1 Introduction

Landslides can be classified through different approaches such as the type of the movement, the involved materials, the state of activity, the velocity of the displacement, the stage of the movement (Hutchinson 1988; WP/WLI 1993; Cruden and Varnes 1996; Hungr et al. 2001, 2014). Cruden and Varnes (1996) distinguish the landslides through the velocity of the displacements. Seven classes were identified, each of which spans two orders of magnitude, with upper and lower thresholds, respectively, equal to 5 m/s and 16 mm/yr.

Three of the most widespread landslides classes are represented by extremely slow, very slow and slow-moving landslides. These categories group phenomena whose rate of displacement ranges between 16 mm/yr and 1.6 m/yr and between 1.6 m/yr and 13 m/month for very-slow-moving and slow-moving landslides, respectively. These landslides can develop both in rock or in earth slopes, with kinematical behaviors and morphological features related to roto-translational slides, flows, complex landslides or Deep-Seated Gravitational Slope Deformation (DSGSD) (Varnes 1978).

The extremely slow, very slow and slow-moving landslides are characterized by long periods of activity and by displacements occurring along one or several shear surfaces. Their kinematic is characterized by steady rates of movement, sometimes close to the detection limit of the traditional monitoring equipments (e.g., tenths of mm/yr), with occasional or seasonal phases of reactivation and accelerations of the movements (Cruden and Varnes 1996; Leroueil et al. 1996).

Although they are rarely associated to loss of human lives, these types of landslides can cause slight but progressive damages to the structures, due to their continuous displacements or during the most intense reactivation phases. The most significant effects of the displacements are evident in the exposed facilities, especially the buildings and the roads, which are located in the area affected by the slope instability (Blochl and Braun 2005; Mansour et al. 2011; Muceku et al. 2016; Peduto et al. 2017, 2021; Muceku and Jaupaj 2018). The most significant consequences are generally the detrimental effects to these facilities and the attainment of their serviceability/ultimate limit states, with also social consequences for the people living in the affected areas (Corominas et al. 2014; Peduto et al. 2017). Furthermore, when the kinematical behavior of these types of landslides is characterized by a significant (especially, exponential) increase on the rate of the displacement (Petley et al. 2002, 2005; Cascini et al. 2014; Pepe et al. 2021), a paroxystic event could occur (Fukozono 1985; Segalini et al. 2018; Intrieri et al. 2019). For these reasons, a deep characterization of the kinematics and of the trends of the displacement of extremely slow-moving to slow-moving landslides is required for a correct land use planning and in order to identify the most suitable risk mitigation strategies (Corominas et al. 2014; Gili et al. 2021).

The displacement trends are identified and investigated in time by means of monitoring techniques. One of the most adopted procedure is the Advanced-Differential Interferometric Synthetic Aperture Radar (A-DInSAR). The datasets of displacements acquired through this technique have been available for more than 20 years (Canuti et al. 2004; Meisina et al. 2008; Herrera et al. 2013; Bovenga et al. 2017; Bordoni et al. 2018; Imaizumi et al. 2018; Raspini et al. 2018; Solari et al. 2019; Urgilez Vinueza et al. 2022). This technique is particularly suitable to monitor entire slope instabilities in areas of hundreds to thousands of square kilometers, thanks to a typical resolution of millimetric-centimetric ground deformations (Ferretti et al. 2001, 2011). Instead, monitoring of landslides displacements through A-DInSAR cannot be implemented in all the contexts affected by slope instabilities, due to the intrinsic limitations of this technique: movements along the line of sight not completely seen due to the hillslope morphology; absence of measuring points for the presence of materials with low reflectance features; rate of displacements higher than the resolution of the technique (Ferretti et al. 2001; Plank et al. 2012; Notti et al. 2015).

As a consequence, conventional in situ monitoring techniques (i.e., inclinometers, extensometers, GPS systems, topographic leveling) are still used widespread to reconstruct and analyze the temporal trends of displacement. In the last years, the use of automatic probes (Lollino 1992; Lollino et al. 2002; Simeoni and Mongiovì 2007; Crosta et al. 2014; Vallet et al. 2016; Loew et al. 2017; Guo et al. 2019; Stumvoll et al. 2022; Zhang et al. 2022), which allow to monitor continuously in field the trends of the displacements, improved the quantitative analysis and the reconstruction of the kinematical behaviors of these types of landslides, thanks to (Crosta et al., 2017): (i) the representation of the long-term landslides behavior at high temporal resolution (i.e., hourly, daily); (ii) the identification of different phases of activity or of acceleration in displacement trends; (iii) the response of the phenomenon toward the different factors which could determine a change in the rate of the displacements (i.e., rainfalls, snow-melting); (iv) the estimation of the conditions leading to a partial or complete collapse of the unstable mass.

A displacement monitoring shows peculiar features according to the type of used device (Cascini et al. 2014; Corominas et al. 2014). Wire extensometers and automatic GPS can measure cumulated ground displacement, which could be not correlated to the kinematic behavior of the monitored landslide in correspondence of the sliding surface or the shear zone. Furthermore, the measures of superficial probes can be affected by thermal effects due to the alternance of cold and hot periods across a day (light hours, night) or the seasons (Malet et al. 2002). In-place automatic inclinometers can measure the displacement rates and trends directly in correspondence of the landslides sliding surfaces, with a higher temporal frequency of measurements compared to mobile inclinometers. However, the measured time-series acquired by an automatic inclinometer could be affected by errors or anomalous measurements, which are not easy to discern from real movements (Simeoni and Mongiovì 2007; Stark and Choi 2008). These anomalies have to be deleted from the displacement time-series, in order to obtain a filtered trend which describe the real changes in the rate of deformation due to a particular slope instability (Palshikar 2009). Automatic inclinometers allow to monitor time-series of displacements characterized by long period of activities and accelerations in the deformations, alternated to phases of relative stability. The active phases can be correlated to the triggers which influence the intensity of the changes in the rate of deformation of a landslide (Guzzetti et al. 2007; Berti et al. 2012; Wei et al. 2019). All these steps of the analysis are typically treated with an empirical point-of-view, which limits the repeatability of the methodological approach to different test-sites (Vallet et al. 2016). Thus, it becomes fundamental the development of a systematic methodology able to cover the entire process of analysis of displacement time-series acquired at high temporal resolution by automatic inclinometers, for the characterization of the deformation time-series measured by a probe at site-specific scale.

