Document Actions

ijege-13_bs-hungr-aaron.pdf

background image
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
51
DOI: 10.4408/IJEGE.2013-06.B-04
STABILITY AND FAILURE BEHAVIOUR OF THE VAIONT SLIDE
O
ldrich
HUNGR & J
Ordan
AARON
University of British Columbia, 6330 Stores Rd., Vancouver, B.C., V6T 1Z4, Canada
which the failure scenario unfolded. No-one expected
the gigantic, sudden release of energy, which produced
a wave overtopping the Vaiont dam by a height of 140
m and sent a deadly surge of water towards the town of
Longarone in the Piave Valley.
The Vaiont Slide has been the subject of a fair
amount of investigation and data gathering both before
and after 1963 and a very large number of publications.
However, due to the large scale of the event, its timing
in the nineteen-sixties and economic circumstances, the
factual data base is still quite limited, compared to data
sets commonly available for contemporary mining and
civil geotechnical slope problems. This makes quantita-
tive analyses very difficult. The recently-acquired Lidar
topography and detailed structural analyses compiled by
S
uperchi
(2012) are a significant addition to the data base.
The purpose of this invited paper is to attempt a
simple three-dimensional analysis of the mechanism
of failure and propagation of the landslide, based on
a summary of existing data. Specifically, the goal is
to attempt a fresh reconstruction of the sliding surface
and examine its stability and dynamics using best es-
timates of material properties and piezometric con-
ditions. The instability of the north slope of Mt. Toc
is not difficult to explain. The primary focus of this
analysis is the failure behaviour. Why was energy re-
leased so suddenly and why did the enormous mass of
rock and soil move so rapidly and cover such a large
distance? What was the mechanism of interaction with
the water stored in the reservoir?
ABSTRACT
The statics and dynamics of the Vaiont Slide have
been studied using several models based on the theory
of Limit Equilibrium, in two and three dimensions.
The analyses confirmed the need to consider low bed-
ding-parallel strength of much of the rupture surface,
combined with high piezometric pressures. The role
of internal strength of the rock mass is also important,
to a degree that depends on the mobilization of rock
mass cohesion. The slide was asymmetric and later-
ally constrained and is likely to have detached in two
stages, separated by a surface under diagonal tension.
A displacement wave analysis indicates that the slide
velocity is unlikely to have exceeded 10 m/s.
K
ey
words
: Landslide, rock slide, limit equilibrium analysis,
dynamic analysis, displacement wave
INTRODUCTION
The Vaiont rock slide of October 9, 1963 was the
second deadliest single landslide event in European his-
tory. It is further remarkable in that both the landslide it-
self and the disastrous displacement wave which caused
more than 2000 fatalities, were the result of the artificial
impoundment of a reservoir. Even more important for
geologists and engineers is the fact that the full extent of
the landslide was recognized, investigated, measured,
monitored and predicted by knowledgeable profession-
als right up to the moment of failure. What was not
anticipated, however, was the catastrophic speed with
background image
O. HUNGR & J. AARON
52
International Conference on Vajont - 1963-2013 - Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
The authors consider most of these conclusions to
be still largely valid at the present time.
Detailed structural analysis and a geomechanical
characterization of the rock masses was conducted re-
cently by a research group from the University of Pado-
va (S
uperchi
2012, S
uperchi
et alii, 2010). Its findings
are that the limestone beds are folded not only in the
north-sound trending syncline, but also in a less pro-
nounced east-west trending (Messalezza) syncline. The
two perpendicular superimposed folding episodes create
oblique dips in the upper part of the sliding surface and
small interference structures in the central part of the
sliding surface. This research also advanced a hypothe-
sis that the failure occurred in two closely-related stages.
RECONSTRUCTION OF THE SLIDING
SURFACE
The rupture surface of the 1963 slide was recon-
structed by the following means:
1) By accepting the three downslope sections drawn
by D. Rossi and E. Semenza and reproduced by
h
endrOn
& p
attOn
(1985) in their Fig. 15, 17 and
19. It is noted that these sections coincide well
with the levels of the main sheared zones iden-
tified in a number of boreholes drilled in 1964,
following the slide.
2) By ensuring that the downslope (toe) outline of the
rupture surface coincides with the outcrop of a
PREVIOUS ANALYSES
Detailed original studies of the Vaiont reservoir
slopes were made by geologists, as summarized by
S
emenza
& G
hirOtti
(2000). These studies, supported
by extensive field mapping and limited drilling site in-
vestigations, produced a reliable trace of the surface
outline of the sliding mass, a series of interpolated
cross-sections and proof that a large part of the sliding
surface follows a bedding-parallel zone, pre-sheared
by a pre-historic landslide of similar geometry. This
data, supplemented with additional fieldwork, was
used in a comprehensive engineering analysis of the
event by Hendron & Patton (1985). The latter authors
carried out approximate analysis of slope stability in 2
and 3 dimensions, as well as a two-dimensional anal-
ysis of landslide motion. Influenced by earlier ideas
by m
encl
(1966), V
OiGht
& F
auSt
(1982) and others,
they contributed the following key findings:
The major part of the Vaiont sliding surface fol-
lowed clay-coated bedding planes in Late Jurassic lime-
stone units, pre-sheared by the prehistoric landslide. Al-
though the bentonitic clay fillings on the bedding planes
had laboratory residual friction angles of 5° to 16°, the
average value for the shear zone, accounting for some
rock-to rock contact, was estimated as 10° to 12°.
