Mechanical response of a jointed rock beam—numerical study of centrifuge models

In this paper we present a comparison between a set of benchmark centrifuge models of a jointed beam and the predictions of two numerical models: fast Lagrangian analysis of continua (FLAC) and discontinuous deformation analysis (DDA). The primary objective of this paper is a comparison between the measured deformation profiles and thrust evolution to predictions of the numerical methods employed. A secondary objective is an attempt to clarify the issue of compressive arch geometry which is still in controversy among researchers. It is found that both FLAC and DDA result in insufficiently accurate predictions to the measured displacements. The mode of deformation is only partially captured and is dependent on the aspect ratio of the individual blocks which made up the beam. It is shown that the accuracy of the predicted displacements is a function of the assigned interface stiffness. The thrust predicted by both methods is found to be considerably lower than that measured in the model; however, the linear evolution of thrust and equilibrium conditions are correctly captured. The geometry of the compressive arch as predicted by FLAC compares extremely well with the data measured in the physical model. Based on the FLAC analysis it is found that for a beam composed of equidimensional blocks the thickness of the compressive arch varies from 0.8t at the abutment interface to the entire beam thickness (1t) at a distance of a half block width from the abutment face, extending across the interface separating the block and its neighbour, and attains a value of 0.5t at the beam mid span. Copyright © 2006 John Wiley & Sons, Ltd.     

A discontinuous numerical model to simulate rock failure process

Due to the difficulty of the classical fracture mechanics in dealing with multicrack coalescence, the simulation of jointed rock failure has remained a worldwide problem since the middle of the last century. Through a nearly 10-year effort, we have developed a novel but simple discontinuum-based approach, namely DDARF (discontinuous deformation analysis for rock failure), to simulate the progressive failure process of jointed rock mass. In the proposed method, by adopting the FE adaptive mesh generation technique—the advanced front method, the computational model of triangular DDA block system is automatically established. Also, the randomly distributed mechanical parameters statistically satisfying Weibull’s law are assigned to the blocks to simulate the heterogeneity of rock mass. In the generating process of the block system, numerous artificial joints come into being. These artificial joints provide the potential paths along which the cracks generate and propagate. The two blocks beside an artificial joint are glued together through adhesive algorithm, and if the glue is invalid, the artificial joint will break and turn into a real crack. In this way, the rock fragmentation process can be simulated. The results of several verification examples indicate that the DDARF method can simulate the whole process of rock fragmentation, and is suitable for cases of intact rock, rock mass with non-penetrative joints, and even blocky rock.     

分形节理岩体强度与变形尺度效应的试验研究

根据强度与变形尺度效应的研究需要,试验研究了脆性岩石相似模拟材料的配比,提出了预置材料产生模拟节理的方法,解决了随机分布节理试件的制作问题。采用分形分布节理模拟材料试件,研究了脆性岩体轴向抗压强度与变形的尺度效应,获得的规律与实际岩体尺度效应规律一致,并发现岩体变形的尺度效应并非完全由节理闭合和剪切破坏引起,在节理剪切破坏之前,主要是由节理的剪切变形增大引起的。     

A statistically based numerical model for heat conduction in fractured rock masses

A computational procedure for simulating heat conduction in fractured rock masses is proposed and illustrated within the context of the finite element method. The procedure makes use of simple local models for conduction in the vicinity of a single open fracture. The local models allow effective thermal properties for fractured rock to be expressed in terms of fracture characteristics such as spacing, orientation and aperture. The distributions of fractures and fracture properties within the finiteelement model are derived from a statistical representation of geological field data. The procedure is demonstrated to satisfactorily reproduce heat transfer results across single fractures and provide an efficient means of representing conduction in formations with multiple fractures.     

