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Keywords: drilling operation management

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Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2016, August 29–31, 2016

Paper Number: ISRM-EUROCK-2016-182

... Carlo simulation variation deformation modulus estimation GSI rock mass Hoek

**drilling****operation****management**strength input parameter rock mass property deformability property probabilistic approach Rock Mechanics and Rock Engineering: From the Past to the Future Ulusay et al. (Eds) ©...
Abstract

ABSTRACT: The strength and deformability properties of rock mass are required in many mining and civil engineering projects. As rock masses have a complex and uncertain nature, to deal with such complexity the use of probabilistic approaches seems to be more appropriate than the use of conventional deterministic approaches. In this paper, a recently presented quantitative approach was combined with the probabilistic approach to determine GSI value and predict rock mass strength and deformability parameters. Using the estimated GSI and measured intact rock properties the probability density distributions of rock mass strength and deformability properties were calculated through a Monte Carlo method. A comprehensive database is constructed using the information from the drill holes in the mine located in the Eastern part of Turkey. By means of the presented methodology a wide array of strength and deformability parameters to be used in any preliminary design studies were obtained. 1 INTRODUCTION Currently, a vast majority of the mineral extraction is conducted by underground and open pit mining operations. With the improvements in mining industry, mines have become progressively deeper leading to stability problems. To solve these problems empirical, numerical and analytical methods are frequently used. All of the mentioned methods require input parameters such as strength and deformability properties of rock mass. Conventionally, insitu large-scale tests are required to determine the rock mass properties. On the other hand such kind of test are generally considered as both time consuming and expensive, especially at the preliminary design stage. Therefore rock mass classification and characterization systems are frequently used to determine these strength and deformability properties. RMR (Bieniawski 1989), Q (Barton et al. 1974) and the GSI system (Hoek et al. 1995) are the widely used systems among others. In this paper, the GSI system is preferred by the authors for the determination of rock mass properties. The GSI system is based on the description of rock structure and block surface conditions. The strength and deformability properties of rock mass such as rock mass strength, deformation modulus (E m ), Hoek-Brown strength parameters (m, s and a) can be calculated by knowing the UCS, GSI and the material constant (m i ) values. Initially GSI values were determined at the field based on the geological description of rock mass (Hoek et al. 1995). Hoek et al. (2013) mentioned that the observations in the field would be made by qualified and experienced geologists or engineering geologists. Whereas, with the increased use of numerical modelling techniques the observations were made by individuals who did not have strong geological background. Therefore, recently Hoek et al. (2013) proposed the quantification of the GSI chart to increase the interpretability of the GSI chart. In the proposed chart two well established parameters such as joint condition (Jcond89) as defined by Bieniawski (1989) and rock quality designation (RQD) by Deere (1963) are used.

Proceedings Papers

Paper presented at the ISRM Regional Symposium - EUROCK 2015, October 7–10, 2015

Paper Number: ISRM-EUROCK-2015-164

... variable

**drilling****operation****management**realization point random parameter PEM strength parameter probabilistic numerical model dip direction ABSTRACT: Probabilistic wedge stability analyses of a cavern are carried out considering two sets of joints J1 and J2 as random parameters with uncertain...
Abstract

