Process for characterizing a risk of rock falls

Abstract

Method for characterizing a risk of falling blocks detaching from a wall of a rock face of hectometric scale composed of stacks of volcanic rocks made up of alternating massive basaltic flows and inter-flow levels, characterized in that it comprises the following steps: - delimiting blocks on the surface of the rock face from dense three-dimensional topographic data, by hierarchical segmentation by watershed line, - evaluating the stability of each block individually by comparing its sub-excavation depth to its center of mass. Figure for abstract: figure 16

Description

Title of the invention: Method for characterizing a risk of falling blocks State of the art

[0001] Rockfalls and rock falls represent a significant financial and security risk for property and people. To ensure the safety and reduce the vulnerability of people and property located at the foot of rock faces, the authorities responsible for the sites must provide prevention, protection and safeguarding measures. These measures aim respectively to:

[0002] i- Improve knowledge of the phenomenon and inform people;

[0003] ii- Reduce the vulnerability of people.

[0004] As with other dangerous natural phenomena, the rockfall hazard designates the phenomenon itself or the greater or lesser probability that it will occur, regardless of the occupation of the area concerned.

[0005] This is an area of expertise. To characterize the risk of rock fall at the level of a wall, the expert must make a diagnosis of the future evolution of an existing rock slope.

[0006] To do this in the most objective way, he seeks to:

[0007] - identify areas likely to produce rock falls;

[0008] - find stability criteria adapted to the lithology of the wall;

[0009] - quantify the probability of instabilities falling for a certain delay;

[0010] - determine the maximum spreading area;

[0011] - estimate the energy that falling blocks could release.

[0012] The following documents reflect the state of the art known to the inventors.

[0013] Hudson, JA, & Priest, SD. Discontinuity frequency in rock masses. In International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts. Pergamon;

[0014] Asroun, A., & Durville, JL. Stability of fissured rock masses. French Journal of Geotechnics 5-9,

[0015] teach that a fractured rock mass is composed of blocks forming a generally stable structure whose balance can be broken instantly or, in the long term, by aggravating factors. Its susceptibility to rock falls is strongly linked to its morphology and the discontinuities which affect it.

[0016] Bieniawski, ZT. Engineering classification of jointed rock masses. Civil Engineering = Siviele Ingenieurswese, 1973, 335-343;

[0017] Hoek, E., Marinos, P., & Benissi, M.. Applicability of the Geological Strength Index classification for very weak and sheared rock masses. The case of the Athens Schist Formation. Bulletin of Engineering Geology and the Environment, 57, 151-160,

[0018] disclose methods for classifying rock masses according to their properties. These methods are frequently used for the "large-scale" geotechnical characterization of rock walls. The characterization of these criteria is traditionally carried out using expert-based methods which are therefore subjective and have low spatial resolution.

[0019] Abellân, A., Oppikofer, T., Jaboyedoff, M., Rosser, NJ, Lim, M., & Lato, MJ. Terrestrial laser scanning of rock slope instability. Earth surface processes and landforms, 39, 80-97;

[0020] Jaboyedoff, M., Metzger, R., Oppikofer, T., Couture, R., Derron, M. H., Locat, J., & Turmel, D. . New insight techniques to analyze rock-slope relief using DEM and 3Dimaging cloud points: COLTOP-3D software. In Ist Canada-US Rock Mechanics Symposium. OnePetro;

[0021] Gigli, G., & Casagli, N. . Semi-automatic extraction of rock mass structural data from high resolution LIDAR point clouds. International Journal of Rock Mechanics and Mining Sciences, 48, 187-198 ;

[0022] Lato, M. J., & Vôge, M. . Automated mapping of rock discontinuities in 3D lidar and photogrammetry models. International Journal of Rock Mechanics and Mining Sciences, 54, 150- 158;

[0023] Riquelme, A. J., Abellân, A., Tomâs, R., & Jaboyedoff, M. . A new approach for semi- automatic rock mass joints récognition from 3D point clouds. Computers & Geosciences, 68, 38- 52 ;

[0024] Thiele, S. T., Grose, L., Samsu, A., Micklethwaite, S., Vollgger, S. A., & Cruden, A. R. . Rapid, semi-automatic fracture and contact mapping for point clouds, images and geophysical data. Solid Earth, 8, 1241-1253 ;

