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Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
193
DOI: 10.4408/IJEGE.2013-06.B-16
THERMO-HYDRO-MECHANICAL ANALYSIS
FOR THE SIMULATION OF RAPID SLIDING PROCESS
IN A NEW AND FAST RING SHEAR PROTOTYPE
V
ictor
SERRI, E
nriquE
ROMERO, A
ntonio
LLORET, J
osEp
SURIOL & E
duArdo
E. ALONSO
Universitat Politècnica de Catalunya - Department of Geotechnical Engineering and Geosciences
Campus Nord UPC, Building D2 c/ Jordi Girona 1-3 - 08034 Barcelona, Spain
mechanical formulation, applied to the ring shear test,
is proposed in the paper to study pore water pressure
build up and dissipation in a sliding surface being
heated by the frictional work induced by the motion.
Particularly, the proposed model is applied to simulate
the evolution of the shear strength along the sliding
surface during a fast sliding process.
K
ey
words
: thermo-hydro-mechanical analysis, fast landsli-
de, fast sliding ring shear apparatus
INTRODUCTION
If a planar slide loses the conditions for strict
equilibrium an accelerated motion will start. A simple
dynamic calculation involving a rigid block sliding on
an inclined base shows that, if the equilibrium is bare-
ly lost (i.e., the driving force exceeds the resisting one
by a small amount), the increase of sliding velocity
develops at a relatively slow rate. Some case records
indicate, however, that very high velocities may de-
velop in relatively short sliding distances.
For fast sliding, the case of Vajont is an impor-
tant reference. The failure surface had an "open L"
shape, which made even more difficult to explain
why it reached such a high sliding velocity (about
100 km/h) in no more than 30 s (H
Endron
& p
At
-
ton
, 1985). In this case, the recorded slide motions in
the last few months indicated equilibrium conditions
were close to the critical ones (n
onVEillEr
, 1987).
Basically, relatively small changes in pore water
ABSTRACT
Vajont was a case of an extremely fast landslide
and efforts to clarify the failure have been mainly
concentrated in providing a consistent explanation
taking into account this characteristic feature. Par-
ticularly in the case of Vajont landslide, attention has
been essentially focused on the shearing properties of
the sliding surface. An accepted explanation for the
velocity reached is the thermo-hydraulic-mechanical
coupling under saturated conditions, which induces
thermal dilation and effective stress reduction due to
pore pressure build-up. Nevertheless, lack of in situ
and experimental information has become one of the
main drawbacks when trying to explain these coupled
processes. In situ information is difficult to obtain
since temperature and pore pressure development dur-
ing these fast processes are impossible of being meas-
ured. To overcome this limitation, a new fast sliding
prototype -emulating a ring shear apparatus- has been
recently developed at the Universitat Politècnica de
Catalunya (Spain). This prototype can reach relatively
high speeds along the sliding surface (up to 30 km/h)
under relatively high total vertical stresses (up to 3
MPa). Temperature and pore pressure changes can be
locally measured with miniature transducers located
close to the shear band. The design of this complex
prototype requires the use of simulation-aided tech-
niques, to help with the interpretation of the coupled
processes, as well as to estimate the maximum tem-
perature and pore pressure changes. A thermo-hydro-
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V. SERRI, E. ROMERO, A. LLORET, J. SURIOL & E.E. ALONSO
194
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
To get further experimental insight into these
processes, a new fast sliding prototype has been re-
cently developed at the Universitat Politècnica de
Catalunya (Spain). The prototype was designed
maintaining the annular shape of a ring shear appa-
ratus and incorporating electronic control of torque
and speed to emulate force and displacement control
conditions. Numerical simulation tools were used to
better understand the thermo-hydro-mechanical proc-
esses occurring at the sliding surface and design the
prototype. Particularly, the present paper presents the
formulation used in these highly coupled processes,
which involve pore water pressure generation and dis-
sipation in a shear band being heated by the frictional
work induced by the sliding motion. Information on
pressures acting on the sliding surface led probably
to a reduction of the shear strength of the soil, and
as a consequence, to the acceleration of the sliding
motion. Heat-induced pore water pressure rise on
the sliding band, as suggested by (V
oigHt
& F
Aust
,
1982), has been also considered as a tentative mecha-
nism leading to the rapid sliding motion of Vajont
(V
ArdoulAkis
, 2002; A
lonso
& p
inyol
, 2010; p
inyol
& A
lonso
, 2010). A similar mechanism has been also
considered by (r
icE
et alii, 2010; r
icE
, 2006) to ex-
plain the reduction in the shear strength of faults as a
result of fast earthquake slippage. Nevertheless, lack
of in situ and experimental information has become
one of the main limitations when trying to explain
these coupled processes in fast landslides.
