Analysis of crack coalescence in rock-like materials containing three flaws—Part I: experimental approach

Fractures in the forms of joints and microcracks are commonly found in natural rocks, and their failure mechanism strongly depends on the crack coalescence pattern between pre-existing flaws. However, the crack coalescence pattern of rock specimens containing three or more flaws has not been studied comprehensively. In this paper, we investigate experimentally crack coalescence and peak strength of rock-like materials containing three parallel frictional flaws. Three flaws are arranged such that one pair of flaws lines collinearly and the third flaw forms either a non-overlapping pattern or an overlapping pattern with the first flaw. It is found that the mechanisms of crack coalescence depend on the flaw arrangement and the frictional coefficient μ on the flaw surface. Two “rules of failure” for the specimens containing three flaws are proposed. Rule No. 1: the pair of flaws with a lower value of coalescence stress will dominate the process of coalescence. Rule No. 2: mixed and tensile modes of coalescence are always the dominant modes if the coalescence stress of the two pairs of flaws is very close (say within 5%). In addition, it is found that the peak strength of the specimens does not depend on the initial crack density but on the actual number of pre-existing flaws involved in the coalescence. Comparisons of pattern of crack coalescence with the numerical approach are given in Part II of this study, and the two results agree well. The research reported here provides increased understanding of the fundamental nature of rock failure in uniaxial compression.     

含预制裂隙大理岩SHPB动态力学破坏特性试验研究

为了研究端部裂隙形态对岩石动态力学特性以及裂纹扩展的影响,利用50 mm×50 mm圆柱形大理岩加工含不同裂隙倾角的试样,在50 mm杆径分离式霍普金森压杆(SHPB)试验平台上进行冲击加载试验,并使用高速摄影仪实时记录裂纹扩展以及动态破坏全过程。研究表明,大理岩的动态抗压强度、峰值应变、动态弹性模量等力学参数随预制裂隙倾角增大整体呈先减小后增大的趋势;裂纹大多是从裂隙尖端或附近起裂,起裂裂纹为II型剪切裂纹或I–II型复合裂纹(拉剪复合裂纹),起裂角和起裂应力随着预制裂隙角度的增大分别呈M和W型变化,完整和90°裂隙试样最终呈劈裂拉伸破坏,45°裂隙试样呈拉剪复合型破坏,30°和60°裂隙试样呈剪切破坏,存在一个临界角度,临界角两侧裂纹扩展特性表现出较好的对称性;随着预制裂隙角度的增大,岩石的能量吸收率先增大后减小,当端部裂隙与端面成适当角度,会使能量吸收率最大,可以有效提高破岩效率。     

Fracture coalescence in rock-type materials under uniaxial and biaxial compression

Fracture coalescence, which plays an important role in the behavior of brittle materials, is investigated by loading pre-fractured specimens of gypsum, used as a rock model material, in uniaxial and biaxial compression. Several new phenomena and their dependence on geometry and other conditions are observed. The specimens have two pre-existing fractures or flaws that are arranged in different geometries, and that can be either open or closed. Two different test series are performed with these flaw geometries, one under uniaxial loading and one with biaxial loading in which confining stresses of 2.5, 5.0, 7.5 and 10 MPa are applied. As the vertical (axial) load is increased, new cracks emanate from the flaws and eventually coalesce. Flaw slippage, wing crack initiation, secondary crack initiation, crack coalescence, and failure are observed. Two types of cracks occur: wing cracks, which are tensile cracks, and secondary cracks which initiate as shear cracks in a plane roughly co-planar with the flaw. The secondary cracks usually propagate as shear cracks in the same plane but, depending on the geometry, they also propagate out of plane as either tensile or shear cracks. The wing cracks initiate at the flaw tips for uniaxial or low confinement biaxial conditions but move to the middle of the flaw and disappear completely for higher confining stresses. Three types of coalescence, which depend on the geometry of the flaws and to some extent on stress conditions, occur; they can be distinguished by different combinations of wing cracks and secondary cracks. For closed flaw specimens, at least partial debonding and slippage of the flaws is required prior to initiation of a crack. In uniaxial compression coalescence and failure occur simultaneously, while failure in biaxial compression occurs after coalescence.     