[0025] Vasuki, Y., Holden, E. J., Kovesi, P., & Micklethwaite, S. . Semi-automatic mapping of geological Structures using UAV-based photogrammetric data: An image analysis approach. Computers & Geosciences, 69, 22-32,

[0026] disclose the use of 3D images or point clouds as an alternative to traditional methods, with the advantages of being quantifiable and at higher spatial resolution. Automatic or semi-automatic methods have thus been developed to identify, with varying degrees of precision or efficiency, discontinuities within 3D point clouds or the analysis of ortho-rectified images. A detailed review of the methods deployed since 2005 to automatically and semi-automatically detect and characterize discontinuities on rock walls is given in Abellân, A., Oppikofer, T., Jaboyedoff, M., Rosser, N.J., Lim, M., & Lato, M.J. (2014). Terrestrial laser scanning of rock slope instability. Earth surface processes and landforms, 39(1), 80-97. and in Battulwar, R., Zare-Naghadehi, M., Emami, E., & Sattarvand, J. (2021). A state-of-the-art review of automated extraction of rock mass discontinuity characteristics using three-dimensional surface models. Journal of Rock Mechanics and Geotechnical Engineering, 13(4), 920-936.

[0027] With rocks of lower quality or very discontinuous such as volcanic rocks, these methods are not suitable for carrying out traditional stability analyses. Volcanic formations are in fact distinguished by a strong anisotropy induced by thermal discontinuities, called joints, and by rapid alteration degrading their geomechanical properties, a fortiori in a tropical context.

[0028] Estimating the state of stability at the scale of a slope depends on knowledge at every point of the resistance forces that apply to it with respect to the driving forces that stress it. The resistance of the massif depends on the presence of discontinuities and their individual geometry, the position, orientation and quantity of rock bridges, i.e. unbroken zones near a fracture, and their individual resistance. Each cut element, or "block", interacts with neighboring elements to distribute the stress forces.

[0029] External stresses such as rain, frost, vegetation, and tremors can deteriorate the resistance of the rock mass and cause a reduction in its stability. A rock mass therefore oscillates at all times between a stable state and an unstable state.

[0030] Thus, it is understood that the evaluation of stability at the scale of a rock mass, and therefore of its risk of block rupture, is a very difficult exercise due to the natural complexity of a mass and that of the interactions that it maintains with its external environment.

[0031] However, certain typical geometric configurations can give rise to landslides initiated by simple mechanisms such as tilting, overhang failure, etc. This is particularly the case for rock walls formed by the superposition of lava flows. These geometric configurations predispose to block falls.

[0032] A solution provided by Dunham, L., Wartman, J., Olsen, M.J., O'Banion, M., & Cunningham, K. . Rockfall Activity Index: A lidar-derived, morphology-based method for hazard assessment. Engineering geology, 221, 184-192, aims to classify a wall into different block types and apply an activity factor calculated from the wall activity history. This technique does not allow for the delineation of each block individually, nor for its stability to be assessed based on its individual shape.

[0033] Another solution, proposed by Wang, W., Zhao, W., Chai, B., Du, J., Tang, L., Yi, X., 2022. Discontinuity interpretation and identification of potential rockfalls for high-steep slopes based on UAV nap-of-the-object photogrammetry. Computers & Geosciences 166, 105191, aims to:

[0034] 1 / detect families of cracks from an orthophotograph,

[0035] 2 / separate zones of the same orientation delimited by these discontinuities,

[0036] 3 / estimate the depth of overhangs taken from these areas.

[0037] However, crack detection is not always possible and easily leads to errors of assessment. The invention

[0038] An aim of the invention is to propose a method for quantifying the risk of rupture of isolated blocks in the context of volcanic walls.

[0039] An object of the invention is a method for characterizing a risk of falling blocks detaching from a rock face of hectometric scale composed of stacks of volcanic rocks made up of alternating massive basaltic flows and inter-flow levels, characterized in that it comprises the following steps:

[0040] - delineate blocks on the surface of the rock wall from the data dense three-dimensional topographical data, by hierarchical segmentation by watershed line,

[0041] - evaluate the stability of each block individually by comparing its depth of undercutting at its center of mass.

