Characterization of Strength and Deformation of Jointed Rock Mass Based on Statistical Analysis

This paper deals with the statistical analysis of the uniaxial compressive strength and of the elastic modulus of jointed rock masses under different confining pressures. Properties of the rock masses with different joint fabric, with and without gouge have been considered in the analysis. A large amount of experimental data of jointed rock masses from the literature has been compiled and used for this statistical analysis. The uniaxial compressive strength of a rock mass has been represented in a nondimensional form as the ratio of the compressive strength of the jointed rock to the intact rock. In the case of the elastic modulus, the ratio of elastic modulus of jointed rock to that of intact rock at different confining pressures is used in the analysis. The effect of the joints in the rock mass is taken into account by a joint factor. The joint factor is defined as a function of joint frequency, joint orientation, and joint strength. Several empirical relationships between the strength and deformation properties of jointed rock and the joint factor have been arrived at via statistical analysis of the experimental data. A comparative study of these relationships is presented. The effect of confining pressure on the elastic modulus of the jointed rock mass is also considered in the analysis. These empirical relationships are incorporated in a nonlinear FEM code to carryout the equivalent continuum analysis of jointed rock masses. The method presented in this paper recognizes that the jointed rock mass will act both as an elastic material and a discontinuous mass. The results obtained by the model with equivalent properties of the jointed rock mass predict fairly well the behavior of jointed rock mass.     

Creep Modeling in Excavation Analysis of a High Rock Slope

Based on the distinct element method, a numerical procedure is presented for simulation of creep behavior of jointed rock slopes due to excavation unloading. The Kelvin model is used to simulate viscous deformation of joints. A numerical scheme is introduced to create incremental contact forces, which are equivalent to producing creep deformation of a rock-joint system. The corresponding displacement of discrete blocks due to creep deformation of contact joints can be calculated by equilibrium iteration. Comparisons of results between the numerical model and theoretical solutions of a benchmark example show that the presented model has excellent accuracy for analysis of creep deformation of rock-joint structures. As an application of the model, residual deformations of the high rock slopes of the Three Gorges shiplock due to excavation unloading and creep behavior are investigated. By simulating the actual excavation process, the deformation history of a shiplock slope is studied. Good agreement has been achieved between numerical prediction and field measurements. It demonstrates the effectiveness of the presented model in analysis of the creep deformation due to excavation unloading of high rock slopes.     

Method for Estimating the Deformability of Heavily Jointed Rock Masses

Determination of the deformability of jointed rock masses is an important and challenging task in rock mechanics and rock engineering. In this paper, simple expressions are derived for estimating the equivalent isotropic deformation properties of heavily jointed rock masses using the methodology of equivalent continuum approach. The derived expressions are compared with two analytical relations in the literature and the field test data relating rock quality designation (RQD) and deformation modulus ratio Em/Er, where Em and Er are the deformation modulus of the rock mass and the intact rock, respectively. The derived expressions are in reasonable agreement with the existing analytical relations in the literature and satisfactorily predict the range of the field RQD versus modulus ratio Em/Er data. Finally two examples are presented to demonstrate the application of the derived expressions by applying them to estimate the deformation modulus of jointed rock mass at two sites. The results of the paper can be of help in predicting the deformation behavior of jointed rock masses when the properties of the intact rock and discontinuities are available.     

Comparison between Models of Rock Discontinuity Strength and Deformation

One important component in the design of tunnels in urban areas is a correct assessment of the interaction between the underground excavation with other structures in the vicinity. In this sense a correct stress-strain response by the model representing the rock mass behavior is essential. The shear and normal displacement of rock discontinuities and their shear and normal stiffness control the distribution of stress and displacement within a discontinuous rock mass. In conditions where an equivalent continuum based approach is not applicable, the joint material model should be able to describe important mechanisms such as asperity sliding and shearing, post-peak behavior, asperity deformation, and the effect of soft infilling. The distinct element code UDEC was used to simulate the direct shear tests on a natural joint profile, and the prediction of two existing models of discontinuity strength and deformation were then compared with a new soil-infilled joint model and with experimental data for clean and soil-infilled rock joints. A numerical modeling of a cavern excavated in a jointed medium is also presented to illustrate the response of different models. The proposed soil-infilled joint model described more comprehensively the occurrence of dilation and compression with lateral displacements and also better represented the double peak shearing in relation to the adopted squeezing mechanism that could not be captured by the two existing models.     

