Rockfall Hazard Assessment in Volcanic Regions Based on ISVS and IRVS Geomechanical Indices

In volcanic regions, rockfalls represent a major hazard strongly conditioned by the geomechanical behaviour of volcanic materials, the geomorphological characteristics of the relief and the climatic conditions. Volcanic rocks possess very different properties to those of other lithological groups, presenting highly heterogeneous geomechanical behaviours. Nevertheless, they have received little research attention in the field of geological and geotechnical engineering. To date, the application of geomechanical classifications to characterise and estimate volcanic slope stability has not yielded reliable results, indicating the need to establish specific criteria for these rocks. Consequently, we developed indices to estimate rockfall susceptibility, hazard and risk in volcanic slopes. The index of susceptibility for volcanic slopes (ISVS) is designed to estimate slope susceptibility to instability, which is related to the level of hazard, while the index of risk for volcanic slopes (IRVS) is designed to estimate the level of risk as a function of the potential damage or economic loss caused as a result of rockfalls on slopes. Both indices were developed in order to provide an easily applied procedure that facilitates the adoption of short-term preventive measures against rockfalls. The indices were applied in Tenerife (Canary Islands), which presents exceptional conditions for analysing slope stability in volcanic rocks because of its mountainous orography with very steep slopes and a wide variety of materials. These conditions have frequently precipitated slope instability, causing significant damage to housing, beaches, roads and other infrastructures. After applying these indices to a number of slopes representative of the island’s wide variety of geological, geomorphological and climatic conditions, the results obtained were compared with the actual behaviour of the slopes, determined from extensive rockfall inventory data and in situ geomechanical surveys.


Introduction
The processes involved in slope instability and rockfall risk in volcanic regions have received little research attention, despite the high economic losses and significant social impacts these hazards entail, especially in relation to roads, housing, coastal areas and beaches. Instability processes have a significant social impact because they affect road and transport safety and people in urban and recreational areas, and often require short-term preventive measures. Consequently, there is a need for decision-making criteria and proposals for possible solutions [1][2][3][4].
Given the particular geological and geomechanical conditions of volcanic rocks, it is necessary to develop specific methods to estimate slope stability, the probability of rockfalls and the possible economic consequences. Here, we present a method for performing such estimations.
The main factors that determine slope stability in volcanic regions are the geomechanical properties of the rocks and the geomorphologic and climatic conditions of the slopes. As a lithological group, volcanic materials are very distinct from other geological materials because of their atypical geomechanical behaviour. The main properties determining this behaviour include: their high heterogeneity and anisotropy, due to their geostructural and fracture characteristics as well as their geomechanical properties; the existence of substantial differences between deposits; the predominance of discontinuities of thermal origin with very different fracture systems from non-volcanic materials; and the rapid degradation of strength properties by alteration processes, giving rise to secondary, geotechnically unfavourable minerals such as smectites [5,6].
One of the most important factors determining stability is slope geomorphology, which can be very steep, especially in oceanic volcanic islands. Meanwhile, the main factor that triggers rockfalls is rainfall, which exacerbates instability processes, especially in tropical climates [7,8].
In recent decades, the construction of large infrastructures in volcanic regions has aroused interest in advancing geotechnical knowledge of these materials, prompting numerous geotechnical studies aimed at excavation design and slope stabilisation, many of which were presented at the international workshops held on these rocks [9][10][11][12].
These studies have generally used RMR (Rock Mass Rating) [13] and Q-system [14] geomechanical classifications and the geological index GSI (Geological Strength Index) [15,16] to characterise rock masses and their properties. However, these classifications were developed based on rocks whose origin was not, for the most part, volcanic, calling into question the suitability of their application to volcanic rocks. Alternatively, several geomechanical classifications specific to these rocks have been proposed [17][18][19]. These classifications apply different criteria: the first two are based on the RMR, whereas the third proposes a new classification system. Rockfalls in volcanic regions are often difficult to predict and frequently demand short or medium-term preventive measures with little time to perform geotechnical studies or risk analyses. It is therefore highly desirable to develop easily applied procedures to assess slope stability. To this end, we developed two geomechanical indices, one that is designed to identify slopes presenting the highest susceptibility to instability, based on observable in situ data, and the other to estimate the degree of rockfall risk and provide recommendations for the adoption of preventive measures.
The ISVS (index of susceptibility for volcanic slopes) is designed to estimate slope susceptibility (possibility of occurrence) to instability, which can be empirically related to the degree of hazard (probability of occurrence), while the IRVS (index of risk for volcanic slopes) provides a simplified means to estimate the degree of risk as a function of the potential damage or economic loss caused as a result of rockfalls.
The indices were applied in Tenerife (Canary Islands), which presents exceptional conditions for analysing slope stability in volcanic rocks because of its mountainous orography with very steep slopes and a wide variety of materials. These conditions have frequently precipitated slope instability, causing significant damage to housing, beaches, roads and other infrastructures.

