Erratum to: Experimental Investigation on Mechanical Behavior of Coarse Marble Under Six Different Loading Paths

A series of triaxial compression experiments were preformed for the coarse marble samples under different loading paths by the rock mechanics servo-controlled testing system. Based on the experimental results of complete stress-strain curves, the influence of loading path on the strength and deformation failure behavior of coarse marble is made a detailed analysis. Three loading paths (Paths I–III) are put forward to confirm the strength parameters (cohesion and internal friction angle) of coarse marble in accordance with linear Mohr-Coulomb criterion. Compared among the strength parameters, two loading paths (i.e. Path II by stepping up the confining pressure and Path III by reducing the confining pressure after peak strength) are suggested to confirm the triaxial strengths of rock under different confining pressures by only one sample, which is very applicable for a kind of rock that has obvious plastic and ductile deformation behavior (e.g. marble, chalk, mudstone, etc.). In order to investigate re-fracture mechanical behavior of rock material, three loading paths (Paths IV–VI) are also put forward for flawed coarse marble. The peak strength and deformation failure mode of flawed coarse marble are found depending on the loading paths (Paths IV–VI). Under lower confining pressures, the peak strength and Young’s modulus of damage sample (compressed until post-peak stress under higher confining pressure) are all lower compared with that of flawed sample; moreover mechanical parameter of damage sample is lower for the larger compressed post-peak plastic deformation of coarse marble. However under higher confining pressures (e.g. σ ₃ = 30 MPa), the axial supporting capacity and elastic modulus of damage coarse marble (compressed until post-peak stress under lower confining pressure) is not related to the loading path, while the deformation modulus and peak strain of damage sample depend on the difference of initial confining pressure and post-peak plastic deformation. The friction among crystal grains determines the strength behavior of flawed coarse marble under various loading paths. In the end, the effect of loading path on failure mode of intact and flawed coarse marble is also investigated. The present research provides increased understanding of the fundamental nature of rock failure under different loading paths.     

Experimental investigation on strength and failure behavior of pre-cracked marble under conventional triaxial compression

Fractures in natural rocks have an important effect on the strength and failure behavior of rock mass, which are often evaluated in rock engineering practice. The theoretical evaluation of mechanical behavior of fractured rock mass has no satisfactory answer due to the role of confining pressure and crack geometry. Therefore, in this paper, conventional triaxial compression experiments were carried out to study the strength and failure behavior of marble samples with two pre-existing closed cracks in non-overlapping geometry. Based on the experimental results of a number of triaxial compression tests, the effect of crack coalescence on the axial supporting capacity and deformation property were investigated with different confining pressures. The results show that intact samples and flawed samples (marble with pre-existing cracks) have different deformation properties after peak stress, which change from brittleness to plasticity and ductility with the increase of confining pressure. The peak strength and failure mode are found depending not only on the geometry of flaw, but also on the confining pressure. The strength of flawed samples shows distinct non-linear behavior, which is in a better agreement with non-linear Hoek–Brown criterion than linear Mohr–Coulomb criterion. For a kind of rock that has been evaluated as a Hoek–Brown material, a new evaluation criterion is put forward by adopting optimal approximation polynomial theory, which can be used to confirm more precisely the strength parameters (cohesion and internal friction angle) of flawed samples. For intact samples, the marble leads to typical shear failure mode with a single fracture surface under different confining pressures, while for flawed samples, under uniaxial compression and a lower confining pressure (σ₃ = 10 MPa), tests for coarse and medium marble (the coarse and medium refer to the grain size) exhibit three basic failure modes, i.e., tensile mode, shear mode, and mixed mode (tensile and shear). Shear mode is associated with lower strength behavior. However, under higher confining pressures (σ₃ = 30 MPa), for coarse marble, the axial supporting capacity is not related to the geometry of flaw. The friction among crystal grains determines the strength behavior of coarse marble. For medium marble, the failure mode and deformation behavior are dependent on the crack coalescence in the sample. The present research provides increased understanding of the fundamental nature of rock failure under conventional triaxial compression.     

