节理岩体中应力波传播规律研究的进展

讨论了位移不连续模型与特征值法结合的方法,对垂直于单一线性变形节理、多个平行线性变形节理、单一非线性变形节理,分别采用线性变形不连续模型、双曲线变形不连续模型(BB模型)进行的理论与相应的实验研究。用离散元程序UDEC,对上述问题进行数值模拟;用三维离散元程序3DEC,对节理岩体中三维波的传播进行的数值模拟。并用UDEC与有限差分程序AUTODYN-2D耦合,模拟爆炸过程及爆炸波在节理岩体中的传播。同时提出了几个有待研究的问题。     

Comparison of calculational approaches for structural deformation in jointed rock

Results from five different computer models for structural deformation in jointed rock are compared for a problem involving stress-wave loading of a lined circular tunnel in a jointed medium. The computer models include two discrete element codes, The Direct Interacting Block Systems (DIBS) and The Universal Distinct Element Code (UDEC), and three finite element codes, The Finite Element Code for Largely Explicit Calculation (FLEX), The Explicit Calculations of Interacting Bodies Under Rapid Loading Code (EXCALIBUR), and PRONTO. The finite element codes used either slidelines or joint elements to simulate the motion on joints. All codes had some difficulties with a sequence of preliminary problems solved to ‘shake down’ the computer codes. However, most of the shortcomings of each code were readily overcome. Results showed that three codes could obtain similar answers for tunnel closure, stress around the tunnel and slip on the joints.     

Validation study of the distinct lattice spring model (DLSM) on P-wave propagation across multiple parallel joints

A validation study of the distinct lattice spring model (DLSM) for wave propagation problems is performed. DLSM is a microstructure-based numerical model, which is meshless and has advantages in modelling dynamic problems where stress wave propagation is important. To verify the applicability of DLSM to modelling wave propagation through a discontinuous medium, the virtual wave source (VWS) method is used to obtain analytical solutions for wave propagation across a jointed rock mass. Numerical modelling results of the commercial code UDEC are selected as the reference. The effects of particle size and lattice rotation angle on wave propagation are first studied. Then, the results of wave transmission across a single joint with a different joint stiffness and across multiple parallel joints with different joint spacings are derived with DLSM, UDEC and VWS. These results are in good agreement with each other. Therefore, the capability of DLSM to model P-wave propagation across jointed rock mass is verified, which provides confidence for the further application of DLSM to modelling more complex problems.     

基于离散元的强度折减法分析岩质边坡稳定性

将通用离散元UDEC与强度折减法结合,对含多结构面的岩质边坡的稳定性进行了分析。通过对节理岩质边坡的UDEC模型中的可变形块体和节理单元的强度参数进行折减,使模型不能再达到平衡状态,此时的折减系数就是边坡的安全系数,另外,由对应的边坡块体的速度矢量可以确定滑动面和边坡的破坏形态。通过与传统的条分法的结果比较,表明基于UDEC的强度折减法是一种可靠、有效的方法,为复杂节理岩质边坡的滑动面确定与安全系数计算开辟了新的途径。     

A Numerical Study on Wave Transmission Across Multiple Intersecting Joint Sets in Rock Masses with UDEC

This paper presents a numerical study on wave transmission across jointed rock masses with UDEC, where multiple intersecting joint sets exist. The capability of UDEC of studying wave transmission across rock joints is validated through comparison with analytical solutions and experimental data. Through parametric studies on wave transmission across jointed rock masses, it is found that joint mechanical and spatial parameters including joint normal and shear stiffnesses, nondimensional joint spacing, joint spacing ratio, joint intersecting angle, incident angle, and number of joint sets together determine the wave transmission. And for P wave incidence, compared with other parameters, joint normal stiffness, nondimensional joint spacing, and joint intersecting angle have more significant effects on wave transmission. The physical reasons lying behind those phenomena are explained in detail. Engineering applications and indications of the modeling results are also mentioned.     

基于离散元法的节理岩体边坡稳定性分析

节理岩体边坡的稳定性在很大程度上取决于节理的强度及其分布形式。由于节理岩体边坡的失稳破坏具有大变形和非连续的特点,因此,离散单元法成为研究节理岩体边坡破坏机制的最有效方法之一。通过采用离散元软件PFC2D进行数值模拟,对完整岩石及节理的力学性能进行研究,并建立含密集节理的岩体边坡模型,讨论了节理连通率对边坡破坏形式的影响。结果表明,节理岩体边坡的失稳破坏是一个渐进的过程;在多组节理密集分布的岩体边坡中,连通率越大,其稳定性越差;随着连通率的减小,边坡的破坏形式由大范围的滑坡转变为局部崩塌的形式     

Discrete element modelling of an underground explosion in a jointed rock mass

The purpose of this paper is to investigate the application of the discrete element program UDEC for modelling underground explosions in a jointed rock mass. A field underground explosion test has been conducted and UDEC and AUTODYN were utilised in a coupled manner to predict the rock mass response due to the underground explosion. The dynamic equation for the state of the rock material obtained from impact tests was incorporated into the calibration modelling. The comparison of modelling results with test results and empirical formulas shows that UDEC is capable of modelling explosion wave propagation in jointed rock mass with high reliability.     

