Document Actions

ijege-13_bs-paparo-et-alii.pdf

background image
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
583
DOI: 10.4408/IJEGE.2013-06.B-56
THE VAJONT LANDSLIDE, 9
TH
OCTOBER 1963:
LIMIT EQUILIBRIUM MODEL FOR SLOPE STABILITY ANALYSIS
THROUGH THE MINIMUM LITHOSTATIC DEVIATION METHOD
M
aria
a. PaParO, F
iliPPO
ZaNiBONi & S
teFaNO
tiNti
Università di Bologna - Dipartimento di Fisica e Astronomia - Bologna, Italy
INTRODUCTION
The landslide of Vajont, on October 9
th
1963, is
one of the greatest catastrophes in Italy: the mass that
detached from the Mt Toc slope flew into the reser-
voir at high speed, about 20 m/s (Z
aNiBONi
& t
iNti
,
2013, Z
aNiBONi
et alii, 2103) and the water it displaced
swept away or partially destroyed several villages, in-
cluding Longarone. The end result was 1917 victims
of which 1450 belonging to Longarone, 109 to Codis-
sago and Castellavazzo, 158 to Erto and Casso and
200 employees, technicians and their families who
worked for the company operating the dam.
The case of Vajont is still today an important mas-
terpiece for the study of stability, evolution and the
effects generated by a landslide, owing to the large
amount of data collected during the monitoring of the
site since 1936, the year in which the Vajont gulley
was chosen for the construction of the dam. And the
quantity of data increased even more as the conditions
of the slope became critical.
The late 50's and the early 60’s were the golden
years for Italy in industry and civil engineering and it is
in this context that the dramatic event happened. An am-
bitious project like this would have marked a decisive
unprecedented turning in the engineering field for re-
newable energy sources. But the tragedy was around the
corner, and we could say that it had already been written
during the first test of the dam. In a letter dated April 20,
1961, Dr Semenza, the project head, says, “Dopo tanti
lavori fortunati e tante costruzioni anche imponenti, mi
ABSTRACT
Fifty years ago the giant Vajont landslide slipped
in the homonymous lake and caused a disaster. The
purpose of this work is to apply classical limit-equi-
librium methods as well as a the variant developed by
t
iNti
& M
aNucci
(2006, 2008) and called Minimum
Lithostatic Deviation (MLD) method to analyse the
stability of the Mt Toc flank from where the slide de-
tached and to study the effect of the various factors
influencing stability.
The analysis was conducted on two profiles, one
representing the west-side and one representing the
east side of the slide, that were taken from the slid-
ing surface as reconstructed by using pre-slide and
post-slide topographic maps and by using suitable hy-
potheses from the literature on the shape of the hidden
part of the surface (that is the surface that remained
covered even after the slide occurrence).
The analysis shows that the angle of friction is the
most relevant parameter influencing the safety factor
more than the material cohesion. The analysis shows fur-
ther that the Vajont slide was close to instability. With data
used in this paper, a drop of the basin level from 710 m
a.s.l. down to 700 m a.s.l., in conditions of very high pie-
zometric level (790 m a.s.l.) as can be produced by intense
rainfall, may have the effect of drawing the safety factor
below the critical line of 1 and give rise to instability.
K
ey
words
: Vajont landslide, slope stability, limit equi-
librium method
background image
M.A. PAPARO, F. ZANIBONI & S. TINTI
584
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
jont slope opposite to the one that failed (H
eNdrON
&
P
attON
, 1985) are shown in Fig. 1. It can be seen, as
expected, an annual cyclicity (monthly panel) with nar-
row peaks, the highest one occurring in spring 1962.
Notice also that a sequence of precipitation peaks was
recorded in fall and winter of 1960.
The qualitative interpretation of the effect of pro-
longed rainfall is that it may leads to failures in strati-
fied soil over an impermeable layer. This is because rain
water infiltrations penetrate into the ground until reach-
ing the impermeable layer, over which a water saturated
band tends to form with reduced mobilised strength.
Consequently the safety factor – see the formal defi-
nition in the next section – may drastically decrease
(F
redluNd
& r
aHardjO
, 1993; F
redluNd
& X
iNg
,1994;
K
iM
et alii, 2004). In more general terms the increase of
the piezometric level is known to correlate quite well
with the decrease of the safety factor (K
aNeKO
et alii,
2009). It can be stated that creeping processes and ul-
timately slope failures, and in general the attaining of
critical conditions for stability, are more probable to oc-
cur after intense and repeated periods of precipitation.