a)
b)
c)
Fig. 1 - New fast ring shear apparatus a) Photograph of the new prototype (metallic plate at the base 350 mm in diameter);
b) Cross-section of the apparatus; c) Zoom of the annular sample
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THERMO-HYDRO-MECHANICAL ANALYSIS FOR THE SIMULATION OF RAPID SLIDING PROCESS IN A NEW AND FAST RING SHEAR
PROTOTYPE
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
195
GOVERNING
THERMO-HYDRO-ME-
CHANICAL EQUATIONS
Geometrical conditions are axisymmetric (annular
sample shown in Fig. 2a). The problem has been sim-
plified by considering the 2D section shown in Fig. 2b
and 2c, which allows following an equivalent formula-
tion to that described in (p
inyol
& A
lonso
, 2010). The
2D section presents two main zones, separated by the
sliding surface (shear band): a static one at the top and
a movable one at the bottom (Fig. 2c).
Considering that in the sliding surface all the shear
deformation is concentrated –the effective normal
stress does not perform work–, the rate of work input
into the band is given by
(1)
where γ
f
is the shear strength of the band material with
volume V and γ=v
max
/2e the work conjugate (shear)
strain rate (2e is the band thickness and v
max
the slid-
ing velocity). It is important to remark that in the ring
shear apparatus, the velocity depends on the radius. In
this case, the velocity considered is the corresponding
to the average radius. Assuming that all the work input
has been converted totally into heat, it is possible to
write
maximum pore pressure build-up and its dissipation,
as well as temperature increase and its dissipation, are
key data for a better selection of transducers, their lo-
cation and their time response along these fast proc-
esses. The paper presents a simulation of the pore
pressure, temperature and shear strength evolutions
along the sliding surface of a synthetic fast sliding test
carried out on a low permeability material and with
the same geometry of the prototype.
FAST RING SHEAR PROTOTYPE
The ring shear apparatus has been widely used in
the analysis of slope stability, as it provides the ad-
vantage of large shear displacements –the sample can
be sheared at displacements of varying magnitude–,
there is no change in the area of the shear surface as
the test runs, and that fast rotations can be easily im-
plemented. The prototype developed at the Universitat
Politècnica de Catalunya was based on the geometry
of the cell proposed by (B
isHop
et alii, 1971) and en-
hanced - for fast landslides triggered by earthquake
- by (s
AssA
et alii, 2004). To avoid the problems due
to high centrifugal forces, the movable bottom part in-
volved a small mass of soil just to ensure the sliding
surface (B
romHEAd
, 1979). A specially adapted o-ring
ensured the waterproof condition of the cell (no radial
flow condition along the sliding surface). The equip-
ment includes an electronic control of torque or speed,
which can reach relatively high velocities along the
sliding surface (up to 30 km/h) under high total verti-
cal stresses (up to 3 MPa). Total vertical stresses (ap-
plied through an upper piston) and pore pressures are
also automatically controlled. Temperature and pore
pressure changes can be fast and locally measured
with miniature transducers located close to the shear
band. Fig. 1 presents a photograph of the prototype,
together with a cross-section and a zoom of the sam-
ple holder. The main characteristics of the equipment
are summarised in Tab. 1.
Tab. 1 Characteristics of the new fast ring shear prototype
Fig. 2 - Annular sample and 2D scheme for the analyses: a) Annular sample and rotation, b) Top and bottom parts; c) 2D
scheme (zoom of rectangle (b)
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V. SERRI, E. ROMERO, A. LLORET, J. SURIOL & E.E. ALONSO
196
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
• First law of thermodynamics (shear band) given
by Eq. (2).
• Heat balance

(4)
where c
m
is the specific heat of the saturated soil, r is
the saturated soil density and Γ is the thermal conduc-
tivity coefficient.
