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Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
599
DOI: 10.4408/IJEGE.2013-06.B-58
EXPLORATION OF THE KINEMATICS OF THE 1963 VAJONT SLIDE, ITALY,
USING A NUMERICAL MODELLING TOOLBOX
A
ndreA
WOLTER
(*)
, M
ohsen
hAVAEJ
(*)
, L
ucA
ZORZI
(**)
, d
oug
sTEAD
(*)
,
J
ohn
J. cLAGUE
(*)
, M
onicA
gHIROTTI
(***)
& r
inALdo
gENEVOIS
(****)
(*)
Simon Fraser University - Burnaby, British Columbia, Canada
(**)
Golder Associates- Burnaby, British Columbia, Canada
(***)
Alma Mater Universitá di Bologna - Bologna, Italy
(****)
Universitá degli Studi di Padova - Padova, Italy
Col Tramontin Fault and Erto Syncline, as well as block
size, on the failure. Finally, preliminary simulations in
a new 3D lattice-spring code show that crack clusters
developed, and became concentrated in the transition
zone between the back and seat of the chair-shaped fail-
ure surface.
K
ey
words
Vajont Slide; kinematics; numerical modelling; to-
olbox approach; finite element; distinct element; lattice-spring
INTRODUCTION
The 1963 Vajont Slide, Italy is one of the most dev-
astating and significant landslides in history. Although
extensively researched over the past 50 years, certain
aspects of this catastrophic failure remain unknown.
In particular, numerical modeling methods have been
under-utilised in better understanding the kinematics
and dynamics of the failure. Most analyses of the slide
have employed a limit equilibrium approach and have
only considered two dimensions. The first model of
Vajont was a 1:200 scale physical model constructed
in 1961 to investigate the effects of a potentially cata-
strophic failure and resulting displacement wave on
the area (s
eMenZA
, 2010). Since then, few scientists
have researched the displacement wave; for example,
B
osA
& P
etti
(2011), W
Ard
& d
Ay
(2011) and V
Acon
-
dio
et alii (in this volume) show numerical simulations
of the wave. In one of the seminal works on Vajont,
h
endron
& P
Atton
(1985) conducted the first three-
dimensional stability analysis of the Vajont Slide. g
hi
-
ABSTRACT
The Vajont Slide has been studied for half a cen-
tury, yet questions about its kinematics and dynamics
still remain. Application of state-of-the-art numerical
techniques aids in understanding the slide’s mechanical
behaviour. In the current paper, we use four two- and
three-dimensional finite element, distinct element, and
lattice-spring modelling codes in a toolbox approach
to conduct a forensic, exploratory investigation of the
kinematics of the slide. We examined the influence of
rock mass properties and friction along the failure sur-
face using the 2D finite element code. Preliminary re-
sults indicate that weaker units within the sliding mass
deformed more than stronger units, and that a Prandtl
wedge zone of transition developed between the active
upper and passive lower blocks of the slide mass in the
west. The difference between the biplanar western slid-
ing surface and the more circular eastern surface proves
to be significant in terms of stability. Models suggest
a critical friction angle of approximately 18°, above
which the slope is stable. The 2D distinct element mod-
elling results indicate that both failure surface morphol-
ogy and block size are important. Planar and arc-shaped
failure surfaces are most unstable, whereas rough undu-
lating surfaces are stable. As block size increases, over-
all slope stability increases and a lower friction angle
along the failure surface is required to initiate sliding.
Block kinematics were further investigated using a 3D
distinct element code. This numerical code illustrated
the controls of bounding structural features such as the
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A. WOLTER , M. HAVAEJ, L. ZORZI, D. STEAD, J.J. CLAGUE, M. GHIROTTI & R. GENEVOIS
600
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
h
endron
& P
Atton
(1985), may be important. Numer-
ous studies discuss the clay properties, but only h
en
-
dron
& P
Atton
(1985), t
ikA
& h
utchinson
(1999),
and F
erri
et alii (2011) have published laboratory re-
sults of geomechanical properties. Several of the origi-
nal reports, such as
MüLLer
(1968) neglected the clays,
as they were thought to be insignificant.
At present, a still debated characteristic of the Va-
jont Slide is the thickness of the shear zone. The gener-
ally accepted model is that hypothesised by Rossi and
Semenza (in h
endron
& P
Atton
1985) based on cross-
sections which show a discrete primary failure surface
and several secondary shear surfaces. Recently, P
Aro
-
nuZZi
& B
oLLA
(2012) proposed that the shear zone
could have been over 100 m thick.
In this paper, we provide the preliminary results
of four, two- and three-dimensional numerical codes
used in a forensic analysis of the kinematics of the Va-
jont Slide. None of the models should be interpreted
as an accurate representation of actual conditions, but
rather as an aid in examining the effects of different
material properties, discontinuity networks, and slope
geometries on failure. Although groundwater, a critical
aspect of the Vajont Slide, is not explicitly considered
in these preliminary simulations, we approximate its
effects by using low friction properties along the fail-
ure surface and discontinuities. We take a toolbox ap-
proach and highlight the challenges and uncertainties
associated with modelling a failure with such complex
geometry, mechanisms, and behaviour.
BACKGROUND
The Vajont River has eroded a carbonate-dominat-
ed sequence of limestones interbedded with marl, clay,
and clastic rocks. The Vajont Slide involved Jurassic-
Cretaceous units within the Fonzaso Formation and
Calcare di Soccher, which overlie the Calcare del Va-
jont. The Calcare di Soccher is further divided into six
units – A to F – that include fossiliferous limestone, bi-
omicrite, marl, and conglomerate. In terms of geotech-
nical properties, the Fonzaso Formation and unit A of
the Calcare di Soccher can be considered one material
and units C to F of the Calcare di Soccher another. The
conglomerate (unit B) is distinguished from the other
Soccher units (Rossi and Semenza maps in h
endron
&
P
Atton
, 1985). The deposit material in the east is more
disturbed and weaker than that in the west (Fig. 1a and
b), and is densely vegetated, with a fine matrix sepa-
rotti
(1992; 1994) and s
itAr
& M
Ac
L
AughLin
(1997)
completed the first two-dimensional numerical models
of the slide, but little further modeling work has been
conducted until recently. In connection with the 50
th
anniversary conference, several researchers, including
c
AsteLLAnZA
et alii (in this volume) and h
ungr
(in this
volume) have contributed two- and three-dimensional
numerical models.
