Stability analysis of excavations in jointed rocks - the computer program RESOBLOK

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1 Stability analysis of excavations in jointed rocks - the computer program RESOBLOK Thoma Korini Faculty of Geology and Mining, Tirana, Albania Véronique Merrien-Soukatchoff LAEGO, Ecole des Mines de Nancy, Nancy Université, Nancy, France ABSTRACT The paper presents the computer program RESOBLOK able to represent a fractured rock mass in the form of an assembly of blocks. The fractures are represented by plans, (infinite or limited by other fractures) in a statistical or deterministic way or like polygons. RESOBLOK has a downstream module bsa allowing the stability analysis of blocks by limit equilibrium or by minimization of energy. The potential movements considered are the free fall, the slip (according to one or more plans) and the rotation. The blocks are supposed to be rigid. Parameters necessary for the analysis are the density of blocks, cohesion and the angle of friction of the joints. Computation is iterative: in a first phase the stability of the blocks in the vicinity of a free face is examined and those whose factor of safety is lower than a fixed value (generally 1) are considered unstable and removed, which modifies the free face of the model. In the following iterations, the stability of the blocks at the boundary of the new free face is studied until there are no more instable blocks. The geometrical movements and the computation of the resultant of forces are based on a vectorial method developed by Warburton. A bolting pattern, specified by the spacing, the length and the resistance of the bolts can be taken into account in the analysis of stability. The code was used for the representation and dimensioning of the underground excavations (tunnel, mines) or in the road slopes, open pit mines, natural slopes, etc. 1 INTRODUCTION The stability analysis of mining workings must generally take in account the role of discontinuities. The fractures crossing the rock mass, because of their reciprocal intersection, determine blocks of different size and shape. Among these blocks, those that are situated next to the surface of the excavation risk to move toward the excavated area. The instability appears thus as fall or slip of blocks (Figure 1). Its evolution leads, either to obtain a new steady shape of the excavation, either the total loss of the stability while returning the excavation unusable. The progress made the last twenty years has led to better represent the geometry of the discontinuities in the rock mass as well as to improve the representation of the behaviour of the discontinuities and of the rock mass. The geometrical representation of the rock mass has an important influence on the subsequent stability computation. Many computer codes are developed in order to study the fractured rock mass and are able to represent their geometry and their mechanical, hydraulical or thermical behaviour as well as coupled actions. Among these, the code RESOBLOK, that knew its beginnings toward the end of the years '80 (Heliot, 1988), is developed in the

underground excavation goal of creation of databases

Modules able to make a quick stability analysis (Baroudi

1990), to display these databases and the histograms of

the area of the surface have been added to the first

The quite flexible structure of RESOBLOK has able to

by other modelling software either directly or

Although the different 3D discontinuous computer codes

base, due to the richness of joint generation method and

$fractured rock mass represented as blocks assembly and$ included joints.

2 Figure 1. Examples of unstable blocks on the sidewall of an underground excavation goal of creation of databases representing the rock mass. Modules able to make a quick stability analysis (Baroudi et al. 1990), to display these databases and the histograms of the volume of blocks (and of the unstable blocks) or of the area of the surface have been added to the first version. The quite flexible structure of RESOBLOK has able to include in its data base a lot of the information usable by other modelling software either directly or indirectly through appropriate interfaces. Although the different 3D discontinuous computer codes of the rock mechanics have developed their own data base, due to the richness of joint generation method and integrated elements RESOBLOK is useful for numerous practices. 2 PRESENTATION OF COMPUTER CODE RESOBLOK RESOBLOK is an integrated modelling tool taking into account a fractured rock mass represented as blocks assembly and included joints. It architecture is organized in modules as describes below: - at first, a geometrical module able to represent the rock mass as blocks separated by joints "from geological evidence" (Heliot, 1988) and including joints of finite extent; - next, a set of downstream modules allowing to study the blocks assemblage (Figure 2). Figure 2. The modular organization of RESOBLOK