Three-Dimensional Joint/Interface Element for Rough Undulating Major Discontinuities in Rock Masses

Major civil engineering structures are being constructed now a days in complex geological environment with faults, shear zones, and other major discontinuities. These major discontinuities can cause a variety of problems in both surface and underground constructions. Unfavorably dipping major discontinuities may create unstable conditions in underground openings and contribute to the deformations of a rock mass under external static loading. Hence, rock–structure interaction analysis should simulate arbitrarily oriented rough and undulating major discontinuities within the rock mass, as well as the undulating interface along the structure and the rock mass such as dam foundations and underground excavations intersected by fault/shear zones. Realistic simulation of the mechanical behavior of rock joints is a prerequisite for successful numerical modeling of discontinuous rocks. When joint modeling is designed to include different degrees of joint roughness, dilation, and aperture, then realistic response depends upon the appropriate constitutive models and the way these parameters interact with stress change. Due to low values of the normal and tangential module, a unique characteristic of a rock discontinuity is that dilation may occur as soon as relative slip takes place and this may significantly alter the stress distribution, particularly around an underground excavation. In view of these practical requirements, a generalized formulation of a three-dimensional joint/interface element has been proposed here to account for dilatancy, roughness, and undulating surface of discontinuities.     

Numerical Implementation of Anisotropic Continuum Model for Rock Masses

In this technical note, rock mass has been regarded as an equivalent anisotropic continuum. Constitutive relationships for the rock masses have been derived. The approach aims to capture the overall behavior of the rock mass based on the constitutive characteristics of intact rock and rock joints including their orientation, spacing, roughness (waviness), number of joint sets, block size, and normal and shear stiffness, etc. This model has been applied to analyze a tunnel using a software package developed for the purpose, with satisfactory results.     

节理岩体数值模拟及力学参数确定

采用FLAC3D程序和离散裂隙网络技术构建的遍布节理岩体模型能同时考虑节理岩体中节理和岩体的作用,具有概念清晰、建模快捷、计算效率高等特点.首先对现场结构面测绘数据进行统计分析,获得其概率分布特征参数,在此基础上分两尺度考虑节理并确定其离散裂隙网络模型;其次基于离散裂隙网络模型构建相应的节理岩体模型,研究其强度特征并获取工程岩体单轴抗压强度;结合Hoek-Brown、Mohr-Coulomb准则及最大围压拟合综合确定节理岩体力学参数;最后将拟合所得参数用于边坡稳定性分析,分别运用强度折减法和极限平衡法计算两种模型的安全系数,对比发现计算结果基本一致,表明所提出的研究思路用于确定节理岩体参数是可行的.      

等效岩体三维随机节理网络模型构建及其在两河口水电站中的应用

节理的存在对水电高陡岩质边坡的力学性质有重要影响,如何构建反映三维节理分布特征的等效岩体计算模型,是分析与评价岩体力学特性的关键。本文基于损伤力学和统计强度理论,在三维岩石破裂过程分析（RFPA3D）软件的基础上,提出了一种计算等效岩体三维随机节理网络模型的新方法。首先,基于Baecher模型和Monte-Carlo方法,在RFPA3D软件中实现了三维随机离散节理网络（Discrete fracture network,DFN）模型的重构。然后,利用RFPA3D软件内嵌DFN模型,赋予节理和岩石不同的力学参数,构建了工程尺度等效岩体三维随机节理网络模型,实现了三维随机节理岩体破裂过程、变形和强度等力学性质的分析。最后,以两河口水电站左岸边坡坝址区下游节理岩体为研究对象,验证了三维随机DFN模型的准确性,开展了研究区内节理岩体尺寸效应研究,并获得了研究区内岩体的表征单元体（Representative elementary volume,REV）和等效力学参数。该研究成果为等效岩体力学行为分析提供一种新方法。      