Although most of the modelling published has
been conducted in two dimensions, the Vajont Slide
is without doubt a three-dimensional problem. Two-
dimensional cross-sections neglect the structural and
morphological differences across the failure surface,
such as the bowl-shaped failure surface, upstream
plunge of one of the synclines defining the sliding
surface, and the change in its geometry from a chair
shape in the west to a circular surface in the east. Most
modelling results have also been interpreted as rigor-
ous indicators of mobilised shear strength and slide
displacement, rather than as aids in understanding the
kinematics of slide behaviour and an exploration of
different mechanisms and hypotheses.
Sophisticated analyses of the Vajont Slide demand
a relatively large data set. Despite the many studies
and publications on Vajont, relatively few researchers
discuss or attempt to quantify sliding surface and rock
mass properties, and those that do commonly cite dif-
ferent values. This issue becomes apparent when at-
tempting to input parameters into modeling software.
g
hirotti
(1992) bases input parameters on seismic
velocities of the failed rock mass as estimated by M
Ar
-
tinis
(1978), and on published parameter values for
limestone (B
Andis
et alii, 1983). She is one of the few
workers to consider the effects of water directly within
numerical models, but does not explicitly consider the
clays along the shear surface. s
itAr
& M
AcLAugh
-
Lin
(1997) base their 2D Discontinuous Deformation
Analyses (DDA) of block size effects on elastic modu-
lus and Poisson’s ratio, but do not provide the numeri-
cal values they used or the source of the values. Only
s
uPerchi
(2012) provides field estimates and labora-
tory test results of rock mass and intact rock strengths.
If the hypothesis that the landslide mass behaved
as several large intact blocks is accepted, the slope
rock mass properties may be less relevant than those
of the failure zone in understanding the failure. In this
context, the properties of the clay layers and previous-
ly failed material, such as the cataclasite mentioned by
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EXPLORATION OF THE KINEMATICS OF THE 1963 VAJONT SLIDE, ITALY, USING A NUMERICAL MODELLING TOOLBOX
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
601
tions of these two structures are 59°/283° (dip/dip
direction) and 55°/010°, in agreement with results of
other studies (s
uPerchi
, 2012; M
Assironi
et alii, in this
volume). The discontinuities define an asymmetrical
sliding mass with a characteristic M-shape.
The north slope of Monte Toc, which defines the
south-west wall of the Vajont Valley, has been de-
formed by the Massalezza and Erto synclines and as-
sociated parasitic folding related, respectively, to the
Dinaric and Neo-Alpine tectonic events. The Mas-
salezza Syncline is a recently discovered feature that
contributes to the bowl shape of the failure surface
(M
Assironi
et alii, in this volume; W
oLter
et alii, sub-
rating clasts of a variety of sizes. The material in the
west remained more competent as it failed and gener-
ally has a higher strength; it remained relatively intact
and preserved stratigraphy. This difference may be due
to the influence of the Col Tramontin Fault on rocks in
the east.
The Vajont Slide is bounded and kinematically
controlled by several discontinuities and sets of folds
(Fig. 1). Two faults delimit the eastern lateral scarp and
the western headscarp – respectively, the Col Tramon-
tin Fault and Col delle Erghene Fault. An analysis of
long-range terrestrial digital photogrammetric models
(W
oLter
et alii, submitted) indicates that the orienta-
Fig. 1 - Block model illustrating the structures that define the Vajont Slide. DS=discontinuity set, CTF=Col Tramontin Fault,
CEF=Col delle Erghene Fault, ES=Erto Syncline, and MS=Massalezza Syncline. Cross-sections 2 and 10A are from
H
endron
& P
atton
(1985) and cross-sections W and E from are B
istaccHi
et alii (in this volume). Note that the E and
W sections roughly parallel the directions of movement. Insets a) and b) show the difference in character between the
deposits of the east block (densely vegetated, with ponding, clasts of a range of sizes, and a fine matrix) and the west
block (relatively intact rock with stratigraphy preserved). Inset c) illustrates the major step in the east-central area of
the failure scar, which we used as a boundary between the east and west blocks (see text)
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A. WOLTER , M. HAVAEJ, L. ZORZI, D. STEAD, J.J. CLAGUE, M. GHIROTTI & R. GENEVOIS
602
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
nuity properties. This technique reduces the strength pa-
rameters of a slope by a Strength Reduction Factor (SRF)
until it fails and determines the critical SRF, equivalent
to the factor of safety, at failure. We first ran models with
different materials using Rossi and Semenza’s Section 2
(h
endron
& P
Atton
, 1985). The purpose was to observe
the effects of changes in material properties on internal
deformation of the sliding mass. Second, we varied the
friction angle along the Section 2 failure surface from
38° to 5° to investigate the stability of the sliding mass
along a discrete surface. Finally, we used four cross-
sections to investigate the effects of slope and failure
surface geometry on model stability in Phase2: Rossi
and Semenza’s Sections 2 and 10A (h
endron
& P
Atton
,
1985) and B
istAcchi
et alii (in this volume) updated east
and west sections (see Fig. 1 for section locations).
Table 1 lists the rock mass and discontinuity proper-
ties used in all codes, based primarily on
ghirotti
(1992).
All models include the specified failure surface, because
the purpose of the modelling was to back-analyse the
existing Vajont Slide. One joint material (jmat 1) was ap-
plied to all discontinuities in most models. A second set
of joint properties (jmat 2) was applied to sub-vertical
discontinuities in some models (faults, discontinuity sets,
etc., as seen below) to determine their effect on stability.
PRELIMINARY RESULTS
Internal deformation of the sliding mass in the
Phase2 models was concentrated within the zone of
transition between the active back and passive seat of
the chair-shaped failure surface, supporting M
encL
’s
(1966) Prandtl wedge hypothesis. Three zones of high-
mitted). Its axis plunges to the north. The Erto Syn-
cline, the southern limb of which forms the character-
istic chair-shaped profile of the failure surface, plunges
approximately 20° east and defines the axis of the Va-
jont Valley. Both fold systems interact with each other
to produce complex dome-and-basin to crescent-and-
mushroom interference patterns (M
Assironi
et alii, in
this volume). These interference patterns are apparent
over most of the present-day failure scar, and may have
played an important role in the failure.
The failure scar geometry is further complicated
by step-paths associated with folding-related disconti-
nuities that are separated by areas of intact rock. Steps
in the failure scar are oblique to the sliding direction
and could act as release surfaces for smaller rock
masses. The step in the east-central area is an exam-
ple (Fig. 1c). h
endron
& P
Atton
(1985) hypothesised
that, although the failure surface predominantly fol-
lows bedding in the west, with minor steps between
beds, it steps up to ground level in the east.
s
uPerchi
(2012) and B
istAcchi
et alii (in this vol-
ume) propose that the Vajont Slide moved as two main
blocks, an east and a west block. An approximate re-
construction of the failure deposit shows that the loca-
tion of the boundary between these blocks is a parasitic
fold complex and a large step located in the east-cen-
tral area of the failure scar (Fig. 1c). Although the step
is not apparent on pre-failure aerial photographs or on
photographs taken immediately after the 1963 slide,
we tentatively identify it as the approximate boundary
between the east and west blocks.
