresponding

creep structures: the reverses of

dip directions are observed in

continuous drilled cores. The

shear zones are preferably

named in view of the cores with

great degree of fracturing, mud,

fragments, and crushed quartz

grains


123

axial strain, followed by creep axial strain under the con-

stant deviatoric stress of 300 kPa.

Strength reduction

The strength reduction in calculation is associated with the

stress–strain relationships of the Mohr–Coulomb and aniso-

tropic models. From macroscopic and long time scale view-

points, creep and progressive failure of rock slopes are

attributed to strength degradation of rocks. In the numerical

modeling, strength reduction is performed through a Phi-c

reduction approach, which is commonly used for the safety

factor calculation in numerical methods. Herein, the develop-

ment and processes of slope deformation along with the

strength reduction are of concern. The reduction factor RF is

defined as

RF ¼ tan utan ur

¼ C

Cr

ð2Þ

where u is and C are the input strength parameters, i.e.,

friction angle and cohesion; ur and Cr are reduced friction

angle and cohesion in the calculation.

The Mohr–Coulomb model describes isotropic elastic

perfectly-plastic behavior with parameters shown in

Table 3. In addition, the slope model has increments of

Young’s modulus and cohesion from the ground surface to

the depth to reflect the fact that rocks behave stiffer and

stronger with reduced degree of weathering as depth

increases. According to slope height and the difference in

parameters between the highly weathered slate and fresh

slate, the gradient of Young’s modulus and cohesion are

assumed as 70 MPa/m and 10 kPa/m from the surface to

the depth. For example, the stiffness and cohesion reach

7338 MPa and 1044 kPa at a depth of 100 m. The smaller

the gradient, the more the slope deformation extending to

the depth.

The anisotropic model is used to simulate the slaty

cleavage as a set of discontinuity. It has five parameters to

Fig. 7 Numerical creep behavior of the highly and moderately

weathered slate under a triaxial stress state. The instantaneous elastic

and creep strains of the highly weathered slate are distinguished

Table 3 Parameters used in the Mohr–Coulomb model

Highly weathered slate

Unit weight cm (kN/m3) 26

Young’s modulus E (MPa) 338

Poisson’s ratio m 0.3

Cohesion C (kPa) 44

Friction angle u (�) 37

Tensile strength (kPa) 4

Young’s modulus and cohesion have assumed gradients of 70 MPa/m

and 10 kPa/m from the surface to the depth

The dilation angle is set as zero

Table 1 Estimated rock mass parameters applying the Hoek–Brown

failure criterion

Highly

weathered

slate

Moderately

weathered

slate

Fresh

slate

Hoek–Brown parameters

Intact uniaxial compressive

strength (MPa)

20 40 60

Geological strength index 13 29 70

Material constant (mi) 7 7 7

Disturbance factor (D) 0 0 0

Mohr–Coulomb parameters

Cohesion (kPa) 44 176 3,009

Friction angle (�) 37 45 38

Tensile strength (kPa) 4 27 893

Deformation modulus (MPa) 338 1,527 21,984

Table 2 Parameters used in the creep model

Highly

weathered

slate

Moderately

weathered

slate

Fresh

slate

Unit weight cm (kN/m3) 26 26.7 27

Modified compression index k* 1.8E–4 1.6E-4 1.2E-4

Modified swelling index j* 3.5E-5 3.1E-5 2.4E-5

Modified creep index l* 1.0E-04 6.0E-05 1.0E-

06

Cohesion C (kPa) 44 176 3,009

Friction angle u (�) 37 45 38

The dilation angle is set as zero


123

define elastic deformation (Fig. 8). E1 and m1 are Young’s

modulus and Poisson’s ratio for rock as a continuum. The

remaining three elastic parameters describe the behavior

influenced by the staty cleavage. Additional parameters are

cohesion and friction angle, which define the strength along

the cleavage.

Results and discussion

The first part of the results qualitatively simulates observed

creep structures of the bending type, buckling type, and

shear zones around the Lushan landslide. The creep

behavior of a slope is influenced by many factors such as

slope height and inclination, the shape of a slope, and the

anisotropic structure of rock. The second part uses simple

geometry models similar to the Lushan slope to perform a

sensitivity analysis on each of these factors.

