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Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
623
DOI: 10.4408/IJEGE.2013-06.B-60
THE 1963 VAJONT LANDSLIDE ANALYSED
THROUGH NUMERICAL MODELLING
F
ilippo
ZANiBoNi, M
AriA
A. pApAro & S
tefANo
tiNti
Università di Bologna - Dipartimento di Fisica e Astronomia - Bologna, Italy
slide move on a sliding surface with a different shape,
as suggested in the literature, then the corresponding
bottom friction coefficients result to be quite different
from one another, which in turn demands an explana-
tion in terms of lithological difference of the contact
between the slide and the underlying rock body.
K
ey
words
: landslide, numerical modelling, Lagrangian ap-
proach, bottom friction coefficient
INTRODUCTION
The Vajont landslide is a very well-known natural
disaster that occurred in 1963 and destroyed Longar-
one together with some other nearby villages in north-
east Italy: the water, displaced by the mass collapsing
into the Vajont reservoir and mostly channelled west-
ward into the Piave River valley (see Fig. 1), caused
over 2000 casualties. A lot of controversies, of legal,
technical and scientific character, started soon to un-
derstand the responsibilities of the power plant man-
agers and the features of the catastrophe.
The Mt. Toc flank, which forms the southern side
of the basin, was under monitoring even before the
slide occurrence, due to some facts suggesting the
possibility of a slope failure, difficult however to
quantify (M
üller
, 1964 and 1968). After the event
very accurate reconstructions and studies were made,
characterizing the mass deposit, the surface of rupture
and some aspects of the slide motion (e.g. S
elli
&
t
revisAN
, 1964; C
ArloNi
& M
AZZANti
, 1964).
ABSTRACT
The use of numerical modelling to simulate natu-
ral phenomena is increasingly widespread, mainly ow-
ing to computational capacity improving that makes it
possible to face the complexity of the modelling tech-
niques. The 1963 Vajont landslide represents a very in-
teresting case study. The abundance of available data,
before and after the event, allows the reconstruction of
the initial and final mass morphology. Moreover, the
mass compactness and the sudden velocity increase,
as inferred from post-event observations and analyses,
suggests the existence of a well-defined rupture sur-
face, made of exposed clay layers on the western side
of the detachment niche, also under the final deposit.
Furthermore, the very high velocity attained by the slid-
ing mass (presumably 20-25 m/s) is a hint for very low
values of the bottom friction coefficient, considerably
smaller than the usual value for clay material.
In this work we apply to simulate the Vajont
landslide an in-house built numerical code, UBO-
BLOCK1, based on a Lagrangian approach: the slid-
ing mass is split into several along-a-line interacting
blocks, volume conserving and shape changing, and
the motion of each block is computed numerically.
This allows us to simulate the whole dynamics of the
slide and to use observables (mainly the final deposit
mass distribution) to constrain the parameter of the
model, the most influential of which is the bottom fric-
tion coefficient. The main result of our analysis is that,
if it is assumed that the west- and the east-side of the
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F. ZANIBONI, M.A. PAPARO & S. TINTI
624
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
ous studies on the Mt Toc slope stability (p
ApAro
et alii,
2013) and on the Vajont landslide simulations carried out
by two of the authors (T
iNti
& Z
ANiBoNi
, 2004; Z
ANiBoNi
,
2004; Z
ANiBoNi
& T
iNti
, 2013), we concentrate on the
analyses of the bottom friction coefficient that was found
to be heterogeneous on the slide surface, with higher val-
ues on the eastern side and lower on the west. In this
paper we will briefly outline the main features of the in-
house developed numerical code, UBO-BLOCK1, that
was used for the 1963 Vajont landslide simulation; then
we will describe the reconstruction of the sliding surface
morphology and of the initial and final slide deposit;
eventually we will discuss the results of the numerical
simulations showing the need of different basal friction
coefficients to best fit the available data.