含水率和围压对安家岭泥岩峰后力学特性影响的试验研究

为分析含水率和围压对泥岩峰后力学特性的影响,从山西安家岭矿取泥岩,制成不同含水率的5组试样,在YAW2000电液伺服试验机上开展了三轴试验,获得了不同含水率泥岩试样三轴全程应力应变曲线,使用激光共聚焦显微镜观测了泥岩增水过程中微观结构变化。利用试验结果,分析了围压和含水率对泥岩峰值强度、残余强度、弹性模量、破坏应变和脆性模量的影响规律和泥岩增水过程中微观结构的变化规律。引入脆性模量系数和强度退化指数来描述围压对泥岩峰后强度退化过程和残余强度的影响,与FLAC中的SS模型结合,建立了考虑围压影响的泥岩应变软化力学模型,模拟了围压对泥岩应变软化行为的影响。研究结果表明:(1)随着围压增加,泥岩的峰值强度、偏应力峰值、破坏应变和残余强度都增长,峰后强度降低速率趋缓,强度退化指数和脆性模量系数可以较好地描述围压对泥岩残余强度和峰后强度退化过程的影响。(2)泥岩增水过程中,岩样内微裂隙及尺寸增长,泥岩的力学性质劣化。随着含水率增加,泥岩的弹性模量、峰值强度和残余强度降低,破坏应变增长。含水率与泥岩的弹性模量、峰值强度和破坏应变之间近似服从线性关系。(3)本文基于脆性模量系数的岩石应变软化模型能较好地描述三轴压缩泥岩的全程变形行为。     

动力荷载对围压卸载下岩石动态变形模量的影响

利用SHPB岩石动静组合加载实验系统,研究在不同轴压水平下围压以1 MPa/s速率卸载至预加值50%时矽卡岩受频繁冲击作用的动态变形模量变化规律。实验结果表明:高轴压促使岩石内部微裂纹萌发与扩展,降低了岩石抵抗外部冲击的能力。围压的侧向约束阻碍岩石内部裂纹的横向扩展,但在围压卸载时会加剧岩石内部的损伤,这是由于高轴压下,围压卸载导致岩石内部应力重新分布。轴压与围压卸载共同影响着冲击作用下的岩石动态变形模量,通过岩样在冲击荷载下的能量耗散分析岩石动态变形模量的变化规律,有助于了解深部岩体开挖的破坏机制。     

三种红层岩石常规三轴压缩下的强度与变形特性研究

利用MTS815Teststar程控伺服岩石力学试验系统研究了川东地区一红层边坡中的砂岩、粉砂岩和泥岩围压为0³MPa的应力-应变全过程曲线,建立了峰值强度、峰值强度前弹性模量以及峰值强度后的弹性模量和围压的关系。将低围压下红层的全应力-应变曲线概化成5个阶段,分别为压密段、弹性段、屈服段、应变软化段和塑性流动阶段。试验结果得出,红层弹性模量随围压的增加而提高且变化明显,砂岩和粉砂岩在此围压内为脆性破坏,泥岩为塑性破坏的规律。     

高低温加载对大理岩力学特性影响的试验研究

许多工程（如采矿、隧道掘进、地热开采等）都涉及到岩石损伤及破碎问题．传统的岩石损伤破碎技术,如爆破法、水射流法、机械掘进法等均面临着一系列问题,利用岩石的热损伤性质辅助机械破岩有望实现安全、高效破岩的目的．大理岩是一种典型的硬岩,常见许多工程之中,因此本文以大理岩为研究对象,首先将均质性较好的大理岩试样加热至不同温度(20~1000 °C)后放入液氮中进行急速冷处理,然后对其进行了系列的物理力学性质测试．试验结果表明：处理后密度、纵波波速、抗拉强度、单轴抗压强度(UCS)和弹性模量整体上都随温度的上升而下降;当加热温度在100 °C之前,大理岩表现出一定的热硬化现象,即随着温度升高,其UCS、纵波波速以及弹性变形模量均增大;UCS变化的阈值温度为400 °C左右,一旦温度超过400 °C,UCS迅速下降,其速率达到了9 MPa/100 °C,当温度超过500 °C弹性模量迅速下降,其速率达到7.00 GPa/100 °C,表明岩样抵抗变形能力减弱．整体上,热加载降低了大理岩的脆性,使其在单轴作用下的破坏模式由脆性破坏逐渐转化为弹塑性破坏．     

花岗岩破坏过程能量演化机制与能量屈服准则

为了明确岩石破坏的能量演化特性，结合单轴实验和颗粒流程序获得花岗岩的细观力学参数，进行不同应力状态的花岗岩实验，研究不同围压下花岗岩破坏过程的能量演化机理并推导能量屈服准则。获得以下主要结论:花岗岩破坏过程中低围压下内部损伤出现较早而高围压较晚，表明低围压花岗岩内部损伤是渐进发展过程，而高围压下内部损伤一旦出现便快速发展破坏；高围压花岗岩峰值前一定应变范围弹性应变能基本保持不变，吸收的能量全部转化为耗散能，表明高围压破坏时花岗岩内部损伤程度严重；弹性应变能经历不断积累并达到弹性储能极限而后减小的变化过程，而弹性储能极限与围压之间存在线性变化规律，因此高围压下岩体开挖卸荷时极易诱发大量弹性应变能的急剧释放，引起围岩失稳甚至发生岩爆；花岗岩峰值破坏时的能量比与围压无关，为一定值；基于能量原理导出了能量屈服准则，该准则包含岩性参数和所有主应力，能够综合反映岩石破坏影响因素。     

