Corso di Dottorato Regionale in Scienze della Terra
PhD Course in Earth Sciences
XXX Ciclo – 30
thCycle
2014 – 2017
Tommaso Carlà
Time-series analysis of slope monitoring data
for early warning purposes
Tutore - Supervisor:
Prof. Nicola Casagli
Coordinatore del Corso di Dottorato
III
Acknowledgements ... VII
1. Introduction ... 1
2. State of the art on the prediction of geo-mechanical failure ... 5
3. Rationale of the research ... 15
4. Tertiary creep ... 19
Guidelines on the use of the inverse velocity method: data smoothing and 4.1. interpretation ... 19
Methodology ... 20
Results ... 22
Effects of noise on the reliability of failure predictions ... 34
Proposing standard procedures for inverse velocity analyses ... 37
Discussion ... 41
The 10-mile Slide (British Columbia, Canada): inferring behavior and kinematics 4.2. of a landslide from the deformation of a railway retaining wall ... 43
Description of the 10-mile Slide ... 44
Monitored displacement trends ... 50
Inverse velocity and forecasted time to failure ... 58
Discussion ... 63
Markedly brittle slope failures in hard rock masses: a challenge for monitoring 4.3. and early warning ... 66
Overview of the open-pit mine and of the instability case studies ... 67
Analysis of the case studies ... 70
Discussion ... 78
Use of satellite InSAR data for the characterization and prediction of 4.4. catastrophic slope failures ... 83
Introduction to the case study ... 85
Datasets ... 88
Analysis of the slope displacements ... 91
Discussion ... 96
IV
Database of mine slope failures ... 104
Analysis methodology and results ... 107
Implications for the management of unstable slopes and future developments .... 111
6. Numerical analysis of a displacement time series to determine the probability of a flank failure at Stromboli volcano (Southern Italy) ... 114
Introduction to the case ... 114
Geologic and volcanic background ... 115
Materials and Methods ... 117
Definition of probabilistic thresholds and anomalous ground deformation... 119
Results ... 121
Discussion ... 123
7. Remarks on the analysis of slope surface displacements for the prediction of geo-mechanical failure ... 126
8. Conclusions and future research ... 134
9. Full publications list (in chronological order) ... 136
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dei maggiori rischi idrogeologici. La rapidità di movimento del materiale mobilizzato è tale da essere associata ad enorme potere distruttivo, lasciando virtualmente nessun margine di tempo per intraprendere procedure di evacuazione o di messa in sicurezza dopo l’iniziazione dell’evento. Molti fattori possono determinare una slope failure; questi possono essere di natura variabile sia nello spazio che nel tempo. Sebbene sia comunemente accettato che lo spostamento superficiale e le sue derivate (i.e. velocità e accelerazione) siano i più affidabili indicatori diretti delle condizioni di stabilità di un pendio, e che il creep terziario sia l’effetto più evidente di un processo di rottura geo-meccanica progressiva in atto, vari aspetti devono ancora essere studiati e compresi riguardo l’acquisizione ed interpretazione dei dati di monitoraggio in fase di allertamento.
In tal senso, informazioni cruciali possono essere ottenute attraverso un approccio di tipo semi-empirico, cioè attraverso l’analisi a posteriori di un consistente numero di casi di studio. Di conseguenza, la ricerca si è imperniata attorno alla raccolta di vari set di dati di monitoraggio caratterizzati da fasi di accelerazione degli spostamenti. Sono stati considerati sia esempi di versanti in accelerazione che hanno raggiunto il collasso, sia esempi in cui il collasso, sebbene atteso, non è infine avvenuto e si è verificato il raggiungimento di una nuova condizione di equilibrio (i.e. non-failures). Inoltre, i casi di studio hanno riguardato le deformazioni di versanti naturali e artificiali sia in roccia che in terra, e anche le deformazioni di infrastrutture costruite su pendii in frana.
Si può fare riferimento a diverse metodologie per l’analisi di serie temporali di spostamento superficiale. Nello specifico:
Teoria del creep terziario
Metodi “database review”
Metodi numerici
L’applicabilità e lo sviluppo sia teorico che pratico di tutti questi metodi sono al centro dei contenuti di questa tesi. In particolare, a causa della sua diffusione e della sua rilevanza in ambito della gestione del rischio frana, ampio spazio è stato dedicato alla teoria del creep terziario e al relativo metodo del reciproco della velocità (o metodo INV). Relativamente a tale argomento, sono state definite linee guida per la corretta elaborazione ed interpretazione di serie temporali di spostamento superficiale. Dato che è stato rilevato come non necessariamente una fase di creep terziario generi sempre una failure, particolare sforzo è
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stato rivolto all’introduzione di metodologie in grado di indicare quanto una fase di accelerazione sia associabile alla probabilità di un collasso del materiale.
Fra i risultati del lavoro di ricerca, uno dei più importanti è consistito nel rilevamento che, contrariamente a quanto descritto nella letteratura scientifica, fasi di creep terziario (seppur estremamente rapide) sono state osservate anche in antecedenza a failure di natura marcatamente fragile in ammassi rocciosi di alta qualità geomeccanica. È stato quindi possibile concludere che l’osservazione di movimenti apparentemente istantanei in tali tipi di rocce è dovuta in realtà a un’inadeguata risoluzione temporale del monitoraggio, e non a un diverso comportamento cinematico. Un’altra tematica di interesse discussa all’interno della tesi riguarda l’opportunità di utilizzare l’interferometria satellitare per migliorare la caratterizzazione e la previsione di incipienti slope failures. In seguito allo studio del collasso inaspettato di un versante roccioso in una miniera di rame, chiaro creep terziario è stato osservato per la prima volta in misure di spostamento superficiale acquisite tramite questa tecnica. Ciò ha evidenziato come attualmente vi siano le potenziali condizioni per l’applicazione del monitoraggio interferometrico da satellite anche in fasi di allertamento.
Infine, l’ultima parte della tesi propone l’introduzione di due nuove tecniche per l’analisi di dati di monitoraggio di versante: una di esse è riferibile al campo dei metodi database
review, mentre l’altra a quello dei metodi numerici. La prima, basata su dati di spostamento e
velocità relativi a 40 eventi di collasso di pareti rocciose in alcune miniere di carbone, suggerisce l’esistenza di una relazione ricorrente nella curva accelerazione–tempo dei casi di studio analizzati e che l’accelerazione stessa sia un parametro più significativo della velocità in prossimità dell’istante di failure. La seconda, tramite lo sfruttamento di un avanzato modello numerico, è invece finalizzata alla definizione della quantità di spostamento superficiale anomalo mostrato durante un certo lasso temporale dal sito oggetto del monitoraggio; quest’ultimo metodo si adatta allo studio di fasi di deformazione periodicamente ricorrenti.
In ultima analisi è stato osservato come la previsione delle slope failures sia materia estremamente complessa, che abbraccia numerose limitazioni sia teoriche che pratiche. I contenuti proposti nella tesi mirano a superare tali limitazioni e in generale a migliorare lo stato delle conoscenze sui fenomeni di rottura geo-meccanica. In ogni caso è risultato evidente come un approccio a scatola nera, in cui i dati sono analizzati senza giudizio critico e senza considerazione delle specifiche proprietà del sito, sia da evitare. Al contrario, ogni programma di monitoraggio e sistema di allertamento è efficace soltanto se attentamente calibrato e contestualizzato relativamente allo stile deformativo del versante e al rispettivo scenario di rischio.