Modeling of creep structures

The observed creep structures around the Lushan landslide

are simulated using the finite element program with the

creep constitutive model first and then the Mohr–Coulomb

one. For a time duration of 10 years, the creep behavior

yields the greatest displacement at the surface, which is red

color in Fig. 9a. Figure 9b shows that the displacement

decreases with depth in the sections. The creep pattern

corresponds to the bending type that has no defined slide

surface.

Rock slope creep structures could also be reproduced in

the numerical models using the strength reduction tech-

nique and the Mohr–Coulomb constitutive model. The

parameters are shown in Table 3. Figure 10 exhibits the

displacement pattern as strength decreases to a reduced

factor of 2.3. Sections B and C in Fig. 10b show the

bending and buckling types of creep structures. Sections A

and C with different orientations show creep patterns

differently. The creep patterns vary with the position and

orientation of an original planar structure such as foliation.

In view of the occurrence of shear zones such as those in

Fig. 6, the numerical model is further imposed with two

interfaces parallel to the slope surface to represent dis-

continuities underground (Fig. 11). The interface elements

allow for relative movement parallel or perpendicular to

the interface. Both kinds of displacements are composed

of elastic and plastic parts. The elastic displacement par-

allel or perpendicular to the interface is associated with

zx

y

zx

y

zx

y

E2 = / z

2= x / z = y / z

E1 = / z

1= x / z

G2 = yz / yz

Fig. 8 The five elastic

parameters for the anisotropic

model

(a)

(b)Section A Section B

Fig. 9 Simulated results using the creep model: (a) the greatest

displacement of around 5 cm at the surface and (b) displacement

patterns at sections A and B


123

the stiffness and the thickness of the interface. The plastic

displacement parallel to the interface occurs when the

shear stress exceeds the shear strength of the interface,

and the plastic displacement perpendicular to the interface

occurs when the normal stress exceeds the tensile stress of

the interface. The shear zones are qualitatively simulated.

The shear strength of the interfaces is defined as half the

shear strength of surrounding slate. The dark blue plung-

ing layer is an example of exaggeration to represent a

inclined cleavage plane to see shearing along the discon-

tinuities of weakness. The simulated results (Fig. 11) with

a strength reduction factor of 2.3 mimic the shear zones in

Fig. 6, the cause of which may be attributed to the exis-

tence of underground discontinuities as well as rock creep

behavior.

Effects of topography

The sensitivity to the topography investigated includes

varying the slope height, inclination, and slope shapes. The

numerical models vary in slope heights of 250 and 500 m

as well as slope inclinations of 20� and 45�. The surface

rock is the moderately weathered slate with the thickness of

20 m, and the bottom rock is the fresh slate. The corre-

sponding geomechanical input parameters are specified in

Table 2. The creep model is used to compare the greatest

displacements in the four slope models after 1,000 days

(Fig. 12). The results show that for the same slope height,

greater slope inclination yields greater creep displacement.

On the other hand, when the slope inclination is fixed,

greater slope height yields greater creep displacement. That

is, slopes of larger scale or greater inclination facilitate

creep behavior.

For straight slopes, creep behavior develops from the

crown and gradually extends downwards (Fig. 12), and it is

pronounced around the crowns. The influence of the lon-

gitudinal slope curvature is investigated in Fig. 13. As in

the previous models, the state of the slope is investigated

after 1,000 days of displacement, and it has a 20 m thick

layer of moderately weathered slate on top of fresh slate.

The results show that creep behavior is likely to occur at

the toe of a convex slope but at the crown of a concave

slope. The rock slope creep behavior is concentrated at the

steeper portions of both slopes.

