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.     

Crack coalescence in specimens with open and closed flaws: A comparison

A comparison is presented between experimental observations made from gypsum specimens loaded in uniaxial compression, with open and closed flaws. Three types of cracks are observed: wing cracks, coplanar and oblique secondary cracks. Wing cracks are tensile cracks that initiate at or near the tip of the flaws, are stable, and propagate towards the direction of maximum compression. Secondary cracks are shear cracks; they are initially stable and may become unstable near coalescence. Coalescence is produced by the linkage of two flaws by a combination of wing and secondary cracks. When coalescence occurs through wing cracks or a combination of wing and secondary cracks, the process is stable. When coalescence occurs through secondary cracks only, the phenomenon is unstable. Eight types of coalescence have been identified, which apply to specimens with open and closed flaws. The types of coalescence are classified based on the types of cracks that produce linkage, and are closely related to the orientation, spacing, and continuity of the flaws. Interestingly, coalescence produced through the linkage of shear cracks only occurs at higher stress than coalescence produced by a combination of shear and wing cracks. The smallest coalescence stress occurs when produced only by wing cracks. The main difference between experimental results from open and closed flaws is that initiation stresses and coalescence are higher for closed than for open flaws. This is explained by the friction along the closed flaws, which needs to be overcome before a crack can initiate, and also by the capability of closed flaws to transmit normal stresses. Thus the differences are not fundamental, and so a unified conceptual framework and a common terminology are proposed for fracturing phenomena in brittle materials with open or with frictional pre-existing discontinuities.     

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。     

岩石三维表面裂纹扩展机理数值模拟研究

岩石破坏的本质原因是由于内部裂隙的萌生、扩展与贯通过程。从三维的角度出发,采用细观损伤数值模拟方法,模拟单轴压缩下含预制三维表面裂纹的岩石试样的破坏过程。数值模拟得到了表面裂隙内部扩展、贯通过程,动态再现翼型裂纹、壳体裂纹的形态,探讨三维裂纹内部的受力机制,推测可能发生的断裂类型,进一步探讨三维裂纹扩展规律。研究结果表明：①反翼型裂纹并不一定萌生于预制裂纹端部,是由于翼型裂纹扩展后应力释放后的拉应力引起;②壳体裂纹的萌生与扩展阶段是由Ⅲ型加载断裂主导,而翼型裂纹扩展至一定长度之后停滞不前;③除了反翼型裂纹之外,还新发现了一种由壳体裂纹萌生出的次生裂纹,这种裂纹的扩展引起试样整体失稳崩溃;④岩石Ⅲ型加载（反平面剪切）难以获得Ⅲ型断裂破坏,壳体裂纹是由于Ⅲ型加载下的拉应力引起,实际上属于Ⅰ型与Ⅱ型复合裂纹;⑤非均匀性对岩石表面裂纹扩展影响很大,相对均匀岩石中难以出现曲线翼型裂纹或反翼裂纹。研究结果对于岩石三维裂隙扩展机理的物理力学实验与理论分析都具有参考意义。     

基于裂纹扩展模式的岩质斜坡阶梯状滑移破裂机制研究

阶梯状滑移破裂作为节理斜坡的一种典型破坏模式,裂隙间裂纹的扩展模式对其变形破裂机制及斜坡破裂面形态具有重要的意义。通过颗粒流程序研究了不同岩桥倾角(0°,45°,90°,135°)和围压条件下双裂隙间裂纹的贯通模式、基本特征与影响因素,揭示含双裂隙岩体在不同围压作用下裂纹扩展的细观力学机制,并推广到含多裂隙岩体裂纹扩展模式中。主要成果如下:(1)双裂隙的贯通主要通过次生共面裂纹、次生倾斜裂纹和翼裂纹;(2)裂纹扩展具有明显的围压效应,低围压条件下,裂隙的贯通主要通过翼裂纹和次生倾斜裂纹,高围压条件下,裂隙的贯通主要通过次生共面裂纹和次生倾斜裂纹;(3)裂隙的贯通应力受岩桥倾角影响较大,岩桥倾角为45°时,裂隙的贯通应力最小,裂隙最容易贯通。结合双裂隙贯通模式的研究,对多裂隙岩体贯通模式进行研究,多裂隙岩体贯通模式可以理解为多组双裂隙的贯通模式的不同组合,同时,在多裂隙贯通模式中,裂纹会寻找贯通应力最小路径扩展。最后,结合一实际斜坡案例,对阶梯状破坏斜坡的基本破裂特征进行了总结分析,并提出了相应的破裂模式分区。     

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.     