Abstract Probabilistic wedge stability analyses of a cavern are carried out considering two sets of joints J1 and J2 as random parameters with uncertain dip direction and strength parameters. Probabilistic numerical models are constructed employing Monte Carlo and four different point estimate methods. It is represented that due to the variability of the dip directions of the two joint sets J1 and J2, two failure modes are possible to take place comprising sliding on J1 and J2 as well as sliding on J1 only. The investigations reveal that with respect to the calculation of probability of failure, there is a good agreement among all methods but in respect of failure mode, some point estimate methods could never find the failure mode which corresponds to sliding on J1 only while some models are able to find this mode of failure if number of realization points or number of random variables are increased. 1 Introduction When stability of a geotechnical structure is investigated, uncertainties can be taken into account by means of a probabilistic model that in which a probabilistic tool is employed. Since there are various probabilistic methods, different probabilistic models could be created. Nowadays, Monte Carlo Simulation (MCS) as become very popular in geotechnical engineering because it can be used easily without needing to do complicated statistical calculations; as a result, some commercial geotechnical tools were equipped to MCS in order to make probabilistic models (Rocscience Inc. 2015). An important issue that is associated with MCS (Rubinstein & Kroese 2008), is this that when model computation is time consuming, it would be infeasible because small number of simulations leads to inaccurate results and on the other hand large number of simulation leads to inefficiency. Under such circumstances, point estimate method (PEM) (Rosenblueth 1975) is more applicable as it needs smaller amount of computations. Some workers on reliability such as (Zhou & Nowak 1988), (Harr 1989) and (Hong 1998) have commented on Rosenblueth's PEM in order to make some improvements. In previous studies (Ahmadabadi & Poisel 2014a, 2014b, 2014c), authors presented an intensive comparison among aforesaid PEMs and other probabilistic methods including MCS, First-order reliability method (FORM) (Hasofer & Lind 1974) and second-order reliability method (SORM) (Breitung & Hohenbichler 1989) utilizing illustrative examples of rock slope. Also, issues of Harr's and Hong's PEMs in respect of correlated non-normally distributed random parameters was addressed through the NATAF transformation (M.A. 1962). At the present study, abovementioned PEMs and MCS are compared with the help of an example of a cavern highlighting another shortcoming of probabilistic numerical models which employed PEMs.

Proceedings Papers

Paper presented at the ISRM Regional Symposium - EUROCK 2014, May 27–29, 2014

Paper Number: ISRM-EUROCK-2014-247

... methods.

**drilling****operation****management**active friction angle Reservoir Characterization Upstream Oil & Gas resistance rock slope variation Artificial Intelligence Engineering density function random variable rock engineering probabilistic analysis metals & mining reserves...
Abstract

Abstract A probabilistic analysis is applied to rock slope stability with an example case of a rock slope with translational potential failure mode. The capacity and the demand are represented as independent triangular random variables. The distribution of the factor of safety is found analytically and its reliability measures are evaluated, allowing for decisions to be taken in terms of risk and reliability. The same slope is examined in its limit state by applying the partial factors approach of Eurocode 7. The Eurocode design is compared to the traditional factor of safety and probability of failure. 1. Introduction Numerous uncertainties, arising from natural variability in space and time, experimental errors, imprecise information, insufficient knowledge, up-scaling, simplistic assumptions, etc., are pervasive in rock engineering. These are commonly taken into account, indirectly, in the traditional factor of safety design, where acceptable safety factors are selected through experience or regulation, depending on application and its importance (e.g. Priest & Brown 1983). Some drawbacks may be recognized in this approach (Yucemen et al. 1973). The same value of the safety factor is adopted (or imposed) for a particular type of application, regardless of the degree of uncertainty involved (Duncan 2000), the risk level associated with it, or the amount and quality of information available before and acquired during construction. The type of uncertainty is also relevant to rock engineering (Bedi & Harrison 2013) and its assessment essential for reliable design (Bagheri & Stille 2011). Limit States Design (LSD) in Eurocode 7 (CEN 2004) introduced several changes to the previous geotechnical design practice. Verification at the ultimate limit state requires that the design actions, increased to reflect a low probability of occurrence, be lower than the design resistances, which have been factored down to reflect prescribed (or intended) probabilities of being exceeded. The values of the partial factors of the characteristic actions and material parameters are largely associated to variability and other uncertainties and therefore the partial factors approach may be considered as a form of reliability based design, although for complex systems the relation of the partial factors to the intended failure probabilities may be somewhat difficult to observe. Calibration of the partial factor design equations has been primarily based on method a of Figure 1, where the relation between the various calibration methods considered by EN 1900 (CEN, 2002) is presented. There, the probabilistic calibration procedures are divided into Level II reliability and Level III probabilistic methods.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2013, October 23–26, 2013

Paper Number: ISRM-EUROCK-2013-127

...

