Rock slopes risk assessment based on advanced geostructural survey techniques
A.M. Ferrero, M. Migliazza, R. Roncella
Department of Civil Engineering, of the Environment, of the Territory and Architecture, University of Parma, Italy
E.Rabbi
Geodata, Turin, Italy
ABSTRACT: The rock mass structure determines the possible unstable blocks that can induce rock
fall phenomena. The stability analyses must therefore be based on an accurate geo-structural survey. In this work the stability conditions of several steep slopes along a motorway in the Far East have been evaluated through Key Block analysis based on traditional surveys and on laser scanner acquisitions. Discontinuity orientations and positions on the rock face are derived from the point cloud in order to perform the reconstruction of the rock mass and to identify blocks in the slope. Results obtained from both the traditional and the new method is in good agreement.
Stability analyses have been performed for evaluating the kinematic feasibility of different failure mechanisms. The rock block shapes and volumes are computed by performing 2D and 3D analyses whereas the failure mechanisms are examined using the Key Block method. Parametrical analyses have been carried on to evaluate the influence of slope angle variation. DEM models have also been set up. The relative hazard is determined by statistically evaluating the kinematical feasibility of different failure mechanisms. Hazard mapping has been utilised to identify the best methodology for risk mitigation.
1 INTRODUCTION
In mountainous regions transportation corridors are often susceptible to landslides and, in particular, rock falls constitute a major hazard in numerous rock cuts. This is the case illustrated in this work, which concerns a highway segment in North Malaysia (Figure 1.), about 5 km long, excavated through eight slopes and affected by several rock falls that produce a possible risk for highway users.
The aim of the study was to establish the prevailing rock mass characteristics in the eight slopes for the evaluation of instability phenomena based on a traditional geostructural survey coupled with LIDAR technology, in order to assess the relative hazard for the slopes, thus providing recommendations for remedial works.
The analyzed rock slopes have been excavated by blasting technique and are made up by very steep berms of 10m heights with global extension varying between 70 and 760 m in length and 30 and 135 m in height. Protection system and consolidation work design needs the slope hazard evaluation in order to determine optimal works and priority interventions.
Due to the large dimensions of the slope, traditional compass surveys have been coupled with advanced techniques in order to obtain geo structural information even without direct access to the rock mass.
A detailed 3D model of the rock slope topography (Digital Surface Model, DSM) has been acquired by laser scanning that allows the acquisition of a very large number of measurements points forming a “cloud of points”.
Acquired data have than been treated by applying the RANSAC algorithm (RANdom Sample Consensus, Fisher and Bolles, 1981), that allows the segmentation of the point cloud into subsets, each made of points measured on a discontinuity plane of the rock
face. For each subset, the plane’s equation coefficients are first determined by robust estimation and then refined by least-squares estimation after outlier removal. The segmentation algorithm has been implemented in software specifically developed, ROCKSCAN (Ferrero et al., 2008) to facilitate the interaction with the point cloud in the identification of the discontinuities by a virtual projection of the three-dimensional (3D) data on a geo-referenced digital image of the slope.
In this way, selecting a rock mass portion directly on the photographs by either a manual or an automatic system, the code subdivides the area in point subsets belonging to single planes of discontinuity. The code computes each equation orientation and other relevant geometrical data of the plane.
Each slope has been scanned by two different laser scanning surveys. The first one was performed on the entire slope surface in order to determine the global slope DSM (Figure 2a). A second survey with high precision (Figure 2b), was carried out on smaller slope portions (10mx10m windows). The number of high precision windows for each slope was proportional to the slope dimension and to the rock mass structural features.
Data acquired with the two different approaches (compass and LIDAR) have been merged together in a consistent data set and are then statistically treated. This has led to recognition of typical discontinuities for each slope describing them from a geomechanical point of view.
Once both the topography of the slope and the geo-structure were determined, stability analyses were performed using the Key Block method. The different possible kinematic modes (planar and wedge sliding, toppling) were determined and factors of safety and volumes of the possible unstable blocks calculated. An example of the stability analysis based on a complete rock mass geometrical reconstruction is also presented.
An index of stability has then been applied in order to assess a level of relative hazard for the different slopes. This index has been defined introducing parameters such as geometrical characteristics of the slopes and of the berms, global stability and stability of the berms, presence of water, presence of protections. On this base remedial work typologies have also been suggested.
The words “joint”, “fracture” and “discontinuity” are used in an interchangeable way in the text.
The methodological approach followed for stability analyses described in this paper is shown in Figure 3.
2 GEOSTRUCTURAL STUDIES
2.1 Geological setting
The slopes are composed of porphyritic biotite granite of Triassic Age belonging to the Kledang Range. Quartz veins, aplite dykes and pegmatites of variable orientation and size are also present within the granite rock.