Investigation of creep behaviours of gypsum specimens with flaws under different uniaxial loads

The aim of this study is to identify the influence of the dip angle of a pre-existing macrocrack on the lifetime and ultimate deformation of rock-like material. Prediction of lifetime has been studied for three groups of specimens under axial static compressive load levels. The specimens were investigated from 65% to 85% of UCS(uniaxial compressive strength) at an interval of 10% of UCS for the groups of specimens with a single modelled open flaw with a dip angle to the loading direction of 30°(first group), at an interval of 5% of UCS increment for the groups of specimens with single(second group), and double sequential open flaws with a dip angle to the loading direction of 60°(third group). This study shows that crack propagation in specimens with a single flaw follows the same sequences. At first, wing cracks appear, and then shear crack develops from the existing wing cracks. Shear cracking is responsible for specimen failure in all three groups. A slip is expected in specimens from the third group which connects two individual modelled open flaws. The moment of the slip is noticed as a characteristic rise in the axial deformation at a constant load level. It is also observed that axial deformation versus time follows the same pattern, irrespective of local geometry. Specimens from the first group exhibit higher axial deformation under different load levels in comparison with the specimens from the second and third groups.     

The influence of grain size and porosity on crack initiation stress and critical flaw length in dolomites

The influence of rock texture on crack initiation stress (σ_i) and critical flaw length (L_i) is studied by a series of triaxial tests performed on monomineralic dolomites. The critical flaw length, as predicted by analytical models, is shown to be larger than the measured mean grain size (d_m) by two–three orders of magnitude. This discrepancy is explained by rock texture variations, which influence the fracture propagation mode and consequently fracture initiation stress. The quantification of rock texture is accomplished using porosity. Fracture initiation stress is shown to be inversely related to both porosity and mean grain size. When porosity is low, the sensitivity of σ_i to mean grain size is high. This effect is reduced with higher porosity values. A model for initial flaw length is developed by a synthesis of Griffith initiation criteria with our empirical model for fracture initiation stress. Initial flaw length is found to be directly proportional to the elastic modulus, mean grain size and porosity of the rock. When porosity and mean grain size decrease simultaneously, the initial flaw length rapidly decreases and approaches the mean grain size value. Therefore, the classical assumption that grain size scales initial flaw size is shown to be valid only in the very restricted case of low porosity-low grain size rocks. In such textures, where void space is minimal, available crystal faces function as truly initial flaws, and variations in mean grain size influence crack initiation stress significantly. In more porous textures, however, the initial flaw length is shown to be up to two orders of magnitude higher than the mean grain size in the rock, depending upon the porosity and mean grain size values. In such textures crack initiation stress is much less sensitive to variations in mean grain size, indicating that the role of individual grains is less significant.     

数字图像技术在节理岩体裂纹扩展试验中的应用研究

含倾斜裂纹的岩石在单轴压缩下,会发生翼裂纹扩展并逐步损伤破坏。对含预制裂纹的类岩石脆性试件进行单轴压缩试验,采用两台高分辨率相机连续捕捉图像,经过数字图像相关技术(DIC)处理,得到了试件的全局应变场演化过程图,试验结果表明:当荷载达到一定阶段,裂纹端部观察到了明显的微破裂区,其形状为绕裂纹尖端逆时针转动82°的椭圆;荷载增大到最大荷载的85.6%时,微破裂聚集成核,端部开始形成宏观翼裂纹,裂纹的扩展过程就是高应变区不断蔓延的过程,也是微破裂不断发育、成核的过程;次生微破裂区以及反翼微破裂区发育缓慢,且形成过程中也受到了拉伸应力作用,翼裂纹是试件的主要破坏模式。最后基于线弹性断裂力学,比较了裂纹尖端周围应力和应变的变化规律,给出了采用应变方法分析裂纹起裂扩展的理论依据,并且验证了DIC系统试验结果的可靠性。     

公路隧道衬砌裂纹扩展机理

公路隧道衬砌裂缝作为公路隧道的主要病害,其问题日益突出,尤其是带裂纹工作衬砌的等级评价略显不足。为研究公路隧道带裂缝二次衬砌在受荷载作用下裂纹扩展规律,用离散元PFC软件对衬砌裂纹扩展规律进行数值模拟研究,揭示隧道衬砌中裂纹开裂的灾演机理,根据衬砌开裂状态进行病理灾害分析,并建立了相应的预测模型。衬砌的整体安全性受预置裂纹的影响,预置裂纹处往往是衬砌中较危险的位置;预置裂纹的深度对裂纹贯通时间有较大影响,随着预置裂纹深度的增加,预置裂纹贯通衬砌的时间逐渐减小;预置裂纹的深度对裂纹张开度的变化有较大影响,随着预置裂纹深度的增加,预置裂纹张开度逐渐增大,并在贯通衬砌时有明显的突变,这样便于确定衬砌治理时机。     

