The influence of expertise on rockfall failure probability assessment – an original experimentation

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has been used as an ad hoc quantitative method to investigate the effect of the level of quantification within the method.These procedure has been applied on a test site divided into three different sectors.
A statistical treatment of the results (descriptive statistical analysis, chi-square independent test and ANOVA) shows that there is a significant influence of the method used on the rockfall probability assessment, whatever the sector.Furthermore, there is a non-significant influence of the level of expertise of the population for two of the three sectors.On sector 1, there is a significant influence of the level of expertise, explained by the importance of the temporal probability assessment in the rockfall hazard assessment process.The SMR-based method seems highly sensitive to the "site activity" indicator and exhibits an important dispersion in its results.On the other hand, the results are more similar to the LPC qualitative method, even in the case of sector 1.

Introduction
Rockfall instabilities are a major hazard for the population, human activities and infrastructure (Bell and Glade, 2004;Moreiras, 2006) It is thus essential to assess the rockfall hazard in areas over which they are likely to occur, and to propose a mapping of the hazard to manage the risk in urban areas.Natural hazard zoning has been introduced in many countries all over the world.As example, the PPR (Plans de Prevention des Risques Naturels Previsibles) in France (Besson et al., 1999) and the Cartes de Dangers in Switzerland (Leroi et al., 2005) evaluate the hazard level in affected zones, according to a predefined set of hazard classes.Based on this hazard maps, different areas are identified: the ones where construction is restricted, the ones where a monitoring system or a protection system is required for reducing the risk in the studied zone and the ones where no modifications are required (Fell et al., 2008).Because of the implications in the territory management, the rockfall assessment must be as accurate as possible (neither underestimated nor overestimated) and reliable.
Rockfall hazard can be defined as the probability that a specific location at the toe of a studied slope will be reached by a rockfall of a given magnitude (Jaboyedoff et al., 2001).Whatever the magnitude of the expected rockfall, the probability can be divided into two terms: the failure probability and the propagation probability (Jaboyedoff et al., 2005).
Various methods simulate the trajectory of rock masses after rupture and evaluate the propagation probability (Dorren, 2003).However, to date, there is no fully reliable method to estimate the failure probability (Hantz, 2007).Even if some existing methods are quantitative and based on historical inventory (Dussauge-Peisser et al., 2002;Hungr et al., 1999;Luckman, 1976), in most cases, such an inventory is not available.Then, qualitative assessment methods are used to asses the rockfall probability failure.

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Full method considered could likewise has an influence in the hazard assessment.Different research works (Abbruzzese and Labiouse, 2010;Bormioli et al., 2011) have compared different mapping methods and evaluate the influence of the method chosen on the obtained results.These studies highlighted the statistically significance of the method chosen: the use of one method over another gives different levels of failure probability for the same sector.
In this paper, an experiment is undertaken in order to evaluate the influence of the method and the level of expertise on the rockfall failure probability assessment.The failure probability is assessed on a test-site, by three populations with different levels of expertise.Two different methods for rockfall hazard assessment are used: (i) a qualitative one, the Laboratoire des Ponts et Chaussées (LPC) method, which is the method mainly used in France, and (ii) a quantitative one, based on the Slope Mass Rating (SMR).The experiment was conducted in two phases: the first one was realized in May 2012 and the preliminary results were presented in EUROCK Congress (Delonca et al., 2013).The second one was realized in May 2013 in order to confirm the first results, by increasing the size of the three populations and adding statistical procedure to the study.The experimental protocol is presented first, including the assessment methods used.Then, the results are presented and discussed for the two phases together.
The objective of the present paper is to provide a comparison of the methods but more particularly focuses on the influence of the level of expertise of the person making the hazard assessment and its subjective judgment.Indeed, it may interest all, engineers and researchers, in charge of hazard mapping or who are concerned by the development of rockfall assessment methods.Figures

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Selection of the test site
The experiment was realized on a cliff situated in Liverdun, a town close to Nancy in France, which has been previously classified as presenting a high-level rockfall hazard (Moiriat et al., 2008).The site is a 50 m-long cliff of Jurassic limestone that is made up of massive blocks at the base and small blocks in the upper part (Delonca et al., 2013).This site is an old carry that became a climbing site that was closed in the last few years due to rockfall hazard.Three sectors were identified (Delonca et al., 2013): -Sector 1 presents a massive wall with well-defined stratification beds.A pluridecametric fracture isolates a rock panel several hundreds of m 3 in size.At the top, small unstable blocks are present (Fig. 1a).
-In sector 2, two major fractures form a rock wedge of a few m 3 in size.Small unstable blocks are present in the upper part (Fig. 1b).
-In sector 3, limestone beds are overhanging, and some blocks at the top are unstable (Fig. 2).

