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41
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
DOI: 10.4408/IJEGE.2015-01.O-04
A
NTONIO
FEDERICO
(*)
, M
IHAIL
POPESCU
(**)
& A
GNESE
MURIANNI
(***)
(*)
Technical University of Bari - Bari, Italy - E-mail: antoniomario.federico@poliba.it
(**)
Illinois Institute of Technology - Chicago, IL.,USA - E-mail: mihail.e.popescu@gmail.com
(***)
D’Appolonia S.p.A. - Genova, Italy - E-mail: agnese.murianni@dappolonia.it
TEMPORAL PREDICTION OF LANDSLIDE OCCURRENCE:
A POSSIBILITY OR A CHALLENGE?
EXTENDED ABSTRACT
Nell’ottica di una cultura di prevenzione del rischio idrogeologico, purtroppo ancora sostanzialmente mancante, la mitigazione del
rischio da frana, attraverso la previsione del tempo di occorrenza degli accadimenti franosi, è un obiettivo di straordinaria valenza sociale,
economica e scientifi ca. La previsione di un franamento, laddove essa è possibile, consente, infatti ed anzitutto, di evitare - almeno in linea
di principio - la perdita di vite umane; ed, anche, di ridurre i danni economici, di pianifi care l’emergenza operativa e di porre in essere
adeguate contromisure di previsione e di controllo.
Il compito è tutt’altro che semplice, dal momento che è praticamente impossibile introdurre, nella modellazione del fenomeno, la mol-
titudine di variabili e fattori variamente intercorrelati e non tutti defi niti in termini del loro relativo contributo.
L’approccio al problema implica la comprensione del comportamento reologico dei materiali coinvolti nel potenziale movimento fra-
noso, descritto da una curva di creep che correla gli spostamenti di pendio al tempo. L’applicabilità di tale approccio è, tuttavia, alquanto
incerta, non essendo ancora del tutto chiara la fi sica del fenomeno di creep. L’estensione, poi, del modello reologico ad un problema a scala
reale è pressoché impossibile per un vasto insieme di ragioni, tra cui l’eterogeneità delle condizioni geologiche e della massa di terreno o
di roccia ed il fatto che, nella maggior parte dei casi, le pressioni interstiziali sulla superfi cie di potenziale scorrimento, i parametri geomec-
canici e le condizioni al contorno non possono essere defi niti in modo appropriato. A ciò si aggiunge l’impossibilità pratica di prevedere i
fattori esterni che possono innescare l’instabilità.
Al fi ne di rimuovere tali incertezze, viene comunemente impiegato un approccio empirico e fenomenologico per la predizione del
tempo di possibile franamento di un pendio. Basato sull’osservazione ed interpretazione di dati di monitoraggio, l’approccio in parola defi -
nisce tale tempo attraverso una funzione empirica, ottenuta con tecniche di regressione, che descrive l’evoluzione nel tempo di spostamenti
superfi ciali, deformazioni o attività micro-sismica del pendio.
In questo lavoro vengono presentati, per l’essenziale, alcuni metodi di questo approccio, riservando più risalto al metodo di Fukuzono,
del quale vengono pure brevemente illustrate varie applicazioni sia a pendii naturali che a fronti di scavo. Questo metodo, di facile appli-
cabilità, palesa, in generale, buona capacità predittiva a condizione che i) i dati monitorati siano di qualità ed i più rappresentativi della
tendenza cinematica del pendio, ii) le fl uttuazioni dei parametri in gioco non siano di breve periodo rispetto alla durata del creep e iii) sia
applicato con cautela ed i risultati ottenuti interpretati con giudizio.
Vengono poi succintamente presentate, in forma tabellare, varie tecniche avanzate di remote sensing, tra cui, in primis, l’interfero-
metria radar sia terreste che satellitare, con i loro vantaggi, limiti e performance complessiva. Rilievo è, invece, dato alla rifl ettometria
nel dominio del tempo (TDR - Time Domain Refl ectometry) ed agli assai migliorati metodi di emissione acustica (AE - Acoustic Emis-
sion): queste due tecniche presentano anche il vantaggio della possibilità di acquisizione automatica dei dati in tempo reale. Anche in
modalità remota.
Da ultimo, dopo aver delineato qualitativamente il legame tra il fenomeno di creep e quello di rottura progressiva, viene mostrato
un diagramma, che può avere utilità pratica nei casi in cui non si disponga di una serie storica di rilievi di grandezze cinematiche o
deformative. Il diagramma, implementato con ulteriori dati cinematici, fornisce indicazione di probabile imminente collasso se il punto
rappresentativo della situazione cinematica corrente del pendio - ottenibile con solo tre misure di spostamento, tra loro temporalmente
distanziate - si situa in prossimità della retta lungo la quale sono dispersi i valori (ultimi, ovvero a rottura) di velocità di spostamento
e di accelerazione
c
che, attinti dalla letteratura, sono relativi ad un gran numero di casi di frana con documentata evoluzione
temporale degli spostamenti superfi ciali.
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A. FEDERICO, M. POPESCU & A. MURIANNI
42
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
ABSTRACT
In the framework of landslide risk reduction, predicting the
time of occurrence of a slope failure is a goal of major importance.
The task is far from simple, since it is practically impossible to
account for the large number of controlling variables and factors.
For these reasons, an empirical and phenomenological approach is
commonly employed in the time of slope failure prediction, given
that it removes all the uncertainties involved. Based on the observa-
tion and interpretation of monitored data, this approach infers such
time mainly from ground surface displacements using regression
techniques based on empirical functions and neglecting rheologi-
cal soil parameters. The paper presents an overview of the methods
associated with this approach, with particular emphasis on Fukuzo-
no’s method accompanied by a number of its applications. Moreo-
ver, after a short account of advanced remote sensing techniques
and an outline of the qualitative link between creep and progressive
failure, a plot is shown which is potentially useful for early warning
when historical displacement data are not available.
K
EY
WORDS
: landslide, creep, time to failure, prediction, monitoring
INTRODUCTION
Forecasting the time of occurrence t
f
of landslides is a goal of
social, economic and scientifi c signifi cance in the framework
1
of
landslide risk mitigation, given that a reasonably accurate predic-
tion of t
f
would allow human losses to be-at least in principle-
avoided, damage to property to be reduced, adequate counter-
measures to be designed and operative emergencies to be planned.