Other block boundaries may have been discontinu-
ity sets, the Massalezza Gully, and secondary shear sur-
faces, as seen on Rossi and Semenza’s cross-sections
(in h
endron
& P
Atton
, 1985). Although the Massal-
ezza Gully remained intact during sliding, we used it as
a boundary to observe how it may have affected initial
pre-failure block kinematics if it were a release surface.
EFFECT OF MATERIALS AND STRENG-
TH ON FAILURE IN 2D FINITE ELE-
MENT ANALYSES
METHODOLOGY AND MODEL PROPERTIES
We conducted initial investigations of failure be-
haviour and rock mass parameters using Phase2 (r
oc
-
science
, 2012), a 2D finite element code that uses the
Shear Strength Reduction (SSR) technique to model the
degradation of rock and soil materials as well as disconti-
Tab. 1 - Properties used for the two- and three-dimension-
al models, based on G
Hirotti
(1992). The Vajont
limestone was used in all one-material models,
unless otherwise noted
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EXPLORATION OF THE KINEMATICS OF THE 1963 VAJONT SLIDE, ITALY, USING A NUMERICAL MODELLING TOOLBOX
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
603
angle of the failure surface and φ is the friction an-
gle along that plane. The secondary semicircular shear
zones in the weaker material models fall within this
range. Higher angles of potential shear zones require
friction angles of at least 77°. If the inclination of the
failure surface in the upper part of the slope, at 20° to
40°, is taken into account, the other shear zones also
fall within the given range for φ = 12°.
The four-material models further illustrate the ef-
fect of material properties. g
hirotti
(1992; 1994) il-
lustrated the importance of the stronger, more brittle
conglomerate layer (Unit B of the Soccher Formation)
in keeping the rock mass relatively intact. Although no
such conclusions can be drawn from the preliminary
Phase2 results, there is less shear strain concentrated
within this thin layer than in the weaker materials sur-
rounding it, supporting g
hirotti
s
(1992; 1994) con-
clusion (Fig. 2c).
As we reduced the friction angle along the failure
surface, the critical Strength Reduction Factor (SRF),
and thus stability, decreased. The correlation between
friction angle and SRF appears to be linear (Fig. 3).
The critical friction angle was determined to be 18°,
above which the slope was stable.
The different results derived from the east and west
cross-sections indicate the complex nature of the Vajont
failure. Rossi and Semenza’s Section 2 and the west sec-
tion of B
istAcchi
et alii (in this volume) show a biplanar
failure with the Prandtl wedge zone separating the active
back block and passive front block of the sliding mass
(Fig. 2). In contrast, the east sections only show shear
strain concentrations at the toe of the unstable mass.
Rossi and Semenza’s Section 10A has a slightly higher
er shear strain occur at breaks in slope of the failure
surface in all models (Fig. 2). The angles, measured
from horizontal, of each potential shear range from
45° to 90°. The thickest shear zone in each model,
approximately 80 m wide, is inclined about 70°, and
is located in the Prandtl wedge zone. Models with
weaker materials show an additional semicircular in-
cipient shear zone inclined about 45° at the front of the
unstable mass (indicated by a black box in Fig. 2b).
This result may indicate a secondary failure, similar
to the November 1960 failure. Thus, the weaker mate-
rial models show more internal deformation in the rock
mass than the stronger material models, as might be
expected. Assuming that the failure surface has a fric-
tion angle of 12°, the anticipated shear surface angles
within the rock mass are between 39° and 51°, given
the equation θ = 45° ± φ/2, where θ is the expected
Fig. 2 - Preliminary results based on Phase2 models.
Maximum shear strain plots of a) one-material
model based on the Calcare di Vajont, b) one-
material model based on the Fonzaso Formation
and Unit A material, and c) four-material model
including the Calcare di Vajont, the Fonzaso For-
mation, and Units A, B, and C-F of the Soccher
Formation. Dashed white lines and angles (from
horizontal) indicate potential shear zone charac-
teristics. The dashed grey box outlines the search
area used for the SSR analyses. The significance of
the black box in b) is discussed in the text
Fig. 3 - Linear relationship between the friction angle (φ)
along the failure surface and Strength Reduction
Factor (SRF) in Phase2 as the friction angle is
increased over the failure surface
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A. WOLTER , M. HAVAEJ, L. ZORZI, D. STEAD, J.J. CLAGUE, M. GHIROTTI & R. GENEVOIS
604
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
critical SRF than Section 2 (SRF=0.75 versus 0.73).
The failure surface in the east section of
BistAcchi
et alii
(in this volume) dips more steeply than that of the west
section and is thus less stable; it approximates a linear
or curved surface rather than a chair-shaped surface. If
only this section were analysed, the stability of the slope
would be significantly underestimated. The east block
failed last, hence it would give a false impression of
failure if analysed alone. A 2D section cannot simulate
the interactions between the east and west blocks as it
neglects variations in kinematic freedom in the third di-
mension. The results may, however, indicate the differ-
ent potential mechanisms of failure in the east and west,
in a situation where the west block moved to provide
kinematic freedom for the east block.
IMPORTANCE OF FAILURE SURFACE
MORPHOLOGY AND BLOCK SIZE IN 2D
DISTINCT ELEMENT MODELS
METHODOLOGY AND MODEL PROPERTIES
UDEC (Universal Distinct Element Code; ITAS-
CA, 2012c) is a two-dimensional discontinuum code
used to model a variety of rock engineering problems.
We used this code to investigate the importance of fail-
ure surface morphology and failure mass block size.
Using Rossi and Semenza’s Section 2 and
ghirotti
s
(1992) material properties for rigid blocks compris-
ing one and four materials (Tab. 1), we tested a variety
of failure surface geometries involving planar, arc-
shaped, biplanar, and undulating surfaces, as well as
Rossi and Semenza’s original failure surface. Undulat-
ing surfaces were used to assess the potential effect of
a complex failure surface on slide kinematics due to in-
terference between the two fold generations mentioned
above. Following a methodology similar to
sitAr
&
MAcLAughLin
(1997),we also re-examined the signifi-
cance of block size and discontinuity spacing. We input
sub-vertical joints into the models, and changed their
spacing from 50 m to 100, 200, and 500 m.