Population
Three populations were involved in the experiment: -A total of 38 first-year MSc students in the geosciences, confronted to a hazard assessment study for the first time.These students may later be asked to prepare hazard or risk maps, during an internship, for example; -A total of 10 researchers in the geosciences, working in the field of hazard and risk assessment, but not accustomed to regular rockfall assessment studies; Figures

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Full -A total of 8 confirmed experts benefited from a long experience in rockfall hazard assessment and risk studies.
The comparison of the failure probability evaluated by each population is supposed to highlight the influence of the level of expertise on the failure probability assessment.Note that the expert assessment is not necessarily the "best one".

Methods used for the rockfall failure probability assessment
At first, an a priori assessment was requested from each population, without making use of any method.Then, two rockfall hazard assessment methods are used to assess the failure probability: the Laboratoire des Ponts et Chaussées (LPC) method, which is a qualitative method frequently used in France, and a Slope Mass Rating (SMR)-based method that relies on more quantitative information.

"A priori" assessment
The first assessment of the rockfall failure probability was requested from each individual of the three populations.Four failure probability levels were proposed: (i) zero, (ii) low, (iii) medium, and (iv) high.A presentation of rockfall hazard theory was delivered before this work.Before carrying out the experiments on site, and to help beginners develop their approach, a presentation of the methods and parameters used was also delivered.A document describing the site was also provided, containing additional information on the history of the site.The objective of this assessment was to compare it with one based on qualitative and quantitative methods and to estimate the differences between an "a priori" assessment and one based on the use of a guided method.Figures

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LPC method
The LPC method is detailed in Laboratoire des Ponts et Chaussées, 2004.It is a qualitative method that is frequently used in France for official hazard mapping.It consists of two main steps: (1) the collection of preliminary data and (2) the use of these data to localize and characterize the potential instability.
The collected preliminary data incorporate all relevant information regarding the study site, including the following: -Documentary information: the objective is to exploit the archives to avoid duplication of studies already realized; -Historical information: to study the past of the site to determine if events have already occurred on the site; -Geological information: to analyze the lithological and stratigraphic data and the regional geological history to establish the geological context of the study site; -Sectoring: to identify homogeneous areas from the hazard characterization point of view.This step is performed in the study of large zones.
Following the collection of these preliminary data, the potential instabilities are localized and characterized.To do so, three new stages are carried out: i. Localize and identify potential instabilities.In this stage, the expert in charge of the study observes the following parameters: -Nature of the studied area: description of the instable rock mass; lithology; hydraulic and hydrologic data; -Geometric parameters: geometry and dimensions of the potentially unstable compartments; -Geomechanical parameters related to discontinuities: e.g., spacing, roughness, apertures, filling, and orientation of critical discontinuities; and -Triggering factors: e.g., interstitial water, rainfall, high temperature variation, freeze-thaw cycle, and vegetation This stage helps to determine the unstable volume (magnitude) and the potential mechanism of failure.In the experiment proposed in this paper, these parameters were coded to process them statistically.This codification, which has been validated by expert users of the LPC method for the purposes of this experiment, does not belong to the original method.
ii. Define the failure probability.The analysis of the previous parameters helps to define potentially unstable volumes and the potential mechanism of rupture associated with these volumes.For each of these, a coupled "temporal probability/occurrence probability" is assessed.These two terms are qualitatively defined as follows: Introduction