Estimating Rockfall Susceptibility: The ISVS Index
In order to estimate the degree of instability in volcanic slopes, we developed a susceptibility index, the ISVS, based on geological, geomorphological and geomechanical data, with the following objectives: (i) to provide a wide range of professionals-not necessarily experts-with an easily applied, affordable procedure to conduct an initial stability assessment at short notice, prior to geotechnical and risk studies; (ii) to identify areas at greater risk of instability and (iii) to provide criteria for the adoption of short-term preventive measures where necessary.
The ISVS is based on the following parameters: Weaker layers are more susceptible to erosive processes, undermining the base of harder layers and causing rocks or blocks to fall. For example, on slopes with basalt flows, scoria and pyroclastic layers, erosion of the latter causes blocks of the stronger materials to fall. The factors influencing instability are the degree of differential erosion between materials of different strengths and the formation of rock overhangs in hard layers. Figure 1 shows some examples of the types of rock mass described. Tables 1 and 2 give the parameters to consider and their scores.
Sea or gully erosion. Slope proximity to the coast or gullies constitutes a decisive factor for instability. We established a distance of up to 50 m from the sea at high tide, or a gully, as the reference value for applying this penalty factor (Table 1). D.
Instability indicators. The existence of fallen blocks, cracks, escarpments, etc., on a slope, and damage to nearby buildings or roads, are indicators of active instability processes and were included in the ISVS as a penalty factor. This factor is estimated according to the number of indicators observed, both on the ground and in nearby structures ( Table 1).
The ISVS is calculated by applying and scoring the above criteria as indicated in Table 1, establishing four degrees of susceptibility to instability. The score ranges from 0 to 100 points, where 100 is the maximum value for susceptibility, although higher values can be obtained in the calculation. The ISVS is not applicable to highly weathered or altered rocks, colluvial deposits or soils. The flow diagram shown in Figure 2 illustrates the procedure for applying the ISVS.   Table 2 Maximum ISVS score: 100. Not applicable to soils, colluvial deposits or highly weathered rocks. Susceptibility indicates possibility of occurrence. Only one of the options for type of rock mass can be selected: I, II or III. For type III rock mass without differential erosion, types I or II will be selected. Only one option is selected for each parameter in the score assignment.    Large blocks C ≥50 cm and e/C < 2 40 concavity overhangs 10 Medium blocks 25 ≤ C < 50 cm and e/C < 2 30 Large blocks C ≥ 50 cm and e/C < 2 40 Geosciences 2020, 10, x FOR PEER REVIEW 8 of 21 Figure 2. Flowchart for estimating the ISVS (see Table 1).
We also conducted an in situ survey of slopes adjoining Tenerife's road network, selecting those most representative of different geological and geometric conditions from the point of view of stability, noting the number of fallen blocks, and calculating the ISVS for each of them. On the basis of the data collected from 95 representative slopes from Tenerife (see Section 5) and the information obtained by [24,25], we established characteristic intervals for rockfall frequency, return periods and ISVS values (Table 3).
Hazard also depends on the action of factors that trigger rockfalls, such as rainfall, earthquakes and anthropic actions, where rainfall is the most frequent and important factor, and the only triggering factor here considered. Thus, hazard (HA) is expressed as HA = Py · PF, or alternatively, as HA = Pn · PF, where Py and Pn are the abovementioned probabilities and PF is the precipitation factor. This latter factor indicates the rainfall intensity threshold beyond which a significant increase in rockfalls will occur in an area. The relationship between rainfall and rockfalls varies across regions, since other factors are involved, including climatic and geomorphological conditions and the geomechanical properties of rock masses.  Figure 2. Flowchart for estimating the ISVS (see Table 1).