PRELIMINARY RESULTS
The morphology of the failure surface had a strong
effect on failure mechanics. We determined the ap-
proximate value of the critical friction angle for each
configuration (Tab. 2). The most unstable configura-
tions were the linear and arc-shaped failure surfaces,
whereas the most stable configuration was the rough-
est of the three undulating surfaces. The biplanar and
Rossi and Semenza failure surfaces have a similar ef-
fect on stability - the slide mass fails only when the
friction angle along the slide surfaces is reduced to 5°,
assuming dry conditions.
When sub-vertical joints are introduced into the
one- and four-material failure masses, the critical
friction angles along the Rossi and Semenza failure
surface are approximately 16° and 12°, respectively,
indicating a decrease in stability compared to models
without joints. We observed similar decreases in stabil-
ity for all other failure surfaces, except the roughest
undulating surface, which remained stable. The loca-
tions of the individual joints are the same as those used
by g
hirotti
(1992; 1994).
Using the Rossi and Semenza failure surface and
four materials, we found that as the spacing of the sub-
vertical joints and thus block size increased, the failure
mass stabilised and thus the friction angle required
to induce failure decreased. These results are similar
to s
itAr
& M
Ac
L
AughLin
s
(1997) observations us-
ing Discontinuous Deformation Analysis (DDA). An
active-passive mechanism, rather than uniform sliding,
became evident when block size was increased (Fig.
4). As block size increased, the lower blocks became
passive, and a more obvious Prandtl wedge developed
between the active and passive blocks where shear
Fig. 4 - Increasing stability as block size is increased in UDEC. a) Sub-vertical joint spacing is 50 m, and b) sub-vertical joint
spacing is 500 m. The failure mode changes from uniformly sliding to active-passive, accompanied by a significant
decrease in displacement
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EXPLORATION OF THE KINEMATICS OF THE 1963 VAJONT SLIDE, ITALY, USING A NUMERICAL MODELLING TOOLBOX
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
605
of block size (Figs. 1 and 6). The method approximately
follows that employed by c
orkuM
& M
Artin
(2004) in
their investigation of a dam abutment rock slope near
Revelstoke, BC, Canada.
We chose a rigid block model assuming that the
sliding material remained intact and that discontinu-
ity properties dominated failure. We assumed Cou-
lomb-slip area contact constitutive behaviour for all
discontinuities and performed sensitivity analyses on
the friction and cohesion parameters. Two sets of joint
properties, jmat 1 and jmat 2, were introduced in some
models to observe the effects of discontinuity properties
on stability (Tab. 1). We first assigned to all discontinui-
ties the first set of joint properties, which were reduced
in several stages, simulating strength degradation over
time. In further models, we introduced the second set of
joint properties to the back of the chair-shaped failure
surface (i.e., the two surfaces representing the limbs of
the Massalezza Syncline), and/or to secondary discon-
tinuities such as the regularly spaced discontinuity sets
and the plane representing the Massalezza Gully; jmat
2 properties were not changed within each model.
stress and shear strain were localised. Block size thus
has important implications for the modelling of the Va-
jont failure mechanism.
3D–DISTINCT
ELEMENT
MODEL
ANALYSES TO INVESTIGATE BLOCK
KINEMATICS
METHODOLOGY AND MODEL PROPERTIES
3DEC (ITASCA, 2012a), a 3-Dimensional Dis-
tinct Element code that applies an explicit solution
scheme to problems in discontinuous media, was used
to investigate simple block kinematics and interactions
at Vajont. The geometry of the simulations is based
on the GoCAD model of B
istAcchi
et alii (in this vol-
ume). The actual topography is too complex to import
directly into 3DEC for the purposes of our prelimi-
nary kinematic modelling; thus we used it to simplify
the topography by approximating it with intersecting
planes (Fig. 5). We also started with the simplest pos-
sible model, so that an appreciation of the kinematic
controls of the event could be obtained without the
complication of “topographic noise” or unnecessary
model complexity.
We used a variety of different 3DEC model ge-
ometries with different kinematics. Initial models were
created without the Massalezza Gully catchment basin
to compare with those that included it (Fig. 5). The dip
of the part of the basal plane defining the seat of the
chair-shaped failure surface between the Col Tramontin
Fault and the east-plunging Erto Syncline was varied
from 0° to 5° and 10° to the north. The dips and dip
directions of the planes representing i) the Col Tramon-
tin Fault, which forms the east lateral boundary, ii) the
southern limb of the Erto Syncline, which forms part of
the basal surface, and iii) the two limbs of the Massal-
ezza Syncline, which form the rear release or back of
the chair, were varied to ±20° of the values derived from
photogrammetric analyses (W
oLter
et alii, submitted) in
models including a basal plane dipping 5° and a discon-
tinuity set spaced at 200 m. We also varied the number
of blocks. Models first were run with the entire landslide
mass forming one block. Then, discontinuities related to
structural features were added to cut the landslide mass
into two or more blocks. The discontinuities include a
major step in the central-east area of the failure scar that
is associated with folding, the Massalezza Gully, and hy-
pothesized secondary shear surfaces. Finally, we added
regularly spaced discontinuity sets to observe the effect
Fig. 5 - Simplification of a) the complex topography supplied
by B
istaccHi
et alii (in this volume) for use in 3DEC.
b) Plan view. c) Cross-section along the white line
in b). Structural features are represented by planes.
CTF=Col Tramontin Fault. ES=north limb of Erto
Syncline. The basal plane connects the Col Tramon-
tin Fault and Erto Syncline
Tab. 2 - Critical friction angle for the different sliding
surface configurations in UDEC, assuming dry
conditions
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A. WOLTER , M. HAVAEJ, L. ZORZI, D. STEAD, J.J. CLAGUE, M. GHIROTTI & R. GENEVOIS
606
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
a relatively intact, rigid body, clearly contained inter-
nal discontinuities that allowed several large blocks to
move with respect to one another. Block theory (g
ood
-
MAn
& s
hi
, 1985) also dictates that kinematic freedom
should increase as block size decreases and keyblocks
are removed. We therefore conducted a study of block
size (Fig. 6). First, we segregated the failure mass into
two blocks using a possible discontinuity related to
folding in the east-central area and approximating the
boundary between the east and west blocks of s
uPerchi
(2012) and B
istAcchi
et alii (in this volume). We then
used the Massalezza Gully as the boundary between
the two blocks. The discontinuity representing the
Massalezza Gully affected the sliding mass more than
the assumed discontinuity related to the east-central
folding. Maximum displacement increased by more
than three times for a one-joint-material model (Fig.
