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Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
41
DOI: 10.4408/IJEGE.2013-06.B-03
THERMALLY VS. SEISMICALLY INDUCED BLOCK DISPLACEMENTS
IN JOINTED ROCK SLOPES
Y
ossef
H. HATZOR
(*)
& D
agan
BAKUN MAZOR
(**)
(*)
Ben-Gurion University of the Negev - Dept. of Geological and Environmental Sciences - Beer-Sheva, Israel
(**)
Sami Shamoon College of Engineering - Dept. of Civil Engineering, SCE - Beer-Sheva, Israel
INTRODUCTION
It is commonly assumed that large landslides in
rock masses are triggered by a strength failure mecha-
nism either within the body of the rock material in the
case of weak rocks, or along a pre-existing sliding in-
terfaces in the case of strong rocks. Therefore, typically
a static limit equilibrium analysis is employed to study
the stability of rock slopes and the shear strength param-
eters are assumed constant over time. In this paper we
explore the long term stability of a potentially unstable
rock slope by considering two, time dependent, weaken-
ing mechanisms. The first is velocity weakening of the
shear strength of the sliding interface induced by repeat-
ed cycles of shaking which could be triggered by strong
earthquakes. The second is accumulated displacements
along a gently dipping sliding plane due to irreversible
opening of a steeply dipping tension crack at the back
of the sliding mass. We present a model for thermally
induced ratcheting of the tension crack which leads to
progressive displacement of the sliding block over time
due to repeated seasonal temperature fluctuations. We
show that for a seismically active region with high tem-
perature gradients as the Dead Sea rift valley, the ther-
mal mechanism may be more dominant than the seismic
mechanism, provided that the friction angle along the
sliding plane remains constant between earthquake epi-
sodes. We therefore conclude that the thermally induced
ratcheting mechanism is a viable failure mechanism in
rock slopes and it must be considered when assessing
the overall stability of jointed rock slopes.
ABSTRACT
We explore two landslide triggering mechanisms
that are associated with time-dependent, cyclic loading
of the sliding interface. The first is shear strength degra-
dation due to seismic shaking leading to velocity weak-
ening of the sliding interface. We show how a block
that is initially at a state of static limit equilibrium under
constant gravitational load may undergo sliding at in-
creasing velocities when subjected to cyclic vibrations
and demonstrate, using shaking table experiments, how
the observed shear strength degradation may lead to
block run out. The second is sliding initiation due to
cycles of seasonal heating and cooling of the jointed
rock mass. We demonstrate, using field measurements,
analytical and numerical approaches, how repeated cy-
cles of heating and cooling may trigger block sliding
along an inclined sliding plane via a thermally induced
ratcheting mechanics in the sub vertical tension crack.
We show that for Masada rock mass the thermal mecha-
nism may lead to a faster sliding rate than the seismic
mechanism for a given regional seismicity and climatic
conditions for a time window of 5000 years when the
shear strength of the sliding plane is considered con-
stant over time. We therefore conclude that thermally
induced sliding must be considered when studying the
stability of rock slopes that are exposed to strong tem-
perature changes between the seasons.
K
ey
words
: landslides, seismic response, climatic response,
rock slopes, DDA, shaking table
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Y.H. HATZOR & D. BAKUN MAZOR
42
International Conference on Vajont - 1963-2013 - Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
To demonstrate the response of a wedge to a real
earthquake the input motion is replaced with the Impe-
rial Valley earthquake record as recorded at El Centro,
California, and the resulting dynamic displacement of the
wedge is shown in Fig. 3. The step wise block response to
the dynamic excitation is clearly shown in Fig. 3 as well.
FRICTION ANGLE DEGRADATION INDU-
CED BY SHAKING
To further study the dynamic sliding of a wedge a
physical model as shown in Fig. 4 was mounted on a
DYNAMIC BLOCK DISPLACEMENT
The dynamic displacement of a block on an in-
clined plane has been studied by Newmark (n
ew
-
mark
, 1965) and Goodman and Seed (g
ooDman
&
s
eeD
, 1966) who showed that once the acceleration
of the block exceeds the yield acceleration dynamic
block displacement commences in a step wise fashion.