To fill these gaps, this work aims to develop and test a systematic and repeatable methodological procedure for the analysis of the time-series measured by automatic inclinometers installed in extremely slow, very slow or slow-moving landslides. In particular, this method aimed to cover all the steps of the analysis of data acquired by automatic inclinometers, with the aim of: (i) determining the measurements reliability of an automatic inclinometer time-series; (ii) recognizing and removing anomalous measures and noises from the original acquired time-series; (iii) recognizing the most significant moments of change in the rate of displacements measured by a sensor; (iv) describing the type of the kinematic behavior of a phenomenon during its activity phases; (v) identifying the main triggers which influence the displacements and the occurrence of acceleration in measured deformations.

This methodological approach was developed and tested by exploiting the time-series of automatic inclinometers installed in different extremely slow, very slow-moving or slow-moving landslides of Piemonte region (Northern Italy).

2 Materials and methods

2.1 The study area

Piemonte region is located in North-Western Italy and is 25,000 km2 wide. The altitude ranges from few meters to > 4500 m above sea level (a.s.l.). It presents different geological and geomorphological contexts, identified as Alps, Langhe and Monferrato, Apennines, Turin Hills, and Po River Plain (Fig. 1a). The Alps are characterized by high slope gradients, with very steep cliffs (till more than 70°) in the sectors above 2000 m a.s.l. In contrast, the low-lying sectors (below 2000 m a.s.l.) of the Alps, namely the Pre-Alps, have gentler and more vegetated slopes (generally steepness lower than 30°). The alpine geology is characterized by the presence of foliated (especially gneiss and schist) and massive (both magmatic and sedimentary) rocks (Fig. 1b). The Langhe and Monferrato area is characterized by asymmetrical valleys, with steep southeast-facing slopes and gentle northwest-facing slopes and a monocline succession of marls and sandstones (Fig. 1b). The Apennines and Turin hills present less steep slopes (generally, 15°–20°) with sedimentary clay rocks (Fig. 1b). All the previously described contexts are bordered by the alluvial deposits of the Po River Plain, which is the low-lying sector of Piemonte region (generally below 200 m a.s.l.).

Fig. 1
figure 1

The study area, Piemonte region: a main geological and geomorphological contexts; b lithological map at a scale of 1:100,000 (Piana et al. 2017). Coordinates are expressed in WGS84-UTM Zone 32 N

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All the hilly and mountainous contexts of Piemonte region are very susceptible toward landslides. The Landslide Information System in the Piemonte (SIFRAP; http://www.arpa.piemonte.it/approfondimenti/temi-ambientali/geologia-e-dissesto/bancadatiged/sifrap), as an evolution of the Italian national landslide inventory (IFFI; Trigila et al. 2010), identified more than 35,000 slope instabilities. According to Cruden and Varnes (1996)'s classification, different typologies of landslides are present, with different morphological features and trend of displacements. The alpine environment is characterized by the presence of rockfalls/topples, large complex landslides and DSGSD. In the Langhe and Monferrato area, slow-moving translational rock-block slides and fast-moving shallow landslides are significantly predominant. The Apennines area and Turin hills are mainly affected by rotational/translational slides, shallow rapid flows, slow flows and complex landslides. About 45% of the landslides in the SIFraP inventory are rockfalls/topple. While, approximately 40% of the phenomena present in this inventory is represented by various typologies of landslides (DSGSD, rotational/translational slides, rock-block slides, slow flows, complex landslides) characterized by a typical extremely slow to slow velocity of displacement, with temporal or seasonal activation phases alternated with long periods of a substantial absence of significant movements (velocity of the displacement about 0 mm/d).

2.2 Dataset of displacements time-series acquired by automatic inclinometers

Among the landslide inventory of Piemonte region, more than 300 extremely slow to slow-moving landslides are monitored through field devices. All these data are grouped within the landslide regional monitoring network in charge to ARPA Piemonte and Piemonte region (RERCOMF). This extensive monitoring network includes many sites with few conventional instruments (manual inclinometers, piezometers, extensometers, topographic benchmarks, GPS-assisted control networks). Furthermore, 105 automatic inclinometers are installed to monitor different test-sites. These devices have been placed in hillslopes with very slow to slow-moving landslides that were characterized by significant reactivation in past or which moved along sliding surface continuously in time with periodic increase on the rate of displacement.

Automatic inclinometers are present in slope instabilities of all the hilly and mountainous context of Piemonte region (Fig. 2a). The landslides monitored by these devices belong to four types (Fig. 2b):

  1. A.

    Very-slow-moving or slow-moving complex landslides, whose shear surfaces are located at depth higher than 10 m from ground level in correspondence of highly fractured metamorphic rocks. These phenomena are typical of the Alps context, especially of the hillslopes with altitude over 1,000 m a.s.l..

  2. B.

    Translational rock-block slides typical of Langhe and Monferrato area, with sliding surfaces located in the range between 5 and 20 m from ground level, affecting fractured marly and sandy marly rocks.

  3. C.

    Complex landslides that affect eluvial-colluvial cover, where shear surfaces are located at depth generally lower than 15 m from ground level in correspondence of the contact between cover materials and more compact bedrock levels or immediately above this contact.

  4. D.

    Slow flows that affect marly or clayey bedrock levels, with shear surface generally located at depth between 9 and 30 m from ground level. These landslides are typical of the Apennines area.

Fig. 2
figure 2

Location of the automatic inclinometers across the main geological and geomorphological contexts of Piemonte region (coordinates in this map are expressed in WGS84-UTM Zone 32 N) a. Distribution of automatic inclinometers in different landslides types b, in the range of depth of installation c, according to the length of the time-series of acquired data d

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The landslides monitored by automatic inclinometers belong especially to A and C categories (36 and 27 devices, respectively), with a smaller frequency for B and D types (15 and 11, respectively) (Fig. 2b). 61 tools are installed at depth lower than 20 m from ground level, even if 28 sensors are present in deeper levels (Fig. 2c). Most of the devices have acquired data for 1 to 10 years, with a quite equal number of tools whose time-series are long less than 5 years (35 tools) or between 5 and 10 years (37 tools) (Fig. 2d). Whereas, few automatic inclinometers (17) have acquired data for more than 10 years. Only 2 tools have acquired data since 2001, with a corresponding length of the time-series of 20 years.