7), but only the west part of the slide mass moved;
the east side was stable. The difference in behaviour
between models incorporating the east-central folding
discontinuity and those incorporating the Massalezza
Gully may be due to the decrease in the size of the
west block compared to the folding-related disconti-
nuity model. Alternatively, the vertical discontinuity
striking north-south and separating the east and west
blocks perhaps provided better kinematic release than
the discontinuity striking NE-SW. The observation that
the 3DEC models show that the Massalezza Gully may
PRELIMINARY RESULTS
Unlike the majority of the 2D model results, the ini-
tial 3DEC simulations were stable, as expected. The hor-
izontal basal plane on the seat of the chair-shaped failure
surface prevented significant movement until friction
was decreased to zero, clearly an unrealistic scenario.
The very low friction angle necessary for failure may
indicate that: i) increased pore pressures contributed sig-
nificantly to failure, effectively lowering the frictional
resistance along the sliding surface; ii) the models re-
quire more kinematic freedom to fail, either through an
increase in the number of blocks or through removal of
material; or iii) the assumed model geometry is incor-
rect. Models with smaller blocks (see below) and dips of
the basal failure plane of 5° and 10° produced significant
displacements at friction angles of 5° and higher. These
results suggest that block geometry and kinematic free-
dom are critical inputs, as would be expected. The role
of groundwater, although not simulated in the prelimi-
nary models, is, as observed in practice, critical.
As in the case of the UDEC simulations, disconti-
nuity spacing proved to be important. When the land-
slide mass was modelled as one block no significant
movement occurred. This observation suggests that
the sliding mass, although hypothesised to behave as
Fig. 7 - Semi-logarithmic graph of the number of blocks
included in a given model versus maximum total
displacement in metres. Letters correspond to
those in Fig. 6. The two-block model using the
Massalezza Gully (d) as a discontinuity is shown
in comparison to the two-block model using the
east-central fold complex (c). Note that maximum
displacement is roughly three times higher in the
Massalezza model. Models a and b in Fig. 6 are
not plotted as they were stable
Fig. 6 - Sequence of investigation of block size and
number in 3DEC. As block size decreases, stabil-
ity decreases. DS=discontinuity set
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EXPLORATION OF THE KINEMATICS OF THE 1963 VAJONT SLIDE, ITALY, USING A NUMERICAL MODELLING TOOLBOX
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
607
movement of the failing mass toward the NNW or NNE
(Fig. 8), which is in general agreement with published
vectors of movement (for example, B
roiLi
, 1967). How-
ever, some failure masses in the models initiate in the
west corner, some at the west-front corner, and a few at
the east corner of the headscarp, with no discernible rela-
tion to geometric trends. Maximum displacements occur
most commonly in the west-front corner (Fig. 8). Thus,
most models suggest failure initiation in the west, either
at the deposit front (sliding) or at the headscarp (active-
passive), which agrees with previous published research
(s
uPerchi
, 2012; B
istAcchi
et alii, in this volume).
The number of blocks also seems to influence the
displacement direction. For example, the three blocks
in the model shown in Fig. 8a uniformly move to the
NNE. Conversely, a multiple-block model including
DS2 and DS6 (Fig. 8b) shows movement in varying
directions: at the west-front corner, blocks move to the
NNE; in the upper part of the west slope, they move
more to the north; and in the eastern half, they move to
the NNW. A simple kinematic analysis and the h
ocking
(1976) refinement test conducted in DIPS (r
ocscience
,
2012) corroborate the movement directions (Fig. 9).
The east and west limbs of the Massalezza Syncline
show potential for planar sliding, given a slope angle of
40° to the north and an effective friction angle of 10°.
Wedge failure is possible between the east and west
limbs of the Massalezza Syncline, between each limb
and DS2, between each limb and the Col Tramontin
Fault, and between DS2 and the Erto Syncline. Two-
plane sliding could occur along the line of intersection
of the two respective planes, and single-plane sliding
favours one plane. Direct toppling could occur along
have been a more effective zone of separation for the
two blocks is compelling, but contradicts post-failure
observations. The sliding mass must have been com-
petent in the Massalezza area, despite following a fold
hinge. Complex fold interference patterns in that area
may have also inhibited movement.
When we added a plane approximating a second-
ary shear surface, thus creating three blocks, the maxi-
mum displacement increased further (Fig. 7). When
we added three discontinuities determined from photo-
grammetric analyses (W
oLter
et alii, submitted) to the
model to create multiple blocks – DS1 (59°/283°, dip/
dip direction), DS2 (79°/333°) and DS6 (88°/180°) –
the maximum displacement increased by two to three
orders of magnitudes to hundreds of metres. The simu-
lated mechanism of movement also changed. Most
two- and three-block models behaved as active-passive
or uniformly sliding blocks. The blocks in the multi-
block models, however, moved as separate entities with
independent paths. Kinematic freedom and block size
are thus important controls at Vajont, supporting the
observations of c
orkuM
& M
Artin
(2004).
When applied to sub-vertical joints, the second set
of joint properties (Tab. 1) stabilised models. The higher
cohesion and friction values reduced total displace-
ments of the slide mass by 50% to an order of magni-
tude. For example, in a model that included DS2 and
DS6 at 200-m spacing, maximum total displacement de-
creased from 282 m to 127 m. These 3DEC results are
preliminary and further sensitivity studies are required
on stability thresholds and input parameter ranges.
The direction of displacement provides an additional
indicator of model behaviour. All of the models suggest
Fig. 8 - Plots of total displacement (contours) and displacement directions (black lines) for two 3DEC models. a) Three-block
model including the discontinuities representing the east-central fold complex and the secondary shear plane (see
Fig. 6e). b) Multi-block model including DS2 and DS6 at a spacing of 200 m (see Fig. 6g). White arrows represent
general displacement directions; the arrow lengths are not to scale
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608
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
planes oriented parallel to the east limb of the Massal-
ezza Syncline. Field observations support planar and
wedge failure, especially the MSE-MSW wedge seen
in the inset of Fig. 9, but not toppling.
In our exploratory study of the significance of the
orientations of the major planes controlling the Vajont
failure, we determined that the Erto Syncline had a
critical role in failure kinematics, as suggested by h
en
-
dron
& P
Atton
(1985). Varying the dip and dip direc-
tion of the plane representing the east-plunging limb
of the syncline produced both the maximum and mini-
mum total displacements in all models in our study,
which included a basal plane dipping 5°, DS 6 spaced
200 m, and a friction angle of 5°. The maximum to-
tal displacement (222 m) occurred in the model with
the limb of the syncline oriented at 10°/090° (dip/dip
direction), and the minimum total displacement (0.28
m) occurred in the model with the syncline oriented
20°/110°. As the Erto Syncline plane is dipping into
the slope in the latter case, the model is essentially sta-
ble and shows no significant movement. The former
case is more difficult to interpret. In the simple kin-
ematic analysis that we performed, assuming tetrahe-
dral wedges, the plane is not prone to planar or wedge
failure. However, it may have contributed to a complex
pentahedral or hexahedral wedge or wedge-planar fail-
ure as a basal release surface, and thus would not nec-
essarily be stable when interacting with other planes.
