The Various Stress Paths Causing Deformation and Failure in Rocks

The rock deformation and failure tests are performed along various stress paths under true triaxial stress state. The experimental results have shown that the change of three principal stresses (the increase of the maximum principal stress, the decrease of the minimum principal stress, the decrease of the confining pressure and the increase or decrease of the intermediate principal stress ) can lead to deformation and failure in rocks. The strength, the deformability and the failure precursors of rocks are related with stress paths. Based on the results of the study, the problems of the stress path in rock engineering are discussed.     

岩体变形和破坏的各种应力途径

在真三轴应力状态下进行了各种应力途径的岩石变形和破坏实验。实验表明,三个主应力的变化(最大主应力的增加,最小主应力的减小,围压的减小以及中间主应力的增加或减小)都能引起岩石变形和破坏。而且岩石的强度、延性和脆性、体积变化和破坏前兆等都与应力途径有关。据根试验结果探讨了岩体工程中的应力途径问题。     

Deformation modulus of heavily jointed–sheared and blocky greywackes by pressuremeter tests: Numerical, experimental and empirical assessments

Deformability of rock masses influencing their behavior is an important geomechanical property for the design of rock structures. Due to the difficulties in determining the deformability of jointed rock masses at the laboratory-scale, various in-situ test methods such as pressuremeter, dilatometer, plate loading tests etc. have been developed. Although these techniques are currently the best and direct methods, they are time-consuming and expensive, and present operational difficulties. In addition, the influence of the test volume on deformation modulus depending on the method employed is also important. For these reasons empirical equations to indirectly estimate the deformation modulus have also been recommended by several investigators as an alternative approach. In this study; the geomechanical quality of weak, heavily jointed, sheared and/or blocky greywacke rock masses, on which very concentrated civil works are continuing at the southern and southwestern parts of Ankara (Turkey), was assessed. The deformation modulus was determined by pressuremeter tests, the possible effects of variables on the derived deformation modulus from the pressuremeter test were evaluated by numerical methods, and the comparisons between the deformation modulus of the greywackes obtained from the pressuremeter tests and their geomechanical quality (GSI and RMR) were made. Numerical simulations revealed that the presence of a disturbed annulus around the borehole causes underestimation of the deformation modulus, while the effect of length to diameter ratio of the pressuremeter probe on the deformation modulus is minor. Based on the geo-engineering characterization assessments, mainly two greywacke rock masses with different geomechanical qualities were identified. Geotechnical quality of one of these rock masses was verified by the back analysis of two slope failures. The empirical equations to indirectly estimate the deformation modulus of the greywackes using their GSI and RMR values yielded high coefficients of correlation.     

On the role of joint roughness on the micromechanics of rock fracturing process: a numerical study

The deformation process and failure mechanism of rock mass with increased joint roughness subjected to unconfined compression are investigated in this study using discrete element method. A numerical model is developed using soft-bonded particle and validated to realistically replicate the mechanical response of the rock mass. The micro-parameters of the rock material are first determined, and the effects of the joint roughness on the macromechanical response and fracture growth mechanism are then investigated. Analyses are also performed to examine the tensile and shear crack distributions, acoustic emission (AE) characteristics, coordination number, and crack anisotropy to advance the current understanding of the role of joint roughness on the mechanical behavior and deformability of rock mass. The results show that strength and deformability of the jointed rocks are highly dependent on the joint orientation and roughness. Joint roughness is found to restrain the propagation and coalescence of microcracks and AE events from the interlocking of asperities. In addition, the spatial distribution of the contact forces allows for better understanding of the effect of joint inclination angle on the response of the investigated rock samples.

     

Numerical investigation of the effect of joint geometrical parameters on the mechanical properties of a non-persistent jointed rock mass under uniaxial compression

The strength and deformability of rock masses transected by non-persistent joints are controlled by complex interactions of joints and intact rock bridges. The emergence of synthetic rock mass (SRM) numerical modelling offers a promising approach to the analysis of rock masses, but has not been rigorously compared with actual physical experiments. In this work, SRM modelling by the discrete element software PFC3D is used to investigate the effect of geometric parameters of joints on the rock mass failure mechanism, unconfined compressive strength and deformation modulus. Firstly, a validation study is undertaken to investigate the ability of SRM modelling to reproduce rock mass failure modes and strength as determined by uniaxial and biaxial compression testing in the laboratory. The numerical analyses agree well with physical experimentation at low confining pressure. A sensitivity study is then undertaken of the effect of joint configuration parameters on the failure mode, unconfined compressive strength and deformation modulus of the rock mass. Five failure modes are predicted to occur: intact rock, planar, block rotation, step-path and semi-block generation. It is found that the failure mode is determined principally by joint orientation and step angle and the joint orientation with respect to principal stress direction is the parameter with the greatest influence on rock mass properties.     

