Probabilistic stability analysis of open stopes in sublevel stoping method by numerical modeling

Over the past years, maintaining the stability of underground excavations has grabbed attention with the growing tendency of exploitation of deep underground mineral resources. Since sublevel stoping is recognized as the most widely applied method in Canadian underground mines, assessing the open stope stability develops concern for rock mechanics engineers over preserving mining production capacity and providing safety for workers and equipment. Stress-induced failure is among the most common causes of instability for underground open stopes. The probability of failure (POF) depends on a number of factors including rock mass properties, in situ stress state and stope geometry. One of the most reliable approaches for evaluating the influence of the above mentioned factors on open stope stability, is the use of probabilistic methods in conjunction with numerical analysis. Various powerful probabilistic methods (e.g. Monte Carlo Simulation, Random Monte Carlo Simulation and Response Surface Methodology) in conjunction with the finite difference code FLAC3D have been applied throughout our research. In fact, the present research provides a comprehensive methodology to perform a numerical evaluation of the effect of open stope geometrical parameters (i.e., stope strike length, stope width, and etc.) on the potential of rock mass brittle damage, as well as the probability of stope failure (POF) by considering two modes of relaxation-related gravity driven (tensile) failure, and rock mass brittle failure. Monte Carlo Simulation (MCS) and Response Surface Methodology (RSM) are employed to determine the significant individual effects and their interactions of the geometric parameters. This study applies geometrical parameters derived from a survey of numerous open stopes from the Canadian Shield. Evaluation of the effect of stope geometry on the rock mass brittle damage indicates that independent from mining depth, the highest range of brittle damage is observed for the stopes with moderate range of hanging wall hydraulic radius (HR) and high range of hanging wall dip. While the lowest values of brittle damage is observed for the stopes having low-moderate values of hanging wall HR and low-moderate values of hanging wall dip. Also, the individual and interactive effect of stope geometrical parameters on the rock mass brittle damage is found to be significant. Assessing of the effect of stope geometry on the probability of tensile failure (POF) has pointed out that three parameters, which are the stope hanging wall HR, stope span width and stope hanging wall dip, have a strong influence on the stope stability state. Also it was found that the POF is significantly controlled by interaction effects between span width / hanging wall HR and hanging wall dip / hanging wall HR. Moreover, according to the results of the mathematical optimization, the maximum stability (in terms of POF) occurs for shallow dipping narrow stopes having large hanging wall HR. Whereas, the minimum stability would happen in moderately to steeply dipping wide stopes with small hanging wall HR values. Also, a probabilistic stability analysis was performed on seven primary open stopes located in mining blocks V and VI at the Niobec underground mine (Saint-Honoré, Québec). Probabilistic methods with the finite difference code FLAC3D, are employed to evaluate the stability state of each studied stope, taking into onsideration the inherent variability associated with the geomechanical parameters of the rock mass. The stability state is defined via the tensile and compressive probabilities of failure (POF) and the probability of brittle damage initiation (PDI). Monte Carlo simulation generates the probabilistic rock mass input parameters while Random Monte Carlo simulations applied a random spatial distribution of the geomechanical parameters within the rock mass. The results indicate that for the evaluated open stopes, tensile and compressive failures share similar POFs. However, according to the PDI values around all the open stopes, no brittle failure is expected to occur under the existing conditions of rock mass quality and in-situ stress regime in mining blocks V and VI at the Niobec Mine. Pendant les dernières années, le maintien de la stabilité des excavations souterraines a attiré l'attention avec la tendance croissante à l'exploitation des ressources minérales souterraines profondes. Étant donné que la méthode des chantiers ouverts est reconnue comme la méthode la plus largement utilisée dans les mines souterraines canadiennes, l'évaluation de la stabilité de ces chantiers suscite des inquiétudes chez les ingénieurs en mécanique des roches quant à la préservation de la capacité de production minière et à la sécurité des travailleurs et de l'équipement. La rupture induite par la concentration des contraintes est l'une des causes les plus courantes d'instabilité pour les chantiers souterrains ouverts. La probabilité de rupture (POF) dépend d’un certain nombre de facteurs, dont les propriétés du massif rocheux, l’état de contrainte in situ et la géométrie du chantier. L’utilisation de méthodes probabilistes en conjonction avec l’analyse numérique est l’une des approches les plus fiables pour évaluer l’influence des facteurs susmentionnés sur la stabilité des chantiers. Diverses méthodes probabilistes ayant fait leurs preuves (par exemple, la simulation de Monte Carlo, la simulation de Monte Carlo aléatoire et la méthodologie de surface de réponse), associées au code de différences finies FLAC3D, ont été appliquées tout au long de la présente recherche. En fait, la présente recherche fournit une méthodologie complète pour effectuer une évaluation numérique de l’effet des paramètres géométriques des chantiers ouverts (c’est-à-dire la longueur du chantier, la largeur du chantier, etc.) sur le potentiel des dommages et la probabilité de rupture du chantier (POF) en considérant deux modes de rupture, soit celle due à la gravité (traction) liée à la relaxation et la rupture fragile de la masse rocheuse. La simulation de Monte Carlo (MCS) et la méthodologie de surface de réponse (RSM) sont utilisées pour déterminer les effets individuels et d’interaction significatifs des paramètres géométriques. Cette étude applique des paramètres géométriques dérivés d'un inventaire de nombreux chantiers ouverts dans le Bouclier canadien. L’évaluation de l’effet de la géométrie du chantier sur des dommages fragiles du massif rocheux indique qu’indépendamment de la profondeur des chantiers, les chantiers présentant un rayon hydraulique modéré et une pente élevée montre un plus grand dommage fragile. Par contre, les chantiers avec les valeurs de rayon hydraulique du toit bas à modéré, et un pendage de toit également bas a modéré montrent une dommage fragile minimal. En outre, l’effet individuel et interactif des paramètres géométriques du chantier sur les dommages fragiles du massif rocheux s’avère significatif. L’évaluation de l’effet de la géométrie du chantier sur la probabilité de rupture en traction a montré que trois paramètres, qui sont le rayon hydraulique du toit, la largeur du chantier et le pendage de la paroi, ont une forte influence sur la stabilité du chantier. Il a également été constaté que le POF est contrôlé de manière significative par des effets d’interaction entre la largeur du chantier / le rayon hydraulique du toit, et le pendage du toit / le rayon hydraulique du toit. De plus, selon les résultats de l’optimisation mathématique, la stabilité maximale (en termes de POF) se produit pour les chantiers étroits peu profonds, à faible pendage et ayant de fortes valeurs de rayon hydraulique du toit. Alors que la stabilité minimale se produirait pour des chantiers larges et de pendage modéré à élevé, avec un toit ayant faibles valeurs de rayon hydraulique. De plus, une analyse de stabilité probabiliste a été est effectuée sur sept chantiers principaux parmi les ouvrages souterrains situés aux niveaux V et VI de la mine souterraine Niobec (Saint-Honoré, Québec). Les méthodes probabilistes utilisant le code de différences finies FLAC3D sont utilisées pour évaluer l’état de stabilité de chaque chantier étudié, en tenant compte de la variabilité inhérente associée aux paramètres géomécaniques de la masse rocheuse. L'état de stabilité est défini par les probabilités de rupture en traction et en compression (POF), et la probabilité d'initiation de dégradation fragile (PDI). La simulation de Monte Carlo génère les paramètres probabilistes du massif rocheux tandis que les simulations aléatoires de Monte Carlo ont appliqué une distribution spatiale aléatoire des paramètres géomécaniques dans le massif rocheux. Les résultats indiquent que pour les chantiers ouverts évalués, les ruptures de traction et de compression partagent des POF similaires. Cependant, selon les valeurs de PDI autour de tous les chantiers ouverts, aucune défaillance fragile ne devrait se produire dans les conditions existantes de la qualité du massif rocheux et du régime de contraintes in situ aux niveaux V et VI de la mine Niobec

