Alert threshold assessment based on equivalent displacements for the identification of potentially critical landslide events

Over the past years, the growing number of natural hazards all over the world has led to an increasing focus on activities aimed at studying and controlling the occurrence of these phenomena. In this context, monitoring systems have become a fundamental component for Landslide Early Warning Systems, allowing to understand the evolution of these processes and assess the need for dedicated mitigation measures. This result is achieved thanks to several technological advancements that led to the introduction of more accurate and reliable sensors, as well as automatic procedures for data acquisition and elaboration. However, despite these improvements, the data interpretation process is still a challenging task, in particular when it comes to the identification of critical events and failure forecasting operations. This paper presents a methodology developed to assess if a potentially critical event is displaying a significant deviation from previously sampled data, or if it could be classified as a false alarm. The process relies on the definition of a threshold value based on the landslide behavior preceding the event of interest. In particular, the reference value derives from the evaluation of equivalent displacements, defined as the displacements previously observed in a time interval equal to the one showed by the potentially critical event. This paper reports a series of examples referring to different case studies, involving both false alarms and real collapses, underlining the effectiveness of the proposed model as a useful tool to evaluate the landslide behavior with a near-real-time approach.


Introduction
As previously noted, the processes for the definition of alert levels and thresholds are among the most difficult to entail. Because of their own nature, these should be determined with the intent to represent a critical event in the context of the studied phenomenon, i.e., a condition that may trigger a landslide when exceeded (Guzzetti et al. 2007). For what concerns the landslide monitoring framework, these occurrences are usually associated with slope collapses generated by a situation of irreversible instability of the studied element. In many cases, the threshold assessment process is completely empirical, relying on expert judgment and available monitoring data, and provides values suitable only for the specific landslide for which they are originally defined (Intrieri et al. 2019). Numerical modeling is another possible approach to assess warning levels for a specific landslide. These methods aim to compare displacements measured by monitoring tools installed on-site with values obtained from a reference model. If properly designed and calibrated, the model should be able to represent the behavior of the real slope, thus allowing the definition of one or more thresholds corresponding to different stages of the monitored slope evolution over time (Huggel et al. 2010;Thiebes et al. 2014;Festl and Thuro 2016;Du and Wang 2016;Newcomen and Dick 2016;Zhao et al. 2020;López-Vinielles et al. 2021). This approach can be indeed highly effective, although the large number of components to take into account in the modeling process makes it a quite challenging and time-consuming task. In more recent time, technological improvements regarding the computational ability of modern computers, together with the increased availability of powerful software able to process advanced algorithms, have boosted significantly the research activity in this specific field. As a result, several authors have presented new studies and methodologies based on a wide range of different approaches, such as algorithms relying on Artificial Intelligence (Di Napoli et al. 2020;Guardiani et al. 2021;Liu et al. 2021;Ma et al. 2021) and Neural Networks (Chen et al. 2015;Prakash et al. 2021;Zhang et al. 2022).
On the other hand, other methodologies have been developed over the years focusing on the possibility of creating a more general procedure, not strictly dependent from a specific case study. In these cases, the design process is based on failure forecasting methods (Crosta and Agliardi 2002;Manconi and Giordan 2016;Carlà et al. 2018;Valletta et al. 2020), or derives from a solid observational basis (Brox and Newcomen 2003;Xu et al. 2011). Due to their notable degree of exportability, these methodologies can be integrated in different slope-scale EWS. Nonetheless, they tend to share the same issues affecting the methods from which they derive and should not be used in isolation with a "closed box" approach. In fact, at present, the most reliable approach appears to be the integration of more than one method in order to have a more complete description of the phenomenon (Intrieri and Gigli 2016).

Materials and methods
The methodology here presented relates to this concept, aiming to exploit the availability of a large amount of information regarding the past movements of the monitored landslide as a comparison with determine the impact of newly recorded displacements on the slope stability conditions. In particular, the approach was designed with the main purpose to identify the occurrence of a specific category of false alarms. These consist of events displaying a data trend geometrically compatible with an accelerating pattern, while featuring a displacement magnitude which does not correspond to a critical occurrence if compared to previously observed occurrences. As previously noted, the introduction of new technologies in the geotechnical field has notably increased the monitoring systems reliability and sampling rate, thus making them able to provide a considerable amount of information over time. On this basis, the proposed approach seeks to exploit the availability of available monitoring data to assess one or more alert levels not only for any particular case study, but also specifically for each single event identified by the monitoring instrumentation. Moreover, the methodology was developed trying to balance computational complexity and results reliability, designing a procedure conceptually easy to understand and implement, while being able to provide meaningful information for early warning purposes at the same time.