VII
live up to someone’s expectations.
First of all, I would like to thank Prof. Nicola Casagli for giving me the opportunity and the tools to undertake and complete my PhD program. Particular thanks are directed to Dr. Emanuele Intrieri and Dr. Paolo Farina, whose continuous and unmatched support was essential in developing my research. I am thankful to Dr. Paolo Farina also for providing me with several of the case studies presented in this thesis, which invaluably enhanced the value of the results. On another note, I cannot forget how much being at work was enjoyable by having the original “red roommates” Dr. Federica Bardi, Dr. Giulia Dotta, and Dr. Teresa Salvatici next to my door: thanks for enduring my presence and for the many good times together. My thoughts go then to Prof. Giovanni Gigli, Dr. Massimiliano Nocentini, Dr. Luca Lombardi, and Dr. Veronica Tofani, who always helped me keep a positive mood and deal with any doubts or concerns I may have had. Ultimately I thank all the people of the engineering geology research group at the University of Florence.
During my PhD I had the chance to work for 6 months at the Department of Civil Engineering of the University of Alberta in Edmonton, Canada. I cannot possibly tell how much of an exceptional experience that was. I will always feel indebted to Prof. Derek Martin for making it happen, and I would like to extend this thought also to Dr. Renato Macciotta and Prof. Michael Hendry. Your teaching and advice allowed me to greatly improve both my competences and my attitude to research. An additional thank you is due to Dr. Renato Macciotta, who treated me not only as a colleague, but also as a true friend.
All the above cannot be even closely compared to the gratitude that I owe to my parents Roberto and Susanna, my brother Lorenzo, and my sister Giulia. I will not elaborate further, since I would need at least 3 or 4 times the number of pages of this thesis if I had to tell everything they have done for me in my life.
Finally, last but not least, I would like to reserve a special mention to my beloved Teresa. You already know what are my feelings for you. I will certainly not use these lines to make them public, but I will just repeat: thank you.
VIII “If a landslide comes as a surprise to the eyewitnesses, it would
be more accurate to say that the observers failed to detect the phenomena which preceded the slide”.
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1. Introduction
Landslides are one of the most frequent type of geo-hazards, and have an enormous impact on society, economics, and environment (Guzzetti et al., 2003). They can be defined as any mass of earth material (soil or rock) displaced under any action of the gravity. In Italy alone, at least 10 000 people died in consequence of landslides between 1279 and 1999 (Guzzetti, 2000), and 8077 people were killed or injured in at least 1398 events at 1239 different areas during the 20th and 21st century (Salvati et al., 2015). In recent times, factors such as excessive land use, uncontrolled urbanization, and improper urban planning have led to an alarming worldwide increase in the frequency of landslides occurrence (Nadim et al., 2006; Petley, 2012).
The risk posed by landslides is related to their rate of displacement (Guzzetti, 2000), as well as to factors such as volume, runout, exposure, etc. Fast-moving phenomena such as rockfall, rockslides, rock avalanches, and debris flows are typically the most difficult to manage. In particular, great destructive power is associated with the so-called “slope failures”: resulting from a sudden strength drop over one or more controlling rupture planes, these involve physical detachment and consequent total collapse of rock and/or earth material at local or global scale (“very rapid”, as for Cruden and Varnes, 1996). Geo-mechanical failure occurs when the acting loads or stresses exceed the strength of the material forming the slope. As strain levels increase, strain softening may in fact lead to non-recoverable deformation and failure development (Zavodni and Broadbent, 1980). Both natural and engineered slopes can experience failure. Famous examples of large catastrophic failures affecting a natural and an engineered slope are the Vajont landslide and the Bingham Canyon mine failure (Figure 1).
Generally speaking, landslide risk can be reduced in several ways: stabilization works can be undertaken to improve the factor of safety of the slope; physical barriers can be installed to prevent the moving mass from reaching the exposed elements; or existing buildings and infrastructures can be reinforced. Unfortunately, these defensive techniques are often not adequate to counteract the size and rapidity with which slope failures commonly occur, and are also limited by economical/logistical constraints that may not be possible to overcome. In such cases, the timely evacuation of the dangerous area remains the only viable procedure for protecting vulnerable communities (Kilburn and Petley, 2003).
Any evacuation strategy is closely dependent on the implementation of an effective early warning system (EWS). EWSs aimed at reducing the risk from natural hazards are defined as “monitoring devices designed to avoid, or at least minimize, the impact imposed by a threat on humans, damage to property, the environment, or/and to more basic elements like livelihoods” (Medina-Cetina and Nadim, 2008; Intrieri et al., 2013), and include the following activities (Intrieri et al., 2012): monitoring, data analysis/forecasting, dissemination of alarms,
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and definition of response actions (Figure 2). All of these need to be calibrated and contextualized in the frame of the studied scenario.
Concerning the phases of monitoring and forecasting, one of the most crucial aspects is determining which are the variables that should be measured in order to have an accurate understanding of the investigated phenomenon and of its possible evolution. When conducting analyses at basin/regional scale, the preferred and often only practical approach is to relate the landslide distribution to one or more triggering factors. For example, several authors have proposed statistical or probabilistic models of landslide occurrence and susceptibility that are dependent on rainfall intensity–duration relationships (e.g. Keefer et al., 1987; Guzzetti et al., 2008; Rosi et al., 2012; Segoni et al., 2014; Lagomarsino et al., 2015), seismic activity (e.g. Kamp et al., 2008; Lee et al., 2008; Gorum et al., 2011), or a combination of predisposing geological and geomorphological features (e.g. Çevik and Topal, 2003; Ermini et al., 2005; Catani et al., 2013). However, these methods are necessarily approximated at larger scales, as the nature and effect of the variables driving slope instabilities can vary sharply both in space and time.
Figure 1. (a) The Vajont landslide and (b) the Bingham Canyon mine failure.
On the other hand, effective early warning of slopes prone to catastrophic geo-mechanical failure requires the analysis of site-specific data. In this context, the near real-time monitoring of key parameters selected as stability indicators assumes pivotal importance. Regardless of the mechanism of instability and of the type of destabilizing forces in effect, it has been long observed that substantial information about the kinematics of a landslide can be obtained by measuring the deformation of the slope surface (Gili et al. 2000; Brückl et al. 2006; Baldi et al. 2008a; Teza et al. 2008). Variations in slope surface deformation trends may in fact be the result of changes in the internal strength-stress regime or indicate the evolution of the moving mass towards failure (Macciotta et al., 2016). Moreover, long-term slow deformations have been repeatedly observed to anticipate the geo-mechanical failure of slopes and of geomaterials under laboratory testing. For this reason, displacement and its derivatives (i.e. velocity and acceleration) are widely considered the best indicators of slope stability conditions (Rose and Hungr, 2007; Lacasse and Nadim, 2009; Mufundirwa et al., 2010).
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Figure 2. Flow chart of a generic EWS (from Intrieri et al., 2012).
