Effects of confinement on rock mass modulus: A synthetic rock mass modelling (SRM) study

The main objective of this paper is to examine the influence of the applied confining stress on the rock mass modulus of moderately jointed rocks (well interlocked undisturbed rock mass with blocks formed by three or less intersecting joints). A synthetic rock mass modelling (SRM) approach is employed to determine the mechanical properties of the rock mass. In this approach, the intact body of rock is represented by the discrete element method (DEM)-Voronoi grains with the ability of simulating the initiation and propagation of microcracks within the intact part of the model. The geometry of the pre-existing joints is generated by employing discrete fracture network (DFN) modelling based on field joint data collected from the Brockville Tunnel using LiDAR scanning. The geometrical characteristics of the simulated joints at a representative sample size are first validated against the field data, and then used to measure the rock quality designation (RQD), joint spacing, areal fracture intensity (P₂₁), and block volumes. These geometrical quantities are used to quantitatively determine a representative range of the geological strength index (GSI). The results show that estimating the GSI using the RQD tends to make a closer estimate of the degree of blockiness that leads to GSI values corresponding to those obtained from direct visual observations of the rock mass conditions in the field. The use of joint spacing and block volume in order to quantify the GSI value range for the studied rock mass suggests a lower range compared to that evaluated in situ. Based on numerical modelling results and laboratory data of rock testing reported in the literature, a semi-empirical equation is proposed that relates the rock mass modulus to confinement as a function of the areal fracture intensity and joint stiffness.     

Influence of degree of interlock on confined strength of jointed hard rock masses

The strength of jointed rock mass is strongly controlled by the degree of interlock between its constituent rock blocks. The degree of interlock constrains the kinematic freedom of individual rock blocks to rotate and slide along the block forming joints. The Hoek–Brown (HB) failure criterion and the geological strength index (GSI) were developed based on experiences from mine slopes and tunneling projects in moderately to poorly interlocked jointed rock masses. It has since then been demonstrated that the approach to estimate the HB strength parameters based on the GSI strength scaling equations (called the ‘GSI strength equations’) tends to underestimate the confined peak strength of highly interlocked jointed rock masses (i.e. GSI > 65), where the rock mass is often non-persistently jointed, and the intact rock blocks are strong and brittle. The estimation of the confined strength of such rock masses is relevant when designing mine pillars and abutments at great depths, where the confining pressure is high enough to prevent block rotation and free sliding on block boundaries. In this article, a grain-based distinct element modeling approach is used to simulate jointed rock masses of various degrees of interlock and to investigate the influences of block shape, joint persistence and joint surface condition on the confined peak strengths. The focus is on non-persistently jointed and blocky (persistently jointed) rock masses, consisting of hard and homogeneous rock blocks devoid of any strength degrading defects such as veins. The results from this investigation confirm that the GSI strength equations underestimate the confined strength of highly interlocked and non-persistently jointed rock masses. Moreover, the GSI strength equations are found to be valid to estimate the confined strength of persistently jointed rock masses with smooth and non-dilatant joint surfaces.     

Bayesian data analysis to quantify the uncertainty of intact rock strength

One of the main difficulties in the geotechnical design process lies in dealing with uncertainty. Uncertainty is associated with natural variation of properties, and the imprecision and unpredictability caused by insufficient information on parameters or models. Probabilistic methods are normally used to quantify uncertainty. However, the frequentist approach commonly used for this purpose has some drawbacks.First, it lacks a formal framework for incorporating knowledge not represented by data. Second, it has limitations in providing a proper measure of the confidence of parameters inferred from data. The Bayesian approach offers a better framework for treating uncertainty in geotechnical design. The advantages of the Bayesian approach for uncertainty quantification are highlighted in this paper with the Bayesian regression analysis of laboratory test data to infer the intact rock strength parameters σ_(ci) and m_i used in the Hoek-Brown strength criterion. Two case examples are used to illustrate different aspects of the Bayesian methodology and to contrast the approach with a frequentist approach represented by the nonlinear least squares(NLLS) method. The paper discusses the use of a Student's t-distribution versus a normal distribution to handle outliers, the consideration of absolute versus relative residuals, and the comparison of quality of fitting results based on standard errors and Bayes factors. Uncertainty quantification with confidence and prediction intervals of the frequentist approach is compared with that based on scatter plots and bands of fitted envelopes of the Bayesian approach. Finally, the Bayesian method is extended to consider two improvements of the fitting analysis. The first is the case in which the Hoek-Brown parameter, a, is treated as a variable to improve the fitting in the triaxial region. The second is the incorporation of the uncertainty in the estimation of the direct tensile strength from Brazilian test results within the overall evaluation of the intact rock strength.     