A variety of structural discontinuity planes cut the granitic rock; the discontinuity planes are of variable orientation, spacing and extent and they produce rock blocks of variable size and shape. The slopes belong to the same geological domain although they show a different weathering degree: fresh to slightly weathered granite rock is only exposed in the lower benches of the selected slope cuts, the upper benches being excavated in moderately to completely weathered rock.
2.2 Geostructural survey
Geological-geostructural mapping was carried out for the 8 slopes through the definition of geostructural domains and the geomechanical description of the rock mass (Ferrero et al., 2007).
For each slope a preliminary geometric description was given with the definition of geostructural domains and principal joint sets (Figure 4); then a series of geostructural surveys along scanlines of 10m lengths were performed.
More than 50 geostructural traverses were performed with a total of about 2400 discontinuities collected in terms of orientation (dip, dip direction), spacing, persistence, roughness, general condition (alteration, aperture, filling) according to ISRM suggested method (1978).
In order to identify the predominant joint sets, all data collected were statistically analysed separately for each traverse and together for the 8 different slopes, using a commercial code (DIPS, Rockscience) . The combined use of these tools permitted the determination of dispersion around the mean value, in terms of a cone of confidence for each family of joints.
During the traditional survey in situ observations of local instabilities, water presence and existing protective structures, were noted separately to be compared with and for integrating the results of the surveys.
2.2.2 Laser scanner survey
The Digital Surface Model (DSM) generation for the eight slopes has been obtained by using the LIDAR (Light Detection And Ranging) terrestrial laser scanner technique, which utilizes a system consisting of a laser telemeter and a scanning mechanism. A pulse emitted from the laser source is reflected by the object surface, its echo is captured by the optics: measuring the time-of-flight, the sensor-to-object distance is computed. Terrestrial lasers are equipped with two mirrors mounted on two orthogonal axes; when the instrument is levelled, the synchronized rotation provides scanning in azimuth and zenith. The polar coordinates of the target are then converted to a local Cartesian frame with the origin in the instrument centre, z-axis vertical and x-axis in an arbitrary direction. Point clouds of rock faces, (operating ranges of lasers are from 100 to 800 m and more), with accuracies of the 3D coordinates in the range 5 10-3 ÷3 10-2 m and a scanning role from
2000 to 12000 pts/s have been obtained. Angular scanning resolutions are in the order of 100 mrad and allow for a very high sampling density on the object in relatively short acquisition times, resulting in millions of points measured on the object surface.
The survey of the slopes was carried out with a Riegl LMS-Z420i with a calibrated Nikon D70 digital camera mounted on it. During the survey, many scan positions were adopted in order to avoid hidden zones. In addition, in each slope two different survey resolutions were adopted:
for the general description of the slope a point every 0.05x0.05 m2 was acquired,
while for taking the digital images a 20 mm calibrated focal lens was used;
a detailed survey was carried out in zones, having a dimension of 10 m x 10 m (a point every centimetre, 84 mm lens).
The examined slopes have been excavated by means of blasting techniques (Figure 4). Therefore, the free surfaces of discontinuities present very little contrast and the survey requires high point density and digital images having a very high resolution.
A local network has been implemented, documented and surveyed by means of a fast static GPS survey with a Trimble 4000 ssi double-frequency receiver and a Trimble 4600 single-frequency receiver, in order to provide reference points to georeference the scanning.
From these points a topographic survey was carried out by means of a Leica TC 1105 total station to connect the reflecting targets placed on the rock slope to the reference vertices.
In this way it was possible to convert all the local measurements into a mapping system and reference all data to the north direction.
The laser scanner supplies the coordinates of points in space. The next step to realise a geometrical model of the rock mass is the determination of the discontinuity planes. For this purpose, points have to be divided into groups belonging to a single plane. In other words, the point cloud has to be analysed in order to identify the points belonging to each discontinuity plane existing in the slope. For this purpose laser scanner measurements have been superimposed onto images of the slope in order to determine both slope geometry and identify rock discontinuities by means of a software called ROCKSCAN developed by the authors (Figure 5). This tool is based on a segmentation algorithm capable of identifying the number of planes present in a point cloud and compute their geometrical parameters. By knowing the plane equation, dip and dip direction of each plane can be computed. A detailed description of the applied survey technique is given in Ferrero et al. (2008) where a description of the software ROCKSCAN developed by the authors is also given.