The installation mode and the main features of the considered automatic inclinometers are the following. Each probe is placed in an inclinometer casing, where sometimes the measurements can be carried out also through a mobile inclinometer. The probe is connected to a datalogger for the acquisition of the data and to a wireless communicating device to transfer the data from the test-site. In the tube, more sensors could be installed at different depths, in order to monitor the deformation trends of the analyzed phenomenon at different depths and to establish whether the landslide moves as a whole or it is characterized by different kinematic behavior along depth. Each sensor provides the measure of the time-series of the amount of displacements and of the direction of the movement respect to the north direction. The displacements (Di) are measured in mm, in terms of cumulated amount of this parameter since the beginning of the monitored time spans. The direction of the displacement vector (Ai) is expressed in degrees (°). The temporal resolution of the acquisition can be daily or of 2–3 measures per day. The accuracy of the displacement measures ranges between 0.05 and 0.1 mm, while the one of the direction of the movement is typically lower than 5°.

2.3 Methodology for the analysis of time-series acquired by automatic inclinometers

Figures 3 and 5 summarize the methodology developed to analyze and interpret time-series acquired by an automatic inclinometer. The methodological approach is composed by the following steps: step (I) evaluation of the reliability (accuracy) of the instrument; step (II) identification and elimination of the anomalous measures; step (III) identification of the significant accelerations in the trends of the displacements; step (IV) identification of the kinematic behavior of a landslide during its activity phases; step (V) identification of the main triggers which influence the displacements and the occurrence of acceleration in measured deformations.

Fig. 3
figure 3

Flowchart of steps I-IV of the developed methodology

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Step I: Evaluation of the reliability of the instrument

Once daily time-series displacements was acquired, the accuracy of the measures was estimated considering if each daily displacement measure was above the standard deviation of all the measures. This process estimated the relative shifting of each movement measure from the time-series standard deviation and enlight the potential anomalies. Accurate measures were the ones characterized by values below the standard deviation of the standard deviation of all the measures.


Step II: Identification and elimination of anomalous measures

The measures acquired by automatic inclinometer time-series can be affected by different kind of errors (Simeoni and Mongiovì 2003, 2007). The most common errors detected in the analyzed time-series are outliers or spikes in cumulative displacement in correspondence of less than 5 continuous measures (1–5 days). In other cases, anomalous measures of cumulative displacements equal to 0 or decreases in cumulative displacements could occur for few days (1–10 days). Anomalous measures can occur also if there is a significant shifting of the measured displacement direction respect to the main direction of landslide displacement (Simeoni and Mongiovì 2007). These anomalies can be due to (Simeoni and Mongiovì 2003): noise due to the acquisition system; systematic errors associated to damages to the acquisition system or to the probes; shifts caused by the removal of the in-place probe; occasional errors due to unforeseen and unknown phenomena.

For the detection and the elimination of anomalous measures, the sub-daily measures (2 or 3 according to the instruments) were firstly averaged into daily values, to make uniform the analysis for all the inclinometers present in the considered dataset. The anomalies were, then, detected in the daily time-series of an automatic inclinometer by means of an objective and repeatable procedure. In particular, a series of measures represented a spike or an anomalous Di due to a new origin if two conditions were verified: (i) daily Di over the standard deviation of the Di of the entire time-series, typically lower than 5 mm/d for these devices; (ii) value of daily Ai over a range of tolerance, averagely equal to the characteristic Ai of the phenomenon ± 30°. These two conditions allowed to distinguish the anomalies from the real increases on the rate of Di due to a real change of the landslide kinematic behavior, that were characterized by Ai within the range of the landslide Ai ± 30°. This range was chosen analyzing the differences between real landslide Ai and Ai measured in correspondence of a daily anomaly, that were generally higher or lower of 30° than the characteristic Ai of the landslide. Local Ai was defined analyzing the direction of the movements measured by both the automatic and the mobile inclinometers present within a landslide. Furthermore, an error was recognized if daily Ai was over the range local Ai ± 30° even if daily Di was below the standard deviation of the entire time-series. For the identification of errors due to significant decrease in cumulated Di, daily velocity of the displacement (Vi) was defined, according to Eq. (1), as:

$$V_{i} = D_{i, n} - D_{i, n - 1}$$
(1)

where Di,n and Di,n-1 were Di measured in correspondence of a particular and of the previous one, respectively.

Since the automatic inclinometers have to measure a positive cumulative displacement along time (Simeoni and Mongiovì 2003, 2007), Vi in a day lower or equal to − 0.1 mm/day represented an anomaly and was removed. The threshold of negative Vi was set according to the absolute value of the highest value of accuracy of daily Di (0.1 mm) detected for the analyzed inclinometers, even if it could be set to a different value according to the analyzed phenomenon and probe.

The identification of all of these anomalies was done implementing a specific R code (R Core Team 2017) for the analysis of the time-series. The identified errors with this procedure were compared to a dataset of the daily measures recognized as anomalies during a preliminary analysis of the time-series of automatic inclinometers. This allowed to verify the reliability of the implemented procedure, by the calculation of the probability of detection (POD), which is the percentage of daily anomalies correctly predicted respect to the total amount (Gariano et al. 2015).

Identified anomalies on Di and/or Ai daily time-series of each automatic inclinometer were then removed to obtain filtered daily time-series, containing only real measures not affected by anomalies. These filtered time-series were then used in the following steps of the developed methodology.