The task is far from simple however, since it is practically impos-
sible to account, in the modellation of the phenomenon, for the
large number of variables and factors to be considered, that are
variously intercorrelated among themselves and not all clearly
defi ned in terms of their relative contribution. The approach to the
problem entails understanding the rheological behaviour of the
geomaterials involved, which can be substantiated in a displace-
ment versus time creep curve. However, the applicability of this
relationship is still doubtful, given that the fundamental physics
underpinning the creep phenomenon has not yet been fully eluci-
dated (H
UTCHINSON
, 2001). Furthermore, extension of the relation-
ship to the full scale problem is questionable for various reasons,
among them: the heterogeneity of the soil/rock mass and the fact
that, in most cases, pore pressures, mechanical parameters and
boundary conditions of the problem cannot be properly defi ned.
Moreover, it is impossible to forecast the triggering factors origi-
nating outside the sliding mass (e.g. heavy rainfall).
(1)
About 50 helpful reports on assessment and quantifi cation of landslide
risk and on most appropriate risk management strategies can be found at
the web site http://safeland-fp7.eu/.
Safeland was a large,integrating research project under the European
Commission’s 7
th
Framework Programme (FP7) started on 1 May 2009
and went on for 3 years, ending on 30 April 2012
For these reasons, an empirical approach, hereinafter named
“phenomenological”, is commonly employed, because it removes
all the uncertainties involved. It determines the time of occur-
rence (t
f
) of a landslide by means of a function, derived from the
results of laboratory creep tests, that empirically describes the
evolution over time of the monitored displacements/deformations
or microseismic activity of a slope.
In the following, a selection of predictive methods of this ap-
proach is briefl y presented to defi ne the conditions under which
they are applicable, referring a more detailed description to F
ED
-
ERICO
et alii (2012). Emphasis is given to the Fukuzono method and
several examples of its application are shown. This method pro-
vides an easy tool which can be quite reliable for t
f
prediction, as
long as i) the monitored data are of good quality, ii) the variations
of the involved parameters are not of short period in comparison
to creep duration and iii) it is applied with caution and the result
interpreted with care. Moreover, a short account is given of sev-
eral advanced remote sensing techniques with their advantages and
limits and of the possibilities offered by time domain refl ectometry
and improved geoacoustic methods. Then, after an outline of the
qualitative link between creep and progressive failure phenomena,
a plot is shown, that can be of practical usefulness when historical
series of slope displacement are not available.
FIRST PREDICTIONS OF SLOPE FAILURE
Historically, the fi rst successful time of slope failure predic-
tion is that of the Motto (alias Monte) d’Arbino rockfall in Tessin,
not far from Bellinzona (Switzerland). The rockfall occurred on
October 2
nd
1928, when 30 to 40x10
6
m
3
of rock blocked the
Arbedo valley, creating a small, 1.5 km long, lake (Fig. 1) (J
ÄG
-
GLI
, 1928; B
ONNARD
, 2006).
Fig. 1 - View of Motto d’Arbino rockfall dam in the Arbedo valley just
after the event, in 1928 (after B
ONNARD
, 2006)
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TEMPORAL PREDICTION OF LANDSLIDE OCCURRENCE: A POSSIBILITY OR A CHALLENGE?
43
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
The most interesting aspect of this case is that trigonometric
surveys had been conducted by the Federal Topographic Bureau
since 1888 (H
EIM
, 1932), supplying the fi rst scientifi c and duly
measured evidence (Fig. 2) of the acceleration phase before the
rockfall, allowing the evacuation of the 16 houses that were sub-
sequently destroyed (E
NGEL
, 1986).
Shortly afterwards, this technique was applied by Heim
(ibid.) to a rock slope above the town of Linthal in the Swiss
Alps, for which two separate predictions of catastrophic slope
failure were made, neither of which was successful. Heim re-
ported that “lack of experience” was the reason for the inac-
curate prediction.
A few decades later, a case that caught the world’s attention
was the slope failure forecast made for at the Chuquicamata mine
in Chile (Fig. 3), fi ve weeks before the event.
The date of failure (February 18
th
, 1969) was exactly pre-
dicted by rough hand-drawn extrapolation of the displacement
data of the fastest moving target on the slope surface. The predic-
tion allowed the rockslide to be managed and worked around in
such a way that production was stopped for only 65 h (K
ENNEDY
& N
IERMEYER
, 1970; H
OEK
& B
RAY
, 1977). However, as shown
by F
EDERICO
et alii (2011), the accuracy of the prediction is
questionable - and the prediction rather imprudent - given that a
hand-extrapolation beyond the last date of observation (January
13
th
, 1969) could have led to a number of other possible dates of
failure, within a time span of about two months, most of them
subsequent to the actual date of the event.
Fig. 2 - Reconstruction of movements at Motto d’Arbino from 1888 to 1933 (after E
NGEL
, 1986, modifi ed)
Fig. 3 - The Chuquicamata copper mine
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A. FEDERICO, M. POPESCU & A. MURIANNI
44
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
GROUND MOVEMENTS THAT PRECEDE A
LANDSLIDE
As the cases of Motto d’Arbino and Chuquicamata show,
displacement monitored data of a slope can be usefully analysed
for the prediction of the timing of a landslide.
Indeed, signifi cant creep
2
deformations develop in all slopes
before failure occurs (T
ER
-S
TEPANIAN
, 1980; T
AVENAS
& L
EROUE
-
IL
, 1981). These slope displacements against time before failure
can take the form of the third stage of a creep curve (Fig. 4),
i.e. of the stage of self-feeding instability, wherein accelerating
slope displacements are taken as a warning of imminent failure
(E
BERHARDT
, 2008). In this regard, the diagram (Fig. 5) in T
ER
-
ZAGHI
(1950) illustrating the ground movements
3
that precede a
landslide is substantially still valid.
If the slope is adequately monitored, its possible failure can
be predicted, commonly using an empirical approach. It consists
of defi ning the timing of a landslide through semi-empirical for-
mulations that describe the evolution of the displacement versus
time. Such functions usually, but not exclusively, derive from the
results of laboratory creep tests and relate the prefailure moni-
tored surface displacements to the time of slope failure. Herein
this approach is named “phenomenological”, to highlight that it
(2)
A comprehensive, overview on creep of geomaterials has been presen-
ted by V
ARNES
(1982).