NUMERICAL MODEL
Complex phenomena like landslides need a lot
of simplifications to be simulated, that however have
to catch all essential aspects of the involved physi-
cal processes to provide meaningful results. Keeping
this in mind the code UBO-BLOCK1, developed by
the University of Bologna Tsunami Research Team,
adopts a centre of mass (CoM) lumped model, mean-
ing that the dynamics is computed on some points (the
CoM) representative of the whole mass, through a
Lagrangian approach, i.e. an approach where the com-
putational grid moves together with the sliding mass.
The sliding mass is split into different blocks along
the motion direction, obtaining a sort of a “chain” of
interacting blocks, whose CoM movement is computed
numerically. This “block” approximation allows one to
follow accurately the fall of the mass and the consequent
shape changes, simplifying significantly the motion
equations: at each time step the acceleration, velocity
and displacement of each block are calculated in the or-
der, as well as its geometry (namely the block bounda-
ries) and consistently the geometry of the entire slide,
providing all data necessary to pass to the subsequent
time step. As regards the block acceleration, it is given
by the sum of the following contributions:
- the main acceleration term, comprehending the
body forces (gravity and buoyancy, in case of un-
derwater slides) and the bottom friction resistance
resulting from the mass-sliding surface contact;
- the resistance term, accounting for all the interac-
tions between the exposed mass surfaces (frontal
and lateral) and the ambient;
Further contributions came from C
Aloi
(1966),
who estimated a slide velocity of around 20 m/s bas-
ing on seismic records, and from H
eNdroN
& P
AttoN
(1985), who collated all the preceding studies and data
and got confirmation of previous findings: in particu-
lar, that 1) the slide moved over well-defined clay lay-
ers (exposed in the upper part of the sliding surface),
and 2) the mass speed passed suddenly from a few
cm/day to tens of m/s, which justifies also why it re-
mained compact with almost undisturbed layers as is
still visible in the final deposit.
Many studies concentrated on the friction coeffi-
cient μ characterizing such sliding surface. The usual
value for the clay (friction angle 17°-22°, correspond-
ing to μ = 0.3-0.4) seemed too high to account for the
large velocity reached. C
iABAtti
(1964), basing only
on dynamics considerations, estimated a value of
0.236 for that parameter. Further studies (G
hirotti
,
1994; S
eMeNZA
& G
hirotti
, 1998; T
ikA
& h
utchiN
-
soN
, 1999; S
eMeNZA
, 2000; V
ArdoulAkis
, 2002; C
eci
-
NAto
et alii, 2011) substantially lowered it down to μ
= 0.07-0.09 invoking auxiliary concurrent processes,
such as for instance the pore water pressure increase,
due to the heat generated during the slide motion.
Numerical simulations of the landslide and its
consequences were the last to appear in the literature
of the Vajont case. The recent works by P
ANiZZo
et alii
(2005) and by B
osA
& P
etti
(2011) dealt with the wa-
ter displaced by the slide impacting the Vajont lake.
W
Ard
& D
Ay
(2011) applied their model, where the
slide mass and the water basin are seen as an ensemble
of a great number of particles interacting together.
In this work, following and complementing previ-
Fig. 1 - Map of the 1963 slide detaching from Mt. Toc
flank and collapsing into the Vajont Lake. Initial
mass in green, final deposit boundary in red, pre-
slide water basin extent in blue
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THE 1963 VAJONT LANDSLIDE ANALYSED THROUGH NUMERICAL MODELLING
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
625
final deposit. Stratigraphic analyses carried out also
on the unaffected slope around the detachment niche
show that clay layers along Mt. Toc flank exhibit a
40°-45° slope angle in the upper part, and are found to
be almost horizontal downslope in the valley bottom.
As can be deduced from Fig. 1 the run-out dis-
tance of the Vajont slide is rather limited and the final
deposit is largely superimposed to the initial body. Ac-
cordingly, the sliding surface can be subdivided into
three main areas:
- the upper portion, that is uncovered now, and hen-
ce coincides with the post-event topography;
- the lower surface that was initially exposed and
downslope the slide toe and that resulted to be co-
vered by the final mass deposit. Therefore this can
be obtained from the pre-slide topography;
- the intermediate part covered by the depletion
mass (as defined in WP/WLI 1993).