[0042] The method of the invention makes it possible to identify blocks in a situation of potential instability when it comes to volcanic walls exhibiting alternations of massive basaltic flows and scoria for which a dense topographic survey acquired for example by lidar or photogrammetric method.

[0043] According to a particular embodiment of the characterization method, the density of the topographic data is in line with the dimensions of the blocks and overhangs to be distinguished.

[0044] Thus, according to a particular embodiment of the characterization method, this adequacy means that the density of points is of the order of 2.5% to 5% of the height of the benches, with a density which can in particular reach 400pts / m2 on 95% of the wall with a proportion seeking to equal or exceed 1600 pts / m2. A bench corresponds to a layer of homogeneous rock, delimited by a “wall” and a “roof”. These established terms are inherited from mining language. The wall corresponds to the lower base of the bench. The roof corresponds to the top of the bench.

[0045] The method involves singling out the blocks within a 3D point cloud and determining their stability status by comparing the depth of the sub-excavation to its center. of mass. The exhaustive detection of instabilities at the scale of an outcrop then makes it possible to construct an inventory of the blocks of a wall including the geometric attributes, the instability indices and the estimates of the potential energy of fall of the individual blocks.

[0046] According to a particular embodiment of the characterization method, the steps of the method are repeated regularly, for example once a year.

[0047] This regular reiteration gives a temporal depth to the stability analysis and refines the probability of a given block falling. This analysis can in particular make it possible to calibrate the definition of safety thresholds, i.e. the criteria from which a block is considered to have a high probability of falling.

[0048] According to a particular embodiment of the characterization method, the three-dimensional topographic data are acquired by lidar or photogrammetric or radargrammetry method.

[0049] According to a particular embodiment of the characterization method, a spatial approximation of the coordinates of the points is carried out using a discretization of the three-dimensional data in the form of a 3D or 2.5D grid, to which the block delimitation processing is applied.

[0050] According to a particular embodiment of the characterization method, a reference system of cartographic axes or one adjusted locally to the wall is applied in the 3D or 2.5D grid.

[0051] According to a particular embodiment of the characterization method, the stability of a block is evaluated as insufficient if the block has a ratio L / P < 2, where L is the width of the block and P, its depth inferred from the width of the block, considered as a proxy for the width in this type of configuration.

[0052] According to a particular embodiment of the characterization method, once the unstable blocks have been identified, the energy of each block is determined if it were to fall at the foot of the wall. Brief description of the figures

[0053] The invention will be better understood on reading the following description given solely by way of example and with reference to the appended drawings in which:

[0054] [Fig-1] is a representation of a raw colorized 3D point cloud obtained by photogrammetry,

[0055] [Fig.2] is a representation of the filtered point cloud of densely vegetated,

[0056] [Fig.3] illustrates the saliency of the wall blocks in the filtered point cloud,

[0057] [Fig.4] illustrates the principle of segmentation by watershed line applied to a topography,

[0058] [Fig.5] illustrates the principle of hierarchical segmentation by watershed line applied to a watershed,

[0059] [Fig.6] represents the spectra of the different parameters explored in the regions of the rock face delimited by hierarchical segmentation. [Fig. 6a]: perimeter as a function of height, [Fig. 6b]: height as a function of size, [Fig. 6c]: degrees of compactness as a function of size,

[0060] [Fig.7] is a map of the identified rock overhangs,

[0061] [Fig.8] shows the distribution of the volumes of the identified overhanging blocks,

[0062] [Fig.9] shows the distribution of the depths of the identified overhangs,

[0063] [Fig. 10] is a graph representing the volumes of the blocks in an unstable situation,

[0064] [Fig. 11] represents a mapping of the stability of rock blocks,

[0065] [Fig. 12] shows the distribution of the kinetic energy of the delimited rock blocks corresponding to the selection criteria,

[0066] [Fig. 13], [Fig. 14] and [Fig. 15] represent the location of the blocks considered unstable, as a result of the implementation of the method,

[0067] [Fig. 16] is a block diagram representing four phases of the process. Detailed description

[0068] The wall studied extends over a surface which can generally be assimilated to a plane, even if it is obviously not flat, with a longitudinal direction which measures its width, a vertical direction which measures its height and a depth which measures its inclination. Photogrammetric data are obtained with a density of lpt / 10 cm2.

