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- 1. Original Paper Landslides (2011) 8:221–231 DOI 10.1007/s10346-010-0246-4 Received: 16 March 2009 Accepted: 1 November 2010 Published online: 2 December 2010 © Springer-Verlag 2010 Anna M. Ferrero I Maria Migliazza I Riccardo Roncella I Elena Rabbi Rock slopes risk assessment based on advanced geostructural survey techniques 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 utilized to identify the best methodology for risk mitigation. Keywords Rock slopes . Risk assessment . Advanced geostructural survey techniques 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 (Fig. 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 Light Detection and Ranging (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 10 m 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 RANdom Sample Consensus (RANSAC) algorithm (Fischler 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 (Fig. 2a). A second survey with high precision (Fig. 2b), was carried out on smaller slope portions (10×10 m 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, and 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 Fig. 3. Geostructural studies Geological setting The slopes are composed of porphyriticbiotite 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. Landslides 8 & (2011) 221
- 2. Original Paper GPS LIDAR Compass on traverse Georeferenced Points Clouds of Georeferenced Points Georeferenced Digital Image ROCKSCAN 3D Digital Terrain Georeferenced Model Geological and Geostructural Survey Statistical Analysis Fig. 1 Profile of one (W4) of the eight slopes present along the highway segment 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. Geostructural survey Traditional methods Geological-geostructural mapping was carried out for the eight 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 (Fig. 4); then, a series of geostructural surveys along scanlines of 10 m lengths were performed. More than 50 geostructural traverses were performed with a total of about 2,400 discontinuities collected in terms of Joint sets definition Editing protection measures Rock Fall Hazard Maps Propose of typological remedial works Fig. 3 Methodological flow chart 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 analyzed separately for each traverse and together for the eight 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. Fig. 2 Solid model obtained by laser scanning of the slope W4: a whole slope, b high precision survey on a berm window 222 Landslides 8 & (2011) Stability Analysis
- 3. Fig. 4 Principal joint sets observed on one of the eight rock slopes (W4) 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. Laser scanner survey The DSM generation for the eight slopes has been obtained by using the LIDAR 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-ofﬂight, the sensor-to-object distance is computed. Terrestrial lasers are equipped with two mirrors mounted on two orthogonal axes; when the instrument is leveled, the synchronized rotation provides scanning in azimuth and zenith. The polar coordinates of the target are then converted to a local Cartesian frame with theorigin in the instrument center, 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 2,000 to 12,000 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 LMSZ420i 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 0.05× 0.05 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 10×10 m (a point every centimeter, 84 mm lens). The examined slopes have been excavated by means of blasting techniques (Fig. 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. Fig. 5 Positions of surveyed planes, by using RockScan program, in one of the survey window Landslides 8 & (2011) 223
- 4. Original Paper rectangle base b = 1; grid spacing = k*min(b,h) rectangle height h 0.2 1 grid spacing (k=0.1) # pts grid spacing (k=0.2) # pts grid spacing (k=0.5) # pts grid spacing (k=1) # pts 0.02 561 0.04 156 0.1 33 0.2 12 0.1 121 0.2 36 0.5 9 1 4 5 0.1 561 0.2 156 0.5 33 1 12 Topographical survey direction grammetry) 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 (Fig. 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 10–100% (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 Fig. 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 ¼ Ax þ d 224 Landslides 8 & (2011) a 1.4 12 pts 33 pts 156 pts 561 pts 1.2 Dip accuracy [deg] A local network has been implemented, documented, and surveyed by means of a fast static GPS survey with a Trimble 4,000 ssi double-frequency receiver and a Trimble 4,600 singlefrequency 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 1,105 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 realize 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 analyzed 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 (Fig. 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 photo- 1 0.8 0.6 0.4 0.2 0 10 b Dip Direction accuracy [deg] Fig. 6 Geometrical discontinuity plane characteristic and point density value considered to define the accuracy of the orientation plane definition with parameters x and observables y (Felus 2006). Without loss of generality, the equation of a plane through the origin ax þ by þ cz ¼ 0 has been considered; the functional model is of the form F(y, x)=0 and must be linearized with 20 30 40 50 60 DIP [deg] 70 80 90 7 12 pts 33 pts 156 pts 561 pts 6 5 4 3 2 1 0 10 20 30 40 50 60 70 80 90 DIP [deg] Fig. 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