For this last portion of sliding surface some assump-
tions were made by H
eNdroN
& P
AttoN
(1985), basing
on previous geological studies from r
ossi
& S
eMeNZA
(1965) and on profiles prior drawn by S
elli
& T
revisAN
(1964): the western side of the rupture surface suppos-
edly follows a chair-like profile, steeper upslope and
very low-angle downslope (see profiles 1-4 in Fig. 7),
while the eastern side is conjectured to exhibit a para-
bolic trend (profiles 5-6 in the same Figure). The pre-
existing clay layers, well visible in the upper part of the
sliding surface, deepens eastward: s
elli
& t
revisAN
(1964) supposed that the sliding motion provoked the
cut, in the downslope part of the eastern sliding surface,
of calcareous rocks overlaying the clay, creating a new
rupture surface with a higher friction coefficient, provid-
ing then the explanation for the observed slight eastward
rotation experienced by the mass during sliding (h
eN
-
droN
& p
AttoN
, 1985). The lithological heterogeneity of
the sliding surface has implications on the basal friction
coefficients of the two sides as will be seen later.
In virtue of the above considerations and tak-
ing advantage from the along-slope profiles drawn
S
elli
& T
revisAN
(1964) and by H
eNdroN
& P
AttoN

(1985), we reconstructed and digitized eight south-
north transects, using them as the basis to obtain the
intermediate unknown part through an interpolation
procedure. Together with the other two parts obtained
digitising the post- and pre-slide maps, this provided
eventually a regular grid representing the topography
of the entire sliding surface.
- the internal interaction term, providing the reci-
procal pushes between the blocks and controlling
their lengthening or shrinking.
In order to adopt such approach, the code UBO-
BLOCK1 needs as input the initial sliding mass and
the undisturbed sliding surface: in our model the vol-
ume of the landslide is conserved, there is not deposi-
tion during the motion nor sliding surface erosion and
volume increase. Also the pre-defined CoM trajectory
has to be provided to the code, together with the lat-
eral boundaries controlling the mass spreading.
It is worth mentioning that the code UBO-
BLOCK1, further details of which can be found in T
iNti
et alii (1997), is a module of a more complex set of
codes to investigate landslide-generated tsunamis and
has been successfully applied to several case-studies,
such as the Stromboli 2002 landslide tsunamis (T
iNti
et
alii, 2006; T
iNti
et alii, 2008); the Stromboli Holocene
landslide (T
iNti
et alii, 2000; T
iNti
et alii, 2003); the
evaluation of the effects of the speculative tsunami
induced by the Ischia Debris Avalanche (T
iNti
et alii,
2011); the investigation on the source of the 1693 east-
ern Sicily tsunami (T
iNti
et alii, 2012); the evaluation
of the tsunamigenic potential of the North Gorringe
Avalanche - Atlantic Ocean (Lo I
AcoNo
et alii, 2012).
DATA ELABORATION: THE SLIDING
SURFACE AND THE INITIAL MASS
MORPHOLOGY
In order to run the numerical simulation of the
Vajont landslide, an accurate reconstruction of the
sliding surface and of the sliding mass is needed.
The large amount of data available both before and
after the event allowed us to reconstruct the morphol-
ogy of the sliding surface and of the collapsing body.
Hereafter we outline the most significant steps of this
procedure, starting with the digitalization of two maps
containing the pre- and post-slide topography of the
Vajont valley (D
i
S
oprA
, 1997).
THE SLIDING SURFACE
One of the most striking features of the Vajont
slide case is that in the upper part of the slope, more
precisely on the western side, the slide left exposed
well-defined clay layers that can be then easily consid-
ered the upper portion of the sliding surface, and that
can be further assumed to constitute the sliding sur-
face also in the part that remained covered under the
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F. ZANIBONI, M.A. PAPARO & S. TINTI
626
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
and higher than the initial one (green line) and more
asymmetric, with the peak closer to the front. The
transversal profiles 3 and 4 are taken respectively on
the rear and on the frontal part of the initial and final
deposits and are designated as 3pre, 4pre and as 3post
and 4post in Fig. 2. What appears with evidence is that
the sliding body, starting from a two-lobes mass distri-
bution (profile 3pre, green line) compacts while mov-
ing downslope, showing a mass concentration on the
eastern side (profile 3post red line). In the front, the
initial body still presents a double lobe, though less
prominent (profile 4pre, green line), while at the end
of the motion one sees that the mass concentrates in
the central part, reaching more than 270 m thickness.