The accuracy (i.e. the degree of closeness of measurements of a quantity to its true value) of the dip and dip direction estimation by mean of non contact method of survey (laser scanning or photogrammetry) has been analyzed with mathematical and stochastic models to define it as a function of the most relevant parameters: the accuracy on 3D coordinates of the points surveyed on the discontinuity plane, the orientation, the size and the shape of the plane respect to the direction of the survey and the number of points measured per unit area of the surveyed discontinuity. In this approach the discontinuity plane (Figure 6) is represented by a rectangular surface having the base b fixed and the ratio b/h (where h is the rectangle height) varying from 1/5 to 5 to represent elongated shapes in height and width (as well as a square). The measurement points are distributed on the rectangle on a square grid with a point density k ranging in 10% to 100% (the percentage is referred to the shortest rectangle side). The number of grid points measured on each rectangle is a function of grid spacing and the point density increases with the factor k and the rectangle height decreases (table in Figure 6). The accuracy of dip and dip direction, as a function of measurement accuracy, has been computed by variance propagation within a generalized least squares model:
Dy = Ax + d with parameters x and observables y (Felus, 2006).
Without loss of generality, the equation of a plane through the origin ax + by + cz = 0 has been considered; the functional model is of the form F(y, x)=0 and must be linearized with respect to the observables as well as with respect to the parameters. We have therefore:
D=
∂
F
∂
y
; A=−
∂
F
∂
x
; d=−F ( x
o, y
o)
where D contains the parameters of the plane and A the coordinates of the points which define the plane, while xo, yo are respectively approximations of parameters and point
coordinates. The stochastic model is defined by the covariance matrix of the observations CYY, which is taken as block diagonal, neglecting correlations between measurement
points.
The theoretical accuracy of the parameters is given by the covariance matrix CXX
computed by covariance propagation: CXX = (At (D CYY Dt)-1A)-1
The orientation of the plane unit normal vector (pole) pointing upwards can be expressed as a function of the plane’s coefficient as
where k is 0° or 180° depending on the quadrant. The accuracy of dip and dip direction determination can be derived by a new error propagation, with the full covariance matrix CXX.
The analyses carried out have been shown as the accuracy of dip depends only on the accuracy of the z component of the vector normal to the plane, while the accuracy of dip direction depends on the accuracy of both the x and y components (but x and y components accuracies are strongly influenced by the z component itself ). Consequently the accuracy in estimating the plane dip direction is strongly influenced by the plane dip angle for nearly horizontal planes (below 30°) as well. To evaluate the accuracy value obtainable for both dip and dip direction , several simulations have been performed, using different shapes and size plane and density of points on the face plane. The results show as the accuracy always increases with a higher point density. The dip accuracy, it strongly depends on the shape of the plane and less from the dip value of the plane; while, the dip direction accuracy depends on both shape and dip value of the plane. In Figure 7 an example of the result obtained is illustrated. In this case the results regard a rectangular shape of the plane and the dip and dip direction accuracies are referred to different values of plane inclination (dip) and number of points in the plane.
One can observe as the error in the estimation of the plane orientation decreases with plane dip. It is necessary to note that the values of mean square error have been obtained by considering an horizontal survey direction; the relation between the measure error and the dip value is correlated to the direction of the survey in relation to the slope direction (for instance if the survey is vertical the error is higher for vertical planes and minimal for horizontal planes).
Graphs similar to those reported in Figure 7 have been developed for planes with different shapes and orientations for the design of a laser scanning survey with a known accuracy. In this way, the survey orientation with respect to the rock slope and the point density to be measured can be defined.
For what it concerns persistence, spacing and discontinuity position in the space, the code ROCKSCAN allows to determine all geometrical characteristics of each identified plane and trace. In particular, persistence can be computed by the code by selecting two opposite extreme points on the rock face.
Spacing can be defined in two ways: the first one simulates the classical compass survey along scanline by reproducing a virtual scanline on the photographs and counting the distance of each intersected plane by an interactive tool; the second way is to select two discontinuities between which the code computes the minimum distance in mathematical way. The plane localization is done automatically by the code knowing the 3D coordinate of the plane centroid.
2.2.3 Geo-structural data analysis and comparison
Orientation data calculated from LIDAR and those measured through compass have been compared to validate the system. In Figure 8 an example of the comparison of the two stereonets obtained plotting the data resulting from the traditional compass method and from LIDAR data is reported. The results refer to the data collected along a traverse (37 data plane collected) and in a LIDAR survey windows placed in the same zone (251 data plane collected). The results appear in good correspondence with the preliminary in situ observations apart from the sub-horizontal plane, that cannot be detected by laser scanner since all acquisition have been done at the same high.
Data have been analyzed after subdividing the slope into homogeneous domains, and discontinuity data have been statistically analyzed to define the joint sets and their average orientation, spacing and persistence (Table 1). The rock mass has shown a relatively homogeneous structure in that the main joint sets are present in all slopes although some of the slopes have shown a local variation. In particular, in some slopes a joint set parallel to the rock face has been observed by the in situ survey that cannot be identified from the LIDAR data.