As for the Vajont case, the slope that was to fail in
1963 and whose movements were being monitored by
means of a system of benchmarks exhibited a remark-
able peak of downslope creep velocity (up to 5 cm/
day) after the heavy precipitations in the fall of 1960,
as shown in Fig. 2.
trovo veramente di fronte ad una cosa che per le sue di-
mensioni mi sembra sfuggire dalle nostre mani” (After
many lucky works and impressive constructions, I really
face something that for its size seems to me to escape
from our hands) (B
uSettO
& g
aiaNi
, 1964).
In this paper our main goal is to apply the model
for the analysis of slope stability based on limit equi-
librium theory that was developed between 2006
and 2008 by Tinti and Manucci (t
iNti
& M
aNucci
,
2006 and 2008) and later revised by two of the au-
thors (P
aParO
& t
iNti
). This model will be designated
as MLD (Minimum Lithostatic Deviation) model
throughout the paper. We will also compare some of
our results with those obtained by using the classical
methods found in the literature and reformulated in a
way coherent with the MLD model.
THE GEOLOGY OF THE SLIDE
The Vajont valley is located in the north of the
Venetian Prealps and the homonymous torrent incised
the gorge along an E-W trending axis, by eroding it
along a synclinal (g
iudici
& S
eMeNZa
, 1960; g
HirOtti
,
1992). The particular shape of the valley is mainly due
to two erosive phases: the widest part formed in the
Würmian glacialism, and the deepest and narrow part
during an intermediate or post-glacial phase (C
arlONi
& M
aZZaNti
, 1964
B
; c
arli
, 2011).
The slope of the Mt Toc from which the slide de-
tached and the slide body itself were the object of very
many geological and geotechnical investigations espe-
cially over the years immediately before and after the
slide occurrence. The slope was found to be formed by
a succession of layers of dolomitic limestone, spaced
by thin layers of clays (g
eNevOiS
& g
HirOtti
, 2005).
But for some years after the disaster, the presence of
clay in the rock layers was not commonly accepted and
considered questionable (B
rOili
, 1967; M
üller
, 1968).
In our analysis we assume that the slope is composed of
Jurassic rocks and that the slide took place in the Fonza-
so formation along a slipping surface corresponding to
interbeds of clay (r
OSSi
& S
eMeNZa
, 1965; S
eMeNZa
,
1965; g
eNevOiS
& g
HirOtti
, 2005).
In addition to the specific characteristics of the soil,
rain was considered soon a key factor for the stability
of the Vajont slopes. During the four years of filling and
lowering of the basin level after the dam was built, rain-
fall was object of careful monitoring. Official monthly
and daily precipitation records taken at Erto on the Va-
Fig. 1 - Precipitation in mm recorded at Erto from 1960
to 1963 (after H
endron
& P
atton
, 1985). Monthly
(upper panel) and daily (lower panel) values
background image
THE VAJONT LANDSLIDE, 9TH OCTOBER 1963: LIMIT EQUILIBRIUM MODEL FOR SLOPE STABILITY ANALYSIS
THROUGH THE MINIMUM LITHOSTATIC DEVIATION METHOD
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
585
φ(x) is the angle of shearing resistance (F
elleNiuS
,
1936; t
erZagHi
, 1943, B
iSHOP
, 1955).
Let’s consider a 2D generic slice of the body with
vertical side walls placed at x-dx/2 and x+dx/2 where
dx is the horizontal slice width, and let’s denote the
slip surface and the top surface of the body by the
functions z
1
(x) and z
2
(x) respectively. If the base and
the top surfaces have local inclination angles α and β,
then the following equilibrium conditions should hold
(see t
iNti
& M
aNucci
, 2006, for details):
The first two equations come from imposing the
equilibrium of the horizontal and vertical components
of the forces acting on the slice, while the third one
comes from the momentum balance. In the above
equations P and S denote the respective normal and
shear components of the stress taken at the base of the
slice, E and X are internal normal and vertical forces
applied on the vertical slice walls, A is related to the
momentum associated with internal forces, D is a load
function applied on the slice top, ρ is the soil density
and g the gravity acceleration. In the problem, the
functions X(x), E(x) and A(x) have to satisfy the con-
ditions at boundaries of the slide, i.e. in the positions
x
i
and x
f
where the slide starts and ends:
The functions P(x), S(x), X(x), E(x) and A(x) are
unknown and since their number is greater than the
number of equations which describe the problem,
there cannot exist a unique solution (t
iNti
& M
a
-
Nucci
, 2006, 2008).