These features confirm what has been found in the lit-
erature: the mass concentration in the central part of
the front in the valley bottom and a slight eastward
rotation of the mass, probably being connected with
the different behaviour of the rupture surface.
SLIDE STRIPPING
The input data of the slide evolution code UBO-
BLOCK1 are the initial sliding mass and the sliding
surface, that have been obtained as specified in the
previous sections, and in addition the common trajec-
tory of the block CoM and the lateral boundaries of
the surface within which the slide is “channelled” (see
t
iNti
et alii, 1997).
THE SLIDING BODY AND THE FINAL DEPOSIT
After reconstructing the complete sliding surface,
obtaining the initial thickness of sliding body is a triv-
ial matter since it is simply given as the point-to-point
difference between the initial topography (pre-slide
map) and the topography of the sliding surface.
Likewise, the thickness of the final deposit is by
definition the difference between post-slide topogra-
phy and the sliding surface.
By the procedure summarised here above we
have been able to obtain a total volume of around
258.8x10
6
m
3
for the initial slide, that is a value com-
patible with the estimates found in the literature. The
final deposit turns out to be of a slightly lower vol-
ume, namely 248.5
x
10
6
m
3
. The lack of mass can be
probably explained as the consequence of a second
minor slide affecting the eastern lobe of the mass,
occurring at the end of the main event according to
H
eNdroN
& P
AttoN
(1985). Since in our model the
slide conserves the volume, this discrepancy will af-
fect the final simulated deposit.
In Fig. 2 the pre- and post-slide thicknesses are
graphed: the transects are taken longitudinally (1 and
2) and transversally (3 and 4) with respect to the mass
motion direction, mainly south-north oriented. Some
features are evident: the mass concentrates more to-
wards the slide front, as is visible in profiles 1 and 2
where the final deposit (red line) seems to be shorter
Fig. 2 - Reconstruction of the initial (green) and final (red) slide body, starting from the obtained sliding surface. The 1-4
lines marks the positions of the slices reported on the right panels, accounting for longitudinal transects (1 and 2) and
transversal (3-4) ones with respect to the sliding motion (south-north). The 3 and 4 lines are taken along the rear and
frontal parts of the pre- (green) and post-slide (red) body, and then respectively compared
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THE 1963 VAJONT LANDSLIDE ANALYSED THROUGH NUMERICAL MODELLING
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
627
RESULTS OF THE NUMERICAL SIMU-
LATION
EXAMPLE OF SIMULATION: SUB-SLIDE 3
The slide motion was computed separately in each
strip by means of the code UBO-BLOCK1. Each sub-
slide was partitioned into a “chain” of 10 blocks, with
approximately equal volume.
Figures 3 and 4 show some results of the landslide
simulation for strip 3 with friction coefficient value μ
= 0.14, and more precisely the mass profile evolution
and block velocities respectively.
We can notice that the sub-slide maintains its
compactness, tending further to concentrate towards
the front and to slightly shorten from the initial length
of around 1300 m down to approximately 1200 m
(Fig. 3). This is confirmed also by the quasi uniform-
ity of the velocity of the individual blocks (black dots
in Fig. 4), with differences smaller the 3-4 m/s at any
time. The maximum velocity attained is 18 m/s after
almost 20 seconds as concerns the average value (red
line in Fig. 4), while some blocks approach 20 m/s.
The motion mainly stops after about 35 s, after
which only one block still moves, though quite slowly.