Step III: Identification of significant acceleration

Generally, the movements of an extremely slow, very slow or slow-moving landslide presents moments of change in its rate in a large range of duration and cumulated displacements. An event was defined as a period characterized by an increase in the rate of Di respect to the typical trend of the deformation measured by an inclinometer. Previous approaches (Brox and Newcomen 2003; Dick et al. 2014; Vallet et al. 2016; Carlà et al. 2016, 2017; Crosta et al. 2017; Segalini et al. 2018; Intrieri et al. 2019) identified an event basing only on the detection of those time spans when the velocity of the displacement increased over a certain threshold, defined in an empirical way or since statistical indexes (e.g., mean, median, quartiles) of the time-series of displacement measured through inclinometers.

In the proposed approach, an event occurred along a displacement time-series when two conditions were verified: (i) velocities of displacement above a statistically-defined threshold; (ii) cumulated displacement over a certain level of significance. First, the time-series of Di, measured by an automatic inclinometer and filtered by anomalies, was transformed in a time-series of daily Vi applying the first derivative. Then, the threshold of Vi (Vi,thre) was defined using a statistical indicator on the frequency distribution of Vi values measured in the time-series acquired by all the tools present in the analyzed dataset.

Monitored landslides belong to A and D categories were characterized by long seasonal state of activity alternated with other long and seasonal moments when Vi was close to 0 mm/d (Fig. 4a). For these phenomena, Vi,thre corresponded to the 95th percentile of the frequency distribution of the all the measures acquired by tools installed in correspondence of such slope instabilities and was set equal to 0.2 mm/d (Fig. 4b). Instead, landslides of B and C types were characterized by prolonged periods with Vi close to 0 mm/d interrupted by phases of increase in the rate of displacement, with duration of few days (Fig. 4c). For these landslides, due to the bigger distribution of Vi values close to 0 mm/d, Vi,thre was set equal to the 99th percentile of the of the frequency distribution of the all the measures acquired by tools installed in correspondence of such slope instabilities, corresponding to 0.5 mm/d (Fig. 4d). The choice of these statistical indexes was consistent with the detection only of the moments in the statistical distribution that represented really significant increase in the rate of displacements that could be linked to peculiar triggers (Krishnamoorty 2016).

Fig. 4
figure 4

Typical time-series of cumulated Di and Vi a of landslides of type A and D (Borgata landslide, automatic inclinometer at 16.8 m from ground level) and Pareto chart of the distribution of Vi for landslides of type A and D b. Typical time-series of cumulated Di and Vi c of landslides of type B and C (Cantalupo Ligure landslide, automatic inclinometer at 2.5 m from ground level) and Pareto chart of the distribution of Vi for landslides of type B and C d

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An event was, then, identified in correspondence of every period when daily Vi kept above the threshold and when the total Di of the same period, without anomalies, was of at least 1 mm, since lower values were not able to provoke significant effects in terms of modification on landslide kinematics (Mansour et al. 2011). Vi of a very-slow-moving or of a slow-moving phenomenon could fluctuate during an activity phase also below a defined threshold. Thus, a period with Vi above Vi,thre was merged with another one close to it if the length of the time span with rates of the displacement below the defined threshold (X) was equal to 5 days for B and C landslides and to 14 days for A and D landslides. The choice of these different values are due to difference in the typical response toward triggers peculiar of these different slope instabilities. A and D landslides, characterized by longer and more seasonal activity phases than B and C ones, required to consider longer time spans of Vi below the threshold.

Also this step of the methodology was implemented on a specific R code (R Core Team 2017). The identified events with this procedure were compared to field evidences of acceleration events (e.g., cracks and other morphological evidences, damages to buildings or roads) collected during the preliminary analysis of the time-series of automatic inclinometers. POD index, in terms of percentage of events correctly predicted respect to their total amount, was calculated to verify the reliability of the implemented procedure.


Step IV: Identification of typical kinematic behaviors of a monitored landslide

Once identified events of acceleration in each displacement time-series, the characterization of the typical kinematic behaviors of the monitored landslides can be obtained identifying typical patterns of motion, described by common features within different events. A similar framework was adopted by Casini et al. (2014) and Scoppettuolo et al. (2020), who characterized and distinguished the time-series of the displacements monitored with field tools (e.g., inclinometers, extensometers) in order to find the typical trends and the kinematic behaviors of slow-moving landslides, within a dataset of monitored landslides in different geological contexts and with different depths of sliding surface and geotechnical-geomechanical properties of the unstable mass. These authors analyzed the cumulative displacements and the duration of phases of acceleration, in order to distinguish different kinematic behaviors of slow-moving landslides.

A similar approach was adopted to exploit the database of the events obtained analyzing the considered inclinometers time-series. The events, identified during step III of the methodology for each automatic inclinometer, were characterized in terms of the displacement Di, duration of the event d and average velocity Vi. The database of the events was exploited by means of a Hierarchical Cluster Analysis (HCA), in order to group events with similar features in terms of cumulative displacement, duration and average rate of motion. Adopted clustering was an iterative procedure (Aldendorfer and Blashfield 1984), with the following steps: (i) an initial random partition of the dataset into some specified number of clusters; (ii) the computation of the centroids of the clusters; (iii) the allocation of each data point to the cluster that has the nearest centroid; (iv) the computation of the new centroids of the clusters; (v) the alternance of steps iii and iv until no data points changed. HCA aimed at creating groups of events with similar features, limiting the variability within the cluster and keeping high differences respect to the other ones. The goodness of HCA application was evaluated through the calculation of Dunn Index, given by the ratio between the minimum inter cluster separation and the maximum intra cluster distance (Pakhira et al. 2004). HCA was performed through the software Orange 2.7, while its reliability was estimated through a specific R code (R Core Team 2017) for the calculation of Dunn Index. This step of the methodology allowed to distinguish different clusters of events, that could be useful to characterize the kinematic behavior monitored by a particular automatic inclinometer.