Discontinuity spacing and persistence distributions have been computed and average values of spacing are utilised in the rock slope stability evaluation. Concerning persistence, the computed values have been high for most joint sets (above 90%) with very high dispersions and, consequently, several values of persistence have been assumed, with a maximum value of 95%.
3 STABILITY ASSESSMENT
Fractured rock masses are often geometrically complex and can be regarded as an assemblage of many individual polyhedral blocks whose shape and volume are connected to number, orientation and spacing of the discontinuity systems present in the rock mass. When such a rock mass is subjected to mechanical disturbance, through for example the excavation of slopes, the rock blocks can displace, rotate and detach from the rock mass. To assess the slopes stability conditions several analyses have then been performed by applying the limit equilibrium method (LEM). Several analyses were performed by considering the statistical distribution of geometrical characteristics of the joint sets identified in each slope.
In order to identify shape, dimension, type of kinematism and factor of safety of the blocks that can detach from the rock mass, the commercial code Rock3D (geo&soft) has been utilized. The code allows to conduct slope stability analyses following four steps: cluster analysis to identify the joints sets by the hierarchic clustering procedure; kinematic analysis based on the Key Block Theory (Goodman & Shi, 1985); geometrical reconstruction of the blocks by creating a map of the discontinuities on the rock face, based on the statistical distribution of the discontinuities measured on the slope; stability analysis by applying the limit equilibrium method to compute the factor of safety of each finite and removable block and, in case of unstable blocks, the stabilization forces.
Cluster analyses leads to the identification of the joints sets by hierarchic clustering procedures based on multivariate analysis applied to the bi-dimensional spherical space instead of the n-dimensional Cartesian space (Dillon and Goldstein, 1984). This procedure leads to the determination of an optimal number of joint sets and their average orientations. The stability analysis are carried out by identifying the possible kinematic mechanism (vertical fall, planar and wedge sliding) with the Key Block method, evaluating the rock block volume and determining its safety factor (SF) on the base of the shear strength of the discontinuities and by applying the limit equilibrium method (LEM).
Joint shear resistance has been determined on the basis of discontinuity roughness and compressive strength collected by in situ measurements. In particular, since all discontinuities constantly showed low roughness values and a high weathering degree a precautionary friction value equal to 32° have been adopted for all stability analysis. This code allows, note the rock face dimension and orientation, to determine a map of the discontinuity traces in two different ways: by introducing the orientation and position of each discontinuity on the rock face (deterministic way) or by an automatically traces generation based on statistical distribution of geometrical discontinuity characteristics (orientation, spacing and length) measured on the slope (random way). In this way the survey results can be expanded and applied to larger slope portions. Statistical analyses of spacing and persistence are carried independently for each joint set identified by the cluster analysis. For each kinematic analysis, the block shape and size is defined by the joint intersection, spacing and persistence; so they can be characterized by simple or complex shape and the volume of each detachable block (defined as free and removable in the Key Block method) can be easily determined by simple analytical geometric equations. The dip, dip direction and spacing variation for each joint set was quantified and applied in the block stability evaluation by considering a random combination of this variability. Several analyses for each block type were performed until the maximum volume for each kinematics type was determined.
Stereographic projection analyses have been performed for each slope both considering average slope dip and berm dip. These analyses allow to identify toppling of free and removable blocks and to define their safety factors (SF) on the base of the block geometrical conditions (ratio between block height and width) and the base plane dip. This method has been applied to each analysed slope, considering all the acquired discontinuity data obtained from traditional and laser scanner surveys. The results of the key block analysis are: a map of the discontinuities crossing the rock faces, the type of kinematics and the geometrical features of free and removable blocks. For each free and removable block the factor of safety (SF) was computed by the limit equilibrium method. Results are reported in Figure 9 for slope W8.
In Table 2 the results obtained for all the eight slopes analyzed are summarized.
A parametrical analysis has been performed in order to evaluate the influence of the slope orientation on the slope stability.
The slopes considered with average inclination were analysed with special care since it gives an important indication on the whole slope stability conditions. In particular a decreasing dip can determine a decreasing number of possible kinematism types since it determines a decreasing of the “space pyramid”.
Average and standard deviation dip for each slope have been computed analytically by the developed code as the plane that interpolates the whole cloud points. Computed dip range has been utilised for performing parametric analysis.
Some of the slopes did not show any major variation (slope W1, W2 zones 1 and 3, W3, W6 and W7) in the stability condition because the decreasing dip did not determine any variation in the block pyramid in terms of finite and removable blocks.
Some slopes (W2 zone 2, W4, W5 and W8) show variations indicated in Table 2.
In practice some of kinematism are not present any more with these slope inclination decrease. As smaller number of blocks reduces the number of unstable blocks and, consequently, the unstable volume per unit slope area. However, the maximum volume block did not change with slope inclination since in all cases the kinematism that determined that maximum volume is constantly the same.
