Analytical simulation of the dynamic compressive strength of a granite using the sliding crack model

A sliding crack model is employed to simulate rock strength under dynamic compression. It is assumed that the growth and nucleation of a sliding crack array presented results in the shear fault failure and dominate the mechanical properties of rock material. The pseudo‐tractions method is used to calculate the stress intensity factor of the sliding crack array under compression. With the utilization of a dynamic crack growth criterion, the growth of the sliding crack array is studied and the simulated strengths of a granite under dynamic compression are correspondingly obtained. It is concluded that the simulated rock strengths increase with increasing strain rates at different confining pressures, and the rising rates have a trend to decrease with increasing confining pressures. It is also indicated that the simulated rock strengths increase with increment of confining pressure at different strain rates, and the rising rates are almost identical at different strain rates. The simulation results are validated by the experimental data for the granite. Copyright © 2001 John Wiley & Sons, Ltd.     

高温作用后花岗岩三轴压缩试验研究

为综合考察温度、围压对花岗岩力学性质及破坏方式的影响,在高温（25℃～1 000 ℃）作用后,利用MTS815.02电液伺服材料试验系统对花岗岩岩样进行不同围压作用下的三轴压缩试验。研究结果表明,（1）围压一定时,经历不同高温作用后花岗岩三轴压缩全应力-应变曲线经历了压密、弹性、屈服、破坏、塑性流动5个阶段;（2）经历不同高温作用后岩样三轴抗压强度与围压呈非线性二次多项式增长关系,围压为40 MPa时的抗压强度比单轴抗压强度提高了382.30%;常规三轴压缩条件下,400 ℃是花岗岩力学参数的阀值温度;（3）经历高温作用后,岩样弹性模量随围压升高呈增大趋势,围压为40 MPa时的弹性模量比单轴时提高了90.26%;随温度升高呈二次非线性减小,1 000 ℃时的弹性模量比25℃时降低了57.16%;（4）花岗岩的失稳型式同时取决于围压和温度。单轴压缩状态下,随着温度的升高,岩样变形破坏型式由脆性破裂向塑性变形过渡,失稳型式在低温时为突发失稳、中高温为准突发失稳,温度高于800 ℃为渐进破坏;三轴压缩状态下,随着围压的增大,岩样破裂型式由脆性张拉破裂逐渐向剪切破裂过渡,岩样的失稳型式以突发失稳为主。在试验温压范围内,影响花岗岩力学性质的首要因素是温度,其次是围压。     

花岗岩动三轴抗压强度的裂纹模型研究(Ⅱ):应用

根据压缩载荷作用下的滑移型裂纹模型，结合裂纹的动态断裂准则，模拟了花岗岩在应变速度从10^-4-10^0s^-1以及围压力20，50，80MPa时的强度特性。结果表明，模拟结果与实验结果基本一致。还探讨了地从裂纹扩展和聚合特性入手揭示岩石材料强度随应变速率以及围压变化的机理。     

An experimental study on deformation and failure mechanical behavior of granite containing a single fissure under different confining pressures

Fissures in natural rocks play an important role in determining the strength, deformability and failure behavior of rock mass. However in the past, triaxial compression experiments have rarely been conducted for rock materials containing three-dimensional (3-D) fissures and the failure mechanical behavior of fissured rocks is not well known due to the difficulty of conducting triaxial experiments on fissured rocks. Therefore in this research, conventional triaxial compression experiments were performed to study the strength, deformability and failure behavior of granite specimens with one preexisting open fissure. Thirty-one specimens were prepared to perform conventional triaxial compression tests for intact and fissured granite. First, based on the experimental results, the effects of the confining pressure and the fissure angle on the elastic modulus and the peak axial strain of granite specimens are analyzed. Second, the influence of the confining pressure on the crack damage threshold and the peak strength of granite with respect to various fissure angles are evaluated. For the same fissure angle, the crack damage threshold and the peak strength of granite both increase with the confining pressure, which is in good agreement with the linear Mohr–Coulomb criterion. With increasing fissure angle, the cohesion of granite first increases and later decreases, but the internal friction angle is not obviously dependent on the fissure angle. Third, nine crack types are identified to analyze the failure characteristics of granite specimens containing a single fissure under conventional triaxial compression. Finally, a series of X-ray microcomputed tomography (CT) observations were conducted to analyze the internal damage mechanism of granite specimens with respect to various fissure angles. Reconstructed 3-D CT images indicate obvious effects of confining pressure and fissure angle on the crack system of granite specimens. The study helps to elucidate the fundamental nature of rock failure under conventional triaxial compression.     