Effects of anisotropy

Slaty cleavage is a metamorphic structure associated with

the arrangement of platy minerals that results in anisot-

ropy, which influences not only strength but also defor-

mation behavior of rock. The structure may be thought of

infinite parallel planes of weakness, and no certain weak

plane can be determined at certain position. The studied

slope geometry is similar to the landslide site at Lushan

with height of 400 m and surface slope of 27�. The slope

stratigraphy assumes highly weathered slate of 20 m

thickness at top and fresh slate at bottom. The cleavage

structure is considered in the anisotropic model, whose

parameters are shown in Table 4. The parameters for a

continuum are Young’s modulus E1 and Poisson’s ratio m1

(a)

(b)

Section A Section B Section C

Fig. 10 Simulated results using strength reduction: a selected sec-

tions and b displacement patterns at sections A, B and C. The red

represents the relatively greatest displacement on the slope

(a)

(b)

Section ADiscontinuities

Fig. 11 Displacement patterns of shear zones with the two parallel

discontinuities


123

with shear modulus G1 = E1/[2(1 ? m1)]. Additional

parameters are Young’s modulus E2, Poisson’s ratio m2,

and shear modulus G2 to account for the anisotropic

behavior. The anisotropy is named cross anisotropy or

transverse isotropy, in which material is isotropic within a

plane and symmetric about an axis. For slate, it is iso-

tropic in a plane of cleavage, and the axis of symmetry is

in the direction normal to the cleavage planes. From

Amadei (1996), we know that the ratios of E1/E2 and G1/

G2 are usually greater than unity, and no particular trend

for m1 and m2. Thus, the ratio of E1/E2 and G1/G2 is

assumed as 2, and m2 the same as m1 (Table 4). The

cohesion and friction angle are the Mohr–Coulomb con-

stitutive model strength parameters along the cleavage.

Six slope conditions with different cleavage orientations

are subjected to strength reduction to a factor of 3

(Fig. 14). The comparison of critical positions and dis-

placement levels are shown in Table 5. The slopes with

horizontal and vertical cleavage have critical positions near

slope toes (Fig. 14a, b). Other slope conditions have criti-

cal positions near crowns or upper portions of the slopes

(Fig. 14c–f). The cleavage dips of 30� and 60� represent

gentle and steep structures, respectively. The consequent

slope with cleavage dip of 27� represents a dip slope,

where the dips of the slope surface and of the cleavage

coincide (Fig. 14e). Among the critical positions of the six

slope conditions, lower displacement values appear at the

slopes with horizontal and vertical cleavage (Fig. 14a, b),

the obsequent slope with gentle cleavage (Fig. 14c), and

the consequent slope with steep cleavage (Fig. 14f).

However, it is noted that deep slide may evolve from the

crown in the consequent slope with steep cleavage

250m

0

250m

0

0 0

500m500m

(a) (b)

(c) (d)

Slope angle: 20 Slope angle: 45Fig. 12 Displacements after

1,000 days of creep. The red

represents the relatively greatest

displacements in the slopes,

which are 1.1 cm in (a), 3.1 cm

in (b), 1.6 cm in (c), and 3.6 cm

in (d)

Fig. 13 Displacements in the convex and concave slopes after 1,000 days of creep. The red represents the relatively greatest displacements in

the slopes

Table 4 Parameters used in the anisotropic model

Highly weathered slate Fresh slate

Unit weight cm (kN/m3) 26 27

Young’s modulus E1 (MPa) 338 21,984

Poisson’s ratio m1 0.3 0.3

Young’s modulus E2 (MPa) 169 10,992

Poisson’s ratio m2 0.3 0.3

Shear modulus G2 (MPa) 65 4,228

Cohesion C (kPa) 44 3,009

Friction angle u (�) 37 38

The dilation angle along the planes of weakness is set as zero


123

(Fig. 14f). The Lushan landslide is of this type, where the

slide surface evolved along the cleavage from the crown of

the slope (Fig. 2). The great dip of the cleavage in the

consequent slope enables the development of a deep slide

surface, but it has not yet extended to the lower slope. On

the other hand, the results show that anisotropy plays an

important role in the obsequent slope with steep cleavage

(Fig. 14d) and the dip slope (Fig. 14e), which yield much

greater displacements than other slope conditions.