Many of the downslope cross-sections had a lis-
tric compound shape resulting from the synclinal
geometry of the calcareous strata (Erto Syncline), so
that the sliding stability was influenced by the inter-
nal strength of the displaced rock, in order to make
downslope motion kinematically feasible (m
encl
,
1966, h
utchinSOn
, 1988).
The bedding structure plunged to the west,
so that the sliding surface had to pass through the
limestone rock mass in order to daylight on the right
(east) flank of the landslide.
There was high piezometric pressure within the
unstable rock mass, caused by a combination of toe
submergence by the reservoir and infiltration coincid-
ing with heavy rainfalls preceding the event.
A substantial loss of strength of the sliding mass was
required to enable the landslide to reach the observed
total displacement and velocity. Hendron and Patton (in
an analysis carried out by D. Anderson) assumed that
strength loss occurred on the part of the sliding surface
controlled by the bedding planes and that it was due to
pore-pressure increase caused by heating (as proposed
by V
OiGht
& F
auSt
, 1982, see discussion below).
Fig. 1 - Reconstructed rupture surface of the Vaiont Slide,
related to the boundaries of the mesh used in the sta-
bility analyses. Boreholes with reported elevations of
the main shear zone are shown. Dimensions in me-
tres. The UTM coordinates of the origin lower right
corner of the map (-300,-500 are 2313965,5127994)
and the azimuth of the vertical axis is 190ᵒ
background image
STABILITY AND FAILURE BEHAVIOUR OF THE VAIONT SLIDE
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
53
shape are unlikely to have a major influence on the
balance of forces. Other factors, especially the distri-
bution of shear strength on the surface and the internal
strength of the sliding body, are more important.
LIMIT EQUILIBRIUM ANALYSES
GEOTECHNICAL MODEL
The initial geotechnical model was derived from
the conclusions of h
endrOn
& p
attOn
(1985) and
uses the sliding surface described on Fig. 1. The mod-
el recognizes two types of shear strength, mobilized in
different areas:
The main (western) part of the sliding surface is as-
sumed to follow pre-sheared bedding planes or pre-ex-
isting shear zones, with an average friction angle of 12ᵒ,
corresponding to a smooth, clay-filled discontinuity at
residual strength. This assumption is based on the ob-
servation of the exposed southern parts of the surface,
where shearing often clearly follows the rock structure.
However, the relationship between the bedding at-
titudes and the sliding surface is not simple. For exam-
ple, the average bedding strikes measured by S
uperchi
(2012) in the eastern and western structural domains
of the exposed surface are not exactly parallel with
the average contours of the sliding surface. Therefore,
the surface must be curved and/or stepped in these do-
mains. The relationship between the bedding and the
sliding surface is even more complex in the central
structural domain, which exhibits complicated folding
interference features and crushed zones. The blanket
assignment of the 12ᵒ residual friction angle is there-
fore not unambiguous and will be discussed further.
The internal strength of the limestone rock mass
was estimated using the h
Oek
-B
rOwn
(1980) rock
mass strength model. The rock mass strength enve-
lope was derived by the software RocLab, Version 1
of RocScience, Ltd. and is based on empirical equa-
tions developed by E. Hoek and co-workers during the
nineteen-nineties (h
Oek
et alii, 2002). The mean prop-
erties of the rock mass were determined using typical
indices based on detailed field and laboratory work
by S
uperchi
(2012): Uniaxial Compressive Strength
of 50 MPa and an average Geological Strength Index
(GSI) of 50. With a rock pressure corresponding to a
depth of 250 m, these indices yield an equivalent co-
hesion of 1500 kPa and a friction angle of 34ᵒ. These
values were considered as an upper limit of rock
strength on surfaces perpendicular or oblique to the
"tectonized" zone on the left bank of the pre-1963
Vaiont Gorge, as mapped by S
elli
& t
reViSan
(1964) and identified as the outcrop of the pre-
historic slide surface.
3) By matching the large part of the sliding surface
exposed by the landslide in the upper levels of the
slope and mapped recently by aerial Lidar (S
u
-
perchi
, 2012).
4) By limiting the eastern margin of the sliding mass
along the trace of the steep Col Tramontin fault
(S
uperchi
, 2012).
5) By ensuring that the sliding surface is reasonably
smooth in the downslope direction, although steps
transverse to the direction of movement are accepted.
The reconstruction of the sliding surface was
carried out using the three-dimensional slope stabil-
ity program CLARA-W, which is designed to form a
three-dimensional surface by interpolation between ad-
jacent downslope cross-sections (h
unGr
et alii, 1988).
The input cross-sections were constructed at 200 m
spacing, and drawn so as to satisfy Points 2), 3) and
5) above. Three of the sections were coincident with
Rossi and Semenza Sections No. 2,5 and 10a, which
are the best constrained by borehole information.