**operation****management**jakubowski wedge geological modeling Upstream Oil & Gas stability analysis orientation Rock mechanics international journal support design geometry Reservoir Characterization reserves evaluation Simulation Mining Science plane rock mass kPa probability stochastic...
Abstract

Abstract In engineering practice, rock ledge stability analysis is often performed as a two-dimensional failure analysis, where the single sliding plane is defined by the problem geometry and not the actual joints geometry. This was the case with the Yard Trench Lead in Sunnyside Yard, an element of the East Side Access Project in NYC. A probabilistic wedge stability analysis, including surcharge load and rock bolt reinforcement, was presented and discussed as a design alternative. The transition from 2D to 3D and from a deterministic to a stochastic approach, with the use of the geological joint orientation data, was shown to provide a more realistic view of the initial support design and to have the potential of leading to reductions in the initial support costs. Introduction Reinforcement and support requirements in blocky rock mass have commonly been assessed by means of a rigid blocks limit equilibrium stability analysis. This approach has been confirmed by site observations and proven in engineering practice when empirical, rock mass quality classification-based methods are unable to project structural failure. The relevant solutions have been presented, inter alia, by Wittke (1965), Priest (1980), Lucas (1980) and Bray & Brown (1976). The problem of arbitrary polyhedral block stability analysis was solved by Warburton (1981), Goodman and Shi (1985), Lin and Fairhurst (1988) and others. The method put forward by Goodman and Shi (1985) was used in this study for computations. It is popular and refers not only to a particular block, but to blocky rock mass in general, as well. While most of the methods consider the sliding and falling modes of failure, the problem of rotational failure has also been addressed (Mauldon 1995a,Wittke 1990). As a result of the limited information on discontinuities and their highly stochastic nature, uncertainty constitutes the central problem of analyses and their interpretation in jointed, blocky rock mass. A solution to this problem is brought about by probabilistic methods, either analytical or simulation (for example, McMahon 1971, Priest & Brown 1983, Park et al. 2005, Hatzor 1993, Hoerger & Young 1990, Mauldon 1995b, Jakubowski & Tajdus 1995, Jakubowski 2011). The statistical description of a joint network is crucial for stochastic joint geometry modeling and probabilistic stability analysis in a blocky rock mass (Hudson & Priest 1983, Mauldon et al. 2001, Zhang & Einstein 2000, Kulatilake 2001, Shanley & Mahtab 1976, Chiles 1987, Dershowitz & Einstein 1988).

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2013, October 23–26, 2013

Paper Number: ISRM-EUROCK-2013-010

... on the model adopted to characterise and propagate uncertainty. machine learning Artificial Intelligence

**drilling****operation****management**reserves evaluation information Upstream Oil & Gas characterisation fuzzy number epistemic uncertainty Engineering agreement curve knowledge Bayesian...
Abstract

Abstract In this paper we show how the appropriate uncertainty model to apply in an analysis depends on the nature of the available information. We explore this through the analysis of a rock slope using probabilistic models that incorporate alternative subjectively assigned probability distributions. These alternatives mimic the opinion of multiple experts. The results are shown to depend strongly on the shape of the input distributions, and hence the expert opinion utilised. We conclude by showing that an analysis using fuzzy mathematics is more appropriate than a probabilistic approach when objective data are limited or absent, and present a novel technique for decision making using the results of a fuzzy analysis. Introduction In rock engineering, practitioners are often required to make critical decisions based on little or no objective data. This lack of information requires subjective estimation of parameters used in any analysis, and thus introduces uncertainty. Some have suggested that even with little or no information, stochastic methods can be used to make pragmatic decisions by adopting a subjective view of probability (Aven 2010, Lindley 2000). This forms the basis of the Bayesian approach, which suggests that expert opinion can be applied to assign precise probability distributions (so-called ‘priors’) based solely on the knowledge or judgement of an expert. Within this framework, a probability distribution function (PDF) represents an expert's subjective degree of belief in a value's probability of occurrence. However, others argue that the subjective assignment of priors can lead to misinformed decisions and dissonance amongst experts (Ferson & Ginzburg 1996). In this paper, we investigate the latter argument via a case study on slope stability – that of the previously published Sau Mau Ping Road slope in Hong Kong (Hoek 2007). In this paper we compare the results from Monte- Carlo simulation based on a subjectivist approach to probability and a non-probabilistic approach using fuzzy sets. We show the significant differences in design decisions that may result depending on the model adopted to characterise and propagate uncertainty.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2012, May 28–30, 2012