凌海花岗岩变形特点与脆性评价

以凌海花岗岩为研究对象,进行了一系列常规三轴高压试验,研究了花岗岩的变形特点及脆性演化规律。基于试验结果,分析了不同围压下的全应力-应变曲线,探讨了静态应变采集试验中花岗岩表面变形特点、峰前损伤规律及其与裂隙扩展的关系,总结了动态采集试验中典型的裂纹扩展模式,并基于改进的峰后能量平衡法评价岩石的脆性。研究结果表明：多应变片静态采集三轴试验中岩样不同位置变形规律差异明显,压缩应变较大的区域往往是裂隙产生、扩展的位置;动态应变采集三轴试验中识别了3种典型的裂隙扩展模式,且与应力加载方式存在一定联系;在70 MPa围压范围内,岩样都表现出明显的脆性破坏特征,其脆性指数随围压增加呈现出先减小后增加再减小的变化趋势。该研究成果对进一步开展其他硬岩的变形破坏机制研究和地下工程的稳定性分析具有一定参考价值。     

不同应变率下砂岩动态强度准则的试验研究

分别利用RMT－150C和多功能分离式霍普金森压杆（SHPB）试验系统对砂岩进行了不同应变率下的单轴压缩、三轴压缩和拉伸试验。结果表明,在围压为0或围压一定的情况下,应变率低于102 s-1时,抗压强度的增加与应变率的量级呈正比;在应变率高于102 s-1时,岩石的抗压强度增加趋势与应变率的1/3次方呈正比。拉伸强度也存在类似规律。针对101～102 s-1应变率范围内缺少岩石动态强度准则这一现状,根据上述试验规律,结合Mohr-Coulomb准则、Hoek-Brown准则和Griffith准则的原理,给出了不同应变率范围内动态Mohr-Coulomb准则和动态Hoek-Brown准则的具体表达形式。研究结果表明,在低应变率情况下,动态Mohr-Coulomb准则和动态Hoek-Brown准则均适用,但Griffith准则判别结果误差很大。在高应变率情况下,动态Mohr-Coulomb准则比较适用,Griffith准则仅适用于评估高应变率单轴抗压强度和抗拉强度之间的关系。     

基于试验的花岗岩渐进破坏本构模型研究

对取自大渡河流域大岗山电站的花岗岩进行了系统的试验研究,得到了不同围压下的应力-应变曲线。根据岩样受力过程中内部微裂纹的活动状态,定义了4个特征应力,即闭合应力、起裂应力、破损应力、峰值应力,来反映花岗岩的渐进破坏过程,特征应力也反映了岩石内部的损伤程度。依据特征应力,将试验曲线分为4个阶段,并对每一阶段分别求取变形模量和泊松比。结果表明,变形模量不仅与围压有关,且与岩石的损伤程度有关,而泊松比只取决于岩石的损伤程度。特征应力可由体积应变曲线结合线性回归技术准确求取。在此基础上,提出了一个考虑花岗岩渐进破坏的本构模型。在该模型中,变形参数(弹性模量、泊松比)是应力状态的函数,强度参数（凝聚力、内摩擦角）是塑性变形的函数。将该模型嵌入大型有限元分析软件ABAQUS,对不同围压下的花岗岩室内压缩试验进行模拟,结果表明,模拟所得的应力-应变曲线与试验曲线的吻合程度较高,模型能反映花岗岩等脆性岩石的峰前非线性力学行为。     