The resulting surface is shown in Fig. 1. The 1964
boreholes are posted with interpreted elevations of the
main sliding surface. The shaded area in the top part
of the slope indicates the zone where the reconstructed
surface coincides approximately with the recent Lidar
topography and thus shows the areas where the 1963
sliding surface is presently exposed.
The borehole information is shown to be ap-
proximately consistent with the reconstructed surface,
except in Borehole 16, near the eastern flank of the
landslide, where drilling information shows several al-
ternative shear zones and the position of the main slid-
ing surface is very uncertain. The surface outline of the
slide also closely follows the outline determined from
airphotos. The upper part of the reconstructed sliding
surface coincides with the exposed area surveyed by
Lidar. The volume of the landslide, based on this sur-
face, is 294 million m
3
. It is recognized that, in a land-
slide as large and complex as this, the sliding surface
may consist of more than one discrete shear zone. In
particular, the rupture surface is likely stepped in its
eastern part and its reconstruction there is less certain.
However, given the great volume of material in-
volved, departures from the assumed sliding surface
background image
O. HUNGR & J. AARON
54
International Conference on Vajont - 1963-2013 - Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
greater, western part of the sliding surface, while the
higher rock mass strength was used for that part of the
surface extending from x=1500 m to the eastern margin.
Also, the internal strength of the slide was assumed
to be the rock mass strength, in sections where internal
deformation is required to make motion kinematically
feasible.
The piezometric surface associated with the rup-
ture surface of Fig. 1 was obtained by interpolation of
the highest piezometric lines assumed for Sections 2, 5
and 10a by h
endrOn
& p
attOn
(1985). Guided by the
limited water well level observations made prior to the
landslide and by the record of landslide behaviour rela-
tive to precipitation, h
endrOn
& p
attOn
assumed that
the piezometric surface was determined partly by the
water level in the reservoir, but increased significantly
due to heavy rainfall infiltration. The assumed surface
exhibits artesian pressures along the reservoir shoreline,
in a narrow band parallel with the landslide toe.
A standard toe submergence procedure of includ-
ing the weight of the reservoir water above the sliding
surface and adding a total horizontal hydrostatic thrust
force was used in the analysis. The hydrostatic thrust
force amounted to 1.1% of the slide weight and the cor-
responding increase in the Factors of Safety due to toe
submergence was of the order of 4%.
TWO-DIMENSIONAL ANALYSIS
Three different 2D methods of limit equilibrium
analysis were utilized in this case. The first one, Bishop's
Simplified Method, with modifications due to F
redlund
bedding. There are reasons to consider that the cohe-
sion value may be substantially less in some locations,
as discussed below.
Rock structure has a very strong influence on the
geotechnical model. The bedding structures daylight
along the western margin of the landslide, which al-
lows the blanket assignment of the weaker bedding-
parallel strength in the western region. The distribu-
tion of shear strength is particularly complex in the
eastern part of the sliding surface. Even though new
geological observations and the discovery of the
north-south trending Messalezza Syncline have com-
plicated the picture, it is still apparent that the bedding
planes plunge into the rock mass bordering the right
flank of the landslide. This likely happens in step-like
manner, as proposed by h
endrOn
& p
attOn
in Figs.
21 and 22 of their report. The existence of this phe-
nomenon is supported by the multiplicity of sheared
zones intersected by Boreholes 9 and 16. Also, the
shape of the sliding surface near the eastern flank de-
parts from the characteristic chair-shaped morphology
of the central region. A near-vertical cliff, more than
100 m high, bounds the eastern margin of the slide,
corresponding approximately with the trace of the Col
Tramontin fault. The pre-failure displacement meas-
urements reported by m
üller
(1964 and 1968) indi-
cated clockwise rotation of the slide mass, suggesting
that the right (eastern) flank was constrained by an
increased strength of the rupture surface in this area.
Based on the above arguments, the geotechnical
model used the lower (bedding) shear strength for the
Fig. 2 - Cross-sections of the sliding surface, used in the 2D analyses
background image
STABILITY AND FAILURE BEHAVIOUR OF THE VAIONT SLIDE
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
55
cohesion). Sarma analyses were completed only for
the first two sections. For the remaining two (10a and
x=1700) the Sarma program did not converge. In any
case, these sections are close to a circular shape, so
are unlikely to benefit very strongly from mobiliza-
tion of internal strength. Therefore, the Sarma Factor
of Safety for these sections is likely similar to that of
Morgenstern Price.
The results reported in Table 1 indicate that the in-
fluence of mobilized internal strength is not very great,
unless the full value of internal cohesion is included.
Without internal cohesion (although a high internal fric-
tion angle of 34ᵒ is used), the Sarma results exceed the
Bishop Factors of Safety by 10-16% for the two chair-
shaped Sections 2 and 5 and likely much less for the
remaining sections. Only with fully-mobilized internal
cohesion does the internal strength account for about
40% stability increase in Sections 2 and 5 and likely
less in the remaining sections. The Morgenstern-Price
Method predicts a much smaller influence of internal
strength of less than 10% (Spencer's Method was also
used and yielded very similar results). Because the non-
rotational Cross-sections 2 and 5 represent only about
one half if the slide volume, the overall effect of mobi-
lized strength on the stability of the slide is likely in the
range of 20-25% with cohesion and 5% without. This
is significant, because loss of internal cohesion due to
large-scale deformation during movement will lead to a
significant reduction of the resisting forces, leading to
brittle acceleration of the landslide.