Estimating Rockfall Hazard
Hazard refers to the probability (P) that an event of a given intensity or magnitude will occur in a given spatial area within a given period of time [22,23]. This can be estimated from the return period (T) of the event concerned (P = 1/T) and is expressed as the annual probability of exceedance (P y ) or the probability of occurrence during the service life of a given exposed structure or element (P n ). The return period can be estimated from observation of the number and size of rockfalls over a given period of time.
To estimate rockfall frequency in a volcanic zone, we used records of rockfalls affecting the road network in Tenerife, with more than 2000 events in the last 25 years [24,25]. In addition, we compiled other data on rockfalls in urban areas, coasts and beaches, gullies, etc., from publications, technical reports, newspaper archives and city councils, with events that date back more than 100 years.
We also conducted an in situ survey of slopes adjoining Tenerife's road network, selecting those most representative of different geological and geometric conditions from the point of view of stability, noting the number of fallen blocks, and calculating the ISVS for each of them. On the basis of the data collected from 95 representative slopes from Tenerife (see Section 5) and the information obtained by [24,25], we established characteristic intervals for rockfall frequency, return periods and ISVS values (Table 3). Hazard also depends on the action of factors that trigger rockfalls, such as rainfall, earthquakes and anthropic actions, where rainfall is the most frequent and important factor, and the only triggering factor here considered. Thus, hazard (HA) is expressed as HA = P y · PF, or alternatively, as HA = P n · PF, where P y and P n are the abovementioned probabilities and PF is the precipitation factor. This latter factor indicates the rainfall intensity threshold beyond which a significant increase in rockfalls will occur in an area. The relationship between rainfall and rockfalls varies across regions, since other factors are involved, including climatic and geomorphological conditions and the geomechanical properties of rock masses.
In order to estimate PF values in a volcanic region according to the rainfall-rockfall relationship, we analysed databases for rockfalls affecting roads in Tenerife [24,25] and the rainfall recorded during the events [26]. The results are given in Figure 3, while Figure 4 shows the relationship between rockfall probability and rainfall intensity [27]. Lastly, based on these data we estimated the precipitation factor (PF) and hazard (HA) ( Table 4).
Geosciences 2020, 10, x FOR PEER REVIEW 9 of 21 In order to estimate PF values in a volcanic region according to the rainfall-rockfall relationship, we analysed databases for rockfalls affecting roads in Tenerife [24,25] and the rainfall recorded during the events [26]. The results are given in Figure 3, while Figure 4 shows the relationship between rockfall probability and rainfall intensity [27]. Lastly, based on these data we estimated the precipitation factor (PF) and hazard (HA) ( Table 4).

Estimating Rockfall Risk: The IRVS Index
The index of rockfall risk for volcanic slopes (IRVS) was developed with the same general objectives as those for the ISVS: i) to provide a means to estimate the degree of risk at short notice; ii) to facilitate decision-making in situations requiring the adoption of short-term preventive measures and iii) to conduct zoning according to the relative level of risk. Its scope is limited to a preliminary assessment prior to quantitative risk analyses procedures (QRA) [28,29].
The IRVS is expressed as a function of the hazard or probability of occurrence of a rockfall and the possible damage or losses caused to elements potentially exposed to risk [22,23,30]. The IRVS is calculated according to the expression IRVS = HA · LI, where HA is the hazard, and LI is the loss index. HA is obtained as described above, and the LI is calculated using the following expression LI = V · EC · CC, where V is vulnerability, EC is the energy increment coefficient for impact energy due to the height of the fall, and CC is the cost coefficient for damage or loss.

Estimating Rockfall Risk: The IRVS Index
The index of rockfall risk for volcanic slopes (IRVS) was developed with the same general objectives as those for the ISVS: (i) to provide a means to estimate the degree of risk at short notice; (ii) to facilitate decision-making in situations requiring the adoption of short-term preventive measures and (iii) to conduct zoning according to the relative level of risk. Its scope is limited to a preliminary assessment prior to quantitative risk analyses procedures (QRA) [28,29].
The IRVS is expressed as a function of the hazard or probability of occurrence of a rockfall and the possible damage or losses caused to elements potentially exposed to risk [22,23,30]. The IRVS is calculated according to the expression IRVS = HA · LI, where HA is the hazard, and LI is the loss index. HA is obtained as described above, and the LI is calculated using the following expression LI = V · EC · CC, where V is vulnerability, EC is the energy increment coefficient for impact energy due to the height of the fall, and CC is the cost coefficient for damage or loss. Figure 5 summarises the procedure for applying the IRVS. Social and environmental costs are not included in this index. This was estimated by simulating rockfalls at different heights and slope angles, for blocks weighing 0.5, 1 and 2 t, and slope heights measuring between 10 and 90 m ( Figure 6). Rockfall simulations were carried out using Rockfall 6.011.2008 program from Rockscience Inc. Coefficients of restitution Rn = 0.53 and Rt = 0.95 were applied according to the experience on basaltic rock masses from the Canary Islands [26].
• The cost coefficient (CC) refers to the economic losses of an exposed element affected by rockfalls.    Tables 4 and 5). The parameters considered to calculate V, EC and CC are shown in Table 5, according to the following criteria:

•
The vulnerability of exposed elements (V) that may be affected by the rockfall and the degree of loss that such elements may experience due to a hazard of a given intensity. Vulnerability varies depending on the characteristics of an element and the magnitude or intensity of the event, and is expressed according to the percentage that may be affected, either in percent or on a scale of 0-1.