In the following we briefly outline the MLD meth-
One additional factor playing a role is the level
of the Vajont reservoir. Since the dominant mate-
rial of the valley is limestone, whose permeability
is higher than that of clay, if on increasing the basin
level a limestone layer is intercepted, then the basin
water may infiltrate laterally the underwater slope and
form an aquifer confined on the top by impermeable
clay layers, and this may cause a decrease of the shear
stress along the sliding surface (F
auKKer
& r
utter
,
2000; c
rawFOrd
et alii, 2008; v
aN
d
e
r
eeP
, 2009)
and favour slope destabilisation.
LIMIT EQUILIBRIUM THEORY
There is a variety of methods proposed for the as-
sessment of the stability of a slope. We focus here on
the limit equilibrium approach that is one of the most
commonly used in the engineering field. For the sake
of brevity and clarity, we will provide only an outline
of the method, and present the main formulas we ap-
plied in our study.
The limit equilibrium method is widely used since
it represents a simple and practical approximation to
describe the equilibrium of a mass having the potential
to detach and slide along a slope. Usually and also here
it is applied to two-dimensional profiles and the mass
is divided into blocks or slices by vertical cuts (B
iSHOP
,
1955). It is based on the definition of the parameter F,
which takes the name of safety factor, given by the ratio
where S
max
(x) is the mobilized shear strength at any
point along the slip surface and S(x) is the shear stress
at the corresponding point. This parameter can assume
different values, depending on the condition of the
slope: when it is equal to 1 the blocks are subject to the
maximum shear stress sustainable along their base.
Therefore when the ratio falls below 1 the blocks are
no longer in balance and the whole system becomes
unstable and is ready to move. On the contrary, if the
value is greater than 1, the system is stable.
The mobilized shear stress can be expressed by
means of the failure criterion introduced by Mohr-
Coulomb in the following way
S
max
(x)=c(x)+[P(x)-u(x) ] tan φ (x)
where c(x) is the cohesion, P(x) is the normal stress
along the slip surface, u(x) is the pore pressure and
Fig. 2 Rate of creeping recorded on the slope that was in-
volved by the Vajont slide from 1960 to 1963 (after
H
endron
& P
atton
, 1985)
background image
M.A. PAPARO, F. ZANIBONI & S. TINTI
586
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
means the MLD method and some of the most com-
mon classical methods. In the application of the
MLD method, the solution was searched by imposing
that X(x) is a sine series truncated to the third order
(see t
iNti
& M
aNucci
, 2006, for details). The curves
shown in the Figs. 3, 4 and 5 are the unknown func-
tions E(x), X(x) and A(x) and should vanish at the be-
ginning and at the end of the trial slide as imposed by
the boundary conditions. It can be seen that the plot-
ted curves do not differ too much from one another,
but only the curves calculated through the Spencer’s
method and through the MLD method fulfil the con-
ditions in all the graphs.
od by t
iNti
& M
aNucci
(2006) that introduces a mini-
mization principle to find a solution to the problem.
MINIMUM LITHOSTATIC DEVIATION
METHOD
The method of the Minimum Lithostatic Devia-
tion (MLD) was developed from 2006 to 2008 by Tin-
ti and Manucci (t
iNti
& M
aNucci
, 2006; 2008). Since
an infinite number of solutions exist to the problem of
equilibrium in the formulation of the limit equilibrium
theory, it was noted that one can always find a solution
where F is smaller than 1 or larger than 1, and there-
fore find that the slope is at the same time unstable
and stable. This inherent ambiguity was corrected by
introducing a minimization criterion and by consider-
ing F not as an unknown like it is assumed in the clas-
sical methods (F
elleNiuS
, 1936; B
iSHOP
, 1955; j
aNBu
,
1957, 1973; a
ryal
et ali, 2006; S
PeNcer
, 1967), but
as a free parameter. The best solution was assumed to
be the one minimising the lithostatic deviation, that
was defined as:
This is the ratio of the average magnitude of the
inter-block forces and the total weight W of the sliding
mass. A range of values of F is given as input, [F
min
;
F
max
], where F
min
is smaller than 1 and F
max
is larger, and
for each of them the problem is solved. The value of F
providing the solution with the smallest value of δ is
taken as the safety factor of the slope.