In certain cases if the slope inclination increases of few degrees (and this can happen locally for large size slopes) the kinematism can be formed by the discontinuity intersection. For this reason a parametrical analysis has been performed in order to evaluate when a dip variation can determine major slope stability variations too (dip max in Table 3).
This is the case of slope W2 zone 2 where an increase of 8° (up to 67°) can determine the formation of blocks of large dimensions (up to 20 m3). For slopes W5 and W8 the slope dip
variations (down to 40° and 48° respectively) determine an increase in the slope stability conditions.
In Figure 10 some pictures reporting the in situ sliding phenomenon are shown, these observations confirm the results obtained with key block methods and have been carried on for each analyzed slope.
Stability analyses based on the complete geometrical model of the slopes based on the above described survey have been done by applying the code Resoblock. (Heliot, 1988 a e b). The analyses follow the tectonic history of the formation as a continuous medium is transformed into a block system. The joint sets have been introduced in the code in such a way that only the first one can determine planar and continuous discontinuity whilst the following joint set have to stop against existing planes. Discontinuities can be introduced in a deterministic way, as in the case of faults or singular discontinuities directly detected on site; the joint sets are automatically generated in a statistical way on the basis of surveyed discontinuities, by means of statistical distributions.
Figure 11 shows the Resoblock model (1265 blocks reproducing a rock mass volume of 100x40x40 m3 (X,Y,Z)) set up on this basis for one slope and the sliding phenomena
computed by the BSA (Block Stability Analysis) code based on the Limit Equilibrium Method. These analyses have determined the same kind of kinematics obtained with the Rock3D code in all examined cases.
4 HAZARD ASSESSMENT METHODOLOGY AND RESULTS
In order to plan and define the eventual remedial works needed to reduce the rockfall risk level, an hazard level assessment procedure based on the use of intensity-frequency matrix diagram (OFAT, OFEE, OFEFP, 1997; Interreg IIc, 2001; Crosta et al., 2006; Corominas et al. 2003, Jaboyedoff et al., 2005) has been applied. For this purpose the hazard is calculated in term of probability of occurrence of a dangerous phenomenon in a given location and time period (Varnes and IAEG Commission on Landslides, 1984). Consequently hazard level derives from a cross analysis between probability of rock failure and danger, as reported in the diagram of Figure 12.
The eight slopes have been preliminary analyzed focusing on the characterization of danger (intensity or magnitude of a localised existing or potential phenomenon of slope instability, with specific geometric and mechanical characteristics). The danger has been correlated to the number and the volume of the unstable blocks. The rock block volume has been evaluated by considering the discontinuity orientations, persistence and spacing of each characteristic joint set.
The probability of rock failure is calculated for a portion of rock mass, with a specific volume within the considered slope. For this study this item has been correlated to the factor of safety (SF) coming from the analysis developed on the slopes for the theoretical unstable blocks and to the type and number of possible instability phenomena, as focused on the basis of the kinematic analysis.
The risk is defined as the product between the slope hazard and the vulnerability. Since the slopes are all directly hanging on the motorway, they all show the same degree of vulnerability (100%) and, consequently, the risk zonation corresponds to the hazard zonation.
In order to assess the exposition to the risk associated with rock fall and to prioritize interventions, a classification scheme was developed, to identify, the most dangerous slopes among the eight slopes studied and those of them requiring more urgent remedial works. Since all slopes are hanging on the motorway the level of vulnerability is constantly high for all slopes and consequently the level of hazard can be directly compared. The very small space between the slope and the road corridor do not leave any other possibility.
To define the level of danger, and then the hazard level, the following items and ratings have been taken in account:
- Geometrical characteristics of the berm (height, gradient, length of the road below the slopes), considered as part of global stability and stability of single berm;
- Global stability of the slope expressed in terms of unstable theoretical volumes per slope square meter (unit volume), varying from 0 to 10 m3/m2;
- Stability of the single berm expressed as unstable theoretical volumes per square meter of slope, on slope height (varies from 0 to 4.4);
- Presence of water: dry (0), damp (1) or seepage (2) are distinguished;
- Presence of existing protection measures, ranging from 0 (absence or presence of non consistent protections) to -1 (existing protections).
According to the above mentioned index, a final rating was assigned to each slope (or geo – structural homogeneous sub-domain), as reported in Table 4. Taking in account the total rate, 3 levels of hazard were distinguished (Figure 12) and applied for the various slopes and domains.
The above defined hazard levels allowed for setting up a “Map of Rock Fall Hazard”. The maps were set up by subdividing each slope in regular mesh of 30 m x 30 m; for each mesh cell n hazard level was assigned on the bases of the above reported parameters. According to this, some preliminary typological remedial works have been proposed, for different levels of hazard, as shown in Table 5.
