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 FLAC^(3D),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.

Determination of uncertainties of geomechanical parameters of metamorphic rocks using petrographic analyses

Geomechanical parameters of intact metamorphic rocks determined from laboratory testing remain highly uncertain because of the great intrinsic variability associated with the degrees of metamorphism.The aim of this paper is to develop a proper methodology to analyze the uncertainties of geomechanical characteristics by focusing on three domains,i.e.data treatment process,schistosity angle,and mineralogy.First,the variabilities of the geomechanical laboratory data of Westwood Mine(Quebec,Canada)were examined statistically by applying different data treatment techniques,through which the most suitable outlier methods were selected for each parameter using multiple decision-making criteria and engineering judgment.Results indicated that some methods exhibited better performance in identifying the possible outliers,although several others were unsuccessful because of their limitation in large sample size.The well-known boxplot method might not be the best outlier method for most geomechanical parameters because its calculated confidence range was not acceptable according to engineering judgment.However,several approaches,including adjusted boxplot,2MADe,and 2SD,worked very well in the detection of true outliers.Also,the statistical tests indicate that the best-fitting probability distribution function for geomechanical intact parameters might not be the normal distribution,unlike what is assumed in most geomechanical studies.Moreover,the negative effects of schistosity angle on the uniaxial compressive strength(UCS)variabilities were reduced by excluding the samples within a specific angle range where the UCS data present the highest variation.Finally,a petrographic analysis was conducted to assess the associated uncertainties such that a logical link was found between the dispersion and the variabilities of hard and soft minerals.

Modelling of the variation of granular base materials resilient modulus with material characteristics and humidity conditions

This study aims to quantify the susceptibility of granular materials used in pavements to changes in moisture content and propose a correlation model to incorporate this susceptibility into seasonal analyses.The fines content and the percentage of fractured coarse aggregates were identified as direct indicators of the resilient modulus susceptibility to changes in water content.The results showed that the percentage of fractured coarse aggregates particles(FR)has a more significant impact on the resilient modulus(Er)of crushed granular materials used in pavement construction than the combined indicator of the fines content and sample volumetrics(nf).Crushed granular materials with a higher percentage of fractured coarse aggregates are relatively insensitive to changes in the degree of saturation,but become more sensitive as the fine fraction porosity decreases.An adjusted model was proposed based on the existing formulation,but considers a complex parameter to describe and adjust the sensitivity of base granular materials to variations in moisture content with respect to fabrication charac-teristics,fines content and volumetric properties.The model shows that the variation of Er values is below10%for fully crushed granular materials.However,it reaches approximately±12%for materials with 75%of crushed coarse aggregates andþ40%and-25%for materials with FR=50%.This model could help select good ag-gregates characteristics and adjust grain-size distribution for environments where significant moisture content variations can occur in the pavement system,such as in the Province of Quebec(Canada).As it is based on pa-rameters that can be easily determined or estimated,it also represents a valuable tool for detailed design and analysis that can consider material characteristics.

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.

Determining relative block structure rating for rock erodibility evaluation in the case of non-orthogonal joint sets

The most commonly used method for assessing the hydraulic erodibility of rock is Annandale's method.This method is based on a correlation between the erosive force of flowing water and the capacity of rock resistance. This capacity is evaluated using Kirsten's index, which was initially developed to evaluate the excavatability of earth materials. For rocky material, this index is determined according to certain geomechanical factors related to intact rock and rock mass, such as compressive strength of intact rock, rock block size, discontinuity shear strength and relative block structure. To quantify the relative block structure, Kirsten(1982) developed a mathematical expression that accounts for the shape and orientation of the blocks relative to the direction of flow. Kirsten's initial concept for assessing the relative block structure considers that the geological formation is mainly fractured by two joint sets forming an orthogonally fractured system. An adjusted concept is proposed to determine the relative block structure when the fractured system is non-orthogonal where the angle between the planes of the two joint sets is greater or less than 90°. An analysis of the proposed relative block structure rating shows that considering a non-orthogonally fractured system has a significant effect on Kirsten's index and, as a consequence, on the assessment of the hydraulic erodibility of rock.

A method to determine relevant geomechanical parameters for evaluating the hydraulic erodibility of rock

Among the methods used for evaluating the potential hydraulic erodibility of rock,the most common methods are those based on the correlation between the force of flowing water and the capacity of a rock to resist erosion,such as Annandale’s and Pells’methods.The capacity of a rock to resist erosion is evaluated based on erodibility indices that are determined from specific geomechanical parameters of a rock mass.These indices include unconfined compressive strength(UCS)of rock,rock block size,joint shear strength,a block’s shape and orientation relative to the direction of flow,joint openings,and the nature of the surface to be potentially eroded.However,it is difficult to determine the relevant geomechanical parameters for evaluating the hydraulic erodibility of rock.The assessment of eroded unlined spillways of dams has shown that the capacity of a rock to resist erosion is not accurately evaluated.Using more than 100 case studies,we develop a method to determine the relevant geomechanical parameters for evaluating the hydraulic erodibility of rock in unlined spillways.The UCS of rock is found not to be a relevant parameter for evaluating the hydraulic erodibility of rock.On the other hand,we find that the use of three-dimensional(3D)block volume measurements,instead of the block size factor used in Annandale’s method,improves the rock block size estimation.Furthermore,the parameter representing the effect of a rock block’s shape and orientation relative to the direction of flow,as considered in Pells’method,is more accurate than the parameter adopted by Annandale’s method.

Rockburst in underground excavations:A review of mechanism,classification,and prediction methods

Technical challenges have always been part of underground mining activities,however,some of these challenges grow in complexity as mining occurs in deeper and deeper settings.One such challenge is rock mass stability and the risk of rockburst events.To overcome these challenges,and to limit the risks and impacts of events such as rockbursts,advanced solutions must be developed and best practices implemented.Rockbursts are common in underground mines and substantially threaten the safety of personnel and equipment,and can cause major disruptions in mine development and operations.Rockbursts consist of violent wall rock failures associated with high energy rock projections in response to the instantaneous stress release in rock mass under high strain conditions.Therefore,it is necessary to develop a good understanding of the conditions and mechanisms leading to a rockburst,and to improve risk assessment methods.The capacity to properly estimate the risks of rockburst occurrence is essential in underground operations.However,a limited number of studies have examined and compared yet different empirical methods of rockburst.The current understanding of this important hazard in the mining industry is summarized in this paper to provide the necessary perspective or tools to best assess the risks of rockburst occurrence in deep mines.The various classifications of rockbursts and their mechanisms are discussed.The paper also reviews the current empirical methods of rockburst prediction,which are mostly dependent on geomechanical parameters of the rock such as uniaxial compressive strength of the rock,as well as its tensile strength and elasticity modulus.At the end of this paper,some current achievements and limitations of empirical methods are discussed.