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).     

基于GSI值量化和修正方法的岩体力学参数确定

为了准确确定岩体力学参数,通过综合分析多种地质强度指标(GSI)量化方法,提出了一种改进的GSI值量化和修正方法。首先,利用测线法估算结构面平均间距(d)和岩体块度指数(RBI)的改进型岩体块度率(RBR),根据岩体三维结构面网络,获得岩体体积节理数(Jv)和岩体结构等级(SR),然后采用上述参数和结构表面条件(SCR)及结构表面特性参数(Jc)进行了GSI值的定量化处理。为了克服GSI体系的缺点,考虑结构面产状和地下水对岩体力学性质的影响,提出了GSI值的修正方法和公式。以某铅锌矿体的矿岩体为例,根据改进的GSI值量化和修正方法及Hoek-Brown强度准则来确定矿岩体力学参数,通过与原位变形试验的对比分析,验证了该方法的精确性和可行性。该方法为从室内岩石力学试验合理地获取节理岩体力学参数提供了理论及实现的依据。     

经历剪切变形历史的岩石节理表面粗糙特性分析

基于两类岩石节理剪切试验，采用非接触式激光测距仪，实测了剪切前后节理表面粗糙数据，统计分析了岩石节理表面粗糙特性的三维粗糙参数的物理含义，并将这些参数与相应的二维参数进行了充分比较。结果表明，三维参数与二维参数间存在的近似线性关系，而多个三维参数相对比单一的二维参数更全面有效地描述了节理表面粗糙特性。     

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。     

多尺度节理岩体力学特性的颗粒流分析

以白云鄂博露天铁矿东矿岩质高边坡为工程背景,结合现场地质调查、室内岩石和节理力学试验等数据,采用等效岩体技术,构建能充分反映节理分布特征的实验室、现场原位试验和工程尺度等多尺度等效岩体模型。通过对各类等效岩体模型进行单轴压缩试验,研究岩体单轴抗压强度、弹性模量等力学特性的尺寸效应和各向异性。研究表明：节理的存在使岩体表现出尺寸效应和各向异性,且随着尺寸的增大,这种特性基本呈逐渐减弱的趋势;研究区域岩体的表征单元体积、单轴抗压强度和弹性模量分别为20 m×10 m×10 m、1.46 MPa和3.91 GPa;岩体单轴抗压强度、弹性模量与轴向尺寸的关系,近似符合渐进式指数函数关系,且该函数能直观地给出工程尺度岩体的力学特性。     

Indirect determination of weighted joint density (wJd) by empirical and fuzzy models: Supren (Eskisehir, Turkey) marbles

Correct block size assessment is the most important stage for rock quarry management. Although volumetric joint count (J_v) and weighted joint density (wJd) were proposed for this purpose, simple prediction method for these indices is not encountered in literature. Due to the fact that some rock masses such as marbles contain less discontinuity, collection of representative amount of data from in situ line surveys for statistical assessments is highly difficult. For this reason, the main targets of the present paper are to apply photoanalysis approach for collecting additional discontinuity data and to obtain some simple statistical and fuzzy models for predicting weighted joint density to evaluate block size in engineering practice for marbles around Supren (Eskisehir, Turkey). In addition, a new and simple approach to predict volumetric decrease caused by chemical weathering is introduced. For these purposes, extensive field and photoanalysis studies were performed and the data obtained from both field and photoanalysis studies were assessed by regression and fuzzy approaches. The results revealed that the prediction performance of the fuzzy inference system is higher than that of the regression equation.     