Progressive failure

Progressive failure is studied using the Phi-c reduction

approach to approximate rock degradation. The stress–

strain behavior is defined as the Mohr–Coulomb model

with the parameters of highly weathered slate at the surface

(Table 3). Straight and concave slopes show similar evo-

lution processes of failure (Fig. 15). For the straight slope,

the displacements concentrate at the crown of the slope as

the reduction factor increases to 1.3. The deformation

extends to the middle of the slope at a reduction factor of

1.6. The slide surface further develops to the lower slope as

the reduction factor reaches 2.4. Similarly, the concave

slope has initial displacements or deformation at the crown,

which is the steeper portion of the entire slope. The

deformation extends downwards with further strength

reduction, eventually forming a continuous failure surface.

Convex slopes, which may be caused by expeditious

undercutting of rivers or uplift of mountains are not as

common as straight and concave slopes. The initial strength

reduction results in the displacements concentrated near the

toe of the convex slope (Fig. 16). Further strength reduc-

tion results in the deformation or displacements towards

upslope until the formation of a continuous through going

failure surface. Unlike the straight and concave slopes,

with the degradation of rock the failure surfaces develop

upwards from the toes of convex slopes.

Discussion

Rock slope creep behavior is a process of slope failure, and

recognition of its geomorphic expression may be useful for

the prediction of the time of slope collapse. Deep-seated

landslides are commonly controlled by geologic structures.

The formation of the slide surfaces may be progressive

through a period of time before total collapse. The geo-

morphological precursors due to the progressive develop-

ment of a large-scale slide surface can help delineate areas

that are prone to a catastrophic landslide.

The numerical results from the creep constitutive model

and from the Mohr–Coulomb constitutive model with

strength reduction show the same trend of rock slope creep

behavior. In other words, the initial critical position

appears at the crowns of straight and concave slopes,

whereas it appears at the toes of convex slopes. Apart from

the convex slopes, which are unusual and generally near

rivers, it is believed that the slide surfaces of deep-seated

landslides evolve from the crowns of slopes and extend

downwards if slope masses are homogeneous without the

influence of discontinuities or defects. Margielewski

(2006) also mentioned that most head scarps of the studied

landslides form at heads of valleys along a joint set. The

initiation of a slide surface may cause scarps on slope

surfaces, and the downward movements of the upper slope

Fig. 14 Deformation after strength reduction. The orientations of

cleavage are a horizontal, b vertical, c 30� in the obsequent slope,

d 60� in the obsequent slope, e parallel to the surface of the

consequent slope as 27�, and f 60� in the consequent slope. The red

shows positions where relatively greatest displacements occur

Table 5 Effects of cleavage orientations on slope creep behavior

Inclination of cleavage with respect to the slope

Horizontal Vertical Obsequent 30� Obsequent 60� Consequent 27� Consequent 60�

Critical position Around toe Around toe Around crown Upper portion Upper portion Upper portion

Greatest displacement 2 9 10-3 m 5 9 10-3 m 6 9 10-3 m 0.73 m 2.7 m 6 9 10-3 m


123

compress the lower slope, resulting a slight convex shape at

that section. The Lushan slope is the case (Fig. 2).

Therefore, scarp or subsidence may be signs of movements

at top of a potential slide body and thought of precursors of

large-scale landslides. The time of collapse depends on

when a slide surface extends to its lower slope, which is

influenced by the geologic structures, speed of weathering,

fracturing of rock mass, the magnitude of triggering, etc. In

view of the great uncertainty, monitoring of a potential

landslide will be helpful. After the movements at the upper

slope, the monitoring should concentrate more on the lower

slope. When the displacement rate at the lower slope

becomes greater than before, the fractures underground

coalesce and the slide body is ready to collapse (Petley

et al. 2005). A critical displacement rate will be reached

where the slope can be regarded in imminent danger of

rapid and catastrophic collapse. The critical displacement

rate on a slope surface may depend on the lithology of

rocks, thickness of a weak or slide layer, depth of a slide

surface, stress levels, etc.

The results of the slope stability analyses with anisotropic

structures show that dip slopes and obsequent slopes with a

steep anisotropic structure yield greater displacements

under the same strength reduction (Table 5). This is con-

sistent with that sliding and toppling are two of the most

commonly reported failure mechanisms. With the same rate

of weathering and critical displacement, dip slopes and

obsequent slopes with a steep anisotropic structure have

more possibility than other slopes to yield displacement

greater than the critical displacement, leading to landslides.