单轴加载条件下花岗岩声发射及波传播特性研究

 采用声波、声发射一体化装置,研究单轴压缩下花岗岩波速与声发射演化规律,通过宏细观方法确定各应力门槛值,研究裂纹扩展不同阶段声发射演化及波传播规律。结果表明：细观裂纹的演化与宏观变形直接对应,由于微裂纹主要沿轴向扩展,导致轴向刚度对裂纹起裂及贯通的敏感度弱于非线性增长的侧向变形,瞬时泊松比曲线斜率变化点与应力门槛值对应,声发射测试确定的起裂应力比宏观应变法偏小,但反映了微裂纹的初始萌生;采用实测波速变化分析声发射震源的时空及幅值演化分布,较好地描绘了裂纹的扩展过程,由于不同阶段声发射信号的幅值及能量存在差异,导致声发射特征参数演化规律差异较大(尤其在损伤应力之后),AE能量在破坏前呈突发性增长,可作为灾害性破坏的前兆;加载初始阶段,由于微裂隙的闭合,波速及波幅均随应力逐渐增大,但增加速率逐渐下降,侧向波速在闭合应力附近基本达到峰值,此后一定阶段基本保持不变,但其他方向波速则继续增大,随着波传播方向与径向夹角的增大,波速增加幅度及波速下降点对应的应力(损伤应力前、后)逐渐增大,峰值应力附近对应波速下降幅度减小;波速受损伤演化的影响要滞后于声发射事件。     

Analysis of stress and failure in rock specimens with closed and open flaws on the surface

The influence of closed and open surface flaws on the stress distribution and failure in rock specimens is investigated. Heterogeneous finite element models are developed to simulate the compression tests on flawed rock specimens. The simulated specimens include those with closed flaws and those with open flaws on the surface. Systematic analyses are conducted to investigate the influences of the flaw inclination, friction coefficient and the confining stress on failure behavior. Numerical results show significant differences in the stress, displacement, and failure behavior of the closed and open flaws when they are subjected to pure compression; however, their behaviors under shear and tensile loads are similar. According to the results, when compression is the dominant mode of stress applied to the flaw surface, an open flaw may play a destressing role in the rock and relocate the stress concentration and failure zones. The presented results in this article suggest that failure at the rock surface may be managed in a favorable manner by fabricating open flaws on the rock surface. The insights gained from this research can be helpful in managing failure at the boundaries of rock structures.     

Strain localization analyses of idealized sands in biaxial tests by distinct element method

This paper presents a numerical investigation on the strain localization of an idealized sand in biaxial compression tests using the distinct element method (DEM). In addition to the dilatancy and material frictional angle, the principal stress field, and distributions of void ratio, particle velocity, and the averaged pure rotation rate (APR) in the DEM specimen are examined to illustrate the link between microscopic and macroscopic variables in the case of strain localization. The study shows that strain localization of the granular material in the tests proceeds with localizations of void ratio, strain and APR, and distortions of stress field and force chains. In addition, both thickness and inclination of the shear band change with the increasing of axial strain, with the former valued around 10–14 times of mean grain diameter and the later overall described by the Mohr-Coulomb theory.     

三维裂隙组扩展及贯通过程的试验研究

 采用一种透明性良好、在低温下呈脆性破裂特征的非饱和树脂材料,制作一些含三维裂隙组的试样(原生裂隙采用薄铝片进行模拟),研究单轴压缩条件下平行三维裂隙组的扩展与贯通过程。试验结果表明：试验早期阶段,各裂隙在端部均以包裹式翼裂纹起裂,并独立地扩展。随着各裂纹间相互作用的加强,会引起次生裂纹在预置裂隙端部附近反向扩展的现象,并形成一种新的断裂模式——包裹式反翼裂纹。最终,试样被包裹式翼裂纹与反翼裂纹主导的宏观破裂面所劈裂,并且裂纹在整个断裂过程中能够始终保持一种稳定的扩展。此外,裂隙组的分布方式将影响着三维裂纹的扩展参数,尤其是对裂纹初始扩展角的影响较大,使得包裹式翼裂纹的扩展角约偏转了10°。最后,讨论了三维裂隙组断裂的基本模式与断裂机制。     

Strain localization analyses of idealized sands in biaxial tests by distinct element method

This paper presents a numerical investigation on the strain localization of an idealized sand in biaxial compression tests using the distinct element method (DEM). In addition to the dilatancy and material frictional angle, the principal stress field, and distributions of void ratio, particle velocity, and the averaged pure rotation rate (APR) in the DEM specimen are examined to illustrate the link between microscopic and macroscopic variables in the case of strain localization. The study shows that strain localization of the granular material in the tests proceeds with localizations of void ratio, strain and APR, and distortions of stress field and force chains. In addition, both thickness and inclination of the shear band change with the increasing of axial strain, with the former valued around 10–14 times of mean grain diameter and the later overall described by the Mohr-Coulomb theory.     

