Time-dependent multilaminate model of rocks—a numerical study of deformation and failure of rock masses

A new model for rocks and rock-like material with multiple planes of weakness is proposed. The behaviour of the assembly applies tensile and Mohr-Coulomb shear limits on each such plane with possible strain dependence of frictional properties. The visco-plastic algorithm which allows the incorporation of time effects is used to obtain static solutions. The model is illustrated in actual context by applications to stability of rock slopes and behaviour of tunnels. A generalization of the model to include arbitrary three-dimensional distribution of laminae in ‘quasi-plane strain’ is included. The effect of various flow rules adopted for plastic straining is indicated.     

均匀离散分布的平面应变过程和Fry法应变测量

本文运用 Apple Macitonsh 计算机对无应变的均匀离散点分布进行系列平面应变模拟,应变叠加模式分别采用具普遍意义的成岩压实+顺层缩短(LPS)+压溶作用和成岩压实+简单剪切+压溶作用。对各应变阶段的变形点分布进行相应的 Fry 法应变测量,并配合低变形砂岩样品的 Fry 法应变分析实例.证实 Fry 法应变测量方法为一非常有用的应变测量方法,其结果不仅能较好地揭示全岩总应变特征,而且能揭示出许多应变叠加的信息,Fry 法揭示的全岩有限应变椭球主面的方位也较为真实可靠。而 Fry 法运用于应变分布不均匀的劈理化岩石中时,能揭示不同变形域的应变特征,从而达到应变分解的目的。     

Plane Strain Testing with Passive Restraint

A plane strain condition for testing rock is developed through passive restraint in the form of a thick-walled cylinder. The so-called biaxial frame generates the intermediate principal stress that imposes a triaxial state of stress on a prismatic specimen. Major and minor principal stresses and corresponding strains are accurately measured, providing data to calculate the elastic (Young’s modulus and Poisson’s ratio), inelastic (dilatancy angle), and strength (friction angle and cohesion) parameters of the rock. Results of experiments conducted on Indiana limestone in plane strain compression are compared with the results of axisymmetric compression and extension. With proper system calibration, Young’s modulus and Poisson’s ratio are consistent among the tests. The plane strain apparatus enforces in-plane deformation with the three principal stresses at failure being different, and it allows one to determine the Paul-Mohr-Coulomb failure surface, which includes an intermediate stress effect.     

Elastoplastic analysis of jointed rocks using a coupled finite element and boundary element method

This paper presents a coupled, elastoplastic, finite element and boundary element method for the two-dimensional, non-linear analysis of anisotropic jointed rock. The non-linear and anisotropic behaviour of a jointed rock mass is simulated by representing the mass as an equivalent anisotropic, elastoplastic continuum, so that the influence of the jointing system is ‘smeared’ across the continuum, i.e. the individual joints are not modelled as discrete entities. Numerical examples have been solved to verify the capability, accuracy and efficiency of the present technique. The proposed technique has also been applied to the analysis of tunnel excavation problems in plane strain. The effects of anisotropy and non-linearity of the jointed rock mass during excavation have been investigated in some detail.     

The rheology of plasticine

Plasticine rheology has been investigated in plane strain compression and stress relaxation tests. Constant strain rate tests indicate Reiner-Rivlin fluid characteristics or alternatively the deformation properties of plasticine may be described by a constitutive flow law of the type e = K σ^N where N= 6–9. This relationship was found for the three types of plasticine studied. Relaxation data indicate complex behaviour with probable structure changes during deformation. Under plane strain conditions at 25°C inhomogeneous flow characterized by ductile shears often occurs at high strains in all three types of plasticine. These effects were not apparent during 45°C tests. The application of plasticine analogues to simulate rock structures is discussed.     

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.     

