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.     

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.     

Revisiting rock classification to estimate rock mass properties

This paper presents the results of ongoing research carried out by the author exploring methods to provide a more robust estimate of rock mass properties specifically for use in tunnel design. Data from various large-scale rock mass failures are introduced, including coal pillars. The damage-initiation,spalling-limit approach is compared to the coal pillar database. New comparisons of estimating the geological strength index(GSI) and relationships to estimate the Hoeke Brown failure criterion parameters, mb, s and a, are presented.     

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.     

A new estimation method and an anisotropy index for the deformation modulus of jointed rock masses

The deformation modulus of a rock mass is an important parameter to describe its mechanical behavior.In this study,an analytical method is developed to determine the deformation modulus of jointed rock masses,which considers the mechanical properties of intact rocks and joints based on the superposition principle.Due to incorporating the variations in the orientations and sizes of joint sets,the proposed method is applicable to the rock mass with persistent and parallel joints as well as that with nonpersistent and nonparallel joints.In addition,an anisotropy index AIdmfor the deformation modulus is defined to quantitatively describe the anisotropy of rock masses.The range of AIdmis from 0 to 1,and the more anisotropic the rock mass is,the larger the value of AIdmwill be.To evaluate the proposed method,20 groups of numerical experiments are conducted with the universal distinct element code(UDEC).For each experimental group,the deformation modulus in 24 directions are obtained by UDEC(numerical value)and the proposed method(predicted value),and then the mean error rates are calculated.Note that the mean error rate is the mean value of the error rates of the deformation modulus in 24 directions,where for each direction,the error rate is equal to the ratio of numerical value minus predicted value to the numerical value.The results show that(i)for different experimental groups,the mean error rates vary between 5.06%and 22.03%;(ii)the error rates for the discrete fracture networks(DFNs)with two sets of joints are at the same level as those with one set of joints;and(iii)therefore,the proposed method for estimating the deformation modulus of jointed rock masses is valid.     

Slope stability assessment of an open pit using lattice-spring-based synthetic rock mass (LS-SRM) modeling approach

Discontinuity waviness is one of the most important properties that influence shear strength of jointed rock masses, and it should be incorporated into numerical models for slope stability assessment. However, in most existing numerical modeling tools, discontinuities are often simplified into planar surfaces. Discrete fracture network modeling tools such as MoFrac allow the simulation of non-planar discontinuities which can be incorporated into lattice-spring-based geomechanical software such as Slope Model for slope stability assessment. In this study, the slope failure of the south wall at Cadia Hill open pit mine is simulated using the lattice-spring-based synthetic rock mass (LS-SRM) modeling approach. First, the slope model is calibrated using field displacement monitoring data, and then the influence of different discontinuity configurations on the stability of the slope is investigated. The modeling results show that the slope with non-planar discontinuities is comparatively more stable than the ones with planar discontinuities. In addition, the slope becomes increasingly unstable with the increases of discontinuity intensity and size. At greater pit depth with higher in situ stress, both the slope models with planar and non-planar discontinuities experience localized failures due to very high stress concentrations, and the slope model with planar discontinuities is more deformable and less stable than that with non-planar discontinuities.     

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.     

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.     

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.     

Anisotropic characteristics of jointed rock mass: A case study at Shirengou iron ore mine in China

Rock mass is characterized by the existence of distributed joints whose properties and geometry strongly affect the mechanical behavior of jointed rock masses. A finite element model considering the anisotropic characteristics of fractured rock mass was proposed which could deal with a wide variety of joint distribution in rock mass and then applied in Shirengou iron ore mine in Tangshan, China. First, the scale effects and anisotropy were investigated by using multi-scale discrete fracture network models under uniaxial compression tests. Then, the principal direction of elasticity was found and used in the constitutive law of the equivalent continuum model. Finally, the deformation and failure behavior were studied and verified through site-specific microseismic data. It is found that the stress and damage zone are influenced by joint orientation. This proposed model can efficiently study the effects of rock joints on rock mass behavior and thus contribute to a more reasonable explanation on the dominant effect of the joint sets on deformation and failure of rock mass.     