•
The energy increment coefficient (EC) is related to the height from which a block on a slope falls. This was estimated by simulating rockfalls at different heights and slope angles, for blocks weighing 0.5, 1 and 2 t, and slope heights measuring between 10 and 90 m ( Figure 6). Rockfall simulations were carried out using Rockfall 6.011.2008 program from Rockscience Inc. Coefficients of restitution Rn = 0.53 and Rt = 0.95 were applied according to the experience on basaltic rock masses from the Canary Islands [26].

•
The cost coefficient (CC) refers to the economic losses of an exposed element affected by rockfalls. Hazard (HA) and the loss index (LI; Tables 4 and 5 respectively) were used to estimate the IRVS (IRVS = HA · LI) and degree of risk (Table 6). Table 6 gives some recommendations for preventive measures.
The different degrees of risk considered might vary according to subjective criteria such as social perception of risk, an aspect that is not considered in the IRVS but which would be of interest in a possible situation of social risk [22,31]. To analyse the potential impact of this aspect, we conducted a survey among university graduates unfamiliar with the geosciences, asking them how they would classify the level of risk of a rockfall that could affect a house according to the different levels of hazard and losses obtained from the IRVS. The results obtained (Figure 7) show some differences with respect to the degrees of risk considered in the IRVS (Table 6): respondents proposed three degrees of risk instead of four, due to difficulties in differentiating between the high and very high degrees; we also noted a tendency to overestimate the degree of risk with respect to that estimated using the IRVS. These results may be useful in possible situations of personal injury or social consequences.  Hazard (HA) and the loss index (LI; Tables 4 and 5 respectively) were used to estimate the IRVS (IRVS = HA · LI) and degree of risk (Table 6). Table 6 gives some recommendations for preventive measures. The different degrees of risk considered might vary according to subjective criteria such as social perception of risk, an aspect that is not considered in the IRVS but which would be of interest in a possible situation of social risk [22,31]. To analyse the potential impact of this aspect, we conducted a survey among university graduates unfamiliar with the geosciences, asking them how they would classify the level of risk of a rockfall that could affect a house according to the different levels of hazard and losses obtained from the IRVS. The results obtained (Figure 7) show some differences with respect to the degrees of risk considered in the IRVS (Table 6): respondents proposed three degrees of risk instead of four, due to difficulties in differentiating between the high and very high degrees; we also noted a tendency to overestimate the degree of risk with respect to that estimated using the IRVS. These results may be useful in possible situations of personal injury or social consequences. Figure 7 are out of place !!!

Application of the ISVS in Tenerife and Discussion of the Results
The ISVS was applied in Tenerife (Canary Islands) because it offers ideal conditions for analysing rockfalls in volcanic slopes (Figure 8). Based on the information available on previous rockfalls affecting roads [24,25], urban areas, coasts and beaches, we identified a number of areas of interest for applying the ISVS. These areas were geologically and geomechanically characterised, selecting 95 slopes representative of the different types of rock mass and geomorphological and climatic zones in Tenerife [32]. The location of the slopes and their corresponding rock mass type are given in Figure 9. Appendix A gives detailed data on the slopes analysed.
We estimated the ISVS value for the selected slopes according to their history of rockfalls (ISVS assigned ), and then compared this value with the one calculated in situ (ISVS in situ ). Figure 10 shows the relationship between the two, which obtained a correlation coefficient of 0.97. These results reflect the successive adjustments made to the scores during development of the ISVS, until the results obtained agreed with the actual behaviour of the slope, thus verifying the validity of the parameters considered in the ISVS. We estimated the ISVS value for the selected slopes according to their history of rockfalls (ISVS assigned), and then compared this value with the one calculated in situ (ISVS in situ). Figure 10 shows the relationship between the two, which obtained a correlation coefficient of 0.97. These results reflect the successive adjustments made to the scores during development of the ISVS, until the results obtained agreed with the actual behaviour of the slope, thus verifying the validity of the parameters considered in the ISVS. Recently, studies have been conducted in Tenerife to analyse application of the abovementioned geomechanical classifications to slope stability in volcanic rocks [33]. The results obtained from an analysis of 42 slopes show that the classification described by [18] cannot be used to assess the degree of slope stability, although it may be suitable to estimate the geomechanical quality of the rock mass. Meanwhile, the classification proposed by [19] evidences significative differences with respect to the actual behaviour of the slopes, with a tendency to overestimate slope stability. When the ISVS was applied, a correlation coefficient of 0.95 was obtained between the index values and those estimated according to actual slope behaviour.
The ISVS can be applied to other volcanic regions since its parameters do not depend on local factors. In this respect, further studies are being conducted in Mexico, which have obtained positive results to date [34]. However, it is evident that more data is required on other volcanic areas and regions. When applying the IRVS, the precipitation factor must be adjusted to the climatic conditions of each region.