5 CONCLUSION
The paper aims to demonstrate the importance of advanced techniques in the slope geo-structural and geometrical survey to improve the quality of the stability analysis.
The study of the stability conditions of 8 rock slopes hanging on a motorway in Far East have been carried on by means of the key block method based on accurate rock mass surveys. The surveys have been performed by both classical techniques and laser scanning acquisition; the last one has allowed to determine the DSM and the slope point clouds that have then been treated by a specific software developed by the University of Parma for the determination of the rock discontinuities visible on the rock faces by means of the application of a segmentation algorithm. Discontinuity dip, dip direction and position have also been computed. Statistical data analysis at different scales supported by in situ observation allowed the determination of the rock mass structures in terms of joint set orientation and spacing
Consequently finite and removable rock blocks have been determined in terms of kinematics mode and maximum and average unstable volumes. The acquired data will then be utilised for the design of stabilization works and for the slope risk assessment. On the basis of stability computations and in situ observations a stability index has been defined for both the global slope and singular berm. Using this index coupled with geometrical characteristics of the slopes, derived from DSM file, a rating system has been adopted for the hazard zonation. This procedure has also allowed to set up a quantitative way to compare the hazard among the slopes thus suggesting typological remedial and hazard mitigation works, for the various kinematisms.
REFERENCES
Costa G, Carrara A, Agliardi F, Campedel P, Frattini P (2006). Valutazione della pericolosità da caduta massi tramite un approccio integrato statistico e deterministico. Giornale di Geologia Applicata 4, pp. 41-48.
Corominas J, Copons R, Vilaplana JM, Altimir J, Amigò J (2003). Form landslide hazard assessment to management, the Andorran experience. Int Conf on Fast Slope Movements, Prediction and Prevention for Risk Mitigation, AGI, pp. 111-118.
Dillon WR, Goldstein M (1984). Multivariate Analysis Methods and Applications, Wiley, New York, 587 pp.
Felus YA (2006). On linear transformations of spatial data using the structured total least norm principle. Cartography and Geographic Information Science, vol. 33, July 2006, pp. 195-205.
Ferrero AM, Forlani G, Grasso PG, Migliazza M, Rabbi E, Roncella R (2007). Analysis of stability condition of rock slope lying a far East motorway based on laser scanner surveys. 11th ISRM Congress, Lisbon.
Ferrero AM, Forlani G, Roncella R, Voyat HI (2008). Advanced geo structural survey methods applied to rock mass characterization. Rock mechanics and Rock Engineering. Springer Wien New York, vol 4(2), pp. 631-665.
Fischler M and Bolles R (1981). Random sample consensus: a paradigm for model fitting with application to image analysis and automated cartography. In Commun. Assoc. Comp. Mach., 24(3), pp 81-95.
Goodman RE, Shi GH (1985). Block theory and its application to rock engineering. Prentice Hall, London 338pp.
Héliot D (1988a). Conception et Réalisation d’un Outil Intégré de Modélisation des massifs Rocheux Fracturés en Blocs. Thèse, Institut National Polytechnique de Lorraine
Héliot D (1988b) Generating a Blocky Rock Mass. Int. J. Rock Mech. Sci.& Geomech. Abstr. Vol. 25(3), pp. 127-138.
Interreg IIc (2001). Prévention des mouvements de versants et des instabilités de falaises: confrontation des méthodes d’étude d’éboulements rocheux dans l’arc Alpin, Interreg Communauté européenne.
ISRM (1978). Suggested Methods for the Quantitative Description of Discontinuities in Rock Masses, Commission for standardization of Laboratory and field test.
Jaboyedoff M., Dudt J.P., Labiouse V., 2005. An attempt to refine rockfall hazard zoning based on the kinetic energy, frequency and fragmentation degree, Nat. Hazards Earth Syst. Sci., vol. 5, pp. 621-632.
OFAT, OFEE, OFEFP, 1997. Recommendations. Prise en compte des dangers dus aux mouvements de terrain dans le cadre des activités de l’aménagement du territoire. Edited
by OFAT/OFEE/OFEPF, Bern, avaible
at:http://www.planat.ch/resources/planat_product_fr_1032.pdf.
Rock3D. Key block theory based three-dimensional rock block analysis. Manual. Geo&Soft.
Varnes DJ and IAEG Commission on Landslides and Other Mass-Movements (1984). Landslide hazard zonation: a review of principales and practice. UNESCO Press, Paris, 1984.
LIST of CAPTATIONS
Figure 1. Profile of one (W4) of the 8 slopes present along the highway segment.