& k
rahn
(1977) to allow the use of non-rotational slid-
ing surfaces, explicitly neglects the internal strength of
the sliding body. Its advantage here is that a three-di-
mensional version is available, which permits searching
for the critical direction of sliding. The Morgenstern-
Price Method is a "rigorous method” in that it satisfies
all equations of equilibrium and does include the influ-
ence of internal strength. However, the internal strength
is not specified as a function of material properties, but
is assigned by the solution algorithm so as to simultane-
ously satisfy the moment and force equilibrium (F
red
-
lund
& k
rahn
, 1977). There is also a 3D version of this
method implemented in the program CLARA-W, but it
cannot at present be optimized with respect to the di-
rection of sliding. The third method used is the Sarma
Method as programmed by h
Oek
(1997). The Sarma
Method is also a rigorous method. It relies on an explicit
assignment of strength on internal surfaces of the sliding
body. In this, the method resembles the technique used
by h
endrOn
& p
attOn
(1985).
Using the program CLARA-W, limit equilibrium
analyses were first conducted on four cross-sections
drawn in the downslope direction, as presented in Fig.
2. The first three of these sections coincide with the
Rossi-Semenza sections mentioned previously. Their
locations can be determined using the x-coordinates
on Fig. 1. Sections 2 and 5 were also simplified in the
form of blocks separated by vertical boundaries as
shown in Fig. 3 and analysed using a Sarma program
kindly provided to the author by Prof. e. h
Oek
and
based on h
Oek
(1997).
Strength properties and piezometric levels were
assigned as described in the previous section. For
Sections 2, 5 and 10a, the shear strength of the sliding
surface is based on ϕ=12ᵒ and zero cohesion, while
the internal strength for the Sarma Method involves
ϕ=34ᵒ, with or without a cohesion of 1500 kPa. The
additional section at x=1700 m, close to the eastern
flank, was assigned a basal friction angle of 34ᵒ (no
Fig. 3 Cross-sections 2 and 5, represented as block assemblies for analysis using the Sarma Method
Tab. 1 - Two-dimensional factors of safety for four rep-
resentative cross-sections
background image
O. HUNGR & J. AARON
56
International Conference on Vajont - 1963-2013 - Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
All of the sections located within the part of the
sliding surface that exposes bedding-parallel shears are
highly unstable, even with full mobilization of internal
strength. Only the section at x=1700 m, considered to lie
within the constraining zone, has a much higher Factor
of Safety, derived from the strength of the rock mass.
The stability of the slide thus relies to a very large de-
gree on the strength and spatial extent of the easterly
constraining zone of rock mass, as was also concluded
by h
endrOn
& p
attOn
(1985). It is possible that the
presented geotechnical model exaggerates this phenom-
enon. A further discussion of this is provided below.
Basal friction angles that would be required for
each section to be stable on its own would be 26ᵒ, 18ᵒ,
26.5ᵒ and 32ᵒ for Sections 2,5,10a and x=1700 respec-
tively, using the Morgenstern-Price Method. These
represent the maximum strength values that the sliding
surface could possibly have had.
THREE-DIMENSIONAL ANALYSIS
A 3D model was assembled in CLARA-W, us-
ing the sliding surface shown in Fig. 1 and Fig. 4. The
strength parameters, a piezometric surface and toe
submergence are the same as used in the 2D analyses
shown in Fig. 2. The assumed distribution of the two
types of shear strength on a plan of the sliding surface
is shown in Fig. 5
The strength of the constraining zone was consid-
ered both with and without a cohesion of 1500 kPa. Be-
cause large parts of the constraint are probably subject
to tensile stresses, as considered by Hungr and Amann
(2010), cohesion is likely to have been destroyed in a
large proportion of the constraint surface. Thus, the c=0
model is considered more realistic.
The results of the 3D analyses are shown in Table
2. The analyses show that the constraint is essential in
order to maintain marginal stability of the landslide,
even if an allowance for increased resistance due to in-
ternal shear strength of the cross-sections is allowed for
(up to a maximum of 25%, as discussed earlier). This
finding is in accord with the conclusions of h
endrOn
& p
attOn
(1985). Cohesion within the constraint ap-
pears especially important and the slide could not be
stable without it with the assumed strength parameters.
A loss of cohesion within the constraint could reduce
the overall resisting forces within the landslide by 50%
and marginal stability could not be achieved.
The analysis provides some other conclusions. If
there is cohesion within the constraint, a rotation of the
direction in which the forces are resolved by 10ᵒ coun-
ter-clockwise from the negative-y-axis could reduce the
Factor of Safety by more than 10%. But this effect is
not observed without cohesion.
The high piezometric surface proposed by Hen-
dron and Patton is necessary for instability. If the piezo-
metric surface was reduced to the level of the reservoir,
the minimum 3D Factor of Safety would be 1.10.