渗透水压作用下类岩石材料张开型裂纹启裂特性研究

 在探讨渗透水压和远场应力共同作用下张开型裂纹的启裂规律及裂纹尖端应力强度因子的演化规律的基础上,建立压剪应力场和渗流场共同作用下含预置裂纹类岩石材料的损伤断裂力学模型和裂纹尖端应力强度因子演化方程,提出运用裂纹尖端应力强度因子作为判断压剪岩石裂纹的启裂准则。研究结果表明：张开型裂纹尖端应力强度因子受围压、渗透水压力、裂纹尖端曲率半径以及裂纹倾角等因素的影响;裂纹启裂角随预制裂纹角度的变化不大,其值约为70.5°;裂纹启裂强度与渗透水压力、裂纹长度、裂纹尖端曲率半径成反比,与围压的大小成正比,此外还与裂纹倾角有关。算例验证表明,运用不同的断裂判断准则均可得出岩石裂纹初裂强度随渗透水压力的增大而呈减小的趋势。且进一步的试验也验证了启裂强度与渗透水压成反比而与围压成正比;当裂隙角度为30°时裂纹启裂强度最大,60°次之,45°最小。提高渗透水压可显著降低张开型裂纹的启裂强度,这一结果可为深部高应力岩体诱导破裂提供新的思路。     

A state-of-the-art review of mechanical characteristics and cracking processes of pre-cracked rocks under quasi-static compression

The mechanical characteristics and failure behavior of rocks containing flaws or discontinuities have received wide attention in the field of rock mechanics. When external loads are applied to rock materials, stress-induced cracks would initiate and propagate from the flaws, ultimately leading to the irreversible failure of rocks. To investigate the cracking behavior and the effect of flaw geometries on the mechanical properties of rock materials, a series of samples containing one, two and multiple flaws have been widely investigated in the laboratory. In this paper, the experimental results for pre-cracked rocks under quasi-static compression were systematically reviewed. The progressive failure process of intact rocks is briefly described to reveal the background for experiments on samples with flaws. Then, the nondestructive measurement techniques utilized in experiments, such as acoustic emission (AE), X-ray computed tomography (CT), and digital image correlation (DIC), are summarized. The mechanical characteristics of rocks with different flaw geometries and under different loading conditions, including the geometry of pre-existing flaws, flaw filling condition and confining pressure, are discussed. Furthermore, the cracking process is evaluated from the perspective of crack initiation, coalescence, and failure patterns.     

单轴压缩下基于全局应变场分析的岩石裂纹扩展及其损伤演化特性研究

 采用自主开发的图像分析软件结合数字图像相关技术对含预制单裂纹的类岩石材料在单轴压缩下的变形破坏特性进行试验研究。基于试件全局应变场角度从细观层次量化分析、总结裂纹起裂、扩展的规律及岩石变形损伤演化特征。并采用断裂分析软件FRANC2D/L对相似模型进行数值模拟,分析在加载全程不同阶段的裂纹扩展路径及其应力场分布特征。结合试验与数值研究结果,细致地探讨裂隙岩石的细观力学机制与宏观力学响应之间的内在联系,该研究有助于提升人们对节理岩体工程灾变机制的认识。     

基于单轴压缩的岩体破坏机制细观试验研究

 岩石在荷载作用下产生宏观破坏,其断裂面的细观形态变化,可以间接地反映岩石内部损伤演化进程,并与其宏观力学状态和结构破坏特性之间存在必然联系。主要对巴西劈裂试验和剪切试验试样的断裂面进行电镜扫描,总结典型力学特征下试样断裂面的细观形貌特征,建立裂纹断裂面细观形貌与宏观力学特性匹配的判断标准。进而对含不同倾角预制单裂纹试样单轴压缩试样的破坏全断面进行细观扫描分析,采用判断标准对其细观形貌判别,得到断裂面的拉剪应力分布权重,探究断裂面拉、剪应力分布随裂纹扩展过程的变化规律。试验结果表明：全断面拉剪应力权重与预制裂纹倾角有密切关系。预制裂纹倾角小于45°时,断裂面以拉应力为主,且随着裂纹扩展拉应力权重逐渐减小,剪应力权重逐渐增大;当裂纹倾角大于45°时,其结论与前述结论相反;预制裂纹倾角为45°时,拉、剪应力共同作用产生翼裂纹及次生裂纹2种扩展方式,翼裂纹扩展由拉应力主导向剪切应力主导过渡,次生裂纹扩展过程中主导应力变化规律与之相反。     