[0069] The method of the invention, in the implementation which will be described, makes it possible to identify, position and delimit the blocks present in the wall and to evaluate their degree of stability as a function of their undercutting.

[0070] This implementation takes place in four phases 1, 2, 3 and 4, which are represented in the block diagram of [Fig.16]. Phases 1 and 4 are optional.

[0071] Phase 1: Capturing rock face geometry as dense 3D topographic data.

[0072] In the example, topographic data obtained by photogrammetric method applied to aerial images are used. These images were taken at a distance from the wall of approximately 40m (see p.32 of the report) and with a field of view, or “swath” or “field of view”, of 72”. The pixels of these images have an individual physical dimension of 3.3pm.

[0073] These shots make it possible to obtain a 3D point cloud by photogrammetry, like the one shown in [Fig.l].

[0074] From the 3D point cloud thus obtained, certain processing must be applied to make block detection possible.

[0075] First of all, if the wall to be studied is not close to a north-south or east-west orientation, the point cloud is placed in an orthogonal coordinate system relative to the outcrop. Thus, the Y axis is parallel to the longitudinal direction, the X axis is directed towards the interior of the rock mass and the Z axis is the vertical direction. This processing allows the use of specialized software that only calculates in the X, Y or Z directions, as is the case with the software from the Open Source Project “CloudCompare” available at https: / / www.cloudcompare.org / .

[0076] A second treatment consists of filtering the vegetation using the software using geometric characteristics of the point cloud: sphericity, planarity, as well as the connection between the points of the 3D cloud. These parameters are calculated for each of the points in a neighborhood of radius r, using the eigenvalues Xi with ie [1;3] such that X3 < X2 < XL

[0077] - Sphericity is defined by the ratio X3 / X1. The selected radius is r= 0.206615. Based on the values obtained, points with a sphericity greater than 0.25 are considered as points belonging to vegetation and are removed from the point cloud.

[0078] - The planarity P, defined as P = X2-X3, is calculated on a radius r=0.4m. The XI zones with a P<0.65 are rough areas i.e. potentially vegetated and are therefore filtered.

[0079] - On the residual cloud, after filtering on planarity and on sphericity, we apply a second processing called point gathering. For this purpose, an algorithm called connected-component is applied. This algorithm allows the connected points to be gathered into a single set. The number and size of the sets depends on the chosen decomposition level. The higher the level, the more the medium is decomposed into numerous sets. In the present embodiment, the neighboring voxels at level 11 of the octree are searched for. The corresponding physical dimension is calculated by L / 2n l, where L is the largest dimension of the point cloud, n is the octree level. For example, for a point cloud whose maximum footprint length is 500 m, L=500 and the size of a level 11 voxel is then 0.48 m.

[0080] Finally, a manual selection on the sets makes it possible to exclude residual vegetated areas.

[0081] At this stage we have a cloud of collected points, cleaned of vegetated areas, as visible in [Fig.2].

[0082] Phase 2: Delimitation of the blocks

[0083] We will now use the salience to begin preparing the individualization of the blocks.

[0084] Salience is a parameter calculated to highlight potential overhanging areas.

[0085] In the present embodiment, the salience is the difference according to the X component between the wall and the surface adjusted to the minima of the wall in the same component according to a wavelength of 3 m. This definition corresponds to the depth of the undercut, within the meaning of the method of the invention. The result is illustrated by [Fig. 3], where the salience is displayed as the distance to the average surface of the cliff. The areas in an overhanging situation have a positive salience, indicated in red, while the recesses have a negative salience, indicated in blue. The more salient an area is, the greater its projection.

[0086] It is on this data that the individualization of the blocks is carried out, as will now be explained.

[0087] The objective here is to partition the cloud of points gathered into several connected regions and select those corresponding to blocks in an overhanging situation, that is to say with positive saliency.

[0088] To achieve this objective, the method of hierarchical segmentation by watershed line is used.

[0089] Although known to the specialist, we recall here the general principle of the watershed line algorithm.

[0090] The watershed is a segmentation tool that allows an image to be partitioned into several regions using a topographical approach: the different regions of the image are separated by ridge lines, as illustrated in [Fig.4].

