Developments in the Assessment of In-situ Block Size Distributions of Rock Masses

Summary  The block sizes in a rock mass play an important role in many rock engineering projects and therefore the assessment of in-situ block size distribution (IBSD) has been an increasing pursuit of researchers in mining, quarrying and highway cutting operations. This paper discusses further developments in the assessment of IBSD which build upon a broadly accessible approach for engineers published previously by the Geomaterials Unit. The original research provided look-up tables appropriate for field data, with theoretical joint set spacing distributions and an assumption that discontinuities extend indefinitely. The developments reported in the paper include: the prediction of IBSD with special reference to discontinuity sets with fractal spacing distributions; the influence of impersistence of discontinuities on the prediction of IBSD; and the use of grey correlation analysis when selecting a closely fitting theoretical distribution for discontinuity spacing data. Various approaches to IBSD assessment are discussed.     

Prediction of in-situ block size distributions with reference to armourstone for breakwaters

Understanding a quarry in terms of its potential for breakwater construction materials presents a special challenge for the engineering geologist. Unlike blasting in aggregates and mining operations, optimisation of the extraction process has a focus on the potential for production of large blocks for armourstone. These blocks weighing many tonnes are used for cover layers to resist wave action. The quarry-run is used for breakwater core. If the quarry has been developed as a source of materials dedicated to a breakwater construction project, the success of the project depends greatly on the blasting and production of rock sizes that are required and the avoidance of leaving a massive quantity of unused materials behind in the quarry after project completion. Prediction of in-situ block sizes such as from joint spacing data, provides the most critical input for the prediction of the blast pile block size distribution (BBSD), which in turn is a vital early design input if the constructed breakwater is to be economical as well as effective.This paper is part of a series of papers that introduces the coastal engineering motivation for this work on engineering geology, giving reasons why the prediction of the fragmentation curve of the blast products in a dedicated quarry is of such economic importance for breakwater projects. The first step towards blasted block size distribution (BBSD) prediction is the prediction of the in-situ block sized distribution (IBSD), the main subject of this paper. Drawing together research methods from the 1990s and the rock mechanics principles of discontinuity analysis, a practical step by step methodology for IBSD assessment that includes approaches that are not reliant on specialised computer software is presented. Continuing on the practical theme, a new extension of the volumetric joint count approach is suggested for IBSD prediction for the case when sparse borehole data is all that is available. A case study of IBSD assessment and the associated BBSD and blast assessment is presented from a Carboniferous limestone quarry. For clarity, details of blast design and yield curve prediction that are recommended for use in the context of armourstone production, have been presented in a companion paper. The Rosin-Rammler equation is used as an example form for the BBSD prediction of a dedicated quarry and the potential for breakwater project optimisation is illustrated. The final section sets out a method for directly comparing yield curves together with the demand for materials set by the breakwater design. On the same plot, sizes where there is a relative shortfall in production can be identified. The dependence of effective breakwater design on accurate quarry yield prediction and quarry blasting performance is discussed.     

Performance Prediction of Large-Diameter Circular Saws Based on Surface Hardness Tests for Mugla (Turkey) Marbles

Surface hardness tests such as Shore hardness (SH) and Schmidt hammer rebound hardness (SR) may provide a quick and inexpensive measure of rock hardness, which may be widely used for estimating the mechanical properties of rock material such as strength, sawability, drillability and cuttability. In the marble industry, circular sawing with diamond sawblades constitutes a major cost in the processing. Therefore, several models based on the relations between hourly slab production (P _hs), rock surface hardness (SH and SR) and mineral grain size (S _cr) were developed using the data obtained from field and laboratory measurements on five different marbles quarried in the Mugla Province of Turkey. The models which include surface hardness and crystal size may as well be used for the prediction of sawability (hourly slab production) of carbonate rocks using large-diameter circular saws.     