岩石强度时效性演化模型

在一定的外界荷载作用下,岩石材料的强度会随时间不断降低,在工程上常表现为由于强度的弱化而导致岩体的突发性破坏行为以及岩体的长期强度等不同现象和问题。因此,岩石强度的时间效应研究对岩体工程施工安全和工程长期稳定性都具有重要的指导意义。在对大量试验结果分析的基础上,总结了岩石强度演化规律与内在机制,发现岩石强度的损失与岩石本身的固有强度、所受应力状态（屈服接近度）以及应力作用的持续时间有关,在此基础上,提出了以岩石凝聚力和内摩擦角随上述因素变化为核心的岩石强度时效性演化模型。通过对多组试验数据的模拟分析表明,提出的岩石强度时效性演化模型能很好地描述岩石强度的演化规律,可以较好地定量反映不同应力水平下岩石强度弱化过程,且物理意义明确,为岩石强度的时间效应研究开拓了一个新的思路和方法。     

岩体波速与坝基岩体变形模量关系

岩体变形模量是岩体工程设计最重要的参数之一,尽管其可以通过各种现场试验来获得,但因其耗时、费力、投资大,使得许多中小型工程及大型工程的初步设计阶段无法通过试验来得到这一参数。因此,许多研究者建立了诸多岩体变形模量与岩体物理力学参数或岩体质量分级之间的相关关系,如岩体变形模量与RQD、RMR分级、Q分级、岩体纵波速度等之间的关系,从而利用这些关系估算岩体变形模量。总结了已有估算岩体变形模量的各种方法,讨论了其应用条件及预测结果,重点分析了利用岩体纵波速度估算岩体变形模量的方法及存在的问题,并以玛尔挡坝址为实例,建立了相关预测公式。通过与已有估算方法的对比研究,阐明了各种方法预测结果的异同,表明其建立的估算公式与Barton等公式具有较好的一致性,可以用来估算岩体的变形模量     

多节理岩体裂纹扩展及变形破坏试验研究

为了研究不同倾角下多节理岩体力学行为,采用10 MN微机控制电液伺服大型多功能动静力三轴仪,开展包含较多预制非贯通节理类岩石试件的单轴压缩试验,研究了多节理岩体裂纹的特征、贯通模式、破坏模式、应力-应变特征等与节理倾角之间的关系。试验结果表明,（1）多节理岩体的裂纹类型主要有翼裂纹和次生共面裂纹,翼裂纹的扩展路径与单个节理情况下的扩展路径差异较大,翼裂纹起裂后沿起裂方向存在较长的扩展长度,直接与相邻节理或翼裂纹形成贯通,并且裂纹的贯通表现出四种不同的模式;（2）多节理岩体的破坏模式归纳为3种类型：平面破坏、块体转动式破坏和台阶式破坏;（3）根据多节理岩体的应力-应变曲线在应变软化阶段所表现出的不同非线性变形行为特征,可以将曲线归纳为4种类型;（4）多节理岩体的强度和变形各向异性特征非常显著,强度和弹性模量均在节理倾角30°时最小,90°时最大。     

基于黏聚力裂缝模型的反倾层状岩质边坡倾倒破坏模拟

反倾层状岩质边坡的倾倒破坏是一种常见的地质灾害。为探究开挖条件下反倾层状岩质边坡的倾倒破坏机制以及层间剪切强度、岩层厚度因素对破坏特征的影响,利用ABAQUS有限元软件,建立黏聚力裂缝模型（Cohesive Crack Model,CCM）,基于连续-离散方法,经参数标定和对比,建立反倾层状岩质边坡CCM,采用开挖并增重的方式诱发边坡倾倒破坏。数值模拟结果与古水水电站坝前倾倒变形体离心模型试验结果基本一致,验证了CCM的正确性。进一步,基于以上参数及模型,研究了反倾层状岩质边坡的破坏演化过程和应力分布特征,并探讨层间剪切强度对边坡倾倒破坏特征的影响。结果表明:坡体前缘首先发生局部折断,后缘出现明显拉裂缝,反倾岩层由下往上依次折断直至倾倒体中部（一级破裂面）。随后,坡体前缘的表层岩层被挤出,形成二级破裂面,最后一级破裂面扩展至坡体后缘,形成连通宏观的破裂面。最后,二级破裂面扩展至坡体中部,边坡完全倾倒破坏;破裂面基本沿层间法向应力峰值位置连线发育;层间剪切强度对边坡倾倒破坏特征具有显著的影响,随着层间剪切强度的增大,岩层初始折断位置逐渐降低,垮塌范围逐渐减小,破裂面倾角增大;坡体层厚越大,一级破裂面分布越深,垮塌区范围越大,坡体滑动的整体性越强。研究成果可为反倾层状岩质边坡倾倒破坏的分析和监测提供有效计算方法及依据,为此类滑坡灾害的防治提供一定参考。     