The Hoek–Brown failure criterion and GSI – 2018 edition

The Hoek–Brown criterion was introduced in 1980 to provide input for the design of underground excavations in rock. The criterion now incorporates both intact rock and discontinuities, such as joints, characterized by the geological strength index (GSI), into a system designed to estimate the mechanical behaviour of typical rock masses encountered in tunnels, slopes and foundations. The strength and deformation properties of intact rock, derived from laboratory tests, are reduced based on the properties of discontinuities in the rock mass. The nonlinear Hoek–Brown criterion for rock masses is widely accepted and has been applied in many projects around the world. While, in general, it has been found to provide satisfactory estimates, there are several questions on the limits of its applicability and on the inaccuracies related to the quality of the input data. This paper introduces relatively few fundamental changes, but it does discuss many of the issues of utilization and presents case histories to demonstrate practical applications of the criterion and the GSI system.     

Influence of data analysis when exploiting DFN model representation in the application of rock mass classification systems

Discrete fracture network (DFN) models have been proved to be effective tools for the characterisation of rock masses by using statistical distributions to generate realistic three-dimensional (3D) representations of a natural fracture network. The quality of DFN modelling relies on the quality of the field data and their interpretation. In this context, advancements in remote data acquisition have now made it possible to acquire high-quality data potentially not accessible by conventional scanline and window mapping. This paper presents a comparison between aggregate and disaggregate approaches to define fracture sets, and their role with respect to the definition of key input parameters required to generate DFN models. The focal point of the discussion is the characterisation of in situ block size distribution (IBSD) using DFN methods. An application of IBSD is the assessment of rock mass quality through rock mass classification systems such as geological strength index (GSI). As DFN models are becoming an almost integral part of many geotechnical and mining engineering problems, the authors present a method whereby realistic representation of 3D fracture networks and block size analysis are used to estimate GSI ratings, with emphasis on the limitations that exist in rock engineering design when assigning a unique GSI value to spatially variable rock masses.     

Estimating the geotechnical properties of heterogeneous rock masses such as flysch

The design of tunnels and slopes in heterogeneous rock masses such as flysch presents a major challenge to geologists and engineers. The complex structure of these materials, resulting from their depositional and tectonic history, means that they cannot easily be classified in terms of widely used rock mass classification systems. A methodology for estimating the Geological Strength Index and the rock mass properties for these geological formations is presented in this paper. Electronic Publication     

A comparative review in regards to estimating bearing capacity in jointed rock masses in northeast Jordan

There are a number of different methods used for estimating the bearing capacity in jointed rock masses. In this paper, the geological strength index (GSI) introduced by Hoek et al. (1995) was used to estimate the bearing capacity of the rock mass via rock mass rating (RMR). An empirical relationship is proposed to estimate the bearing capacity of the rock mass using the GSI-dependent toughness factor (TF). The proposed formula was correlated with bearing capacity equations used in the literature. The regression analyses showed exponential relationships with a high correlation coefficient.     