In Figure 1 the dynamic displacement of a block rest-
ing on an inclined plane with a dip of 20 degrees and
a friction angle of 30 degrees is plotted for three dif-
ferent methods of analysis, namely the classical New-
mark’s and Goodman and Seed solutions (referred to
here as Newmark solution for brevity), a three dimen-
sional analytical vector solution developed by Bakun-
Mazor et al. (B
akun
-m
azor
et alii, 2012), and results
obtained with the numerical 3D-DDA (s
Hi
, 2001). The
input motion is sinusoidal in direction parallel to the
dip of the sliding plane and is shown as well.
Using the three dimensional generalization of the
Newmark’s approach the dynamic displacement of
a wedge which rests on two inclined planes can be
studied as well. In Fig. 2 the dynamic displacement
of a wedge resting on two planes dipping to 52/063
and 53/296 and subjected to a sinusoidal input motion
vector given by:
(1)
is plotted. The line of intersection of the two planes
dips 30 degrees and the friction angle on both planes
is 20 degrees.
Fig. 1 - The typical step-wise dynamic displacement of a
block subjected to sinusoidal input motion
Fig. 2 - Dynamic displacement of a wedgesubjected to si-
nusoidal input motion
Fig. 3 - Dynamic displacement of a wedge subjected to
the Imperial Valley earthquake (Lower panel) up-
scaled by a factor of 5
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THERMALLY VS. SEISMICALLY INDUCED BLOCK DISPLACEMENTS IN JOINTED ROCK SLOPES
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
43
clearly obeys the Coulomb-Mohr shear strength cri-
terion when tested under a constant sliding velocity,
but with increasing testing velocity the coefficient of
friction clearly decreases (see Fig. 8).
When the interface was tested at much higher
sliding velocities in the shaking table experiments the
same velocity weakening behavior was observed, up
to six orders of magnitude of velocity (see Fig. 9).
A very interesting phenomenon was observed
however during many shaking table experiments. Once
dynamic sliding was initiated, the classical step wise
shaking table with a single degree of freedom aligned
with the direction of the line of intersection of the two
inclined planes. The shaking table assembly is shown in
Fig. 5 and Fig. 6.
The concrete interface material was tested in a
servo-controlled direct shear system where both nor-
mal and shear pistons were servo-controlled under
either load or displacement control. Several velocity
stepping tests were performed and it was established
that the interface material clearly exhibits velocity
weakening characteristics. An example of four veloc-
ity stepping segments obtained with the servo-control-
led direct shear assembly is shown in Fig. 7.
Moreover, the tested concrete interface material
Fig. 4 - Physical model of a wedge which was mounted on
a shaking table
Fig. 5 - Shaking table assembly used in this research
Fig. 6 - Direct shear assembly used in this research
Fig. 7 - Results of velocity stepping tests obtained with the
direct shear assembly
F
ig. 8 - A) Example of a segment direct shear test with a
constant imposed sliding velocity, B) Coulomb-
Mohr failure envelopes for increasing levels of
imposed sliding velocities
Fig. 9 - Velocity weakening of the tested interface from
slow (direct shear) to high (shaking table) impo-
sed sliding velocities
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Y.H. HATZOR & D. BAKUN MAZOR
44
International Conference on Vajont - 1963-2013 - Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
which is determined by the available friction angle of
the sliding interface. We have also seen that the nomi-
nal value of the friction angle degrades as a response
to shaking, and that when the sliding mass is at a state
which is close to limiting equilibrium shaking induced
friction angle degradation may lead to block run out.
In this section we present another source of block
instability that is derived from temperature fluctuations.
Consider the model of a block shown in Fig. 11 where
the tension crack is filled some detrital material from
the surrounding rock mass.
displacement was only observed up to a certain point,
beyond which block run out was detected. An example
of such an experimental output is shown in Fig. 10.
Inspection of Fig. 10 reveals that a friction angle
degradation amounting to only 2.5 degrees was suf-
ficient to prompt block run out. There are two pos-
sible sources for the observed friction degradation:
either due to accumulated displacement, as originally
proposed by Goodman and Seed (g
ooDman
& s
eeD
,
1966), or due to sliding velocity, as originally pro-
posed by Dieterich (D
ietericH
, 1972). Either way,
our experimental results clearly suggest that frictional
degradation does take place as a consequence of dy-
namic shaking of discrete blocks resting either on a
single infinite plane or on two planes in the form of a
wedge. When the discrete blocks are close to a state
of limiting equilibrium under static conditions, strong
ground motions induced by earthquake could rapidly
reduce the available shear strength below the value re-
quired for static stability and consequently sliding will
commence. When the sliding interface exhibits veloc-
ity weakening characteristics, once sliding is initiated
the sliding velocity could increase progressively, cul-
minating in a catastrophic landslide.