This is the first (uppermost) block of the chain, as vis-
ible also from Fig. 3, where one can appreciate that the
t=40 s (black) profile almost coincides with the final
one (t=64 s, blue dotted line), apart from a small differ-
ence in the rear part. It is worth remarking that the fi-
nal simulated profile shows a very good approximation
with the observed one. A quantitative way to measure
the discrepancy between the final computed and ob-
The Vajont slide shows a considerable width
(~1850 m) compared to the longitudinal extension
(~400 m), while the model we adopt suits more
“chain”-like slides, where the aspect ratio (length over
width) is greater than 1. Using a single central path for
the CoM would represent a too crude approximation,
because this would imply neglecting the heterogeneity
of the sliding surface.
In order to cope with the Vajont landslide lateral
extension, we decided to split the landslide into differ-
ent parallel strips, applying on each of them the UBO-
BLOCK1 code and running them independently each
other. Each “chain”-like sub-slide simulation needs
its own sliding surface, initial sliding mass, CoM path
and lateral boundaries, and also a final deposit thick-
ness used as a constraint for the tuning of the model
parameters. The subdivision was realized by trying to
conserve the volume inside each strip, and accounting
also for the slight easterly rotation already mentioned.
Strips are shown in the first panel of Fig. 5. Most of the
volume is included in strips 2 to 5, and here the percent-
age differences between the pre- and post-slide volumes
are not more than 3% in each strip. The side strips show
larger discrepancies. The westernmost strip, close to the
Vajont dam, no. 1, involving only about 6% of the total
volume, shows a slightly larger percentage difference
(about 4%). But the eastern strip, no. 6, which includes
15% of the volume, has a deviation of about 29% of less
volume which is mainly due to the already mentioned
secondary slide, taking place after the main occurrence
and bringing mass out of the computational boundaries.
Fig. 3 - Slide thickness taken at different times for sub-slide
3, compared with the observed initial (purple dashed
line) and final (red line) thickness. Values are com-
puted along the CoM trajectory. Curves correspond-
ing to 40 and 64 s are almost totally superimposed
Fig. 4 - Velocity of the blocks CoM (black dots) and av-
erage velocity (red line) vs. time for sub-slide 3.
Notice that after 35 s only one block is still mov-
ing, though slowly, while the velocity of the other
CoMs is zero
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F. ZANIBONI, M.A. PAPARO & S. TINTI
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International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
served deposits is the misfit index, ranging from 0-1 and
measuring the degree of lack-of-overlapping between
to mass distributions (see Z
ANiBoNi
& T
iNti
, 2013; for
further details). In this case the computed misfit index
is 0.058, which means that the two distributions deviate
from one another by less than 6%, or, alternatively, that
overlap by more than 94%.
SENSITIVITY ANALYSIS THROUGH THE
FRICTION COEFFICIENT
By varying the bottom friction coefficients in each
strip one can obtain different final sub-slide deposits
and different speed curves. In playing with the value
of μ within the reasonable range 0.10-0.40 we noticed
that the results for the side strips 1 and 6 (see Fig.
5 for their position) were always the least satisfac-
tory, which has induced us to neglect them in the rest
of the analysis and to focus on the central strips ac-
counting for the largest portion of the slide volume
(about 80%). We noticed further that sub-slides tend
to remain compact during the motion as occurs in the
exemplary case of strip 3 with μ = 0.14 given in the
previous section, since individual blocks tend to move
with similar speed at any time. Therefore, the time-
history of the average speed (red line in Fig. 4) can be
taken as representative of the velocity of all blocks.
In performing our analysis we consider three ba-
sic issues:
1) The first is that the final deposit poses a severe con-
straint to the simulation, so that the goal is the mi-
nimisation of the misfit, i.e. the achievement of the
maximum overlapping between the simulated de-
posit and the observed one in the strips considered.
2) The second key point is that, in consequence of
the evidence that the whole Vajont slide remai-
ned compact during the motion, differential velo-
cities between the different sub-slides are hard to
accept. Therefore the second goal to attain is the
minimisation of deviations between the curves of
the average speeds of the various sub-slides. It is
worth observing here that to measure the deviation
among speed curves, one exploit the same quantita-
tive misfit used for the volume distribution but with
two main differences: in this case the objects to
compare are curves instead of surfaces and second
they are in number of four (corresponding to the
velocity curves of sub-slides 2-5) instead of two.