Step V: identification of the main triggers which influence the displacements and the occurrence of acceleration in measured deformation trends

The moments, when a extremely slow, very slow or slow-moving landslide increase its rate of the displacements, are due to particular amounts of the triggers which influence the movements (Terlien 1998). The geological and geomorphological features and the complex groundwater hydrodynamics of a wide and deep-seated landslide generally determine complicated hydro-mechanical relationships between rainfalls, groundwater table depth, snow-melting and the resulting deformation. Different models can be applied to evaluate the main factors which influence the deformation trends. The application of physically-based methods to assess the effects of triggers to the displacement trends is limited in the implementation and calibration phases because of the scarcity of measured soil and rock geotechnical and mechanical properties and of quantification of hydrogeological processes for the reconstruction of the landslide boundary condtions (Guzzetti et al. 2007). Therefore, in the case of large amounts of available meteorological data, groundwater depth measures and monitored periods of displacements, the definition of a data-driven model able to estimate statistically the response in terms of deformation to the changes of the most important triggers could be preferred (Guzzetti et al. 2007; Vallet et al. 2016; Guo et al. 2019).

Machine learning techniques were tested to achieve this aim, thanks to their strong capability in reconstructing linear or more complex relationships between the predictors (factor influencing the rate of displacement at a particular temporal resolution) and the response variable (this rate of displacement) and in forecasting future trends of the response variable according to different scenarios of the triggers (Liu et al. 2014; Vallet et al. 2016; Krkac et al. 2017; Zhou et al. 2018; Guo et al. 2019). Liu et al. (2014) compared different techniques generally used to predict displacement time-series of slow-moving and deep-seated landslides, identifying the Gaussian Process (GP) as the best performer for the prediction of the trends of the displacements and of their changes in time, according to the main factors influencing the displacements. A GP model (Fig. 5) was, then developed in order to reconstruct time-series of Vi derived from the displacement data acquired by an automatic inclinometer in the analyzed dataset and corrected from the errors and anomalies during step II of the developed method. For a detailed explanation on the main functioning of a GP model, we refer to Rasmussen and Williams (2006) and Liu et al. (2014).

Fig. 5
figure 5

Flowchart of step V of the methodology

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The predictors used in a GP model were selected within the meteorological and hydrogeological parameters which could influence the trend of deformation measured by an automatic inclinometer. For landslides of type A and D, the model was reconstructed for monthly Vi, since the seasonal and longer periods of acceleration typically of these phenomena. Cumulated amounts of rainfall from 1 to 12 months, mean groundwater table in 1–12 antecedent months and the mean snow depth in 1–12 antecedent months were, then, considered. Instead, for landslides of type B and C, the model was reconstructed for daily Vi, since the limited temporal length of acceleration periods typical of these slope instabilities. Cumulated amounts of rainfall from 1 to 180 days, mean groundwater table in 1–180 days and the mean snow depth in 1–180 antecedent days were, then, considered.

In each model, Vi was estimated considering only the most significant predictors, representing the factors that are the most influencing the displacements trends measured in correspondence of an automatic inclinometer. These predictors were identified after a sensitivity analysis, carried on to assess the influence of each predictor in the modeling of the real trend of Vi used as a response variable of a model. Then, the most significant predictors adopted for the final modeling of Vi trend were dentified calculating the Spearman’s rank correlation coefficient (ρ) which represents a non-parametric measure of statistical dependence between two variables that could be also nonlinear (Myers et al. 2010), between a predictor and the Vi. Only those variables whose ρ was higher than 0.7 were then considered in the model. For the reconstruction of the final model, the time-series was divided in a training and in a test part. The training part corresponded to 75% of the time span covered by the entire time-series and was required to reconstruct the GP model for interpreting the relations between predictor and response variables. The remnant part of the considered time-series (25%) constituted the test part. According to Eq. (2), the root mean square error (RMSE) was used for evaluating the performances of each model for both the training and the test phase:

$${\text{RMSE}} = \sqrt {\frac{{\left( {y_{i} - y_{i} *} \right)^{2} }}{n}}$$
(2)

where n is the number of the measures in the training or test sets, yi and yi* are the measured and predicted values, respectively. This step of the methodology can be applied to each displacement time-series acquired by an automatic inclinometer, furnishing indication about the main factors driving the kinematic behavior at a particular monitored point.

3 Results

3.1 Reliability of the instruments and elimination of anomalies along time-series of displacement

The daily time-series of the displacement measured by automatic inclinometers were investigate to detect the different types of anomalous measures (new origin of the measures, spike, negative Vi, measure of Ai not coherent with the real direction of the displacement) which limited the accuracy of the available measures (Fig. 6). In the time-series of the analyzed dataset, a total amount of 62 measures were detected as anomalous. The developed methodology allowed to identify correctly 59 of these anomalies, for a POD index of 95% (Table 1). The correct identification of the anomalous measures was similar for both landslides characterized by seasonal movements (types A and D) and for landslide with strong response toward intense meteorological events (types B and C), as confirmed by POD indexes of 93 and 100%, respectively. The methodology allowed also to recognize several other anomalous measurements (290) in the set of the analyzed time-series, especially due to anomalous measures of Ai or for the decrease in the cumulated Di. According to the demonstrated well capability of this step of the methodological approach in the detection of anomalies along displacement time-series, all the identified anomalous measures were deleted from each time-series. Filtered trends were, then, obtained and investigated for the following analyses.

Fig. 6
figure 6

Identification of the different types of anomalous measures, affecting automatic inclinometers time-series of cumulated displacement Di a and of direction of the movement Ai b: Borgata landslide, automatic inclinometer at 16.8 m from ground level. In the legend: (1) new origin of the measures of Di; (2) spike of the cumulated Di; (3) moment of decrease in the cumulated Di; (4) measure of Ai that is not coherent with the real direction of the deformation

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Table 1 Assessment of the performance of the developed methodology in identifying errors in the analyzed time-series acquired by automatic inclinometers
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3.2 Identification of moments of significant increase in the rate of displacement and of the kinematic behavior of a landslide

The time-series of displacement, filtered by the anomalous measures, were interpreted to identify events of significant increase in the rate of displacement. A dataset of 81 real events, involving different automatic inclinometers, was used to quantify the reliability of this step of the methodology. 77 real events were correctly indentified (POD index of 95%; Table 2). The number of correctly reconstructed events was similar for all the types of landslides (POD indexes of 95 and 94% for landslides types A and D and for landslides types B and C, respectively).