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

By using a Rock Failure Process Analysis code, RFPA^2D, numerical simulations on samples of rock-like material containing three flaws under uniaxial compressive loading are conducted to investigate the failure mechanism and crack coalescence modes. The pre-existing flaws are arranged in different systematic geometries. Friction in closed flaws is modelled by inserting ideal elasto-plastic materials into the flaws. As the uniaxial compression load is increased, new cracks propagate from the flaws and eventually coalesce. The simulations replicate most of the phenomena observed in actual experiments, such as initiation and growth of wing and secondary cracks, crack coalescence, and the macro-failure of the sample. For the samples containing three pre-existing flaws, four types of crack coalescence mode are obtained: the tensile mode (T); the compression mode (C); the shear mode (S); and the mixed tension/shear mode (TS). The C mode is mainly formed by coalescence of small tensile fractures in the form of a shear band, and is believed to correspond to the formation and growth of en-echelon cracks. The applied load required to initiate coalescence depends on which mode (tensile or shear) dominates the coalescence process. A higher load is required to cause coalescence in the shear mode (S) than that for coalescence in the tensile mode (T) and mixed mode (TS). A total of four types of samples containing three parallel inclined frictional flaws and nine samples containing two parallel inclined frictional flaws are numerically simulated. It is concluded that crack coalescence will occur following the weakest coalescence path among all possible paths between any two flaws. The results obtained in the simulations are qualitatively in good agreement with experiments presented in Part I of the accompanying paper and other reported experimental observations.     

含交叉多裂隙类岩石材料单轴压缩力学性能研究

 以类岩石材料模拟岩体,考虑了主次多裂隙、等长多裂隙两类交叉多裂隙形式,制作含交叉多裂隙试件,对试件进行单轴压缩实验,研究了含交叉多裂隙岩体在单轴压缩下的力学性能。研究表明：含2条交叉裂隙试件强度高于含单一裂隙试件,当裂隙数量超过2条(不含)时,含主次多裂隙试件峰值强度与含单一裂隙试件接近,含等长多裂隙试件的峰值强度及试件破坏所需外力功都低于含单一裂隙试件;次裂隙数量增加对含主次多裂隙试件强度影响不明显,裂隙数量增加对含等长多裂隙试件的强度降低作用非常明显;绝大部分含交叉多裂隙试件峰值强度对应应变低于含单一裂隙试件;含主次多裂隙试件起裂应力高于含单一裂隙试件,大部分含等长多裂隙试件起裂应力低于含单一裂隙试件;含单一裂隙试件破坏面为剪切裂隙,含交叉多裂隙试件破坏面以张拉裂隙为主。     

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.     

类岩石材料有序多裂纹体单轴压缩破断试验与翼形断裂数值模拟

为研究断续岩石裂纹产状特性对岩体强度的影响和岩桥破断规律,在水泥砂浆中预制有序多裂纹体,开展单轴压缩下类岩石材料有序多裂纹体破断试验。研究发现：有序多裂纹体破断模式主要为排间翼形拉裂纹贯通、排间拉伸—剪切裂纹贯通和排内倾斜剪切裂纹贯通。当裂纹倾角较小（如倾角为25°和45°）时,随裂纹密度的增加,试件表征峰值强度总体上呈衰减趋势,而残余强度总体上呈增加走势;裂纹倾角较大（如倾角为75°和90°）时,裂纹密度对表征峰值强度无显著影响,其残余强度特性表现不明显;相同裂纹密度下倾角从25°变化到90°,试件表征峰值强度总体上呈增加趋势。提出主控岩桥贯通模式的概念,倾角25°试件的主控岩桥贯通模式大都是斜对角线上排间拉伸-剪切裂纹贯通;倾角45°试件的主控岩桥贯通模式为：翼形裂纹贯通和斜对角线方向上共面次生剪切裂纹贯通两种模式。裂纹尖端应力-应变集中特性揭示了压剪裂纹尖端的拉应变集中是岩石翼形裂纹萌生的本质原因,而裂纹端部的双向压应力-应变集中导致次生剪切裂纹萌生。从岩石断裂力学基本理论出发,引入点剪切安全系数,构建基于ANSYS的岩石多裂纹体翼形断裂扩展的数值分析模型,阐明了单轴压缩下有序多裂纹体翼形断裂贯通的力学机制,其数值结论与物理试验基本相吻合。     

类岩石裂纹压剪流变断裂与亚临界扩展实验及破坏机制

进行双轴压缩条件下类岩石裂纹的压剪流变断裂实验,采用双扭试件的常位移松弛法对类岩石材料进行亚临界裂纹扩展与断裂韧度试验。在实验室尺度上证实了类岩石裂纹流变断裂现象的存在,并且得到了翼形裂纹–翼形裂纹贯通、翼形裂纹–原生裂纹贯通和翼形裂纹–翼形裂纹–剪切裂纹贯通的 3 种流变断裂贯通模式。类岩石材料的流变断裂是一种稳定的裂纹扩展,其本质原因是类岩石裂纹的亚临界扩展。以黏弹性断裂力学、流变力学和能量准则为理论依据,推导以应力强度因子、翼形裂纹长度和时间为内变量的相应势函数,建立多种破坏机制的 压剪岩石裂纹的流变断裂 判据和计算模型。 利用 流变断裂 实验对计算模型进行验证,得出裂纹流变 贯通的 理论时间与实验时间较为吻合,当翼形裂纹的扩展方向与最大压应力方向偏离较大时实验结果与理论模型误差较大。提出的计算方法和理论判据为研究岩石裂纹的流变断裂的细观机理及岩体工程流变破坏的宏观机制提供了一个新而实用的研究手段。     