频繁动力扰动对围压卸载中高储能岩体的动力学影响

基于冬瓜山铜矿深部巷道围岩开挖过程中面临的高应力和频繁爆破扰动问题,利用改进的SHPB动静组合加载系统,开展了频繁动力扰动对围压卸载中高储能岩体动力学影响的研究。研究结果表明,围压卸载中的矽卡岩受到动力扰动时,其动态峰值应力和弹性模量随动力扰动次数非线性变化。围压卸载中的高储能矽卡岩受到动力扰动时会释放能量。轴压促使岩样内微裂隙轴向发育,造成岩样抵抗动力扰动能力减弱;围压减缓岩样内微裂隙轴向发育,造成岩样抵抗动力扰动能力增强。动力扰动对微裂隙扩展有促进作用,使围压卸载中的岩样由拉伸破坏向剪切破坏转变。     

砂岩峰后卸除围压过程的渗透性试验研究

为了探讨煤层开采引起的围岩卸除围压过程中砂岩渗透性的变化规律,本文用数控瞬态渗透法在电液伺服岩石力学试验系统MTS815.02上进行了砂岩试样的渗透特性试验。得出了试样峰前渗透系数-应变与应力-应变的关系曲线,以及在峰后保持轴向应变一定卸除围压过程中试样的渗透系数-围压与主应力差-围压的关系曲线;对试验砂岩在变形破坏过程中渗透性变化规律进行了总结,重点分析了其峰后卸除围压过程中渗透性的变化规律;并对试验砂岩峰后渗透系数与有效围压关系进行了拟合,得出了拟合方程式,为煤层开采引起的围岩体应力场与渗流场耦合问题提供参考。     

复杂加载下混凝土的弹塑性本构模型

混凝土材料在不同应力路径下或复杂加载条件下会表现出差异性显著的应力应变关系,在小幅循环加载条件下,其应力应变关系会表现出类似于弹性变形的滞回曲线.在不同应力水平下,混凝土的应力应变关系以及破坏特性都具有静水压力相关特点,即随着静水压力增大,各向异性强度特性弱化.此外,混凝土受压及受拉破坏机理不同,因而对应于混凝土硬化损伤亦有不同,即可分为受压硬化损伤,受拉硬化损伤及两者的混合硬化损伤类型.基于Hsieh模型,对该模型进行了三点改进.（1）针对小幅循环加载下混凝土无塑性变形的试验规律,而模型中在应力水平较低的循环加载条件下始终存在塑性变形的预测问题,采用在边界面模型框架下,设置了应力空间的弹性域,初始屈服面与后续临界状态屈服面几何相似的假定.（2）基于广义非线性强度准则将原模型采用变换应力方法将其推广为三维弹塑性本构模型,采用变换后模型可合理的考虑不同应力路径对于子午面以及偏平面上静水压力效应形成的影响,并避免了边界面应力点奇异问题.（3）分别对拉压两种加载损伤模式建议了相应的硬化参数表达式,可分别用于描述上述加载中产生的应变软化及强度退化行为.基于多种加载路径模拟表明:所建立的三维弹塑性本构模型可合理地用于描述混凝土的一般应力应变关系特性.      

Micro-scale behavior of granular materials during cyclic loading

This study presents the micro-scale behavior of granular materials under biaxial cyclic loading for differ- ent confining pressures using the two-dimensional （2D） discrete element method （DEM）. Initially, 8450 ovals were generated in a rectangular frame without any overlap. Four dense samples having confining pressures of 15, 25, 50, and 100 kPa were prepared from the initially generated sparse sample. Numeri- cal simulations were performed under biaxial cyclic loading using these isotropically compressed dense samples. The numerical results depict stress-strain-dilatancy behavior that was similar to that observed in experimental studies. The relationship between the stress ratio and dilatancy rate is almost indepen- dent of confining pressures during loading but significantly dependent on the confining pressures during unloading. The evolution of the coordination number, effective coordination number and slip coordina- tion number depends on both the confining pressures and cyclic loading. The cyclic loading significantly affects the microtopology of the granular assembly. The contact fabric and the fabric-related anisotropy are reported, as well. A strong correlation between the stress ratio and the fabric related to contact normals is observed during cyclic loading, irrespective of confining pressures.     