[0091] The algorithm is applied to a gradient image, that is to say when a spatial derivative operator is applied to a field of scalar values (any numerical values, including for example the altitude field when considering topography).

[0092] The gradient image is likened to a landscape where the altitude of each point is given by the intensity of the corresponding pixel. High intensity pixels correspond to peaks, while low intensity pixels correspond to valley bottoms.

[0093] The algorithm makes it possible to determine the set of ridge lines 5 which separate the different watersheds 6 by a flooding process. The watersheds are flooded progressively with altitude, that is to say that the sources of the flooding correspond to the local minima 7. This method is notably described in the document Beucher, S., 1994. Watershed, Hierarchical Segmentation and Waterfall Algorithm, in: Serra, J., Soille, P. (Eds.), Mathematical Morphology and Its Applications to Image Processing, Computational Imaging and Vision. Springer Netherlands, Dordrecht, pp. 69-76. https: / / doi.org / 10.1007 / 978-94-011-1040-2_10.

[0094] This reminder of the general principle of the algorithm being made, its application to the present embodiment allows the delimitation of the blocks by watershed line, but in the hierarchical version of this algorithm.

[0095] The hierarchical segmentation algorithm by watershed line is also known to the specialist. It is notably described in Cousty J. Najman. L., Incremental algorithm for hierarchical minimum spanning forests and saliency of watershed cuts. 10th International Symposium on Mathematical Morphology (ISMM'l 1), Jul 2011, Verbania-Intra, Italy. pp.272-283, 10.1007 / 978-3-642-21569-8_24hal- 00622505; in Perret B., Cousty J., Guimarâes S., Maia D. (2018) - Evaluation of hierarchical watersheds. IEEE Transactions on Image Processing, Institute of Electrical and Electronics Engineers, 2018, 27 (4), pp.1676-1688. 10.1109 / TIP.2017.2779604. hal-01430865v4 ; and in Maia, DS, Cousty, J., Najman, L., & Perret, B. (2019, March). Recognizing hierarchical watersheds. In International Conference on Discrete Geometry for Computer Imagery (pp. 300- 313). Springer, Cham.

[0096] We recall the general principle.

[0097] This algorithm consists of generating a region tree 8 from the result obtained by watershed line. From the initial watershed line segmentation, the regions resulting from this segmentation are merged according to regional attributes.

[0098] Two regions will be merged if they are neighbors and if a criterion is met. The criterion can be scalar, morphometric - area, volume -, or topological. Neighboring regions are merged step by step until there is only one region encompassing all those from the initial watershed line.

[0099] Each of the levels of the tree corresponds to a partition, as illustrated by [Fig.5], where each of the branches of the tree corresponds to a region defined by a local minimum and a watershed.

[0100] The regions produced by the segmentation process can be initialized using markers, i.e. pixels identified as being part of a particular region.

[0101] Each of the regions can be described according to statistical parameters and morpho-mathematical characteristics. A selection according to one or more of these criteria makes it possible to isolate certain regions and thus retain only certain elements of the image.

[0102] This reminder made, we now explain the application of the principle to the characterization of blocks.

[0103] For this, we use the python watershed tree code developed by F. Guiotte [https: / / python-sap.readthedocs.io / en / master / source / sap.trees.html#sap.trees;] from the higra library [https: / / higra.readthedocs.io / en / st2able / python / watershed_hierarchy.html].] This code takes as input the inverse of the "saliency" collected point cloud for which it calculates the gradient.

[0104] No marker is defined. The watershed is drawn and the regions are hierarchized.

[0105] The regions are hierarchized according to their area. In practice, this means that the lowest level of the tree is the partition corresponding to the initial segmentation of the point cloud gathered "saliency" by watershed line. Each partition of the tree corresponds to a neighboring region merging level. The regions of a partition are characterized by an area included in a given interval. The top of the tree is a single region encompassing the entire image.

[0106] Once the segmentation is carried out, several statistical and morphomathematical parameters characterizing elements of the tree are explored.