Effect of Block Size and Joint Geometry on Jointed Rock Hydraulics and REV

The effect of joint geometry parameters and the size of jointed rock block on the hydraulic properties of jointed rock, including the equivalent continuum behavior, was investigated through numerical experimentation. The chance to reach equivalent continuum behavior for a rock mass having a certain joint configuration increases with the increase of block size. The REV (representative elementary volume) size to show hydraulic equivalent continuum behavior for a jointed rock system was found to depend on the orientation of the joint sets; the REV size seems to decrease with increasing joint density and joint size. The REV does not seem to exist for some rock masses having joint systems with low relative orientation angles (systems with two joint sets) and low densities. The average block permeability (K0) value at the REV size for a joint system increases with increase in joint size and joint density. The equivalent continuum behavior of a joint system can be expressed with respect to a cut-off value for the first invariant of fracture tensor (F0). The block size corresponding to the aforementioned cut-off F0 (between 10 and 30 for the joint systems investigated in this study) can be considered to provide the REV size for a given joint configuration. A threshold value for F0 (a joint network having two perpendicular joint sets produced 2.75) can be used to find the chance for a given joint network to have nonzero block permeability. A strong power functional relation seems to exist between the directional permeability and the fracture tensor component for the connected joint configuration when rock blocks contain minor discontinuities.     

3D Modeling of Ripping Process

Due to environmental constraints and limitations on blasting, ripping as a ground loosening and breaking method has become more popular than drilling and blasting method in both mining and civil engineering applications. The best way of estimating the rippability of rocks is to conduct direct ripping runs in the field. However, it is not possible to conduct direct ripping runs in all sites using different dozer types. Therefore, the utilization of numerical modeling of ripping systems becomes unavoidable. A complex ripping system can better be understood with three-dimensional (3D) models rather than two-dimensional models. In this study, 3D distinct element program called 3DEC was used to investigate the ripping process. First, the ripping mechanisms were investigated and then the individual factors that affect the rippability performance of dozers were reviewed. The rippabilities of rocks depend not only on the rock properties, but also machine or dozer properties. Thus, ripper production and rock rippability with D8 type of dozers were also determined by direct ripping runs on different open pit lignite mines within the scope of this research. Production values obtained from numerical modeling were compared with field production values obtained from the case studies. This comparison shows that the model gives consistent and adequate results. Hence, a link has been established between the field results and the 3D models.     

Three-Dimensional Hoek-Brown Strength Criterion for Rocks

A great number of rock strength criteria have been proposed over the past decades. Of these different strength criteria, the Hoek-Brown strength criterion has been used most widely, because: (1) it has been developed specifically for rock materials and rock masses; (2) its input parameters can be determined from routine unconfined compression tests, mineralogical examination, and discontinuity characterization; and (3) it has been applied for over 20?years by practitioners in rock engineering, and has been applied successfully to a wide range of intact and fractured rock types. The Hoek-Brown strength criterion, however, does not take account of the influence of the intermediate principal stress, although much evidence has been accumulating to indicate that the intermediate principal stress does influence the rock strength in many instances. In this paper, a three-dimensional (3D) version of the Hoek-Brown strength criterion has been proposed. The original Hoek-Brown strength criterion is just a two-dimensional (2D) version of the proposed 3D strength criterion. The 3D strength criterion not only inherits the advantages of the original Hoek-Brown strength criterion, but can take account of the influence of the intermediate principal stress. Polyaxial or true triaxial compression test data of intact rocks and jointed rock masses has been collected from the published literature and used to validate the proposed 3D Hoek-Brown strength criterion. Predictions of the proposed 3D Hoek-Brown strength criterion are in good agreement with the test data for a range of different rock types. The proposed 3D Hoek-Brown strength criterion is also compared with a simplified 3D Hoek-Brown strength criterion proposed by Pan and Hudson. The Pan-Hudson criterion cannot be considered a true 3D version of the Hoek-Brown criterion, because it does not reduce to the form of the original Hoek-Brown criterion at either triaxial or biaxial state. The Pan-Hudson criterion underpredicts the strength at the triaxial state, but overpredicts the strength at the biaxial state.     