- 5. respect to the observables as well as with respect to the parameters. We have therefore: D ¼ @F ; @y A¼À @F ; @x d ¼ ÀF ðxo ; yo Þ 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: À À1 ÁÀ1 CXX ¼ At ðD CYY Dt Þ A The orientation of the plane unit normal vector (pole) pointing upwards can be expressed as a function of the plane’s coefﬁcient as dip ¼ arccosðcÞ dip direction ¼ k Æ arctanða; bÞ 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 Fig. 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 Fig. 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 (a) Major joint sets J1 J2 J3 Slope (b) Compass survey Dip Dip Direction 76 242 72 006 37 192 88 200 Dip 77 88 44 88 LIDAR survey Dip Direction 241 195 224 200 Fig. 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) Landslides 8 & (2011) 225
- 6. Original Paper 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. 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 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 thehierarchic clustering procedure; kinematic analysis based on the key block theory (Goodman and 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 226 Landslides 8 & (2011) Joint Sets Dip [°] Dip Dir [°] 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 J1 87 42 0.7 J2 81 341 0.7 J3 51 160 0.45 J4 54 232 1.5 J1 33 285 1.2 J2 77 329 0.6 J3 71 248 0.5 J4 84 63 0.6 J1 69 10 0.6 J2 82 239 1 J3 35 212 0.65 J4 62 136 0.7 J1 79 9 0.4 J2 77 239 1.2 J3 83 132 0.8 J4 48 191 0.6 J5 Geo-structural data analysis and comparison Orientation data calculated from LIDAR and those measured through compass have been compared to validate the system. In Fig. 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 utilized 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%. Slope 26 207 1.0 J1 70 264 0.5 J2 80 12 0.7 J3 49 168 1 J4 79 134 0.7 J5 76 302 1 2 (1,100 data) 3 (338data) 4 (376 data) 5 (419 data) 6 (400 data) 7 (467 data) Spacing [m] 82 212 0.3 50 187 0.6 J3 41 288 0.7 J4 45 40 0.5 J1 77 63 0.4 J2 75 215 0.43 J3 44 215 0.5 J4 70 268 0.64 J5 8 (515 data) J1 J2 78 11 0.5 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
- 7. 0111 4 0011 0110 0101 0001 1001 Kinematism 1 0100 Planar sliding 0000 1100 1000 slope Wedge sliding Joint / Intersectio n Block ID J3 J3-J4 J2-J4 10001 10011 10101 Max Block Volume [m3] 5.200 0.008 0.134 Safety Factor SF 0.937 0.900 0.510 1011 3 1110 2 1010 Fig. 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 Fig. 4) are reported 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 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 Table 2 Geometrical characteristics of the analyzed slopes and results obtained in terms of number of possible kinematisms, number, and volume of detachable (free and removable) blocks Slope Height Length Dip [m] [m] [°] Number of Kinematism # Free and Removable Blocks # Max Block Volume 3 Average Block Volume [m ] [m3] 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 Landslides 8 & (2011) 227
- 8. Original Paper to deﬁne their 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 analyzed 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 SF was computed by the limit equilibrium method. Results are reported in Fig. 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 analyzed 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 utilized 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 Fig. 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 (Héliot 1988a, 1988b). The analyses follow the tectonic history of the formation as a continuous medium is 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 Slope Laser scanner Dip Dip direction W1 57 164 W2 59 161 Parametric analysis Dip “max” Notes Observed variation in the stability conditions with slope dip No changes 67 Zone 1–3 (DD 155°). No changes Zone 2 (DD 170°). With dip equal 59° kinematism 1,110 (3D sliding along J1–J4) is not more present. This kinematism is present from a slope minimum dip equal 67° W3 65 255 W4 54 196 No changes 65 Kinematism 1,010 (sliding along J2–J4) and 1,001 (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 10,101 (sliding along J3–J4), 10,001 (sliding along J4) and 10,011 (sliding along J2–J3). Kinematism with max volumes (10,101: > 3.5 m3 e 10,001>2 m3) are present from a minimum slope dip equal 62° Zone 2 (DD 180°) With dip equal 40° kinematism 11,001 (sliding along J2–J4), 10,001 (sliding along J4) and 10,011 (sliding along J2–J3). Among these kinematism with max vol. (10,001>7 m3) is present from minimum slope dip equal 51° W6 178 No changes W7 64 198 No changes W8 228 71 49 207 Landslides 8 & (2011) 52–71 Kinematism 10,001 (planar sliding along J3) e 00,111 (sliding along J1–J2) are not more present with slope dip equal 49°. Minimum dip equal for one sliding 52° and 71° for both