(3)
Terzaghi (ibid.) emphasized the role of these movements: “It has often
been stated that certain slides occurred without warning. Yet no slide can
take place unless the ratio between the average shear strength and the
average shearing stress on the potential surface of sliding has previously
decreased from an initial value greater that one to unity at the instant
of the slide...(The landslides) are preceded by a gradual decrease of the
ratio which, in turn, involves a progressive deformation of the slice of
the material located on the potential surface of sliding and a downward
movement of all point located on the surface of the slice. Hence, if a lan-
dslide comes as surprise to the eyewitness, it would be more accurate to
say that the observers failed to detect the phenomena which preceded
the slide... The clay slides which occurred in the spring of 1935, during
the construction of the German superhighway from Munich to Saltzburg,
came as a surprise to the supervising engineers, but one week before the
movements started the laborers claimed that the slope becomes alive...”.
is based only on the available monitoring data, such as displace-
ment /deformation versus time or acoustic emission counts of a
slope and to distinguish it from other approaches based on the
application of specifi c constitutive viscous-elastic-plastic laws
implemented in numerical models.
OUTLINE OF THE PREDICTION METHODS USED
IN THE PHENOMENOLOGICAL APPROACH
As already said, a phenomenological approach is commonly
employed for forecasting a landslide, since it removes all the un-
certainties involved.
Prediction methods based on this approach can be divided
into two categories:
i) physically-consistent: the regression curve usually com-
plies with the rheological behaviour of the rock mass;
ii) regression-only: the regression curve is not driven by the
physics of the phenomenon.
Within the fi rst category, an additional distinction can be made:
1) methods for a “critical” prediction, i.e. a prediction per-
formed close to the failure, presumably in the tertiary
creep phase;
2) methods for medium and long-term predictions, where the
observations refer to a signifi cant part of the whole creep
period.
In addition to t
f
- time to slope failure, the following notations
are used below: η-displacement, ε-strain, t-time and t
0
-initial time
of the measurements or of the creep stage. The letters a, b, c and
α indicate empirical parameters derived from data fi tting, and are
specifi c to each method.
Fig. 4 - Ideal creep curve of a material
Fig. 5 - Diagram illustrating the ground movements that precede a
landslide (after T
ERZAGHI
, 1950)
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TEMPORAL PREDICTION OF LANDSLIDE OCCURRENCE: A POSSIBILITY OR A CHALLENGE?
45
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
Physically-consistent methods
Although philosophically seminal, the prediction technique
used in the Swiss Alps remained little known and did not benefi t
practically from further applications and developments. Indeed, it
was to be decades before research on the subject resumed.
The need for reliable methods to forecast slope failure has been
a vital subject of research over the last 50 years, especially in Japan,
where the second documented successful forecasting of slope failure
was made (S
AITO
& U
EWAZA
, 1961; S
AITO
, 1965). This was the land-
slide which occurred on December 14
th
, 1960 along the Ooigawa
railway line . It was predicted (...”forecasting was successful and
railroad traffi c was interrupted at 10.30 on December 13
th
,the day
before collapse” (S
AITO
, ibid.) on the basis of comparison of slope
displacement records and laboratory measurements of the strain rate
during secondary creep using load-controlled triaxial tests.
CRITICAL OR SHORT TERM PREDICTION
S
AITO
(1969) extended the mentioned method to the tertiary
creep phase, obtaining:
Equation 1 indicates that the time to failure during tertiary
creep is inversely proportional to the current strain rate.
Using this equation, S
AITO
(1979) predicted the Takabayama
landslide (January 1970) well in advance, while S
UWA
(1991) pre-
dicted the collapse of a rocky cliff-face on National Highway 327
in the village of Saigo, Japan. Thanks to the restriction of traffi c
following the prediction, no human life was lost.
By differentiating Equation 1, a linear relationship between the
logarithm of the acceleration and the logarithm of the time to fail-
ure is obtained. P
ICARELLI
et alii (2000), based on the monitoring
data of P
ELLEGRINO
& U
RCIUOLI
(1996) on a large number of slopes
monitored until failure, confi rmed the validity of Equation 1.
C
RUDEN
& M
ASOUMZADE
(1987) used a statistical distribution
method to better estimate the constants of Eq. 1, while A
ZIMI
et alii
(1988) suggested a graphical procedure for solving such equation
and estimating t
f
, based on the method proposed by A
SAOKA
(1978)
for determining one-dimensional consolidation settlement. The un-
derlying idea is to fi nd the time for which the displacement rate
tends to infi nity. Equations not dissimilar to Equation 1 were de-
rived by Y
AMAGUCHI
(1978) and H
AYASHI
et alii (1988a and 1988b).
Based on an experimental study of small-scale slope models
run until failure under monotonically increasing load, F
UKUZONO
(1985) found that for rapid failure the logarithm of acceleration
i
is proportional to the logarithm of the velocity
of
ground surface displacement, i.e.:
The a and α values may be estimated from a regression pro-
cedure. C
ROSTA
& A
GLIARDI
(2003) used a non-linear regression
method to derive a and α for the assessment of the alert-velocity
threshold of the Ruinon rock slide in northern Italy.
Integrating this equation for α
>
1, one obtains:
or
The plot 1/ vs t is linear for α
=
2, concave for α
<
2 and con-
vex for α>2. Extrapolating this plot, its intersection with the
abscissa should correspond approximately to the time of failure.
The assumption of linearity (α =2) usually provides a reasonable
estimate of t
f
. The relevant procedure is shown in Fig. 6. A simi-
lar graphical procedure is available for the case when the 1/
i
vs t
is not linear. Note that Equation 4 can be rewritten as
where (t
f
-
t) is the time interval until the slope collapse and that,
for α = 2, Equation 5 - if expressed in terms of strain ε-coincides
with Equation 1 proposed by S
AITO
(1969).
Fukuzono’s Equation 2 was manipulated and interpreted by
V
OIGHT
(1988a, 1988b and 1989) as a fundamental physical law
governing various forms of material failure under conditions
of constant stress and temperature. For the case of rock failure
due to accelerated creep, the variable η is a characteristic de-
formation, e.g. strain, rotation, displacement or seismic-energy
release. Moreover, drawing an analogy between failure mecha-
nisms and volcano eruption processes, η can also be interpreted
in terms of conventional geodetic, seismic or geochemical ob-
servations, enabling Equation 2 to provide a consistent basis
for eruption prediction (V
OIGHT
, 1988a and 1990; C
ORNELIUS
&
V
OIGHT
, 1995).