Geomechanical characterization of a heterogenous rock mass using geological and laboratory test results: a case study of the Niobec Mine, Quebec

To conduct a successful geomechanical characterization of rock masses, an appropriate interpretation of lithological heterogeneity should be attained by considering both the geological and geomechanical data. In order to clarify the reliability and applicability of geological surveys for rock mechanics purposes, a geomechanical characterization study is conducted on the heterogeneous rock mass of Niobec Mine (Quebec, Canada), by considering the characteristics of its various identified lithological units. The results of previous field and laboratory test campaigns were used to quantify the variability associated to intact rock geomechanical parameters for the different present lithological units. The interpretation of geomechanical similarities between the lithological units resulted in determination of three main rock units (carbonatite, syenite, and carbonatite-syenite units). Geomechanical parameters of these rock units and their associated variabilities are utilized for stochastic estimation of geomechanical parameters of the heterogeneous rock mass using the Monte Carlo Simulation method. A comparison is also made between the results of probabilistic and deterministic analyses to highlight the presence of intrinsic variability associated with the heterogeneous rock mass properties. The results indicated that, for the case of Niobec Mine, the carbonatite-syenite rock unit could be considered as a valid representative of the entire rock mass geology since it offers an appropriate geomechanical approximation of all the present lithological units at the mine site, in terms of both the magnitude and dispersion of the strength and deformability parameters