岩石圆孔结构破坏过程变形场演化的实验研究

采用自行设计的岩石材料破坏过程变形场监测系统(Geo-DSCM系统),观测了受单轴压缩的岩石圆孔结构破坏过程中的变形场演化。圆孔结构由大理岩方板在中心钻孔加工而成,以0.02 mm/min的位移加载速度进行单轴压缩至破坏。实验结果表明,载荷水平较低时圆孔结构的拉应力集中部位发生变形集中现象;当载荷水平接近加载曲线的峰值点时,变形集中在两条共轭的与加载方向成一定角度的局部化带上;之后,变形的集中迁移到其中一条带上集中,结构最终在此带上形成宏观裂纹而破坏。     

Limits on strength and deformation properties of jointed basaltic rock masses

Summary A study of strength and deformation measurements for basaltic rocks, along with consideration of the influence of fracturing using a rock mass classification system, documents the range of brittle response for basaltic rock masses. Although basalts vary widely in composition and other physical factors, many of the properties of a basaltic rock mass appear to vary within a factor of about 10. Typical values of strength parameters for intact basalt at ambient temperature (20°C) and negligible confining pressure are Young's modulus, 78±19 GPa; Poisson's ratio, 0.25±0.05; tensile strength, –14.5±3.3 MPa; unconfined compressive strength, 266±98 MPa; and conhesion, 66 MPa. Corresponding values for a basaltic rock mass that incorporate the weakening effects of scale are deformation modulus, 10–40 GPa; Poisson's ratio, 0.3; tensile strength, –0.1 to –2.5 MPa; uniaxial compressive strength, 10–90 MPa; and cohesion, 0.6–6 MPa. A measured deformation modulus for ambient pressure in the vertical direction, 20 GPa, is 1.5–3 times larger than that in the horizontal directions, 13.5 and 6.5 GPa, reflecting strength anisotropy due to column or block geometry for one particular basalt. Values of tensile and cohesive strength for the basaltic rock mass are generally one to two orders of magnitude lower than corresponding values for intact basalt. The shear strength of joints appears to vary considerably from flow to flow.     

软岩应变软化数值模型的建立与研究

根据三轴压缩试验的应力-应变曲线,运用Hoek提出的由主应力圆包络线确定粘聚力和内摩擦角等效值的方法和曲线拟合的方法,研究了围压对软岩峰后软化特性的影响和软岩的宏观物性参数峰后应变软化规律,建立了峰后应变软化数值模型。利用该数值模型对三轴试验进行数值模拟,其结果与试验数据吻合。     

浅埋人防隧洞围岩破坏机理分析

以埋深为6～13 m的某浅埋人防隧洞为研究对象,应用快速拉格朗日有限差分程序（FLAC）对不同跨距、不同岩性的隧洞顶板在不同荷载作用下的破坏规律及破坏机制进行数值模拟研究,确定了隧洞围岩破坏域,并对拱顶敏感块体进行跟踪分析。研究结果表明：隧洞跨距为2 m且顶板岩层为泥岩时,隧洞顶板有一定的承载能力,当上部荷载达到0.7 MPa时隧洞才破坏;隧洞跨距为3 m且顶板岩层为泥岩时,当上部荷载达到0.33 MPa时,隧洞就已经破坏;隧洞顶板为卵石层时,即使上部不施加荷载,在自重应力的作用下,隧洞亦破坏。该研究对类似的浅埋地下工程围岩稳定性分析具有实际意义。     

