Determination of asperity damage parameters for constitutive models of rock discontinuities

Dilatancy and contact surface damage are important phenomena affecting the behaviour of rock joints and other geological discontinuities. Effective constitutive laws that incorporate these behaviours have recently been developed but require the specification of new material parameters that govern damage of asperity surfaces. Determination of the parameters that control damage is currently a difficulty that confronts practitioners. This brief will summarize the findings of Hutson and Dowding's investigation of joint surface asperity degradation and elaborate on the implications for application.     

Thermodynamical approach for CamClay-family models with Roscoe-type dilatancy rules

The CamClay model has been extensively used in numerous research programmes for constitutive modelling in Soil Mechanics during the past quarter of a century. Several derivations of this model are now available and routinely used for numerical simulations in the geomechanical engineering field. However, to the authors' knowledge the thermodynamical basis of this model in its original form has never been established, at least in a modern thermodynamics framework. The thermodynamics principle proposed by Ziegler is very expedient for this purpose as the non-associated flow rule may be considered. This approach is applied to the CamClay model with the Roscoe dilatancy rule. A dissipation function and free energy are specified in terms of kinematic variables (i.e. state and internal variables), and the material response is derived entirely from these functions.     

Stress deformation properties of rock and rock discontinuities

The results of an extensive literature survey on the stress deformation properties of rock materials and rock discontinuities are summarized. The results show that: (1) for rock tested under uniaxial conditions, the range of modulus is from about 1 to 100 GN/m², and the Poisson's ratio range is from 0.02 to 0.73 (0.46 if dilatant values are excluded) with an average value of 0.20; (2) for rock tested under triaxial conditions, the effects of nonlinearity and stress-dependency of the rock modulus are minor with hard, crystalline or homogeneous rock of low porosity, but are significant in porous, clastic or closely jointed rock; (3) anisotropy of the rock modulus is demonstrated mainly by variations in the modulus number or initial stiffness, while the nonlinearity and stress-dependency parameters are fairly constant with sample orientation; (4) nonlinearity and stress-dependency of the rock Poisson's ratio may be significant depending upon the magnitude of stress changes imposed, with the nonlinearity being more significant; and (5) limited data on rock discontinuities indicate that nonlinearity and stress-dependency effects may be quite large.     

岩体结构面新型本构模型研究

对于涉及需要单独考虑岩体结构面的工程岩体结构分析,采用能反映岩体结构面主要力学特性的合理的本构模型是取得合理解答的关键问题之一。针对在经典连续介质力学理论框架内建立岩体结构面本构模型的缺点,基于岩体结构面的实际受力变形特性,采用直接法建立了一种新型岩体结构面本构模型。所建立的模型依据岩体结构面切向应力变形曲线及剪胀曲线的实际特征,将其分为峰前线性段、峰前非线性段以及峰后软化段,并分别给出了用于描述岩体结构面变形和强度等主要力学特性的数学模型,进而推导建立了结构面各变形阶段的增量型本构模型。最后,编写相关计算程序,采用所建立的新型本构模型以及被广泛采用的Plesha模型对经典的岩体结构面直剪试验成果进行拟合分析。结果表明,所建立的新型本构模型能更为合理的描述岩体结构面的主要力学特性,且模拟能力优于Plesha模型     

岩体不连续面迹长与直径间的概率关系模型分析

由于“随机”概念的模糊性,在假定不连续面为薄圆盘及弦长作为迹长的前提下,基于迹线端点在圆周上均匀分布、迹线中点在直径上均匀分布、迹线中点在圆面域内均匀分布这3种明确而又不同的“随机”含义,可以得到3种合理的迹长 与直径 间的概率关系模型。通过对这3种模型进行分析认为：其在各自的“随机”含义下都是正确的,只是适用条件各异;野外实际可行的条件是介于模型2 和模型3之间的,合理地分析应该同时考虑这两种模型。在实际应用中,应该首先对所有取样面产状之间的关系进行分析,根据其结果来分配给模型2和模型3以某种权重,这样得到的迹长与不连续面直径之间概率关系更具合理性,其结果弥补了目前国内外进行的相关研究仅仅考虑到第2类模型的不足。     

压剪应力条件下各向异性岩石损伤本构模型和渗流模型(Ⅱ)：三轴压缩应力状态下理论模型及算例

在文[1]的基础上，推导了所建立本构模型和渗流模型的三轴压缩情况下的方程，并给出了1个算例。结果表明，建立的本构模型能够反映微裂纹闭合摩擦滑移、微裂纹发生自相似扩展和微裂纹发生弯折扩展对变形的影响；建立的本构模型能够反映岩石剪胀特征；弯折微裂纹分支张开是使岩石渗流明显地增大原因     