THERMAL TRIGGERING OF BLOCK DI-
SPLACEMENT
We have seen in the previous section the typical
downslope stepwise block displacement triggered by
dynamic shaking whenever the input acceleration ex-
ceeds the yield acceleration required for sliding, a value
Fig. 10 - Example of an experimental output from the
shaking table experiments of the concrete wedge
block. Sinusoidal input motion at 2 Hz frequency
and 0.21 g amplitude. The back calculated friction
angles for the run-out segments are also shown
Fig. 11 - Model of a block resting on a shallowly dipping
sliding plane with a tension crack at the back that
is filled with some debris. Sd is the “thermal skin”
depth
Fig. 12 Proposed thermally-induced ratcheting mechanism
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THERMALLY VS. SEISMICALLY INDUCED BLOCK DISPLACEMENTS IN JOINTED ROCK SLOPES
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
45
ture difference between the seasons (∆T). The predicted
seasonal plastic displacement that would be obtained
by Pasten’s model for a dolomitic rock mass for three
different sliding plane inclinations under maximum
temperature difference of 20° is shown in Fig. 13. It is
worthwhile to point out here that dolomite has a rela-
tively high thermal expansion coefficient in comparison
to other rock types and therefore it is more susceptible
to the thermally induced ratcheting mechanism.
To test the viability of the analytical model predic-
tions let us examine the temperature fluctuations and the
resulting tension crack response in the dolomitic rock
mass of Masada world heritage site which is used here
as a case study. The opening and closure of several clean
and tight joints at the western slope of Masada mountain
were monitored over a period of several years as a func-
tion of temperature (B
akun
-m
azor
et alii, 2013). The
layout of the monitoring system is shown in Fig. 14. The
joint meter and temperature outputs for one annual cy-
cle, from May 2010 to May 2011, are shown in Fig. 15.
The left panel of Figure 15 shows the raw data whereas
the right panel shows the same data after correction for
electrical drift that was detected by comparison to the
output of the neutral transducer that was mounted on an
intact rock surface (WJM4). Inspection of the data pre-
sented in Fig. 15 reveals that the maximum temperature
difference over an annual cycle at Masada is indeed in
For a given annual temperature cycle from the
warm to the cold period the sliding block is expected
to undergo much more thermal strain in comparison to
the rock mass material because of its much smaller size.
Consequently, during the cold season the sliding block
is expected to experience shortening and as a result the
tension crack is expected to open slightly. The climati-
cally controlled opening of the tension crack will al-
low penetration of the fragments dipper into the ten-
sion crack as schematically illustrated in Fig. 12 with a
wedge block that represents the detritus. When the sea-
son changes to the warm season, the sliding block will
experience elongation prompting closure of the tension
crack. But since the wedge block has already penetrated
into the tension crack, the sliding block will be forced
to move downslope incrementally (see Fig. 12). This
process will be repeated from one season to the next,
leading to cumulative downslope block displacement,
the magnitude of which depends on the amplitude of
the thermal fluctuation between the seasons in the re-
spective region, the thermal conductivity, and thermal
expansion coefficient of the rock.
Pasten (P
asten
, 2012) developed an analytical solu-
tion for the expected “plastic” downslope displacement
of a block subjected to the thermally induced ratchet-
ing mechanism over one annual cycle, once the elastic
displacement due to asperity shortening (scaled by the
shear stiffness of the sliding plane), has been overcome.