动载下节理岩体破坏过程的数值试验研究

节理岩体是工程中最常见的一类岩体,其在地震、爆炸等动载下的力学响应及破坏过程对相关工程安全性的影响至关重要。采用基于有限元应力分析和统计损伤理论开发的动态版RFPA2D数值模拟软件,对动载下节理岩体的动态破坏过程进行了模拟,重点讨论了节理条数、节理贯通度、节理倾角及应力波峰值对岩体动态破坏过程的影响规律。计算结果表明,断续节理岩体动态破坏过程及破坏强度与节理构造形态、应力波峰值密切相关。相同动载下,随着节理条数的增加,岩体破坏程度以及应力波能量损失增强,但当节理条数数超过一定值后,岩体破坏程度及应力波能量损失逐渐趋于稳定;节理贯通度较小时,岩体破坏程度较低且破坏单元自上而下均匀分布。随着节理贯通度的增加,岩体破坏增强,且破坏主要出现于节理上部岩体;节理倾角较小时,节理上部岩体破坏严重,易形成次生贯通裂纹。随着节理倾角增加,破坏范围逐渐变大,不易形成次生贯通裂纹;倾角为45°～60°时,岩体破坏效果最佳;动载荷的峰值越大,试样的破坏越严重。当峰值达到一定值时,节理附近发育出多条裂隙并向上下方不断发展而导致岩体完全破坏。在不同节理贯通度工况下与岩石霍布金森压杆（SHPB）试验结果进行比较,结论吻合,证明该数值模拟的合可行性和结论的可靠性。     

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).     

基于摩尔-库仑准则的断续节理岩体复合损伤本构模型

针对工程实际中断续节理裂隙岩体的损伤本构模型,假设岩石微元强度服从Weibull随机分布,以摩尔-库仑破坏准则作为描述微元强度的表示方法,推导出细观损伤变量。利用能量和断裂力学理论,综合考虑节理几何特征及力学特性,推导宏观损伤变量计算公式。基于Lemaitre应变等效假设,考虑宏细观缺陷耦合作用,推导出复合损伤变量,建立了基于摩尔-库仑准则的宏细观缺陷耦合作用的断续裂隙岩体损伤本构模型。研究结果表明：（1）采用摩尔-库仑准则作为描述微元强度的统计分布变量建立的损伤模型能够较好地反映岩石内部缺陷分布和变形特征,该模型真实地反映岩石微元强度受应力状态的影响。（2）该模型建立的理论曲线与断续节理岩体的试验曲线吻合较好。（3）节理裂隙岩体宏观损伤变量及峰值强度随节理倾角的变化规律与综合考虑宏细观耦合作用下的损伤变量及裂隙岩体峰值强度随节理倾角的变化规律基本一致。（4）宏细观耦合作用下的等效弹性模量与节理贯通率呈非线性负相关;在节理倾角一定的情况下,损伤变量与节理长度呈非线性正相关;在贯通率较小时,岩体的宏观损伤变量与内摩擦角的关系呈线性负相关变化,贯通率达到一定程度,线性关系变成非线性关系。     

节理岩体蠕变特性研究

在已知岩石和节理蠕变规律的前提下,推导了节理岩体蠕变模型的一般表达式。假定岩石体积变形和节理法向压缩变形为弹性变形,忽略节理的剪胀现象,认为只有岩石畸变和节理剪切滑移与时间有关,从而推导了含三组相交节理的岩体蠕变模型及其参数。根据反演出的岩石和节理蠕变模型,计算了含三组相交节理的岩体在单轴应力作用下一些节理参数对岩体单轴蠕变的影响。分析表明,节理间距、剪胀系数以及节理夹角都对岩体的单轴蠕变变形有明显影响。节理间距越大,剪胀系数越大,节理夹角越小,节理岩体的单轴蠕变柔量也就越小,岩体的蠕变变形也越小。     

Numerical Simulation of the Process of Fracture of Echelon Rock Joints

The effect of joint overlap on the full failure behavior of a rock bridge in the shear-box test was numerically investigated by means of the particle flow code in two dimensions (PFC2D). Initially, the PFC2D was calibrated by use of data obtained from experimental laboratory tests to ensure the conformity of the simulated numerical model’s response. Furthermore, validation of the simulated models was cross-checked with the results from direct shear tests performed on non-persistent jointed physical models. By use of numerical direct shear tests, the failure process was visually observed and the failure patterns were seen to be in reasonable accordance with experimental results. Discrete element simulations demonstrated that macro shear fractures in rock bridges are because of microscopic tensile breakage of a large number of bonded discs. The failure pattern is mostly affected by joint overlap whereas the shear strength is closely related to the failure pattern. The results show that non-overlapping joints lost their loading capacity when nearly 50 % of total cracks developed within the rock bridge whereas the overlapping joints lost their loading capacity as soon as cracks initiated from the joint walls. Furthermore, progressive failure or stable crack growth was seen to develop for non-overlapped joints whereas brittle failure or unstable crack growth was seen to develop in overlapped joints.     