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Full -The occurrence probability is subjectively assessed from the parameters presented in Fig. 3.It answers the question "Will the rockfall occur?"The qualitative scale of the level of occurrence probability is presented in Table 1; -The temporal probability corresponds to the annual frequency or return period of the rockfall on the study site.It answers the question "When will the rockfall occur?"The periods are defined on a scale from "imminent" to "long-term".The definitions of the terms are presented in Table 2.
Then, for each volume under consideration, these two probabilities are combined in a matrix (Table 3).The plotted couples are then used to provide the best response to the risk: quick action for the shortest terms and the strongest issues and the planning of preventive actions for the longest terms.
iii.Qualification of the probability of propagation.With the LPC method, it is proposed to carry out a qualitative trajectory analysis before considering a more advanced study using numerical simulations.We do not detail this last step because it has not been considered in the experiment.
The use of the "temporal probability/occurrence probability" matrix is not easy for beginners.Therefore, we have proposed a new matrix, developed with experts, to assess the failure probability level.The temporal probability and the occurrence probability are combined to assess the level of the susceptibility to instability (Table 4).
Finally, the susceptibility is coupled with the volume (magnitude of the phenomenon) to determine the failure probability (Table 5).Three levels of failure probability are defined: low, medium and high.As mentioned, the assessed level can be used to define the best response to the risk.Several volumes can be identified on a single site, and then, several values for the level of failure probability can be assessed.The global failure probability of the site corresponds to the worst hazard on the study site.Figures

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SMR-based method
The Slope Mass Rating (SMR) index, proposed by Romana (1985), is a geomechanical classification commonly used for the characterization of rock slopes (Corominas Dulcet and Mavrouli, 2009;Irigaray et al., 2003) and derived from the Rock Mass Rating (RMR) as follows: where RMR b is the basic RMR index resulting from Bieniawski's rock mass classification without any correction (Bieniawski, 1972).It is obtained by adding rating values for the following five parameters -The strength of the intact rock; -The Rock Quality Designation (RQD) (Deere and Miller, 1966).This parameter gives a quantitative estimate of the rock mass fracturing based on the study of cores obtained by drilling.The RQD is defined as the percentage of intact pieces of length greater than 10 cm over the total length of the hole.It can also be estimated from surface measurements; -The spacing of discontinuities; -The condition of discontinuities: the roughness, weathering and opening of the discontinuities are assessed; -The water inflow through discontinuities and/or the pore pressure ratio; where F 1 , F 2 , F 3 and F 4 are defined as follows: -F 1 characterizes the angle (A) between the slope face strike and joint azimuth.It ranges from 0.15 to 1.00, according to the relationship F 1 = (1 − sin(A)) -F 2 refers to the joint dip angle.For a plane sliding mechanism, its value ranges from 0.15 to 1, according to the relationship F 2 = tan(B j ) 2 , where B j denotes the joint dip angle.For a toppling mode of failure, F 2 is equal to 1.00; -F 3 reflects the relationship between the slope and joint dips.This parameter uses the Bieniawski adjustment factors that range from −60 to 0 points and reflects the probability that outcropping blocks will be subjected to planar and wedge failure mechanisms; -F 4 is an adjustment factor to take into account the method of excavation (natural slope, presplitting, smooth blasting, blasting or mechanical, and deficient blasting).Its value ranges from −8 to 15, and it is chosen empirically.
The SMR calculation leads to five stability classes (Romana, 1985).Then, based on the work of El-Shayeb et al. (1997) or El-Shayeb (1999), a level of the site activity is evaluated.There are four different levels of activity corresponding to the following: i. Sleeping: morphological traces are faded, and there is no alteration of the rock mass; ii. Inactive: few morphological traces and superficial alteration; iii.Low active: recent morphological traces and deeper rock mass alteration; iv.Active: numerous morphological traces and deep rock mass alteration.
The combination of the SMR class and the site activity provides a level of occurrence probability (Table 6), which is coupled to the volume of unstable masses to obtain the failure probability level (Table 7).

Complementary data
The on-site observations took place at the foot of the cliff.Each individual had a compass, a sclerometer and a geologist's hammer with him and had to report his Introduction

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Full observations and measurements on a separate form for each sector.On this form, each method was presented again, and all the used parameters were listed (cf.Fig. 3 for the LPC method).