MEDIUM / LONG-TERM PREDICTION
The possibility of medium/long-time prediction was dealt
with by K
AWAMURA
(1985), who developed a method which ac-
counts for the entire creep phenomenon and is therefore - in prin-
ciple - applicable to medium/long-term prediction.
(1)
(2)
(3)
(4)
(5)
Fig. 6 - Diagrams illustrating the procedure for predicting the time to
failure (after F
UKUZONO
, 1990)
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A. FEDERICO, M. POPESCU & A. MURIANNI
46
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
The derived relationship is:
This model is the outcome of numerical analyses based on
creep theory and a large quantity of monitoring data.
F
UKUZONO
(1996) also introduced a creep-deformation model
related to the entire creep stage which makes it possible to predict
t
f
at an earlier stage. The related equation is:
Lastly, another physically consistent method for t
f
prediction
was more recently developed by M
UFUNDIRWA
et alii (2010), who
claim it is also suitable for slope failures governed by processes
and mechanisms not affected by creep (e.g. structural failures).
The adopted equation is that of F
UKUI
& O
KUBO
(1997), and it
represents strain divergence in the terminal phase of creep failure
in rocks:
where (t
f
-
t) is the life expectancy.
REGRESSION-ONLY METHODS
There are some other predictive methods which are based
only on different regression functions.
Building on a previous study by Y
AN
(1987), L
I
et alii (1996)
used the V
ERHULST
function, which is applied to the growth of
biological organisms and which is the solution of the following
differential equation:
The inverse V
ERHULST
function-whose shape (Fig. 7) is that
of a standard creep curve-is obtained as the symmetrical function
with respect to η
=
0 line in a η vs t plot.
With the initial condition η
=
η
0
at t
=
t
0
, the solution of Equa-
tion 9 is:
The inverse function derived from Equation 10 is:
If η
, failure occurs. This implies, if to
0, that (a
-
bt) →
0,
i.e. t
=
t
f
. The parameters a and b are provided by the best fi t of the
monitored data.
Li et alii (1996) reported two examples of this application,
where the observed data were in good agreement with the pre-
dicted values of the inverse function, and claimed that the predic-
tions based on this theory had an error ranging from 0 to 15 days.
M
IAO
& A
I
(1988) applied the “catastrophe theory” (P
OST
&
S
TEWART
, 1978) and proposed the following governing equation,
strictly limited to a purely cohesive soil:
By integrating Equation 12, one obtains:
When
α
=
2, Equation 13 - if expressed in terms strain ε - co-
incides with the Saito’s equation.
C
HEN
& W
ANG
(1988) applied the “Grey System Theory” ,that
is a method for studying problems for which few monitored data
and poor information is available. The limited knowledge of the
factors controlling the creep deformation and failure of a slope
and the inherent complexity of the slope system make a landslide
similar to a “Grey System”.
The derived solution (not reported here) is compared with the
accumulated displacement and the time at which the gradient of the
accumulated displacement tends to infi nity is the time to failure.
In the last two decades Artifi cial Neural Networks (ANN)
have been increasingly employed as effective tool in geotechnical
engineering. They are statistical methods and take their name from
the networks of nerve cells. Although they are a simplifi ed ver-
sion of biological neural networks, they retain enough of the struc-
ture observed in the brain to provide insight into how biological
neural networks might operate. Like these, an ANN can learn and
be trained to fi nd a solution, recognize patterns, classify data and
forecast future events (S
AKELLARIOU
& F
ERENTINOU
, 2005). A pecu-
liar feature of neural networks is that they do not require knowl-
edge of the relationship connecting input and output variables.
This computational tool has had a number of applications in
slope stability prediction (e.g. M
AYORAZ
et alii, 1996; A
LEOTTI
(7)
(8)
(9)
Fig. 7 - V
ERHULST
inverse function (after L
I
et alii, 1996)
(10)
(11)
(12)
(13)
(14)
(6)
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TEMPORAL PREDICTION OF LANDSLIDE OCCURRENCE: A POSSIBILITY OR A CHALLENGE?
47
Italian Journal of Engineering Geology and Environment, 1 (2015)
© Sapienza Università Editrice
www.ijege.uniroma1.it
& C
HOWDHURY
, 1999; G
AO
, 2008; Z
HANG
et alii, 2008; G
HAF
-
FARI
, 2010; K
AUNDA
et alii, 2010; SAFELAND Project-D1.5) A
detailed description of their use for the prediction of pore pres-
sures and slow displacement movements of slopes can be found
in M
AYORAZ
& V
ULLIET
(2002).
CREEP AND PROGRESSIVE FAILURE
All the prediction methods so far outlined account for the creep
phenomenon and do not mention the progressive failure phenom-
enon. In reality, these two phenomena are strongly connected and
hypotheses about the relationship between them have been circu-
lating for several decades (e.g. N
ELSON
& T
HOMPSON
, 1977; P
UZRIN
& S
CHIMD
, 2011). However a defi nitive theory encompassing creep
and progressive failure is not yet available, and the following com-
ments are offered as a schematic introduction to this problem.
Typical curves from creep tests are shown in Fig. 8. The early
part of these curves indicates a decreasing strain rate (primary
creep), reaching a minimum value that may be sustained for time
periods representing sizable strain (secondary creep). Eventually,
this prolonged straining leads to accelerated creep culminating in
failure of the specimen (tertiary creep).
As pointed out by N
ELSON
& T
HOMPSON
(1977), the accumula-
tion of plastic strains during primary and secondary creep stages
results in continuous deterioration of the soil’s internal bonds.
On the basis of published creep data (e.g. C
AMPANELLA
& V
AID
,
1974; M
URAYAMA
& S
HIBATA
, 1961) there is evidence that a critical
threshold of accumulated strains exists - specifi c to each type of
soil - at which all the variable components of strength have been
destroyed or overcome, causing the reduction of the shear strength
of the soil to its residual value. Then, if the locally applied stress
τ is greater than the residual strength
τ
r
, equilibrium is no longer
maintained and, as a result, progressive failure and stress redistri-
bution begin. On the other hand, if the applied stress is lower than
the residual strength, the system remains in equilibrium and pro-
gressive failure will not be triggered. However, as shown in Fig.
8, creep will continue at its slow rate. Obviously, from a physical
point of view, even this low strain rate can eventually lead to the
onset of progressive failure, depending on the
τ
/
τ
r
ratio.