Influence of Stochastic Discontinuity Network Parameters on the Formation of Removable Blocks in Rock Slopes

Summary  We study the effects of discontinuity network parameters on the formation of removable wedges in rock slopes. Discontinuities are simulated using the Poisson disk model, and removable wedges are identified using block theory. The formation of removable wedges of different sizes is assumed to follow a Poisson process. Poisson regression and Monte Carlo simulation are then used to identify statistically relevant parameters of the model, and to study the effects that variations in their values have on formation of removable blocks. The sensitivity of the results as a function of the mean orientations of the discontinuity sets forming the blocks is also studied by means of a parametric study. The volumetric intensity of discontinuities in the rock mass is found to have a significant impact on the computed estimates of removable block formation. As predicted by theory, our results indicate that, everything else being equal, the expected rate of formation of removable wedges is proportional to the square of the intensity measure. Estimates are also sensitive to changes in discontinuity size, especially in cases in which discontinuities are smaller than one to two times the height of the slope. The interaction between the mean size of discontinuities and the coefficient of variation of discontinuity sizes is found to be significant as well. Finally, results of our sensitivity analysis suggest that the orientation of discontinuity sets significantly affects the rate of formation of removable blocks in rock slopes. Author’s address: Dr. Rafael Jimenez-Rodriguez, ETS Ing. de Caminos, Canales y Puertos. Universidad Politecnica de Madrid, Spain     

Evaluating rock mass geometry from photographic images

Summary The importance of discontinuities in controlling rock mass behaviour in any engineering project involving excavations calls for a sound and spatial characterization of the discontinuity structure present. Such a characterization necessitates field work that requires sufficient rock exposures in order to obtain an adequate number of data, time and considerable cost. Photoanalysis techniques can help in overcoming the above difficulties equally well or better than other techniques. This paper refers to simple photographic techniques and their implementation for computer aided analyses for the characterization of the rock mass fracturing features. In particular attention is focused on scale problems and on reconstruction of fracture density stereoplots on the basis of data collected from one or two images according to different lithologies and outcropping conditions. The methodology for evaluating the volumetric fracture intensity follows in a slightly modified way a technique previously suggested in the literature. Certain reported examples allow to validate the photoanalytical technique used and the proposed method of analysis. Furthermore, analyses on planar density, spacing, frequency, terminations in solid rock or against other discontinuities and spatial correlation have been implemented in a software to yield a more complete rock mass characterization. At the same time input data and analysis results are produced in data files available as input for numerical analyses.     

Numerical Homogenization of Jointed Rock Masses Using Wave Propagation Simulation

Homogenization in fractured rock analyses is essentially based on the calculation of equivalent elastic parameters. In this paper, a new numerical homogenization method that was programmed by means of a MATLAB code, called HLA-Dissim, is presented. The developed approach simulates a discontinuity network of real rock masses based on the International Society of Rock Mechanics (ISRM) scanline field mapping methodology. Then, it evaluates a series of classic joint parameters to characterize density (RQD, specific length of discontinuities). A pulse wave, characterized by its amplitude, central frequency, and duration, is propagated from a source point to a receiver point of the simulated jointed rock mass using a complex recursive method for evaluating the transmission and reflection coefficient for each simulated discontinuity. The seismic parameters, such as delay, velocity, and attenuation, are then calculated. Finally, the equivalent medium model parameters of the rock mass are computed numerically while taking into account the natural discontinuity distribution. This methodology was applied to 17 bench fronts from six aggregate quarries located in Tunisia, Spain, Austria, and Sweden. It allowed characterizing the rock mass discontinuity network, the resulting seismic performance, and the equivalent medium stiffness. The relationship between the equivalent Young’s modulus and rock discontinuity parameters was also analyzed. For these different bench fronts, the proposed numerical approach was also compared to several empirical formulas, based on RQD and fracture density values, published in previous research studies, showing its usefulness and efficiency in estimating rapidly the Young’s modulus of equivalent medium for wave propagation analysis.     

On Distance Measures for the Fuzzy K-means Algorithm for Joint Data

Summary  The analysis of data collected on rock discontinuities often requires that the data be separated into joint sets or groups. A statistical tool that facilitates the automatic identification of groups of clusters of observations in a data set is cluster analysis. The fuzzy K-means cluster technique has been successfully applied to the analysis of joint survey data. As is the case with all clustering algorithms, the results of an analysis performed with the fuzzy K-means algorithm for discontinuity data are highly dependent on the distance metric employed in the analysis. This paper explores the significant issues surrounding the choice and use of various distance measures for clustering joint survey data. It also proposes an analogue of the Mahalanobis distance norm (used for data in Euclidean space) for clustering spherical data. Sample applications showing the greater flexibility and power of the new distance measure over the originally proposed distance metric for spherical data are given in the paper.     