The process to define the alert threshold value can be divided into a series of consecutive steps, starting from the acquisition of landslide displacement data. When the elaboration software detects a potentially critical event, it extracts the corresponding dataset and evaluates the displacement generated d * 0 and its duration t * . The event identification can be performed starting from available monitoring data, and the corresponding dataset is expected to follow an increasing trend in the displacement-time plot. The authors developed a multi-criteria algorithm specifically designed for the identification of the onseton-acceleration (OOA) and the subsequent acceleration phase, relying on a drop-down procedure composed of four steps that are applied to each single data sample to detect specific variations in the landslide behavior (Valletta et al. 2021). The method is based on the hypothesis that the monitored landslide would display a transition from a linear to a nonlinear behavior, corresponding, respectively, to a constant and increasing displacement rate. Therefore, if the elaboration process identifies a trend that fulfils all criteria, it is possible to define a displacement dataset representing an increasing velocity over time.
Taking as a reference the date t x of the first point d x (i.e., the OOA) included in the dataset, the software retrieves all monitored data sampled by the same sensor during the 30 days preceding the event. These values are going to serve as a term of comparison for the event identified at the previous step, using t * as the time interval reference for the calculation of equivalent displacements. This term defines the slope displacements measured before the event occurrence and developed over a time interval equal to the one showed by the potentially critical event. By doing this, the algorithm produces a series of displacements d * n generated over the same time interval t * . Table 1 reports an example of this procedure for a dataset composed of six displacement values, under the hypothesis of constant sampling frequency during the monitoring activity (i.e., the time interval is equal for datasets featuring the same number of values).
Therefore, it is possible to assess an alert threshold d * th based on the values of mean S and standard deviation S referred to the dataset of the equivalent displacement previously calculated: Finally, it is possible to compare this outcome with the displacement d * 0 , in order to verify if the event generated a displacement with a magnitude similar to values previously observed during the considered time period, or if the resulting values overcome the alert threshold, thus indicating an unusually intense phenomenon. The flow diagram reported in Fig. 1 summarizes the procedure outlined above.
The reference time interval for the evaluation of equivalent displacements, and the related threshold value, was assessed on the basis of a series of considerations regarding the monitoring activity of a landslide, and after calibrating the model on several datasets sampled with automatic instrumentation installed in different sites of interest. The main observation concerns the number of monitoring data to be included in the dataset, which should be large enough to allow an appropriate definition of a typical trend of the landslide before the event occurrence. In fact, by choosing a too short time interval, the threshold fluctuations induced by single equivalent displacement would be too prominent, resulting in an unreliable threshold definition process. At the same time, taking into account a very long time interval for this operation would force to wait a prolonged time period after the installation of the monitoring tools, severely limiting the effectiveness of the warning system. The introduction of automatic instrumentation able to achieve sampling frequencies of hours, and even minutes, could potentially play an important role when addressing this issue. However, it should be also taken into account that a very high number of data collected in a short time period could not provide a comprehensive representation of the general behavior of the monitored landslide. The time period here proposed was chosen by taking into consideration these remarks together with empirical observations coming from the application of the methodology to different datasets. Nonetheless, while the 30-day interval provided positive results during the calibration and testing phases, the possibility to select a more appropriate time window according to on-site observations in specific case studies should not be entirely discarded. Figure 2 reports four examples obtained during the calibration process. Each plot shows the equivalent displacement evaluated according to the previously discussed procedure and displays the alert threshold value evaluated by considering a varying number of monitoring data. The first three datasets relate to case studies where the sampling frequency was set (1) d * th = S + 3 S Fig. 1 Flow diagram summarizing the main steps for the assessment of an alert threshold based on equivalent displacements to six readings per day, resulting in a total number of monitoring values equal to 180 for each month. The 4th dataset refers to a monitoring system configured with an hourly sampling frequency, thus producing a 720-point dataset. These examples show how the threshold experiences very prominent variations when its assessment relies on smaller datasets and reaches a more stable value when more data are added to the calculation process. It is worth noting that the presence of some peaks in the equivalent displacement dataset is still able to influence the threshold value even if large datasets are taken into account, as can be observed for example in dataset #3 and #4. However, this should not be seen as an issue, since higher equivalent displacement values are an indication of the occurrence of past events generating more noticeable slope movements, which should not be neglected when assessing the standard behavior of the monitored landslide.

Results and discussion
The threshold assessment process has been applied to a wide range of dataset recorded in real-time, working in synergy with the previously mentioned methodology designed to identify accelerating trends in landslide displacements. In the following sections, three different case studies involving a total of four events are described, in order to present some examples of the methodology application and outcomes in a real scenario. The examples provided in this paper include also a back-analysis performed on a case study where the detected event led to an actual collapse of the monitored slope (thus representing a "true" positive in terms of early warning).