From a mathematical point of view, modelling tertiary creep
requires a time dependent constitutive model (i.e. a viscosity
model) that is able to capture strain localization in a shear band
during progressive failure. As it is well known, local softening
plasticity is associated with strong mesh dependency and serious
problems of convergence as soon as strain localization occurs. In
order to avoid these problems, viscoplastic constitutive models or
higher-order continuum theories can be employed. Elasto-visco-
plastic constitutive models seem to be particularly suitable, as ex-
perimental evidence shows that the mechanical behaviour of all
geomaterials is time-dependent (D
I
P
RISCO
& I
MPOSIMATO
, 1996).
One regularization technique applied with success in the last
few years (D
I
P
RISCO
& I
MPOSIMATO
, 2003; T
RONCONE
, 2005; C
ONTE
et alii, 2010; M
URIANNI
, 2011) is the non-local elasto-viscoplastic
approach. The viscosity accounts for the time-dependent behaviour
of the soil thanks to the introduction of two viscous parameters
[calibrated on the basis of creep tests or parametric analysis (M
U
-
RIANNI
, ibid.)], while the non-local approach makes it possible to
overcome the numerical problems of the softening laws.
However, a great deal of research is necessary to render this
approach suitable for the analysis of slope stability.
A SHORT ACCOUNT OF ADVANCED MONITO-
RING TECHNIQUES FOR PREDICTING TIME TO
SLOPE FAILURE
The t
f
prediction methods outlined above are based exclusive-
ly on the measurement of displacement or deformation.
During the past 10 years there has been a rapid development of
remote sensing methods for monitoring slope displacement or de-
formation, enabling automated high -precision surveys. Table 1 lists
the main remote sensing methods and their (multiple) acronyms
along with their performance when applied to slopes instabilities.
The advantages and limitations of such methods are compared in
Table 2,while the rating of their mean features is shown in Table 3.
However, measurements can also be made of acoustic emis-
sions and time domain refl ectometry.
Geoacoustic methods were fi rst developed mainly to obtain
warnings of the occurrence of rockburst in mines (e.g. O
BERT
&
D
UVALL
, 1945, apud H
UTCHINSON
, 1983). Application of these
methods to rock slope stability problems came later (e.g. C
ADMAN
& G
OODMAN
, 1967; K
ENNEDY
, 1972; M
C
C
AULEY
, 1975; N
OVOSAD
et alii, 1977) when the Acoustic Emission (AE) count rate was
recognized as an early indicator of slope instability.
In Fig. 9 the extensometer data are compared to the accumulated
AE count measured during a slope-failure experiment carried out by
F
UJIWARA
et alii (1999). The similarity of the two curves is apparent
Fig. 8 - Constant stress creep curves (after N
ELSON
& T
HOMPSON
, 1977)
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A. FEDERICO, M. POPESCU & A. MURIANNI
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Italian Journal of Engineering Geology and Environment, 1 (2015)
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Tab. 1 - Main remote sensing methods
Tab. 2 - Advantages and limitations of the methods for remote monitoring of displacement or deformation (after M
AZZANTI
, 2012, modifi ed)
REMOTE MONITORING METHOD
ACRONYM(S)
PERFORMANCE
Terrestrial/Airborne Laser Scanning
also referred to as
Terrestrial/Airborne Light Detection and Ranging
TLS/ALS
Terrestrial/Airborne LiDAR
High
Terrestrial Interfermetric Synthetic Aperture Radar
also referred to as
Ground Based Interfermetric Synthetic Aperture Radar
TInSAR
GBInSAR
Extremely high
Satellite Interfermetric Synthetic Aperture Radar
also referred to as
Differential Interfermetric Synthetic Aperture Radar
SInSAR
DInSAR
Medium
Permanent Scatterers Interfermetric Synthetic Aperture Radar PSInSAR
Medium-High
Robotic Total Station
also referred to as
Automatic Total Station
or
Automated Motorized Total Station
RTS
ATS
AMTS
High
Refl ectorless Robotic Total Station
RRTS
Medium
Digital Photogrammetry
DP
Medium
Differential Global Positioning Systems
D-GPS
Low-Medium
ADVANTAGES
LIMITATIONS
TLS
• High density of information
• Good view of results thanks to the 3D models
• Long distance measurements
• Low accuracy
• Diffi cult data management
• Not effective in rainy and cloudy weather
ALS
• High density of information
• Wide-area coverage (up to regional scale
• Can obtain results also in vegetated areas
• Low measurement precisions (cm-dcm)
• Generally too expensive for repeat surveys
• Not effective in rainy and cloudy weather
TInSAR
• High density of information
• High accuracy and precision
• Effective in any weather conditions
• Diffi cult data processing
• Unidirectional measurement of deformation
• Phase ambiguity
SInSAR
• Monitoring at regional scale (large areas)
• Analysis of historical deformation (since 1992)
• High information density
• Low temporal frequency
• Unidirectional measurement of deformation
• Low spatial resolution
PSInSAR
• Monitoring at regional scale (large areas)
• Analysis of historical deformation (since 1992)
• High information density under favourable conditions
• Sensitivity to land cover conditions
• Unidirectional measurement of deformation
• Limitations on detectable displacement velocity
RTS
• High accuracy and precision
• 3D monitoring
• Easy to use
• Interaction with ground/structure (target required)
• Not effective in some lighting and weather conditions (fog, rain, etc.)
• Low accuracy at large distances
RRST
• Cost effective
• 3D monitoring
• Easy to use
• Limited range and incidence angle
• Not effective in some lighting and weather conditions (fog, rain, etc.)
• Limited number of investigated points
DP
• Simultaneous monitoring of large areas
• Cost effective
• Analysis of historical deformation
• Low accuracy and precision
• Not effective in some lighting and weather conditions (fog, rain, etc.)
• Low temporal frequency
D-GPS
• Monitoring of deformation along the three main directions
• Effective in any weather conditions
• Easy to use
• Strong interaction with ground/structure
• Low precision in the short term analysis
• Low information density
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and both resemble a typical displacement-time creep curve. Appli-
cation of rate process theory to AE activity gives better results than
techniques based on graphical analysis (S
HIOTANI
& O
HTSU
, 1999).