3 2.1 Creation of blocks database The geometrical representation is computed by a blocks generator named "bg". This generator needs as input a "scenario file" which gathers the information representing the studied rock mass and supply an output file describing the blocks assemblage generated. The output file is the so-called "data base" and depict the geometry of the blocks, the joints and the mechanical properties associated with both the joints and the rock mass. The studied zone called "zone of interest" defined as a rectangular parallelepiped is subdivided in blocs by the progressive insertion of discontinuities (fault, strata ) defined deterministically or stochastically. In the last case a set of fractures is defined by a first statistical law characteristic of the orientation and a second one defining the spacing. The fractures persistence is taken into account by stopping their extension on another set of fractures or by defining the fracture as polygonal (Bennani, 1990, Thoraval et al, 2005) In order to help the data input, and to manage the data error a processing specific language named BGL (Block Generation Language) has been developed (Heliot, 1988). BGL allow writing a scenario-file which will be interpreted by the "bg" command for generating the blocks assemblage as a database file. When the discontinuities are stochastically defined, the same scenario file allows generating, via the module bg, different blocks assemblies distinguished by a so called "simulation number". The exploitation of the database thus created is done by different modules (Figure 2). Among these, we can distinguish the module bd (Block Display), the module bh (Block Histogram) and the module bsa (Block Stability Analysis). 2.2 Stability Analysis module (bsa) The module bsa has been realized in order to perform a stability analysis of the Figure 3. Block stability analysis

4 excavations realized in blocky rock masses. It allows analysing the stability of blocks in contact with an excavation by simple computations based on limit equilibrium (Asof, 1991). bsa checks if isolated blocks next to an underground or an open pit excavation are able to detach. If possible, the boundaries of excavation change and the computation can goes one iteratively, until no more blocks are unstable. The stability analysis is based on Warburton s algorithm (Warburton, 1981) and followed two stages (see Figure 3): - the geometric analysis permit to exclude of further analysis the blocks that are geometrically unremovable, - the mechanical analysis look at the possible movement of geometrically removable blocks and if possible compute the safety factor of the block taking into account the geotechnical properties of discontinuities and the density of blocks that are introduced in the scenario file. The potential movements examined are successively: Direct fall. If, due to gravity, direct fall is possible the block is declared unstable, but no safety factor can be computed (except in the case of support) because the joint is supposed to have no tension resistance, Movement parallel to one or several faces. In this case a factor of safety can be computed. If the movement is parallel to one or two faces limit equilibrium analysis is possible and the only parameters needed are the cohesion and friction angle of discontinuities that border the block as well as the density of the block. If the movement is parallel to more than two faces, limit equilibrium analysis is not possible but an energy based analysis can be used. The energy based analysis required additional parameters as normal and shear stiffness of the discontinuities. A bsa run need 3 stages: the data input, the computation and the output analysis. In * Zone of interest * Discontinuities sets - deterministic - statistical --> geological scenario * Excavation bg realisation1 blocks data base realization n 1 bsa realisation 1 Data file with BGL bg realisation 2 bg realisation i blocks data base realization n 2 bsa realisation 2 bsa realisation i Mean stability analysis bg realisation n bsa realisation n blocks data base realization n n Figure 4. Stochastic aspects of RESOBLOK and bsa

5 the case fracture are stochastically defined, for a unique scenario file there are several realisations of the blocks assembly (identified by different simulation number). bsa module realizes a stability analysis for each blocks assemblage and the results can be processed statistically: number and volume of unstable block, min, max volume (see Figure 4). One of the advantage of RESOBLOK software lies on the fact that the result of the stability analysis can be analysed statistically. Baroudi et al. (1990 and 1992) have shown on a case of slope stability problem that a minimum of 50 geometrical simulations was to be performed in order to achieve a reasonable outcome in the stability analysis. Running 50 simulations, in this case allows getting stable values of the mean, the standard deviation and the histogram of variables such as the mean volume of unstable blocks, the total unstable volume and the number of unstable blocks. This result is also confirmed by later studies (Merrien-Soukatchoff et al., 2007). 2.3 Stability calculation of blocks reinforced by bolting If the number of unstable blocks is important, in order to ensure the stability of the working, one possible remediation can be the use of bolts or cables to reinforce the ground. Its role is taken into account in BSA by the fact its resistance prevents the direct fall or the sliding of isolated block and may avoid the propagation of instability by stabilizing the key blocks Calculation of factor of safety of blocks reinforced by bolting Two types of behaviours can be taken into account in the analysis: the active reinforcement or the passive reinforcement. The first one rather corresponds to prestressed bolts and the second one to fully grouted anchor (Seegmiller, 1982). In both cases the effect of bolts is taken into account (Korini et al., 1993) by adding in the forces balance a force which module is the strength of the bolt and acting in the direction of the bolt. The force induced by the bolt is resolved in: - A force parallel to the movement (opposite direction); - A force perpendicular to the movement direction. In the case of direct fall of the block only the first component is taken into account (suspension role). In the case of sliding along one or more faces the force parallel to the movement direction is added to the shearing of the discontinuity and the force perpendicular to the movement direction increase the normal stress, so the limit shear strength. For active reinforcement the force resolved parallel to the movement is numbered among the driving forces whereas for passive behaviour it is numbered among the resisting forces. Depending on the case (active or passive reinforcement) the factor of safety is calculated as: a) active reinforcement Fc + Fnwtanϕ + Fnb tanϕ fsa = F F b) passive reinforcement Fc + Fnw tanϕ + Fnb tanϕ + Ftb fsp = Ftw with: f sa and f sp factor of safety (respectively for active and passive reinforcement); F c cohesion force on the sliding face; F nw normal component of active forces; F nb normal component of the force induced by bolts; F tw tangent component of active forces; F tb tangent component of the force induced by bolts. For all possible cases of instability (direct fall, sliding along a single face, wedge sliding, etc.) the formulation of factor of safety calculation is performed (Korini et al., 1993) Setting up a bolting pattern Generally, bolting is applied according to a regular pattern and the problem arising for tw tb