Table 2 Assessment of the performance of the developed methodology in identifying events of significant increase in the rate of displacement in the analyzed time-series acquired by automatic inclinometers
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HCA technique grouped these events in different clusters, according to their similar features in terms of d and Di. Three clusters of events were identified (Fig. 7, Table 3). Dunn Index of the obtained clustering was 0.75, testifying a well-performing clustering (Pakhira et al. 2004). The first cluster, named as C1, grouped all the events characterized by long duration, in the order of weeks or months, and cumulated displacement till 10.2 mm. The second and the third ones, named as C2 and C3, respectively, indicated events with duration of few days, between 1 and 8. C2 cluster grouped events which caused a limited increase in the rate of displacement, as testified by typical cumulated displacement between 1.3 and 10.0 mm, while C3 cluster merged events which provoked a stronger acceleration in the displacement, till about 50.0 mm, in few days.

Fig. 7
figure 7

Clusters of the events characterized by similar duration and cumulated displacement. The type of landslides is indicated close to each point a. Boxplot of cumulated displacement b and of duration c for each cluster

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Table 3 Main statistical indexes of cumulated displacement and duration of the events for the identified clusters through HCA method
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The recognized clusters represented a description of the main kinematic behaviors characterizing a displacement time-series monitored through an automatic inclinometer. Events of cluster C1 were typical only of inclinometric time-series collected in landslides of type A and D, where the acceleration on the displacement rate occurred mostly during long time spans (more than a week) in correspondence of particular seasons in a year. The events of shorter duration grouped in clusters C2 and C3 were more common of inclinometric time-series collected in landslides of type B and type C. Events with these features could be detected also in inclinometric time-series collected in landslides of type A. Events of these clusters could characterize more rarely also inclinometric time-series collected in landslide of type D, even if they were not affected by increases in the rate of displacement higher than 6 mm in few days (cluster C3).

3.3 Data-driven model of landslides displacements at local scale

Once identified the anomalous measures, the events of acceleration and the kinematic behaviors in the displacement time-series acquired through automatic inclinometers, the step of the methodology of identification of the main factors which influence the displacements and the occurrence of acceleration in measured deformation trends was applied to two different test-sites, for the validation of this approach. The first test-site corresponded to Borgata landslide (north-western Piemonte region, Alpine sector), a slope instability of type A characterized by seasonal movements occurring especially in spring and summer months. The second one was located in Cantalupo Ligure landslide (south-eastern Piemonte region, Apennine sector), where the activity of the landslide was intermittent and consequent to strong rainfall events.

3.4 Borgata landslide

Borgata landslide is a complex landslide, located in the Chisone river catchment (Fig. 8a). It occupies an area of 191,800 m2, at elevation between 1840 and 2300 m a.s.l. The displacement occurs along a planar sliding surface located at 12–18 m below ground level. In its terminal part, the landslide is characterized by a slow flow-like behavior, which affects the village of Borgata and municipal and provincial roads. The landslide affects a steep (mean slope angle of 22°) south-eastern facing slope, where a DSGSD is present (Fig. 8a). The hillslope is characterized by the presence of quartz-rich calcic schists, which are fractured in blocks plunged in sandy or sandy-silty matrix in correspondence of the sliding surface of the complex landslide (Fig. 8b). Below the landslide sliding surface, more compact quartz-rich calcic schists are present.

Fig. 8
figure 8

Borgata landslide: a location of the slope instabilities and of the monitoring tools; b representative geological section of the landslide; c correlation between cumulated displacements measured by automatic inclinometers, cumulated snow cover of 1 month and cumulated snow cover of 4 months; d comparison between observed and modeled by GP trends monthly displacement velocity of the analyzed automatic inclinometer (S6SSTA0A at − 16.8 m from ground level)

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The landslide has been monitored through 5 automatic inclinometers since 2004. Manual inclinometers and GPS are also present (Fig. 8a). Until 2010, the deep drainage networks guaranteed the flows of the underground waters away from the sliding surface of the landslide, making slower the deformation. The displacements started to increase since winter 2010 and is still going on, in correspondence of the levels between 12.5 and 16.8 m from ground level (Fig. 8c). The displacement time-series of the inclinometers located in the shallowest layers did not highlight significant events of increase in the rate of displacement, while only one acceleration event in March–May 2016 was measured in correspondence of the automatic inclinometer S6SSTA0B at − 32.5 m from ground level (Fig. 8c).

Borgata complex slope instability is a type A landslide, characterized by seasonal active phases which occur mostly in spring months between March and June. Events of increase in the displacement rate are rarer in other periods of the year. Analyzing the times-series of the displacements filtered by the errors for the automatic inclinometers S6SSTA0A (− 16.8 m from ground) and S6SSTA1C (− 12.5 m from ground level), the significant events of increase in displacement velocity belonged mostly to the cluster C1. These events were characterized by duration between one week and one month and by cumulated displacement between 8 and 22 mm.

The seasonal activity of the landslide and the typical event length of several weeks-months detected by the different field sensors were consistent with the choice of modeling monthly time-series of displacement velocity Vi through the GP model. Monthly Vi time-series of S6SSTA0A automatic inclinometer was chosen as a representative example, due to the presence of the sensor in correspondence of the sliding surface (− 16.8 m from ground) and to the highest length of monitored time span (2004–2019). For the input parameters of the model, piezometric levels were acquired in a piezometer located less than 50 m from the two vertical of automatic inclinometric sensors, while rainfall and snow cover data were measured in a meteorological station (Pragelato Trampolino a Valle station, ARPA Piemonte meteorological network), located at 6 km from the unstable area in a similar range of altitude. Monthly Vi were not correlated (ρ < 0.15) to monthly cumulated rainfall amounts and to average piezometric levels (depth of groundwater table steady between − 29 and − 26 m from ground level). Instead, it was strongly correlated to snow cover depths, in particular to the cumulated snow cover of that month (ρ = 0.75) and of the last 4 months (ρ = 0.80). The highest correlation between 4 months cumulated snow cover and monthly Vi was in agreement to the seasonality of the displacements. The events of increase in the deformation occurred mostly in March-June in a year, as a consequence of the infiltration of water melted after the peaks in snow cover during the winter months, especially December February (Fig. 8c). GP model was, then, built using only one month and 4 months cumulated snow cover. It allowed to reconstruct the real time-series of monthly Vi in a reliable way, as shown by RMSE values of only 0.14 and 0.12 mm/month for training and test set, respectively (Fig. 8d).