Conclusions
In response to the need for specific criteria to analyse slope stability in volcanic rocks, we developed a rockfall susceptibility index, the ISVS, and a rockfall risk index, the IRSV. Both indices were developed in order to provide an easily applied procedure that facilitates the adoption of shortterm preventive measures against rockfalls.
The ISVS is based on four parameters that exert a considerable influence on stability: type of rock Recently, studies have been conducted in Tenerife to analyse application of the abovementioned geomechanical classifications to slope stability in volcanic rocks [33]. The results obtained from an analysis of 42 slopes show that the classification described by [18] cannot be used to assess the degree of slope stability, although it may be suitable to estimate the geomechanical quality of the rock mass. Meanwhile, the classification proposed by [19] evidences significative differences with respect to the actual behaviour of the slopes, with a tendency to overestimate slope stability. When the ISVS was applied, a correlation coefficient of 0.95 was obtained between the index values and those estimated according to actual slope behaviour.
The ISVS can be applied to other volcanic regions since its parameters do not depend on local factors. In this respect, further studies are being conducted in Mexico, which have obtained positive results to date [34]. However, it is evident that more data is required on other volcanic areas and regions. When applying the IRVS, the precipitation factor must be adjusted to the climatic conditions of each region.

Conclusions
In response to the need for specific criteria to analyse slope stability in volcanic rocks, we developed a rockfall susceptibility index, the ISVS, and a rockfall risk index, the IRSV. Both indices were developed in order to provide an easily applied procedure that facilitates the adoption of short-term preventive measures against rockfalls.
The ISVS is based on four parameters that exert a considerable influence on stability: type of rock mass, slope angle, incidence of erosive processes and presence of instability indicators. The IRVS is based on currently used methods for estimating hazard and risk, and on the use of empirical relationships to estimate the probability of rockfalls and the influence of rainfall on such events.
The ISVS was applied in Tenerife, analysing 95 slopes representative of the island's geological, geomorphological and climatic conditions. The information available on rockfalls affecting roads, urban areas, coasts and beaches was used to obtain the history of rockfalls on the slopes analysed. These data were used as a reference to analyse the validity of the ISVS. The relationship obtained between the ISVS estimated in situ, in accordance with the developed procedure, and the ISVS assigned in accordance with historical rockfalls on the slope, showed a high degree of correlation.
The ISVS can be applied to any volcanic region, within the previously established limitations. However, when applying the IRVS, the precipitation factor must be adjusted to the climatic conditions specific to each region, although the values suggested in the present study may provide tentative guidance should other data be unavailable. The information provided by the ISVS and IRVS will help ensure the safety of infrastructures and people by enabling identification of those slopes with a higher risk of rockfalls and adoption of the necessary preventive measures.

Acknowledgments:
The authors thank Ing. Javier Jubera, from the Construction Laboratory and Quality Service of the Government of the Canary Islands, and Ing. Sergio Leyva, from the Roads and Landscape Technical Service of the Island Council of Tenerife, for their comments and discussions; and Dr. Eduardo González-Díaz, from the Department of Engineering and Architecture Techniques and Projects at the University of La Laguna (Tenerife), for his contribution to statistical analyses. We also thank the Academy of Engineering of Mexico for permission to publish part of the data included in the present study, in particular Dr. Demetrio Santamaría Orozco and Ing. Rolando de la LLata. We thanks to Marco Rollino from the Universitá degli Studi di Torino for his contribution during the field survey in Tenerife. The studies conducted in Tenerife were funded by the European project MACASTAB (2018), in collaboration with the Construction Laboratory and Quality Service, Regional Department of Infrastructures and Transport of the Canary Islands Government. The authors are grateful to anonymous reviewers for their comments and suggestions.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.