Figure 2. Solid model obtained by laser scanning of the slope W4: a) whole slope; b) high precision survey on a berm window. Figure 3. Methodological flow chart
Figure 4. Principal joint sets observed on one of the 8 rock slopes (W4).
Figure 5. Positions of surveyed planes, by using RockScan program, in one of the survey window
Figure 6. Geometrical discontinuity plane characteristic and point density value considered to define the accuracy of the orientation plane definition
Figure 7. Dip (a) and dip direction (b) accuracy computation for a rectangular shape (h=5 and b=1) of discontinuity plane for different value of plane inclination (dip) and point density.
Figure 8. Joint set identification determined by the compass survey (a) and by laser scanner DTM (b) on the same zone of the slope: slope W4 – traverse 3 (lower hemisphere).
Figure 9. Joint pyramids obtained for slope W4 and relative types of kinematics, maximum volume of the free and removable blocks and corresponding safety factor. In the lower side of the figure a statistical reconstruction trace map and free and removable blocks identified for three-dimensional sliding along the intersection J3-J4 (red and blue lines in Figure 4) are reported.
Figure 10. Some pictures reporting the in situ planar (a and b) and 3D (c and d) sliding phenomena. Figure 11. Resoblock rock slope reconstruction of slope W2 and sliding blocks computed by BSA code.
Figure 12. Danger – Probability of rock failure diagram to obtain the hazard level (from OFAT, OFEE, OFEFP, 1997 modified).
TABLES
Table 1. Joint sets orientation angles and average spacing value obtained by statistical analysis of the data collected along each slope by traditional and LIDAR surveys.
Table 2. Geometrical characteristics of the analysed slopes and results obtained in terms of number of possible kinematisms, number and volume of detachable (free and removable) blocks.
Table 3. Parametric analysis results by varying the slope dip between dip value obtained by laser scanner results DTM, up to the minimum dip determining unstable blocks
Table 4. Partial and total hazard rating obtained for each slope. Table 5 Typological proposed remedial works for the different slopes.
FIGURES
Figure 2. Solid model obtained by laser scanning of the slope W4: a) whole slope; b) high precision survey on a berm window.
Figure 3. Methodological flow chart
Topographical survey direction
rectangle base b = 1;
grid spacing = k*min(b,h)
rectangle
height h
0.2
1
5
grid spacing
(k=0.1)
0.02 0.1 0.1
# pts
561 121
56
1
grid spacing
(k=0.2)
0.04 0.2 0.2
# pts
156
36
15
6
grid spacing
(k=0.5)
0.1 0.5 0.5
# pts
33
9 33
grid spacing
(k=1)
0.2
1
1
# pts
12
4 12
Figure 6. Geometrical characteristic of planes and point density value considered to define the accuracy of the orientation plane definition.
Figure 7. Dip (a) and dip direction (b) accuracy computation for a rectangular shape (h=5 and b=1) of discontinuity plane for different value of plane inclination (dip) and point density.
(a) (b)
Major joint sets
Compass survey LIDAR survey Dip DirectionDip Dip DirectionDip
J1 76 242 77 241
J2 72 006 88 195
J3 37 192 44 224
Slope 88 200 88 200
Figure 8. Joint set identification determined by the compass survey (a) and by laser scanner DTM (b) on the same zone of the slope: slope W4 – traverse 3 (lower hemisphere).
Kinematis m Joint / Intersec tion Block ID BlockMax Volume [m3] Safet y Facto r SF Planar sliding J3 1000 1 5.200 0.937 Wedge sliding J3-J4 1001 1 0.008 0.900 J2-J4 1010 1 0.134 0.510
Figure 9. Joint pyramids obtained for slope W4 and relative types of kinematics, maximum volume of the free and removable blocks and corresponding safety factor. In the lower side of the figure a statistical reconstruction trace map and free and removable blocks identified for three-dimensional sliding along the intersection J3-J4 (red and blue lines in Figure 4) are reported.
Figure 10. Some pictures reporting the in situ planar(a and b) and 3D (c and d) sliding phenomena. c) W4. intersection J2 – J4. b) W2. along set J3(160°/51). a) W4. along set J3 (212/35) d) W2. intersection system J3 – J4. 3D sliding Planar sliding
HAZARD LEVEL and RATING
Low to medium 0 ÷ 1 Medium to High
High to Very High
1 ÷ 5 > 5 DANGER High to very high Medium to high Low to medium High to
very highMediumto highLow to medium PROBABILITY OF ROCK FAILURE
Figure 11. Resoblock rock slope reconstruction of slope W2 and sliding blocks computed by BSA code.
TABLES
Table 1. Joint sets orientation angles and average spacing value obtained by statistical analysis of the data
collected along each slope by traditional and LIDAR surveys.