3) The third item is that since the bottom friction
coefficients are essentially determined by the
properties of the rocks that are in contact and that
the western side of the sliding surface (including
strips 2-4) is different from the eastern side (strip
5), hence we assume the same friction coefficient
for the set of sub-slides 2-4 and a possible different
friction coefficient for the other sub-slide, no. 5.
An immediate observation is that satisfying the first
two items above is impossible because searching for
the least deposit misfit was found to lead to discrepant
velocities and vice versa, minimising the velocity misfit
resulted to lead to an unsatisfactory deposit misfit. The
most appropriate strategy to follow therefore seems to
be to search for a compromise, where none of the two
indices are minimised but rather a combination of the
two. Indeed it is simple to define a global misfit index
that is weighted average of the deposit and velocity
Fig. 5 - Calculated footprints of the six sub-slides shown
at different times superimposed to the sliding sur-
face topography. Strips are numbered from 1 to 6
starting from the westernmost strip (top left pan-
el). Strips are separated by black lines. The blue
lines within each strip are the CoM pre-defined
trajectories, that are required as input data by the
landslide simulation code UBO-BLOCK1. The
central strips, involved in our sensitivity analysis,
are marked in green, while the lateral ones, 1 and
6, are light green. The red line in the final map
(bottom right) delimits the final deposit
background image
THE 1963 VAJONT LANDSLIDE ANALYSED THROUGH NUMERICAL MODELLING
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
629
The velocity plot of Fig. 6 confirms that slides
in strips 1 and 6 move quite different from the oth-
ers with higher speed and longer motion. Restricting
to the central core of the slide, we observe that sub-
slides 2, 4 and 5 go rather coherent with similar speed
curves, but sub-slide 3 moves slower than the other
and is the one that most contributes to the value of the
velocity misfit. The average velocity (red line) goes up
to 23 m/s at about t = 20 s, fully compatible with the
findings by S
elli
& T
revisAN
(1964), suggesting 20
m/s, and later by S
eMeNZA
(2002), increasing the value
to 20-25 m/s. The whole slide motion, in addition,
seems to last 35-40 seconds, slightly shorter than the
value of 40-50 s estimated by S
elli
& T
revisAN
(1964)
and C
Aloi
(1966) studying seismic records.
To complete the picture of the final results, cross-
sections of the slides taken along the CoM trajectories
(see their location in Fig. 5) are given in Fig. 7. Here,
for each strip, the profile of the sliding surface forms
the basis above which the initial profile of the slide as
well as the computed and the observed deposits are
shown. In general a good agreement can be noticed
between the observed deposit (light grey) and the final
position of the simulated slide (blue line). Notice also
that in the simulation the mass mainly deposits in the
bottom of the valley and only partially climbs up the
northern opposite flank, reaching farther than the real
slide. This occurs for example for strip 2 and slightly
for strip 5. This is evident also for the side strip 1 and
much more for the side strip 6 and was already men-
tioned in commenting the maps of Fig 5.
misfit (see Z
ANiBoNi
& T
iNti
, 2013, for further details).
The result of the minimisation process described
here is that the best global misfit has the value of 0.106,
corresponding to a velocity misfit of 0.091 and a de-
posit misfit of 0.129, and this is achieved when the fric-
tion coefficient used for the west-side sub-slides 2-4 is
μw = 0.14 and that for the east-side sub-slide 5 is μ
e
=
0.27. With this parameter setting, the Vajont slide, seen
as the composition of the six sub-slides, moves as is de-
picted in Fig. 5, where the footprints of each sub-slide
at different times are portrayed (in green). For the side
strips no 1 and no 6 we used respectively the west- and
the east-side value of the friction coefficients, i.e. μw =
0.14 and μ
e
= 0.27. Since the results of these simula-
tions were not taken into account in the global misfit
minimisation procedure, they are marked distinctly in
light green. Our attention concentrates on the central
strips 2-5, showing a satisfactory homogeneity during
the sliding motion and presenting an almost compact
front moving northward, downslope, with only strip
4 moving slightly ahead of the others. After t = 30 s
the slide picture seems not to change significantly, and
the t = 40 and t = fin views are practically coincident.