In Figures 3 to 5 the solutions we found for the
profile 2 of the Vajont slide (see next section) by
Fig. 3 - Curves of the horizontal inter-slice force E(x) for
different methods. At the boundaries the function E
should vanish. Notice that none of the Bishop meth-
ods (simplified and generalised) provide a solution
that goes to zero at the right boundary. Curves refer
to the profile 2 of the Vajont slide in case of dry soil
and water basin at the level of 700 m a.s.l
Fig. 4 - Curves of the vertical inter-slice force X(x) for
different methods. Notice that, like in Fig.3, the
generalised Bishop method provides a solution
that does not vanish at the right boundary. Notice
further that X is assumed to
be identically equal
to zero by the simplified Bishop method. The
horizontal x axis is the same as in Fig.3. See
caption of Fig. 3 for further details
Fig. 5 - Curves of the momentum A(x) for different methods.
Only for the Spencer and MLD method A vanishes
at both boundaries. The horizontal x axis is the
same as in Fig. 3.Other details in caption of Fig.3
background image
THE VAJONT LANDSLIDE, 9TH OCTOBER 1963: LIMIT EQUILIBRIUM MODEL FOR SLOPE STABILITY ANALYSIS
THROUGH THE MINIMUM LITHOSTATIC DEVIATION METHOD
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
587
the slide experienced very different basal friction in the
two sides (Z
aNiBONi
et alii, 2013).
The reconstructed topography over which the mass
slid down is depicted in Fig. 6, where also the boundary
of the area that was swept by the moving slide is giv-
en. In this paper we have selected two profiles as trial
curves for the stability analysis, also plotted in the Fig.
7: profile 1 on the west and profile 2 on the east side.
Cross-sections of both profiles are portrayed in
Fig. 7, where also the top of the slide (pre-failure to-
pography) together with the level of water basin and
of a possible piezometric line are shown. The trial
surfaces are approximated by circumference arcs,
also plotted in Fig. 7, we used to apply classical limit
equilibrium methods
Tables 1 and 2 report the geotechnical param-
eters we used to study the stability of the respective
profiles 1 and 2, that are taken from the literature
(H
eNdrON
& P
attON
, 1985). As the first step of the
analysis we have considered profile 2 and have used
the assumptions that there is no water in the basin
ANALYSIS OF STABILITY
To analyse the stability of a slope one needs a
trial basal curve representing the boundary where the
rupture is going to take place. In principle, the rupture
surface in 3D analyses, or the rupture curve in 2D, is
unknown. In this case a number of potential curves
are examined and one takes the one giving the small-
est value of the safety factor, under the assumption that
it is the most prone to break. This kind of approach is
appropriate to examine stability before failures, which
is the most common application. In this paper we study
a slope, namely Mt Toc flank, where a failure already
occurred, and that therefore showed to be unstable. The
purpose therefore is to find the main factors leading to
the instability over a surface that is already known.
We take advantage of the reconstruction of the slid-
ing surface of the Vajont slide that was made by the
authors to investigate the dynamics of the slide (see
Z
aNiBONi
& t
iNti
, 2013 and Z
aNiBONi
et alii, 2013). The
surface was obtained by exploiting the available topog-
raphies of the pre-slide (in front of the slide) and of the
post-slide (in the detachment niche) slopes and by con-
necting them in the intermediate section on the basis of
the conjecture that the west side and the east side of the
surface have distinctly different shapes: namely chair-
like downslope cross-sections on the west and parabol-
ic on the east (see S
elli
& t
reviSaN
, 1964 & H
eNdrON
& P
attON
, 1985). The conjecture is based on the main
observation that breaking occurred in correspondence
of an exposed clay layer on the west while affected
limestone on the east and it was proven to imply that
Fig. 6 - Topography of the sliding surface (after Z
aniboni
et alii, 2013) and boundary of the area swept by
the slide during its motion. The slide is subdivided
in two parts. For each part we selected one profile
Fig. 7 - Cross-sections of the profiles 1 and 2 selected for
the stability analysis. The best fitting circumfe-
rence arcs are the trial curves we used for the
classical stability methods. The basin level and a
possible piezometric level
are also shown
background image
M.A. PAPARO, F. ZANIBONI & S. TINTI
588
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
and that the soil is perfectly dry. The computed val-
ues of the safety factors are given in Fig. 8. Classical
methods were conceived for arc-like trial curves only
and hence the profile base has been approximated by
a circumference arc. On the other hand, we mention
that an extension of those methods was developed
by two of the authors (P
aParO
& t
iNti
) to allow the
application to generic trial curves.