Fig. 4 - An isometric view of the assumed rupture surface
(see also Fig. 1). Published slide outline shown
Fig. 5 - A plan of the sliding surface output from CLARA-
W. The green area on the right is the part of the
sliding surface following bedding-parallel shears.
The yellow area on the left is the constraint, where
rock mass shear strength is assumed to prevail
T
ab. 2 - Summary of the 3D LE analyses carried out with
the reviewed geotechnical model, with bedding-
parallel friction angle of 12ᵒ and a constraint
placed as shown in Fig. 5
background image
STABILITY AND FAILURE BEHAVIOUR OF THE VAIONT SLIDE
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
57
of the 3D stability model, as shown in Fig. 1. Cer-
tain material which ran into the valley upstream of the
eastern boundary of the model is not accounted for.
Also, there could be some difference between the pre-
1963 topography and the recent Lidar-derived model.
In any case, there is no evidence of substantial bulk-
ing of the deposit, which confirms the hypothesis of a
nearly-intact sliding block
The dynamic analysis therefore utilized two ex-
perimental semi-flexible block models, which are
currently under development at the University of
British Columbia. The premise of the modelling is
that the planar layout of the landslide mass remains
essentially intact, like a semi-flexible blanket which
is able to shear in the vertical direction, but remains
coherent in plan. A similar model was used at Vaiont
in two dimensions by r
OmerO
& m
Olina
(1974).
A two-dimensional motion analysis was first car-
ried out using a modification of the 2D shallow flow
model DAN-W (h
unGr
, 1995). The modification in-
volved forcing the assembly of reference blocks to
remain coherent in the downslope direction. In order
to achieve this, instead of solving the equation of
motion separately for each element, the driving forc-
es and resisting forces for all elements, without the
pressure term, were each summed into a single re-
sultant force in each time step and the net force was
used to accelerate the flexible body down the slope.
Fig. 6b shows the resulting analysis, compared with
the actual cross-section before and after the slide, as
obtained from the digital terrain models as shown in
Fig. 6a. The analysis assumed that the friction angle
on the base of the slide was 23°, combined with a
constant pore-pressure coefficient ru (ratio of pore-
pressure to total vertical stress) which corresponds to
the high piezometric pressure as assumed in previous
analyses. The analysis shows a fair agreement with
the observation. The slide is displaced by about 270
m, having reached a maximum velocity of 14 m/s.
The basal friction angle of 23°, back-analysed by
the dynamic model is substantially higher than the 12°
used in the stability analyses. One reason for this is that
the dynamic calculations neglect internal strength of
the sliding body. This was seen to be able to increase
the stability of this cross-section by 11% to 40%, de-
pending on whether cohesion is fully active (as seen in
Table 1 by comparing the Sarma and Bishop results).
The second reason is that, according to the 3D analyses,
A further discussion of these results is provided
in the Conclusions.
ANALYSIS OF MOTION
TWO-DIMENSIONAL DYNAMIC ANALYSIS
Dynamic analysis of landslide motion is not yet a
routine procedure at present, although significant ad-
vances in the application of models have been made
in recent years. Most current models are unsteady
flow models based on an integrated ("shallow wa-
ter") solution of the equations of motion (e.g. h
unGr
et alii, 2005). However, such solutions cannot be ap-
plied to the Vaiont Slide, which is known to have
moved by several hundreds of metres as a nearly
solid block. Evidence of this is provided by the pre-
served stratigraphy around the margins of the deposit
and on the surface (S
uperchi
, 2012).
The overall volume of the detached mass, as es-
timated by subtracting the assumed sliding surface of
Fig. 1 from the pre-1963 ground surface is 294 million
m
3
. The deposit volume, obtained by subtracting the
sliding surface from the post-slide topography is 286
million m
3.
The latter number could be larger because
the calculation was carried out only within the limits
Fig. 6 a) Cross-section 2 (x=540 m), before and after the
1963 slide. b) Cross-section 2 before and after the
slide, analysed with the 2D flexible block model,
with ϕ=23° and an ru of 0.4. The thin lines are
profiles at 10 second intervals. The inset shows the
velocity profile of the front
background image
O. HUNGR & J. AARON
58
International Conference on Vajont - 1963-2013 - Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
the sliding body. Rotation of the sliding block around
the vertical axis was then determined from the torque
exerted by the driving and resisting resultants and di-
viding by the moment of inertia of the sliding mass.
The accelerations were integrated to obtain both
translatory and rotational velocities and displace-
ments and these were distributed to the individual
columns, depending on their radial distance from the
centre of rotation.
The initial analysis was made using the same
strength properties of the sliding surface as used for
the LE analysis. The larger, western part of the sur-
face was given a friction angle of 12° and a constraint,
at x>1500 m was given the friction angle of the rock
mass, 34°. The slide was seen to rotate strongly clock-
wise and overshot the observed displacement on the
western side by several hundred metres. As shown in
Fig. 8, a better correspondence with observations was
obtained by increasing the bedding-parallel strength
to 23°. This result compares favourably with the
above-described 2D analysis of Section 2 and can be
explained using the same arguments.