Results
To statistically treat the results, the level of the failure probability was coded as follows: i. Low failure probability level: code value equal to 1 ii. Moderate failure probability level: code value equal to 2 iii. High failure probability level: code value equal to 3 This coding allows the level of failure probability to be quantified and reflects its intuitive increase.Other encodings have been tested, as discussed in Sect.4.3.

Methods for the statistical treatment
Each individual had to make three types of failure probability assessment: an "a priori" assessment, an assessment with the LPC method and an assessment with the SMRbased method.After the experiments were carried out, a descriptive statistical analysis was performed to compare the levels of the failure probability assessment.Then, the results were analyzed using the chi-square independence test and the analysis of variance (ANOVA) method (Scheffé, 1959) to assess the significance of the influence of the level of expertise and of the influence of the method used in determining the failure probability level.Finally, the means of the LPC and SMR-based method parameters were compared to identify those that most influence the failure probability assessment.Introduction

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Preliminary descriptive analysis
An initial statistical treatment has been performed for the three sectors.Figure 4 and Table 8 present the results and show the following: -Regarding the "a priori" assessment, there is a wide dispersion (standard deviation higher than 0.5) of the results in terms of failure probability levels for all populations in all sectors, except for the experts in sector 3. Except for sector 3, where the populations give similar results, the students more often give a higher value for the probability failure level, followed by the experts and finally the researchers.This can be explained by the level of inexperience of the students, who were initially impressed by the presence of cracks and overhanging blocks on the cliff; -Regarding the LPC method, the results are similar for all population groups, with less dispersion than with the "a priori" assessment.Students achieved the highest mean score whatever the sector.-With the SMR-based method, the results exhibit more dispersion for the three sectors, with the standard deviations being higher than 0.5 except for the students in sector 2. We also note that the mean failure probability level is always lower than that from the LPC method.For comparison, a random sampling on the SMR matrix (Occurrence probability -Magnitude) gives the following results Introduction

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Full The influence of the level of expertise and of the chosen method on the level of failure probability could not be clearly determined from this preliminary descriptive analysis.This is the reason why statistical tests have also been performed.

3.3
Influence of the level of expertise and the method on the level of failure probability

Chi-square independence test (χ 2 )
The chi-square independence test allows the dependence between two qualitative variables to be investigated.Let x 1 , . . ., x i , . . ., x p and y 1 , . . ., y j , . . ., y q be the terms (categories) of two qualitative variables X and Y .A sample of n individuals from whom the values of the two variables were simultaneously taken yielded the following results: n i j is the number of individuals who presented both the x i value of X and the y j value of Y .n i .and n. j are, respectively, the total of line x i and the total of column y j .It is then possible to build the contingency table of the observed values (Table 9).
Under the hypothesis that variables X and Y are independent, we can also build a contingency table of theoretical values equal to at the intersection of row i and column j .It is then possible to calculate the following quantity which obeys a χ 2 distribution with (p − 1)(q − 1) degrees of freedom.Introduction

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Full This test is performed side-by-side, between (i) the method and the level of failure probability and (ii) the level of expertise and the level of failure probability.As an example, tables 10 and 11 present the contingency tables of the observed and theoretical values, respectively, for the chi-square test to be performed between the level of expertise (variable X ) and the level of failure probability (variable Y ) for sector 1.
The χ 2 distance is then calculated following Eq.(3): Table 12 shows the distances computed for the two-independency test carried out on each sector together with their p values.A p value lower than 0.05 indicates that the independency hypothesis should be rejected.

This table highlights the following:
-A non-dependency between the level of expertise and the level of failure probability for sectors 2 and 3; -A dependency between the level of expertise and the level of failure probability for sector 1; -A dependency between the method and the level of failure probability for the three sectors.