复杂构造条件下大型地下工程开挖局部不稳定块体分析与预测

锦屏一级水电站泄洪洞位于雅砻江右岸埋深大于100m的大理岩中,构造条件复杂,在施工开挖过程中产生大量不稳定块体,严重影响工程安全。本文以泄洪洞0＋210～0＋230m段中导洞现场工程为依托,根据所揭露出的工程地质条件,采用赤平投影、统计分析和块体理论等手段,对该工程段可能存在的不稳定块体进行了分析和预测。分析得到如下结论：（1）未开挖段不稳定块体由fxh-14、fxh-16断层与②、④组节理和开挖临空面切割产生,主要分布在右侧拱脚部位;（2）可能的大小主要取决于②、④组结构面的延伸长度;（3）搜索结果表明：未开挖段右侧拱脚处存在两处大型块体。经块体理论计算,其中由L一。。与②、④组节理和临空面组合而成的不稳定块体体积26．8m3,稳定性系数2．89。而fxh-14、fxh-16断层、②组节理与临空面切割而成的不稳定块体体积25．40,破坏模式为直接掉落,应施以相应的工程支护补强措施。     

Estimation of Block Sizes for Rock Masses with Non-persistent Joints

Summary  Discontinuities or joints in the rock mass have various shapes and sizes. Along with the joint orientation and spacing, the joint persistence, or the relative size of the joint, is one of the most important factors in determining the block sizes of jointed rock masses. Although the importance of joint persistence on the overall rock mass strength has long been identified, the impact of persistence on rock strength is in most current rock mass classification systems underrepresented. If joints are assumed to be persistent, as is the case in most designs, the sizes of the rock blocks tend to be underestimated. This can lead to more removable blocks than actually exist in-situ. In addition, a poor understanding of the rock bridge strength may lead to lower rock mass strengths, and consequently, to excessive expenditure on rock support. In this study, we suggest and verify a method for the determination of the block sizes considering joint persistence. The idea emerges from a quantitative approach to apply the GSI system for rock mass classification, in which the accurate block size is required. There is a need to statistically analyze how the distribution of rock bridges according to the combination of joint orientation, spacing, and persistence will affect the actual size of each individual block. For this purpose, we generate various combinations of joints with different geometric conditions by the orthogonal arrays using the distinct element analysis tools of UDEC and 3DEC. Equivalent block sizes (areas in 2D and volumes in 3D) and their distributions are obtained from the numerical simulation. Correlation analysis is then performed to relate the block sizes predicted by the empirical equation to those obtained from the numerical model simulation. The results support the concept of equivalent block size proposed by Cai et al. (2004, Int. J. Rock Mech. Min. Sci., 41(1), 3–19).     

Stability analysis and optimization of the support system of an underground powerhouse cavern considering rock mass variability

Input parameters, such as rock mass strength parameters and deformation modulus, considered in the design of underground openings involve some uncertainty. The current uncertainty in these parameters is due to the inherent variability of these parameters. To quantify these parameters and design underground openings, the statistical methods must be utilized. In this research, a statistical method was used to define the GSI of rock mass (Geological Strength Index), block volume (V_b), and joint conditions (J_c). Using the GSI distribution function obtained from field data and intact rock strength characteristics, the statistical distribution functions of rock mass parameters were defined using the Monte Carlo method. The statistical analysis of the stability in Azad-pumped storage powerhouse cavern was carried out through the point estimate method. The appropriate support system was suggested according to the support pressure and the plastic zone around the cavern. This study showed the application of the statistical method, by combining the uncertainties of the intact rock strength and discontinuity parameters, in the assessment of the strength and deformability of rock masses and the support selection process in comparison with the deterministic methods.     

Probabilistic key block analysis of a mine ventilation shaft stability – a case study

In this study, the probabilistic key block analysis was applied to evaluate the stability of a mine ventilation shaft developed in a rock mass of granite. The key blocks were identified based on the block theory. The variations of discontinuity orientations were fitted with the Beta distribution and taken into consideration. The key block forming probabilities were analyzed. For simplification of calculations the first-order second-moment (FOSM) approximation was employed for probability estimation. With the considerations of the rock properties as random variables and applications of several statistical analysis tools, the key block failure probabilities, the probabilistic distribution of safety factors, and the probabilistic distribution of potential maximum key block volumes were analyzed. The analysis indicated that although the safety factor calculated based on the mean values of the variables was above 1.0 for the stability of the most critical key block, the block had a considerable probability of failure with a significant rock volume due to variations in discontinuity orientations and rock properties. Without promptly applying supports to the rock excavation, the shaft had a significant likelihood of failure.     