Analysis of a Powerhouse Cavern in the Himalaya

A powerhouse cavern in the Himalaya has been analyzed using the finite element method under various stages of excavation. A constitutive model based on disturbed state concept has been used to depict the strain softening behavior of the rock mass. The material parameters for the rock mass have been determined from the tests on the intact rock samples from the field. The behavior of the cavern is presented and discussed. The instrumentation used to study the behavior of the cavern during excavation is presented. The predicted and observed behavior of the cavern are compared. It is shown that the predictions are satisfactory.     

断续节理对岩体力学性能的影响

采用颗粒流数值模拟程序,建立不同节理状态的岩石试样模型,对其进行双轴试验模拟,从岩桥长度、节理长度和倾角三个方面对断续节理影响下的岩体破裂形式和力学性质进行了数值模拟分析.岩桥的破裂方式为翼裂纹扩展下的拉剪复合破坏,模型破裂大致经历了翼裂纹的扩展、次生裂纹的延伸以及岩桥的贯通三个过程,而且表现出明显的蠕变特性以及延性破坏.岩桥长度的变化对峰值强度和弹性模量影响较小;相比岩桥长度,节理岩样的力学特性对节理长度更加敏感.对于不同的节理倾角,岩石试件表现出不同的初始破裂形式,0°倾角岩样的破裂方式为翼裂纹的扩展和次生裂纹的延伸,中间岩桥没有被贯通,15°倾角岩样的初裂强度和峰值强度最大.      

山东焦家金矿床工程岩体稳定性分类研究

在矿山开采中常因不良岩体失稳造成很大的损失,因此,在施工前迫切需要对岩体稳定性进行合理的评价研究。本次研究结合焦家金矿的工程地质条件,根据矿区节理裂隙调查统计的结果,在矿区工程地质、节理裂隙素描统计岩石力学性质实验的基础上,采用现场调查统计分析、室内岩石力学试验、不同分类方法组成的岩石综合分级评价法及非线性有限元数值分析相结合的方法,对节理裂隙与地下巷道围岩稳定性的关系进行深入的探讨与研究,针对各区域不同安全等级顶板岩层情况,确定相应的开采技术方案,并对节理裂隙与地下巷道围岩稳定性的关系进行深入探讨。     

基于PEM-JFEM方法的节理岩质边坡稳定性评价

以赞比亚一露天铜矿南帮边坡(矿体下盘)为研究对象,将Rosenbluth点估计方法与节理有限元方法相结合应用于该节理发育的岩质边坡稳定性评价中.建立以边坡岩体材料强度参数(内摩擦角和黏聚力)为输入变量,安全系数为输出变量的概率模型,点估计状态函数的求解过程引入节理有限元方法.通过现场节理及结构面调查,建立边坡节理有限元模型求解边坡安全系数,得到基于安全系数的边坡变形破坏概率统计指标,对边坡稳定性进行了概率分析,分析结果与现场失稳情况一致.该方法既考虑了岩体材料参数在赋值过程中实际存在的不确定性,同时也考虑了节理岩质边坡的节理属性,充分体现了岩层接触作用的非线性关系,使得对节理岩质边坡的稳定性评价更加合理.      