Measuring the slope surface displacements has therefore become the standard practice for the setup of monitoring systems, and a variety of instruments may be used to this aim. These include total stations and prisms, wire and rod extensometers, inclinometers, tiltmeters, Global Positioning System (GPS) devices, and geo-phones to record the intensity of ground noise as an indirect measure of deformation and rock disaggregation. In recent years, significant improvement of the accuracy and sampling rate of slope displacement data has been obtained with the introduction and development of radar interferometry. Ground-based radar devices calculate displacements by measuring the phase difference of the back-scattered microwave signal between two or more coherent acquisitions (Antonello et al., 2004; Luzi et al., 2006; Casagli et al., 2010; Di Traglia et al., 2014a; Monserrat et al., 2014; Bardi et al., 2017; Casagli et al., 2017), without the need to install artificial reflectors on the slope. This technology presents the advantages of high measurement accuracy, high spatial and temporal resolution, long-range capabilities, and limited impact of atmospheric noise (Farina et al., 2013). In this sense, mine operations are important laboratories of slope failure research: advanced slope monitoring programs are in fact commonly deployed to preserve the safety of the personnel and the integrity of the mining equipment, and at the same time maximize the extraction of the mineral resources (Figure 3). The amount and detail of data collected in such environments are hardly matched by any monitoring system in natural slopes. Moreover, the frequency of active instabilities in mines is greatly enhanced by the variations in stress deriving from the continuous man-induced changes in slope geometry and loading conditions (Crosta et al., 2017).
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Following the considerations above, in scenarios of near real-time slope monitoring it is common practice to establish arbitrary thresholds of displacement or velocity representative of different alarm levels. The main limitation of this “observational” approach is that it relies heavily on the experience and interpretation of the user, and therefore is usually very conservative. Thresholds are in fact mostly defined through the back-analysis of events occurred in similar morpho-climatic settings (Bhandari, 1988; Crosta and Agliardi, 2002). Unfortunately, displacements and velocities in proximity of failure have been observed to vary across a wide range of values (Ryan and Call 1992, Cabrejo et al., 2012), even among case studies where the type of failure mechanism and the mechanical properties of the sheared material were similar.
Figure 3. Ground-based interferometric radar installed in an open-pit mine for slope displacement monitoring.
The object of this thesis is to further develop the knowledge, methodologies, and procedures for the time-series analysis of displacement data of unstable slopes. Specifically, the main goal is to provide a framework for improving the ability to effectively anticipate catastrophic events of geo-mechanical failure and set up corresponding alarms. The research was crucially supported by several datasets of slope displacement measurements that have been collected and reviewed during the 3 years of research as a Ph.D. student. These included both cases of failure and “non-failure” (i.e. events of rapid acceleration that ultimately did not evolve into failure) in natural slopes, engineered slopes, and artificial structures built on landslides. Part of the research was carried out during a 6-month research period at the School of Petroleum and Mining Sciences, Department of Civil Engineering, of the University of Alberta (Edmonton, Canada), under the supervision of Prof. Derek Martin, Prof. Michael Hendry, and Dr. Renato Macciotta.
Section 2 presents an overview on the current state of the art concerning the analysis of slope displacement data for assessing the probability of geo-mechanical failure. Then, the following sections describe the reviewed case studies of slope instability, and the consequent findings and insights that are relevant to the practices of landslide risk management and early warning.
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2. State of the art on the prediction of geo-mechanical failure
The onset of rapid movements of hazardous slopes is one of the main sources of concern in the field of geo-hazard management. Anticipating events of catastrophic slope failure can allow human casualties to be avoided, damages to infrastructures and private properties to be reduced, and appropriate response actions to be designed and implemented (Federico et al., 2012). At the same time, alarm thresholds and failure-time predictions that are too conservative can lead to an excessive number of false alarms and indirect economic losses, as well as to a lack of credibility to the eyes of the population at risk. Early and reliable assessment of impending failure conditions is therefore essential in order to define appropriate emergency response plans and mitigate landslide risk.A universal law able to predict failure by comprehensively taking into account all the physical aspects of the landslide does not exist. This is because the heterogeneity of landslide forms, soil/rock mass mechanical properties, boundary conditions, and triggering factors cannot be uniquely defined and/or modelled. The proportions of the issue increase with the scale and complexity of the investigated phenomenon. As previously mentioned, great importance is thus assumed by the empirical analysis of the slope surface displacements. The interpretation of the displacements in terms of the probability of slope failure occurrence can be performed according to different approaches.
The concept of creep is at the basis of the vast majority of methods of landslide displacement analysis. Creep can be defined as “time dependent deformation of solids under stress”, and it has been observed extensively prior to events of slope failure (Tavenas and Leroueil, 1981). During the life of a slope, three main creep phases may be identified (Federico et al., 2012; Figure 4):
1. Primary creep: decrease of strain rate with time. This is particularly evident in artificial cuttings, as the relatively rapid exposure of the new rock face determines an initial phase of stress relief and elastic rebound;
2. Secondary creep: strain rate at a constant minimum. No strength loss occurs within the slope;
3. Tertiary or “accelerating” creep: exponential increase in strain rate up to failure. The deformation is non-recoverable, as material cohesion is quickly lost with the development of internal fracturing.
Tertiary creep, termed also “progressive deformation” of the slope, is considered the most indicative precursor to failure (Zavodni and Broadbent, 1980; Cruden and Masoumzadeh, 1987; Azimi et al., 1988; Cornelius and Scott, 1993; Hutchinson, 2001; Crosta and Agliardi, 2003; Helmstetter et al., 2004; Rose and Hungr, 2007). Accelerating slope displacements are in fact considered to indicate a critical decrease in the factor of safety of the slope, and therefore to represent a warning of imminent failure (Eberhardt, 2008). This phase has been
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associated by some authors with fracture nucleation and propagation (Kilburn and Petley, 2003; Petley, 2004; Kilburn, 2012; Sättele et al., 2016), followed by the degradation in joint cohesion due to the breaking of rock bridges (Kemeny, 2003).
As a result, several mathematical relationships for modelling the tertiary creep curve and predicting the time of failure of a slope have been proposed (e.g. Saito, 1969; Fukuzono, 1985; Hayashi et al., 1988; Voight, 1988; Voight, 1989; Hao et al., 2016). These typically correspond to exponential or power-law functions calibrated through the empirical regression of displacement-time measurements of laboratory creep tests, and subsequently verified on monitoring data of failing slopes. For this reason, these models are also regarded as “phenomenological” approaches (Federico et al., 2012), i.e. based only on an available collection of datasets.
The first author to propose an equation for failure-time prediction was Saito (1969), who argued that:
(𝑡𝑓− 𝑡)𝜀̇ = 𝑎 [1]
With 𝑡𝑓 indicating the time of failure, 𝜀̇ the strain rate, and 𝑎 being a constant.