Case study #1
The first case study involves the monitoring activity of a slope located in Southern Italy, where a series of instability phenomena were identified after the construction of a viaduct connected to a State Road crossing the area. As a consequence, a multi-parameter monitoring system was installed in order to study the phenomenon evolution, focusing on its interaction with the infrastructure. The instrumentation included seven Vertical Array automatic inclinometers, based on MUMS (Modular Underground Monitoring System) technology developed and produced by ASE S.r.l. (IT). The instrumentation is an array composed of different nodes (named Links) connected by a quadrupole electrical and an aramid fiber cables in order to form an arbitrary long chain of sensors (Segalini et al. 2014;Carri et al. 2015). It can be equipped with 3D MEMS, electrolytic cell, piezometer, thermometer, and other typologies of sensors, while a dedicated data logger connected to the Array automatically queries each different Link. The on-site location and composition of each array should be carefully considered in the project phase with the aim of providing a comprehensive description of the landslide, focusing on different sectors of the monitored slope. This aspect is essential for any monitoring activity intended for early warning purposes. For this case study, the length and composition of each Array varied according to the on-site position of the equipment. The monitoring system included also three Piezo Arrays, each one integrating a series of analog piezometers to record the pore pressure and water level variation over time; seven tilt meters, installed on the viaduct piles to control the stability conditions of the structure; three barometers to monitor the atmospheric pressure; and a rain gauge for the measurement of rainfalls in the area. Table 2 summarizes the main features of the monitoring system. On 24 September 2020, the elaboration software reported the presence of an accelerating pattern detected by Vertical Array DT0074 in correspondence of Tilt Link 15, located at a depth of 16 m (Fig. 3). The automatic routine for the determination of the onset-of-acceleration identified the beginning of the event at 06:13. After the definition of the dataset of interest, the first step for the alert level assessment process involves the determination of the displacement generated by the event itself and the corresponding time interval. In this case, since this device was set to sample new data every 6 h, the monitoring data showed a displacement 1.5 mm over a time period of approximately 30 h.
The subsequent operation consists of retrieving monitoring data from the 30 days preceding the event of interest, in order to assess the equivalent displacements and the correlated threshold. Taking the OOA as a reference, displacements recorded since 24 August 2020 06:13 were retrieved in this phase. Each equivalent displacement value is computed by considering a time interval equal to the one obtained from the event, resulting in 118 equivalent displacements. By exploiting the mean and standard deviation values calculated on this dataset, respectively, equal to 0.74 and 0.56 mm, the alert threshold based on equivalent displacements is equal to 2.5 mm ( Table 3). As a result, it is possible to state that the identified event does not display a concerning behavior if compared to previously sampled monitoring data, since the corresponding displacement does not overcome the computed threshold (Fig. 4).

Case study #2
The second case study deals with the monitoring of a slope located in Southern Italy, crossed by a high-speed railway tunnel currently under construction. After the identification of a quiescent landslide in the area, it was decided to install an automatic monitoring system with the objective of verifying the design hypotheses and control the deformations induced by the excavation works. The monitoring system included a total of four Vertical Array automatic inclinometers, featuring different lengths and number of sensors. Interspace between Links also varied depending on their vertical position, with a distance of 2 m between each node in the supposedly stable area, reducing to 0.5 m in proximity of the sliding surface for an increased degree of detail in the phenomenon description. Additionally, the system comprises four Piezo Arrays, each one composed of two analog piezometers, to record the water level variations over time. The characteristics of each Array are summarized in Table 4. During the entire monitoring period, all Vertical Arrays evidenced a relevant degree of activity of the monitored site, even without displaying any significant evidence of critical instabilities taking place in the area of interest. For this case study, two events are going to be analyzed, involving two different Arrays in May 2020 and August 2020. Datasets recorded by each Tilt Link that identified an unexpected displacement trend were processed with the algorithm previously detailed, assessing an equivalent  displacement threshold to verify how the event magnitude compared to the landslide's past behavior. The first event here analyzed was detected on 13 August 2020, when the elaboration software indicated the presence of an upward trend in a six-point dataset sampled by Vertical Array DT0112-Tilt Link 48, located 17.50 m below the ground level. The algorithm defined the onset-of-acceleration for the event at 21:51 of the previous day (Fig. 5). According to this information, displacements recorded since 12 July 2020 21:51 were retrieved for the alert threshold assessment procedure. As a result, a total of 184 equivalent displacements were computed by taking as a reference the time interval obtained from the event, i.e., 24 h. Finally, the algorithm evaluated the mean and standard deviation values for the dataset, obtaining an alert threshold equal to 2.9 mm.