Paper Number: ISRM-EUROCK-2012-042

... variation coefficient numerically probability

**drilling****operation****management**uniform random variable triangular distribution safety factor diagram safety reserves evaluation probability density eurock 2012 random variable rock mass uniform distribution mean factor analytical evaluation...
Abstract

Abstract: Most serious problems encountered in mining and tunnelling, that plagued for decades in countries throughout the world, are associated with falling or breakouts of rock from the roofs and the sidewalls. They constitute hazards by injuring people, damaging workings, and delaying production. It is therefore desirable to consider the problem in some detail, because with the increasing extent and depth of mining, it becomes more serious. The factor of safety, defined as the ratio of the capacity of the rock to the pertinent demand, allows for the estimate of the structural reliability of mining operations. However, this factor does not account for the variability of the parameters involved. A probabilistic approach enables the evaluation of the reliability by taking into account the randomness of the involved parameters. Nevertheless, for such estimates sophisticated probabilistic models and large computing resources are required. By representing the capacity and the demand as uniform random variables, analytical solutions for the probability distribution of the factor of safety may be em-ployed. Application of these solutions for the probabilistic analysis of two under-ground mining cases follows straight forward. The first case concerns the potential for spalling rock in an underground nuclear waste repository. The spalling strength and the stress field are considered as random variables, and the more sophisticated numer-ical evaluations for the probability of spalling are compared to the analytical ones. The second one concerns the potential for falling rock from the Excavation Disturbed Zone (EDZ) of a bolted underground opening. Analytical and numerical evaluations are employed to define the probability of failure, and a parametric study illustrates a methodology to design the support. 1 INTRODUCTION Most serious problems encountered in mining and tunnelling are associated with fal-ling or breakouts of rock from the roofs and the sidewalls.

Proceedings Papers

Paper presented at the ISRM Regional Symposium - EUROCK 2009, October 29–31, 2009

Paper Number: ISRM-EUROCK-2009-067

... and facilitates more sophisticate simulation tool. hydraulic fracturing orientation Artificial Intelligence Upstream Oil & Gas stability analysis equilibrium bolt pattern fluid modeling equation of state strength discontinuity lognormal 4 excavation

**drilling****operation****management**reserves...
Abstract

Abstract Block stability analysis around a large excavation is analyzed with both Probabilistic Kinematics Limit Equilibrium (PKLE) and Discrete Fracture Network-Distinct Element Method (DFN-DEM) approaches. Different combination of geometric parameters of fracture sets are selected in PKLE method and a series of numerical DEM modeling are performed on generated and validated DFN models in DFN-DEM approach to measure volume of potential unstable blocks and also minimum required support patterns. The mean volume of unstable blocks for PKLE with limited joint length assumption is fairly close to DFN models and they are far from mean value of PKLE when the joint length is extended infinitely. The minimum required support pattern for PKLE is smaller than DEM models which means that the PKLE design tool is underestimated compared with DFN-DEM method which benefits more realistic conceptual model and facilitates more sophisticate simulation tool.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2002, November 25–27, 2002

Paper Number: ISRM-EUROCK-2002-021

... of frequencies or histograms that represents the number of times that each value of the variable is repeated in the collected sample. Upstream Oil & Gas Artificial Intelligence frequency hemispherical projection statistical homogeneous region Rock mechanics