New approaches to quantify progressive damage and associated dynamic rock mass blockiness

In the past decade, numerical modelling has been increasingly used for simulating the mechanical behaviour of naturally fractured rock masses. In this paper, we introduce new algorithms for spatial and temporal analyses of newly generated fractures and blocks using an integrated discrete fracture network (DFN)-finite-discrete element method (FDEM) (DFN-FDEM) modelling approach. A fracture line calculator and analysis technique (i.e. discrete element method (DEM) fracture analysis, DEMFA) calculates the geometrical aspects of induced fractures using a dilation criterion. The resultant two-dimensional (2D) blocks are then identified and characterised using a graph structure. Block tracking trees allow track of newly generated blocks across timesteps and to analyse progressive breakage of these blocks into smaller blocks. Fracture statistics (number and total length of initial and induced fractures) are then related to the block forming processes to investigate damage evolution. The combination of various proposed methodologies together across various stages of modelling processes provides new insights to investigate the dependency of structure's resistance on the initial fracture configuration.     

基于纵波波速的块状岩体GSI系统

 为减少目前GSI系统对现场地质观察的依赖程度,降低其应用难度,且使其能更加准确地反映一定深度范围内的岩体特性,根据现有研究成果与GSI系统输入参数的定性、定量对应关系,建立基于纵波波速的GSI系统,据此获得大岗山坝区岩体的GSI,通过对比分析此结果与经验公式的结果及基于GSI的岩体变形模量的预测值与实测值的分布规律及其相关性,探讨了将岩体完整系数和岩石风化程度系数作为GSI系统输入参数的可行性。结果表明：基于岩体完整系数和岩石风化程度系数的GSI系统基本可行;风化程度输入参数采用风化岩石与未风化岩石的波速比平方较为合理;岩体完整系数和岩石风化程度系数丰富了GSI系统的输入参数。     

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.     

基于区间理论与GSI的岩质边坡稳定可靠性分析方法

针对采用结构面表面特征与岩体结构的定性描述确定岩体地质强度指标GSI存在较强主观性的特点,首先以结构面表面等级SCR与岩体结构等级SR对其进行量化处理,并根据组成SCR与SR的量化指标取值过程中所具有的不确定性,采用区间值表示参数取值,建立岩体量化GSI区间值确定方法;其次,根据Hoek-Brown准则等效岩体抗剪强度参数转换关系,采用区间数学理论建立出岩体力学参数区间值确定方法;然后,通过区间组合法求解岩质边坡安全系数区间值,并在确定安全系数要求值的基础上采用非概率可靠性分析方法进行稳定可靠性评价,进而建立出基于区间理论与GSI的岩质边坡稳定可靠性分析方法;最后,将其应用于分析湖南省柘溪水电站进水口高边坡稳定性,结果表明该方法具有一定的合理性与可行性。在缺乏现场岩体力学试验与大量样本数据的情况下,该方法为岩质边坡从岩体力学参数确定到稳定可靠性评价提供了一条新途径。     

Interaction of shotcrete with rock and rock bolts—A numerical study

The shotcrete–rock interaction is very complex and is influenced by a number of factors. The influence of the following factors was investigated by a series of numerical analyses: the surface roughness of the opening, the rock strength and Young's modulus, the discontinuities, the extent and properties of the excavated disturbed zone, the mechanical properties of the interface between shotcrete and rock, and the thickness of the shotcrete lining and the rock bolts. The study was carried out as a sensitivity analysis. The results showed that the rock strength and the surface roughness had significant impact on the number of failures at the rock–shotcrete interface and in the shotcrete lining. Furthermore, the behaviour of the lining is sensitive to small amplitudes of the surface roughness. In all the cases investigated, a high interface strength was favourable. The results indicate that if a thick shotcrete lining is dependent on the bond strength. The benefit of using a thicker lining can be doubtful. The analyses showed that for an uneven surface the extent of the EDZ had a minor effect on the behaviour of the shotcrete lining. Furthermore, if rock bolts were installed at the apex of the protrusion instead of at the depression, the number of failures decreased both at the interface and in the lining.     