PRELIMINARY TENSILE FAILURE SIMU-
LATIONS IN LATTICE-SPRING MODELS
METHODOLOGY AND MODEL PROPERTIES
Slope Model (ITASCA, 2012b) is a lattice-spring
code recently developed as part of the Large Open Pit
(LOP) project that simulates complex rock mass be-
haviour using an explicit time-stepping, discrete ele-
ment approach. Slope Model incorporates the Synthet-
ic Rock Mass (SRM) approach to simulate rock masses
as a combination of intact rock and discontinuities and/
or Discrete Fracture Networks (DFNs). Large-scale,
important discontinuities such as faults and bedding
planes should be considered separately in models. For
the preliminary models in this paper, a rock mass with
degraded properties was simulated with major discon-
tinuities that intersect the sliding mass included explic-
itly. We used the code to investigate tensile behaviour
in the Vajont failure mass, given the complex geometry
of the pre- and post-failure topography (B
istAcchi
et
alii, in this volume). We imposed similar block limits
in these simulations as in the 3DEC models. Our mod-
els were based on one- or two-block sliding masses.
The properties used for the preliminary Slope
Model simulations are listed in Table 1 and are based
on accepted values for limestone, s
uPerchi
s
(2012)
laboratory testing, and g
hirotti
s
(1992) rock mass
estimates. The friction angle of the discontinuities and
the elastic modulus of the SRM were varied, respec-
tively, from 10° to 45° and 9 GPa to 40 GPa. The value
of 9 GPa was derived from the properties used by g
hi
-
rotti
(1992; 1994). The value of 40 GPa represents a
strong, granite-like rock mass, and is consistent with
Superchi’S laboratory results, degraded to rock mass
properties. For each model, total displacement and
the number of new cracks generated were recorded to
monitor failure.
PRELIMINARY RESULTS
The preliminary Slope Model simulations in which
the failure mass is one continuous block and the fric-
tion angle is 13° indicate failure, unlike the one-block
3DEC simulations. When the discontinuity related to
the folding in the east-central area was incorporated,
displacement patterns were similar to the one-block
Fig. 9 - Stereonet plot showing possible wedge intersec-
tions occurring between planes included in the
3DEC models, given a slope angle of 40° to the
north and an assumed low friction angle of 10°.
Two- and single-plane sliding was determined us-
ing the method of H
ockinG
(1976). Inset shows an
example of a wedge between the east (MSE) and
west (MSW) limbs of the Massalezza Syncline.
CTF=Col Tramontin Fault, DS2=discontinuity
set 2, ES=Erto Syncline,
ESmin=Erto Syncline
orientation yielding minimum displacement,
and ESmax=Erto Syncline orientation yielding
maximum displacement (see text)
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EXPLORATION OF THE KINEMATICS OF THE 1963 VAJONT SLIDE, ITALY, USING A NUMERICAL MODELLING TOOLBOX
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
609
of crack formation decreased and the number of new
cracks became constant (L
orig
et alii, 2010; h
AVAeJ
et alii, 2012). Using this cracking criterion, the critical
friction angle of the Vajont slide mass is approximately
14°. With a friction angle of 15°, the slope is stable.
If the friction angle of the material is reduced to 13°,
displacement increases exponentially, demonstrating
continued failure, and cracks continue to generate at a
constant rate. The Slope Model critical friction angle is
between those generated by the UDEC and 3DEC mod-
els and those of the Phase2 models. Thus, the prelimi-
nary Slope Model simulations appear slightly less sta-
ble than the UDEC and 3DEC models, but more stable
than the 2D finite element models. Further work is on-
going to include DFNs in the lattice scheme in order to
obtain a more realistic representation of the rock mass.
The elastic modulus value assigned to model
materials affects the behaviour of those materials. A
lower value represents a more ductile material and
a higher modulus represents a more brittle material.
The Slope Model simulations on the Vajont rock mass
show this effect. Although the locations of new cracks
models but tensile cracks developed in clusters trending
roughly E-W (Fig. 10). These clusters are approximate-
ly parallel to the secondary shear surfaces proposed by
Rossi and Semenza (h
endron
& P
Atton
, 1985) and to
the compressional ridges and extensional depressions
in the debris (W
oLter
et alii, in this volume). The high-
est concentration of newly created fractures is in the
area of highest curvature between the back and seat of
the chair-shaped failure surface. This result supports the
Phase2 and UDEC modelling, as well as M
encL
(1966),
and may indicate the onset of deformation, fracturing,
and disintegration of the failure mass in the Prandtl
wedge zone where stress concentrations and thus de-
formations are expected to be highest. It may also ex-
plain why the Slope Model simulations failed, whereas
the rigid 3DEC ones remained stable: the former allow
internal deformation of the sliding mass and thus pro-
gressive weakening of the material.
h
AVAeJ
et alii (2012) used the number of new
cracks as an indicator of failure in their Slope Model
simulation of a conceptual non-daylighting wedge fail-
ure. As the models approached equilibrium, the rate
Fig. 10 - Preliminary results of a Slope Model simulation. a) Displacements in different parts of the sliding mass when
separated by an assumed discontinuity related to folding in the east-central area. Black line shows location
of cross-section below. b) Clusters of newly created cracks (black disks) with trends similar to those observed
in the field and determined by Rossi and Semenza (in H
endron
& P
atton
, 1985). Black line shows location of
cross-section below, and white curves indicate general trends in microcrack clusters
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610
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
changed little as the modulus of the rock mass (E
rm
)
was reduced, indicating similar stress distributions, the
number of cracks decreased for a constant model run
time (15 s). The material was allowed to deform more
ductiley and thus there was less brittle deformation, or
fracturing. The lowest E
rm
material contained the low-
est number of new cracks, and the highest E
rm
mate-
rial the highest number of new cracks. Trends in crack
propagation are nonetheless similar, indicating that all
models are unstable. Overall, the assumed elastic mod-
ulus, although affecting results, was not dominant. The
tensile strength of the modelled rock mass was much
more important to stability.