**drilling****operation****management**...
Abstract

Rock joints determine the size of the blocks and the rock fracture degree; at the same time joints influence the mechanic and hydraulic behaviour of the rock mass due to its geometrical and mechanical characteristics. Considering major discontinuities, presents in little amount (faults, dikes etc.) and minor discontinuities in great amount and a very variable space distribution (fissures, contacts and discontinuities), former ones (or joints) should be studied statistically and modelled its space distribution applying probabilistic methods, Kulatilake (1993). In this work is presented a probabilistic model of joint distribution applied to the Southeast Slope of Timbopeba iron mine, the fractured rock mass was adopted homogeneous and isotropic, with joints considered as plane circular disks, with parameters like orientation, diameter and location. With the probabilistic model for each joint parameter and the Monte Carlo method, it was simulated and built the fractured rock mass in three dimensions of the Timbopeba Southeast Slope. The contribution of this model is the probable representation of the rock mass structure and its inference in future excavations of slopes in the rock mass. This tool aids in the determination of critical situations where the joint concentration could be higher than a mean concentration value normally used. 1. INTRODUCTION The mechanical and hydraulic behaviour of a fractured rock is very influenced by the joint sets which have complex characterization due to, its geometric variability, limitation in the observation and quantification of their geometric parameters, when made in outcrops, rock cores, or tunnel surfaces. With help on a survey joint mapping in a sampling plane of the Southeast Slope, the probabilistic model proposed will have the function of predict the distribution of joints in a no accessible volume of rock. Later it was simulated a traverse cut of the slope where the most probable joints are observed for the geological type formation of the case study. This probabilistic model of joint distribution allows to enlarge the knowledge of the structure of the rock mass, for the case study, and in the future it will be possible, with help on limit equilibrium methods and numeric tools, to simulate the mechanical and hydraulic behaviour of the rock mass, aiding this way in projects in fractured rock. 2. STATISTICS AND PROHABILITY APPLIED TO GEO-SCIENCES In most of the geo-science areas, the studies focus the external part of the globe, basing their studies on observations of the surface and to a certain depth of the Earth crust. These observations have a lot of uncertainties as for the own heterogeneous formation of the Earth, in this sense the statistics is an important tool of research in this area. In a statistical study the random variables can be described approximately in terms of parameters, as the measures of central tendency and measures of dispersion (mean and standard deviation respectively). Also we can use the distribution of frequencies or histograms that represents the number of times that each value of the variable is repeated in the collected sample.

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 2002, November 25–27, 2002

Paper Number: ISRM-EUROCK-2002-018

... reserves evaluation failure mode stability Goodman UDEC geometric parameter boundary condition tg 1 rock block friction angle stability condition rock slope boundary shear strength equation

**drilling****operation****management**Bray plane geometry dip angle probabilistic analysis...
Abstract

Though sliding and toppling conditions of rock blocks on an inclined plane are easily established from static or dynamic equations, safety assessment of natural rock slopes against toppling failure is quite difficult. The paper presents the equations, which distinguish the static and dynamic approaches of this type of problems, followed by a numeric procedure implemented on a worksheet for the safety evaluation of a toppling slope. A commercial program (UDEC) was used to validate the numerical procedure, after being tested against the dynamic equations of a rigid block on an inclined plane. A probabilistic model considering the Spacing variability of the discontinuity spacing was developed. 1. STABILITY OF A RIGID BLOCK ON AN INCLINED PLANE It is commonly referred that the failure modes in rock slopes are sliding and toppling. Sliding occurs due to a translation movement of a rock block or a rock mass along a plane failure surface. Toppling involves rotation of rock blocks or columns around a fixed point on its base. The simplest assumption for the study of rock slopes is to consider a single rigid block on an inclined plane (Figure 1). This figure allows to establish the regions where the block is stable, where it slides or where it tilts. However, it can be seen that there is a zone where the block can slide and tilt at the same time. In this region, the correct instability mode cannot be deduced from the limit equilibrium equations (1) and (2) because they are not formally valid. In fact, the zone where both sliding and tilting may occur does not correspond to the intersection of both equations, since it is required that the force acting at the toe is large enough to provide block fixity (Bray & Goodman). As Sagaseta (1986) states, to define correctly the boundaries between the regions where sliding, tilting and sliding plus tilting occur it is necessary to establish the limit equilibrium equations starting by the dynamic motion equations of the block and then by imposing the particular conditions associated with the different modes of failure. The stability analysis of rock blocks on a slope was performed using a limit equilibrium analysis (Goodman & Bray, 1976; Hoek & Bray, 1977; Bobet, 1999) implemented in a common worksheet (Excel). The relative errors were found to be very small (less than 0.25%). Finally, the UDEC single block model was used to define the boundaries between the sliding, toppling and mixed sliding and toppling failure modes. Again, values of friction angle ranging from to 20° to 45° were used. The results showed that equations (5.2) or (7.1) - boundary between sliding and sliding+toppling - and equations (6.2) or (7.2) - boundary between sliding+toppling and toppling - were well modelled by UDEC, as the relative errors were small (in the range of the values already shown). 2. TOPPLING OF ROCK BLOCKS A 2D problem involving the toppling of a group of rock blocks on an excavation slope was analysed.