[0107] - The surface: the surface of a node of the tree corresponds to the number of pixels of the region of the image represented by the node in question. For the cliff studied, as a first approach, a selection on the surface makes it possible to exclude regions which encompass too large portions of the cliff (> 10 m2) and not representative of potential instabilities of the rock fall type of the lower part of the cliff and also to remove regions below 0.1 m2 which could correspond to unfiltered vegetation residues. These parameters are linked to the cliff studied and to the resolution of the point cloud used.

[0108] - The perimeter: the perimeter of a node of the tree corresponds to the perimeter of the node region. It is given in number of pixels of 10 cm side.

[0109] - Compactness: the degree of compactness of a node is defined by the Polsby- Popper as: 4irA / P2

[0110] where A is the knot and P is its perimeter.

[0111] Compactness varies between 1 (compact) and 0 (not compact). A disk has a capacity of 1, a square of 0.78, a rectangle twice as long as it is wide, of 0.69. A block can be seen as a relatively compact area of the cliff.

[0112] - Height: Height is the difference in altitude between the altitude of the parent of the node and the altitude of the deepest node in the subtree rooted in the node. The height is directly related to the salience of a given region of the wall. Overhangs have a positive height, i.e., salience.

[0113] The spectra of the different parameters explored on the rock face are represented in [Fig. 6a], 6b and 6c. In [Fig. 6a], we see the perimeter as a function of the height expressed in meters. In [Fig. 6b], we have represented the height, expressed in meters, as a function of doing, expressed in number of pixels. In [Fig. 6c], the degrees of compactness are represented as a function of doing, expressed in number of pixels. In these three figures, the more a characteristic is represented, the greater the value of the spectrum.

[0114] We then proceed in two stages: first, extract the rock overhangs, then, select the rock blocks.

[0115] a) Extraction of rock overhangs

[0116] The morpho-mathematical and statistical characteristics of the different elements of the tree are used to isolate the areas in an overhanging situation.

[0117] In order to define the thresholds, the matrix of manually mapped rock overhangs is crossed with that of automatically mapped overhangs. A percentage of overlap results from this crossing. The mapping is also visually evaluated by superimposing the overhang map on the orthophotography.

[0118] We note that with the following selected criteria:

[0119] - Area (number of pixels of 0.1 m2) included in [1; 100]

[0120] - Compactness > 0.25,

[0121] - Height > -0.05,

[0122] we obtain the rock overhangs illustrated in [Fig.7], on which 86% of the pixels identified on the orthophotography as belonging to overhangs are mapped. The 14% not identified are areas where there are no points on the 3D point cloud, pixels located on the periphery of an overhang or areas where the salience is not sufficient. Only 4% of the pixels manually identified as overhangs but covered by vegetation were automatically mapped as overhangs.

[0123] This verification qualifies the reliability of the method followed and provides the desired thresholds. We can now move on to the selection of rock blocks.

[0124] b) Selection of rock blocks

[0125] Due to their geological nature, the rock blocks of basalt flows are mainly cut at the level of cooling cracks (joints). A strong hypothesis is considered to retain rock blocks having a ratio L / P < 1, where L is the width of the block and P, its depth. Thus, polygons whose width is 1.1 times greater than their depth are discarded. This filtering can have the effect of excluding from the selection contiguous blocks and emerging with this method as a single block with, therefore, a ratio L / P>1.

[0126] The volume is estimated from the saliency, the calculation of which has already been explained. It corresponds to the sum of the saliency of each pixel belonging to it, multiplied by the surface area of a pixel.

[0127] In a variant not illustrated, the volume is estimated by multiplying the surface area of the pixels by the width of the block, itself approximated as identical to its depth. The depth of a block is known to the specialist, for example in Gonzalez de Vallejo L, Hemândez-Gutiérrez L, Ana Miranda and Mercedes Ferrer Rockfall Hazard Assessment in Volcanic Regions Based on ISVS and IRVS Geomechanical Indices Geosciences 2020, 10, 220; doi:10.3390 / geosciences 10060220.

[0128] In another variant not illustrated, two volume estimates are made using the two previous methods, then an average value and a standard deviation are deduced to validate the volumes thus calculated.