Geotechnical Parameters of Landslide-Prone Laflamme Sea Deposits, Canada: Uncertainties and Correlations

Due to inherent variability arising from unpredictable geological depositional and post-depositional processes, the geotechnical parameters of Laflamme sea clay deposits remain highly uncertain. This study aims to develop and apply a methodology to assess the uncertainties of geotechnical parameters using statistical distributions for a landslide-prone Saguenay Lac-Saint-Jean (SLSJ) region. We used the measured physical and mechanical parameters of Laflamme Sea clays of various locations in the SLSJ region to characterize the geotechnical parameters in a representative manner. Goodness-of-fit tests assign each physical and mechanical parameter a distribution function for their descriptive analysis. We found that the quality of these tests is significantly influenced by outliers. The detected outliers in the dataset considerably impact the distribution type and the uncertainties of the specific geotechnical parameter. Subsequently, appropriate distribution functions for each parameter were assigned after treating the outliers. The derived coefficient of variability values for the SLSJ region were significantly high in comparison to the literature with cone penetration test data being only the exception. Finally, the results indicated that the uncertainties of geotechnical parameters of the Saguenay-Lac-Saint-Jean region marine clays are high as compared to Scandinavian clays and are relatively comparable to other eastern Canadian clays

A methodology for damage evaluation of underground tunnels subjected to static loading using numerical modeling

We have proposed a methodology to assess the robustness of underground tunnels against potential failure. This involves developing vulnerability functions for various qualities of rock mass and static loading intensities. To account for these variations, we utilized a Monte Carlo Simulation (MCS) technique coupled with the finite difference code FLAC3D, to conduct two thousand seven hundred numerical simulations of a horseshoe tunnel located within a rock mass with different geological strength index system (GSIs) and subjected to different states of static loading. To quantify the severity of damage within the rock mass, we selected one stress-based (brittle shear ratio (BSR)) and one strain-based failure criterion (plastic damage index (PDI)). Based on these criteria, we then developed fragility curves. Additionally, we used mathematical approximation techniques to produce vulnerability functions that relate the probabilities of various damage states to loading intensities for different quality classes of blocky rock mass. The results indicated that the fragility curves we obtained could accurately depict the evolution of the inner and outer shell damage around the tunnel. Therefore, we have provided engineers with a tool that can predict levels of damages associated with different failure mechanisms based on variations in rock mass quality and in situ stress state. Our method is a numerically developed, multi-variate approach that can aid engineers in making informed decisions about the robustness of underground tunnels

The damage-failure criteria for numerical stability analysis of underground excavations: A review

Failure of rock mass in deep underground excavations could be attributed to a broad range of performance malfunction, from plastic yielding of rock, generation of macro cracks on the boundary of the excavation, gravity driven rockfalls or even complete stress-induced collapse. The failure criteria determine the stress level (or strain level) at which the rock mass loses its load-carrying (or strain-carrying) capacity. Determination of the state of underground stability can be successfully achieved through implementation of appropriate failure criteria within the numerical analyses’ tools. The choice of failure criteria in numerical stability analysis plays a key role in defining the behaviour of an underground excavation. A failure criterion will be useful only if selected based on the correct mechanism of failure. Plus, a right choice of failure criterion, significantly reduces the errors of quantifying an excavations behaviour. Therefore, this paper offers a critical review of the most common stress-based and strain-based failure criteria used in numerical stability analysis of underground excavations. Particular attention is paid to characterize different mechanisms of underground failure and recommendations are formulated for each failure mode. In addition, this paper addresses the theoretical considerations for the applicability of different failure criteria and highlights the practical limitations for their numerical implementation

Review of Applicable Outlier Detection Methods to Treat Geomechanical Data

The reliability of geomechanical models and engineering designs depend heavily on high-quality data. In geomechanical projects, collecting and analyzing laboratory data is crucial in characterizing the mechanical properties of soils and rocks. However, insufficient lab data or underestimating data treatment can lead to unreliable data being used in the design stage, causing safety hazards, delays, or failures. Hence, detecting outliers or extreme values is significant for ensuring accurate geomechanical analysis. This study reviews and categorizes applicable outlier detection methods for geomechanical data into fence labeling methods and statistical tests. Using real geomechanical data, the applicability of these methods was examined based on four elements: data distribution, sensitivity to extreme values, sample size, and data skewness. The results indicated that statistical tests were less effective than fence labeling methods in detecting outliers in geomechanical data due to limitations in handling skewed data and small sample sizes. Thus, the best outlier detection method should consider this matter. Fence labeling methods, specifically, the medcouple boxplot and semi-interquartile range rule, were identified as the most accurate outlier detection methods for geomechanical data but may necessitate more advanced statistical techniques. Moreover, Tukey’s boxplot was found unsuitable for geomechanical data due to negative confidence intervals that conflicted with geomechanical principles