In addition to the geometrical variables shown in Figure
11, Pasten’s solution depends on the Young’s modulus
of the rock material, the shear stiffness of the sliding
interface, the thermal conductivity and thermal expan-
sion coefficient of the rock, and the maximum tempera-
Fig. 13 - One cycle plastic displacement for three plane in-
clination angles η for a dolomitic limestone with
maximum temperature difference between seasons
of 20° (P
asten
, 2012). For definition of LW and LB
see Fig. 11
Fig. 14 - Joint displacement and temperature monitoring
campaign at the west slope of Masada mountain
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Y.H. HATZOR & D. BAKUN MAZOR
46
International Conference on Vajont - 1963-2013 - Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
the vicinity of 20°. Moreover, the relationship between
temperature increase and joint closure (negative joint
meter output) and between temperature decrease and
joint opening (positive joint meter output) is clearly por-
trayed in Fig. 15.
COMPARISON BETWEEN THE SEISMICALLY
AND THERMALLY INDUCED DISPLACE-
MENTS
It is interesting to compare between the sources of
instability discussed above and ask: in a given region
where everything else is kept equal, which mecha-
nism would amount to a greater block displacement
over time? To try and address this question we use a
single discrete block in the East slope of Masada that
is shown in Figure 16 with geometrical dimensions
similar to those shown in Fig. 11.
Let us consider a time window of 5000 years dur-
ing which the east slope of Masada can be safely as-
sumed to have been exposed in its current topographi-
cal and geomorphological configuration. Since its
exposure the block has undergone an accumulated dis-
placement of 200 mm, the amount of opening of the
tension crack that can be readily measured in the field
(see Fig. 16). This cumulative joint opening distance
provides a physical constraint on the total amount of
displacement that could have taken place in the past in
either one of the two triggering mechanisms discussed
Fig. 15 - Joint meter and temperature transducer output
from Masada rock slope over one annual cycle
Fig. 16 - A displaced block that was mapped in the East
slope of Masada mountain that could have been
subjected to both seismically as well as thermally
induced displacements
Fig. 17 - DDA results vs. analytical (Newmark’s) solution
for the dynamic displacement of the analyzed
Block (Figs 11, 16) when subjected to asinusoidal
input function with 0.5g amplitude and the two
dominant frequencies for Masada (H
atzor
et alii,
2004): 1.3 Hz (a) and 3.8 Hz (b). (k is the numeri-
cal contact spring stiffness used in DDA)
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THERMALLY VS. SEISMICALLY INDUCED BLOCK DISPLACEMENTS IN JOINTED ROCK SLOPES
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
47
record corrected for rock response and amplified to
the topographic site effect measured at Masada as ex-
plained elsewhere (H
atzor
et alii, 2004, B
akun
-m
azor
et alii, 2013). The assumed attenuation law for the re-
gion in terms of magnitude, distance from source, and
expected ground acceleration is adopted from (s
HaPira
et alii, 2007) and is plotted in Fig. 18. Also shown in
Fig. 18 are the “stable” and “sliding” modes of the ana-
lyzed block with respect to regional earthquake magni-
tude and distance based on pseudo-static analysis.
Inspection of Fig. 18 reveals that the relevant
earthquakes to cause seismically induced displace-
ments of the studied block are between magnitudes 6.0
and 7.5 and a distance from Masada of up to 20 km.
Using the attenuation relationship the Nuweiba earth-
quake was up-scaled so as to represent each relevant
earthquake magnitude with the corresponding accel-
erogram for input directly into the centroid of the ana-
lyzed block at top of Masada (B
akun
-m
azor
et alii,
2013). The scaled records were applied to the analyzed
block using DDA after the contact spring stiffness
value has been properly optimized, and the resulting
dynamic block displacements for single earthquake
episodes of different magnitudes at a distance of 1km
from Masada are shown in Fig. 19. Using the mapped
joint opening as a physical constraint on the numerical
results shown in Figure 19 we may conclude that the
analyzed block at the top of the east Masada cliff has
here. We can safely assume that no block run-out due
to frictional degradation has taken place because the
block exhibits a finite amount of displacement, and
therefore it would be permissible to use a constant
friction angle in the dynamic analysis.
We shall use the analytical solution derived by
Pasten (P
asten
, 2012) to compute the accumulated
displacement over time due to the proposed thermal-
ly induced ratcheting mechanism, and the numerical
discrete element DDA method (s
Hi
, 1993) to com-
pute the dynamic displacement of the block due to
shaking that is expected to have struck the mountain
during the past 5000 years.