Slope Joint Sets Dip[°] Dip Dir [°] Spacin g [m] 1 (311 data) J1 80 309 0.5 J2 89 174 0.6 J3 72 75 0.8 J4 53 146 0.5 J5 48 83 0.7 2 (1100 data) J1 87 42 0.7 J2 81 341 0.7 J3 51 160 0.45 J4 54 232 1.5 3 (338data) J1 33 285 1.2 J2 77 329 0.6 J3 71 248 0.5 J4 84 63 0.6 4 (376 data) J1 69 10 0.6 J2 82 239 1 J3 35 212 0.65 J4 62 136 0.7 5 (419 data) J1 79 9 0.4 J2 77 239 1.2 J3 83 132 0.8 J4 48 191 0.6 J5 26 207 1.0 6 (400 data) J1 70 264 0.5 J2 80 12 0.7 J3 49 168 1 J4 79 134 0.7 J5 76 302 1 7 (467 data) J1 82 212 0.3 J2 50 187 0.6 J3 41 288 0.7 J4 45 40 0.5 8 (515 data) J1 77 63 0.4 J2 75 215 0.43 J3 44 215 0.5 J4 70 268 0.64 J5 78 11 0.5
Table 2. Geometrical characteristics of the analysed slopes and results obtained in terms of number of
possible kinematisms, number and volume of detachable (free and removable) blocks.
Table 3.
Parametric
analysis results by varying the slope dip between dip value obtained by laser scanner results DTM, up to
the minimum dip determining unstable blocks
Slop e scanner Laser Parametr ic analysis N OTES
Dip directioDip n
Dip
"max" Observed variation in the stability conditions with slope dip W1 57 164 No changes
W2 59 161 67
Zone 1-3 (DD 155°). No changes Zone 2 (DD 170°).
With dip equal 59° kinematism 1110 (3D sliding along J1-J4) is not more present. This kinematism is present from a slope minimum dip equal 67°.
W3 65 255 No changes W4 54 196 65
Kinematism 1010 (sliding along J2-J4) and 1001 (sliding along J3-J4) are not more present with dip equal 54°.
This kinematism is present from a slope minimum dip equal 65°. Kinematism with max volume (> 5 m3) is always present
W5 40 190 62-51
Zone 1 (DD 220°). With dip equal 40° Kinematism 10101 (sliding along J3-J4), 10001 (sliding along J4) and 10011 (sliding along J2-J3). Kinematism with max volumes (10101: > 3.5 m3 e 10001 > 2 m3) are present from a minimum slope dip
equal 62°.
Zone 2 (DD 180°) With dip equal 40° kinematism 11001 (sliding along J2-J4), 10001 (sliding along J4) and 10011 (sliding along J2-J3). Among these kinematism with max vol. (10001 > 7 m3) is present from minimum slope dip equal 51°. W6 71 178 No changes
W7 64 198 No changes
W8 49 207 52-71 Kinematism 10001 (planar sliding along J3) e 00111 (sliding along J1-J2) are not more present with slope dip equal 49°. Minimum dip equal for one sliding 52° and 71° for both.
Table 4. Partial and total hazard rating obtained for each slope
Slop e
Domai n
Berm Stability Global Stability [m3/m2] Wate r Existing protection Total rating W1 0.7 1 1 -1 1.7
Slo
pe
Heig
ht
Leng
th
Di
p
Number
of
Kinemat
ism
Free
and
Remova
ble
Blocks
Max
Block
Volu
me
Averag
e Block
Volume
[m]
[m] [°]
#
#
[m
3]
[m
3]
W1
40
180 60
4
23
1,118 0,291
W2 135
750 75
6
59
23,0
1,830
W3
30
100 75
3
15
0,556 0,107
W4
30
90
75
3
9
5,217 0,614
W5
40
50
80
6
31
5,430 0,896
W6
50
130 82
3
28
3,411 0,336
W7
50
250 85
3
38
4,342 0,588
W8
50
50
80
4
22
0,983 0,134
W2 a 0.1 1.3 1 -1 1.4 b 3.5 10 1 -1 13.5 c 0.4 0 1 0 1.4 W3 0.3 0 0 0 0.3 W4 0.1 1 0 0 1.1 W5 ab 0.90.4 22 22 00 4.94.4 W6 4.4 1 2 0 7.4 W7 0.1 0.3 2 0 2.4 W8 0.1 0.2 0 0 0.3
note: the grey hues are the same of the hazard levels reported in figure 12
Table 5. Typological proposed remedial works for the different slopes.
Remedial work SLOPES 3 8 4 2a 2c 1 7 5b 5a 6 2b Monitoring X X X X X X X X Real time monitoring X X X X Scaling X X X X X X X X X X X Bolting X X X X X X X X X Mesh X X X X X X Fences X X X Re-profiling X X X X Canopy X