动载下两条断续预制裂隙贯通机制研究

采用预制断续裂隙类砂岩模型试样单轴动载试验，对不同裂隙空间位置（雁行、共面排列）条件下两条裂隙的贯通机制进行了研究。静、动荷载下的对比研究成果显示：不同窄间位置的裂隙贯通方式存在较大差异，且对动载的响应不同：动载下分支裂纹扩展及贯通具有惯性效应，即动载下裂尖翼裂纹及次生兆面裂纹起裂后易朝原起裂方向快速发展，动载下易在两预制裂隙内端部产生直接贯通。这与静载下岩桥处的贯通常通过分支裂纹拐折扩展、相连不同，这也是导致裂隙试样中低应变速率下强度增大（即速率效应）的主要原因。同时，试验结果也揭示：动载下次生共面裂纹扩展长度增加、预制裂隙尖端易产生直接贯通是地震荷载下易发生宏观Ⅱ型剪切断裂的又一原因。     

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.     

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.     

基于应变局部化的双裂纹岩样贯通模式及强度试验研究

含裂隙岩体在外力作用下,内部裂纹会发生扩展,这会显著影响强度以及损伤特性。基于前期验证可靠的DIC系统,对含双裂纹的类岩石材料进行单轴压缩试验,捕获全过程的应变场演化云图以及岩桥区域应变局部化过程,研究发现:岩样呈现出显著的变形局部化渐进破坏特性;试验初期形成的应变局部化带基本确定了加载全程全局应变场的变化范围与变化趋势;基于试验研究,双裂纹岩样的贯通破坏模式可归总为4类:岩桥不贯通模式、裂纹内尖端贯通模式、裂纹内外尖端贯通模式以及裂纹外尖端贯通模式;岩桥角度及其空间排布在细观上影响了应变场局部化带的演化过程,宏观上决定了裂纹的扩展路径及岩样的破坏模式;岩桥贯通时应变局部化带的融合造成了应力–应变曲线的"峰前波动",使得岩样强度降低,并且融合越慢岩样强度越高。     

Systematic evaluation of cracking behavior in specimens containing single flaws under uniaxial compression

This paper presents the results of an experimental study in which molded gypsum and Carrara Marble specimens containing a pre-existing flaw were tested in uniaxial compression. The main purpose of this study was to observe and characterize the cracks that emanate from a single pre-existing flaw. Seven different crack types were identified based on their geometry and propagation mechanism (tensile/shear). Specifically, they include three types of tensile cracks, three types of shear cracks, and one type of mixed tensile–shear crack. In addition to the geometry and mechanism, it was also possible to determine the temporal sequence of different crack types. These observations form the basis for a re-evaluation of cracking processes reported in the literature. It is possible to apply the classification obtained in the present research to previously conducted experiments by others. This eliminates much of the confusion that has existed when comparing different research results.     

Application of the expanded distinct element method for the study of crack growth in rock-like materials under uniaxial compression

The expanded distinct element method (EDEM) was used to investigate the crack growth in rock-like materials under uniaxial compression. The tensile-shear failure criterion and the Griffith failure criterion were implanted into the EDEM to determine the initiation and propagation of pre-existing cracks, respectively. Uniaxial compression experiments were also performed with the artificial rock-like samples to verify the validity of the EDEM. Simulation results indicated that the EDEM model with the tensile-shear failure criterion has strong capabilities for modeling the growth of pre-existing cracks, and model results have strong agreement with the failure and mechanical properties of experimental samples. The EDEM model with the Griffith failure criterion can only simulate the splitting failure of samples due to tensile stresses and is incapable of providing a comprehensive interpretation for the overall failure of rock masses. Research results demonstrated that sample failure primarily resulted from the growth of single cracks (in the form of tensile wing cracks and shear secondary cracks) and the coalescence of two cracks due to the growth of wing cracks in the rock bridge zone. Additionally, the inclination angle of the pre-existing crack clearly influences the final failure pattern of the samples.     

双轴加载下断续预置裂纹贯通机制的研究

通过物理实验和数值模拟,研究双轴作用下不同几何分布和不同围压的断续预置三裂纹的萌生、扩展和贯通机制。结果清楚显示裂纹贯通机制主要受加载条件与预置裂纹几何分布的影响。在双轴加载条件下,裂纹贯通的模式包括拉贯通、剪贯通、压贯通和混合贯通。拉裂纹在双轴加载下, 其扩展速度减慢或停止,且在岩桥间出现剪裂纹,从而形成混合贯通或剪贯通。压裂纹是在侧压下产生的次生裂纹,其贯通受制于两非共线的重叠裂纹间的岩距。当1相似文献   

含预制裂隙大理岩SHPB动态力学破坏特性试验研究

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