A simplified approach to directly consider intact rock anisotropy inHoekeBrown failure criterion

Many rock types have naturally occurring inherent anisotropic planes, such as bedding planes, foliation,or flow structures. Such characteristic induces directional features and anisotropy in rocks＇ strength anddeformational properties. The HoekeBrown （HeB） failure criterion is an empirical strength criterionwidely applied to rock mechanics and engineering. A direct modification to HeB failure criterion toaccount for rock anisotropy is considered as the base of the research. Such modification introduced a newdefinition of the anisotropy as direct parameter named the anisotropic parameter （Kb）. However, thecomputation of this parameter takes much experimental work and cannot be calculated in a simple way.The aim of this paper is to study the trend of the relation between the degree of anisotropy （Rc） and theminimum value of anisotropic parameter （Kmin）, and to predict the Kmin directly from the uniaxialcompression tests instead of triaxial tests, and also to decrease the amount of experimental work.
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Strength of massive to moderately jointed hard rock masses

The Hoek-Brown(HB) failure criterion and the geological strength index(GSI) were developed for the estimation of rock mass strength in jointed and blocky ground where rock mass failure is dominated by sliding along open joints and rotation of rock blocks. In massive, veined and moderately jointed rock in which rock blocks cannot form without failure of intact rock, the approach to obtain HB parameters must be modified. Typical situations when these modifications are required include the design of pillars,excavation and cavern stability, strainburst potential assessment, and tunnel support in deep underground conditions(around s1/s ci 0.15, where s1 is the major principal compressive stress and s ciis the unconfined compressive strength of the homogeneous rock) in hard brittle rocks with GSI ! 65. In this article, the strength of massive to moderately jointed hard rock masses is investigated, and an approach is presented to estimate the rock mass strength envelope using laboratory data from uniaxial and triaxial compressive strength tests without reliance on the HB-GSI equations. The data from tests on specimens obtained from massive to moderately jointed heterogeneous(veined) rock masses are used to obtain the rock and rock mass strengths at confining stress ranges that are relevant for deep tunnelling and mining;and a methodology is presented for this purpose from laboratory data alone. By directly obtaining the equivalent HB rock mass strength envelope for massive to moderately jointed rock from laboratory tests,the HB-GSI rock mass strength estimation approach is complemented for conditions where the GSIequations are not applicable. Guidance is also provided on how to apply the proposed approach when laboratory test data are not or not yet available.     

A generic method for rock mass classification

Rock mass classification (RMC) is of critical importance in support design and applications to mining, tunneling and other underground excavations. Although a number of techniques are available, there exists an uncertainty in application to complex underground works. In the present work, a generic rock mass rating (GRMR) system is developed. The proposed GRMR system refers to as most commonly used techniques, and two rock load equations are suggested in terms of GRMR, which are based on the fact that whether all the rock parameters considered by the system have an influence or only few of them are influencing. The GRMR method has been validated with the data obtained from three underground coal mines in India. Then, a semi-empirical model is developed for the GRMR method using artificial neural network (ANN), and it is validated by a comparative analysis of ANN model results with that by analytical GRMR method.     

Face stability analysis of circular tunnels in layered rock masses using the upper bound theorem

An analysis of tunnel face stability generally assumes a single homogeneous rock mass. However, most rock tunnel projects are excavated in stratified rock masses. This paper presents a two-dimensional (2D) analytical model for estimating the face stability of a rock tunnel in the presence of rock mass stratification. The model uses the kinematical limit analysis approach combined with the block calculation technique. A virtual support force is applied to the tunnel face, and then solved using an optimization method based on the upper limit theorem of limit analysis and the nonlinear Hoek–Brown yield criterion. Several design charts are provided to analyze the effects of rock layer thickness on tunnel face stability, tunnel diameter, the arrangement sequence of weak and strong rock layers, and the variation in rock layer parameters at different positions. The results indicate that the thickness of the rock layer, tunnel diameter, and arrangement sequence of weak and strong rock layers significantly affect the tunnel face stability. Variations in the parameters of the lower layer of the tunnel face have a greater effect on tunnel stability than those of the upper layer.     