斜入射线弹性节理应力波传播特征的数值模拟

依据弹性波理论,应力波斜入射线弹性节理时会发生波场分解。根据入射、透射及反射各波形的不同到时,运用离散元软件UDEC模拟应力波在含倾斜节理岩体中的传播并计算其透射、反射系数,并分析其波型转换规律。应力波斜入射单节理时,模拟得到的透射、反射系数随节理刚度、入射角度的变化规律,与已有的理论解是吻合的。应力波斜入射一组平行节理时,随着节理间距的增大,其同类波的透射系数Tpp、Tss先增大后减小,最后趋于稳定值;节理条数越多,Tpp、Tss越小。此外,不同条数的节理,透射系数达到最大值的临界节理间距值基本一致,但趋于稳定时的节理间距值随节理条数的增加而逐渐增大。     

Modeling strategy for jointed rock masses reinforced by rock bolts in tunneling practice

This paper deals with the modeling of jointed rock masses reinforced by rock bolts. It is well known that rock bolts are extremely effective in reinforcing jointed rocks. However, if a continuum approach is adopted for modeling jointed rock masses, it is often misleading to evaluate the effectiveness of the rock bolts by numerical analyses such as the finite element method. This may be due to the fact that since no more joints exist in the continuum, the effectiveness of the rock bolts in constraining the relative displacements along the joints cannot be evaluated properly. In order to investigate the reinforcement effect of rock bolts, physical model tests were performed in the laboratory. The test results revealed that jointed rock masses should be modeled as an equivalent continuum after the installation of rock bolts and that the mechanical parameters of the equivalent continuum should be evaluated by considering the reinforcement effect of the rock bolts. Therefore, the values of the mechanical parameters differ from place to place in accordance with the relation between joint orientation and rock bolt direction, even though joint systems are homogeneous. In conclusion, in the continuum approach for modeling jointed rock masses, it should be emphasized that rock bolts and jointed rock masses should not be modeled separately but should be modeled simultaneously by considering the reinforcement effect of the rock bolts in constraining joint movement. The modeling of shotcrete reinforced by steel ribs is also discussed in comparison to the modeling by rock bolts.     

Strength and dilatancy of jointed rocks with granular fill

It is well recognised that the strength of rock masses depends upon the strain history, extent of discontinuities, orientation of plane of weakness, condition of joints, fill material in closely packed joints and extent of confinement. Several solutions are available for strength of jointed rock mass with a set of discontinuities. There is a great multiplicity in the proposed relationships for the strength of jointed rocks. In the present study, the author conceives the effect of increasing stresses to induce permanent strains. This permanent strain appears as micro crack, macro crack and fracture. A fully developed network of permanent deformations forms joint. The joint may contain deposits of hydraulic and hydrothermal origin commonly known as gouge. The joint factor numerically captures varied engineering possibilities of joints in a rock mass. The joints grow as an effect of loading. The growth of the joints is progressive in nature. It increases the joint factor, which modifies the failure stresses. The dilatancy explains the progressive failure of granular media. Hence, a mutual relationship conjoins effectively the strength of jointed rock and a dilatancy-dependent parameter known as relative dilatancy. This study provides a simple and integral solution for strength of jointed rocks, interpreted in relation to the commonly used soil, and rock parameters, used for a realistic design of structure on rock masses. It has scope for prediction of an equivalent strength for tri-axial and plane strain conditions for unconfined and confined rock masses using a simple technique.     