The final (bottom right) panel of Fig. 5 shows also the
boundary of the Vajont slide deposit, depleted however
of the mass involved in the secondary eastward slide
(compare it with the one given in Fig. 2). The agree-
ment between observed and computed boundaries is
very satisfactory in the central strips, while in lateral
strips is quite bad since they both lengthen too much
and go well beyond the observed front.
Fig. 6 - Average velocities of the six sub-slides vs. time, for
the case μw=0.14 and μ
e
=0.27. The curves for sub-
slides 1 and 6, plotted with black and grey dashed
lines, did not enter the misfit minimisation proce-
dure, but are reported for the sake of completeness
Fig. 7 - Cross-sections for the six strips, with the sliding
surface marked in grey. The initial thickness is
represented by a dashed red line, the simulated de-
posit by a blue line. The observed deposit is shown
in light grey
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F. ZANIBONI, M.A. PAPARO & S. TINTI
630
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
part was built on the hypothesis (advanced by H
eN
-
droN
& P
AttoN
, 1985) of a “chair”-like downslope
profile for the western side and of a parabolic shape
for the eastern part, basing also on S
elli
& T
revisAN
(1964) transects. The initial geometry of the slide and
the final deposit were straightforward products of the
sliding surface reconstruction, and turned out to be
of almost similar volumes (260
x
10
6
m
3
vs. 250x10
6
m
3
), the small deficit being explainable by invoking a
secondary slide evacuating some mass after the main
slide occurrence. Volume matching found a posteriori
is in support of the correctness, or at least strong plau-
sibility, of the reconstructed surface of sliding.
Stripping of the slide into six sub-slides with length
predominant over width was made to meet the class
of application for which the numerical code UBO-
BLOCK1 was conceived. Strips were defined in such
a way that they intercept similar volume in the initial
slide body and in final deposit. In our simulations the
six sub-slices move independent from one other.
The most important parameter in the model is the
bottom friction coefficient, influencing the velocity of
the blocks, the duration of the motion and the run-out
distance. Differences between the west- and east-side
of the sliding surface induced us to use two values for
this coefficient, one for the western strips 1-4, where
supposedly the bottom surface is clay and another for
the eastern strips 5-6, where instead it is characterized
by a calcareous rock component. The bulk of the anal-
ysis was however performed only on the central strips
2-5 involving 80% of the total volume, neglecting the
side strips 1 and 6.
The main slide features we have chosen to relate
are the position and geometry of the final deposit and
the fact that the slide moved with the same velocity
as a unique body, though our modelling implies that
it is the ensemble of independent sub-slides. Fitting
both items turned out to be a conflicting issue, and
hence it was opted for a combined minimization of
discrepancies. These were measured by introducing
a quantitative index of misfit measuring the similar-
ity of distributions. For the deposit, a deposit misfit in-
dex was defined measuring the difference between the
computed and observed distributions of mass for the
set of sub-slides 2-5. Further for the velocity, the slide
velocity curves of these sub-slides were compared in
pairs and a total velocity misfit was then obtained as
an average. Eventually, the deposit and the velocity in-
The final remark regards the sliding surface. From
the cross-sections it appears clear that on the south-
ern flank (left on the figure) profiles 1-4 (on the west
of the slide) exhibit a sharp change of gradient from
steep to mild around mid-slope, while profiles 5 and
6 (on the east) do not: this is the consequence of the
hypothesis we adopted in reconstructing the sliding
surface as described in a previous section: chair-like
shape profiles for the clay layer located on the west
and parabolic shape for the calcareous rock rupture
surface one finds on the east.