3.5 Cantalupo ligure landslide

Cantalupo Ligure landslide is a slow flowslide, located in the Rio di Cognola creek catchment and affecting the village of Costa Merlassino (Fig. 9a). It occupies an area of 295,778 m2, at elevation between 560 and 440 m a.s.l. The landslide affects a medium-steep (mean slope angle of 12°) south-western facing slope, where a more deep complex landslide is present (Fig. 9a). The displacement occurs along a planar sliding surface at 2–3 m below ground level. The sliding surface is located at the contact between the colluvial cover, formed by silt ad sand with arenaceous and marly blocks, and the weathered bedrock, constituted of low permeable marls locally alternated with thin arenaceous layers (Fig. 9b).

Fig. 9
figure 9

Cantalupo Ligure landslide: a location of the slope instabilities and of the monitoring tools; b representative geological section of the landslide; c correlation between cumulated displacements measured by automatic inclinometers, cumulated rainfall of 3 days and cumulated rainfall of 30 days; d comparison between observed and modeled by GP trends daily displacement velocity of the analyzed automatic inclinometer (S1CPLC0A at − 2.5 m from ground level)

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The landslide was monitored in 2006–2014 time span through 2 automatic inclinometers (S1CPLC0A at − 2.5 m from ground, S1CPLC0B at − 14.0 m from ground), whose sensors was located at different depths in correspondence of one vertical. The monitoring time-series showed that the deformation occurred only in the shallowest layer, while the deepest sensor did not measure significant events of increase in the rate of displacement (Fig. 9c).

Cantaloupe Ligure flowslide is a type C landslide, characterized by discontinuous active phases that follow intense meteorological events that could occur in every seasons. Analyzing the times-series of the displacements filtered by the anomalous measures for the automatic inclinometer S1CPLC0A, 12 significant events of increase in displacement velocity belonged to the clusters C2 and C3 were identified. They were characterized by duration between 1 and 5 days and by cumulated amounts between 2 and 13 mm.

The typical event length of few days was consistent with the choice of modeling daily time-series of displacement velocity Vi through the GP model. Daily Vi time-series of S1CPLC0A automatic inclinometer was chosen as a representative example. For the input parameters of the model, the rainfall data were measured in a meteorological station (Roccaforte Ligure station, ARPA Piemonte meteorological network), located at 5 km from the unstable area and at a similar range of altitude. Daily Vi time-series was correlated significantly to cumulated rainfall amounts of the last 3 (ρ = 0.71) and 30 days (ρ = 0.74). The events of increase in the rate of deformation detected by the analyzed inclinometer occurred in correspondence of intense and prolonged rainy periods (Fig. 9c). Daily Vi in the range 2–5 mm/d occurred in correspondence of cumulated rainfall amounts in 3 days of 64.0–101.2 mm and cumulated rainfall amounts in 30 days of 297–514.6 mm, while velocity of more than 5 mm/d occurred in correspondence of cumulated rainfall amounts in 3 days of 89.0–102.2 mm and cumulated rainfall amounts in 30 days of 546.4–555.2 mm. GP model was, then, built using only cumulated rainfall of 3 and 30 days, allowing to reconstruct the real time-series of daily Vi effectively, as shown by RMSE values of only 0.17 and 0.18 mm/d for training and test set, respectively (Fig. 9d).

4 Discussions

Although the use of automatic inclinometers devices is common for monitoring extremely slow, very slow and slow-moving landslides, an integrated methodological scheme was developed for the first time, in order to cover all the steps of data interpretation. The developed method has significant advantages.

First, the methodological scheme can be implemented to different test-sites monitored with automatic inclinometers, guaranteeing a uniform and objective application for different monitored points (Guo et al. 2019). Furthermore, it has the potential to be applied also for the analysis of displacement datasets collected through other types of automatic field probes (e.g., extensometers, GPS).

The initial assessment of the reliability of the measured data furnish a time-series of displacement clean by anomalies which could limit the interpretation of the real deformation trend of a landslide (Simeoni and Mongiovì 2007). This step of the method stress that also the measured direction of the movement, acquired by the inclinometer, can be used as an indicator of the measures reliability.

The identification of the moments of significant increase in the rate of landslides displacement is a procedure which is generally based on the comparison between average velocities. Instead, in this methodology, an event of significant acceleration occur also if the cumulated displacement, during the activity phase of the landslide, is over a threshold. In this way, the detection of the event takes into account both the significant change in the state of activity of a landslide and the minimal amount of deformation that could lead to provoke detrimental effects on the unstable area (Mansour et al. 2011; Peduto et al. 2017, 2021).

The definition of the parameters and the thresholds for the detection of events of acceleration cannot be homogeneous at large scale, due to differences on slope instability kinematics, geomorphological and geological settings at the test-sites, heterogeneities of the properties of unstable mass, monitoring depths and landslide sliding surfaces. However, typical kinematic mechanisms, represented by different types of events in terms of duration and cumulated amounts, can give indications on the typical deformation patterns which could be detected in a dataset of displacement time-series acquired by automatic inclinometers. In the analyzed dataset of Piemonte region, the displacement time-series acquired by the automatic inclinometers can present events of acceleration during rapid or prolonged phases of water infiltration till the sliding surface, in consequence of intense rainfalls or snowmelt. These displacement trends are in agreement with trend-type III identified by Cascini et al. (2014) and Scoppettuolo et al. (2020) for several active slow-moving landslides in Italy, Spain and Japan.

The last step of the methodological approach is related to the identification of the main factors which influence the displacements and the occurrence of acceleration in a measured deformation trend. Even if the proposed approach can be applied to different displacement time-series acquired by automatic inclinometers, the identification of the main triggers is local and representative only to that monitored time-series (Guzzetti et al. 2007). However, this analysis is fundamental to understand the factors influencing the kinematic behavior of a landslide or of a part of it, with practical consequences for both land use planning and early prediction systems (Crosta et al. 2017). Furthermore, only the most influencing factors of a displacement trend are considered, limiting misinterpretation or bias (Krkac et al. 2016).