Development of a new classification system for assessing of rock mass drillability index (RDi)

The drilling process and its results are affected by various parameters of the rock material and rock mass. The effects of rock material have been emphasized in various studies; however lack of perfect knowledge of rock mass structural parameters may lead to unpredictable results. This paper presents a new classification system for specifying the rock mass drillability index (RDi). For this purpose, six parameters of the rock mass, including texture and grain size, Mohs hardness, uniaxial compressive strength (UCS), joint spacing, joint filling (aperture) and joint dipping have been investigated by physical modeling and rated. Physical modeling in particular has been used for investigating the effects of joint characteristics on drilling rate. In the proposed RDi system, each rock mass is assigned a rating from 7 to 100, with a higher rating corresponding greater ease of drilling. Based on the RDi rating, the drilling rate may be classified into five modes: slow, slow-medium, medium, medium-fast, and fast.     

Analytical solutions for the stresses and deformations of deep tunnels in an elastic-brittle-plastic rock mass considering the damaged zone

The excavation impact (e.g. due to blasting, TBM drilling, etc.) induces an excavation damaged or disturbed zone around a tunnel. In this regard, in drill and blast method, the damage to the rock mass is more significant. In this zone, the stiffness and strength parameters of the surrounding rock mass are different. The real effect of a damage zone developed by an excavation impact around a tunnel, and its influence on the overall response of the tunnel is of interest to be quantified. In this paper, a fully analytical solution is proposed, for stresses and displacements around a tunnel, excavated in an elastic–brittle–plastic rock material compatible with linear Mohr–Coulomb criterion or a nonlinear Hoek–Brown failure criterion considering the effect of the damaged zone induced by the excavation impact. The initial stress state is assumed to be hydrostatic, and the damaged zone is assumed to have a cylindrical shape with varied parameters; thus, the problem is considered axial-symmetric. The proposed solution is used to explain the behavior of tunnels under different damage conditions. Illustrative examples are given to demonstrate the performance of the proposed method, and also to examine the effect of the damaged zone induced by the excavation impact. The results obtained by the proposed solution indicate that, the effects of the alteration of rock mass properties in the damaged zone may be considerable.     

含断续节理岩体强度的各向异性研究

根据断续节理岩体结构的力学效应和压剪断裂破坏特征，用Ｈｏｅｋ－Ｂｒｏｗｎ经验准则预测含断续节理岩体的强度，建立强度参数ｍ，ｓ值与断续节理的几何尺寸、结构形式以及岩桥和节理面物理力学参数之间的定量关系，阐明含断续节理岩体强度的各向异性特征，提出合理确定断续节理岩体强度参数ｍ，ｓ的定量分析法。     

Tunnel behaviour and support associated with the weak rock masses of flysch

Flysch formations are generally characterised by evident heterogeneity in the presence of low strength and tectonically disturbed structures. The complexity of these geological materials demands a more specialized geoengineering characterisation. In this regard, the paper tries to discuss the standardization of the engineering geological characteristics, the assessment of the behaviour in underground excava- tions, and the instructions-guidelines for the primary support measures for flysch layer qualitatively. In order to investigate the properties of flysch rock mass, 12 tunnels of Egnatia Highway, constructed in Northern Greece, were examined considering the data obtained from the design and construction records. Flysch formations are classified thereafter in 11 rock mass types （I-XI）, according to the siltstone -sandstone proportion and their tectonic disturbance. A special geological strength index （GSI） chart for heterogeneous rock masses is used and a range of geotechnical parameters for every flysch type is presented. Standardization tunnel behaviour for every rock mass type of flysch is also presented, based on its site-specific geotechnical characteristics such as structure, intact rock strength, persistence and complexity of discontinuities. Flysch, depending on its types, can be stable even under noticeable overburden depth, and exhibit wedge sliding and wider chimney type failures or cause serious deformation even under thin cover. Squeezing can be observed under high overburden depth. The magnitude of squeezing and tunnel support requirements are also discussed for various flysch rock mass types under different overburdens. Detailed principles and guidelines for selecting immediate support mea- sures are proposed based on the principal tunnel behaviour mode and the experiences obtained from these 12 tunnels. Finally, the cost for tunnel support from these experiences is also presented.     