However, the technique has two shortcomings: the levels of
AE in fi ne-grained soils during shearing are very low (K
OERNER
et alii, 1981) and even in relatively noisy soils (i.e. coarse-grained
soils) attenuation may be high as a consequence of local energy
losses when AE is transferred from one particle to another. To
improve the detection of AE when dealing with deep soil strata,
K
OUSTENI
(2002) and D
IXON
et alii (2003a) proposed using of active
waveguides which consist of a steel tube installed in a pre-drilled
borehole with a coarse-soil backfi ll placed around it. The steel of
the waveguide transmits the signal generated by the soil deforma-
tion with low attenuation to a sensor at the ground surface (Fig. 10).
This technique is very promising and, being very sensitive to
small pre-failure slope deformations, can be used specifi cally as
an early-warning system. Based on the analysis of L
AMB
wave ar-
rival times, D
IXON
et alii (2003b) developed a method to locate the
AE sources along the waveguide; once the loci of these sources
are identifi ed, a developing or existing reactivated shear surface
can be located. The technique has been further improved to quan-
tify the displacement rate and to locate a developing or existing
reactivated shear surface (S
PRIGGS
, 2005; D
IXON
& S
PRIGGS
, 2007).
Originally developed to locate breaks and faults in communi-
Tab. 3 - Remote sensing methods: qualitative
rating of the main relevant features
(after M
AZZANTI
, 2012, modifi ed)
Fig. 9 - Comparison of extensometer results and accumulated AE count
(after F
UJIWARA
et alii, 1999)
Fig. 10 - Schematic of the AE monitoring system, including active
waveguide (after D
IXON
et alii, 2003 b)
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cation and power lines, Time Domain Refl ectometry (TDR) has
been extended to the monitoring of slope movements (K
ANE
&
B
ECK
, 1994; M
IKKELSEN
, 1996; O’C
ONNOR
& D
OWDING
, 1999). The
technique consists of logging the impedance to a pulsing electronic
signal along a coaxial cable. The impedance changes are correlated
with the distortions of the cable, such as crimping or shearing due
to rock deformations. Therefore, by installing either vertical or
horizontal cables in slopes, movements of slip planes, shear zones
and tension cracks can be easily detected. The location of the TDR
cable spikes correlates with the zone of movement and the rate of
spike growth correlates with the rate of slope movement (Fig. 11).
TDR cables have longer time effi ciency than inclinometers
and their functionality is rarely compromised. A signifi cant ad-
vantage of TDR, as well as of AE, is automatic data acquisition,
even remotely.
PREDICTION IN THE ABSENCE OF HISTORICAL
SERIES OF MONITORED DATA
The use of the above-described predictive approaches re-
quires long-term measurements of slope displacement or defor-
mation. However, sometimes it is necessary to evaluate the be-
haviour of an unstable slope even when long-term measurements
are not available.
A number of case histories of landslides, with well document-
ed temporal evolutions of recorded displacements, are reported
in the literature. In this study, the last monitored values of accel-
e r a t i o n
a
and velocity
before failure were derived
from the displacement time histories of different case studies. The
obtained values, reported in a log-log plot, were found to be scat-
tered along a straight line (Fig. 12) whose equation
is formally equal to Equation 2 from F
UKUZONO
(1985) and sim-
ilar to the equation derived by F
UKUZONO
& T
ERASHIMA
(1982)
from tests on small-scale models.
This plot can be of practical use when historical series of slope
displacements are not available: indeed, it indicates a probable im-
minent collapse if the representative point of the current slope’s
kinematic situation - which can be obtained using just three tempo-
rally spaced measurements - is close to the straight line.
EXAMPLES OF APPLICATION OF THE FUKUZO-
NO METHOD
The formulation by F
UKUZONO
(1985, 1989 and 1990), im-
plemented by Voight, is universally known as the F
UKUZONO
’s
method or the “inverse velocity method”. It is the most commonly
applied predictive method and is based on the consideration that
when the mean velocity of slope surface displacements becomes
high, its inverse tends to zero. Therefore, the intersection of the
curve 1/
w
with the abscissa represents the time of maximum
velocity, that is the time t
f
of the slope collapse.
The analysis of slope surface displacements on different time
windows along with the use of straightforward statistical methods
can further increase the potential of the Fukuzono method (A
L
-
LASIA
et alii, 2013; M
ANCINI
& G
IORDAN
, 2014).
In the following, several applications of this method will be
briefl y described.
SUCCESSFUL PREDICTIONS
A well known example of “post-factum” or backward pre-
diction (an oxymoron) using the Fukuzono method is the Vajont
landslide (Fig. 13).
Figure 14a illustrates the monotonic curve of increasing slide
velocity for the last phase of pre-failure movement at Vajont. In
this, the displacement velocities for survey points 5 and 63 for the
last 68 days before the failure are plotted versus time.
The same data are replotted as the reciprocal of the displace-
ment velocity versus time in Fig. 14b, where, even the simplest
extrapolation technique indicates, with the benefi t of hindsight,
that the catastrophic Vajont failure of 9
th
October, 1963 could
have been forecast more than a month and a half before this date.
As is well known, the slide created a surge of water in the res-
ervoir, overtopping the dam and killing more than 2000 people.
The comparison of fi gures 14a and 14b shows the clear pre-
dictive advantage of plotting the reciprocal of displacement ve-
locity against time instead of using the hyperbolic curve of dis-
placement velocity against time (H
UTCHINSON
, 2001).
Anyway, this method has had a number of successful and use-
ful applications with both natural and man-made slopes.
The case of a coal mine waste dump failure prediction is re-
ported by H
UNGR
& K
ENT
(1995): the dump failure, monitored by
Fig. 11 - Comparison of inclinometer and TDR measurements (after
C
ORSINI
et alii, 2005)
(15)
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TEMPORAL PREDICTION OF LANDSLIDE OCCURRENCE: A POSSIBILITY OR A CHALLENGE?
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Fig. 12 - Slope velocity
against acceleration
b
before failure for a number of landslides
Fig. 13 - The Vajont landslide (Italy) (courtesy of Prof. Paronuzzi)
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A. FEDERICO, M. POPESCU & A. MURIANNI
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An automatic monitoring system was immediately put in place.
Due to the fast movements, most of the rockslide body was not
accessible for the installation of benchmarks, with the exception
of the upper area. For this reason, it was decided to employ a re-
mote sensing technique based on radar interferometry (in particu-
lar, the GBInSAR technique), which allowed the highly precise
defi nition of the boundaries of the moving mass and the evolution
of the movement in space and time, as well as the magnitude,
failure mechanism and the runout distance of the rockslide.