Figure 4. Conceptual representation of the three phases of slope creep behavior leading to failure. The most notorious description of tertiary creep was produced by Voight (1988; 1989), who formulated a relation between the displacement rate and two dimensionless parameters A and α:
𝛺̇−𝛼𝛺̈ − 𝐴 = 0 [2]
Where Ω is displacement and the dots refer to the order of differentiation with respect to time (i.e. 𝛺̇ is velocity and 𝛺̈ is acceleration). The constants A and α control the shape of the
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velocity curve and the sensitivity to accelerating activity, respectively (Crosta and Agliardi, 2002). Voight’s method involves the integration of [2] for α > 1, which yields:
𝛺̇ = [𝐴(𝛼 − 1)(𝑡𝑓− 𝑡) + 𝛺̇𝑓1−𝛼]1/(1−𝛼) [3]
Where 𝛺̇𝑓 is the velocity at failure. Then, by manipulation of [3], it follows that:
𝑡𝑓− 𝑡 = 𝛺̇1−𝛼− 𝛺̇𝑓1−𝛼⁄𝐴(𝛼 − 1) [4]
And for 𝛺𝑓 assumed infinite:
𝑡𝑓− 𝑡 = 𝛺̇1−𝛼⁄𝐴(𝛼 − 1) [5]
It is necessary to estimate the parameters A and α for deriving the time to failure from [5], which can be attempted by: solving a set of simultaneous equations like [3], using observed velocities up to the current time; or by extrapolating the best-fit regression line in a log 𝛺̈ vs log 𝛺̇ plot.
The accuracy of the described analytical solution is heavily influenced by the precision and frequency of the monitoring data, since A and α are effectively constant only under time-invariant external conditions (e.g. load and temperature). However, such an assumption is hardly satisfied in the natural environment (Voight, 1989). Following Saito’s pioneering study, Fukuzono (1985) had previously proposed a graphical solution to predict the time of slope failure during stages of tertiary creep. This was based on the observation that, as velocity tends asymptotically to infinite towards failure, then the value of the inverse of velocity correspondingly approaches zero, consistently with the following equation:
𝛬 = 1 𝑣⁄ = [𝐴(𝛼 − 1)]1 𝛼−1⁄ (𝑡
𝑓− 𝑡)1 𝛼−1⁄ [6]
Where A and α have the same meaning than in [5].
By extrapolating the downward trend in an inverse velocity vs. time plot, the predicted time of failure is thus considered as the projected intercept point on the horizontal axis (i.e. point of infinite slope velocity). While it is true that Voight (1988; 1989) mathematically substantiated the tertiary creep theory, Fukuzono’s inverse velocity method is regarded as a very powerful tool of analysis thanks to its apparent simplicity of use and wide applicability. Several cases of failure in natural and engineered slopes, that were successfully predicted with the inverse velocity method, have been reported in the literature (e.g. Voight, 1988; Rose and Hungr, 2007; Doyle and Reese, 2011; Gigli et al., 2011; Dick et al., 2015; Figure 5 and Figure 6).
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Figure 5. Prediction of the Mt. Beni rockslide with the inverse velocity method (from Gigli et al., 2011).
Figure 6. Plot of inverse velocity and velocity vs. time for three prisms monitoring a failure at the Betze-Post open-pit mine (from Rose and Hungr, 2007).
The shape of the inverse velocity curve is dictated by the parameter α. In particular, the trend is linear for 𝛼 = 2, convex for 𝛼 > 2, and concave for 𝛼 < 2 (Figure 7). In any case, for formulation of the inverse velocity method, Fukuzono (1985) assumed that α is always greater than 1. The variability of α can introduce significant uncertainty to the extrapolation of a prediction, since the long-term trend in the plot may not be clear until the failure process is well underway. On the other hand, experience has shown that in most cases the inverse of the velocity approaches linearity, especially in close proximity to the time of failure
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(Fukuzono, 1985; Rose and Hungr, 2007; Dick et al., 2015). The commonly recommended procedure thus involves the continuous definition of a linear best-fit regression, updated on an ongoing basis by using the latest available data (Rose and Hungr, 2007). Several authors have indeed demonstrated that, in theory, the inverse velocity plot should be expected to be linear given ductile, accelerating creep occurring under constant effective stress conditions in soils, rock, and other materials (Voight, 1988; Voight, 1989; Kilburn and Petley, 2003).
Rose and Hungr (2007) compiled a list of disturbing elements that can cause unexpected variations of displacement rates and thus hamper the quality of inverse velocity analyses. These include: measurement error and random noise, local movements of the slope, influence of seasonal or periodically changing factors, action of sudden destabilizing forces (e.g. earthquakes, intense rainfall, etc.), and cases of brittle failure (i.e. failures characterized by an apparent lack of precursory deformation). Moreover, the onset of tertiary creep does not always imply an inevitable evolution towards failure: at some point the slope may in fact start to decelerate and then assume a constant rate of displacement if a new condition of equilibrium is reached (Hutchinson, 2001; Dick et al., 2015).
Figure 7. Influence of α on the shape of the inverse velocity vs. time curve approaching failure (from Rose and Hungr, 2007).
Under the observation that some slope failures may be dominated by mechanisms that are not affected by creep, Mufundirwa et al. (2010) proposed that 𝑡𝑓 corresponds to the slope
of the 𝑡(𝑑𝑢 𝑑𝑡⁄ ) vs. 𝑑𝑢 𝑑𝑡⁄ curve (where 𝑑𝑢 𝑑𝑡⁄ is the displacement rate). Known also as “SLO”, this method has not been able to replace the regression of inverse velocity data as the preferred way of deriving the geo-mechanical failure-time, mainly because of its tendency to provide overly conservative, or safe, predictions (“safe” is a failure-time prediction that
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precedes the actual failure-time). Contextually to their work, Mufundirwa et al. (2010) introduced the concept of “Life Expectancy Plot” (or PLE), which can be applied to any method aimed at producing failure-time predictions. For predicted life expectancy, it is intended the difference between the predicted time of failure and the time the prediction is made. This allows to evaluate whether the predictions, performed systematically as a new measurement of displacement is acquired, converge towards a consistent (and therefore more reliable) datum (Figure 8). As a result, PLE plots have become a common tool for integrating inverse velocity analyses (Dick et al., 2015).
The downsides and limitations that are inherent to the inverse velocity method will be discussed in the next sections of this thesis, as part of the description of the research work.
Figure 8. Example of life expectancy plot for a slope failure event (monitoring continued also after the main failure) and for a temporary acceleration event (from Dick et al., 2015).
Among the phenomenological approaches, it is also worth mentioning the method proposed by Hayashi (1988), who considered tertiary creep to be divided in two different phases: the first one, which includes the largest part of tertiary creep, immediately follows secondary creep and is characterized by a linear relationship between velocity and displacement; the second one, relatively short, where the logarithm of velocity increases proportionally with the displacement. The latter phase is made explicit by the following equation (Federico et al., 2012):
(𝑡𝑓− 𝑡)𝛺̇𝛼 = 𝑎𝛺𝛼 [7]
According to Hayashi (1988), the main theoretical advantage is that, while Saito’s and Fukuzono’s methods are able to deliver predictions only in close proximity of failure (i.e. during the second phase of tertiary creep), equation [7] is valid as soon as tertiary creep begins and thus provides the ability to predict failure earlier. Ultimately, this interpretation of creep has never been really acknowledged by the scientific community. Another important limitation is represented by the estimation of the parameters a and α, which can experience significant variations from case to case.
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More recently, Hao et al. (2016) proposed a general derivation of Voight’s relation [2] for 𝛼 > 1, according to which:
𝛺̇𝛺̈ = (𝛼 − 1)(𝑡𝑓− 𝑡) [8]
The equation above yields a new method for predicting the time of failure by linearly extrapolating the ratio 𝛺̇/𝛺̈ towards zero, and has the advantage of not needing the estimation of the parameters A and α (Hao et al., 2017; Figure 9). However, this solution has been applied only to observations from precursors to volcanic eruptions and from laboratory tests of creep strain rupture. Its suitability to the prediction of slope failures and, in general, to data of landslide displacement still needs to be verified.
