Environ Earth Sci (2015) 73:275–287
DOI 10.1007/s12665-014-3423-2
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 bending, 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
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
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 geomorphic 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 geological 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 investigated 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–
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dependent behavior with slide velocity increasing before
total collapse, the characteristics of creep velocity is typically used for the time prediction of total collapse (Mufundirwa 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 deformation over decades whether induced by raining or earthquake, 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 summarized 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; Fernández-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 discontinuities 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 influence 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
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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 different aspects of slope failure processes. In the long term, both
macroscopically involve strength degradation of rocks.
Many geological structures observed in the field are associated with creep behavior of rock mass. Creep structures
can form over very large time scales including the geological 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 processing the relocation of the village. Surface investigation
shows that the strikes of cleavage range from N10 to
40E, 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 N30E/57SE.
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 Conservation 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
Environ Earth Sci (2015) 73:275–287
277
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
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. Chigira (1992) classified four types of creep structures based
on field observations (Fig. 3). Figure 4a, b are creep patterns 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–
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Fig. 3 Four types of creep patterns proposed by Chigira (1992)
Coulomb model is an elastic-perfectly plastic simple
model, and the anisotropic model can reflect the anisotropic 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
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Fig. 4 Creep structures observed in the field. a The bending type and
b Buckling type
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 weathered 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
K
ð1Þ
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
Environ Earth Sci (2015) 73:275–287
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
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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
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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
Cohesion (kPa)
44
176
3,009
Friction angle ()
37
45
38
4
27
893
338
1,527
21,984
Mohr–Coulomb parameters
Tensile strength (kPa)
Deformation modulus (MPa)
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*
Modified creep index l*
3.5E-5
1.0E-04
3.1E-5
6.0E-05
2.4E-5
1.0E06
Cohesion C (kPa)
44
176
3,009
Friction angle u ()
37
45
38
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
3
Unit weight cm (kN/m )
26
Young’s modulus E (MPa)
338
Poisson’s ratio m
0.3
Cohesion C (kPa)
44
The dilation angle is set as zero
Friction angle u ()
37
axial strain, followed by creep axial strain under the constant deviatoric stress of 300 kPa.
Tensile strength (kPa)
4
Strength reduction
The dilation angle is set as zero
The strength reduction in calculation is associated with the
stress–strain relationships of the Mohr–Coulomb and anisotropic models. From macroscopic and long time scale viewpoints, 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 development and processes of slope deformation along with the
strength reduction are of concern. The reduction factor RF is
defined as
RF ¼
tan u
C
¼
tan ur 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.
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Young’s modulus and cohesion have assumed gradients of 70 MPa/m
and 10 kPa/m from the surface to the depth
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
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281
Fig. 8 The five elastic
parameters for the anisotropic
model
z
x
y
y
E1 = /
z
z
z
1= x / z
E2 = /
x
x
y
G2 =
z
yz
/
yz
2= x / z = y / z
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 technique 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
(a)
Section A
Section B
(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
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 discontinuities 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 parallel or perpendicular to the interface is associated with
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shear strength of surrounding slate. The dark blue plunging layer is an example of exaggeration to represent a
inclined cleavage plane to see shearing along the discontinuities 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 existence of underground discontinuities as well as rock creep
behavior.
Effects of topography
(a)
Section A
Section B
Section C
(b)
Fig. 10 Simulated results using strength reduction: a selected sections and b displacement patterns at sections A, B and C. The red
represents the relatively greatest displacement on the slope
(a)
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 corresponding 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 longitudinal 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
Discontinuities
Section A
(b)
Fig. 11 Displacement patterns of shear zones with the two parallel
discontinuities
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
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Slaty cleavage is a metamorphic structure associated with
the arrangement of platy minerals that results in anisotropy, which influences not only strength but also deformation 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
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283
Fig. 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)
Slope angle: 20
Slope angle: 45
250m
250m
0
0
(a)
(b)
500m
500m
0
0
(c)
(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
3
Highly weathered slate
Fresh slate
Unit weight cm (kN/m )
26
27
Young’s modulus E1 (MPa)
338
21,984
0.3
Poisson’s ratio m1
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
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 isotropic 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 constitutive 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 displacement 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 critical 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
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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 reduction 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.
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
(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 evolution 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
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 geomorphological precursors due to the progressive development 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
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
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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
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
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
285
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 consistent 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 landslide 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 additionally influenced by groundwater, hard and weak layers,
in situ stress, and discontinuities in a complex threedimensional condition. Brideau and Stead (2012) investigated the three-dimensional influence of the orientations of
three discontinuity sets on slope failure mechanisms. Nevertheless, 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 certain thickness, which cannot reflect gradual increases of
stiffness and strength distributed perpendicularly to the
slope surface. The vertical layering and downward increases
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286
Environ Earth Sci (2015) 73:275–287
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 progressive 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 Science Council, Taiwan through the Grant NSC 99-2625-M-005-006MY3 is gratefully acknowledged.
123
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