[0129] [Fig.8] shows the distribution of the volumes of the identified blocks (number of blocks as a function of the volume, expressed in m3). The median of the volumes is 0.045 m3, the quantiles at 17% and 83% are equal to 3x10 4 m3 and 1.53 m3 respectively, which means that 50% of the blocks delimited by the method correspond to blocks of less than 501, or approximately 120 kg for basalt.

[0130] The overhang depth of a given block is approximated by the 83% quantile of the saliency values contained in the delimited block. The distribution of the depths of the identified overhangs is represented in [Fig.9] (number of blocks as a function of the overhang depth, expressed in meters). The median depth of an overhang is 0.45 m. The measured overhang depths do not exceed 1.6 m. There is no obvious relationship between block size and overhang depth.

[0131] Phase 3: Evaluation of the stability of each individual block

[0132] The rock mass becomes unstable when the tensile, bending and shear forces due to a geometric imbalance can no longer be compensated by the strength of the material. It is assumed that rock blocks in basalts are cut by background cracks that develop at a distance equivalent to the width of the block due to a pseudo-hexagonal flow with a slenderness orthogonal to the flow surface. This teaching is already known from Aydin, A., Degraff, J., 1988. Evolution of Polygonal Fracture Patterns in Lava Flows. Science (New York, NY) 239, 471-6. and from Goehring L. & Stephen W.M. Scaling of columnar joints in basait. Journal of Geophysical Research, Vol. 113, B10203, doi:10.1029 / 2007JB005018, 2008.

[0133] In this case, where the dip direction is almost coplanar with the direction of the wall, the bed of the blocks is considered perpendicular to the wall. Then, it is considered that when the depth of the overhang (P) is greater than half the width (L), the center of gravity is beyond the overhang line. The block would therefore be in unstable equilibrium. After filtering, the volume of these unstable blocks varies from 103 to 10 m3, as seen in [Fig. 10], which represents the distribution of the L / P ratio as a function of volume, expressed in m3. Above the broken line 9, the blocks are considered stable. Below, as unstable. These stability criteria would have to be adapted in the event of an unfavorable slope, i.e. in the event of a downstream slope, or favorable, i.e. in the event of an upstream slope, of the block seating surfaces.

[0134] The blocks considered in stable and unstable equilibrium are located on the wall of [Fig.11].

[0135] Blocks in unstable equilibrium (L / P < 2) represent approximately 15% of the mapped blocks.

[0136] A comparison with a catalog of natural events makes it possible to associate a probability of occurrence with the instability criteria and allows a probabilistic quantification of the hazard.

[0137] Thus, among the twelve detections of block falls, unnatural because caused by purges, more than half appear with a width / depth ratio <2.

[0138] Phase 4: Determination of the energy of each block

[0139] The intensity of the rockfall phenomenon is quantified by the kinetic energy of the event. The greater the kinetic energy, the greater the damage caused by the impact of the block can be. Damage to structures and energy levels are linked in a known manner, notably from the MEZAP guide

[2021] .

[0140] The kinetic energy of the blocks at first impact is calculated by considering that the block is in free fall such that:

[0141] [Math.l] mv2 )2 pV^2gH)2 Bc = — = -------=---= pVgH

[0142] where m is the mass of the block, v its speed, p being the density, equal here to 2,650 kg / m3 for basalt, V the volume of the block, g=9.81 m / s2 the acceleration of gravity at the surface of the earth and H the height of fall. The dissipation of energy during propagation, during rebounds or fragmentation on impact is not considered here.

[0143] The fall height is approximated by the difference in altitude between the foot of the wall and the barycenter of the block in question. It should be noted that large volumes can detach from the lower part of the wall, as well as from the upper part.

[0144] The smallest volumes (volume <102 m3, or 101), are filtered because they correspond to blocks of decimetric dimensions close to the resolution (10 cm) of the analyses carried out.

[0145] [Fig. 12] shows the distribution of kinetic energy (in kJ) of the delimited rock blocks corresponding to the selection criteria (depth > 0.9 width, volume <10m3). The left ordinate represents the frequency and the right ordinate the cumulative frequency.