Figure 9. Failure-time prediction by means of Hao’s method: (a) seismic energy release of Bezymyanny Volcano, and (b) creep strain rupture tests of Hanley clay (after Hao et al., 2016).
“Data-review” approaches are instead based on the analysis of monitoring data from a collection of several case studies in order to identify a set of characteristic conditions for failure triggering. Rather than providing time predictions, the goal is to define recurrent correlations between specific variables in close proximity to the instant of failure; or, in other words, to determine common slope behaviors in anticipation of failure. Knowing what are the requisites that must be met for failure to occur is in fact of crucial support when assessing the risk associated with ongoing events of slope deformation. This research field has not yet been explored comprehensively in the literature, mainly because of the logistical difficulties implied in retrieving large and consistent databases of monitoring data from a large number of different failure case studies. Unlike the phenomenological methods to failure-time prediction, a key advantage of data-review approaches is that they allow the evaluation of
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data trends by grouping the results according to different types of failure mechanism and to specific properties of the failing material.
An example of data-review approach was given by Zavodni and Broadbent (1980), who proposed that velocity at failure can be calculated as:
𝑣𝑓 = 𝐾2𝑣0 [9]
Where 𝑣0 is the velocity at the onset of acceleration and K is a constant to be estimated from
past failures where 𝑣0 and 𝑣𝑚𝑝 (i.e. velocity at the mid-point of the acceleration phase) are
known. A velocity of 5 cm/d was also interpreted as a signal that failure would occur within the next 48 days. The application of [9] is limited by the need to arbitrarily define in every instance the onset of acceleration and, consequently, also the mid-point of the acceleration.
Federico et al. (2012) derived the last measured values of acceleration and velocity from 30 slope failure case histories, and noticed that, in an acceleration vs. velocity plot in logarithmic scale, these are roughly scattered along a straight line (Figure 10). However, the use of logarithmic scales generates insensitivity of the data that cannot be captured. Another issue is that the database lacks consistency, meaning that the time of the last measurement of acceleration and velocity is not the same for each event.
Figure 10. Relationship between acceleration and velocity at failure for 30 slope failure case histories (after Federico et al., 2012).
Another notable example was proposed by Newcomen and Dick (2015), who explored the correlation between the Rock Mass Rating index (RMR) and the slope strain percentage for a large number of failures occurred in open-pit mines (“strain-based” method). The strain was defined by the authors as the total surface movement divided by the height of the slope
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failure. After classification of the results based on the type of failure mechanism, they concluded that RMR can be used to estimate a range of strain values that should be expected for failure to occur (Figure 11).
Ryan and Call (1992) reviewed displacement records of 14 rock slope failures in open-pit mines and reported that the ratio of measured velocity 24 h prior to collapse to measured velocity 48 h prior to collapse was consistently between 1.7 and 2.3. They also observed that in the final 48 h the magnitude of the acceleration may be a more consistent failure indicator than velocity.
Figure 11. Pit wall strain percentage vs. RMR at failure (from Newcomen and Dick, 2015).
Finally, “numerical” approaches aim at predicting mathematically the future displacements of the slope. The basic idea is that measurements of displacement can be compared to displacements simulated by numerical models to confirm that the slope is responding as initially predicted (Newcomen and Dick, 2015). Such an analysis methodology is usually challenging and site-specific, as it requires the availability of a long record of measurements in order to fit and calibrate a model that describes appropriately the specific kinematics of the examined phenomenon. The displacement pattern can also be related to changes in groundwater level, pore pressure, or rainfall intensity–duration. For example, Corominas et al. (2005) attempted to predict the displacement and velocity of the Vallcebre landslide by solving the momentum equation in which a viscous term (Bingham and power law) was added. Du et al. (2013) adopted a back-propagation neural network model with selected rainfall–water level factors to predict the displacements of active colluvial landslides in the Three Gorges Reservoir in China. Bernardie et al. (2015) used a combined
statistical-14
mechanical model to predict changes in landslide displacement rates from observed changes in rainfall amounts at the Super-Sauze landslide. Further examples have been published by Lu and Rosenbaum (2003), Feng et al. (2004), Randall (2007), Li et al. (2012), Miao et al. (2017), and others.
It follows that numerical models may be considered particularly suitable for dealing with slopes affected by periodical cycles of acceleration and deceleration. Eventually, anomalous slope deformation may be detected if the measured displacement exceeds a pre-determined threshold or confidence interval of the predicted displacement, and then the probability of failure occurrence may be associated with a certain amount of anomalous slope deformation. In this regard Crosta and Agliardi (2002), through the application of non-linear estimation techniques, and in accordance with Voight’s accelerating creep model, derived characteristic displacement and velocity curves of the Ruinon rockslide in the Central Alps (Italy) based on the available historical record of displacements (Figure 12). Consequently, they defined threshold points of 30, 15, and 7 days before failure in order to activate respectively a state of pre-alert, alert, and emergency.
Figure 12. Example of fitting of cumulative displacements of the Ruinon rockslide by using Voight’s model through a non-linear estimation analysis (after Crosta and Agliardi, 2002).
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3. Rationale of the research
Despite the importance of the topic, answering the question “when is geo-mechanical failure going to occur?” still poses major concerns (Mufundirwa et al., 2010). Mufundirwa et al. (2010) also reckoned that “there is a need to focus on simple and quick methods that are extensive in application and with minimal sensitivity to different lithology, size/volumes of failure and more importantly to failure mechanisms”. While such a solution would be ideal and deserves to be pursued, in practice it is difficult to assume that all slopes can be reduced to a unique deformation behavior prior to failure. In fact, according to Rose and Hungr (2007), “assessment of rock slope failure mechanisms requires an understanding of structural geology, groundwater and climate, rock mass strength and deformability, in situ stress conditions and seismicity”. In particular, material strength and deformability play a key role in the development of the failure process in terms of ductility or brittleness (i.e. magnitude and abruptness of the precursory displacement increments), and consequently in influencing the amount of forewarning that is available between the identification and the occurrence of the failure. While precursors to failure are usually evaluated through the back-analysis of sets of displacement data, at the same it is often neglected whether it would have been practically possible to derive acceptable predictions in a scenario of near real-time monitoring. An “acceptable” prediction is here intended as one that is accurate, reliable, and provides sufficient notice for undertaking the necessary response actions. If that cannot be achieved, then the formulation of failure prediction methods becomes solely an exercise of pure academic interest.
The trend of the inverse of velocity surely represents the main point of emphasis for the analysis of phases of accelerating displacement. Nonetheless, the tertiary creep theory is based on several simplifications and assumptions that can hamper its reliability and practical use (Rose and Hungr, 2007; Hao et al., 2017), and therefore it is typically recommended that the inverse velocity method should be used with caution and only by experienced users (Fell et al., 2000; Dick et al., 2015). Among such downsides, it is worth noting that the velocity at failure is assumed infinite; this condition is obviously never verified in nature, and velocity at failure may actually vary for different rock types, volumes, mechanisms of failure, and slope angles (Newcomen and Dick, 2015). Another limitation consists of the identification of onsets of acceleration and points of trend change: this may be an obvious procedure only if carried out in hindsight or when failure is already well underway. Most notably, the physical aspects of the landslide and the mechanical properties of the sheared material are not considered in terms of their influence on the development of the failure (Federico et al., 2012). As a result, the shape and temporal evolution of creep curves may be extremely variable, and the margin of error of failure-time predictions can be markedly wide (Crosta and Agliardi, 2003; Sättele et al., 2016). A considerable amount of key points still remain unaddressed concerning the behavior of progressively deforming slopes, as well as the appropriate procedures of data acquisition and interpretation to be followed for a successful early warning strategy.