Proceedings Papers

#### Evaluation of Sliding Instability Factor of Safety Using Fuzzy Analysis of Discontinuity Orientation

Paper presented at the ISRM International Symposium - EUROCK 96, September 2–5, 1996

Paper Number: ISRM-EUROCK-1996-068

... stability analysis plane Artificial Intelligence discontinuity orientation data trim 0

**drilling****operation****management**orientation data wedge machine learning orientation centroid discontinuity fuzzy method safety algorithm cumulative distribution Computation partition identification...
Abstract

ABSTRACT: The stability of rock slopes is known to be controlled by the geometry and strength of discontinuities, and amongst several rock mass features, the discontinuity orientation has the principal influence on instability phenomena. In this paper, a method is presented for the evaluation of discontinuity orientation data such that these data may be used in stability analyses. This method is a procedure for the robust statistical interpretation of discontinuity orientation data using the actual form of the data; this contrasts sharply with classical analysis using discontinuity orientation contour diagrams. Fuzzy partitioning algorithms have been applied to discontinuity orientation data, and membership levels - representing "degree of certainty" - are computed directly from the data without the use of an assumed analytical function. These membership values are then directly used in the computation of the factor of safely of sliding wedges. This new approach appears to show advantages over the classical statistical analyses, where models fitted to real data are used in the analysis. In addition, the use of fuzzy partitioning algorithms has been found to offer an improved analysis, as degree of certainty is immediately applicable in an engineering context. RESUME: La stability des talus rachises est. lie aux caracteristiques geometriques et de resistance des discontinuites naturelles, I'orientation etant Ie facteur d'instabilite Ie plus important. Dans cat article on propose une method pour l'evaluation de la structure des donnees collectees in situ, au fin de les utilize dans des analyses de stability pregnant en compete les limits de conveyance. Cite method constitute un demarche pour I' interpretation statistique des donnees d'orientation qui considere la formed effective des donnees On a applique les algorithms du "fuzzy partitioning" aux donnees d'orientation et determine les niveaux d'appartenance, representants Ie "degree d'incertitude", directement à partir des donnees, sans devoir assumer une fonction analitique. Enfin, Ie novae d'appartenence de chaque discontinuity a tee utilize directement pour I' evaluation des factures de security du glissement d'un coin. ZUSAMMENFASSUNG: Es ist bekannt daß die Standsicherheit von Felsböschungen von der Rampage und Scherfestigkeit von Trennflachen kontrolliert wird Ouch bee violin andiron Gebirgseigenschaflen hat die Rampage der Trennflachen einen entscheidenden Einfluß auf die Standsicherheit. Der vorliegende Aufsatz stellt ein Verfahren fur die Auswertung von Kluftorientierungen vow, so daß sie direkt nil' Standsicherheitsanalysen benutzt werden conmen. Das Verfahren stellt eine leistungsfahige sratistische Interpretation der Daten in hirer erhobenen Form dar. Dies stet in scharfem Gegensatz zu den herkömmlichen Analysemethoden, die auf der Auswertung von Isolinien birchen. Bee dem Verfahren werden Aufleilungsalgorithmen angewandt, die auf der Theorie der unscharfen Menden basemen. Dobie werden Zugehörigkeitsgrade, die einem Grad von Gewissheit entsprechen, direkt aus den geometrischen Eingangsdaten berechnet, hone daß dabbed Verteilungsfunktionen vorausgesetzt werden. Diese Zugehörigkeitsgrade gehen dann direkt in die Berechnung der Sicherheit eines Gleitkeils ein. Dieser neue Ansatz scheint Vorteile gegenueber den klassischen statistischen Verfahren aufzuweisen, bee denim die gemessenen Daten an angenommene Verteilungen angepasst werden. Die Verwendung von Aufteilungsalgorithmen auf der Grundlage unscharfer Menden hat sich zoomed ales ein verbessertes Verfahren herausgestellt, da der Grad an Gewissheit unmittelbar ingenieurmaßig umgesetzt werden ken. 1 INTRODUCTION The stability of rock wedges is influenced by rock parameters that display variability In deterministic stability analysis, the dispersion of parameters is taken into consideration by using reduced or modified mean values and calculating the safety factor for different combinations of parameters. With probabilistic methods, it is possible to calculate the probability of failure of a system depending on the combinations of parameters, and to quantify the potential risk of a geotechnical construction (Trunk, 1993, Muralha et al., 1993).