Numerical investigation of the effect of joint geometrical parameters on the mechanical properties of a non-persistent jointed rock mass under uniaxial compression

The strength and deformability of rock masses transected by non-persistent joints are controlled by complex interactions of joints and intact rock bridges. The emergence of synthetic rock mass (SRM) numerical modelling offers a promising approach to the analysis of rock masses, but has not been rigorously compared with actual physical experiments. In this work, SRM modelling by the discrete element software PFC3D is used to investigate the effect of geometric parameters of joints on the rock mass failure mechanism, unconfined compressive strength and deformation modulus. Firstly, a validation study is undertaken to investigate the ability of SRM modelling to reproduce rock mass failure modes and strength as determined by uniaxial and biaxial compression testing in the laboratory. The numerical analyses agree well with physical experimentation at low confining pressure. A sensitivity study is then undertaken of the effect of joint configuration parameters on the failure mode, unconfined compressive strength and deformation modulus of the rock mass. Five failure modes are predicted to occur: intact rock, planar, block rotation, step-path and semi-block generation. It is found that the failure mode is determined principally by joint orientation and step angle and the joint orientation with respect to principal stress direction is the parameter with the greatest influence on rock mass properties.     

基于蒙特卡罗随机模拟的矿岩崩落块度预测研究

基于实测节理面空间几何参数,采用蒙特卡罗方法对某大型镍矿III矿区节理空间进行了模拟。采用自主研发的三维矿岩块度预测软件MAKEBLOCK对其矿岩块度分布进行了预测和分析。结果表明,该矿区大多数矿岩块体体积小于 0.2 m3,绝大多数块体形状为盘状和块状,块体等效尺寸大多在0.2 m到1.5 m之间。预测结果可以作为自然崩落法工程设计与实施的参考依据。     

岩体结构面各向异性变异系数的尺寸效应研究

岩体结构面的各向异性与尺寸效应特征对其力学性质影响较大,综合考虑两者之间的相互关系对工程岩体稳定性评价具有重要意义。全面分析不同尺度结构面的各向异性分布,提出考虑正交方向三维形貌参数的各向异性变异系数AVC3D。通过渐进覆盖法统计4组天然岩体结构面10种不同采样尺寸的各向异性变异系数及其尺寸效应规律。结果表明：各向异性变异系数均随结构面尺寸增大而减小至定值,其与结构面尺寸具有较好的负对数函数关系;通过归一化处理,各向异性变异系数与结构面尺寸呈现较好的线性函数关系,表明各向异性变异系数具有分形结构,分维数D可以实现其尺寸效应的规律统计。该方法揭示了影响结构面形貌特征方向性变化的最大有效倾角 和粗糙系数C的增长幅度会随采样尺寸增大趋于稳定的变化机制,体现了当结构面达到各向异性尺寸效应的阈值后,会呈现出稳定的各向异性规律。     

REV and its properties on fracture system and mechanical properties,and an orthotropic constitutive model for a jointed rock mass in a dam site in China

Fracture data available for one of the rock masses (limestone) in the dam site of Yujian River Reservoir were used to build and validate a stochastic 3-D fracture network model, and to perform a REV and equivalent continuum study in 3-D. A number of relations are developed in the paper between the rock mass mechanical parameters and fracture tensor components in 3-D. Based on the mechanical parameter values obtained in every 45° direction in 3-D, the principal parameter values, principal directions and tensors are developed for rock mass mechanical parameters to represent the REV block size properties. An incrementally linear elastic, orthotropic constitutive model is suggested to represent the equivalent continuum pre-failure mechanical behavior of the jointed rock mass by incorporating the effect of joint geometry network by the fracture tensor components.     

Shear deformation and strength of the interphase between the soil–rock mixture and the benched bedrock slope surface