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Data-review and numerical approaches have been explored much less extensively in the scientific literature. While these may be more complicated to use and/or be characterized by some practical or logistical drawbacks, they can offer new insights and perspectives into the behavior of geo-materials in proximity of failure, and thus provide meaningful tools of analysis that are alternative to the classical creep theory. Specifically, the integrated review of different sets of slope monitoring data gives the opportunity to look for new parameters or variables that may deemed as indicators of impending failure conditions.
This thesis highlights the advancements and innovative contributions in the fields of slope displacement analysis and predictability of slope geo-mechanical failure that have been produced in the framework of the three years of Ph.D. The research has been focused both on the development of the existing inverse velocity method associated with the tertiary creep theory, and on the preliminary introduction of new methods for the interpretation of slope monitoring data. Ultimately, all the activities were aimed at improving the knowledge and best practice for the early warning of slope failure risk.
A considerable part of the research concerned a careful selection and scrutiny of the case studies. For instance, it was of fundamental importance that monitoring and field data were collected in a consistent, reliable, and methodical way. When the frequency of the deformation measurements was too variable, data were resampled over a fixed time interval. Some of the presented datasets were retrieved from the literature; others were made available to the author of this thesis thanks to the activities carried out over the years by the Department of Earth Sciences of the University of Florence in support of the Italian Civil Protection department. With regards to the open-pit case studies, data were either picked first-hand by accessing the storage systems of the monitoring instruments installed in situ (when given permission), and/or by close interaction and collaboration with the geotechnical engineers in charge of safety at the mine sites. Slope instabilities of different nature and involving different geological materials were taken into consideration, in order to substantiate the validity and suitability of the proposed methodologies over a wide field of application. The characteristics of the case studies, which include both failures and “non-failures”, and instabilities in both loose materials and consolidated materials, are summarized in Table 1.
In light of the research findings, some of the contents and results of this thesis have also been published in several international scientific journals during the course of the 3-year PhD program. Such publications are all distributed free of charge in Open Access format. Data analysis and writing of the manuscripts have been performed by the author of this thesis under the guidance and support of the respective co-authors. Specifically, in chronological order:
Carlà T, Intrieri E, Di Traglia F, Casagli N (2016). A statistical-based approach for determining the intensity of unrest phases at Stromboli volcano (Southern Italy) using one-step-ahead forecasts of displacement time series. Natural Hazards 84(1):669– 683.
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Carlà T, Intrieri E, Farina P, Casagli N (2017). A new method to identify impending failure in rock slopes. International Journal of Rock Mechanics and Mining Sciences 93:76‒81.
Carlà T, Intrieri E, Di Traglia F, Nolesini T, Gigli G, Casagli N (2017). Guidelines on the use of inverse velocity method as a tool for setting alarm thresholds and forecasting landslides and structure collapses. Landslides 14(2):517‒534.
Carlà T, Farina P, Intrieri E, Botsialas K, Casagli N (2017). On the monitoring and early-warning of brittle slope failures in hard rock masses: examples from an open-pit mine. Engineering Geology 228:71‒81.
Carlà T, Macciotta R, Hendry M, Martin D, Edwards T, Evans T, Farina P, Intrieri E, Casagli N (2017). Displacement of a landslide retaining wall and application of an enhanced failure forecasting approach. Landslides, DOI: 10.1007/s10346-017-0887-7.
Carlà T, Farina P, Intrieri E, Ketizmen H, Casagli N (2018). Integration of ground-based radar and satellite InSAR data for the analysis of an unexpected slope failure in an open-pit mine. Engineering Geology 235:39‒52.
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Name Event Geological
material Triggering factors Monitoring instrument Monitoring frequency Method
Mt. Beni F Basalts, ofiolitic breccias
Quarrying activity
Distometric
bases Weekly INV, Tfw Mt. Toc F Limestone Reservoir
filling
Benchmark survey
Weekly,
daily INV, Tfw Volterra F Clayey and sand
deposits
Pore
pressure GBInSAR 8 h INV, Tfw Stromboli
talus F
Volcaniclastic debris
Volcanic
activity GBInSAR Daily INV, Tfw 10-mile NF Mixed landslide
deposits
Highway
undercutting Total station Weekly INV, Tfw Pit 1 F Intrusive Mining GBInSAR 20 mins INV, vel./acc. Pit 2 F Intrusive Mining GBInSAR 20 mins INV, vel./acc. Pit 3 F Intrusive Mining GBInSAR 20 mins INV, vel./acc. Pit 4 F Intrusive Mining GBInSAR 3 mins INV, vel./acc. Pit 5 F Intrusive Mining GBInSAR 3 mins INV, vel./acc. Pit 6 NF Intrusive Mining GBInSAR 3 mins INV, vel./acc. Pit 7 NF Intrusive Mining GBInSAR 3 mins vel./acc. Pit 8 NF Intrusive Mining GBInSAR 20 mins INV, vel./acc. Pit 9 NF Intrusive Mining GBInSAR 15 mins vel./acc. Pit 10 F Metamorphic Mining GBInSAR,
satellite InSAR 6 mins INV ACARP #78 F Unknown Mining GBInSAR Unknown acc./acc. Stromboli
flank F Volcanic
Volcanic
activity GBInSAR Daily ARMA
Table 1. Summary table of the case studies presented in the thesis. F = failure; NF = non-failure; INV = inverse velocity method.
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4. Tertiary creep
Tertiary creep was at the center of a large part of the research because of the wide acknowledgement of the inverse velocity method in both the theory and practice of slope failure risk management. This involved the consideration of several different issues that are inherent to the monitoring of slopes prone to phases of accelerating displacement. Specifically, these are:
data processing and frequency of acquisition;
extraction of valuable information concerning the kinematics and controlling mechanisms of slope instabilities;
predictability of markedly brittle failures in hard rock masses;
use of satellite interferometry for enhancing the reliability of monitoring data and improving the predictability of large catastrophic failures.
All these aspects are addressed in the following sub-sections.
Guidelines on the use of the inverse velocity method: data smoothing
4.1.
and interpretation
In inverse velocity analyses, one of the key aspects is to correctly process data in order to reduce noise as much as possible. Noise, defined as any additional meaningless information affecting the fundamental trend of a measurable quantity, can be associated to two different sources:
Instrumental noise (IN): related to the accuracy of the monitoring device;
Natural noise (NN): related to the discrepancy between the real behavior of geomaterials and the theoretical assumptions of the tertiary creep theory.
Data filtering is essential to help locating points of onset of acceleration (OOA) and points of trend change (or “trend update”, TU), and to increase the degree of fitting in the regression of inverse velocity measurements.