Proceedings Papers

Paper presented at the ISRM International Symposium - EUROCK 93, June 21–24, 1993

Paper Number: ISRM-EUROCK-1993-030

... like mean value and standard deviation. Artificial Intelligence reserves evaluation deviation

**drilling****operation****management**limit state importance measure discontinuity Reservoir Characterization Upstream Oil & Gas wedge state function reservoir simulation orientation mean value...
Abstract

ABSTRACT: For the probabilistic stability analysis of rock wedges formed by two discontinuities the First and Second Order Reliability method is used. This asymptotic method needs a continous formulation of the limit state. In the stochastic model the orientations, trace lengths and shear parameters are defined as basic random parameters. The importance measures of the variables are determined. The possibility to use of partial safety factors for the wedge analysis is discussed. The influence of water pressure on safety level is examined in an example. RÉSUMÉ: L' analyse probabiliste de la stabilite de roches tetraedriques formees par deux discontinuites est effectuee à I' aide des methodes du premier et du second ordre de la theorie de la fiabilite. Ces methodes asymptotiques necessitent une fonction d'etat limite continue. L' orientation des plans de glissements, les longueurs d' affleurement et les coefficients de cisaillement sont modelises par des variables aleatoires, Les importances relatives de ces variables sur les resultats des calculs fiabilistes sont precisees. La possible utilisation de coefficients de securite pour s 'assurer de la stabilite de roches tetraedriques est consideree. Enfin, l' influence de la pression de l 'eau sur le niveau fiabilite est etudiee dans un example. ZUSAMMENFASSUNG: Die Zuverlassigkeitstheorie erster und zweiter Ordnung wird fuer die probabilistische Standsicherheitsanalyse tetraedrischer Felskeile verwendet. Fuer die Anwendung dieses asymptotischen Verfahrens ist eine stetige Formulierung der Grenzzustands erforderlich. Die Trennflachenrichtungen, die Ausbiβlangen und die Scherparameter werden im stochastischen Modell als Zufallsvariable definiert. Die Gewichte und Sensitivitaten der Basisvariablen werden bestimmt. Es wird untersucht, ob die Verwendung von Partialsicherheitsfaktoren fuer die Standsicherheitsanalyse von Felskeilen möglich ist. Der Einfluβ von Wasserdruck auf das Sicherheitsniveau wird an einem Beispiel untersucht. 1. INTRODUCTION The stability of rock wedges is influenced by random rock parameters. In deterministic stability analysis, the dispertion of parameters is taken into consideration by using reduced or modified mean values and calculating the safety factor for different combinations of parameters. However it is not possible to calculate the probability of failure or the reliability in this way. With probabilistic methods, it is possible to evaluate the reliability of systems depending on random and fixed parameters and quantify the influence of deterministic and random parameters on the reliability. Design rules are often based on limit state definitions, e.g. failure of slopes or foundations. Therefore it is necessary to find a mechanical model representing the real problem. Sliding of tetrahedral rock wedges is such a model often used for the design of rock slopes and walls of underground openings (JOHN, 1970; HOEK and BRAY, 1974 and 1981; WITTKE, 1965). As a rigid block method, this gives only information about the ultimate limit state and not about the serviceability limit state. It is necessary to keep in mind that the limitations and necessary simplifications of the model influence the results for the deterministic safety factor as well as for the reliability or probability of failure. A more detailed discussion of the theoretical background is given in MURALHA and TRUNK (1993) and TRUNK (1993). 2. MECHANICAL AND STOCHASTIC MODEL To evaluate the influence of random rock parameters, the model of the tetrahedral rock wedge is chosen. In the first step, only failure by sliding is calculated. The failure by rotation and toppling of wedges is not considered. The use of a simple and established mechanical model makes an interpretation of the probabilistic results easier. The model determines the parameters that must be described in the stochastic model by means of distribution functions and their parameters like mean value and standard deviation.