Mechanical Behaviour of Cyclically Heated Fine Grained Rock

Summary The most vital difference between rock and rock mass are fractures and fissures. They affect the behaviour and strength of rock masses. According to their origin, size, and shape, rock mass contains several types of weakness planes varying from microfissure to faults. Other parameters such as underground water, temperature, time and stress state affect the rock's behaviour in its natural environment. The frequency of discontinuities in fractured rock is one of the basic parameters for reducing its strength. However it is generally difficult to test undisturbed fractured rock in a laboratory environment. In this study it was tried to open and loosen the grain boundaries of fine-grained rock specimens by cyclical heating and cooling. This should serve as a physical simulation of fractures in the rock mass and enables a discussion of the changes in mechanical behaviour of fractured rock. For this reason, laboratory test specimens of Carrara marble and Buchberger sandstone were used. The heating cycles were varied from 0 to 16. From the results of uniaxial compression, Brazilian and “Continuous Failure State” triaxial tests, it was pointed out that all of the mechanical parameters decreased gradually with an increasing number of heating cycles. Uniaxial compressive strength was reduced to about 50%, while the tensile strength decreased to about 60% for both types of rock. It was also observed that the variations of strength parameters were higher after the first heating cycles. As a result of cyclical heating, the slopes of pre-failure and post-failure curves in the stress-strain plane changed similarly, but the variations of modulus of elasticity were higher than the slopes of the post-failure curves for sandstone. The ratio between compressive and indirect tensile strength rose to a value of 98 after the last heating cycle. For unheated specimens of Carrara marble this ratio is 20. The axial strain at the failure point increased suddenly after the first heating cycle and the failure developed entirely intergranular in cyclically heated specimens.     

柱状节理玄武岩隧洞破坏模式及其力学机制模拟

柱状节理岩体由于其内部赋存大量的隐节理面,开挖卸荷后极易出现隐节理面开裂松弛等特征,导致其破坏模式异于一般岩体。其破坏模式主要受到异常发育的节理面和较高地应力的共同作用影响。由于柱状节理岩体节理面发育,岩体结构控制型破坏占主要部分,包括单临空面节理面滑移（塌方）、多临空面节理面滑移（塌方）、与错动带、断层等弱面相组合的坍塌等破坏模式;应力控制型破坏主要为河谷侧顶拱喷层开裂;应力-结构面型破坏主要为岩性交界处的节理岩体塌落等。柱状节理岩体表层主要发生柱内竖直隐节理面和柱间节理面的拉破坏,而围岩内部的柱状节理主要发生柱间节理面的剪切破坏。因此,现场柱状节理的支护也应主要包括两个方面：以喷射混凝土钢纤维来阻止柱状节理岩体表层的张性开裂,以系统锚杆来控制柱状节理岩体内部的剪切破坏。     

A material model for inelastic rock deformation with spatial variation of pore pressure

This paper sets forth the theoretical background and basic numerical expressions for the incorporation of elastic-plastic constitutive equations for ductile rock into a finite element computer code. The derivation of an expression for the total strain rate is performed both for a total stress formulation and for a formulation that employs the concept of effective stress for inelastic behaviour. Specific expressions for the incremental strain rate are presented for the case of a porous material having a quadratic initial yield surface and observing the associated flow rule with a special hardening law for subsequent plastic deformation. A final section of the paper summarizes the expressions required to insert the quadratic yield surface model into a finite element code.     

Experimental and numerical studies of rock salt strain hardening

The work presented in this paper comes as part of a research program dealing with the thermomechanical behaviour of rock salt. It aims to study laboratory and in-situ long-term behaviour by means of creep tests with deviator and temperature changes. The laboratory results, using a triaxial multi-stages creep tests, highlighted the strain hardening character of rock salt. Furthermore, the in-situ results, using a borehole dilatometer multi-step creep test, have shown that the drilling is carried out in a weakly stressed pillar. The interpretation of the laboratory results, using the J.LEMAITRE law, did not indicate full agreement with all the test results. As a result a ‘double’ J.LEMAITRE model, which takes into account a double strain hardening variable, has been put forward. The validation of this model on the laboratory creep tests is very satisfactory. Furthermore, the activation energy seems satisfactory to represent the influence of the temperature. The in-situ behaviour modelling is clearly more complex than the modelization based on laboratory tests. In fact, it seems that if the rock salt behaviour is maintained by J.LEMAITRE law, it is necessary to vary with the stress, at least, one of the parameters assumed constant in the basic law.     

Prediction of dilation and permeability changes in rock salt

A numerical procedure has been developed for predicting dilation (porosity) and gas permeability changes in rock salt. The hierarchical single-surface constitutive model of Desai and co-workers is used a finite element program to calculate the state of stress and strain surrounding excavations in rock salt. The elastoplastic constitutive model accounts for strain hardening, a non-associative volumetric response and stress-path-dependent behaviour. The calculated stress and strain fields are used in a flow model based on the equivalent channel concept to predict permeability. Parameters for both the mechanical and permeability models are developed from laboratory test results. Two field experiments adjacent to underground excavations are modelled. The extent of the dilated rock zone around the excavation is predicted well, but the magnitude of the porosity and gas permeability is underpredicted very near the excavations. This discrepancy is attributed to model parameters derived from loading-only laboratory tests, whereas significant unloading occurs in the field. The shape of the yield surface was found to be an important factor in dilation and permeability predictions. Similar stress, strain and permeability fields were obtained with different model types (plane strain or axisymmetric) and initial stress states, and with instantaneous and progressive excavation.     