DISCUSSION AND CONCLUSIONS
All of the exploratory models presented in this
paper, whether two- or three-dimensional, continuum
or discontinuum, illustrate the significance of discon-
tinuities or zones of weakness on failure. The friction
angles required to produce significant movement in all
models are less than or equal to 18°, indicating that the
failure was controlled predominantly by weak surfaces.
In all cases, significant movement required secondary
shear surfaces that separated the sliding mass into mul-
tiple blocks, as suggested by M
Artin
& k
Aiser
(1984).
The critical friction angles obtained using Phase2 were
roughly equivalent to previous values of approximately
20° (h
endron
& P
Atton
, 1985). The UDEC models
suggested critical friction angles of between 12° and
16°. 3DEC critical friction angles were less than 15°,
depending on block size and shape, whereas Slope
Model sensitivity analyses implied a critical angle of
14°. The 3D codes generally required lower friction an-
gles, as they considered the effects of lateral and rear
release surfaces. That is, 3D models were inherently
more stable than 2D simulations, and thus required
lower friction angles along the sliding surface to fail.
Assumptions in the preliminary models aid in explain-
ing low friction angles. First, the simulations that treat-
ed the failed mass as one block were predominantly
stable at friction angles above 5°. Second, the clays and
other weak material were not explicitly included in the
models; rather, they were approximated by the discon-
tinuity properties along the failure surface. Third, as the
focus for the current paper is geometry and disconti-
nuity properties, groundwater was not explicitly con-
sidered. As many researchers have demonstrated, pore
pressures within the unstable mass were clearly impor-
tant. Groundwater would have reduced friction, and
thus was approximated by incorporating low friction
values. However, this approach does not account for
important seepage forces that will be incorporated in
future models. Finally, most of the models highlighted
in this paper used rigid blocks. Preliminary deformable
models indicate that stability decreases slightly when
more complex constitutive behaviour is included.
The kinematics of the Vajont Slide are critical to
realistic modelling of its behaviour. The difference be-
tween the east and west blocks highlights the three-di-
mensional nature of the failure. The east block appears
to have failed along a circular surface and is thus less
kinematically controlled than the west block. The ma-
jor release plane in the east is the Col Tramontin Fault.
The east block also seems to have failed in weaker
material, possibly related to the fault, than the west
block, which is dominated by large blocks of intact
limestone. The west block failed predominantly along
a biplanar surface and was kinematically controlled. Its
behaviour during failure was influenced by the active-
passive mechanism, the bowl-shaped failure surface,
and the east-plunging south limb of the Erto Syncline,
which guided movement to the north-east. The west
block may have acted as a buttress, preventing failure
of the east block until it had moved, thus creating the
kinematic freedom necessary for the second failure.
Therefore, although 2D cross-sections may indicate
that the east block is equally or less stable than the
west block, 3D models indicate the required kinematic
freedom prior to failure of the eastern slope.
The kinematic role of the Massalezza Gully re-
mains unclear. The 3DEC models suggest that the
west block fails more easily when the failure mass is
separated by the gully than the fold-related discontinu-
ity in the east-central area. However, field and aerial
photograph interpretations clearly show that the Mas-
salezza Gully remained intact during sliding and that
the smaller east block overrode the larger west block.
The Massalezza could, however, have been important
in the initial stages of slope instability. As the failure
developed, weaker shear zones in the east could have
surpassed the Massalezza zone in importance. Future
investigations will include sensitivity analyses of fric-
tion and water pressures on these release surfaces.
Block size is one of the most significant param-
eters in all models, as demonstrated previously by
c
orkuM
& M
Artin
(2004). Both the UDEC and 3DEC
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EXPLORATION OF THE KINEMATICS OF THE 1963 VAJONT SLIDE, ITALY, USING A NUMERICAL MODELLING TOOLBOX
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
611
ed different constitutive models in each code, and used
continuum and discontinuum codes, but a comparison
of the codes was not the principal objective of the paper.
Preliminary exploratory modelling in Phase2,
UDEC, 3DEC, and Slope Model highlights a number
of characteristics of the Vajont Slide. The low fric-
tion angles required for failure along the sliding sur-
face indicate that pore water pressures, kinematic
freedom, and clay layers were important in enabling
failure. Kinematics and block size are also important
factors, both in two and three dimensions. The smaller
the blocks within the sliding mass, the less stable the
slope becomes. The mechanism also changes from an
active-passive mode to sliding of individual blocks as
block size decreases. To occur as an active-passive,
catastrophic failure, the Vajont slide mass must have
comprised large blocks separated by shear or joint
surfaces as suggested by h
endron
& P
Atton
(1985),
yet these large blocks enabled movement. Finally, the
internal deformation of the slide mass, in the form of
shear strain concentrations within the Prandtl wedge
zone (Phase2 and UDEC) and tensile failure clusters
(Slope Model) contributed to the disintegration of the
failed mass into smaller blocks and decreased stability.
Future work includes explicitly including groundwa-
ter, using deformable blocks, investigating the varia-
tion of shear zone thickness, and incorporating more
sophisticated fracture network geometries.
ACKNOWLEDGEMENTS
Research was funded by an NSERC scholarship
to A. Wolter and NSERC Discovery Grants to D.
Stead and J.J. Clague. The authors thank A. Bistacchi
for providing the GoCAD model for numerical mod-
elling, and Loren Lorig and John Read for providing
the Slope Model code. Slope Model was developed
as part of the Large Open Pit (LOP) project, which
is sponsored by Anglo-American, AngloGold Ashanti,
Barrick, BHP Billiton, Compañia Minera Doña Ines
de Collahuasi, De Beers, Newcrest, Newmont, Ok
Tedi Mining Ltd., RioTinto, Teck Resources Ltd, Vale,
and Xstrata Copper.
results indicate that failure geometry, mechanism, and
stability change as block size changes. Increasing the
number of blocks in the 3DEC models was required
for failure to occur. As block size decreased, the
mechanism in two and three dimensions changed from
active-passive to semi-independent displacement of
individual blocks. Realistic simulation requires several
blocks to be included; however, more investigation
using field observations is required to determine the
actual number of blocks involved.