DISCUSSION AND CONCLUDING RE-
MARKS
In this paper we have carried out the numerical
simulation of the Vajont landslide by using a code
UBO-BLOCK1 implementing a block Lagrangian
model. The features of the slide that were relevant for
the simulations are:
1) clay layers remained exposed uphill on the west
side of the detachment niche;
2) mass deposit compactness with preserved layer
sequences, which suggests the existence of a
well-defined sliding surface;
3) the mass deformed as the effect of the slide, so-
mewhat shortening and concentrating toward the
centre of the front;
4) a slight eastward rotation of the sliding mass;
5) the slide moved fast reaching peak speed around
20-25 m/s, and lasted around 40-50 s, which sug-
gests small values for the bottom friction coeffi-
cient, lower than the usual one for clay surfaces.
The numerical code used for simulations repre-
sents the sliding body as a chain of contiguous blocks,
preserving mass and able to deform. Needed inputs for
the code are the sliding surface, the initial geometry of
the slide, the lateral boundaries of the area swept by the
slide, and the common path of the CoM of the blocks
forming the slide. Relevant outputs are the position, ve-
locity and acceleration of all the block CoMs vs. time,
and, in addition, the basal area and height of each block.
From all of this, the shape of the entire slide is known
as a function of time and in particular the computed
final shape can be compared with the observed deposit.
Great attention was devoted to reconstructing
the sliding surface. The uphill and downhill parts of
the surface were derived by making use of pre- and
post-slide topographic maps, while the intermediate
background image
THE 1963 VAJONT LANDSLIDE ANALYSED THROUGH NUMERICAL MODELLING
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
631
a scenario can be imagined where the failure started
on the west involving the contact of the mass with the
clay layer and then propagated eastward where rup-
ture passed across different layers.
This analysis needs refinement and probably code
improvements. Using a fully 2D landslide simulation
code accounting for lateral interaction between adja-
cent blocks (in terms of the present discretisation, this
would involve interaction between adjacent sub-slides)
will lead to a coherent movement of the whole slide in a
natural way, without the need of making recourse to the
speed misfit index. Further, in our model all sub-slides
move only in one direction, and are not allowed to re-
verse their motion. Some authors however claimed that
evidence was found that the Vajont mass, after climbing
up the opposite flank, returned back to the bottom of the
valley (e.g. S
eMeNZA
& G
hirotti
, 2000), which would
imply a longer duration of the motion and a longer slide
path, and, consequently, smaller friction coefficients.
What our simplified modelling proved is the strict
association between the two-shape geometry of the
sliding surface and the two-value friction coefficient.
Though more sophisticated models can expectedly lead
to some correction to these values, we are confident that
this chief feature will be maintained. Confirmation or
falsification of this findings demands for more specific
geological investigations on the properties of the rock
material involved in the sliding process.
dices were combined together to get the global misfit.
The result was that the friction coefficients leading
to the smallest global misfit are very different from one
another, μw = 0.14 for the western side of the sliding
surface, and μ
e
= 0.27 for the eastern. The slide simu-
lated by using these parameters showed a satisfactory
agreement with the observed final deposit (see Figs. 5
and 7). Moreover, the average speed of the whole slide,
obtained as the weighted mean of the individual sub-
slide speeds, was consistent with estimates given in the
literature. The mass reaches 23 m/s in about 20 s and in
the next 15 s it decelerates (see Fig. 6), and reaches the
valley bottom, showing a compact front moving north-
ward (see Fig. 5). The total duration of the slide mo-
tion is about 35 s, slightly smaller than the one deduced
in the literature from the analysis of seismic records.
Further, the sub-slides move with similar velocities, but
sub-slide 3 has a speed always somewhat smaller than
the others, which is unsatisfactory.
The main results of our analysis is that assum-
ing a different geometry of the sliding surface, one in
the west-side (chair-like profile) and another on the
east side (parabolic profile), implies that the friction
coefficients must be very different, and much smaller
on the west-side. This may have some geological ex-
planation in the lithological difference of the sliding
surface, consisting respectively of clay layer and of
calcareous rocks. Going further with this hypothesis,
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