压剪应力条件下各向异性岩石损伤本构模型和渗流模型(Ⅰ)：理论模型

采用细观力学研究了岩石损伤变形过程和渗流过程。在本构模型中增加了对剪胀变形机理和渗流对变形影响的内容,同时按照微裂纹发展过程建立了考虑微裂纹扩展、变形和渗透压影响的岩石各向异性渗流模型,使得模型能够更好地表述岩石的变形特性和渗流特性。所建立的模型能够考虑微裂纹闭合摩擦滑移、微裂纹发生自相似扩展和微裂纹发生弯折扩展等过程。     

Estimation of a surface with known discontinuities for automatic contouring purposes

As an aid to automatic contouring, a method has been designed to estimate a surface with known discontinuities. Through a primary estimation process the surface is assumed to be known at the nodes of a regular grid. These known values are termed data points. A distance r_EI is defined between a known data point I, and any given point E to be estimated. This distance is increased, as explained, by a penalty if one discontinuity (or more) is found in between these points. At each data point I the tangential quadric to the surface is computed, using the data points K in a neighborhood of I, which will be defined. The value at E is then a linear combination of these tangential quadrics in the neighborhood of E. For this combination, a weighting p_EI is used, related as a decreasing function of r_EI. The underlying assumptions of the method are given, together with the way to compute quadrics and the properties of the weights p_EI. An application package has been written in FORTRAN and two examples are given in this paper.     

Strain parameters of discontinuities in rock for finite element calculation

The bulk strain induced by excavation of rooms for storage of highly radioactive waste is usually unimportant, but the change in aperture and shear displacement of permeable fractures may be of practical importance. Hence, the normal and shear of such discontinuities have to be considered and are commonly predicted by using special deformation moduli termed “normal” and “shear” stiffnesses in numerical calculations. For the use of some finite element methods, these have to be converted to compression and shear moduli ,which, in turn, requires that the thickness of the discontinuity is known. The normal and shear strain can be expressed in terms of soil mechanical parameters, yielding the compression modulus M and the shear modulus G, with the required form for finite element calculations. By definition they are functions of the normal and shear stiffness K_n and K_s. It is concluded that calculation of the normal and shear strain of discontinuities with clastic fillings by the use of finite element methods and deformation moduli derived from stiffness numbers is very uncertain except when the geometry of the weaknesses can be accurately defined.     

考虑岩体扩容和塑性软化的软岩巷道变形解析

考虑岩体的扩容和塑性软化特性,引进扩容梯度和软化模量的概念,推导出均匀介质中软岩巷道应力和变形的理论解答。与其他理论模型进行比较,验证了理论模型的正确性。通过算例分析了岩体的扩容梯度和软化模量对围岩塑性区、破裂区半径以及围岩变形和压力的影响。分析结果表明,考虑岩体的扩容和塑性软化特性使得分析更加准确,研究成果对软岩巷道支护设计与施工具有一定指导意义。     

The evolution of rock failure with discontinuities due to shear creep

A two-dimensional brittle creep model for rock provides insight into the initiation of shear fracture along weak discontinuities in rock. The model accounts for material heterogeneity and introduces the concept of a mesoscopic renormalization to capture the cooperative interaction between cracks in the transition from distributed to localized damage. A series of shear creep tests on rock with discontinuities were performed to simulate the initiation and propagation of crack along a pre-existing weakness under sustained shear stress and normal stress. The investigation showed that shear stress level and the normal stress level might have significant effect on the long-term behavior of rock with weak discontinuities. Moreover, a case study of rock slope instability was also investigated, where the numerically simulated instability failure of rock slope with discontinuities showed that both tensile and shear damage at the weakest elements are the trigger for the failure surface initiation in the rock slope. Once damage occurs, redistributed stress concentrations would then intensify fracture propagation and coalescence within these damage zones, leading to the progressive development of a failure surface. Moreover, failure surface extending is not only dominated by the properties and the position of discontinuities but also influenced remarkably by the complex interaction between existing discontinuities and fracture propagation. The results are of general interest because they can be applied to the investigation of time-dependent instability in rock masses, to the mitigation of associated rock hazards in rock engineering, and even to a better understanding of the physical phenomena governing the stability of rock slope.     