基于残余强度修正的岩石损伤软化统计本构模型研究

岩石随着围压的增大,残余强度的增加幅度比峰值强度大,残余强度逐渐成为影响岩石全应力-应变曲线峰后段的主要因素,因此,建立岩石损伤软化统计本构模型时,对残余强度进行修正是非常必要的。基于岩石应变强度理论以及岩石微元强度服从Weibull随机分布的假设,考虑岩石峰后残余强度对损伤变量进行修正,在微元破坏符合Hoek-Brown屈服准则条件下,建立了能够反映岩石峰后软化特征的三维损伤统计本构模型;依据岩石试验全应力-应变曲线的几何特征,推导出本构模型参数的数学表达式,并基于花岗岩室内试验数据对模型参数进行探讨,研究了Weibull分布参数与本构模型的关系,探讨了损伤修正系数的取值和岩石累积损伤的扩展过程;将建立的本构模型理论曲线与4种岩石（斑状二长花岗岩、细晶大理岩、砂岩和粉砂质泥岩）不同围压下的常规三轴压缩试验曲线进行对比分析,结果表明,该模型能很好地描述岩石破裂过程的全应力-应变关系和表征岩石残余强度特征。这对于岩石损伤软化问题以及岩石加固处理措施的研究均具有重要的意义。     

基于岩石统一能量屈服准则的硬岩损伤模型

为了更准确、便捷地确定深埋地下工程中硬岩的力学行为,开展了如下研究：根据损伤与塑性演化存在相似机制,假设损伤阈值与初始屈服采用相同的确定方法,将岩石统一能量屈服准则作为损伤阈值的判定准则;基于Rabotnov对损伤变量的定义和Lemaitre应变等效性假设,并考虑未损伤部分的应力-应变关系符合广义虎克定律,提出了简化形式的硬岩损伤本构方程;为了更好地表达硬岩从低围压到高围压条件下的脆-延转化特性,提出了改进的Mazars损伤演化方程;基于锦屏T2b大理岩常规三轴压缩试验结果,对损伤模型参数进行求解,并分别与基于Mazars损伤演化方程和Mohr-Coulomb准则为损伤阈值判定准则的损伤模型进行对比,结果表明：提出的损伤模型可更好地表达硬岩从低围压的脆性到高围压的延性转变过程,特别是对损伤阈值后岩石的损伤演化过程的模拟更为精确,对硬脆性岩石的工程计算有一定的借鉴意义。     

脆性岩石侧向变形特征及损伤机理研究

进行了三峡花岗岩常规三轴压缩、保持轴向应变和保持轴向应力的卸围压试验,研究了脆性岩石在不同应力路径和不同加载控制方式下的侧向变形特征,可见临界侧向应变均稳定在（?0.004 ? 0.000 5）范围内。进一步进行三峡花岗岩的全过程应力-应变曲线和损伤力学分析,发现脆性岩石在不同应力路径和不同加载控制方式下均以侧向损伤为主,且侧向损伤曲线的形态近似,达到临界破坏状态时损伤值稳定在0.7?0.8左右。最后以侧向损伤变量表征花岗岩脆性破坏过程,建立了基于应变空间的、可以考虑卸荷应力路径的损伤模型和应变型破坏准则。     

Microplane damage model for jointed rock masses

The paper presents a new microplane constitutive model for the inelastic behavior of jointed rock masses that takes into account the mechanical behavior and geometric characteristics of cracks and joints. The basic idea is that the microplane modeling of rock masses under general triaxial loading, including compression, requires the isotropic rock matrix and the joints to be considered as two distinct phases coupled in parallel. A joint continuity factor is defined as a microplane damage variable to represent the stress‐carrying area fraction of the joint phase. Based on the assumption of parallel coupling between the rock joint and the rock matrix, the overall mechanical behavior of the rock is characterized by microplane constitutive laws for the rock matrix and for the rock joints, along with an evolution law for the microplane joint continuity factor. The inelastic response of the rock matrix and the rock joints is controlled on the microplane level by the stress–strain boundaries. Based on the arguments enunciated in developing the new microplane model M7 for concrete, the previously used volumetric–deviatoric splits of the elastic strains and of the tensile boundary are avoided. The boundaries are tensile normal, compressive normal, and shear. The numerical simulations demonstrate satisfactory fits of published triaxial test data on sandstone and on jointed plaster mortar, including quintessential features such as the strain softening and dilatancy under low confining pressure, as well as the brittle–ductile transition under higher confining pressure, and the decrease of jointed rock strength and Young's modulus with an increasing dip angle of the joint. Copyright © 2014 John Wiley & Sons, Ltd.     