For obsequent slopes, creep behavior is pronounced and

antiscarps are common on slope surfaces (Bovis and Evans

1996; Jarman 2006). Qi et al. (2010) pointed out that land-

slide events were more frequent at consequent slopes and

obsequent slopes during the 2008 Wenchuan earthquake.

Dip slopes with the favorable anisotropic structure may

form deep-seated landslides. On the other hand, obsequent

slopes with the steep anisotropic structure may be prone to

shallow landslides unless additional discontinuities or joints

of favorable orientation form a deep failure surface.

For simplicity, the numerical modeling only considers

the effects of topography and anisotropy in two dimensions.

In a large natural slope, slope creep behavior may addi-

tionally influenced by groundwater, hard and weak layers,

in situ stress, and discontinuities in a complex three-

dimensional condition. Brideau and Stead (2012) investi-

gated the three-dimensional influence of the orientations of

three discontinuity sets on slope failure mechanisms. Nev-

ertheless, they did not consider the influence of the basal

discontinuity dip angle, and the spacing of discontinuities

had to be specified in the distinct element modeling. The

slaty cleavage is thought of infinite planes of weakness that

causes anisotropic behavior, and the persistence of the

cleavage is much more pronounced than that of joints. In

addition, a natural slope has highly weathered rock on the

surface and gradually less weathered rock distributed below

the surface. The simulations using the creep model and

anisotropic model need to specify weathered layers of cer-

tain thickness, which cannot reflect gradual increases of

stiffness and strength distributed perpendicularly to the

slope surface. The vertical layering and downward increases

Fig. 16 Displacements of the convex slop after strength reduction at

a RF = 1.3, b RF = 1.6, and c RF = 1.9. The red represents the

relatively greatest displacements in the slopes

Fig. 15 Displacements after strength reduction. The straight slopes at

a RF = 1.3, b RF = 1.6, and c RF = 2.4. The concave slopes at

d RF = 1.1, e RF = 1.4, and f RF = 1.7. The red represents the

relatively greatest displacements in the slopes


123

of stiffness and cohesion in the Mohr–Coulomb model are

expected to approximately reflect field conditions.

The numerical modeling involves several constitutive

models and slopes of great height, in which stress levels

vary greatly from slope surface to the bottom. The model

parameters are based on a review of the published literature

and with careful assumption. However, the study does not

aim at quantified numerical results, but to simulate some

creep structures and show how slope creep behavior is

influenced by slope height and inclination, the shape of a

slope, and the anisotropic structure of rock.

Conclusions

Creep behavior describes strain under constant effective

stress. It applies to the long term behavior of slopes under

gravity while being affected by the weathering of rock

mass leading to degradation of rocks. The variation of

cleavage orientations may be partly attributed to slope

creep behavior. The numerical modeling with the creep

model and the strength reduction approach is first used to

simulate the phenomena or creep patterns observed around

the Lushan landslide site. Then, the study is extended to the

influence of slope height and inclination, the shape of a

slope, anisotropic geologic structures, as well as progres-

sive development of failure surfaces. Other features

obtained from the numerical modeling are as follows.

• The bending type of structures commonly develops

near the slope surface, and the buckling type of

structures is associated with the deformation or slides

of a slope. The creep pattern depends on the orientation

and position of an original planar structure in the

deformed slope. In addition, the shear zone involves a

joint or fracture along which sliding has occurred.

• Topography has influence on slope creep behavior.

Slopes with greater inclination or height result in greater

creep behavior. Moreover, creep is more pronounced at

the steeper portions of either concave or convex slopes.

• With the same topographic conditions, the orientation

of an anisotropic geologic structure influences creep

behavior as well. Consequent slopes with coinciding

cleavage and obsequent slopes with steep cleavage

result in greater creep behavior.

• Without the effects of anisotropic structures, failure

surfaces develop downwards from the crowns of

straight or concave slopes, whereas they develop

upwards from the toes of convex slopes.

Acknowledgments Support for this research by the National Sci-

ence Council, Taiwan through the Grant NSC 99-2625-M-005-006-

MY3 is gratefully acknowledged.

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