不同围压下煤岩变形与剪胀扩容模型

在RMT-150B岩石力学试验系统上进行了煤岩的变形和剪胀特性研究,获得如下结论:随着围压增加煤岩均质性明显提高,峰值前变形特性基本趋于一致,屈服阶段逐渐增长;煤岩体变扩容初始点发生在应变硬化阶段,最大扩容率在应变软化阶段,且随着围压增加体变对围压的敏感性减小;为了准确表达煤岩在破坏过程中的非线性体积变化行为,建立了同时考虑塑性剪切应变和围压影响的煤岩剪胀角模型,该模型表明在较小塑性剪切应变下剪胀角即达到峰值,之后不断缓慢回落,围压越小对应的剪胀角峰值越大,小围压下峰值剪胀角对应的塑性剪切应变也较小。     

Constitutive and numerical framework for modeling joints and faults in rock

A three‐dimensional constitutive model for joints is described that incorporates nonlinear elasticity based on volumetric elastic strain, and plasticity for both compaction and shear with emphasis on compaction. The formulation is general in the sense that alternative specific functional forms and evolution equations can be easily incorporated. A corresponding numerical structure based on finite elements is provided so that a joint width can vary from a fraction of an element size to a width that occupies several elements. The latter case is particularly appropriate for modeling a fault, which is considered simply to be a joint with large width. For small joint widths, the requisite equilibrium and kinematic requirements within an element are satisfied numerically. The result is that if the constitutive equation for either the joint or the rock is changed, the numerical framework remains unchanged. A unique aspect of the general formulation is the capability to handle either pre‐existing gaps or the formation of gaps. Representative stress–strain plots are given to illustrate both the features of the model and the effects of changes in values of material parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

结构面对程潮铁矿东区地表及岩体移动变形的影响研究

以程潮铁矿东区为例,通过现场结构面调查、地表及深部岩体变形监测,分析了该区地表及岩体移动变形与结构面的关系。结果表明：程潮铁矿东区地表及岩体移动变形主要受该区复杂的地质条件控制,特别是结构面的影响,变形方向和变形量值均与理论预期不同。NNE、NE向结构面的存在控制着岩体向采空区运动的侧向边界条件,同时导致变形方向的向西偏转,NWW向结构面的松动导致东主井区岩体向采空区的倾倒变形,地表变形在南北剖面上呈三级阶梯分布;西风井相对东西采空区的特殊位置以及NE向结构面的影响使其变形值小于预期,是该区相对安全的主要原因。     

岩体结构面的多参数优势分组方法研究

岩体中的结构面对岩体的水力和力学性质有很大影响,因此,弄清岩体中结构面的发育规律是岩体稳定性评价的基础。当结构面的产状一致,其他性质不一致时,结构面的水力学特性和力学性质是不同的。而传统的结构面优势分组方法仅根据产状数据分组,无法分辨产状相同、其他性质不同的结构面。因此,提出了一种基于量子粒子群优化算法的多参数结构面的优势分组方法。该方法通过结构面的相似性度量建立目标函数,运用量子粒子群优化算法通过搜索目标函数的全局最优解来确定聚类中心,可用于结构面多个参数的优势分组。通过对计算机模拟的多参数结构面数据的分组,验证了该方法的可靠性。最后,将该方法应用于怒江松塔水电站坝址区实测的多参数结构面数据的划分,得到了符合实际的分组结果。     

Effect of rock discontinuities on certain rock strength and fracture energy parameters under uniaxial compression

Summary Five series of test blocks of Pendeli marble with artificially created discontinuities of different crack densities (simulating three mutually orthogonal joint sets) were tested in uniaxial compression in order to study the effect of discontinuities on: (a) the compressive strength and the modulus of elasticity, and (b) certain fracture energy parameters expressed by the ratio W _A/W _V, where W _A is the surface energy and W _V the volume elastic strain energy. Mathematical relationships are derived similar to those suggested by other authors relating strength parameters to crack densities. Such relationships clearly show a reduction in strength with increased crack density. The experimental results obtained permit the extension of Persson's relation (which refers to ideal intact rock) to the more realistic case of discontinuous rock mass by introducing the appropriate term that takes into consideration the effect of rock mass discontinuities on the energy ratio W _A/W _V. A comparison between laboratory results and field observations was subsequently carried out assuming the rock mass to behave as a linearly elastic material, obeying the Hoek and Brown failure criterion. This comparison showed that laboratory results can be extended to larger scale. Furthermore, in order to predict the in situ strength and stability of a rock mass in uniaxial compression (which is of major importance in underground excavations) certain concepts are proposed based on laboratory tests, in situ investigations and first principles of linear elastic fracture mechanics.