Fig. 9 shows perspective views of the slide be-
fore failure, after 1963 as surveyed by Lidar and a
comparison with the 3D analysis result. The model
shows unrealistic distortion of the debris surface at
the location of the Vailont Gorge, because no attempt
was made to simulate the filling of the gorge.
The 3D dynamic analysis is reasonable qualita-
tively, but it again shows the need to better account
for the internal strength of the sliding body. It also
seems to exaggerate the degree of rotation of the
sliding mass. This indicates that the initial geotechni-
cal model may be underestimating the shear strength
of the western part of the sliding surface.
Section 2 could not be stable without contribution from
the 3D effects. A third possible explanation, however is
that the 12° bulk friction of the western lobe of the slide
is, perhaps an underestimation.
Internal strength acts in the first vertical curve of
the chair-shaped profile, as pointed out previously by
m
encl
(1966) and others. However, an even greater
influence of internal strength is likely to play a role
during motion, as the landslide front impacts the right
side of the Vaiont gorge and is forced upward. This
impact was so powerful that a part of the right bank
was, in fact, entrained by the slide and thrust upward
(h
endrOn
& p
attOn
, 1985).
3D DYNAMICS OF A SEMI-FLEXIBLE BLOCK
The above-described method of dynamic analy-
sis of a flexible block was extended into three dimen-
sions. The model was configured in the same manner
as the 3D Limit Equilibrium analysis, by simulat-
ing the landslide mass by an assembly of over 2000
vertical columns. The driving force on each column
was determined as the downslope component of
its weight. The forces from all columns were then
summed into one driving force resultant. In the same
way, the resisting forces on the column bases were
determined by assuming zero frictional stresses on
vertical column boudaries and taking into account
the friction of the sliding surface and the piezometric
pressure prevalent at the moment of failure. Again,
these forces were combined into a single resultant.
The translatory motion of the slide was determined
in time steps, by determining a constant acceleration
as the ratio of the net resultant force and the mass of
Fig. 7 - Truncated" sliding surface of the Stage 1 failure
used in the analyses summarized in Tab. 3
Fig. 8 - Isopachs of the Vaiont deposit. a) as obtained from
the Lidar survey. b) Calculated using the flexible
block model
background image
STABILITY AND FAILURE BEHAVIOUR OF THE VAIONT SLIDE
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
59
mass would be associated with diagonal tension, acting
at a direction oriented 45ᵒ to the planes of maximum
shear, oblique to the direction of sliding. As proposed by
S
uperchi
(2012), the sliding mass may have separated in
course of failure along an oblique plane perpendicular
to this tensile stress field. A corresponding "truncated"
rupture surface was constructed as shown in Fig. 7. The
volume of the first stage failure is approximately 280
million cubic metres. A remnant volume of approxi-
mately 40 million m
3
is left in place. The analysis used
the same strength and piezometric properties as used for
the whole landslide.
The 3D LE analyses are summarized in Table 3, and
can be compared with Lines 2 and 3 of Table 2. This
comparison indicates that the truncated volume is about
20% less stable than the full volume of the slide. This
confirms that the two-stage failure hypothesis (S
uper
-
chi
, 2011 and S
uperchi
et alii, 2010) is very plausible.
The motion of the truncated Stage 1 landslide
was simulated using the flexible block model as
shown in Fig. 10. The block is predicted to shift
downslope and rotate clockwise, exposing a high
cliff in the north-east corner and removing support
from the 40 million m
3
remnant block. Although this
second failure stage was not modelled, in all likeli-
hood, the remnant block would fail almost simulta-
neously and follow the main mass to form the final
deposit, as described by S
uperchi
(2012).
LANDSLIDE WAVE
A variety of closed form and numerical tech-
niques exist to simulate the water waves generated by
the displacement of reservoir water by landslides (e.g.
S
linGerland
& V
OiGht
, 1978, h
eller
et alii, 2009).
The Vaiont case is not easily adaptable to routine anal-
ysis, because the volume of the water is much smaller
than the volume of the landslide masses displacing it.
TWO-STAGE FAILURE
The concentration of strength near the right (east)
flank gives the landslide a tendency to rotate clockwise
around a vertical axis. This trend is confirmed by pre-
failure displacement observations (m
üller
, 1964 and
1968), as well as by the behaviour of the 3D dynamic
model. During the pre-failure deformation period, this
tendency to rotate must have generated high shear stress-
es on downslope-oriented vertical planes near the right
margin of the slide, associated with tensile streses in the
east-west direction. Such stress conditions were analysed
by h
unGr
& a
mman
(2011), with examples of asymmet-
ric, laterally constrained planar and wedge slides. A ten-
dency of the tensile stress to destroy cohesion within the
rock mass forming the constraint was noted.
The highest value of tensile stresses within the rock
Tab. 3 - Summary of the 3D LE analyses representing the
first stage of a two-stage failure (see Fig. 7 and
Fig. 10)
Fig. 10 - Stage 1 failure runout, as analysed using the
3D flexible block model. The remnant block re-
mains in its original position
Fig. 9 - Isometric views of the Vaiont slide. a) before the slide, b) after the slide as surveyed by Lidar, c) Result of the flexible
block dynamic calculation
background image
O. HUNGR & J. AARON
60
International Conference on Vajont - 1963-2013 - Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
Also, the moving landslide forces the reservoir
volume against a steep and uneven opposing slope.