裂隙岩体宏观力学参数的二维数值模拟

岩体通常含许多不同尺度的裂隙,因而力学性质非常复杂。由于现场测试及常规实验室试验常受各种条件的限制,因而其不能准确反映岩体的宏观物理力学性质。本文基于有限元分析软件对二维情况下的完整岩体和含不同倾角的软弱夹层的岩体在单轴和双轴压缩下进行了数值模拟,得到岩体变形的应力-应变曲线。该类曲线能反映裂隙对岩体力学参数的影响,对于指导工程实践有一定的意义,并且为获取岩体力学参数提供了新的途径。     

煤岩两体模型变形破坏数值模拟

采用拉格朗日元法,在弹性岩石与弹性-应变软化煤体所构成的平面应变两体模型的上、下端面上不存在水平方向摩擦力条件下,模拟了模型的破坏过程、岩石高度对模型及煤体全程应力-应变曲线、煤体变形速率、煤体破坏模式及剪切应变增量分布的影响。结果表明,当模型的全程应力-应变曲线达到峰值时煤体内部的剪切带图案已经十分明显,在模型的应变硬化阶段,煤体中的应变局部化可视为模型失稳破坏的前兆,随岩石高度的增加,模型应力-应变曲线的软化段变得陡峭,这与单轴压缩条件下的解析解在定性上是一致的;煤体应力-应变曲线的软化段变得平缓,煤体消耗能量的能力增强;弹性阶段煤体的变形速率降低;煤体内部的剪切应变增量增加。煤体应力-应变曲线的软化段的斜率、弹性阶段煤体的变形速率、煤体内部的剪切应变增量及塑性耗散能都受岩石高度的影响,说明了岩石几何尺寸对煤体的影响(煤岩相互作用)是不容忽视的。     

岩石破坏非连续变形分析弹脆性本构模型的二次开发

岩石非连续变形分析方法DDARF成功实现了模拟岩体裂纹萌生、扩展、贯通、破碎的全过程,但算法只考虑了岩体的线弹性本构模型,没有分析岩体的非线性应力-应变关系。为更符合真实岩体工程,同时扩展岩石非线性本构模型的应用范围,分别采用摩尔-库仑强度准则和最大拉应力强度准则对岩体进行剪切和拉伸破坏判断;对理想弹脆性本构模型进行算法分析,并在VC++平台下程序实现;对“自定义”的岩体非连续变形分析方法弹脆性本构模型与室内单轴压缩试验进行比较分析;将岩体非连续变形分析方法弹脆性本构模型应用于大型地下洞室开挖,并与线弹性本构模型进行对比。结果表明,非连续变形分析方法中自定义岩体弹脆性本构模型是可行的,它能够反映岩体变形的非线性特征,与室内试验吻合度较好;非连续变形分析方法弹脆性本构模型应用于大型地下工程,能更安全且真实地分析洞室围岩的稳定性,进而更好地指导地下洞室的防护措施。     

Slope failure analysis considering anisotropic characteristics of foliated rock masses

Weak planes affect the strength and deformational behaviors of rock slopes, and the anisotropic characteristics of rock mass should be considered in slope stability analysis. Effects of joint plane orientations on failure mechanism and strength response of inherently anisotropic rock samples were firstly investigated. The specimens with various orientations of joints were evaluated under uniaxial compression, Brazilian tensile, and direct shear tests. By treating the foliated rock as transversely isotropic materials, the relevant elastic constants and strength parameters were obtained from experimental results. The slope damage zone was then investigated using Comsol Multiphysics code based on Hoffman criterion. It is indicated that the failure mechanism and strength response depend highly on the inclination of specimens with respect to the loading direction. For disks with the same inclination angle, the value of tensile strength has an increasing trend with the total fracture length. Numerical results show that partial slope mass failed in single slope and no large-scale landslide occurred. The failure pattern in numerical results agrees well with the field observations. The cooperation between the experimental results and the numerical results allows an in-depth analysis of the experimental results and thus better understanding the dominant effect of joints on the deformation and failure of rock mass.     