By looking at Fig. 8 it is clear that all the meth-
ods predict that the slope is stable with F ranging
however between 1.10 and 1.4, with the generalized
Janbu’s method giving the smallest value and the gen-
eralized Bishop’s method the largest one. Further, it is
also evident that approximating the bottom surface by
a circumference arc leads to a systematic increase of
the estimates for F. Differences between the computed
values are small, but not negligible. For the rest of the
analysis we will use only the MLD method and drop
the unnecessary approximation of the arc-like bottom.
The stability of profiles 1 and 2 was studied with
the goal of examining the influence of the various fac-
tors intervening in the process. The main idea is that
the slope is affected by lateral infiltration of the water
from the basin and by infiltration from the top of rain
water. Both processes determine the increase of the pi-
ezometric level with consequent increase of the inter-
stitial pore pressure. We make the further hypothesis
that varying the water level in the basin affects also
the properties of the rock, passing from unsaturated
to saturated soil conditions (see Tabs 1 and 2) (l
ee
& d
e
F
reitaS
, 1989; K
iM
et alii, 2004). Our analy-
sis is static, that is time-independent and neglects the
time needed to transform dry soil into saturated soil.
Further we assume that the soil is saturated below the
level of the water in the basin and unsaturated above,
which means that increasing the basin level increases
the portion of the bottom surface characterised by
saturated soil properties.
We have examined the cases listed in Tab. 3 and
the results are shown in Figs. 9 and 11 for profile 2 and
in Figs. 10 and 12 for profile 1.
The general trends of the curves are similar for
both profiles but differ significantly from case to case.
In case 1 we use the properties of a dry soil (see Tables
1 and 2) and we consider the load of hydrostatic na-
ture exerted by the water in the reservoir on the slope,
Tab. 1 - Geothecnical parameters for profile 1 (H
endron
&
P
atton
, 1985)
Tab. 2 - Geothecnical parameters for profile 2 (H
endron
&
P
atton
, 1985)
Fig. 8 - Values of the factor of safety computed for profile
2 with unsaturated soil by means of all the meth-
ods mentioned in the paper
Fig. 9 - Trend of F with varying reservoir level for cases
from 1 to 5 of Tab. 3 for profile 2
Tab. 3 - Cases analyzed in the slope stability study
background image
THE VAJONT LANDSLIDE, 9TH OCTOBER 1963: LIMIT EQUILIBRIUM MODEL FOR SLOPE STABILITY ANALYSIS
THROUGH THE MINIMUM LITHOSTATIC DEVIATION METHOD
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
589
expected. It is worth noting that in these cases the pi-
ezometric level is also changed exactly as in case 2.
The effects of cohesion and friction angle changes are
studied separately. It is seen that lowering cohesion
(case 3) is much less effective than lowering the fric-
tion angle (case 4). And this is also confirmed where
both effects are considered together (case 5), since
the safety factor curve of case 5 is yet lower but only
slightly than the curve of case 4.
Case 5 is the one providing the lowest values of
the safety factor and the smallest value of F is ex-
pectedly corresponding with the highest basin level
considered in the analysis. If we compare findings
for profiles 1 and 2, we see that both profiles remain
stable for any level of the water and that profile 2 is
closer to instability conditions than profile 1. Further
we observe that curves of in Fig. 10 are more regular
than the ones of Fig. 9. Especially when the changes
of friction angle are taken into account (cases 4 and 5)
curves show a quick decrease (around level 660-690)
for profile 2, where they decrease steadily for profile
1, which is probably to be linked with the different
geometries of the two profiles.
Case 6 considers a condition where the water
basin is kept constant at the level of 710 m asl, and
the piezometric line is increased from 710 m to 790
m (H
eNdrON
& P
attON
, 1985). This increase can be
viewed as the consequence of heavy rains and rain
water infiltration in the slide from the top surface.