Influences of the valley morphology and rock mass strength on tunnel convergence: With a case study of Khimti 1 headrace tunnel in Nepal

Underground structures are constructed at the bottom of the valley sides for various purposes and for different reasons. Hydropower projects and transport tunnels are some of the examples of such structures. In this paper, literatures on topographical effects on the in situ stresses in valley and fjord sides are reviewed. An attempt is made to correlate stress anisotropy problems with the valley side topography by using Phase² numerical modelling. Based on an underground construction case study, fifteen in situ stress measurements and the Phase² analysis, stress induced problems have been found to be influenced by the valley morphology. This influence can be monitored by the convergence measurement and by the stress measurement. In addition to the overburden height, the total valley height and the slope need to be considered in the assessment of the stress induced problem. The second aspect dealt with is the influence of the rock strength on the tunnel convergence. In the Khimti 1 headrace tunnel and 66 cases from 15 countries, it has been observed that the tunnel convergence is larger in the weaker rocks than in the stronger rocks though they may have similar Q-values. Rock type such as gneiss or phyllite (corresponding to the rock mass strength) is not considered in the Q-system but it has influence on the convergence that takes place in underground works. Thus, it also needs to be considered in the assessment of potential convergence of an underground structure.     

一种基于GSI弱化的应变软化模型

Mohr-Coulomb和Hoek-Brown破坏模型是目前运用最广泛的两种岩体破坏模型。为了能够直观地描述围岩高应力条件下的脆性破坏,众多学者提出基于这两种破坏模型的岩体参数取值方法,主要包括基于Mohr-Coulomb模型的CWFS模型以及基于Hoek-Brown模型的DISL模型和BDP模型。上述模型在表征岩石的脆性破坏方面均有一定的适应性,但是由于存在高围压条件下的硬化现象以及参数取值物理意义不明确等问题,其在实际工程中的应用受到一定限制。在上述模型的基础之上进一步研究Hoek-Brown破坏模型的参数取值规律,在分析地质强度指标GSI值在岩石压缩变形过程中的变化规律的基础上,通过构建地质强度指标GSI值与围压以及塑性应变的函数关系式,建立一种新的基于GSI弱化的应变软化模型——GSI弱化应变软化模型;然后通过锦屏二级水电站白山组大理岩以及Tennessee大理岩三轴压缩试验数值模拟对该模型进行验证。分析表明：该应变软化模型能够较好地模拟大理岩的三轴力学特性。最后运用该模型评价锦屏二级水电站引水隧洞开挖松弛范围,可为岩体开挖支护提供一定参考。     

A discrete model for prediction of radon flux from fractured rocks

Prediction of radon flux from the fractured zone of a propagating cave mine is basically associated with uncertainty and complexity. For instance, there is restricted access to these zones for field measurements, and it is quite difficult to replicate the complex nature of both natural and induced fractures in these zones in laboratory studies. Hence, a technique for predicting radon flux from a fractured rock using a discrete fracture network (DFN) model is developed to address these difficulties. This model quantifies the contribution of fractures to the total radon flux, and estimates the fracture density from a measured radon flux considering the effects of advection, diffusion, as well as radon generation and decay. Radon generation and decay are classified as reaction processes. Therefore, the equation solved is termed as the advection-diffusion-reaction equation (ADRE). Peclet number (Pe), a conventional dimensionless parameter that indicates the ratio of mass transport by advection to diffusion, is used to classify the transport regimes. The results show that the proposed model effectively predicts radon flux from a fractured rock. An increase in fracture density for a rock sample with uniformly distributed radon generation rate can elevate radon flux significantly compared with another rock sample with an equivalent increase in radon generation rate. In addition to Pe, two other independent dimensionless parameters (derived for radon transport through fractures) significantly affect radon dimensionless flux. Findings provide insight into radon transport through fractured rocks and can be used to improve radon control measures for proactive mitigation.     

Strength and deformation characteristics of irregular columnar jointed rock mass: A combined experimental and theoretical study

The irregularity of jointed network poses a challenge to the determination of field mechanical parameters of columnar jointed rock mass (CJRM), and a reasonable prediction of deformation and strength characteristics of CJRM is important for engineering construction. The Voronoi diagram and three-dimensional printing technology were used to make an irregular columnar jointed mold, and the irregular CJRM (ICJRM) specimens with different dip directions and dip angles were prepared. Uniaxial compression tests were performed, and the anisotropic strength and deformation characteristics of ICJRM were described. The failure modes and mechanisms were revealed in accordance with the final appearances of the ICJRM specimens. Based on the model test results, the empirical correlations for determining the field deformation and strength parameters of CJRM were derived using the dip angle and modified joint factor. The proposed empirical equations were used in the Baihetan Project, and the calculated mechanical parameters were compared with the field test results and those obtained from the tunneling quality index method. Results showed that the deformation parameters determined by the two proposed methods are all consistent with the field test results, and these two methods can also estimate the strength parameters effectively.