6 an excavation is to find a bolting pattern to prevent the block fall. Given that the distribution of fractures it s known, generally, only statistically, we obtain, by simulations, various block models ( bg command) and for every model are performed stability calculations with various bolting patterns. The bolting pattern is applied over a given surface, which corresponds to one or multiple faces defining the excavation. It can be the roof or the roof and the lateral faces of the underground room or gallery, or the slope of an open pit. The necessary parameters to define a bolting pattern ensure to obtain various patterns that we can be meet during the practice of exploitations Optimization of the bolting pattern The stability analysis consists of the determination of factor of safety of potentially instable blocks that eventually we reinforce with bolting. For every simulation and for every bolting pattern, the results are presented as number of unstable blocks, volume and weight of every unstable block and the total weight of unstable blocks. It is possible also to furnish the results by number (or volume) of blocks corresponding to various types of instability (free fall, plan sliding,... etc). Finally, for the set of simulations it is possible to calculate the average volume (and/or the average weight) of instable block for every bolting pattern. So, it is possible to choose as the best pattern the one that minimize the block instability. That choice can be confirmed by the use of histograms presenting the distribution of the number and the volume of unstable blocks for all the simulations (these histograms allows to verify if the blocks still unstable after bolting have a limited volume). In fact, the fall of small blocks going throw the bolting mesh is not really significant, because in practice the bolting goes with wire mesh that prevent the fall of small blocks. It is to remember that the choice of an optimal pattern must include the economical considerations. 3 STABILITY ANALYSIS EXAMPLE The analysis concerns an underground mining gallery (a length of 100m) realized in a blocky rock mass. The main sets of discontinuities are summarized in the Table 1 and are the result of a statistical analysis of the orientation and the interfractural distance. The zone of interest is a parallelepiped of 100m of length (x axis), 20m of width (y axis there) and 15m of height (z axis), while the excavation is composed of a mining gallery with dimension 4x4m (Figure 5a). The purpose of our analysis was to study the influence of discontinuity sets to the stability of the gallery and to propose solution to the improvement of the stability. Three sets of calculations were performed: 1- a model with no support and with a flat roof (Figure 5a); 2- a model with no support but with a cylindrical roof (Figure 5b); 3- a model with a flat roof and with a bolting support (Figure 5c). The Table 1. Data for discontinuity sets Set Mechanical Dip K of Spacing (m) Dip properties of joints Direction Langevin ( ) Standard Cohesion Friction ( ) Fisher Law Law Average deviation (kpa) angle ( ) Exp Lgnor Nor Exp

7 Figure 5. Models for stability analysis: a) no support and with a flat roof; b) no support with a cylindrical roof; c) flat roof with bolt support; d) representation of blocks for the case of a cylindrical roof. schema adopted is the one with a density of 0.7 bolts/m 2, length of 2m and a bearing capacity of 200kN. Figure 5d shows the representation of blocks for the case of a cylindrical roof. The module bsa were used to calculate the stability of each model. For each set of calculations were realized 60 simulations. Figure 6 shows the evolution of average volume of unstable blocks vs. number of simulations. It is clearly shown that the average volume of unstable blocks is divided by two when the roof is changed from flat to circular one and the reduction of unstable blocks is very remarkable for the model using a bolting mesh. The figures Figure 7, Figure 8 Figure 9 show examples of unstable blocks for particular simulations for the three models used for calculations. Average volume (in m 3 ) of unstable blocks Simulation number Flat roof (without bolts) Cylindrical roof (without bolts) Flat roof (with bolts) Figure 6. Variation in the average volume of unstable blocks vs. number of simulations