Attempts to model the Vajont Slide include sig-
nificant challenges with respect to both model and
parameter uncertainties, especially in the case of three-
dimensional modelling. The challenges include decid-
ing how much detail to incorporate in the models, and
model geometry and material properties. The explora-
tory modelling that we performed aided in identifying
important characteristics. For example, incorporating
the complex topography in the Slope Model simula-
tions did not increase accuracy, and topography may
have been well-represented by the simplified forms
used in the 3DEC models. Including the stratigraphy in
the Phase2 models did not appear to significantly influ-
ence results when the failure surface was incorporated,
and the stratigraphy was reasonably approximated by
using the weakest unit throughout the slide mass. Of
course, the level of detail included in any model de-
pends on the research question to be answered. For our
purposes, high levels of detail were considered inappro-
priate given the level of uncertainty and the objectives
of the study. The two main sources of uncertainty in
the models are parameter and model uncertainty. Pa-
rameter uncertainty relates to the input properties used
in the modelling. Despite the large amount of research
on Vajont, material and discontinuity properties remain
poorly constrained. We performed sensitivity analyses
on important properties such as friction angle and elas-
tic modulus, and different geometries were investigated
to examine the effects of properties on stability. Our
models are forensic back-analyses, with the objective
of validating and constraining simulations. We did not
analyse model uncertainty in this study. We implement-
REFERENCES
B
Andis
s., L
uMsden
A.c. & B
Arton
r.d. (1983) - Fundamentals of rock joint deformation. International Journal of Rock Me-
chanics and Mining Sciences & Geomechanics Abstracts, 20 (6): 249-268.
B
osA
s. & P
etti
M. (2011) - Shallow water numerical model of the wave generated by the Vajont landslide. Environmental
Modelling & Software, 26 (4): 406-418.
background image
A. WOLTER , M. HAVAEJ, L. ZORZI, D. STEAD, J.J. CLAGUE, M. GHIROTTI & R. GENEVOIS
612
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
B
roiLi
L. (1967) - New knowledges on the geomorphology of the Vaiont Slide slip surfaces. Felsmechanik und Ingenieurgeologie,
5 (1): 38-88.
c
orkuM
A.g. & M
Artin
c.d. (2004) . Analysis of a rock slide stabilized with a toe berm: a case study in British Columbia,
Canada. International Journal of Rock Mechanics & Mining Sciences, 41: 1109-1121.
F
erri
F., d
i
t
oro
g., h
irose
t., h
An
r., n
odA
h., s
hiMAMoto
t., Q
uAresiMin
M. & d
e
r
ossi
n. (2011) - Low- to high-velocity
frictional properties of the clay-rich gouges from the slipping zone of the 1963 Vaiont slide, northern Italy. Journal of Geo-
physical Research, 116: B09208, doi:10.1029/2011JB008927.
g
hirotti
M. (1992) - Aspetti geomeccanici e modellazione numerica della frana del Vajont. PhD thesis, Universitá di Parma,
Ferrara, Firenze e Pavia, Italy.
g
hirotti
M. (1994) - Nuovi dati sulla frana del Vaiont e modellazione numerica. Geologica Romana, XXX: 207-215.
g
oodMAn
r.e. & s
hi
g. (1985) – Block theory and its application to rock engineering. Prentice Hall, Englewood Cliffs, NJ,
USA, 338 pp.
h
AVAeJ
M., s
teAd
d., L
orig
L. & V
iVAs
J. (2012) – Modelling rock bridge failure and brittle fracturing in large open pit rock
slopes. Proceedings of the 46
th
US Rock Mechanics/Geomechanics Symposium, 24-27 June 2012, Chicago, IL.
h
endron
A.J. & P
Atton
F.D. (1985) - The Vaiont Slide: a geotechnical analysis based on new geologic observations of the failure
surface. US Army Corps of Engineers, Technical Report GL-85-5, 324 pp.
h
ocking
g. (1976) - A method for distinguishing between single and double plane sliding of tetrahedral wedges. International
Journal of Rock Mechanics and Mining Science Geomechanical Abstracts, 13: 225-226.
i
tAscA
(2012a) - 3-Dimensional Distinct Element Code (3DEC, v. 4.1). Itasca Consulting Group, Minneapolis, MN, USA.
i
tAscA
(2012b) - Slope Model. Itasca Consulting Group, Minneapolis, MN, USA.
i
tAscA
(2012c) - Universal Distinct Element Code (UDEC, v.5.0). Itasca Consulting Group, Minneapolis, MN, USA.
L
orig
L., c
undALL
P.A., d
AMJAnAc
B. & e
MAM
s. (2010) − A three-dimensional model for rock slopes based on micromechan-
ics. Proceedings of the 44
th
US Rock Mechanics Symposium and 5th US-Canada Rock Mechanics Symposium, 27-30 June
2010, Salt Lake City, Utah.
M
Artin
c.d. & k
Aiser
P.k. (1984) - Analysis of a rock slope with internal dilation. Canadian Geotechnical Journal, 21(4): 605-
620.
M
Artinis
B. (1978) - Contributo alla stratigrafia dei dintorni di Erto-Casso (Pordenone) ed alla conoscenza delle caratteristiche
strutturali e meccaniche della frana del Vajont. Memorie di Scienze Geologiche, Universitá di Padova, 32: 1-33.
M
encL
V. (1966) - Mechanics of landslides with non-circular slip surfaces with special reference to the Vaiont slide. Geotech-
nique, 16 (4): 329-337.
M
üLLer
L. (1968) - New considerations on the Vaiont Slide. Felsmechanik und Ingenieurgeologie, 6: 1-91.
P
AronuZZi
P. & B
oLLA
A. (2012) - The prehistoric Vajont rockslide: an updated geological model. Geomorphology, 169-170:
165-191.
r
ocscience
(2012) - DIPS (V. 6.0) & Phase2 (v. 8.0). Rocscience Inc., Toronto, ON, Canada.
s
eMenZA
e. (2010) - The story of Vaiont told by the geologist who discovered the landslide. K-flash ed., Ferrara. 205 pp. [avail-
able at www.k-flash.it].
s
itAr
n. & M
AcLAughLin
M.M. (1997) – Kinematics and discontinuous deformation analysis of landslide movement. Proceed-
ings of the 2
nd
Panamerican Symposium on Landslides, Rio de Janeiro, Brazil, 65-73.
s
uPerchi
L. (2012) – The Vajont Rockslide: new techniques and traditional methods to re-evaluate the catastrophic event. Ph.D
thesis, Università degli Studi di Padova, Italy, 187 pp.
t
ikA
t.e. & h
utchinson
J.n. (1999) - Ring shear tests on soil from the Vaiont slide slip surface. Geotechnique, 49 (1): 59-74.
W
Ard
s.n. & d
Ay
s. (2011) - The 1963 Landslide and Flood at Vaiont Reservoir Italy: A tsunami ball simulation. Bollettino
della Società Geologica Italiana, 130: 16-26.
W
oLter
A., s
teAd
d. & c
LAgue
J.J. (submitted) - A morphologic characterisation of the 1963 Vajont Slide, Italy, using long-
range terrestrial photogrammetry. Geomorphology.
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