深部岩石考虑残余强度时三轴试验离散元定量模拟及参数分析

深部岩石在工程中具有高应力、大变形等典型特点,因此,高围压下考虑岩石残余强度的三轴试验对于分析深部岩石力学特性具有重要意义。离散单元法是分析岩石力学特性的重要数值方法,但是长期以来采用离散单元法定量模拟岩石的三轴试验一直存在诸多挑战,即数值模拟与室内试验得到的应力-应变全过程曲线难以定量匹配。采用改进的三维胶结抗弯-扭模型对深部砂岩考虑残余强度时的三轴试验进行了定量模拟,实现了数值模拟与室内试验应力-应变全过程曲线的定量匹配,获得了岩石较大的峰值/残余内摩擦角及非线性强度包线,克服了经典BPM模型存在的3个突出问题。通过参数分析,研究了峰值/残余内摩擦角及黏聚力与离散元微观参数之间的关系,同时这些大量的算例也证明了该模型具有较高的计算效率,可以满足模拟三维室内常规试验的要求。     

Empirical Formula of Shear Strength of Rock Fractures Based on 3D Morphology Parameters

The prime objective of this work is to provide a reference to predict the peak shear strength of rock fractures. The paper studied some shear properties of rock fractures and proposed an empirical formula for the peak shear strength of rock fractures based on 3D morphology parameters. The rock fractures were induced in cylindrical sandstone and marble specimens by means of indirect tension. A rock direct shear apparatus (RDS-200) was adopted to conduct direct shear tests on five groups of rock fractures under different levels of normal load. Before the direct shear test, 3D morphology parameters of rock fracture surfaces were obtained using a 3D optical scanner. By analyses of direct shear test data, the relationships between peak shear strength, peak shear displacement, peak dilatancy angle, residual friction coefficient and peak normal stress were found. According to the evolution trends of peak shear strength and peak dilatancy angle along with the normal stress, an empirical formula was proposed to predict the peak shear strength of rock fractures in both sliding and cutting failure modes considering the 3D morphology parameters of rock fracture surfaces. The empirical formula could be commonly used for different types (sandstone and marble) and grain sizes (powder-grained, fine-grained, medium-grained and coarse-grained) of rock fractures.     

Effects of pre-existing discontinuities on the residual strength of rock mass – Insight from a discrete element method simulation

When rock failure is unavoidable, the designer of engineering structures must know and account for the residual strength of the rock mass. This is particularly relevant in underground coal mine openings. Pre-existing discontinuities play an important role in the mechanical behavior of rock masses and thus it is important to understand the effects of such pre-existing discontinuities on the residual strength. For this purpose, the present study demonstrates a numerical analysis using a discrete element method simulation. The numerical results indicate that fracture intensity has no significant influence on the residual strength of jointed rock masses, independent of confining conditions. As confining pressures increase, both peak and residual strengths increase, with residual strength increasing at a faster rate. The finding was further demonstrated by analyzing documented laboratory compressive test data from a variety of rocks along with field data from coal pillars. A comprehensive interpretation of the finding was conducted using a cohesion-weakening-friction-strengthening (CWFS) model. The effect of rock bolts on rock mass strength was also evaluated by using a discrete element method model which suggested that rock bolts can significantly increases residual strength but have limited effect on increasing the peak strength of rock masses.     

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.     

基于一种脆性指标确定岩石残余强度

岩石的残余强度是岩石力学的重要指标,准确地评价岩石残余强度对于评价地下工程的稳定性以及优化岩体支护设计具有重要意义。基于岩石的三轴力学特性提出一种表征岩石峰后强度衰减行为的力学指标--岩石强度衰减系数,该指标可反映岩石的脆性程度,并提出岩石强度衰减系数与围压关系的幂函数模型。对22组不同成因的岩石常规三轴压缩试验数据进行幂函数模型参数拟合,发现不同岩石拟合所得参数离散性较大,分析其原因主要与岩石矿物组成和岩石结构特征等因素相关。在此基础上提出基于强度衰减方法确定岩石残余强度的方法,分析表明,该方法能够很好地拟合岩石残余强度试验数据,并能反映岩石结构性质对残余强度的影响。     