海底隧道风化花岗岩流变试验研究

采用全自动三轴流变试验机对厦门东通道海底隧道风化槽地段岩石进行三轴压缩流变试验,研究了岩石在不同围压和不同应力水平作用下轴向应变随时间的变化规律。试验表明,强风化花岗岩时效特性较全风化花岗岩更加明显;围压对岩石蠕变变形存在很大影响,围压越大,蠕变变形量越小。通过分析岩石压缩流变过程中应力-应变关系可知,蠕变变形在弹性阶段不对岩石整体构成明显损伤。而进入塑性阶段后,黏塑性变形对岩石破坏影响较大。建议通过支护增加围压,以提高隧道围岩屈服强度和减小流变变形,防止隧道失稳破坏。     

Numerical simulation on excavation-induced damage of rock under quasi-static unloading and dynamic disturbance

During the excavation of underground opening, the rock may experience a complex loading path that includes the highly confined compression before excavation, unloading of confining stress and further disturbance of dynamic loading after excavation. By using Rock Failure Process Analysis for Dynamics (RFPA-Dynamics), the failure of rock sequentially subjected to this complex loading path is numerically simulated, in order to examine the rock failure mechanism induced by excavation. The RFPA-Dynamics is firstly used to reproduce the failure of rock under confined compression, followed by unloading of confining pressure, and it is validated against with the existing experimental observation. Then, the failure characteristics of rock specimen sequentially subjected to the quasi-static triaxial loading, unloading of confining pressure and dynamic disturbance are numerically simulated, where the effect of magnitude of axial loading and confining pressure, and duration and amplitude of the dynamic disturbance on the final failure patterns of rock are examined. The numerical results indicate that the arc-shaped spalling damage zone is prone to develop with the increase in the axial pressure and lateral pressure coefficient. As for the effect of dynamic disturbance, the contribution of duration and amplitude of dynamic disturbance on the energy input are similar, where the area of damage zone increases with the energy input into the rock specimen. In this regard, the area of the damage zone is influenced by both the magnitude of in situ stress and waveform of dynamic disturbance. This study denotes that it is of great significance to trace the complex loading path induced by excavation in order to capture the rock failure mechanism induced by underground excavation.     

有侧向压力的岩石材料动态直接拉伸试验装置

岩石材料的动态拉伸力学特性是评价爆炸以及地震等动荷载作用下岩体工程响应以及安全的基本参数。介绍了一种有侧向压力的岩石动态直接拉伸试验研究装置,同时采用石膏和花岗岩材料对试验装置进行了尝试性试验。研究结果表明,岩石类脆性材料的抗拉强度随应变速率以及侧向压力的变化规律,与前人进行的岩石间接动态拉伸试验和及岩石类脆性材料（混凝土）双轴试验的变化规律具有一定相似性,因此所介绍的试验装置可以应用于岩石类脆性材料动态直接拉伸试验研究。     

考虑围压影响的岩石峰后应变软化力学模型

试验表明,随着围压增加,岩石峰后残余强度和割线模量增加,如何模拟围压对岩石峰后应变软化力学行为的影响是岩石峰后力学行为研究的关键。利用Z. Fang[1]提出的峰后强度下降指数描述围压对岩石峰后残余强度和割线模量的影响,与摩尔-库仑模型结合,建立了考虑围压影响的岩石峰后应变软化力学模型。在FLAC环境下,利用Fish函数方法开发了相应的数值计算程序。数值算例研究了Tennessee大理岩在不同围压下的应变软化过程,模拟结果与试验数据基本一致,表明建立的模型合理,可以应用于岩石峰后软化过程的模拟。     

Three-dimensional numerical modelling of falling rock protection barriers

This paper presents a new numerical strategy for the design and verification of flexible falling rock barriers: passive protection measures for risk mitigation of potentially unstable rock slopes. The key point of the proposed approach is that notwithstanding the complexity of the simulated phenomenon, the resulting highly non-linear, dynamic model is simple and produces an accurate prediction of all the relevant parameters for barrier design, such as anchorage forces, net panel elongations and residual heights.The modelling procedure has been assessed using detailed experimental data obtained from a set of full-scale tests on three barrier prototypes with various energy absorption capacities (5000 kJ, 3000 kJ and 500 kJ). By comparison with the experimental results, the numerical model has shown to be reliable in capturing very accurately the barrier response to a block impact. Consequently, this method can be extended to investigate the behaviour of flexible falling rock protection barriers under conditions different from those encountered in full-scale tests. Therefore, the numerical procedure can be regarded as an effective tool used for designing and testing these structures.     