8 Figure 7. Unstable blocks for the flat roof, without support, for the simulation number1. Figure 8. Unstable blocks for the flat roof, with bolting support, for the simulation number1 Figure 9. Unstable blocks for the cylindrical roof, without support, for a particular simulation. 4 CONCLUSIONS The software RESOBLOK is a powerful computer tool permitting the simulation of the jointing of the rock mass from deterministically or statistically processed data. Associated to a method of analysis of stability of isolated blocks, it becomes a mean to forecast the instability risks and permits, the choice of optimal excavation orientation and shape as well as the calculation of bolting support. The bolting, introduced according to regular patterns, plays its role of support by anchoring the unstable blocks to the unremovable part of the rock mass. The answer on the stability of a bolted block is given by the calculation of the factor of safety, using the vectorial method of Warburton. The formulation of the security factor is given for all the possible cases of instability. The modelling has been limited to the only behaviour in traction of the bolt, what excludes some other modes of ruptures (shearing etc.). In the general case, the choice of a bolting pattern is made by the analysis of several possible propositions. The retained criterion is the minimization of the number of unstable blocks and their size, while also taking in account of the economic considerations and the complementary technical solutions (wire mesh and shotcrete). The method of calculation adopted, relatively simple, returns the fast stability analysis and permits the analysis of several patterns of bolting for several geometries of joints. The methodology of stability analysis has been partially illustrated by one example. Nevertheless, the application to real cases must be made progressively while comparing the results of the model to the observations and measures in situ and while improving progressively the knowledge concerning the jointing of the rock mass, the mechanical features and the hypotheses of the calculations.

9 REFERENCES Asof M. (1991), Etude du comportement mécanique des massifs rocheux fracturés en blocs (méthode à l'équilibre limite) : réalisation et application, Ph.D. thesis, LAEGO, Ecole des Mines, INPL, France, 142 p. Baroudi H., Hantz D., Asof M., Piguet J.P. (1992), Bench stability in open pit Mines: A methodology for jointed Rock masses, Régional Conference on fractured and jointed rock masses, Lake Tahoe, California, June 3-5, 1992 Baroudi H, Piguet J.P., Chambon C., Asof M. (1990), Utilization of the block generator "Resoblok" to complex geologic conditions in an open pit mine, Proceedings of the International conference on Mechanics of jointed and faulted rock, Vienna, Austria, April 18-20, 1990, Edited by A. A. Balkema. pp Bennani M. (1990), Maintenance et developpement d un outil intégré de modélisation de massifs rocheux fracturé en blocs, Rapport de D.E.S.S. Informatique, I.S.I.A.L. Nancy, 85p. Heliot D. (1988), Generating a blocky Rock Mass, International Journal of Rock Mechanics and Mining Science & Geomechanics Abstracts, Vol. 25, No. 3, June 1988, pp Korini, T., Merrien-Soukatchoff V., Bennani, M. (1993), Optimisation du soutènement par boulonnage des excavations creusées dans un massif rocheux fracturé en blocs. 4ème Colloque Franco-Polonais:Géotechnique et Environnement, Nancy, novembre 1993, pp (ISBN ). Merrien-Soukatchoff, V., Gasc-Barbier, M., Korini T. (2007), Influence from Geomodelling of a Fractured Rock Mass on the Mechanical Assessement, Felsbau, Rock and Soil Engineering, Journal for Engineering Geology, Geomechanics and Tunnelling, 4/2007, pp Seegmiller B.L. (1982), Artificial support of rock slopes, Third Int. Conference On Stability in Surface Mining, June 1981, Volume 3, New York, pp Thoraval A. (2005), Aide au dimensionnement de l exploitation de marbre en carrières souterraines par modélisation numérique, Evaluation et gestion des risques liés aux carrières souterraines abandonnées Séminaire de restitution et de valorisation des travaux, INERIS Réseau des LPC, ENPC, Paris, 11 mai, pp

Structurally controlled instability in tunnels

Structurally controlled instability in tunnels Introduction In tunnels excavated in jointed rock masses at relatively shallow depth, the most common types of failure are those involving wedges falling