The outcomes of this operation are summarized in Table 5, while Fig. 6 presents a graphical comparison between the equivalent displacements and the threshold computed at the previous step. It is possible to observe how the resulting value referred to the event of interest is comparable to previously recorded displacements, not overcoming the threshold value. It is also worth noting that equivalent displacements evaluated for this event do not show any significant peak in the reference time period.
The second event here analyzed was recorded by Vertical Array DT0113 on 24 May 2020, approximately four months after its installation. In this case, the movement detected by the instrumentation was recorded by two Links, namely Tilt Links 43 and 55, placed, respectively, at a depth of 12.50 and 6.50 m. The datasets identified by the software were composed of five monitoring values each, and the beginning of the accelerating phase was set at 04:37. Analyzing the available monitoring data, it is possible to notice a strong similarity between the trends displayed in Figs. 7 and 8, representing the slope displacements for Tilt Link 43 and Tilt Link 55, respectively. Since these values refer to cumulative displacements, it could be assumed that a single movement located at a lower depth influenced the behavior of both Links.
Following the retrieval of displacement data starting from 24 April 2020 04:37, two datasets of 185 equivalent displacements were obtained for the analysis. The operations relating to the evaluation of the displacement generated by the event, the extraction of  equivalent displacements from previous monitoring data, and the threshold assessment, are summarized in Table 6. All Vertical Arrays on this specific site were set on a sampling rate of 4 h, recording six monitoring values each day. Therefore, since each dataset includes five velocity values, the time interval to evaluate the equivalent displacements for this example is equal to 20 h. Figures 9 and 10, referring, respectively, to Tilt Link 43 and 55, present a graphical visualization of the analysis outcomes, evidencing how the detected event did not cause a displacement significant enough to overcome the threshold values assessed for the two Links. As seen in the previous case, it is quite easy to notice how the event entity does not appear to be significantly higher than other equivalent displacements, therefore   representing an occurrence where the early warning elaboration was triggered only by the geometric pattern of monitoring data. Moreover, a strong similarity in displacement trends for the Tilt Links considered for this analysis can be observed from available graphs. Since these values are obtained from cumulative displacements, it is possible to assume that both Links were influenced by a common movement located at a lower depth.

Case study #3
The third case study here discussed refers to the monitoring of a landslide, located in Central Italy, that persists on the construction site of a state road connecting the Adriatic and Tyrrhenian Seas, through Abruzzo and Molise regions. The site is affected by the presence of several landslides in the western sector of the area of interest, showing fast kinematics and sliding surfaces at a depth between 8 and 10 m, with other instabilities appearing in the first meters of material in the Eastern areas. Following a series of preliminary surveys evidencing further problems related to settlements and damages to pre-existing instrumentation, a MUMS-based monitoring system was designed, with a total of nine Vertical Arrays installed on site over approximately 4 years starting from the end of 2016. Each Array featured a different number of Tilt Link HR 3D V, equipped with 3D MEMS and electrolytic tilt sensors, and customized interspace between nodes, as in Table 7. The event here analyzed, extensively discussed in Segalini et al. (2019), occurred in March 2017, some months after the installation of the Vertical Array DT0014. At that time, DT0014 was the only automatic monitoring device present on site, and the acquisition process was set on a sampling frequency of 1 h. Starting from the end January 2017, the inclinometer recorded a series of displacements involving the first six meters of soil, with some datasets activating the early warning criteria implemented in the software. The phenomenon evolved over the following weeks, leading to a major displacement recorded on March 8 th that damaged the Array, partially compromising its functionality. The event was identified by the elaboration software, which issued a series of alert messages to authorities responsible of the monitoring activity.
Ultimately, MUMS inclinometer DT0014 became completely inactive on March 13th due to excessive deformations. In the following days, an on-site inspection confirmed the landslide occurrence, highlighting the presence of a complex dynamic featuring several failures and scarps, settlements, and displacements (Fig. 11). Additionally, an in-depth check of the conditions of previously installed instrumentation reported severe damage caused by the event (e.g., inaccessible inclinometer casings).