不同温度条件下饱水风化花岗岩强度及变形特性分析

为研究温度和围压对风化花岗岩抗压强度、 剪切强度参数及变形特性的影响规律, 以新疆天山某一矿区的风化花岗岩为研究对象, 对不同温度（15、 -5、 -15 ℃）、 不同围压（0、 4、 7、 10 MPa）条件下的饱水风化花岗岩进行单轴和三轴压缩试验。结果表明： 相同温度条件下, 围压在0 ~ 10 MPa变化时, 风化花岗岩三轴抗压强度随围压线性增大。在相同围压下, 抗压强度随温度的降低而明显提高, 风化花岗岩的黏聚力c随温度降低而增大, 内摩擦角φ随温度的降低呈增长趋势。弹性模量随围压的增大不断提高, 但随着温度的降低, 增长幅度逐渐减小。泊松比也随温度降低和围压的增加呈增大趋势。温度和围压对风化花岗岩试样的破坏形态影响机制不同。温度降低使矿物颗粒及内部的微裂纹和间隙收缩, 进而胶结强度增大; 荷载和围压的增大会使岩石内部形成微裂隙并逐渐贯通, 同时孔隙冰破碎裂隙充分接触, 进一步增加摩擦力提高岩石强度。     

Genesis of the Proterozoic Mangabeira tin–indium mineralization,Central Brazil: Evidence from geology,petrology, fluid inclusion and stable isotope data

The Mangabeira deposit is the only known Brazilian tin mineralization with indium. It is hosted in the Paleo- to Mesoproterozoic Mangabeira within-plate granitic massif, which has geochemical characteristics of NYF fertile granites. The granitic massif is hosted in Archean to Paleoproterozoic metasedimentary rocks (Ticunzal formation), Paleoproterozoic peraluminous granites (Aurumina suite) and a granite–gneiss complex. The mineralized area comprises evolved Li-siderophyllite granite, topaz–albite granite, Li–F-rich mica greisens and a quartz–topaz rock, similar to topazite. Two types of greisens are recognized in the mineralized area: zinnwaldite greisen and Li-rich muscovite greisen, formed by metasomatism of topaz–albite granite and Li-siderophyllite granite, respectively. Cassiterite occurs in the quartz–topaz rock and in the greisens. Indium minerals, such as roquesite (CuInS₂), yanomamite (InAsO₄·2H₂O) and dzhalindite (In(OH₃)), and In-rich cassiterite, sphalerite, stannite group minerals and scorodite are more abundant in the quartz–topaz rock, and are also recognized in albitized biotite granite and in Li-rich muscovite greisen. The host rocks and mineralized zones were subsequently overprinted by the Brasiliano orogenic event.Primary widespread two-phase aqueous and rare coeval aqueous-carbonic fluid inclusions are preserved in quartz from the topaz–albite granite, in quartz and topaz from the quartz–topaz rock and in cassiterite from the Li-rich muscovite greisen. Eutectic temperatures are − 25 °C to − 23 °C, allowing modeling of the aqueous fluids in the system H₂O–NaCl(–KCl). Rare three-phase H₂O–NaCl fluid inclusions (45–50 wt.% NaCl equiv.) are restricted to the topaz–albite granite. Salinities and homogenization temperatures of the aqueous and aqueous-carbonic fluid inclusions decrease from the topaz–albite granite (15–20 wt.% NaCl equiv.; 400 °C–450 °C), to the quartz–topaz rock (10–15 wt.% NaCl equiv.; 250 °C–350 °C) and to the greisen (0–5 wt.% NaCl equiv.; 200 °C–250 °C). Secondary fluid inclusions have the same range of salinities as the primary fluid inclusions, and homogenize between 150 and 210 °C.The estimated equilibrium temperatures based on δ¹⁸O of quartz–mica pairs are 610–680 °C for the topaz–albite granite and 285–370 °C for the Li-rich muscovite greisens. These data are coherent with measured fluid inclusion homogenization temperatures. Temperatures estimated using arsenopyrite geothermometry yield crystallization temperatures of 490–530 °C for the quartz–topaz rock and 415–505 °C for the zinnwaldite greisens. The fluids in equilibrium with the topaz–albite granite have calculated δ¹⁸O and δD values of 5.6–7.5‰ and − 67 to − 58‰, respectively. Estimated δ¹⁸O and δD values are mainly 4.8–7.9‰ and − 60 to − 30‰, respectively, for the fluids in equilibrium with the quartz–topaz rock and zinnwaldite greisen; and 3.4–3.9‰ and − 25 to − 17‰, respectively, for the Li-rich muscovite greisen fluid. δ³⁴S data on arsenopyrite from the quartz–topaz rock vary from − 1.74 to − 0.74‰, consistent with a magmatic origin for the sulfur. The integration of fluid inclusion with oxygen isotopic data allows for estimation of the minimum crystallization pressure at ca. 770 bar for the host topaz–albite granite, which is consistent with its evolved signature.Based on petrological, fluid inclusion and isotope data it is proposed that the greisens and related Mangabeira Sn–In mineralization had a similar hydrothermal genesis, which involved exsolution of F-rich, Sn–In-bearing magmatic fluids from the topaz–albite granite, early formation of the quartz–topaz rock and zinnwaldite greisen, progressive cooling and Li-rich muscovite greisen formation due to interaction with meteoric water. The quartz–topaz rock is considered to have formed in the magmatic-hydrothermal transition. The mineralizing saline and CO₂-bearing fluids are interpreted to be of magmatic origin, based on the isotopic data and paragenesis, which has been documented as characteristic of the tin mineralization genetically related to Proterozoic within-plate granitic magmatism in the Goias Tin Province, Central Brazil.     