The DDA solution is quite sensitive to the user’s
choice of the penalty value, or the so called “contact
spring stiffness” (k). Indeed, our research indicates
that the optimal k value also depends on the motion
frequency. A topographic site response study per-
formed at Masada (H
atzor
et alii, 2004) indicates that
the two dominant frequency modes of the mountain
are 1.3 Hz and 3.8 Hz. An optimization of the best
value of k for these two frequencies for the geometry
of the modeled block is shown in Fig. 17.
In order to assess the expected seismically induced
displacement of the studied block we need to consider:
1) a characteristic earthquake input motion, 2) the at-
tenuation law for the region, and 3) the recurrence times
of earthquakes of different magnitudes in the studied
region. For the input motion we use the 1995 Nuweiba
Fig. 18 - Assumed attenuation curves for Dead Sea Rift
earthquakes (s
HaPira
et alii, 2007) (dashed lines)
with amplification due to topographic site effect
at Masada (H
atzor
et alii, 2004) (solid lines and
symbols). Shaded region delineates conditions at
which seismically-induced sliding of the analyzed
block 1 at Masada (Block 1) is not possible
Fig. 19 - DDA results for dynamic displacement of the ana-
lyzed block when subjected to amplified Nuweiba
records corresponding to earthquakes with moment
magnitude between 6.0 to 7.5 and epicenter dis-
tance of 1 km from Masada. Mapped joint opening
in the field is plotted (dashed) for reference
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Y.H. HATZOR & D. BAKUN MAZOR
48
International Conference on Vajont - 1963-2013 - Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
SUMMARY AND CONCLUSIONS
We present in this paper the possibility for a ther-
mally induced wedging mechanism for rock slopes
using the monitored rock blocks at Masada Mountain,
Israel, as a case study. The thermal mechanism involves
the rock mass, a wedge filled tension crack, a sliding
block, and a sliding interface with the rock mass. We
show that for the dolomites of Masada the seasonal
temperature amplitude is sufficient to induce perma-
nent plastic displacement of rock blocks via a wedging
- ratcheting mechanism, although the blocks are situated
on relatively shallow dipping planes.
Since Masada is situated on the margins of a seismi-
cally active rift, we use numerical discrete element anal-
ysis to compute the seismically induced displacement of
the same block we use to demonstrate the thermal load-
ing mechanism and find that for the assumed seismicity
of the region, the 200 mm displacement of the studied
block is more likely to have been thermally, rather than
seismically, induced.
We conclude that the thermally induced sliding
mechanism should be considered when quantitatively
assessing surface erosion or rock slopes with thermal
and mechanical properties that permit this failure mech-
anism to take place. This mechanism may explain rock
failure episodes occurring more frequently than is gen-
erally assumed or explained.
ACKNOWLEDGEMENTS
Financial support from the U.S. - Israel Bi-na-
tional Science Foundation (BSF) through contract No.
2004122 is gratefully acknowledged. Dr. Ulrich Cors-
meier from Karlsruhe Institute of Technology is thanked
for sharing his data from the West Masada metrological
station. The Israel Nature and Parks Authority (INPA)
and Eitan Campbell from Masada National Park are
thanked for supplying the high quality photographs of
the West slope of the Mountain and for assistance in the
installation of our monitoring devices.
never been subjected to Dead Sea rift type earthquakes
with magnitudes greater than 6.5 with epicenter at a
distance from Masada greater than 1 km.
Using published forecasts for recurrence times of
earthquakes of different magnitudes in the Dead Sea
region (B
egin
, 2005) we can now compare between
the seismic and thermal loading mechanisms for a time
window of 5000 years, keeping in mind that since the
studied block has not run out we use the constant fric-
tion angle value in our analyses. The results of such a
comparison are shown in Fig. 20. Inspection of Fig. 20
reveals that the seismic loading mechanism, given the
seismicity of the region, would amount to a total of 600
mm overt a period of 5000 years, taking into considera-
tion all the earthquakes and their respective magnitudes
that could have hit the region during that period. The
thermal mechanism, however, if allowed to continue
for 5000 years, would lead to greater block displace-
ments, and at a greater displacement rate.
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THERMALLY VS. SEISMICALLY INDUCED BLOCK DISPLACEMENTS IN JOINTED ROCK SLOPES
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
49
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