Analysis of variance (ANOVA)
The analysis of variance (ANOVA) is a statistical test indicating the influence of qualitative variable(s) on a quantitative variable to be assessed.It is based on the comparison of the mean values of the quantitative variable for each category of the qualitative variable.Introduction

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Full Before performing the ANOVA, the normality of the level of failure probability (the quantitative variable) and its homoscedasticity have to be verified.The levels of failure probability are discrete data, which make the condition of normality difficult to assume.However, authors such as Legendre and Borcard (2008) and Underwood (1996) state that in a balanced experimental design, ANOVA has problems with the heterogeneity of the variance when the variance is in high contrast to others, but the ANOVA is little affected by non-normality.This condition is considered as not discriminating to achieve the ANOVA.
To test the homogeneity of the variances, there are several tests, including Levene's test, that are insensitive to the normality of the data (Legendre and Borcard, 2008).If Levene's test is statistically significant, the assumption of the homogeneity of variances should be rejected.We used the software program R to perform this test.For the three sectors, Levene's test has shown that we can consider the variances to be homogeneous.
In the ANOVA, the influence of a factor is considered significant when the p value associated with this factor is lower than a given risk such as 5 or 1 % (error chosen here).The ANOVA results are presented in Table 13.To help the reader in the analysis, the significant factors are presented in bold and italic.The analysis of variance shows the following: -A very significant influence of the factor "method" on the level of failure probability assessments for the three sectors; -A very significant influence of the factor "expertise" on the level of failure probability assessments for sector 1; -The non-significant influence of the factor "expertise" on the level of failure probability assessments for sectors 2 and 3 at a 1 % risk (but a significant influence at a 5 % risk); -The absence of interaction between these two factors on the level of failure probability assessments (for all three sectors) at a 1 % risk or even at 10 % risk.Introduction

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Full These results confirm the results given by the test of independence carried out previously.They first exhibit the main importance of the method chosen, as found previously for the three sectors.Then, the great influence of the level of expertise for sector 1 is highlighted.Finally, both tests highlight the negligible influence of the level of expertise for sectors 2 and 3, regardless of the level of confidence we are working with.

Influence of the parameters of the LPC and SMR-based methods
To better understand the influence of the LPC and SMR-based methods on the level of failure probability, a comparison of the mean values of the parameters used in these methods has been conducted (Table 14).
For each parameter presented, a 2 by 2 comparison of the mean values has been carried out.More precisely, we have compared the mean values of the levels given for each parameter by (i) the students and the researchers, (ii) the students and the experts and (iii) the researchers and the experts.The objective was to identify the mean values that are statistically similar and those that are different.This analysis could explain the influence of the chosen method previously highlighted, depending on the sector and the level of expertise.
The first step consists of checking the hypothesis of equal variance for each couple of the population.If the variances can be considered equals, it is then possible to compare the mean values.Let n 1 and s 2 1 be the size and the variance of the first population sample (students, researchers or experts), and let be n 2 and s 2 2 be the size and the variance of the second population sample.In the hypothesis of the equality of population variances, the estimates of the variances are equal.This condition has been verified, and the comparison of the means can then be performed.
Let m 1 and m 2 be, respectively, the mean values of the first and second population samples under test.Both are unbiased estimates of the population means (µ 1 and µ 2 ).Under the assumption that µ 1 = µ 2 , we compute the t ratio (Eq.4), which is supposed to belong to a Student's t-distribution with (n 1 + n 2 − 2) degrees of freedom.This value Introduction

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Full has then to be compared to the interval [−t α/2 , t α/2 ], where α is the risk and (1 − α) the confidence level: where m 1 is the average of the first population tested (students, researchers or experts), and m 2 is the average of the second population tested; n 1 is the sample size of the first population, and n 2 is the sample size of the second population; σ * 2 is the unbiased estimate of the common variance of the two populations based on s 1 , s 2 , n 1 and n 2 .
If t belongs to the interval [−t α/2 , t α/2 ], α being the chosen risk, we can conclude that the two population means are not significantly different.We considered a 5 % risk, so the interval is thus equal to [−2, 2].Table 15 presents the t ratio for the different parameters tested.Table 16 summarizes the results and shows the following: -The susceptibility (LPC method only) is the same, whatever the level of expertise and the sector; -The magnitude is similarly assessed for sectors 2 and 3, regardless of the level of expertise, for both methods (LPC and SMR-based methods); -The magnitude is assessed differently by the students on one side and the experts on the other side, for sector 1; -The SMR classes in the SMR-based method is the same for sectors 2 and 3, but not for sector 1, where there is a significant difference between the students and the experts -The level of activity is assessed differently for the three sectors.Then, seeing that the combination of the SMR classes and the site activity provides the level of occurrence probability, the occurrence probability is assessed differently for the three sectors.