So what is studied here is the effect on stability of
an increased pore pressure, all the rest remaining un-
changed. The results are shown in the plots of Figs.
11 and 12 respectively for profiles 2 and 1. For both
profiles one can observe that the safety factor further
tending to stabilize it. It is seen that the safety factor
increases, along with the level of the water in the ba-
sin. The maximum water level considered in the anal-
ysis is 710 m asl. Though the highest allowed level
according to engineering specification for the Vajont
dam was 722 m asl, the level of 710 m asl was the
highest reached during the reservoir filling tests car-
ried out by the dam engineers.
It is found that on increasing the water level by
about 140 m the safety factors increases by less than
0.1 in both profiles. In addition to the stabilizing water
load, case 2 includes laterally infiltrated water and as-
sumes that the piezometric level is the same
as the basin level. According to the Mohr-Coulomb
criterion, an increment of the pore pressure following
the raise of the piezometric level entails a reduction of
the mobilized shear stress and weakening of the slope.
From Figs. 9 and 10 it seems that the resulting safety
factor remains almost constant, varying only by less
than 0.03. This means that the destabilization effect of
pore pressure increase counteracts and slightly exceeds
the hydrostatic stabilization of the basin.
Cases 3 and 4 consider the effect of the change of
the properties of the rocks in the transition from dry
to saturated values of the cohesion and of the friction
angle. As already enunciated above, it is assumed that
at the interface between the slide and the underlying
rock, that is on the bottom surface of the slide, one
finds the saturated lower cohesion and lower friction
angle values below the basin level, while above that
level the dry values are found. It follows that increas-
ing the water in the basin implies an extension of the
area of the bottom surface where the mobilized shear
strength is lower, and hence a lower safety factor is
Fig. 11 - Trend of F for case 6, profile 2. While keeping the
reservoir level constant at 710 m, we raise the piezo-
metric level from 710 to 790 m (H
endron
& P
atton
,
1985). Lowering the level basin from 710 m to 700 m,
instability conditions are attained (blue dot)
Fig. 10 - Trend of F for profile 1 for different cases from 1
to 5 (see Tab. 3)
background image
M.A. PAPARO, F. ZANIBONI & S. TINTI
590
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
effect of increasing the pore pressure, of decreasing
the inner cohesion and of decreasing the angle of fric-
tion of the material forming the slide. As expected, the
pure hydrostatic load was found to increase stability
(case 1) of the slope, while increasing the piezometric
level and decreasing coherence and friction coeffi-
cient were found to favour instability (cases 2-5). One
of the findings was that after heavy rain and with the
basin level at 710 m both profiles are very close to in-
stability, but still stable. However, lowering the level
down to 700 m causes the safety factor to go below the
critical threshold of 1 (case 6), which reflects the last
sequence of the historical facts leading to the collapse
of the slope on 9
th
October 1963.
The analysis we have performed is still prelimi-
nary and needs both an extension (analysis of more
profiles) and a validation of the geotechnical param-
eters that have been used to study instability. It seems
that the angle of friction is by far more influential than
the cohesion for the stability analysis of this case, and
therefore more specific studies should be addressed
to a better determination of its values and how they
can change in the transition from dry, unsaturated and
saturated rocks. It is worth noting that the hypoth-
esis of a heterogeneous slide surface with the west
side differing from the east side (see Tabs 1 and 2)
is corroborated by the dynamical study of the Vajont
slide performed by Z
aNiBONi
et alii (2013) where it
was found that the friction coefficient has to be much
smaller on the west than on the east to obtain a good
fit between the numerical results and the observations
(namely slide deposit and peak velocity).
ACKNOWLEDGEMENTS
This research has been partly financed by the Eu-
ropean project NearToWarn.
decreases and reaches values quite close to the critical
condition of failure.
As a final consideration we have considered a
sudden decrease of the water level from 710 m to 700
m, without any further change of the other conditions.
As seen in the analysis of case 1, decreasing the level
destabilizes the slope. And indeed what is obtained is
that for both profiles the safety factors drops below 1
(blue dot points in the graphs) and both profiles reach
conditions for failure. This last step, though sounding
artificial, respects indeed what happened in the Vajont
valley on October 9
th
1963. The slide occurred after
the level of the basin was lowered down to 700 m and
after a period of heavy rainfall.