[0146] The blocks considered in unstable equilibrium (L / P<2) have a kinetic energy between 2 kJ and 104 kJ. Half of these blocks have a kinetic energy greater than 594 kJ. 95% have a kinetic energy less than 6500 kJ. The intensity of the phenomena on the studied wall is therefore high. The 95% quantile of the instability energy is recommended for the design of protective structures, according to the National C2ROP Project

[2020] , even if the design assumptions must be adapted according to the level of protection targeted by the project owners. The value of the 95% quantile here exceeds the interception capacities of a conventionally designed gabion barricade (2000 - 3000 kJ). Such blocks could be intercepted by high-energy nets or reinforced barricades.

[0147] In [Fig. 13], 14 and 15, the blocks considered unstable on the studied wall have been located. [Fig. 13] shows the blocks whose length / depth ratio is between 1.2 and 2; [Fig. 14] between 1 and 1.2; [Fig. 15] below 1.

[0148] In summary, the method described is based on

[0149] 1. The description of the relief of a wall;

[0150] 2. Identifying the notion of salience of the blocks on the wall;

[0151] 3. Delimiting the entities in an overhanging situation;

[0152] 4. Using a calculation algorithm derived from mathematical morphology or from geomorphometry to delineate the contours of the overhanging entity;

[0153] 5. Using discretization of point 3D data, gathered point cloud 2.5D or 3D volume elements, including cubic or prismatic voxel, tetrahedral or potential geometric method [called meshfree];

[0154] 6. Calculating the ratio between an estimator of the width of the bounded entity and a overhang amplitude estimator;

[0155] 7. Identifying an estimator of the position of the entity;

[0156] 8. Describing a size metric of the entity [including height, width, surface, volume];

[0157] 9. Relating this size metric to an altitude metric to infer energy including potential or kinetic of the entity at a lower altitude position.

[0158] The method according to the invention finds an industrial application in the following uses:

[0159] - Orientation of purging actions or securing work on a wall extended using unstable block mapping.

[0160] - Statistical definition of instability reference volume useful for dimensioning of protection parade against falling blocks. This sizing criterion is recommended, for example, in the C2R0P guide and is only rarely determinable from an inventory of events, which is generally insufficiently exhaustive.

[0161] The method of the invention makes it possible to individualize and characterize blocks in an overhanging situation. The method is advantageous for several reasons:

[0162] - It is based on a relatively rapid processing chain;

[0163] - The results are objective and reproducible;

[0164] - It is adapted to volcanic walls;

[0165] - It provides relevant information at the block and slope scale which can used to characterize the hazard and size protective measures.

[0166] The invention is not limited to the example described. Other operations could be combined with the method without departing from the scope of the invention, such as the integration of lithological variations (other than volcanic) and the geometry of the flows to allow naturalistic elements to be provided to define the stability of the blocks and the wall.

Claims

Claims

1. Method for characterizing a risk of falling blocks detaching from a rock face of hectometric scale composed of stacks of volcanic rocks made up of alternating massive basaltic flows and inter-flow levels, characterized in that it comprises the following steps: - delimiting (2) blocks on the surface of the rock face from dense three-dimensional topographic data, by hierarchical segmentation by watershed line, - evaluating (3) the stability of each block individually by comparing its sub-excavation depth to its center of mass and in which the three-dimensional topographic data are acquired by lidar or photogrammetric or radargrammetry method.

2. Characterization method according to claim 1, in which the topographic data comprises points whose density is of the order of 2.5% to 5% of the height of the benches, with a density which can in particular reach 400 points / m2 on 95% of the wall with a proportion seeking to equal or exceed 1600 points / m2.

3. A characterization method according to any one of claims 1 and 2, wherein the steps of the method are repeated regularly, for example once a year.

4. Characterization method according to claim 2, in which a spatial approximation of the coordinates of the points is carried out using a discretization of the three-dimensional data in the form of a 3D or 2.5D grid, to which the block delimitation processing is applied.

5. Characterization method according to claim 4, in which a reference frame of cartographic axes or locally adjusted to the wall is applied in the 3D or 2.5D grid.

6. A characterization method according to any one of claims 1, 2, 3, 4, and 5, wherein the stability of a block is evaluated as insufficient if the block has a ratio L / P < 2, where L is the width of the block and P is its depth.

7. A characterization method according to any one of claims 1, 2, 3, 4, 5, and 6, wherein, once the unstable blocks have been identified, we determine (4) the energy of each block if it were to fall at the foot of the wall.

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