Different Approaches for Simulating Brittle Failure in Two Hard Rock Mass Cases: A Parametric Study

One of the aims of rock mechanics analysis is to predict fallouts in underground excavations. The objective of this paper was to study the relative importance of different strength parameters and their significance on the simulation of brittle failure and fallouts. This work was conducted as a parametric study, using numerical modelling and a number of approaches. The results were compared with observed fallouts. More obvious and distinct shear bands could be observed with decreased element sizes close to, and at, the boundary. The maximum shear strain was the most reliable indicator for fallout prediction. The results of the (instantaneous) cohesion softening friction softening models were sensitive to changes of the peak strength parameters and less sensitive to variations in residual parameters. The result from the cohesion-softening friction-hardening (CSFH) model, when using a peak cohesion equal to the intact rock strength, best captured the observed rock behaviour.     

Evolution of Rock Cracks Under Unloading Condition

Underground excavation normally causes instability of the mother rock due to the release and redistribution of stress within the affected zone. For gaining deep insight into the characteristics and mechanism of rock crack evolution during underground excavation, laboratory tests are carried out on 36 man-made rock specimens with single or double cracks under two different unloading conditions. The results show that the strength of rock and the evolution of cracks are clearly influenced by both the inclination angle of individual cracks with reference to the unloading direction and the combination geometry of cracks. The peak strength of rock with a single crack becomes smaller with the inclination angle. Crack propagation progresses intermittently, as evidenced by a sudden increase in deformation and repeated fluctuation of measured stress. The rock with a single crack is found to fail in three modes, i.e., shear, tension–shear, and splitting, while the rock bridge between two cracks is normally failed in shear, tension–shear, and tension. The failure mode in which a crack rock or rock bridge behaves is found to be determined by the inclination angle of the original crack, initial stress state, and unloading condition. Another observation is that the secondary cracks are relatively easily created under high initial stress and quick unloading.     

Evidence for a Long-Term Strength Threshold in Crystalline Rock

The mechanical response of brittle rock to long-duration compression loading is of particular concern in underground disposal of nuclear waste, where radionuclides must be isolated from the biosphere for periods of the order of a million years. Does the strength decrease without limit over such time, or is there, for some rock types, a lower “threshold” strength below which the rock will cease to deform? This paper examines the possibility of such a threshold in silicate crystalline rocks from several perspectives, including: (1) interpretation of the results of short-term creep tests on rock; (2) numerical analysis of the effect of decrease in fracture toughness due to stress corrosion on the strength of a crystalline rock; and (3) evidence from plate tectonics, and observations of in situ rock stress in granite quarries. The study concludes that there is clear evidence of threshold strength. The threshold is of the order of 40% of the unconfined compressive strength or higher for laboratory specimens under unconfined compressive loading, and increases rapidly in absolute value with confinement. Field evidence also leads to the conclusion that the long-term strength of crystalline rock in situ is of comparable magnitude to the laboratory value.     

Application of Rock Mass Characterization for Determining the Mechanical Properties of Rock Mass: a Comparative Study

The results of geotechnical explorations, engineering geological investigation (including laboratory and in situ tests) and field observations have been used, along with borehole logging charts, to obtain the rock mass geotechnical data. Based on the data, the rock mass along the Sabzkuh water conveyance tunnel route was classified by rock mass rating (RMR), Q-system (Q), rock mass index (RMi) and geological strength index (GSI) (3 methods). A new series of correlations were established between the systems based on the data collected from the study area. These relationships were then compared with those reported in the literature, and two new relations were recommended. The classifications were utilized to calculate mechanical properties (rock mass strength and deformation modulus) of the rock mass along the tunnel according to available empirical relations, and to distinguish the upper-bound and lower-bound relations.     