On the role of pre-existing discontinuities on the micromechanical behavior of confined rock samples: a numerical study

The deformation process and failure mechanism of rock mass with increased density of initial joints subjected to confined stress state are investigated in this study using discrete element method (DEM). A numerical model of standard size granite samples is developed and validated using experimental data for both intact and jointed rocks. The micro-parameters of the rock material are first determined, and the effects of the rock discontinuity on strength, deformability, stress–strain relationship, and failure modes are then investigated at the macro-scale level. Analyses are also performed to examine the tensile and shear crack distributions, fragmentation characteristics, particle kinematics, and energy dissipation to advance the current understanding of the deformation processes and failure mechanisms of jointed rock masses. The microscopic evolutions in the fabric and force anisotropy during loading and distributions of contact forces provide insights into the influence of increasing initial jointing on the macroscopic deformational behavior of the rock. The results show how the deceleration in the growth of fabric and contact force anisotropies develops and confirms that the increase in initial jointing and the associated changes in microstructure can restrain the development of anisotropy, thereby reducing significantly the strength of the rock samples.

     

Estimation of the rock mass deformation modulus using a rock classification system

It is often difficult to directly obtain specific design parameters of interest. In these situations, estimation based on empirical correlations is an alternative. The deformation modulus of a rock mass, which is important to know for engineering projects, is measured by in situ tests, such as plate bearing, flat jack, pressure chamber, borehole jacking and dilatometer tests. Nevertheless, these in situ tests are expensive, time consuming and sometimes even impossible. Many attempts have been made to estimate the E modulus using easy-to-obtain parameters of a rock mass. This paper reviews previous studies and the equations that have been developed. In addition, this study presents a new relation developed using a database of 82 dilatometer test results gathered from two dam sites and a tunnel site. Statistical analyses were performed to correlate accessible rock parameters with measured E modulus values from in situ tests. Knowing that discontinuity characteristics and the strength of rock materials are the most important contributors to rock deformability, the focus was on identifying parameters that are affected by the mentioned properties. Among the tested parameters, RMR (Rock Mass Rating) showed the best correlation with the E modulus. Statistical analyses resulted in a new empirical equation that has an acceptable estimation ability.     

Demonstration of spatial anisotropic deformation properties for jointed rock mass by an analytical deformation tensor

This paper develops a joint deformation tensor (JD), which considers all of the joint's mechanical and geometrical parameters that affect the deformability of the rock mass. The method based on JD (JD method) and an elastic deformation anisotropy index (EDAI) are deduced for estimating the spatial anisotropy deformation of a jointed rock mass. The numerical modeling and in situ true triaxial compressive experiments well verified the effectiveness of the EDAI and JD method for the rock mass containing one joint set, orthogonal joint sets or the rock mass containing any types of joint network with unity stiffness ratio.     

Anisotropic Deformation of a Circular Tunnel Excavated in a Rock Mass Containing Sets of Ubiquitous Joints: Theory Analysis and Numerical Modeling

Determining anisotropic deformation surrounding underground excavations for tunnels is an intuitional task that involves many difficulties due to the inherent anisotropies in the strength and deformability of natural rocks. This study investigates joint-induced anisotropic deformation surrounding a tunnel via a numerical simulation that accounts for the mechanical behavior of intact rock, the orientations of joint sets, and the mechanical behavior of joint planes; this numerical simulation can model the complete stress–strain relationship with anisotropic rock mass characteristics. Simulation results demonstrate that the well-known excavation-induced stress variation–decrease in the radial component and increase in the tangential component–decrease shear strength and increase shear stress for the joint plane tangential to the tunnel wall, resulting in joint sliding failure and considerable shear deformation. This joint sliding failure and significant shear deformation account for the joint-induced anisotropic deformation surrounding a tunnel. When a rock mass has two joint sets with unfavorable joint orientations, the area with joint sliding failure can deteriorate mutually, resulting in large anisotropic deformation. Additionally, for a rock mass containing three joint sets with well-distributed orientations, joint sliding in various joint sets and associated stress variations can counter balance each other, resulting in less anisotropic deformation than those of rock masses containing one or two joint sets.     

Failure analysis of the granite for a dam foundation

This paper presents the numerical and experimental investigation of a dam foundation. The site consists of granite and especially weathered granite. Numerical and analytical analyses have been conducted to evaluate suitability of the granite for a dam foundation. Mohr–Coulomb failure criterion has been used to calculate the compressive strength of the rock mass. Finite element implementation of Mohr–Coulomb criterion has been used for deformation and settlement analysis. Packer testing and in-situ estimation of rock mass deformability using the Goodman jack have been performed. The results of the evaluations show that very small normal and differential settlements can be expected in structural regions due to dam construction, and the compacted concrete dam can safely be constructed on either the competent granite or the weathered granite. However, the dam foundation on the weathered granite has high conductivity potential problems for the reservoir.     