In this sense, Dick et al. (2015) carried out a sensitivity analysis for a slope failure in an open-pit mine, which showed that variation of the time of failure (𝑇𝑓) for rates filtered over a
short time period produced larger variations compared to rates filtered over a longer time period. However, the topic was not examined comprehensively, as the main focus of that research was directed toward the correct handling of spatially distributed ground-based radar data for the monitoring of open-pit mine slopes. Moreover, it was not considered that different filters may generate different results depending on the shape of the acceleration curve and on the level of noise, and that several cases of failure should thus be reviewed. A detailed study devoted to testing different methods of data smoothing in order to evaluate thoroughly
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their performances, determine the effects of noise on the reliability of 𝑇𝑓 predictions, and
eventually obtain guidelines for an optimal utilization of the inverse velocity method (INV), has not been yet produced to date.
In retrospect, data smoothing was the main point of emphasis for the review of the deformation measurements from three examples of catastrophic landslides. The analysis was also extended to the collapse of a man-made structure of significant cultural heritage. Each of these events (listed below) displayed accelerating trends prior to failure:
1. Mount Beni rockslide (December 2002): featuring low-medium values of slope velocity prior to failure (i.e. 𝐴 ≈ 0.1, see rest of this Section);
2. Vajont landslide (October 1963), which was anticipated by extremely high values of slope velocity (𝐴 ≈ 0.04, according to Voight, 1988);
3. Roto-translational slide of a debris talus on Stromboli volcano (October 2014);
4. Collapse of a section of medieval walls in the historical town of Volterra (March 2015). Furthermore, two ideal time series of velocity were created in agreement with Voight’s model of tertiary creep, and a set of randomly-generated low- and high-intensity noise was added to them. The resulting effects on the performances of INV were then evaluated, and data smoothing was applied.
Finally, based on the experience gained from the real and simulated case studies, practical procedures for the use of the inverse velocity approach were derived. These proposed guidelines address both the aspect of data handling and the issue of establishing alarm thresholds in emergency scenarios.
The contents of this work have been the object of a research paper published in the journal “Landslides” (Carlà et al., 2017a).
Methodology
The most powerful feature of INV probably relies in its simplicity. In scenarios of risk assessment and management, it is of great advantage if users can rely on quick and practical methods to evaluate the state of the monitored phenomenon and determine the possibility of an imminent calamitous event. This task is not always easy to accomplish because of physical and/or technological constraints. Accordingly, two among the most common and easy-to-use smoothing algorithms were tested, i.e. the moving average and the exponential smoothing. Specifically, three forms of filter were considered:
A short-term simple moving average (SMA), where the smoothed velocity at time t is: 𝑣̅𝑡 =
𝑣𝑡+𝑣𝑡−1+⋯+𝑣𝑡(𝑛−1)
𝑛 [10]
and 𝑛 = 3;
A long-term simple moving average (LMA), where 𝑛 = 7 in [10];
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𝑣̅𝑡 = 𝛽𝑣𝑡+ (1 − 𝛽)𝑣̅𝑡−1 [11]
and the smoothing factor is 𝛽 = 0.5. If the time interval between adjacent measurements is constant, then the type of moving average depicted in [10] is equivalent to the equation described by Dick et al. (2015):
𝑣𝑖 = 𝑑𝑖− 𝑑𝑖−𝑛⁄𝑡𝑖− 𝑡𝑖−𝑛 [12]
Where 𝑡𝑖 is the most recent time and 𝑑𝑖 is the most recent value of cumulative displacement.
There is no formally correct rule or procedure for establishing the order of the moving averages. This is highly dependent on data quality and temporal resolution. High acquisition rates usually require to perform smoothing over a greater number of measurements. Low acquisition rates will hide a greater fraction of the background noise, causing on the other hand the inability to trace short-term movements and delaying the identification of eventual trend changes; in such instance, smoothing should be performed over relatively less measurements, compared to data obtained at high acquisition rates. It follows that the number of data points in the time series does not necessarily hamper the accuracy of the failure predictions. It is difficult to determine a priori the minimum number of acquisitions, in addition to those needed to apply the aforementioned filters (i.e. n), that is required to confidently extrapolate trends of inverse velocity data. Undoubtedly, a populated dataset will help assess how well the time series is fitted by the regression, thus giving a valuable indication about the reliability of the prediction. In any case, modern monitoring technologies, which can measure displacements up to several times per day, ensure that the former is no longer a common issue and typically provide users with a more than acceptable amount of data points (unless monitoring is initiated too close to the failure).
With reference to the data presented in this Section, which were mostly characterized by low acquisition rates (roughly 1 measurement per day or less), using values of 𝑛 > 7 in [10] appeared to smooth out excessively the variations of data trend. Moreover, the wider the temporal window over which smoothing is performed, the higher the lag that is introduced to the time series. In scenarios of near-real time monitoring, it is probably not practical or convenient to use windows of smoothing which span over too long time periods. Therefore an LMA with 𝑛 = 7 (covering a time span of over a month of monitoring data) seems appropriate. Regarding the SMA, equation [10] with 𝑛 = 3 may be considered the most basic filter for smoothing a hypothetical outlier in a linear time series; this moving average (covering a time span of less than a month of monitoring data) responds more quickly to trend changes and is more sensitive to slight fluctuations in the data. For this reason, it was selected for comparison to the less sensitive LMA.
This part of the work was not focused on determining if a certain value of n is the most ideal for treating displacement measurements, since this will certainly vary from case to case depending on several factors such as acquisition rate, landslide velocity, and background
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noise. Both short- and long-term moving averages provide in fact benefits and downsides in time series analysis. The intent was rather to evaluate how these properties influence the reliability of failure predictions and if short-term or long-term moving averages should in general be preferred for the application of INV.
Finally, in [11], a smoothing factor of 0.5 maintains a good balance between smoothing effect and sensitivity to trend changes in the data. An exponential smoothing function has the form of a geometric progression and therefore, differently from a moving average, takes into account all past data, with recent observations having greater weight than older ones.
Results
Mt. Beni rockslide
On 28 December 2002, a landslide occurred on the eastern flank of Mt. Beni (Central Italy), on a slope which had been previously exploited by quarrying activity until the 1980s (Figure 13).
Figure 13. Photo of the Mt. Beni rockslide (after Carlà et al., 2017a).
The failure mechanism, involving jointed massive basalts overlying ophiolitic breccias, was characterized by a volume of approximately 500 000 m3, and has been classified as a rockslide/rock topple (Gigli et al., 2011). Several distometric bases were installed along the perimetric crack (Figure 14), and recorded cumulative displacements since April 2002. Increasing velocities, ranging from few millimeters up to few centimeters per day, were detected by most of the devices starting from September 2002 until the collapse on 28 December. According to eyewitnesses, the event began at about 4:30 a.m. local time. Gigli et al. (2011) made particular reference to distometric base 1-2 for the analysis of the
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precursors to failure, since this recorded the longest and most consistent progressive acceleration of the displacements. Accordingly, they calculated a failure forecast from the linear extrapolation of the trend of the inverse of velocity, starting since 2 August (Figure 5). Although providing an evident indication that failure was going to occur, fitting of these data resulted in a predicted 𝑇𝑓 ahead of the actual failure-time (𝑇𝑎𝑓) by 4 days and a half (i.e.