A simplified analysis was carried out by adapt-
ing an existing two-dimensional depth-integrated
unsteady flow model DAN-W (h
unGr
, 1995). In its
standard configuration, the model accepts a volume
of fluid and allows it to flow in directions dictated by
the inclination of the pressure potential surface. In
the modification developed for this analysis the left
boundary of the model was assumed to be a vertical
wall equal to the depth of the reservoir at the location
of the toe of the sliding surface of the Vaiont Slide
(Fig. 11). This vertical boundary was then forced to
move towards the opposite shoreline at a prescribed
rate of movement, pushing the water in front of it.
Turbulent water flow was assumed.
The prescribed movement rate assumed a para-
bolic velocity distribution in time, by an equation:
V
=
at
2
+
Bt
(Eq. 1)
Integrating Equation [1], one obtains a formula that
permits dimensioning the constants a and b in such
a way as to obtain a user-prescribed maximum ve-
locity and total displacement and an equation tracing
the displacement of the problem boundary in time.
The resulting prescribed landslide velocity profile is
shown by the dashed line in the upper part of Fig.
11 for a maximum velocity of 10 m/s. The maxi-
mum displacement was taken as 200 m to allow for
volume of landslide debris lost in filling the Vaiont
gorge. The slide duration is 30 seconds. As can be
seen by the full line in the upper part of Fig. 11, the
front of the wave advances about 3 times faster than
the motion of the landslide, due to the geometric run-
up magnification. The given input, i.e. maximum ve-
locity of 10 m/s produces good agreement with the
observed wave runup, and the height of overtopping
of the Vaiont Dam.
The same analysis is repeated in Fig. 12 for a
maximum slide velocity of 20 m/s. The predicted
runup is extreme and unrealistic in this case.
Fig. 11 - Prediction of the displacement wave, assuming a
peak landslide velocity of 10 m/s and a total dis-
placement of 200m. The thin lines show the wave
profile at 5 sec. intervals
F
ig. 12 Prediction of the displacement wave, assuming a
peak landslide velocity of 20 m/s and a total dis-
placement of 200m. The thin lines show the wave
profile at 2.5 sec. intervals
background image
STABILITY AND FAILURE BEHAVIOUR OF THE VAIONT SLIDE
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
61
supports this hypothesis.
The analysis of motion carried out during this study
in two and three dimensions also suggests that the as-
sumed 12ᵒ strength of the bedding-parallel surfaces
may be too low. However, this analysis is handicapped
somewhat by being unable to account for the internal
strength of the sliding body. This effect is likely to be
important in the later stages of motion, where the slid-
ing mass contacts the opposite slope of the Gorge.
Another uncertainty connected with the dynamic
analysis is the pore water pressure. Some authors,
including h
endrOn
& p
attOn
(1985) hypothesized a
strength loss due to frictional heating effects on the
sliding surface. On the other hand, the sliding surface
is known not to be perfectly thin and smooth. The pre-
historic slide created a sizeable zone of crushed rock
in the vicinity of the sliding surface. Dilatancy con-
nected with such failure behaviour would negate any
pore-pressure increases that could conceivably result
from heating. In any event, the dynamic behaviour of
the slide is strongly controlled by the process of in-
ternal cohesion strength loss and pore-pressure varia-
tion due to dilatancy, so that a frictional heating model
cannot be reasonably proven or constrained.
An analysis of the displacement wave, carried
out using an original model, concludes that the maxi-
mum slide velocity was of the order of 10 m/s. Given
the geometry of the Vaiont reservoir and the steep
slopes of the right bank, previously-reported veloci-
ties of the order of several tens of m/s would produce
totally unrealistic wave runup.
ACKNOWLEDGMENTS
Prof. R. Genevois, Mr. L. Zorzi and Ms. A. Wol-
ters provided essential data for this study.
DISCUSSION AND CONCLUSIONS
The relatively simple models presented above
are certainly not an exact representation of the com-
plex phenomenon that is the Vaiont Slide. They do,
however, permit some useful conclusions.
The underlying cause of the landslide was the
widespread presence of weak, pre-sheared bedding
planes in the slope. High piezometric pressures, con-
siderably above the level of the reservoir, were also a
necessary condition.
The present analysis confirms the hypothesis of
h
endrOn
& p
attOn
(1985), that internal strength of
the limestone rock mass plays an important role both
in increasing the sliding resistance of cross-sections
characterized by listric compound shape and in pro-
viding a 3D lateral constraint near the right (east-
ern) margin of the slide. The importance of internal
strength depends strongly on the degree in which the
large cohesive component is preserved.
The initial model, studied in this article, assumes
that the bedding-parallel shear strength is very low
(ϕ=12ᵒ) and that the internal cohesion is fully mobi-
lized. An alternative condition could be that the bulk
bedding-parallel shear strength is somewhat higher
(say, 23ᵒ), while the internal rock mass cohesion
is somewhat reduced. This alternative hypothesis
would be in agreement with the observation that the
sliding surface does not generally follow the precise
orientation of bedding, especially in the central por-
tion of the sliding surface and that the limestone lay-
ers overlying the rupture surface showed much dis-
turbance and crushing, before 1963.