It should be noted that only an early version of acceleration criterion was active during the monitoring activity; therefore, no alert threshold based on equivalent displacements was available at the time of the event occurrence. Therefore, a back-analysis was performed on the datasets referring to the displacement observed on 08 March 2017, in order to apply the newly developed methodology to a real case critical scenario. In particular, the sudden increase in displacement rates was identified by Tilt Links 93 and 95, respectively, located 2.5 and 1.8 m below ground surface. For both Links, the analysis returned a sevenpoint velocity dataset with the onset-of-acceleration at 02:28 of March 8th. By looking at both Figs. 12 and 13, it is possible to notice that a portion of the increasing displacement trend was not included in the dataset of the event. This could potentially be attributed to the criteria integrated in the algorithm for the identification of the onset-of-acceleration. As in previous cases, the available monitoring data were processed in order to evaluate the displacement measured by each Link during the event, and to assess the corresponding alert threshold. Given the one-hour sampling frequency of the Vertical Array, and since the detected event involved seven monitoring values, the 30-day time window provided 661 displacement values for each Tilt Link. The outcomes of this procedure are summarized in Table 8, and the graphical representation of the obtained value is displayed in Figs. 14 and 15. It is possible to notice how the event caused a displacement that clearly overcomes the threshold value for both datasets, thus confirming that the monitored phenomenon is showing a critical behavior. It is worth noting that this is the only confirmed slope collapse    (Fukuzono 1985). The time of failure evaluated with this methodology was compared to the date of collapse observed from monitoring data (i.e., the date and time where instrumental data evidenced the damage caused to the Array by soil deformations). As reported by Segalini et al. (2019), both datasets provided a positive prediction of the slope collapse, with a time difference of 3 h for Tilt Link 93, and 1 h for Tilt Link 95.

Conclusions
The importance and effectiveness of Landslide Early Warning Systems has increased considerably over the years, thanks to the introduction of technological developments that allowed to improve their functionality and efficiency. One of the most important elements in a LEWS is represented by failure forecasting and alert thresholds assessment procedures, which represents an essential reference to identify slope instabilities and behaviors potentially leading to collapses and failures. In particular, the correct definition of alert levels should aim to minimize the occurrence of both false positive and missed alerts. This paper deals with this issue by proposing a procedure to assess alert thresholds based on the concept of equivalent displacements, defined as the displacements generated in a time interval equal to the one showed by a specific event identified by the elaboration software. When referred to data sampled prior to the event of interest, they can give an indication of the past behavior of the monitored element. Therefore, they are able to establish a term of comparison in order to understand if the recorded event generated a displacement which does not correspond to a critical occurrence if compared to the entity of previously observed events, despite being geometrically compatible with an accelerating pattern. In order to achieve this objective, the approach here described involves the retrieval of monitoring values sampled in a time window of 30 days preceding the event of interest. These data are exploited to evaluate the equivalent displacements values, taking as a reference the duration of the detected event. Finally, the software is able to assess a threshold value on the basis of the mean and standard deviation values of the reference dataset.
Several examples are included in this paper, underlining the ability of the proposed model to define an effective threshold value to compare the potentially critical event with previously observed trends. In particular, the case studies here presented featured the on-site implementation of automatic monitoring instrumentation that provided an adequate amount of data to apply the methodology. The events here analyzed involve three events that did not lead to any significant effect on the stability conditions, and an occurrence where a collapse was observed following the development of significant slope deformations.
The results obtained can be summarized as follows: -The exploitation of automatic instrumentation played an essential role in providing an appropriate amount of monitoring data for the application of the proposed methodology, giving also the possibility to implement the algorithm in the elaboration process with a near-real-time approach 1 3 -The model parameters selected during the model calibration process (i.e., dataset dimension, number of standard deviations) proved to be effective for the methodology implementation in a real case application -The outcome of the threshold definition process applied to potentially critical events allowed to assess if the detected occurrence displayed a significant deviation from the standard behavior of the monitored slope, identifying also any false alarm generated by displacement trends geometrically compatible with an accelerating pattern The methodology here presented successfully achieved the purpose of this paper, providing an effective and easily applicable procedure for the analysis of potentially critical events and the identification of false alarms. Nonetheless, since the monitoring of slope displacements is only one aspect of a very complex phenomenon, this model should not be applied in isolation. In fact, the most reliable approach should involve the integration of multiple methodologies in order to have a more complete description of the slope evolution over time.
Following the observations previously presented, it is worth mentioning some final considerations on the future developments involving the method here described. In particular, it would be interesting to apply the algorithm to other monitoring devices integrating automatic sampling operations in order to verify its adaptability to different landslide survey approaches. Moreover, another aspect that could be further investigated involves the possibility to exploit the proposed procedure to assess more than a single threshold. This could be achieved by varying the number of standard deviations considered in the equation used to evaluate the d * th value, in order to obtain different alert levels based on the landslide behavior and integrate appropriate safety measures according to the level reached.