Mesoscale modeling of nonlinear elasticity and fracture in ceramic polycrystals under dynamic shear and compression

Dynamic deformation and failure mechanisms in polycrystalline ceramics are investigated through constitutive modeling and numerical simulation. Two ceramics are studied: silicon carbide (SiC, hexagonal crystal structure) and aluminum oxynitride (AlON, cubic crystal structure). Three dimensional finite element simulations incorporate nonlinear anisotropic elasticity for behavior of single crystals within polycrystalline aggregates, cohesive zone models for intergranular fracture, and contact interactions among fractured interfaces. Boundary conditions considered include uniaxial strain compression, uniaxial stress compression, and shear with varying confinement, all at high loading rates. Results for both materials demonstrate shear-induced dilatation and increasing shear strength with increasing confining pressure. Failure statistics for unconfined loading exhibit a smaller Weibull modulus (corresponding to greater scatter in peak failure strength) in AlON than in SiC, likely a result of lower prescribed cohesive fracture strength and greater elastic anisotropy in the former. In both materials, the predicted Weibull modulus tends to decrease with an increasing number of grains contained in the simulated microstructure.     

循环加卸载损伤大理岩的动力学特性

利用MTS 815电液伺服岩石实验系统进行上限应力为80%、85%、90%、95%单轴抗压强度的大理岩单轴压缩循环加卸载实验,每种上限应力条件分别设置20、40、60、80次循环。再利用分离式Hopkinson压杆对损伤岩样进行动力学实验。分析了循环加卸载上限应力及循环次数对大理岩塑性应变的影响,揭示了大理岩动态力学参数和破碎吸收能随损伤变量的演化规律。实验结果表明:塑性应变与循环次数呈正相关,且上限应力越大,塑性应变趋于稳定所需的循环次数也会增大;动态单轴抗压强度、动态弹性模量随损伤变量增加呈指数衰减;破碎吸能占比以损伤变量D=0.343为临界点分为两个阶段,D<0.343时,破碎吸能占比稳定在10%左右,数值约为13 J,当D>0.343时破碎吸能占比随损伤变量增加不断增大。研究结果可为岩体工程的设计、施工及支护参数的选取提供参考。     

考虑围压效应的冻结砂土动态本构模型研究

为描述主动围压作用下冻结砂土的动态力学特性,通过在朱-王-唐模型的非线性体上串联塑性体,建立了能够考虑围压效应的冻结砂土动态损伤本构模型;分析了损伤参数对应力-应变曲线特征、屈服点、峰值应力和峰值应变的影响规律,基于冻结砂土动力学试验数据确定了模型参数;通过将模型和试验数据进行对比,并对不同试验条件下模型的预测误差进行分析,验证了模型的适用性和准确性。结果表明,损伤参数对应力-应变曲线弹性阶段和屈服点无明显影响,而对塑性阶段和破坏阶段的影响较为显著,本构模型预测的应力-应变曲线与试验结果具有较好的一致性。模型能够预测围压引起冻结砂土塑性阶段占比大和屈服点明显的特征,且能够描述围压对冻结砂土动态强度的增强效应;不同负温和主动围压条件下,模型对峰值应力和屈服强度的预测效果优于峰值应变和屈服应变。     

ACOUSTIC EMISSION AND FRACTAL CHARACTERISTICS OF COAL ROCK SAMPLES UNDER TRIAXIAL COMPRESSION

为了研究煤样在不同围压下的声发射及分形特征,利用RMT-150C 型岩石力学伺服试验系统和CDAE-1 型声发射检测仪对煤样试样在不同围压（5MPa,10MPa,15MPa） 进行了实验研究. 对煤样试样的声发射计数和累计计数以及声发射序列的分形特征进行了对比研究. 研究结果表明：不同围压下煤样的声发射特性具有一定的差异性,围压越高前兆信息越明显. 不同围压下煤样都具有分形特征,随着围压的增大,分形特征有所增强. 煤样在失稳破坏过程中声发射序列的分形维值都会出现一个波动-上升-突降的过程,提出可以作为煤样体失稳破坏的前兆信息.     