- 9. Planar sliding a) b) W2. along set J3(160˚/51). d) W4. along set J3 (212/35) W2. intersection system J3 – J4. 3D sliding c) W4. intersection J2 – J4. Fig. 10 Some pictures reporting the in situ planar (a and b) and 3D (c and d) sliding phenomena 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 while 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 (1,265 blocks reproducing a rock mass volume of 100×40×40 m3 (X, Y, Z)) set up on this basis for one slope and the sliding phenomena computed by the 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. Hazard assessment methodology and results In order to plan and deﬁne the eventual remedial works needed to reduce the rockfall risk level, a hazard level assessment procedure based on the use of intensity–frequency matrix diagram (OFAT, OFEE, OFEFP 1997; Interreg 2001; Costa et al. 2006; Corominas et Fig. 11 Resoblock rock slope reconstruction of slope W2 and sliding blocks computed by BSA code Landslides 8 & (2011) 229
- 10. Original Paper DANGER HAZARD LEVEL and RATING High to very high Low to medium 1÷5 High to Very High Medium to high 0÷1 Medium to High >5 Low to medium High to Medium very high to high Low to medium PROBABILITY OF ROCK FAILURE Fig. 12 Danger–probability of rock failure diagram to obtain the hazard level (from OFAT, OFEE, OFEFP 1997 modified) 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 Fig. 12. The eight slopes have been preliminary analyzed focusing on the characterization of danger (intensity or magnitude of a localized 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 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. Table 4 Partial and total hazard rating obtained for each slope Slope Domain Global stability [m3/m2] Berm stability Water Existing protection Total rating 0.7 1 1 −1 1.7 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 a 0.9 2 2 0 4.9 b 0.4 2 2 0 4.4 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 W1 W2 W5 The gray hues are the same of the hazard levels reported in Fig. 12 Table 5 Typological proposed remedial works for the different slopes Remedial work SLOPES 3 8 4 2a 2c 1 7 5b X X X X X X X X X X X X X X X Bolting X X X X X X Mesh X X X X X X X X Monitoring Scaling Fences Re-profiling Canopy 230 Landslides 8 & (2011) 6 2b X Real time monitoring 5a X X X X X X X X X X X X X X X X
- 11. 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 subdomain), as reported in Table 4. Taking in account the total rate, three levels of hazard were distinguished (Fig. 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 30×30 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. 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 eight 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 utilized 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 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 Costa G, Carrara A, Agliardi F, Campedel P, Frattini P (2006) Valutazione della pericolosità da caduta massi tramite un approccio integrato statistico e deterministico. G Geol Appl 4:41–48 Dillon WR, Goldstein M (1984) Multivariate analysis methods and applications. Wiley, New York, 587pp Felus YA (2006) On linear transformations of spatial data using the structured total least norm principle. Cartogr Geogr Inf Sci 33:195–205 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 Mec Rock Eng 4(2):631–665 Fischler M, 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):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 25 (3):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 JP, Labiouse V (2005) An attempt to refine rockfall hazard zoning based on the kinetic energy, frequency and fragmentation degree. Nat Hazards Earth Syst Sci 5:621–632 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. Available 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, IAEG Commission on Landslides and Other Mass-Movements (1984) Landslide hazard zonation: a review of principales and practice. UNESCO, Paris A. M. Ferrero ()) : M. Migliazza : R. Roncella Department of Civil Engineering, of the Environment, of the Territory and Architecture, University of Parma, Parma, Italy e-mail: annamaria.ferrero@unipr.it E. Rabbi Geodata, Turin, Italy Landslides 8 & (2011) 231
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