Use of probabilistic numerical modeling to evaluate the effect of geomechanical parameter variability on the probability of open-stope failure: a case study of the Niobec Mine, Quebec (Canada)

The inherent variability of the geomechanical parameters of a rock mass plays a critical role in affecting underground mine stability. Neglecting this characteristic of a rock mass oversimplifies stability assessment and provides potentially inaccurate results as the actual behavior of rock mass is not considered. Use of probabilistic methods in conjunction with numerical analysis is a reliable approach for evaluating the effect of geomechanical parameter variability on the different modes of underground instability. The degree of stability can be expressed by the probability of failure for different stress-induced instability modes. Here, we use probabilistic methods (random Monte Carlo and Monte Carlo simulations) coupled with the finite difference code FLAC3D to incorporate the variability of rock mass geomechanical parameters into numerical analysis. We assess the stability of seven existing primary open stopes at mining levels V and VI at the Niobec Mine, Quebec, Canada. The stability around each open stope is evaluated by calculating the tensile and compressive probabilities of failure, based on the Hoek–Brown tensile and compressive safety factor, and the probability of brittle damage initiation (PDI), via the brittle shear ratio. For the evaluated open stopes, tensile and compressive failures share similar probabilities of occurrence. Considering the PDI values around all the open stopes, no brittle failure is expected to occur under the existing conditions of rock mass quality and in situ stress regime at the Niobec Mine. Comparison of these probabilistic numerical model results with those run using a deterministic numerical approach highlights the effect of variability of rock mass geomechanical parameters on stope stability

Evaluation of the effect of geometrical parameters on stope probability of failure in the open stoping method using numerical modeling

Stress-induced failure is among the most common causes of instability in Canadian deep underground mines. Open stoping is the most widely practiced underground excavation method in these mines, and creates large stopes which are subjected to stress-induced failure. The probability of failure (POF) depends on many factors, of which the geometry of an open stope is especially important. In this study, a methodology is proposed to assess the effect of stope geometrical parameters on the POF, using numerical modelling. Different ranges for each input parameter are defined according to previous surveys on open stope geometry in a number of Canadian underground mines. A Monte-Carlo simulation technique is combined with the finite difference code FLAC3D, to generate model realizations containing stopes with different geometrical features. The probability of failure (POF) for different categories of stope geometry, is calculated by considering two modes of failure; relaxation-related gravity driven (tensile) failure and rock mass brittle failure. The individual and interactive effects of stope geometrical parameters on the POF, are analyzed using a general multi-level factorial design. Finally, mathematical optimization techniques are employed to estimate the most stable stope conditions, by determining the optimal ranges for each stope’s geometrical parameter. Keywords: Stope stability, Stope geometrical parameters, Probability of failure, General factorial design, Numerical modeling, Sublevel open stopin

The effects of in situ stress uncertainties on the assessment of open stope stability: Case study at the Niobec Mine, Quebec (Canada)

In deep underground mines, a successful development plan to exploit deeper mining levels is highly dependent on adequate consideration of the magnitude and orientation of situ stress state. However, significant uncertainties are associated with the estimation of these parameters. The in-situ stress values that are used in the evaluation of the stability of underground structures in each mine strongly depends on the results of measurement of the stresses as function of the mine depth and the methodology used for the interpretation of the data as well as engineering judgment. These interpretations could produce several scenarios for estimating the stresses in a mine. Each scenario could yield different stability assessment results some of which were not normally used in the current mine stability study. Three different scenarios for estimating stress at the Niobec underground mine (Quebec, Canada) were determined based on the data available from previous stress measurement campaigns. Numerical modeling (FLAC3D) was used to evaluate the potential of brittle, tensile and compressive failure for the vertical transverse and rib pillars. The results demonstrate that in spite of the development of extensive brittle and tensile damage zones within the rock mass, no major brittle or tensile failure is expected to occur at the considered mining levels based on all three stress scenarios. Moreover, meaningful differences in the stability analysis results between the three stress scenarios highlight the importance of appropriate selection of stress estimation approaches in planning deeper mine levels