Probabilistic analysis of rock slope stability and random properties of discontinuity parameters, Interstate Highway 40, Western North Carolina, USA

Probabilistic analysis has been used as an effective tool to evaluate uncertainty so prevalent in variables governing rock slope stability. In this study a probabilistic analysis procedure and related algorithms were developed by extending the Monte Carlo simulation. The approach was used to analyze rock slope stability for Interstate Highway 40 (I-40), North Carolina, USA. This probabilistic approach consists of two parts: analysis of available geotechnical data to obtain random properties of discontinuity parameters; and probabilistic analysis of slope stability based on parameters with random properties. Random geometric and strength parameters for discontinuities were derived from field measurements and analysis using the statistical inference method or obtained from experience and engineering judgment of parameters. Specifically, this study shows that a certain amount of experience and engineering judgment can be utilized to determine random properties of discontinuity parameters. Probabilistic stability analysis is accomplished using statistical parameters and probability density functions for each discontinuity parameter. Then, the two requisite conditions, kinematic and kinetic instability for evaluating rock slope stability, are determined and evaluated separately, and subsequently the two probabilities are combined to provide an overall stability measure. Following the probabilistic analysis to account for variation in parameters, results of the probabilistic analyses were compared to those of a deterministic analysis, illustrating deficiencies in the latter procedure. Two geometries for the cut slopes on I-40 were evaluated, the original 75° slope and the 50° slope which has developed over the past 40 years of weathering.     

Critical review on shear strength models for soil-infilled joints

An infilled rock joint is likely to be the weakest plane in a rock mass. The presence of infill material within the joint significantly reduces the friction of the discontinuity boundaries (i.e. rock to rock contact of the joint walls). The thicker the infill, the smaller the shear strength of the rock joint. Once the infill reaches a critical thickness, the infill material governs the overall shear strength, and the joint walls (rock) play no significant role. Several models have been proposed to predict the peak shear strength of soil-infilled joints under both constant normal load (CNL) and constant normal stiffness (CNS) boundary conditions, taking into account the ratio of infill thickness (t) to the height of the joint wall asperity (a). CNS models provide a more realistic picture of the soil-infilled joint behaviour in the field. This paper presents a critical review on the existing mathematical models for predicting the shear strength of soil-infilled rock joint and verifies the normalised peak shear stress model with further laboratory investigations carried out on idealised saw-tooth rock joints at the University of Wollongong. Based on the prediction of the experimental data, the normalised peak shear stress model is slightly modified by the authors. A simplified approach for using this model in practice is presented and a new expression for prediction of dilatation at peak shear stress is suggested.     

偏压连拱隧道围岩稳定性分析与现场监控量测

针对偏压连拱隧道围岩稳定性问题,采用GeoStudio软件的SIGMA模块进行数值模拟,以数值模拟的计算结果作为判断围岩稳定性的控制指标,结合现场压力盒进行监控量测,并利用加权回归分析方法对监测数据进行处理,得出各监测点实测围岩稳定压力。通过对数值模拟结果与现场监测数据的对比分析,可知隧道围岩处于稳定状态。结果表明,利用有限元对隧道进行数值模拟和加权回归分析对监测数据进行处理,两种方法相结合对判断偏压连拱隧道围岩稳定性具有很好的效果。     

Determining the size and shape of blocks from linear sampling for geotechnical rock mass classification and assessment

Classifying and assessing geotechnical aspects of rock masses involves combining parameters in various ways, guided by empirical considerations, to derive quantitative geotechnical parameters. Geological structures and the deformation history of rocks underpin the nature of rock masses. The kinematics of a deforming rock mass may occur as sliding along throughgoing discontinuities or as distributed sliding on block faces. Distributed sliding will tend to disrupt the continuity of planar structures such that data on the size and shape of blocks is needed, rather than relying on discontinuity orientation data alone. Orientation and spacing data can be combined to provide a geometric analysis of block systems from linear samples, such as drill core. Dihedral angles and spacing of sequential pairs of discontinuities provides a sample of the size and shape of blocks that can be interpreted stereologically. Further detail can be derived by combining neighbouring intersections that enclose or partially enclose individual blocks. The shape and size of a block can be represented on a stereograph with the enclosing faces shown as poles and their perpendicular distance from an arbitrary point inside the block shown as a number. Identifying the size and shape of specific blocks rather than relying on statistical methods is beneficial to critical aspects of design such as analysing keyblocks that would be exposed during excavations. The detailed characterization of block size and shape is also a step toward interpreting the kinematics of rock mass deformation and the analysis of rock masses as ultra-close packed dilatant granular systems.     