Experimental Study of Mechanical Behaviour of Rock Joints Under Cyclic Loading

Summary Evaluation of the effects of small repetitive earthquakes on the strength parameters of rock joints in active seismic zones is of interest of the designers of underground constructions. In order to evaluate these effects, it is necessary to study the behaviour of rock joints under dynamic and cyclic loadings. This paper presents the results of a systematic study on the behaviour of artificial rock joints subjected to cyclic shearing. More than 30 identical replicas have been tested using triaxial compression devices under different conditions of monotonic and cyclic loading. At the first stage a few samples have been tested in monotonic loading modes under various confining pressures and rate of displacement. In the second series of tests, small cyclic loads were applied on the samples for increasing number of cycles, frequency levels and stress amplitudes. These were then followed by monotonic loading again. The variations of maximum and residual shear strengths for each test have been studied. The results show increase of shear strength as a result of the increase in confining pressure and they display decrease of shear strength due to the increase of rate of loading, number of cycles, frequency levels and stress amplitudes.     

峰前循环剪切作用下岩石节理剪切力学特性

微震、工程爆破等低应力循环剪切荷载作用对节理岩体工程失稳破坏具有重要影响。为研究峰前循环剪切加卸载作用下岩石节理剪切力学特性,采用RDS-200型岩石节理剪切试验系统对人工劈裂黄砂岩节理进行了峰前循环剪切下的直剪试验。通过与未进行峰前循环剪切加卸载时岩石节理力学参数预测值对比,得到峰前循环剪切加卸载作用对峰前剪切刚度、峰值剪切强度、峰值剪切位移与残余剪切强度的影响。结果表明：（1）峰前循环剪切加卸载后,当法向应力为2 MPa时,岩石节理峰前剪切刚度增大,当法向应力为4～10 MPa时,岩石节理峰前剪切刚度在循环剪切应力幅值范围内增大,在超出循环剪切应力幅值时减小;（2）峰前循环剪切加卸载后,峰值剪切强度降低了10%～20%,降低百分比随法向应力增大整体呈对数函数增大;峰值剪切位移增加了2%～40%,增加百分比随法向应力增大整体呈对数函数减小;（3）峰前循环剪切加卸载后,岩石节理残余剪切强度无明显变化,峰值剪切强度与残余剪切强度差值减小,峰后剪切应力做功损失百分比降低。     

A Combined Three-Dimensional Geological-Geostatistical-Numerical Model of Underground Excavations in Rock

Summary. This paper exploits geological and borehole geotechnical data obtained in the exploratory phase of a tunneling project to investigate in a first place if the kriging interpolation scheme may effectively reproduce the spatial variability of rock mass quality (Rock Mass Rating, RMR) in the vicinity of tunnels. For this purpose a quick solver in Fortran has been developed that performs variography analysis of 3D spatial data, fast kriging estimations of RMR between borehole sampling locations at the centroids of the elements of the numerical model, and model validation. For the purpose of an integrated underground excavation design, a step further is made by incorporating into the 3D mechanical numerical model of the rock mass, the three-dimensional (3D) solid geological model, thus coupling the geology with the ground (geotechnical) model (i.e. each element of the numerical model is assigned a geological material). The mechanical properties of each finite difference cell (or Representative Elementary Volume) of the ground model were then prescribed according to its geological type, the spatial heterogeneity of the rock mass expressed quantitatively with the kriging model, and the upscaling calculations of the mechanical properties of the intact rocks determined in the laboratory, based on the size-effect (strength dependence on size) and Damage Theory. Furthermore, a preliminary numerical simulation of the advance of unsupported tunnels in the model of the heterogeneous rock mass was performed for illustration purposes.     

NON-LINEAR FAULT BEHAVIOUR NEAR UNDERGROUND EXCAVATIONS — A BOUNDARY ELEMENT APPROACH

A boundary element model for stress/stability analysis of underground excavations in the vicinity of faults is presented. The boundary element formulation adopts the fictitious stress method for the simulation of excavation boundaries and the displacement discontinuity method for the representation of faults. The numerical model employs the Barton–Bandis non-linear joint model for the modelling of the fault behaviour and linear elastic behaviour for the rock. An incremental-iterative in situ stress relaxation algorithm is implemented for the non-linear analysis of the faults. Both deformation and peak strength models of Barton–Bandis are incorporated for modelling the mechanical behaviour of the fault. The non-linear deformation of fault considers the effects of coupling between shear and normal stresses and displacement, joint closure, joint separation, hardening followed by post-peak or residual behaviour. The peak strength model employs a mobilized non-linear shear strength envelope. The differences between linear and non-linear simulation of the fault models are discussed. A comparison of model predictions with the classical Mohr–Coulomb peak strength model with constant joint stiffness is presented. The numerical model is used for a case study of Canadian hard rock underground mine. The shear and normal displacements along the fault during four mining sequences with backfill simulation are presented and discussed.     