• Mass balance (water and solid)
(5)
where n is the porosity, β
w
the thermal expansion co-
efficient of water, β
s
the thermal expansion coefficient
of solid, α
w
the compressibility coefficient of water, m
v
is the soil compressibility coefficient, γ
w
the specific
weight of water, and k
x
and k
z
the permeability in hori-
zontal and vertical directions, respectively.
• Dynamic equilibrium
(6)
where t
uns
is the stress induced by the motor torque of
the equipment that induces shearing and M is the mass
involved in the movement.
To solve these equations it is also necessary to
consider the initial and boundary conditions (the ini-
tial excess pore pressure and velocity are null at an
initial room temperature).
NUMERICAL SOLUTION
The problem is solved using a numerical approxi-
mation. Applying the Taylor approximations, it is
possible to write an explicit model. The step forward
approximation is chosen. The derivative equations are
written as
(7)
Using the finite difference method, the heat and
mass balance equations become
(8)

(2)
where H(t) is the heat generated by friction per unit
volume and time t. The band increases its tempera-
ture as a consequence of this heating source, and pore
water pressure in excess of that initially existing de-
velops induced by thermal dilation of water. This pore
water increase, which develops at relatively small
elapsed times and under undrained conditions, reduc-
es the shear strength of the band material.
Fig. 3 shows the rectangular domain and coordi-
nates used. It represents half of the domain considered
in Fig. 2c for symmetrical reasons (z axis directed
normal to the band plane with origin located on the
mid-plane of the shear band).
The excess pore pressure u
w
(x,z,t) –essentially
caused by the thermal dilation of the water–, tempera-
ture θ(x,z,t), and velocity v(z,t) are functions of the po-
sition in both directions (x,z) and time t. For example,
the maximum excess pore pressure will be developed
in the central plane of the shear band. Other assump-
tions are considered, such as full saturation of the
porous medium and thermal conduction phenomena
(soil and metallic walls of the cell).
As a summary, the set of equations governing the
different thermo-hydro-mechanical processes are:
• Equilibrium conditions and Mohr Coulomb
shear strength law
(3)
where σ
n
is the normal (total) stress applied, p is the
hydrostatic pore pressure, u
w
(t) is the excess pore
pressure induced by heating due to soil friction and ϕ'
is the angle of internal friction.
Fig. 3 - Discretisation used for modelling the 2D section.
The domain is subdivided into n ∆Xm small ele-
ments with the dimensions ∆x and ∆z
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THERMO-HYDRO-MECHANICAL ANALYSIS FOR THE SIMULATION OF RAPID SLIDING PROCESS IN A NEW AND FAST RING SHEAR
PROTOTYPE
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
197
influence on the landslide movement.
The hypothesis considered in the simulations as-
sumes no radial flow along the sliding plane, which is
consistent with the setup of the experimental prototype
(‘o-ring’ between movable base plate and fixed top
cap). On regarding lateral heat dissipation, simulations
carried out by the authors have evidenced small lateral
heat flows –compared to the heat generated- as a con-
sequence of the fast processes involved (around 30 s).
Results for the base case with water permeability
10
-13
m/s for both shear band and sliding mass are sum-
marised in Fig. 4.
The evolution of the following variables has been-
plotted along time: excess pore water pressure and tem-
perature generated in the shear band, shear strength,
as well as sliding displacement and velocity. Some
variables have been plotted in logscale to highlight the
velocity increase with time and the consequent accel-
erated motion undergone by the slide at small elapsed
times, as well as the heat generated even at small dis-
placements. As observed in the figure, a key point in
the simulation is the selection of the shear band thick-
ness, since heat is generated in the band and not outside.
Three different shear band thickness have been selected
to perform the dynamic analyses reported here (2e rep-
resents the thickness), following the approach by (V
Ar
-
doulAkis
, 2000): e=0.5 mm, similar to the proposed
by (m
orgEnstErn
& t
cHAlEnko
, 1967; V
ArdoulAkis
,
2001; A
lonso
& p
inyol
, 2010) for clayey materials,
e=5 mm and e=50 mm. For instance, (V
ArdoulAkis
2001) proposes a thickness of 200 D
50
for clays (i.e.,
2 mm for D
50
=0.01 mm). The code has been stopped at
500 m of horizontal displacement, which is equivalent
to 100 revolutions in the ring shear cell.