A Study of the Failure Mechanism of Planar Non-Persistent Open Joints Using PFC2D

Particle flow code 2D (PFC2D) was adopted to simulate the shear behavior of rocklike material samples containing planar non-persistent joints. Direct shear loading was conducted to investigate the effect of joint separation on the failure behavior of rock bridges. Initially calibration of PFC was undertaken with respect to the data obtained from experimental laboratory tests to ensure the conformity of the simulated numerical models response. Furthermore, validation of the simulated models were cross checked with the results of direct shear tests performed on non-persistent jointed physical models. Through numerical direct shear tests, the failure process was visually observed, and the failure patterns were found reasonably similar to the experimentally observed trends. The discrete element simulations demonstrated that the macro-scale shear zone resulted from the progressive failure of the tension-induced micro-cracks. The failure pattern was mostly influenced by joint separation, while the shear strength was linked to the failure pattern and failure mechanism. Furthermore, it was observed that the failure zone is relatively narrow and has a symmetrical pattern when rock bridges occupy a low percentage of the total shear surface. This may be due to the high stress interactions between the subsequent joints separated by a rock bridge. In contrast, when rock bridges are occupying sufficient area prohibiting the stress interactions to occur then the rupture of surface is more complex and turns into a shear zone. This zone was observed to be relatively thick with an unsymmetrical pattern. The shear strength of rock bridges is reduced by increasing the joint length as a result of increasing both the stress concentration at tip of the joints and the stress interaction between the joints.     

柱状节理岩体原位变形试验力学浅析与模拟

在白鹤滩坝址区柱状节理岩体原位变形试验成果的基础上,针对节理刚度的取值进行讨论,利用柔性中心孔试验值反算得到柱状节理岩体节理面刚度值。岩体变形是由岩块和节理两部分组成,分析含单节理岩体概念模型的单轴加、卸载规律性和其变形特性,发现其滞回特性是节理力学行为造成的;推导得到了岩体变形计算公式,可用于多组相交节理岩体等效弹性模量的计算,能够反映出节理岩体的各向异性特征;建立了柱状节理随机模型,采用离散元方法和反算的刚度值进行了仿真分析,得到等效变形参数在试验结果范围内。     

基于强度折减法的顺层路堑边坡土钉墙支护结构稳定性分析

将非线性有限元分析和极限分析相结合形成强度参数折减有限元法,可以灵活地分析强度不均匀顺层路堑边坡支护结构稳定性问题。将岩体力学理论、非线性有限元分析技术和强度折减系数法相结合,对顺层岩体路堑边坡稳定性进行分析。在对密集假设节理有限元模拟中,假设节理在岩体内连续分布,采用连续介质力学方法建立密集分布节理岩体材料模型。采用强度折减系数法计算岩体结构安全系数,建议采用给定的岩体强度参数计算节理岩质边坡开挖、支护完毕后的内力,再逐渐降低岩体强度参数进行岩体边坡非线性有限元分析,直至岩体边坡达到极限状态,从而求出岩质边坡安全系数。采用该方法对渝怀铁路梅江河右岸DK409+989.4～DK410+020段顺层路堑边坡土钉墙支护结构稳定性进行分析,分析结果表明：采用土钉墙支护后的节理边坡塑安全系数为2.3,支护后的岩质边坡处于稳定状态;土钉墙潜在破裂面为岩体弹性区和塑性区的交界面,与测试得到的各排土钉拉力最大值位置一致。     

节理化岩体复合式滑移破坏的模型试验研究

针对节理化岩体的自身特点,提出沿岩体层面产生的应力集中以及层面与节理之间的残余完整岩桥破坏,将可能导致岩体产生复合式滑移破坏。并在室内利用岩石三轴刚性伺服机,通过模型试验对岩体的层面和一组与层面正交的节理的情况进行模拟研究,分析了结构面性状和围压对复合式滑移破坏的影响,给出了在贯通性结构面(层面)倾角、非贯通性结构面以及围压等因素共同作用下,节理化岩体发生复合式滑移破坏的条件以及破坏面特征。在与前人的试验资料进行对比分析的基础上得到可靠的结论,期望为在将来的实践工作中正确评估节理化岩体的破坏模式提供指导性意见。      

A model for coupled mechanical and hydraulic behaviour of a rock joint

Constitutive laws for rock joints should be able to reproduce the fundamental mechanical behaviour of real joints, such as dilation under shear and strain softening due to surface asperity degradation. In this work, we extend the model of Plesha to include hydraulic behaviour. During shearing, the joint can experience dilation, leading to an initial increase in its permeability. Experiments have shown that the rate of increase of the permeability slows down as shearing proceeds, and, at later stages, the permeability could decrease again. The above behaviour is attributed to gouge production. The stress–strain relationship of the joint is formulated by appeal to classical theories of interface plasticity. It is shown that the parameters of the model can be estimated from the Barton–Bandis empirical coefficients; the Joint Roughness Coefficient (JRC) and the Joint Compresive strength (JSC). We further assume that gouge production is also related to the plastic work of the shear stresses, which enables the derivation of a relationship between the permeability of the joint and its mechanical aperture. The model is implemented in a finite element code (FRACON) developed by the authors for the simulation of the coupled thermal–hydraulic–mechanical behaviour of jointed rock masses. Typical laboratory experiments are simulated with the FRACON code in order to illustrate the trends predicted in the proposed model. © 1998 by John Wiley & Sons. Ltd.