冻融及加卸荷条件下川藏交通廊道典型岩石力学特性的劣化规律

为了探究川藏交通廊道沿线典型岩石冻融循环条件下的劣化规律,选取昌都-林芝段的花岗岩、片麻岩和砂岩为试验对象,开展冻融循环条件下岩石加卸荷试验,结果表明:（1）随着冻融循环次数的增加,岩石抗压强度损失率达30%,粘聚力降幅达18.4%,内摩擦角降幅达10.5%,弹性模量逐渐下降,泊松比逐渐增加;（2）三轴压缩试验中,岩样的变形模量呈现与抗压强度类似的劣化趋势,但是变形模量的劣化幅度比抗压强度劣化幅度大;冻融循环作用下岩石抗压强度越大劣化程度越低,对砂岩的劣化最明显,片麻岩次之,花岗岩最小;（3）与三轴压缩试验相比,在卸围压试验中,冻融循环作用对岩石的卸荷量同样有劣化作用,卸荷程度较小时岩石劣化并不明显,随着卸荷量的逐渐增加,卸荷量大于80%时,岩石的变形模量呈指数型下降,泊松比呈指数型增加;（4）随着冻融循环次数的增加,三轴压缩试验中由拉张和剪切破坏造成的裂纹数量增多;卸围压试验中岩石以拉张破坏为主;岩石微裂纹数量增加的同时,不平整度增加,矿物颗粒之间的胶结状态变差;（5）综合试验结果分析,冻融作用对岩石劣化作用最强的为砂岩,其次是片麻岩,最弱为花岗岩.      

岩盐弹塑性损伤耦合模型研究

岩盐力学模型是进行能源岩盐储存工程稳定性分析的基础,而损伤和塑性机制并存且相互耦合是岩盐力学行为的基本特点。采用云应岩盐,进行了多组围压条件下的三轴压缩试验,分析了不同围压下岩盐的变形特征。在试验分析的基础上,提出了一种能够描述岩盐特性的弹塑性损伤耦合的模型,该模型描述了岩盐损伤的演化和塑性变形的耦合关系,并引入了一种非关联的塑性流动法则来描述岩盐从塑性体积压缩到膨胀的转化。采用该模型对在三轴压缩下的岩盐应力-应变关系进行了模拟分析,并与试验数据进行了对比,结果表明该模型能够较好地描述岩盐的主要力学和变形特性。