基于PFC2D数值试验的异性结构面剪切强度特性研究

天然岩体中广泛发育两侧岩性不同的异性结构面,开展异性结构面变形和强度特性研究旨在为岩体稳定性评价和利用提供依据。选取三峡库区侏罗系典型的砂岩-泥岩异性岩层,首先运用分形几何理论,定量计算了平直和4种不同不规则起伏形态结构面的粗糙度系数JRC值,然后基于PFC2D颗粒流程序,分别开展了以上5种形态异性结构面的数值剪切试验,获得了各形态结构面在不同正应力下的剪切应力-位移曲线。根据数值试验结果,采用巴顿的JRC-JCS模型分析了异性结构面强度特性,并与同性结构面强度性质进行对比研究。最后,在考虑异性结构面剪切破坏机制的基础上,引入强度因子的概念,提出了新的适用于异性结构面强度评价的两类改进巴顿准则。研究结果表明：异性岩体结构面抗剪强度介于相同粗糙度的两种同性结构面强度之间,在较低正应力下接近软岩同性结构面强度,符合Ⅰ型改进巴顿准则;在较高正应力下偏向硬岩同性结构面强度,符合Ⅱ型改进巴顿准则。实际工程中可利用改进准则并根据异性结构面应力状态对岩体稳定性进行评价,弥补了以往研究的不足。     

含两组交叉贯通节理岩体的强度及破坏特征分析

天然岩体中常含有多组相互交叉的贯通节理,它们的存在极大地削弱了岩体的力学性质。为了研究含两组交叉贯通节理岩体的强度及破坏特征,基于弹塑性数值流形方法,对不同应力状态下,节理倾角和节理间距不同的岩体压缩试验进行数值模拟。结果表明：岩体强度随节理倾角的变化曲线呈现出多波峰、多波谷特点,岩体强度随节理间距变化曲线符合负指数函数形式。根据节理状态,两组节理岩体的破坏模式可以分为3种：岩块破坏、沿一组节理滑移和沿两组节理滑移。两组节理均会影响岩体强度,一组起主要作用,另一组起次要作用,并且节理组之间存在相互影响。通过对数值计算结果进行回归分析,基于一组节理岩体强度预测模型,量化节理组之间的相互影响,提出适用于含两组交叉贯通节理岩体的强度预测模型。模型形式简单,使用方便,可为实际工程中正确评估岩体强度提供指导性意见。     

The Influence of Testing Procedures on Uniaxial Compressive Strength Prediction of Carbonate Rocks from Equotip Hardness Tester (EHT) and Proposal of a New Testing Methodology: Hybrid Dynamic Hardness (HDH)

The Equotip hardness tester (EHT) is a portable and non-destructive instrument used mainly for the dynamic rebound hardness testing of metals. Although various versions of the ‘single impacts’ and ‘repeated impacts’ testing procedures have been employed by different authors for different applications, it is not yet known whether a particular testing procedure is more relevant for a specific application in rock engineering. To be able to contribute to the subject, the present study was carried out to determine the suitability of different rebound testing procedures with this instrument for uniaxial compressive strength (UCS) estimations of some selected carbonate rocks. To achieve this goal, as well as four different existing rebound testing procedures, a newly proposed testing methodology involving the parameter hybrid dynamic hardness (HDH) was also employed. The statistical analyses performed on the experimental data, on the whole, showed that the test procedures which are based on single impacts test procedures outperformed the repeated impacts test procedures in terms of UCS prediction accuracy. The prediction capability of the newly introduced testing methodology was found to be superior to those of other procedures considered in this work, suggesting that it could be an efficient tool in practice for preliminary estimates of rock strength. The statistical analyses also indicated that, in practical applications of the EHT using different test procedures, it may be possible to predict the UCS more accurately when apparent density data is available. For the range of specimen sizes considered, no clear evidence of size effect was observed in the mean rebound values. The argument raised by some other authors that the EHT might not be a convenient instrument for the dynamic rebound hardness determination of relatively high-porosity rocks was not confirmed in this study.