The monitoring system at Mt. Beni started in April 2002 and
was carried out until December 19, 2002, just nine days before the
main event, when it was ceased for safety reason and benchmark
damage. It allowed an accurate forecast of the time of failure (Fig.
16), providing public authorities with all the necessary informa-
tion to plan suitable measures for risk management and reduction.
R
OSE
& H
UNGR
(2007) presented three case histories of open
cast mines in the United States, monitored during mining opera-
tions with manual and robotic total station surveys and wireless
extensometers, where t
f
was forecast . Moreover, the same authors
means of simple wire extensometers, involved 3 million cubic
meters of mine waste material.
A prediction was carried out on Mt. Beni (near Florence,
Italy) relative to a landslide that occurred on its eastern fl ank on
December 28
th
, 2002 (Fig 15) (G
IGLI
et alii, 2011).
The collapse was preceded by several forewarning signals.
Fig. 14 - “Post-factum” (after-fact) prediction of the Vajont landslide.
a) Displacement velocity versus time (after L
EONARDS
, 1987, modifi ed apud H
UTCHINSON
,
2001)
b) Application of F
UKUZONO
’s method (after H
UTCHINSON
, ibid., modifi ed)
a)
b)
Fig. 15 - The Mount Beni landslide (courtesy of Prof. Casagli)
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TEMPORAL PREDICTION OF LANDSLIDE OCCURRENCE: A POSSIBILITY OR A CHALLENGE?
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route for passenger vehicles and trucks, fi eld and aerial surveys of
the site were carried out soon after appearance of the fi rst geomor-
phologic evidence of landslide movements and surveying and moni-
toring systems were immediately activated in order to guarantee safe
transit to vehicles. The monitoring system consisted of a warning
device based on extensometers (alarm threshold of 2 mm/h for two
continuous hours) and real time automatic data acquisition system
capable of managing possible alert situations, thus allowing vehicle
circulation to be blocked and evacuation of the population from the
areas at risk. A road was constructed on the opposite bank as a diver-
sion for the worst case scenario of the landslide actually occurring
and was opened on August 9
th
. On August 10
th
a large typhoon-trig-
gered landslide occurred with a forecast of the collapse some hours
in advance (Fig. 18b). Thus, no people were affected and damage
was kept to minimum. The time of failure was quite precisely pre-
dicted using the data recorded by the installed extensometers.
It is interesting to note that, besides the Fukuzono method, the
prediction was also carried out using the Saito relationship (eq.
1) between strain rate in the tertiary creep phase and the residual
time to failure with almost the same precision.
More recent prediction examples regard the Preonzo (Swiss
Alps) landslide (L
OEW
, 2012, pers. comm.) and a landslide in the
Copper Bingham Canyon Mine
4
(southeast of Salt Lake City,
Utah, USA) landslide (Fig. 19), occurred on May 15
th
, 2012 at
11:30 am and on April 10
th
, 2013 at 9.30 pm, respectively.
(4)
Known also as Kennecott Copper mine, it is the largest man-made ex-
cavation in the world. It has been in production since 1906, and features
a pit almost 1 km deep and 4 km wide
presented a set of useful general rules for the use of the Fukuzono
method, together with an example of the method’s usefulness in
planning remedial countermeasures for an unstable rock slope,
using threshold velocity values based on the predicted t
f
. This ex-
ample concerns the instability of 3-10 Mm
3
of rock on the north-
east wall of the Betze-Post (Nevada) open pit mine. From early
May to late June 2002, slope movements within the Midnight/
Pats complex wedge exhibited accelerations. Fig. 17 shows the
plot of inverse velocity versus time for six targets located on the
upper slope, where a consistent linear trend is clear and indicates
a possible failure time of early to mid August 2007.
On the basis of this observation, it was decided to stabilize
the slide by unloading the active part and loading the foot of the
complex wedge.
A threshold movement rate
was selected for remediation activities to ensure that construction
and operation would be completed with a two-week buffer pe-
riod prior to failure, if it were to occur. As the graph shows (Fig.
17), approximately 3 days after construction started, a signifi cant
shift in the trend could be detected, as the slope began decelerating.
Remediation activities were carried out without causing signifi cant
disruption to the mine and continued over a period of about 3 weeks,
until slope displacement rates stabilized to acceptable levels.
The case of the Otomura landslide (Japan) (Fig. 18a) (F
UJISAWA
et alii, 2010) is a textbook example of operative emergency plan-
ning. In January 2004, cracks were found in retaining walls along
national highway 168 near Otomura village in Nara Prefecture (Ja-
pan). Given the strategic role played by this road as a long distance
Fig. 16 - Time of failure forecast for Mount Beni landslide: a): most sensi-
tive baselines; b): distometric base 1-2 (after G
IGLI
et alii, 2011)
Fig. 17 - Plot of inverse velocity versus time for six targets located
on the upper slope of Betze-Post (Nevada) open pit mine
(after R
OSE
& H
UNGR
, 2007)
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Italian Journal of Engineering Geology and Environment, 1 (2015)
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(POSSIBLE) UNSUCCESSFUL PREDICTIONS
As already said, given the empiric and phenomenological
character of the F
UKUZONO
method, its application does not re-
quire a detailed analysis of the factors which contribute to the
evolution of deformations until the collapse. Nevertheless, as
pointed out by H
UTCHINSON
(2001),failures may exhibit quite ir-
regular pre-failure movements, particularly when further vari-
ables are introduced by changes in internal or external condi-
tions. For these reasons, as several examples show, its use can
result in greatly inaccurate predictions. The fi rst example refers
to the already described Vajont landslide, where, as thoroughly
documented by Hutchinson (ibid.) “…increases of slide velocity
with time, somewhat similar to those of October 1963, occurred
in the autumn 1960 and in late 1962,but in neither case leading
to rapid failure. Had anyone been plotting data such as those
prior to the 9
th
October 1963, they may have been infl uenced
by these earlier records into thinking that the rate of movement
would again diminish without failure being reached.
”.
A second and equally impressive example of an unpredicted
trend break in the evolution of a landslide is given by the unusual
kinematic behavior of the la Clapière landslide (Maritimes Alps,
France) (Fig. 20), which is probably the biggest active landslide in
Europe. Its surface displacements have been monitored since 1982.