The individuation of the main factors influencing the displacement trends at the two analyzed test-sites (Borgata and Cantalupo Ligure) allows also to characterize the mechanisms which lead to increase the rate of deformation in the analized automatic inclinometers. GP procedure adopted for these analyses gives good indication of the influencing factors of the deformation, as indicated by values of RMSE lower than 0.2 mm/day or mm/month. Snowmelt controls the deformation pattern of the inclinometer of Borgata landslide, as already demonstrated for slow-moving slope instabilities present in other alpine regions (Crosta et al. 2014; Vecchiotti et al. 2022) or at high latitudes (Nordvik et al. 2010; Grøneng et al. 2011). Antecedent snow cover measures are required to model possible variations of the rate of deformation, with events of significant increase in displacements that could occur during and immediately after snow-melting for high air temperatures. In these periods, generally during spring and summer months in the studied context, water derived from snow-melting can infiltrate in depth till the sliding surface, inducing an increase in pore water pressure enough to determine an active phase of the landslide deformation (Grøneng et al. 2011). For Cantalupo Ligure inclinometer, the events of increase in displacement rate follow phases of intense and continuous rainfalls, which could occur throughout all the year. The meteorological attributes influencing the deformation measured by this sensor are related both to long antecedent rainfalls and to short rainfall periods during few days before the displacement events, as already demonstrated for other slow-moving phenomena affects hilly and mountainous contexts all over the world (Vallet et al. 2016; Krkac et al. 2017; Guo et al. 2019). The activity phases are triggered by strong rainfall events leading to an uprising of water table levels close to the sliding surface of the landslide and a consequent increase in pore water pressure induced by rainwater infiltration (Capparelli and Versace 2011; Tiranti et al. 2013).

A further validation of the model for estimating landslide displacements through the most significant predictors was carried on for January 2019–July 2020 at Borgata and Cantalupo Ligure landslides. At Borgata, the analyzed inclinometer (S6SSTA0A at -16.8 m from ground level) is still measuring. In this time span, snow cover was limited (0–660 mm in a month, 0–4450 mm in 4 months). These conditions did not determine significant acceleration of the rate of displacements (< 1.5 mm/month). The measured trend of monthly rate of displacements was in agreement with the modeled one (RMSE of 0.24 mm/month, Fig. 10a). At Cantalupo Ligure, the analyzed automatic inclinometer was not active in January 2019-July 2020 period. The modeled trend of displacements highlighted two events of acceleration, between 3 and 10 November 2019 (8 mm in 8 days) and between 16 and 22 November 2019 (8.2 mm in 7 days) (Fig. 10b), after intense rainfall events (63.4–88.2 mm in 3 days, 284.2–330.0 mm in 30 days). The cumulative displacements of these events were in agreement with a manual inclinometer, located close to the previously-installed automatic inclinometer, that measured an increase in cumulated displacement of 12 mm between October 2019 and May 2020.

Fig. 10
figure 10

Measured and modeled trends of monthly rate of displacements between January 2019 and July 2020 at Borgata landslide, for automatic inclinometer S6SSTA0A at − 16.8 m from ground level a. Modeled trend of daily rate of displacements between January 2019 and July 2020 at Cantalupo Ligure landslide, for automatic inclinometer S1CPLC0A at  − 2.5 m from ground level

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It is also important to underline limitations and issues of the developed methodology, also for its possible applications to monitored data of other contexts. Besides the robust results obtained through the analysis of automatic inclinometers, the methodology could be extended also to displacements measured by other field devices, with continuous acquisition (e.g., GPS, crackmeters), after a calibration phase, especially for the quantification of the anomalous measures and the determination of the displacement thresholds to define significant events. GP model used only meteorological and groundwater attributes to explain the trend of deformation measured by a particular automatic inclinometer. It is clear that also other factors, such as creeping processes, could play a fundamental role in conditioning the displacement time-series acquired by a sensor (Guo et al. 2019). Moreover, velocities data, acquired by the automatic inclinometers and used for establishing this methodological approach, belong to very slow slow categories (Cruden and Varnes 1996). Thus, more tests are needed to validate the methodology reliability also for faster activity phase, especially the ones which could anticipate a collapse of the unstable mass (Intrieri et al. 2019).

5 Conclusion

A novel methodology for the analysis and the interpretation of displacement data acquired by automatic inclinometers was developed. It allowed to identify the anomalous measures and to interpret the kinematic features of displacement time-series acquired in correspondence of extremely slow to slow-moving landslides monitored in Piemonte region (north-western Italy).

The developed method is reliable in the estimation of the anomalies and in the identification of the events of significant acceleration of the movements, which could also lead to a modification in the kinematic pattern measured by a sensor. The clusters of the events allow to determine similar deformation features between different displacement time-series, helping in the comprehension of the response of displacement trends during particular activity phases. The last step of the methodology regards the identification of the main driving factors which influence the trend of the displacements and the conditions leading to a different response in terms of deformation intensity, measured by an automatic inclinometer. Besides the large heterogeneities in geological, geomorphological and kinematic features of different landslides, the developed data-driven model is able to identify the main attributes which influence more the deformation pattern measured in correspondence of an automatic inclinometer. This could represent an initial step also for the development of thresholds of the driving parameters useful for land planning and early warning strategies.

Overall, this paper demonstrates the effectiveness of the automatic inclinometers in measuring reliable data of displacements and the necessity of integrated methods able to cover all the steps of interpretation of these data. Reliable displacement trends and effective analyses of these data are key factors for establishing an adequate monitoring network of slow-moving landslides. The methodology can be implemented to large networks of in-place automatic inclinometers and, also, of other in-place probes able to measure displacements in the order of extremely slow to slow-moving slope instabilities. In this way, the results achieved through the application of the proposed methodology could represent an important preliminary tool for the development of methods and models which study the damages and the detrimental effects to infrastructures and building due to the movement of a landslide. In these terms, the method could furnish a useful support for land planning and management and for the choice of the best mitigation strategies.