In the case of e=50 mm and during the first 10
s, the generated heat due to frictional work is not
enough to increase the pore water pressure. This is
a consequence of the large band thickness. Never-
theless, as the sliding mass undergoes acceleration
(velocity increase), pore pressure build-up is able to
decrease the shear strength due to vertical effective
stress reduction. The shear strength reduces to a mini-
mum value at elapsed times larger than 25 s. The ef-
fect of reducing the thickness of the band is observed
in the figure, in which a clear increase of the velocity
is detected from the beginning. For e=0.5 and 5 mm,
the shear strength is reduced to a minimum at elapsed
times around 10 s. These results agree well with data
(9)
To obtain a stable solution, the Courant condition
must be satisfied (c
ourAnt
et alii, 1967)
(10)
To simplify the analysis, the permeability is con-
sidered the same in the two directions x and z. With the
restriction indicated in Eq. (10), it is possible to obtain
the interval ∆t used in the numerical simulation.
SIMULATION RESULTS AND DISCUS-
SION
The parameters used in the simulation are summa-
rised in Table 2. Thermal expansion coefficient, spe-
cific heat and compressibility coefficient for water and
the solid particles were taken from (o
liVEllA
et alii.
1996). A soil thermal conductivity of 1.5 W m
-1
K
-1
has
been considered according to (l
imA
et alii, 2009). Po-
rosity and residual friction angle approximate the actual
values of the Vajont sliding clay (H
Endron
& p
Atton
,
1985). The initial temperature is 20ºC. A water perme-
ability of 10
-13
m/s for a high plasticity clay with low
porosity has been considered for the base case (l
imA
et
alii, 2009). Since no precise laboratory information on
the water permeability is available, a complementary
sensitivity analysis has been performed to study how
the output of the numerical model is affected by the
uncertainty of its value. The water permeability has
been changed between 10
-13
and 10
-11
m/s (soils in the
shear band and outside the band). A vertical stress of
100 kPa - not comparable with the real case of Vajont
- has been used to show that even at low stresses these
thermo-hydro-mechanical processes develop and have
Tab. 2 - Parameters used in the simulation
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V. SERRI, E. ROMERO, A. LLORET, J. SURIOL & E.E. ALONSO
198
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
reported by (H
Endron
& p
Atton
1985, A
lonso
&
p
inyol
2010). These fast processes require miniature
and fast response pressure and temperature transduc-
ers, which should be placed as close as possible to the
sliding surface without interfering with the motion of
the bottom sliding end of the prototype. The simu-
lations of changing the water permeability between
10
-13
and 10
-11
m/s of the shear band and the surround-
ing clay indicate that essentially the same response is
obtained as in the base case.
SUMMARY AND CONCLUSIONS
A new experimental apparatus - maintaining the
annular shape of the ring shear - has been designed and
constructed to study fast sliding processes promoted
by heat induced friction. This mechanism has been an
accepted explanation for the high velocity reached in
the case of Vajont landslide. The prototype can reach
high velocity along the sliding surface (up to 30 km/h
and of the order of magnitude of the Vajont case) un-
der relatively high total vertical stresses (up to 3 MPa).
The design of this complex prototype requires the use
of simulation-aided techniques to help with the inter-
pretation of the thermo-hydro-mechanical coupled
processes, which involve pore water pressure genera-
tion and dissipation in the shear band being heated. The
paper presented the coupled formulation, the numeri-
cal solution adopted and the simplified geometry used
for the equipment. The numerical results reported that
shear strength vanishes at elapsed times around 10 s for
Fig. 4 - Simulation results for different shear band thickness with shear band permeability 10-13 m/s equal to the surrounding
clay (base case)
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THERMO-HYDRO-MECHANICAL ANALYSIS FOR THE SIMULATION OF RAPID SLIDING PROCESS IN A NEW AND FAST RING SHEAR
PROTOTYPE
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
199
ACKNOWLEDGMENTS
The authors acknowledge the financial support
provided by BIA2008-06614 research project of the
‘Subdirección General de Proyectos de Investigación’
(Ministerio de Economía y Competitividad, Spain).
relatively small shear band thickness (below 10 mm)
and low permeability (between 10
-13
and 10
-11
m/s).
These synthetic results are used to better know the lo-
cation, range, sensitivity and fast response required for
the temperature and pressure transducers, which are lo-
cated close to the sliding surface.
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