A series of benched excavations were typically carried out on the bedrock slope surface to improve the stability of the soil–rock mixture (S–RM) fill slope. It is difficult to devise an in situ, large-scale direct shear test for the interphase between the S–RM fill and the benched bedrock slope surface. This study introduced a comprehensive approach to investigate the shear deformation and strength of the interphase. First the soil–rock distribution characteristics were analyzed by test pitting, image analysis, and sieve test. Then the PFC2D random structure models with different rock block size distributions were built, and large-scale numerical shear tests for the interphase were performed after calibrating model parameters through laboratory tests. The stress evolution, damage evolution and failure, deformation localization (based on a principle proposed in this paper), rotation of rock blocks, and shear strength were systematically investigated. It was found that as the rock block proportion and rock block size (rock block proportion of 50 %) increase, the fluctuations of the post-peak shear stress–displacement curves of the interphase become more obvious, and the shear band/localized failure path network becomes wider. Generally, smaller rock blocks are of greater rotation angles in the shear band. The peak shear stress and internal friction angle of the interphase increase, while the cohesion decreases with growth of the rock block proportion. However, all these three parameters increase as the rock block size (rock block proportion of 50 %) increases.     

岩体结构对岩质滑坡运动过程和堆积特征的影响研究

我国西南高山峡谷地区,常发生高位岩质斜坡失稳,形成碎屑流,造成巨大人员伤亡与经济财产损失。目前存在着许多关于岩质滑坡的研究理论和物理模型,但这些理论与模型都忽略了岩体结构这一属性,然而对岩质滑坡而言,岩体的结构特征不仅控制着斜坡变形失稳模式,同样影响失稳后滑体碎屑化运动过程,甚至最终的危害范围。因此,文章使用离散元数值模拟方法,通过模拟不同结构面强度、结构面密度、结构面方向和岩块强度下岩质滑坡碎屑化运动过程,研究了不同源区岩体结构对岩质滑坡破碎特征、运动形式和运动距离的影响规律及影响机制。研究结果如下:（1）质心运动距离随结构面强度增大而增大,结构面抗拉强度提升10倍,质心运动距离增加3%;（2）结构面密度的增加使得块体破碎率随之增加,但运动距离和分布面积都呈下降趋势;（3）水平向结构面岩体的前缘运动距离和质心运动距离与其他方向结构面工况相比均降低10%左右,分布面积则缩减接近30%,破碎率最大;（4）随着岩块强度增加,破碎率降低,分布面积最终缩减40%,完整块体工况运动距离最终增大15%左右。结果有助于进一步理解岩质滑坡动力学过程,指导山区防灾减灾工作。     

裂隙岩体块体化程度评价方法的若干问题修正

块体化程度是评价岩体完整性的一种新指标,能从三维角度表征岩体破碎程度,但目前该方法仍存在未充分考虑岩体切割程度及块体规模、未限定基础应用条件、块体化程度等级划分不合理等缺陷。针对上述缺陷,深入分析了其产生原因,并借鉴岩体切割程度、三维块度模数、体积RQD等计算原理,限定了块体体积百分比相关概念,提出了考虑岩体完整性块度尺寸效应的块体体积综合百分比计算方法,确立了块体化程度等级及分级指标取值依据,建立了修正的块体化程度评价方法。通过对比块体化程度评价修正方法、岩土工程规范对岩体完整性的划分结果,分析了修正方法的合理性。分别以广西铜坑矿锌多金属矿体、乌东德水电工程的块体研究数据为基础,开展了修正块体化程度评价方法的实例验证,结果表明：利用修正块体化程度评价方法计算的铜坑矿+255 m中段4#试验区岩体块体体积百分比为11.18%,属轻度块状化岩体;乌东德水电站PD49-1平硐、PD4支硐块体体积百分比分别为12.847%、10.168%,均属于轻度块状化岩体,岩体完整性程度为较完整级别。与现有块体化程度评价方法比较,修正方法计算的块体体积百分比能够更准确地从三维角度表征真实岩体的完整性。研究成果对精确刻画岩体三维完整性具有重要意义。     