岩体等效变形参数研究

岩体变形参数的确定对岩体稳定性模拟至关重要.提出了确定规则裂隙和不规则裂隙岩体等效变形参数的一种模型, 探讨了岩体等效变形参数的规律.通过对不考虑渗流-应力耦合时岩体等效变形性能的研究, 可以发现岩体的等效变形参数不仅与各组结构面的几何形态、结构面变形参数、岩块变形参数等有关, 而且与不同组系结构面间的交切形态有关.岩体的REVs具备以下几点规律: 首先REVs具有多尺度效应和不确定性.其次, REVs与结构面各几何形态要素之间有如下关系: 平均迹长越大, 平均间距越小, 方向角的方差越大, 结构面分布越凌乱, REVs的取值越小.REVs与岩块、结构面变形参数之间有如下关系: 结构面变形参数与岩块变形参数的差异程度对REVs的取值没有明显影响, 但是不同组系结构面或是同一组中的各条结构面, 其变形参数差异越小, REVs的取值将越小.      

岩石在循环荷载作用下的强度及变形特征

本文着重研究了岩石在循环荷载作用下的强度及变形特征。实验结果表明,岩石在循环荷载作用下的强度低于其静力强度,而这个循环疲劳强度极限与振幅、频率有关;岩石在循环荷载作用下的变形特征类似于静力蠕变特征。     

Study of rock joints under cyclic loading conditions

Summary A conceptual model for the behaviour of rock joints during cyclic shear and under constant normal stresses was proposed according to results from shear tests with 50 concrete replicas of rock joints. The shear strength and deformability of joint samples were found to be both anisotropic and stress dependent. Based on these experimental results, a two-dimensional constitutive model was developed for rock joints undergoing monotonic or cyclic loading sequences. The joint model was formulated in the framework of non-associated plasticity, coupled with empirical relations representing the surface roughness degradation, appearance of peak and residual shear stresses, different rates of dilatancy and contraction, variable normal stiffness with normal deformation, and dependence of shear strength and deformability on the normal stress. The second law of thermodynamics was represented by an inequality and used to restrict the values of some of the material parameters in the joint model. The new joint model was implemented into a two-dimensional Distinct Element Method Code, UDEC, and its predictions agreed well with some well-known test results.     

节理岩体锚杆的综合变形分析

在总结国内外对节理岩体中锚杆加固机制的试验研究和理论探讨基础上,综合考虑锚杆的切向和轴向变形能力,建立节理锚固锚杆在剪切荷载作用下的变形模型,将节理锚固锚杆的变形区划分为弹性变形段和挤压破坏段,引入表征挤压破坏段长度的变量,对锚杆与岩体的相互作用机制进行理论分析,推导了剪切荷载与剪切位移和轴向荷载与轴向位移的关系。通过分析锚杆的屈服破坏形式,得到了确定挤压破坏段长度的方法。最后,通过算例分析了挤压破坏段长度与锚杆直径、岩体强度、锚固角度等参数的关系,得到了以下结论：（1）节理锚固锚杆抗剪作用的实质是锚杆调动岩体的抗压强度抵抗节理切向荷载。在抗压强度较高的硬岩中,挤压破坏段局限于节理面附近,锚杆影响范围小;而在抗压强度较低的软岩中,挤压破坏段较大,而且会产生较大的剪切变形,锚杆影响范围较大。（2）锚杆屈服破坏形式与岩质和锚杆直径有关。硬质岩体发生剪切屈服,而较软岩体中容易发生弯曲屈服;小直径锚杆一般直接剪切屈服,而大直径锚杆可能发生弯曲屈服。锚杆屈服破坏后出现塑性铰,挤压破坏段范围在节理一侧约为直径的1～2倍,继续增加剪切荷载,挤压破坏段长度不再增大。（3）随岩质的不同,锚杆锚固节理的最优锚固角变化较大。岩质较硬时,最优锚固角度较小,反之则较大。     