Choice of hazard assessment methods
During the experiment, three methods were used to assess the rockfall failure probability.First, each participant was asked to assess the level of failure probability from his own experience without using any tool, form or measurement.Second, a qualitative method (LPC method), and third, a quantitative method (SMR-based method) were used.In both of these latter cases, a form was provided to guide the process of assessment.We chose to use the LPC method for its wide use in France for most official hazard mapping.This methodology aims to formalize the practice gradually developed over two decades through many field studies produced by both operational services of the French government and local authorities.Many experts contributed to the preparation of this guide, and some of these experts also participated in our experiment.The methodology proposed by the LPC method is somehow classical and follows the following steps as previously described: 1. Literature review: avoids repeating studies or investigations already done; 2. Historical review: its purpose is to make an initial zoning of hazard levels, taking into account past events; 3. Geomorphological analysis: it is during this third step that the level of the rockfall failure probability is actually assessed.

NHESSD Introduction Conclusions References
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Full These steps can be found in many other methods that exist in different countries.In Spain, for instance, Copons and Vilaplana (2008) proposed a similar qualitative method for hazard mapping.Several authors also tried to introduce more quantification to hazard assessment for parameters that are usually qualitatively addressed, such as in the Matterock method developed in Switzerland (Baillifard et al., 2003), the RES method (Hudson, 1993;Mazzoccola and Hudson, 1996;Rozos et al., 2008) and the RHAP method (Ferrero et al., 2011;Lombardia, 2000).Then, even if the LPC method is not an internationally recognized method, we may consider that it treats the hazard analysis in a common manner, similar to other methods.On the other hand, the SMR method, also used in the present work, is commonly used in studies of rock slides along roadways (Budetta, 2004;Corominas Dulcet and Mavrouli, 2009;Irigaray et al., 2003;Tomas et al., 2012).It is derived from the globally used RMR (Rock Mass Rating) method for the stability study of excavated slopes.
Even if it is a qualitative method, the LPC method helps the user to identify the block masses that are potentially instable and the volume concerned and leads to the assessment of the level of failure probability in a similar manner by the three tested populations.However, the introduction of a paper form to assist in the process of the assessment of the level of failure probability could have introduced a bias favoring the LPC method in terms of less dispersion in the assessment results when compared with the results of the SMR-based method.As a result, such a form could be promoted to engineers making use of the LCP method to enforce a common interpretation of some aspects of the method.
The SMR-based method shows similar results to those obtained by the LPC method for students.However, for researchers and experts, the dispersion in the results is more important.The assessment of the site activity is not precise enough to allow the same level of activity to be assessed by all the individuals.Surprisingly, the use of a partly quantitative method does not prevent differences in the final failure probability level, mainly because of the assessment of the site activity, which is a subjective component Figures

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Full of the method.The terms used to describe the activity may be clarified to reduce this effect.

Choice of the test site
For the experiment, one test site was selected, among which three sectors could be defined.These three sectors provide repeatability in the analysis and produce more relevant results.However, because there are three sectors on the site, all of them are composed of the same lithology.Hence, the results obtained in the present study only apply to this case study, and the experiment should be repeated on other sites with different lithology and geological structures to prove that the findings are generic.A national French project is underway that may provide a framework to repeat this experiment on different study sites, with more students, researchers and experts involved, as well as other methods to be tested.However, no sites have yet been chosen to carry out this experiment again.

Coding of the level of rockfall failure probability
As explained previously, to carry out the statistical analysis, the three hazard levels of failure probability were transformed into quantitative variables: the low-failure probability level was coded to "1", the moderate-failure probability level to "2" and the high-failure probability level to "3", so as to reflect the increase of the failure probability in a familiar and convenient way.However, to confirm that this coding has no influence on the results, we performed additional ANOVAs with different encodings.The following cases were used, respectively for low, moderate and high failure probabilities: -"0", "5" and "10"; -"1", "2" and "5"; -"1", "4" and "5"; Introduction