裂隙倾角及数目对岩体强度和破坏模式的影响

为研究不同裂隙倾角和数目下低强度岩体强度和变形破坏特征,对含不同预制裂隙的类岩石材料试件进行常规单轴压缩试验。结果表明:(1)低强度岩体峰值强度随裂隙数目增加而减小,随裂隙倾角增大而增大,裂隙倾角0°的三裂隙试件单轴压缩强度最低;(2)除90°裂隙试件外,随裂隙数量增加,试件弹性模量减小,而轴向峰值应变先增大后减小;(3)随裂隙倾角增大,试件弹性模量和轴向峰值应变总体呈“凹型”变化,最小值发生在30°裂隙试件,且大倾角裂隙试件(α>45°)的轴向峰值应变对裂隙倾角敏感程度大于小倾角裂隙试件(α<45°);(4)随裂隙数目增加,低强度岩体的破坏模式变化趋势:脆性破坏→塑性破坏→塑性流动变形破坏。     

单轴压缩下节理间距和倾角对岩体模拟试件强度和变形的影响研究

通过含一组预置张开裂隙石膏试件的单轴压缩试验,系统地研究了当节理连通率固定时,节理组的间距和倾角对试件强度和变形特性的影响。研究发现：①随着节理间距的增大,试件的应力-应变曲线的由单峰型变为多峰型,延性增大。试验中观察到的应力-应变曲线包括4种类型,单峰型、软化段多峰型、多峰平台后软化型和多峰平台后硬化型。②当节理间距不变时,试件的当量化强度、当量化弹性模量和第一峰值应变随节理倾角的变化曲线都呈V型,其最小值发生在节理倾角为45°处;而残余强度与强度之比和第二峰值应变随节理面倾角的变化规律则反之。③当节理倾角不变时,当量化弹模、当量化强度和第一峰值应变都随节理化系数的增大而减小;而残余强度与强度之比和第二峰值应变则反之。④各节理倾角下,试件的当量化弹模和当量化强度随节理化系数的变化规律可以用相同形式的幂函数来表示。⑤上述宏观力学行为与预制节理闭合、次生裂隙发展等细观损伤力学机制密切相关。上述研究表明,节理间距对岩体的强度和变形特性的影响有显著的各向异性。     

Coalescence of multiple flaws in a rock-model material in uniaxial compression

A number of specimens made of gypsum with three and 16 flaws have been prepared and tested in compression. Results from these experiments are compared with observations from similar specimens with two flaws. The comparisons indicate that the cracking pattern observed in specimens with multiple flaws is analogous to the pattern obtained in specimens with two flaws. Two types of cracks initiate from the tips of the flaws: wing cracks and secondary cracks. Wing cracks are tensile cracks that initiate at an angle with the flaw and propagate in a stable manner towards the direction of maximum compression. Secondary cracks are shear cracks that initially propagate along their own plane in a stable manner. Two types of secondary cracks are possible: coplanar or quasi-coplanar, and oblique. As the load is increased, wing cracks propagate in a stable manner and secondary cracks may propagate in an unstable manner and produce coalescence, which occurs when two flaws are linked together. Nine types of coalescence have been observed, and each type is characteristic of a particular flaw geometry. The stresses at which wing and secondary cracks initiate and coalescence occurs strongly depend on the geometry of the flaws and on the number of the flaws; as the flaw inclination angle increases, the spacing increases, or the number of flaws decreases, initiation and coalescence stresses increase.     

单轴压缩下非贯通节理岩体损伤破坏能量演化机制研究

能量的积聚与释放伴随发生在节理岩体受荷变形全过程。为探寻加载过程中节理岩体能量演化规律,基于单轴压缩试验及岩石能量原理,研究非贯通节理岩体变形破坏过程中总能量U、弹性应变能U~e及耗散能U~d的转化特征,揭示节理岩体损伤破坏能量演化机制,建立了基于弹性能耗比变化率(dK/dε)的非贯通节理岩体裂缝扩展及强度失效准则。研究表明:节理存在对岩体中能量的存储具有明显的削弱作用,峰值点总能量与弹性应变能随节理数量的增加逐渐减小;节理岩体的弹性应变能U~e及耗散能U~d变化曲线存在"阶梯状"突减或突增,双节理岩样弹性应变能和耗散能突增或突减的数值明显小于单节理岩样;峰前与峰后阶段弹性能耗比变化率发生连续突变(dK/dε正负交替变换)与突变(dK/dε保持为正无穷)作为节理岩体裂缝扩展及强度失效判据。