It is certainly surprising that the great deficit of
resisting force in the western part of the slide that, as
implicit in the model, could be transferred to the lat-
eral constraint, without stresses. The present analysis
REFERENCES
F
redlund
d.G. & k
rahn
J. (1977) - Comparison of slope stability methods of analysis. Canadian Geotechnical Journal, 14:
429-439.
h
eller
V., h
aGer
w.h. & m
inOr
h.e. (2009) - Landslide generated impulse waves in reservoirs: basics and computation.
Mitteilungen 211, Versuchsanstalt für Wasserbau, Hydrologie un Glaziologie, R. Boes, Hrsg., ETH Zürich.
h
endrOn
a.J. & p
attOn
F.d. (1985) - The Vaiont Slide, a geotechnical analysis based on new geologic observations of the failure
surface. Technical Report GL- 85-5, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS. I, II.
h
Oek
E. (1997) - General 2-dimensional slope stability analysis. In: B
rOwn
e.t. (e
d
.). Analytical and Computational Methods
in Engineering Rock Mechanics. 95-128, Allen and Unwin, London.
h
Oek
e. & B
rOwn
e.t. (1980) - Underground excavations in rock. Institute of Mining and Metallurgy. Stephen Austin and Sons
Ltd., Hertford, London, 527 pp.
background image
O. HUNGR & J. AARON
62
International Conference on Vajont - 1963-2013 - Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
h
Oek
e., c
aranza
-t
OrreS
c.t. & c
Orcum
B. (2002) - Hoek–Brown failure criterion-2002 edition. In: B
awden
h.r.w., c
urran
J. & t
elSenicki
m. (
edS
.) - Proceedings of the North American Rock Mechanics Society (NARMS-TAC 2002). Mining
Innovation and Technology, Toronto: 267-273.
h
unGr
O., S
alGadO
F.m. & B
yrne
p.m. (1989) - Evaluation of a three-dimensional method of slope stability analysis. Canadian
Geotechnical Journal, 27: 679-686.
h
utchinSOn
J.n. (1988) - General report: morphological and geotechnical parameters of landslides in relation to geology and
hydrogeology. In: Proceedings of the 5
th
International Symposium on Landslides, Lausanne, 1: 3-35.
h
unGr
O., c
OrOminaS
J. & e
Berhardt
e. (2005) - State of the Art Paper #4, Estimating landslide motion mechanism, travel
distance and velocity. In: h
unGr
O., F
ell
r., c
Outure
r. & e
Berhardt
e. (
edS
.). Landslide risk management. Proceedings,
Vancouver Conference. Taylor and Francis Group, London.
h
unGr
O. & a
mann
F. (2011) - Limit equilibrium of asymmetric, laterally-constrained rockslides. International Journal of Rock
Mechanics and Mining Sciences, 48: 748-758.
m
encl
V. (1966) - Mechanics of landslides with non-circular slip surfaces with special reference to the Vaiont slide. Géotechnique,
XVI (4): 329-337.
m
üller
l. (1964) - The Rock slide in the Vaiont valley. Rock Mechanics andEngineering Geology, 2: 148-212.
m
üller
l. (1968) - New considerations on the Vaiont slide. Rock Mechanics and Engineering Geology, 6: 1-91.
r
OmerO
S.u. & m
Olina
r. (1974) - Kinematic aspects of the Vaiont Slide. Proceedings of the 3
rd
Congress ISRM, Denver,
Colorado, 2: 865-870.
S
elli
r., t
reViSan
l., c
arlOni
c.G., m
azzanti
r. & c
iaBatti
m. (1964) - La Frana delVajont. Giornale di Geologia, serie 20,
XXXII (I): 1-154.
S
emenza
e. & G
hirOtti
m. (2000) - History of the 1963 Vaiont slide: the importance of geological factors. Bulletin of Engineering
Geology and the Environment, 59: 87-97.
S
itar
n.m., m
aclauGhlin
m.m. & d
OOlin
D.M. (2005) - Influence of kinematics on landslide mobility and failure mode. Journal
of Geotechnical and Geoenvironmental Engineering ASCE, 131 (6): 716-728.
S
linGerland
r.l. & V
OiGht
B. (1979) - Occurrences, properties, and predictive models of landslide-generated impulse waves. In:
V
OiGht
B. (
ed
.). Developments in geotechnical engineering, rockslides and avalanches, 2: 317-397, Elsevier, Amsterdam.
S
uperchi
l., F
lOriS
m., G
hirOtti
m., G
eneVOiS
r. & S
tead
d. (2010) - Implementation of a geodatabase of published and
unpublished data on the catastrophic Vajont landslide. Natural Hazards and Earth System Sciences, 10: 865-873.
S
uperchi
l. (2011) - The Vajont rockslide: new techniques and traditional methods to re-evaluate the catastrophic event. Ph.D.
Thesis, University of Padova, 188 pp.
V
OiGht
B. & F
auSt
c. (1982) - Frictional heat and strength loss in same rapid slides. Géotechnique, 32 (1): 43-54.
Statistics