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Full isolates a rock panel several hundreds of m 3 in size.After discussions with the three populations, it appears that this particular configuration is a challenge to the students, who tend to overestimate the failure probability.For researchers and experts, the stability of the sector is not an issue in the present state, and the hazard level should be low.Here, we highlight the difficulty of assessing the temporal probability on a specific site.Moreover, the statistical analysis showed a high dispersion in the failure probability assessment for the "a priori" assessment, especially for the students and researchers, explained by their non-experience in this type of exercise.This result, coupled with the previous one, highlights the plus-value of the experts: they do not overestimate the level of failure probability in complex cases, and their assessment is more homogeneous and based on similar cases they have already studied due to their experience.Indeed, for sector 1, which exhibits the above mentioned pluri-decametric fracture, the results show a higher proportion of low-failure probability levels for the experts.This suggests that the experts link the failure probability assessment to the temporal probability assessment.For them, there is no risk of failure within a short time.
Other assessments of the failure probability level will be realized on other sites to enrich this experiment and confirm or challenge the conclusions.The failure probability level will be assessed by other people (students, researchers and experts), and other methods will be used.
If confirmed, the conclusions drawn in the presented paper suggest that the use of a qualitative approach is more relevant for rockfall hazard assessment even if it leaves room for some subjectivity.Nevertheless, the use of a standard form (as exists for many other methods, either basically quantitative or qualitative) could be promoted to engineers making use of the LCP method to enforce a common interpretation of some aspects of the method.Such a form may contribute to a reduction of the subjectivity expected in a qualitative method.rating (SMR), Eng. Geol., 124, 67-76, 2012.Underwood, A. J.: Experiments in ecology: their logical design and interpretation using analysis of variance, Cambridge University Press, Cambridge, 1996.Introduction

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Full  Full  Very High The fall of the rock mass will happen imminently.

High
The fall of the rock mass is more probable than its stability.The temporal probability estimate is approximately 2 years.Moderate The probability of the fall of the rock mass is equivalent to its stability.The temporal probability estimate is approximately 10 years.

Low
The stability of the rock mass is more probable than its fall.The temporal probability estimate is approximately 30-50 years.Very Low The fall of the rock mass will be exceptional, or the temporal probability estimate is approximately 100-150 years.Introduction

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Full  Full  Full  Full Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

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Structural information: to identify the structural characteristics of the study site on different scales and to propose global and local structural models; Morphological information: to identify the main historical steps leading to the actual morphology; -Hydrogeological, hydrological and climatic information: to characterize the fluid intakes, their nature, and their importance.It is also to identify the flows inside the massif and unfavorable climate patterns (e.g., freezing, thawing, and important thermal contrasts); Information regarding vegetation: to identify and characterize the main vegetation on the site and its influence on stability or instability processes; -Potential mechanism of rupture: to identify the potential mechanisms of rupture associated with the studied zone; Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 2 .A value of 1 indicates that the joint azimuth and face strike are parallel; Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Experts and researchers are closer to each other, particularly in sectors 2 and 3.For comparison purposes, a random sampling (using uniform distribution) of the levels of susceptibility and magnitude provided a 6/25 = 24 % low-failure probability level, 9/25 = 36 % moderate-failure probability level and 10/25 = 40 % high-failure probability level (i.e., a mean value of 2.16); the observed values are clearly different from what a random assessment would give; Discussion Paper | Discussion Paper | Discussion Paper | 3/16 = 18.75 % high-failure probability level, corresponding to a mean value of 1.8.Most of the values obtained in the experiment are higher than what would be randomly obtained.
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Table 2 .
Qualitative scale of the level of temporal probability, after the guide of the Laboratoire desPonts et Chaussées (2004).

Table 4 .
Qualitative scale of the susceptibility to instability.

Table 8 .
Mean and standard deviation of the rockfall probability failure levels for the three sectors.

Table 9 .
Contingency table of the observed values of the X and Y variables.

Table 13 .
Results of ANOVA: influence of the level of expertise and the choice of the method on the level of failure probability for the three sectors.The bold and italic values highlight the significantly influencing factors, for which the p values are lower than 1 %.

Table 16 .
Sample mean and standard deviation of the values of the LPC and SMR-based parameters.The bold and italic values correspond to the population means that cannot be significantly differentiated.