DISCUSSION AND CONCLUDING RE-
MARKS
The main purpose of this paper was to study the
stability condition of the flank of Mt Toc that was in-
volved in the Vajont slide and the consequent disaster.
In this paper we have applied the limit equilibrium
theory in a variant, denoted minimum lithostatic de-
viation (MLD) method that was developed by t
iNti
&
M
aNucci
(2006 and 2008).
In the first part of the paper a short outline of
the basic limit equilibrium theory and of the MLD
method was given. It was also noted that the classical
limit equilibrium methods in their original formula-
tion require a slide bottom with an arc shape and that
a generalisation was developed by two of the authors
(Paparo and Tinti) to account for generic bottom sur-
faces. The most common classical methods and the
MLD method were applied to an exemplary case and
were shown to provide similar results though with
differences that cannot be neglected. Indeed the case
examined as an example was the profile 2 of the Va-
jont slide, and the values of F we found are in the
range 1.1-1.4 with a spread that is much higher than
changes produced by physical factors (pore pressure,
cohesion, friction angle).
The analysis of the slope was performed by us-
ing the MLD method and was applied to two profiles
that were obtained by cross-cutting the sliding surface
of the Vajont slide as reconstructed by Z
aNiBONi
et alii
(2013): one profile on the west- and one profile on the
east-side where geometries and conditions are different
following conjectures by H
eNdrON
& P
attON
(1985).
We have examined the separate and the combined
Fig. 12 - Trend of F for case 6, profile 1. See caption of
Fig.11 for further details
background image
THE VAJONT LANDSLIDE, 9TH OCTOBER 1963: LIMIT EQUILIBRIUM MODEL FOR SLOPE STABILITY ANALYSIS
THROUGH THE MINIMUM LITHOSTATIC DEVIATION METHOD
Italian Journal of Engineering Geology and Environment - Book Series (6) www.ijege.uniroma1.it © 2013 Sapienza Università
Editrice
591
REFERENCES
a
ryal
K., g
raNde
l. & S
aNdveN
l. (2006) - A study on interslice force function and line of thrust in slope stability analysis. In:
S
cHweiger
(
ed
.). Numerical methods in geotechnical engineering. Taylor & Francis Group, London: 497-500.
B
iSHOP
a.w. (1955) - The use of the slip circle in the stability analysis of slopes. Geotechnique, 5: 7-17.
B
rOili
l. (1967) - New knoledge on the geomorphology of the Vaiont Slide slip surfaces. Rock Mechanics & Eng. Geol. Jour. Int. Soc.
Rock Mechanics, V (1): 38-88.
B
uSettO
& g
aiaNi
(1964) - Commissione parlamentare d’inchiesta sul disastro del Vajont. I gruppo di lavoro: Nota sugli studi tecnico
scientifici connessi alla concessione delle acque e alla costruzione dell’impianto del Vajont (in Italian).
c
arli
M. (2011) - Thesis of Geological structural mapping and geoelectrical investigation of the North-occidental portion of the Vajont
landslide in the Venetian Prealps. Dipartimento di Scienze Geologiche, Università degli Studi di Padova.
c
arlONi
g.c. & M
aZZaNti
r. (1964 b) - Aspetti geomorfologici della frana del Vaiont. Riv. Geogr. It., 71: 201-231 (in Italian).
c
rawFOrd
B.r., F
aulKNer
d.r. & r
utter
e.H. (2008) - Strength, porosity, and permeability development during hydrostatic and shear
loading of synthetic quartz-clay fault gouge. Journal of Geophysical Research, 113.
F
aulKNer
d.r. & r
utter
e.H. (2000) - Comparisons of water and argon permeability in natural clay-bearing fault gouges under high
pressure at 20°C. Journal of Geophysical Research, 105: 16415-16426.
F
elleNiuS
w. (1936) - Calculation of the stability of earth dams. Proceedings of the 2
nd
Congress on Large Dams, 4: 445-463.
F
redluNd
d.g. & r
aHardjO
H. (1993) - Soil mechanics for unsaturated soils. Wiley, New York.
F
redluNd
d.g. & X
iNg
a. (1994) - Equations for the soil-water characteristic curve. Canadian Geotechnical Journal, 31: 521-532.
g
eNevOiS
r. & g
HirOtti
M. (2005) - The 1963 Vaiont Landslide. Giornale di Geologia Applicata, 1: 41-53.
g
HirOtti
M. (1993) - Nuovi dati sulla frana del Vaiont e modellazione numerica. Geol. Rom., 30: 207-215 (in Italian).
g
iudici
F. & S
eMeNZa
e. (1960) - Studio geologico del serbatoio del Vajont. Unpublished report for S.A.D.E.