Physical and mechanical properties of rock masses at Stromboli: a dataset for volcano instability evaluation

Stromboli island has a complex geological history with repeated changes in the volcanic activity alternating with destructive events, caldera collapses and flank landslides. The last activity resulted in the creation of the Sciara del Fuoco depression which was modified by the recent 2002–2003 landslide. The variation in lithology, degree of tectonization and disturbance has resulted in the presence of a wide spectrum of geotechnical materials. This paper summarises the physical and mechanical properties of Stromboli’s intact rocks, rock masses and loose deposits, based on field surveys and laboratory tests. A new classification of the rock succession is introduced and four lithotechnical units defined: Lava, Lava-Breccia, Breccia and Pyroclastic deposit. The range of variability in bulk volume, porosity, intact rock compressive strength and geological strength index is presented. The Hoek and Brown’s failure criterion was applied for each lithotechnical unit and the rock mass friction angle, apparent cohesion, tensile and compressive strength, global strength and modulus of deformation calculated in a specified stress range.      

Strength classification of rock material based on textural properties

Rock, as a construction material, has great importance during the construction and service phases in a rock environment. The classification of rock materials based on their strength behavior provides a simple and fast solution to determine the type and application of support system as well as the method for opening underground structures. Intact rock materials are generally classified with regard to the strength, such as uniaxial compressive and point load strength. Rock texture, which consists of grains and matrix, directly affects the strength. The relation between the textural and mechanical properties of rock materials has been investigated, and rock texture was quantified from the texture coefficient (TC). The coefficient can be used to put a number on rock textures with experimental studies carried out on thin sections of rock material using image analysis. The main scope of this research is to classify the rock material according to its TC values based on the binary and fuzzy domain. In this study, TC is divided into five classes from very low to very high, and a fuzzy model is proposed to predict the uniaxial compressive strength from TC. A dataset is prepared to construct an objective study with 12 litho-type rock materials from 19 locations in Turkey. The binary and fuzzy classification as well as fuzzy model for the prediction of compressive strength is also applied to the dataset to illustrate the use of the proposed classification and model for underground construction in rock engineering. The model is applied to determine the intact rock material’s rating in rock mass rating classification (RMR) from the proposed classification as well as from the fuzzy model. The results of the example encourage the application of the proposed methods, especially for pre-feasibility studies of rock engineering projects.     

Overhanging rock slope by design: An integrated approach using rock mass strength characterisation,large-scale numerical modelling and limit equilibrium methods

Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlights an integrated approach of designing overhanging rock slopes where the relative dimensions of the slope exceed the scale of fracturing and the rock mass failure needs to be considered rather than kinematic release of individual blocks. The key to the method is a simplified limit equilibrium(LE) tool that was used for the support design and analysis of a multi-faceted overhanging rock slope. The overhanging slopes required complex geometries with constantly changing orientations. The overhanging rock varied in height from 30 m to 66 m. Geomechanical modelling combined with discrete fracture network(DFN)representation of the rock mass was used to validate the rock mass strength assumptions and the failure mechanism assumed in the LE model. The advantage of the simplified LE method is that buttress and support design iterations(along with sensitivity analysis of design parameters) can be completed for various cross-sections along the proposed overhanging rock sections in an efficient manner, compared to the more time-intensive, sophisticated methods that were used for the initial validation. The method described presents the development of this design tool and assumptions made for a specific overhanging rock slope design. Other locations will have different geological conditions that can control the potential behaviour of rock slopes, however, the approach presented can be applied as a general guiding design principle for overhanging rock cut slope.