基于离散元数值模拟的应变分析和裂缝预测技术

应变分析与裂缝预测技术在地学领域具有重要应用意义。离散元方法虽然能有效分析含有大量间断的问题,但目前在地学领域应用较少。文中尝试使用离散元方法表示符合实际性质的岩石,模拟水平挤压环境下滑脱构造的形成过程,并对变形过程中的应变分布变化与裂缝生成规律进行了分析。结果表明:在挤压环境的滑脱构造中,裂缝产生的高峰期先于断层明显活动期,局部区域内聚集的大量裂缝是产生断层的诱因;已经出现明显活动的断层中产生的裂缝较少。裂缝集中区域和应变集中区域相互重叠,裂缝越发育则应变越强烈。受同一个断层影响的裂缝首先在断面上集中出现,随后产生在断面周边区域;在受断层影响的范围内,裂缝距离断面越远则形成时间越晚。该成果还表明离散元方法在应变分析与裂缝预测研究中具有巨大潜力。     

Microplane constitutive model for porous isotropic rocks

The paper deals with constitutive modelling of contiguous rock located between rock joints. A fully explicit kinematically constrained microplane‐type constitutive model for hardening and softening non‐linear triaxial behaviour of isotropic porous rock is developed. The microplane framework, in which the constitutive relation is expressed in terms of stress and strain vectors rather than tensors, makes it possible to model various microstructural physical mechanisms associated with oriented internal surfaces, such as cracking, slip, friction and splitting of a particular orientation. Formulation of the constitutive relation is facilitated by the fact that it is decoupled from the tensorial invariance restrictions, which are satisfied automatically. In its basic features, the present model is similar to the recently developed microplane model M4 for concrete, but there are significant improvements and modifications. They include a realistic simulation of (1) the effects of pore collapse on the volume changes during triaxial loading and on the reduction of frictional strength, (2) recovery of frictional strength during shearing, and (3) the shear‐enhanced compaction in triaxial tests, manifested by a deviation from the hydrostatic stress–strain curve. The model is calibrated by optimal fitting of extensive triaxial test data for Salem limestone, and good fits are demonstrated. Although these data do not cover the entire range of behaviour, credence in broad capabilities of the model is lend by its similarity to model M4 for concrete—an artificial rock. The model is intended for large explicit finite‐element programs. Copyright © 2002 John Wiley & Sons, Ltd.     

脆性岩石三轴压缩渐裂过程中的渗透性演化规律研究

岩石渐进破坏伴随着裂纹的开展发育,岩石的渗透性演化与裂纹的开展规律有着密切的联系。运用三轴渗流伺服装置对凝灰岩进行了不同围压和渗压下的渗流-应力耦合试验,分析了岩石在渐裂过程中不同裂纹开展阶段渗透率的演化规律。结果表明：在裂纹的稳定扩展阶段,渗透率的变化不明显,起裂强度对应的渗透率可用于确定最小渗透率;进入裂纹非稳定扩展阶段后,渗透率出现明显增大,增大过程可以分为两个阶段,裂纹环向应变能较好地反映渗透率增大的两个阶段,其拐点可用于确定起始渗透率的位置;在峰后软化阶段,渗透率出现下降并进入残余稳定阶段,裂纹环向应变率可以反映渗透率的下降阶段,并可用于确定峰值渗透率的位置。     

Post failure behaviour of a rock mass under the influence of triaxial and true triaxial confinement

In this paper results of triaxial and true triaxial testing conducted on physical models of a rock mass are used to describe its post failure behaviour. The specimens comprised of three continuous joint sets and were prepared from blocks of sand lime model material. The testing was performed using a True Triaxial System (TTS) developed by the authors. The results show strain hardening, strain softening and plastic behaviour in the simulated rock mass specimens depending upon joint geometry and stress state. Expressions are suggested to estimate post peak modulus in triaxial and true triaxial stress conditions. Finally, a zonation table is proposed to assess the strain hardening, softening and plasticity behaviour of a rock mass material with the help of joint geometry and confining stress conditions at site.     