H
eNdrON
a.j. & P
attON
F.d. (1985) - The Vaiont slide, a geotechnical analysis based on new geologic observations of the failure surface.
I, II, Technical Report GL-85-5. U.S. Army Eng. Waterways Experiment Station, Vicksburg, MS.
j
aNBu
N. (1957) - Earth pressure and bearing capacity calculations by generalised procedure of slices. Proceedings of the 4
th
International
Conference, SMFE, London, 2: 207-12.
j
aNBu
N. (1973) - Slope stability computations. Embankment dam engineering. Casagrande Volume: 47-86.
K
aNeKO
H., t
aNaKa
H. & K
udOH
y. (2009) - Slope stability consisting of two different layers caused by rainfall. In: O
Ka
, M
uraKaMi
&
K
iMOtO
(
edS
.). Prediction and simulation methods for geohazard mitigation. Taylor & Francis Group, London.
K
iM
j., j
eONg
S., P
arK
S. & S
HarMa
j. (2004) - Influence of rainfall-induced wetting on the stability of slopes in weathered soils.
Engineering Geology, 75: 251-262.
l
ee
S.g. & d
e
F
reitaS
M.H. (1989) - A revision of the description and classification of weathered granite an its application to granites
in Korea. Quarterly Journal of Engineering Geology, 22: 31-48.
M
üller
l. (1964b) - The rock slide in the Vaiont valley. Felsmech. Ingenieurgeol., 2: 148-212
M
üller
l. (1968) - New Considerations on the Vaiont Slide. Rock Mech. Eng. Geol., 6: 1-91.
r
OSSi
d. & S
eMeNZa
e. (1965) - Carte geologiche del versante settentrionale del M. Toc e zone limitrofe, prima e dopo il fenomeno di
scivolamento del 9 ottobre 1963, Scala 1:5000. Istituto di Geologia, University of Ferrara, Ferrara (in Italian).
S
eMeNZa
e. (1965) - Sintesi degli studi geologici sulla frana del Vajont dal 1959 al 1964. Memorie del Museo Tridentino di Scienze
Naturali, 16: 1-52 (in Italian).
S
eMeNZa
e. & g
HirOtti
M. (2000) - History of 1963 Vaiont Slide. The importance of the geological factors to recognise the ancient
landslide. Bull. Eng. Geol. Env., 59: 87-97.
S
PeNcer
e. (1967) - A method of analysis of the stability of embankments assuming parallel interslice forces. Geotechnique, 17: 11-26.
t
erZagHi
K. (1943) - Theoretical soil mechanics. John Wiley & Sons, Inc., New York, N. Y.
t
iNti
S. & M
aNucci
a. (2006) - Gravitational stability computed through the limit equilibrium method revisited. Geophysical International
Journal, 164: 1-14.
t
iNti
S. & M
aNucci
a. (2008) - A new computational method based on the minimum lithostatic deviation (MLD) principle to analyse
slope stability in the frame of the 2-D limit-equilibrium theory. Nat. Hazards Earth Syst. Sci., 8: 671-683.
v
aN
d
e
r
eeP
(2009) - Permeability of limestone-dolomite composite fracture surfaces. Honour Thesis
v
eveaKiS
e., v
ardOulaKiS
i. & d
i
t
OrO
g. (2007) - Thermoporomechanics of creeping landslides: the 1963 Vaiont slide, northern Italy.
background image
M.A. PAPARO, F. ZANIBONI & S. TINTI
592
International Conference Vajont 1963-2013. Thoughts and analyses after 50 years since the catastrophic landslide Padua, Italy - 8-10 October 2013
Journal of Geophysical Research, 112: F03026
Z
aNiBONi
F. & t
iNti
S. (2013) - Numerical simulations of the 1963 Vajont Landslide, Italy: Application of 1D Lagrangian Modelling.
Natural Hazards, submitted.
Z
aNiBONi
F., P
aParO
M.a. & t
iNti
S. (2013) - The 1963 Vajont landslide analysed through numerical modeling. In this volume.
Statistics