As Fig. 21 shows, to a long phase of increasing of displace-
ment velocity peaked at more than 80 mm/d in 1987, an unex-
pected trend reversal followed, with a slow return to a more
reassuring velocity of 20 mm/d in 1988. Currently, the most
active part of the rockslide shows a movement of about 0.4
m/y, slower than the rate of several m/y recorded during the late
1980’s (E
L
B
EDOUI
et alii, 2009).
The above case histories are characterized by a pattern of
surface displacement that is continuous in its evolution and is
described by a smooth concave curve, typical of an accelerating
creep phase, essentially due to a ductile failure of the affected
rocks and soils. When the slope failure has a brittle character,
especially if it involves strong rock masses, the displacement
records may have a step-like shape, characterized by instantane-
ous and abrupt jumps in short time intervals and nearly constant
values over long periods. In those cases, the inverse-velocity
method for the t
f
prediction is harder to apply (R
OSE
& H
UNGR
2007), even though the displacement-time diagram can give indi-
cations of the probable overall trend.
Fig. 18 - a) Otomura landslide (courtesy of Dr Pasuto); b) Plot of inverse velocity versus time for Otomura landslide (after F
UJISAWA
et alii, 2010)
Fig. 19 - Copper Bingham Canyon Mine (USA) landslide (after news.
yahoo.co)
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TEMPORAL PREDICTION OF LANDSLIDE OCCURRENCE: A POSSIBILITY OR A CHALLENGE?
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Italian Journal of Engineering Geology and Environment, 1 (2015)
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the Vajont landslide on October 9
th
, 1963. The theoretical interpreta-
tions of K
ILBURN
& P
ETLEY
(2003) are also important in this regard..
Anyway, the trend to self-stabilization of the la Clapière landslide
Theoretical speculations (H
ELMSTETTER
et alii, 2003), based on
a friction law function of velocity, seem to account for the singular
behavior of this landslide as well as of the catastrophic outcome of
Fig. 20 - Development of La Clapière landslide since 1938 (courtesy of Prof. Marinos)
Fig. 21 - a) Displacement velocity versus time (after R
OCHET
, 1992, modifi ed); b) Inverse of displacement velocity versus time in the period january 1987-
January 1988
a)
b)
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Italian Journal of Engineering Geology and Environment, 1 (2015)
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discussed in this paper, are empirical and phenomenological, gen-
erally relying on surface-based point measurements of displace-
ment/deformation monitored overtime. Inherently, this approach
is “holistic” (E
BERHARDT
et alii, 2008), disregarding the mechani-
cal behaviour of the soil and the infl uence it has on the develop-
ment of the landslide, the actual boundary conditions and details
pertaining to the underlying slope failure mechanism.
The lack of any direct relation to the physics of the phenom-
enon means that the results of these methods would be mainly of
academic interest, especially when the parameters involved have
a limited period of variation in comparison to creep duration. In
such cases, the inverse-velocity method should be applied with
caution, extrapolating the recorded data over varying time inter-
vals where the trend looks consistent, thus avoiding long-term
predictions (R
OSE
& H
UNGR
, 2007).
Regardless of the technique used for extrapolating the time
to failure, the quality of the prediction clearly depends on the
quality of the data, and correct identifi cation of the critical points
or parameters selected for the monitoring is thus essential in or-
der to produce a reliable prediction. This implies the need for
more progress in understanding pre-failure deformations and
other precursory signs of various landslide mechanisms (F
ELL
et alii, 2000). To this aim, the help offered by advanced remote
sensing methods can be considerable.
may be, more simply, the effect of the displacements themselves
5
as well as of the soil masses deposited by the constantly collapsing
toe of the slide which assist the stability (N
IEUWENHUIS
, 2002).
Equally surprising is the trend breaking (Fig. 22) of displace-
ments - due to the combined effects of rain and drawdown - of the
Baishuhe landslide (China), 56 km uphill of Three Gorges dam
along the Yangtze river (L
I
et alii, 2010).
The application to these cases of any one of the prediction
methods would have resulted in a mistaken disaster prediction.
DISCUSSION AND CONCLUDING REMARKS
There is a rich technical literature on the prediction of the
time of failure t
f
of a slope and a general framework for the pre-
diction of t
f
has been herein presented.
The methods for forecasting impending slope failure, briefl y
(5)
V
ERRUIJT
(1995) drew attention to the stabilizing effect of the down-
slope movement of slides along circular surfaces. He considered the
Bishop’s method and added a new formula for a slide displaced over
an angle of rotation β (measured at the centre of the slip circle). N
IEU
-
WENHUIS
(ibid.) considered the last 8 m of the monitored 40 m of displa-
cement, representing the displacements of the second half of 1987. This
displacement implies β=1°. A crude application of the Verruijt analysis
shows that the factor of safety varies from F=1.010 to F= 1.029, with
an increase of 1.9%.The stabilizing effect described by Verruijt is strong
enough to break the trend and slow down the la Clapière slide in its
1987 condition
Fig. 22 - Cumulative slope displacement versus time of Baishuihe landslide (courtesy of Prof. K. Yin)
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complished by means of deterministic methods but nevertheless
they introduce uncertainty. Critical prediction, performed close
to failure when there is strong instability, is relatively accurate,
given that the infl uence of chaos is minimized.
Expert visual examination of the plots of the monitored data
makes it possible to roughly assess the current creep stage of
a slope. If this stage is tertiary creep, the slope is in a critical
condition, close to failure, and the confi dence of the prediction
should be high, because of the reduced impact of factors causing
unpredictability.
In this respect, within the above mentioned limits, the plot in
Fig. 12 could have practical usefulness.
ACKNOWLEDGMENTS
This study was supported with funds from PRIN - National
Interest Research Programs 2008.
Emphasis has been placed on Acoustic Emission and Time Do-
main Refl ectometry because they appear particularly promising.
In several methods the frequency of the observations as well
as the time span of data collection affect the reliability of the
prediction.
In addition to the displacements, the observations would
need to be extended to other parameters such as pore pressure
and crack aperture.
All the methods reviewed in this paper neglect small varia-
tions in the infl uencing factors. This leads to a serious limitation
when dealing with predictions in the long-term. Chaos theory was
applied by Q
IN
et alii (2001) to determine the time scale for which
the prediction is reasonable and to refi ne the prediction within a
specifi c time scale with its relative error. According to these au-
thors, long-term predictions are strongly infl uenced by chaos and
therefore cannot be accurate. Medium-term prediction can be ac-
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Received February 2015 - Accepted May 2015
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