Visco-Plastic Behaviour around Advancing Tunnels in Squeezing Rock

Summary  The visco-plastic behaviour of rocks plays a relevant role in the tunnelling works, especially for deep tunnels subjected to large initial stresses for which squeezing conditions may develop. A rheological model is discussed that accounts for visco-elastic (primary) and visco-plastic (secondary) contributions to rock creep. The effects of tertiary creep are included in the model by way of a gradual mechanical damage governed by the cumulated visco-plastic strains. The parameters of the intact rock are first identified based on laboratory test results presented in the literature. Then, after scaling them to those of the rock mass, the potential applicability of the model is tested through axisymmetric and plane strain finite element analyses of the full face excavation of a deep circular tunnel. The results are discussed with particular reference to the short term redistribution of stresses around the opening and to its convergence. The analyses show the relevant influence of tertiary creep on the tunnel closure. In addition, those based on an axisymmetric scheme turn out to be crucial for the correct long term prediction of the interaction between the rock mass and the supporting structure of the opening.     

A Bounding Surface Plasticity Model for Intact Rock Exhibiting Size-Dependent Behaviour

A new constitutive model for intact rock is presented recognising that rock strength, stiffness and stress–strain behaviour are affected by the size of the rock being subjected to loading. The model is formulated using bounding surface plasticity theory. It is validated against a new and extensive set of unconfined compression and triaxial compression test results for Gosford sandstone. The samples tested had diameters ranging from 19 to 145 mm and length-to-diameter ratios of 2. The model captures the continuous nonlinear stress–strain behaviour from initial loading, through peak strength to large shear strains, including transition from brittle to ductile behaviour. The size dependency was accounted for through a unified size effect law applied to the unconfined compressive strength—a key model input parameter. The unconfined compressive strength increases with sample size before peaking and then decreasing with further increasing sample size. Inside the constitutive model two hardening laws act simultaneously, each driven by plastic shear strains. The elasticity is stress level dependent. Simple linear loading and bounding surfaces are adopted, defined using the Mohr–Coulomb criterion, along with a non-associated flow rule. The model simulates well the stress–strain behaviour of Gosford sandstone at confining pressures ranging from 0 to 30 MPa for the variety of sample sizes considered.     

工程岩体强度的估算方法

岩体是由地质过程中形成的岩块和结构面网络组成。由于试件制备、加荷等均极困难,且昂贵而费时,难于像岩块那样进行大量试验来确定岩体之强度。所以,如何通过室内小试件试验来估算大岩体的强度成为工程地质工作者所关注的问题。本文介绍了两种用小试件资料估算大岩体强度的方法及计算实例。     

Rock slope stability assessment using finite element based modelling – examples from the Indian Himalayas

Numerical modelling of rock slides is a versatile approach to understand the failure mechanism and the dynamics of rock slopes. Finite element slope stability analysis of three rock slopes in Garhwal Himalaya, India has been carried out using a two dimensional plane strain approach. Two different modelling techniques have been attempted for this study. Firstly, the slope is represented as a continuum in which the effect of discontinuities is considered by reducing the properties and strength of intact rock to those of rock mass. The equivalent Mohr-Coulomb shear strength parameters of generalised Hoek-Brown (GHB) criterion and modified Mohr-Coulomb (MMC) criterion has been used for this continuum approach. Secondly, a combined continuum-interface numerical method has been attempted in which the discontinuities are represented as interface elements in between the rock walls. Two different joint shear strength models such as Barton-Bandis and Patton’s model are used for the interface elements. Shear strength reduction (SSR) analysis has been carried out using a finite element formulation provided in the PHASE². For blocky or very blocky rock mass structure combined continuum-interface model is found to be the most suitable one, as this model is capable of simulating the actual field scenario.     

三轴试验下结构面倾角对制备岩样力学特性的影响

结构面倾角对岩样的力学特性有很大影响。人工制备了结构面倾角为15°、30°、45°、60°（水平面为0°面）的单贯通结构面岩样和完整样,并进行了单轴压缩试验和围压为100、200、300 kPa的三轴压缩试验来探讨结构面倾角对其力学和变形特性的影响。试验结果表明：①当倾角小于等于30°时,出现了岩样应力-应变曲线中典型的4个阶段。而当倾角等于45°和60°时,最后阶段变为先软化再硬化的特征;②结构面岩样均先体缩再体胀。随着围压增加,体缩最大值接近,而体胀呈明显减小趋势。随结构面倾角增加,体缩呈缓慢增长趋势,并在30°和45°时出现体缩突变。而体胀显著的减小。最后,指出了耶格尔单结构面判据的不足,并对其进行了修正,验证结果表明改进的耶格尔判据与试验结果吻合较好。