复杂地质条件下顶拱大型不稳定块体分析与预测

锦屏一级水电站2#尾水调压室所处位置地质条件复杂,在桩号0+320~0+360和0+0~0+120之间开挖时局部掉块严重。本文综合分析后,提出了2#尾调室顶拱未开挖域产生大型不稳定块体的必要条件是:(1)由节理①④F183组结构面和开挖临空面切割产生;(2)块体大小主要取决于节理组①和④的延伸长度;(3)较大不稳定块体的产生区域,必然位于F18断层带下盘。对2#尾调室顶拱进行搜索预测,预测结果表明该潜在块体位于未开挖区域桩号0+180～0+260之间,规模约为50m3,重达133.5t。根据块体理论分析,其稳定性系数为1.052,处于临界状态,应采取相应的应急支护补强措施。     

基于三维裂隙网络的裂隙岩体表征单元体研究

岩体表征单元体（REV）的研究一直是岩土工程中的重要问题。裂隙岩体REV是其内部复杂结构在尺寸效应上的体现,归因于岩体内裂隙系统的随机性。在三维网络模型的基础上通过计算体积节理数建立了确定岩体REV的方法。这种方法考虑了岩体内裂隙的三维空间密度的特征,采用体积节理数这一参数的收敛状况确定岩体REV的大小。建立了实际岩体的模拟裂隙系统,用一定大小的立方体来分割裂隙系统,统计不同立方体内的体积节理数,并将均值作为最终裂隙岩体的参数。将此参数作为裂隙岩体的属性,通过判别其收敛状况获得了岩体REV的尺寸。考虑了岩体不连续面的特征,建立了REV的分析模型,得出工程岩体的REV的尺寸是裂隙平均迹长的4倍的结论。     

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     

Risk analysis of fractured rock mass underground structures

Recent accidents in underground structures have raised the risk awareness of the geotechnical engineering community. Geotechnical design is subject to significant uncertainties in load and strength parameters as well as in engineering models. However, engineering models which objectively address such uncertainties in design are still scarce. This paper presents an objective framework for the quantification of the risks involved in underground structures excavated in fractured rock masses, where structural failures may occur due to block falls. The framework considers the structure as a distributed system, where falling block probabilities are integrated over the main structural dimension. Random block size and geometry, arising from random joint orientation, are taken into account, as well as uncertainties in joint strength and geometrical parameters. A cost function is used to quantify failure consequences in terms of the block size. The framework is demonstrated in an application to a case study involving a real structure: the Paulo Afonso IV power station cavern. Results of the case study show that the studied cavern presents high reliability and very low risk. The framework proposed herein is shown to be a practical tool for the risk evaluation of underground structures constructed in rock masses, such as caverns and tunnels.     

基于旋转采样法的结构面粗糙度各向异性评价

岩石结构面粗糙度各向异性评价存在不确定性.本文基于高精度激光扫描技术获得的结构面三维点云数据,提出了一种评价岩石结构面粗糙度系数(JRC)各向异性的旋转采样法.通过典型结构面试样的对比分析,探讨了采样方法和尺寸对JRC各向异性的影响.结果表明:(1)已有的单一轮廓线采样法获得的JRC各向异性数据离散,各向异性评价结果偏...     

Visualization of rock mass classification systems

A rock mass classification system is intended to classify and characterize the rock masses, provide a basis for estimating deformation and strength properties, supply quantitative data for mine support estimation, and present a platform for communication between exploration, design and construction groups. In most widely used rock mass classification systems, such as RMR and Q systems, up to six parameters are employed to classify the rock mass. Visualization of rock mass classification systems in multi-dimensional spaces is explored to assist engineers in identifying major controlling parameters in these rock mass classification systems. Different visualization methods are used to visualize the most widely used rock mass classification systems. The study reveals that all major rock mass classification systems tackle essentially two dominant factors in their scheme, i.e., block size and joint surface condition. Other sub-parameters, such as joint set number, joint space, joint surface roughness, alteration, etc., control these two dominant factors. A series two-dimensional, three-dimensional, and multi-dimensional visualizations are created for RMR, Q, Rock Mass index RMi and Geological Strength Index (GSI) systems using different techniques. In this manner, valuable insight into these rock mass classification systems is gained.