Experimental and Numerical Simulations of Jointed Rock Block Strength under Uniaxial Loading

To simulate brittle rocks, a mixture of sand, plaster of paris, and water was used as a model material. Thin galvanized sheets were used to create joints in blocks made out of the model material. To investigate the failure modes and strength, 30 × 12.5 × 8.6 cm jointed model material blocks having different joint geometry configurations were subjected to uniaxial compressive loading. Results indicated three failure modes: (1) tensile failure through intact material; (2) combined shear and tensile failure or only shear failure on joints; and (3) mixed failure of the above two modes depending on the joint geometry. The fracture tensor component in a certain direction quantifies the directional effect of the joint geometry, including number of fracture sets, fracture density, and probability distributions for size and orientation of these fracture sets. Results obtained from the experiments were used to develop a strongly nonlinear relation between the fracture tensor component and the jointed block strength. The laboratory experiments conducted on jointed model material blocks were simulated numerically using the Universal Distinct Element Code (UDEC). With careful selection of suitable material constitutive models for intact model material and model joints, and accurate estimation and calibration of mechanical parameters of the constitutive models through a combination of laboratory testing and numerical simulations of the intact model material and model joints separately, it was possible to obtain a good agreement between the laboratory experimental and distinct element numerical results.     

FRACOD Modeling of Rock Fracturing and Permeability Change in Excavation-Damaged Zones

The characterization of the excavation-damaged zone (EDZ) around an underground excavation is a major research topic for deep geological disposal of medium- to high-level radioactive waste. Rock fracturing because of excavation and thermal loading and its resultant rock mass permeability change in the EDZ are important for construction projects and long-term safety. A new function to predict rock mass permeability change in fractured rocks has been developed and added to the existing fracture mechanics code FRACOD. The new functions in FRACOD have been applied to predict the extent of EDZ and permeability change in the vicinity of the tunnel sealing experiment (TSX) tunnel of the Underground Research Laboratory (Canada), the zone of excavation disturbance experiments (ZEDEX) tunnel of the ?sp? Hard Rock Laboratory (Sweden), and the deposition tunnels in crystalline and sedimentary rocks (Japan). The predicted EDZ and its permeability are consistent with the measurement data of the TSX tunnel and ZEDEX tunnel. The results from both tests indicate that FRACOD with the new function is capable of realistically predicting the EDZ and permeability change.     

非均质岩石破裂及声发射演化数值模拟

在应变软化本构模型的基础上,考虑岩石材料非均质性和损伤过程中力学性质的弱化特性,建立了非均质岩石损伤软化本构模型,推导了损伤软化本构模型的差分格式,在VC++环境下实现了损伤软化本构模型在FLAC3D中的二次开发。研究了不同均质度对岩石变形强度等力学特性的影响,以及岩石破坏过程中的声发射演化特性。研究表明：随着岩石均质度的增高,岩石的破坏过程由延性向脆性转化,岩石峰值强度和峰值应变不断增大,而残余强度降低;当岩石均质度较低时,岩石破坏剪切带的形成会发生滞后,随着均质度的增加,单轴加载条件下岩石声发射体现出由强度低、频率高向强度高、频率低转化的特性,并表现出群震型、前震—主震—余震型和主震型3种典型模式。     

Lateral Load Capacity of Drilled Shafts in Jointed Rock

Large vertical (axial) and lateral loads often act on the heads of drilled shafts in jointed rock. In current design practice, the p-y curve method used in design of laterally loaded drilled shafts in soil is often also used for shafts in jointed rock. The p-y curve method treats the soil as a continuum, which is not appropriate in jointed rock, particularly when failure occurs due to sliding on joints. A new discontinuum model was developed to determine the lateral load capacity of drilled shafts or piers in a jointed rock mass with two and three joint sets. It consists two parts: a kinematic and a kinetic analysis. In the kinematic analysis, Goodman and Shi’s block theory is expanded to analyze the removability of a combination of blocks laterally loaded by a pier. Based on the expanded theory, a method was developed to select removable combinations of blocks using easily constructed two-dimensional diagrams. In the kinetic analysis, each kinematically selected removable combination of blocks is examined with the limit equilibrium approach to determine the ultimate lateral load capacity. Although the procedure is similar to slope stability analysis, it is more complicated with the addition of a lateral force and the vertical load exerted by the pier. Simple analytical relations were developed to solve for the ultimate lateral load capacity.