基于微观力学特性的脆性岩石变形过程模拟

为了建立能够描述岩石宏观变形及其组成部分的变形模拟方法,考虑微缺陷的不均匀性对岩石宏观变形产生的影响,将岩石视为由空隙部分材料和骨架部分材料两部分组成。首先,基于岩石各组成部分材料变形分析,利用真应变描述方法及非线性变形的特点建立空隙部分材料的变形力学分析方法,同时,引入统计损伤以及固体力学理论建立骨架部分材料的变形力学分析方法。然后,通过岩石及其组成部分的变形力学分析建立岩石宏观变形力学分析方法,从而获得能够模拟岩石变形破坏全过程的统计损伤本构模型,并给出了模型参数的确定方法。最后,将文中模型与既有模型的理论曲线与试验曲线进行了对比分析,且基于文中模型对岩石及其组成部分变形进行了讨论。研究结果表明：文中模型不仅能反映既有模型所描述的主要变形特征,还能克服其难以较好地反映初期宏观变形非线性的不足;同时,该模型还能描述岩石组成部分的变形过程,不仅揭示了岩石宏观变形与其组成部分变形之间的关系,也揭示了空隙部分材料变形是引起岩石宏观变形非线性的根本原因。表明本文模型与方法具有一定的合理性与优越性。     

THE ANALYSIS AND COMPUTATION OF A WHOLE DEFORMATION CURVE OF ROCK UNDER UNIAXIAL PRESSURE

The whole deformation curve of rock represents important mechanical behaviour in the deformation and failure of rock .The problem has been deeply studied by numerous scientists .The author intends to deal with the whole deformation curve of rock .As the first step of study .the analogous calculation has been considered with the whole deformation curve of rock under uniaxial pressure in this paper .The mathematical expressions are developed piecewise ,and the constitutive law is given .Then ,the stress state of a rock specimen is computed for loading and unloading cycles step by step under the uniaxial pressure ,using the finite element method .A satisfactory result is obtained .The author will consider the problem about the deformation and failure of rock under the different confining pressure in another related paper .     

单轴压力下岩石全变形曲线的分析计算

一、问题的提出在实验室内,利用刚性加压设备对于岩石标本进行压缩试验,可以得到岩石标本的全变形曲线.该全变形曲线反映出岩石很多重要的力学属性,诸如压密过程、比例极限、应变强化、强度值、应变软化等等.这些力学属性无论是对于分析岩体的破坏机制,还是评价岩体的稳定性问题都是必需的第一手贫料.但实际上,直接用这些资料进行分析计算确不多.     

Rock Mass Classification and Slope Stability Assessment of Road Cut Slopes in Garhwal Himalaya, India

There are many rock mass classification schemes which are frequently used for different purposes such as estimation of strength and deformability of rock masses, stability assessment of rock slopes, tunneling and underground mining operations etc. The rock mass classification includes some inputs obtained from intact rock and discontinuity properties which have major influence on assessment of engineering behaviour of rock mass. In the present study, detail measurements were employed on road cuts slope faces in Garhwal Himalayas to collect required data to be used for rock mass classification of Rock Mass Rating (RMR) and Geological Strength Index (GSI). The stability assessment of rock slopes were also done by using Slope Mass Rating. In addition the relation between RMR and GSI were also evaluated using 50 data pairs.     

自然与饱水条件下异性结构面的剪切特性研究

利用室内剪切试验装置,开展不同正应力、自然与饱水条件下岩体异性结构面的剪切试验,分析异性结构面的剪切变形和强度特性,利用JRC-JCS抗剪强度力学模型将试验结果与计算结果进行对比分析。结果表明,（1）异性结构面的剪切变形曲线属于弹塑性残余变形类型。相比自然状态试件,饱水试件的弹性区减小,较早进入峰值区或塑性区;（2）异性结构面的剪切刚度均随法向力的增大而增大,但同一正应力下饱水试件的剪切刚度要小于自然状态的剪切刚度,在低法向力下尤为显著;（3）水对岩体异性结构面剪切强度参数有不同程度的弱化,尤其对内摩擦角 的劣化明显;（4）只要计算参数选取得当,并考虑实际岩体的受力及水等情况,JRC-JCS计算模型可以为实际工程岩体的结构面强度提供较为准确的参数。     

考虑膨胀应力和剪胀的深埋隧道弹塑性解

基于湿度应力场理论,推导了考虑膨胀应力和剪胀特性的圆形隧道开挖后围岩力学响应的弹塑性解。将隧道软弱围岩遇水膨胀现象视为湿度-应力耦合过程,基于Fick第二定律,推导了圆形隧洞围岩内湿度扩散非稳态解。采用非关联流动法则,获得了隧道高膨胀势区的应力和位移解答。以两种不同质量岩体开挖的隧洞为例,分析了膨胀围岩应力和变形的影响因素。结果表明,考虑膨胀应力（取决于围岩含水率变化和湿度膨胀系数）时,塑性区扩大,松动圈厚度增加,应力收敛变慢。当膨胀应力增大到一定程度时,塑性区将出现拉应力区。膨胀岩隧洞开挖遇水作用,膨胀应力增加的围岩变形远大于地应力引起的围岩变形。同时,应力剪胀对膨胀性围岩的变形影响不容忽视,尤其是在支护抗力较小的情况下,洞壁处径向位移增加显著。