Incorporating Parameter Variability in Rock Mechanics Analyses: Fuzzy Mathematics Applied to Underground Rock Spalling

Although fuzzy analysis has been widely developed, its use in rock mechanics and rock engineering is limited. Here, it has been used to evaluate the potential for underground rock spalling at the boundary of a circular excavation in terms of rock strength and in situ rock stress, given the uncertainty in both of these input parameters. Using standard techniques from fuzzy mathematics, we develop an expression for the fuzzy factor of safety, and extend this to form the crisp parameters Safety Certainty Value and its complement, the Failure Certainty Value. Plots of the Failure Certainty Value in terms of the in situ stress ratio and rock strength/stress ratio show the effect of uncertainty on the assessment of stability. From these plots, we illustrate how the relative importance of uncertainty in the input parameters can be assessed, with the associated ramifications for site investigation and subsequent engineering design.     

不同倾角节理组和锚固效应对岩体特性的影响

首先采用DDARF(discontinuous deformation analysis for rock failure)分析方法对双裂隙岩块进行单轴和双轴压缩模拟试验,研究了裂隙角度和侧向应力大小对岩块特性的影响,得到了裂隙岩块在这两种加载试验中的破坏过程、应力-应变曲线以及岩块中裂隙的起裂应力和岩块的峰值强度。在双轴压缩模拟试验中绘制了裂隙角度为45°的岩块在不同侧向压力下的强度包络线。其次,采用DDARF分析方法模拟劈裂试验中含裂隙试块的锚固效果,得到了4种不同锚固角度试块的轴向荷载–位移变化曲线和裂隙扩展规律。模拟结果与前人的类似条件下的试验结果相符良好。随后又将双裂隙试块双轴压缩模拟试验中得到的参数运用到一个地下洞室的工程实例中,用等效力学特性的方法分析对比了完整岩体和节理岩体洞室开挖完成后的破损状态的差异。最后运用DDARF分析方法研究了随机生成4组节理岩体的地下洞室的稳定性,得到了洞室节理围岩的裂隙扩展过程。同时通过对关键点位移的监测分析了锚杆的锚固效应。     

岩体应力的现场研究

岩体力学不同于力学的其他分支的主要特点之一,是岩体具有内应力.因而,一切与岩体有关的力学问题的合理解决,脆性破裂理论的实际应用,都离不开对岩体应力状态的了解.     

In Situ Study on Stress in Rock Mass

The Significance of the rock stress measurements for studying state of stress in the crust is elucidated in this paper .A brief introduction on the principles and methods of calculating the rock stress by measuring the deformations of the bore-holes by means of the overcoring technique is given .Generally the error is estimated to be about 10% by the laboratory checking methods .Form the practical examples it is summed up for some laws of the stress distribution within 200 meters of the shallow crust: from the viewpoint of the rock-mass strength and energy accumulation, the relationship between the major principal stress and the elastic modules of the rock is shown in diagrams, and its direction is closed related to the topographical conditions .The practical examples reveal the measurement of rock stress is significant to the ground surface and underground engineering projects .     

Characterization of Strength of Intact Brittle Rock Considering Confinement-Dependent Failure Processes