∆𝑇𝑓= 𝑇𝑎𝑓− 𝑇𝑓= 4.5).
Figure 14. Topographic map of the Mt. Beni rockslide and location of some distometric bases (after Gigli et al., 2011).
Inverse velocity plots for data of distometric base 1-2 filtered by means of SMA, LMA and ESF are shown in Figure 15. The SMA eliminated the small steps in the raw data curve, yielding a significantly improved 𝑇𝑓 prediction (∆𝑇𝑓= 1.1). On the other hand the LMA,
despite determining a slightly better fitting, generated a considerably negative ∆𝑇𝑓 (−4.3), and
most importantly delayed the identification of OOA by 1 month. The latter aspect was even more evident in the velocities smoothed through the ESF. Their poor linearity would have also made their use in the emergency scenario quite troublesome, even if, in retrospect, it was found that the last predicted 𝑇𝑓 was highly accurate.
The respective life expectancy plots (Figure 16) displayed additional information: all datasets, besides the velocities filtered by the ESF, converged parallel to the actual time to failure line. However, raw data consistently gave markedly safe predictions, whereas the
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SMA data got decisively close to the actual time to failure line since November 21. The LMA predictions approached the actual values already on late October, but finally diverged towards significantly negative ∆𝑇𝑓 (i.e. “unsafe” predictions). Exponential smoothing
produced a reliable 𝑇𝑓 in correspondence of the last measurement, but the predicted time to
failure line did not show a regular pattern, if compared to the others.
Figure 15. Inverse velocity analysis based on the displacements measured by distometric base 1-2 at Mt. Beni (after Carlà et al., 2017a).
A slightly different but interesting example from the Mt. Beni rockslide, which was not reported by Gigli et al. (2011), is represented by the displacement rates measured at the distometric base 15-13. Especially in its last phase, the final acceleration presented an irregular shape (i.e. alternating progressive-regressive phases of deformation, Figure 17). Moreover, this appeared to have a slightly concave shape with respect to base 1-2, possibly suggesting a value of α lower than 2. These features may thus be referred to what has been previously defined as NN.
Linear fitting of the raw inverse velocity data resulted to be strongly hampered, and produced a 𝑇𝑓 prediction well ahead of the last actual measurement acquired on December
20 (approximately 8 days). The SMA did not exhibit a noticeable improvement in terms of smoothing, and the consequent ∆𝑇𝑓 was equivalent to that from raw data. Again, exponential
smoothing introduced irregularity to the plot and delayed OOA. In this case, filtering by means of the LMA produced better results under every aspect: OOA was found at the same time than in the raw data, steps in the inverse velocity line were eliminated (thus improving also the degree of fitting), and accuracy of the predicted 𝑇𝑓 was much higher (∆𝑇𝑓= 2). The
related life expectancies converged close to the actual time to failure line already from late November, i.e. 1 month before the event (Figure 18). On the contrary, predicted lines from the ESF data never converged parallel to the actual expectancy line.
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Figure 16. Life expectancy analysis based on the displacements measured by distometric base 1-2 at Mt. Beni (after Carlà et al., 2017a).
Figure 17. Inverse velocity analysis based on the displacements measured by distometric base 15-13 at Mt. Beni (after Carlà et al., 2017a).
Summarizing, the Mt. Beni case study showed that linear fitting of unfiltered inverse velocity data, although surely constituting an indicator of the ongoing acceleration of the slope displacements, produced a predicted 𝑇𝑓 ahead of 𝑇𝑎𝑓 by several days. Smoothing data
with a simple moving average algorithm allowed to benefit from improved qualities of fitting and of 𝑇𝑓 predictions. In particular, the LMA gave optimal results for the noisier, less linear (α
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< 2) time series from distometric base 15-13, while the SMA performed better when applied to the more regular measurements collected by distometric base 1-2. Exponential smoothing did not produce significant improvements to any of the two datasets.
Figure 18. Life expectancy analysis based on the displacements measured by distometric base 15-13 at Mt. Beni (after Carlà et al., 2017a).
Vajont landslide
The 1963 Vajont disaster in Northeast Italy has been one of the most catastrophic landslides in history, and many authors have studied the event under several different perspectives. Without entering into the complex details of the failure mechanism, as these have already been largely described and discussed (and still are), the collapse occurred at about 10:39 p.m. local time on 9 October 1963, when a mostly calcareous rock mass of about 270 million m3 detached from the slope of Mt. Toc and slid at 30 m/s into the newly created Vajont reservoir (Figure 1a). The consequent tsunami wave overtopped the dam and killed 2 500 people in the villages downstream.
The instability was strongly controlled by the water level in the valley floor, as creeping motions began to be observed immediately since the creation of the reservoir (Havaej et al., 2015). The final chain of events started with the April 1963 reservoir filling cycle, and the failure followed 70 days of downslope accelerating movements (Helmstetter et al., 2004). According to measurements from four benchmarks installed at different positions on the mountain slope, pre-failure velocities were extremely high. Among these, benchmarks 5 and 63 in particular were characterized by a clear state of accelerating creep, with displacement rates ranging from ≈5 mm/day up to over 20 cm/day (Figure 19a and Figure 19b), and a total cumulative deformation of a few meters (Muller, 1964). Figure 19 also shows the measurements from Mt. Beni to indicate the different orders of magnitude in the displacement rates between the two landslides, as well as the different shape of the
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respective curves. Distometric base 1-2 at Mt. Beni was indeed associated with significantly lower velocities with respect to the benchmarks at Mt. Toc. Velocities measured at base 15-13 were instead of the same order of magnitude; the acceleration was however “stepped” rather than progressive, further indicating the need to perform high-degree smoothing on this time series (as shown in Figure 17).
Figure 19c describes the inverse velocity plot for the unfiltered measurements of benchmark 63 at Mt. Toc. Even though a slight step-like pattern can be noticed, the graph is remarkably linear as a whole. Most importantly, the linear trend line did fit particularly well the last points leading up to failure. If recorded velocities are regularly high since the initial stages of acceleration (e.g. A ≈ 0.04 as in the Mt. Toc data; Voight 1988), and if the assumption of 𝛼 = 2 is consistently satisfied, it is then suggested to not apply any heavy smoothing, in order to avoid loss of sensitivity with regards to actual downward trends. At most, regression of short-term averaged velocities may also be conducted in parallel to the analysis of the original data. For benchmark 63, the SMA yielded a slightly better fitting and a slightly more accurate 𝑇𝑓 (∆𝑇𝑓 = 0.3) with respect to the original data (∆𝑇𝑓 = 1.1, Figure 19d).
Figure 19. Velocity measurements from benchmarks (a) 5 and (b) 63 at Mt. Toc (modified from Muller, 1964), and from distometric bases (a) 1-2 and (b) 15-13 at Mt. Beni. (c, d) Inverse velocity analysis based on the displacements measured by benchmark 63 at Mt. Toc (after Carlà et al., 2017a).
The inverse velocity plot based on the displacements measured by benchmark 5 (Figure 20a) has a pattern more similar to that of distometric base 15-13 at Mt. Beni (Figure 17a): after the fourth point of the time series, the trend assumes in fact a slight concavity (𝛼 < 2). Consequently, as opposed to benchmark 63, the last data points before failure were not fitted well by the linear regression. This caused a premature 𝑇𝑓 prediction, which preceded also the