循环冲击层理煤岩动力学行为及破坏规律研究

为研究复杂地况下含特征层理煤岩的动态力学行为,采用■50 mm分离式霍普金森压杆实验系统,对含层理(0°、30°、45°、60°、90°)煤岩进行动态三轴循环冲击实验研究,并结合3D轮廓扫描仪量化其断裂界面,分析层理效应和围压效应对煤岩动态力学特性及其损伤破坏规律的影响。研究表明：围压的施加使煤岩应力-应变曲线出现弹性后效现象;较无围压状态,抗压强度提高3.9～4.2倍,失效应变增大2.59～3.05倍。随着层理角度的增大,煤岩的动态抗压强度、弹性模量和能量透射率均呈现先降低后升高的U形分布,在层理角为45°时均达到最小值;能量吸收率和断面粗糙度呈现先增大后减小的∩形分布,损伤变量呈现N形分布,在层理角为45°时达到最大值。煤岩的损伤破坏特征随层理角度的变化可概括为张拉破坏（0°）-剪切破坏（30°、45°和60°）-劈裂破坏（90°）的演变过程,所得特征规律可为实际复杂环境下煤层气资源安全高效开采提供理论支持。     

EXPERIMENTAL STUDY OF MECHANICAL PROPERTIES OF WATER-COOLED GRANITE UNDER HIGH TEMPERATURE1)

通过对高温加热-遇水快速冷却后的花岗岩试样进行单轴和三轴实验,研究了800°C内高温花岗岩遇水快速冷却后的力学性质随温度和围压的变化规律。实验结果表明：(1)400°C为高温加热-遇水快速冷却对花岗岩力学性质影响的阈值;(2)同一温度条件下,峰值偏应力、峰值应变随围压的增大而增大;弹性模量随围压的增大先增大后减小;(3)单轴实验中,温度低于400°C时,岩样表现为复合破坏,随着温度的升高破坏形式转变为拉破坏;三轴实验中,岩样整体上表现为剪切破坏。     

Micro-scale behavior of granular materials during cyclic loading

This study presents the micro-scale behavior of granular materials under biaxial cyclic loading for different confining pressures using the two-dimensional (2D) discrete element method (DEM). Initially, 8450 ovals were generated in a rectangular frame without any overlap. Four dense samples having confining pressures of 15, 25, 50, and 100 kPa were prepared from the initially generated sparse sample. Numerical simulations were performed under biaxial cyclic loading using these isotropically compressed dense samples. The numerical results depict stress–strain–dilatancy behavior that was similar to that observed in experimental studies. The relationship between the stress ratio and dilatancy rate is almost independent of confining pressures during loading but significantly dependent on the confining pressures during unloading. The evolution of the coordination number, effective coordination number and slip coordination number depends on both the confining pressures and cyclic loading. The cyclic loading significantly affects the microtopology of the granular assembly. The contact fabric and the fabric-related anisotropy are reported, as well. A strong correlation between the stress ratio and the fabric related to contact normals is observed during cyclic loading, irrespective of confining pressures.     

闪长岩单轴加载过程中声发射和弹性波速度变化规律的研究

为研究闪长岩在单轴加载过程中的声发射和各向波速变化规律,在单轴阶段加载和循环阶段加载条件下,对闪长岩岩样破裂过程中的声发射累计数、不同应力水平不同方向的波速、切线模量、轴向应变速率进行了研究。实验结果表明:(1)随着应力水平的增高,声发射事件数不断增加,在高应力水平(约80%峰值强度)时,声发射累计数急剧增多,随后切线模量出现震荡变化。(2)在加载过程中,压密程度及裂纹扩展方向对波速产生了巨大的影响,导致不同方向波速在不同的应力水平呈现出不同的变化规律,由此可以推测破裂面位置和破裂模式。在较高应力水平下(约60%峰值强度),平行于加载方向的波速趋于稳定,而垂直于加载方向的波速则持续下降,故用垂直于加载方向传播的波速预测岩石的破坏更具可靠性。(3)随着应力的增加,应变速率有逐渐减小的趋势,但临近岩石破裂时无异常变化出现,说明利用变形观测难以预测此类岩石的破坏。以上研究表明,根据纵波波速、声发射累计数和切线模量的变化可以有效预测岩石的破坏。     

考虑裂隙间相互作用情况下围压卸荷过程应力应变关系

岩体的稳定性和变形特性主要决定于裂隙，同时裂隙间的相互作用对岩体的稳定和变形产生显著的影响。裂隙岩体在加载和卸荷条件下的力学特性有显著的区别。为此本文首次利用位错模型法结合叠加原理研究在围压卸荷条件下裂隙间的相互作用对岩体的变形的影响问题。文中推导了考虑裂隙间的相互作用情况下裂隙岩体围压卸荷过程的应力应变关系及应力强度因子表达式，且进行了数值计算。