As technologies for deep underground development such as tunneling underneath mountains or mass mining at great depths (>1,000 m) are implemented, more difficult ground conditions in highly stressed environments are encountered. Moreover, the anticipated stress level at these depths easily exceeds the loading capacity of laboratory testing, so it is difficult to properly characterize what the rock behavior would be under high confinement stress conditions. If rock is expected to fail in a brittle manner, behavior changes associated with the relatively low tensile strength, such as transition from splitting to the shear failure, have to be considered and reflected in the adopted failure criteria. Rock failure in tension takes place at low confinement around excavations due to tensile or extensional failure in heterogeneous rocks. The prospect of tensile-dominant brittle failure diminishes as the confinement increases away from the excavation boundary. Therefore, it must be expected that the transition in the failure mechanism, from tensile to shear, occurs as the confinement level increases and conditions for extensional failure are prevented or strongly diminished. However, conventional failure criteria implicitly consider only the shear failure mechanism (i.e., failure envelopes touching Mohr stress circles), and thus, do not explicitly capture the transition of failure modes from tensile to shear associated with confinement change. This paper examines the methodologies for intact rock strength determination as the basic input data for engineering design of deep excavations. It is demonstrated that published laboratory test data can be reinterpreted and better characterized using an s-shaped failure criterion highlighting the transition of failure modes in brittle failing rock. As a consequence of the bi-modal nature of the failure envelope, intact rock strength data are often misinterpreted. If the intact rock strength is estimated by standard procedures from unconfined compression tests (UCS) alone, the confined strength may be underestimated by as much as 50 % (on average). If triaxial data with a limited confinement range (e.g., σ₃ ? 0.5 UCS due to cell pressure limitations) are used, the confined strength may be overestimated. Therefore, the application of standard data fitting procedures, without consideration of confinement-dependent failure mechanisms, may lead to erroneous intact rock strength parameters when applied to brittle rocks, and consequently, by extrapolation, to correspondingly erroneous rock mass strength parameters. It follows that the strength characteristics of massive rock differ significantly in the direct vicinity of excavation from that which is remote with higher confinement. Therefore, it is recommended to adopt a differentiated approach to obtain intact rock strength parameters for engineering problems at lower confinement (near excavation; e.g., excavation stability assessment or support design), and at elevated confinement (typically, when the confinement exceeds about 10 % of the UCS) as might be encountered in wide pillar cores.     

Tensile Strength of Rock Under Elevated Temperatures

Rock strength affects the behaviour of rocks differently under different conditions such as temperature, time, pressure, presence of fluids, rock mass characteristics and stress history of rock in a natural environment. It is not always easy to replicate such conditions of undisturbed rock in a laboratory scale. Hence, it is imperative to study the rock behaviour with respect to every such condition which the rock experiences since its time of formation. Temperature is one of the key parameters which influence the rock throughout its history, ranging from the conditions of formation, experience of depth (loading/unloading) or deformational and metamorphic history. Also, increase in rock temperature; say due to the thermal stress changes like disposal of spent nuclear fuels affects the strength of the surrounding rock. In this work, the effects of temperature on the tensile strength of rock have been studied. The results obtained were interesting as the strength of rock is found to increase considerably up to a particular temperature after which it starts falling by as much as 70% around 250°C.     

不同边界条件下剪切速率对类岩石节理剪切力学特性的影响

为研究不同边界条件下剪切速率对岩石节理剪切力学特性的影响,采用RDS-200型岩石节理剪切试验系统对人工浇筑的具有相同节理形貌的不规则水泥节理试样进行了常法向应力和常法向刚度2种边界条件下5种剪切速率的直剪试验。结果表明：（1）常法向应力边界条件下,随剪切速率增大,相同法向应力下的类岩石节理峰前剪切刚度减速增大,峰值剪切强度和残余剪切强度呈对数降低;随剪切速率增大,类岩石节理黏聚力减速增大,内摩擦角呈对数降低。（2）常法向刚度边界条件下,随剪切速率增大,相同法向应力的类岩石节理峰前剪切刚度减速增大,峰值剪切强度呈对数降低,较高法向应力下的残余剪切强度先增大后减小;随剪切速率增大,类岩石节理黏聚力呈对数降低,内摩擦角减速增大。（3）与常法向应力边界条件相比,常法向刚度条件下,节理黏聚力平均增加了115.85%,内摩擦角平均降低了8.44%;相同初始法向应力和剪切速率下,峰前剪切刚度、峰值剪切强度和残余剪切强度分别平均增加了11.96%、19.47%和32.32%,峰值法向位移平均降低了40.12%。该研究结论可为不同剪切速率下地表和地下工程岩体节理的剪切失稳评价提供一定参考。