The Nigerian manganese-rich iron-formations and their host rocks—from sedimentation to metamorphism

This investigation deals with the Nigerian iron-formations and their host rocks and is based on about 560 mineral analyses (electron-microprobe) and 93 whole-rock analyses (64 iron-formations and 29 host rocks). The manganese-rich and Al-bearing iron-formations occurring in various schist belts of the northern and southern part of West-Nigeria consist of the magnetite-free silicate, the magnetite–silicate and the quartz-rich hematite facies.Iron-formations and host rocks originated from submarine-volcanogenic exhalations enriched in Fe, Mn and CO₂ and from Al₂O₃, SiO₂ and alkali (K₂O and Na₂O)-rich continental-derived pelitic to psammitic material. From these sources and their interaction and controlled by the volcanogenic activity, differently composed protoliths were deposited in the marine basin during the Birimian time. Subsequent metamorphism of greenschist to low amphibolite facies conditions during the Eburnian time led to the formation of the metaprotoliths of the magnetite–silicate (consisting of predominantly magnetite and quartz and subordinate of garnet and amphibole), the silicate facies (consisting of garnet, amphibole and rarely Mn-bearing ilmenite and quartz) and the metasediment phyllite. Garnets are predominantly almandine–spessartine solid solutions, whereas amphiboles are Mn and Ca-bearing grunerite–cummingtonite solid solutions. In the course of a second tectono-metamorphic event of Pan-African age, the magnetite–silicate facies iron-formation/phyllite association was transformed into the hematite facies and muscovite/biotite schists, whereas the silicate facies is characterized by extensive silicification features. The hematite facies and the silicified silicate facies are restricted to southern Nigeria where the second and heterogeneous tectono-metamorphic event is more pronounced (amphibolite facies conditions) than in northern Nigeria.The genesis, summarized as the metamorphic model, shows that the carbonate-rich (siderite, rhodochrosite and subordinate magnesite and calcite) protoliths were metamorphically transformed into the silicate and magnetite–silicate facies. The separation of Mn and Fe, leading to manganese-bearing iron-formations and iron-bearing manganese-formations was explained by varying pH-conditions, under which siderite (pH: 6.8–9.4) and rhodochrosite (pH: 9–11) precipitated.Similar to the Gunfit and Biwabik iron-formations of Minnesota, USA, the iron-formation of Bingi (Maru schist belt), now present in the form of the fayalite bearing silicate facies, was overprinted by contact metamorphism caused by a gabbro intrusion.     

A sensitivity study on the numerical model of displacement and deformation of embedded brittle rock bodies in extension environment during salt tectonics

Many salt bodies contain large rock inclusions (called stringers) such as carbonate or anhydrite bodies. Mostly, large rock inclusions embedded in salt bodies have different ways of movement and deformation, including displacement, folding and fracturing. A finite element model with adaptive remeshing has been built for downbuilding simulation. The standard model set-up is constrained by observations from the South Oman Salt Basin. Based on the generic model in the previous research which shows the fracture, overtrusting or folding deformation during downbuilding process, a sensitivity study has been conducted on the numerical model of the deformation and displacement of brittle rock bodies, including the parameters such as the initial depth and the distance between them. The results of simulation are analyzed based on the data from SOSB and Zechstein salt basin. The study shows that the frequency of the break and the size of stringer fragments are strongly affected by the initial depth and thickness of stringers and the basement configuration.     

脆性岩石破坏数值模拟研究的两个问题

应用数值模拟方法,对脆性岩石单轴压缩情况下破坏规律进行了初步研究,主要讨论了脆性岩石的破坏机理、脆性岩石破坏数值模拟试验中的端部效应问题,并得出了一些初步的结论。在单轴压缩试验中,脆性岩石破坏过程主要以拉伸破坏为主。端部效应则是除了岩石试件本身所具有的材料非均匀性外影响岩石试件破坏形式的另一个重要因素。总体上存在这样的规律,即端部约束越大,岩石试件破坏型式越趋近于“X”型剪胀破坏,端部约束越小,则岩石试件破坏型式越趋近于张拉破坏。