Analyses of Inclined Cracks Neighboring Two Iso-Path Cracks in Rock-Like Specimens Under Compression

Crack propagation process in pre-cracked rock like specimens has been studied experimentally and numerically considering three cracks in the middle part of each specimen. The rock-like specimens are specially prepared from Portland pozzolana cement, fine sands and water. These pre-cracked cylindrical specimens (each containing a single inclined crack in the neighborhood of two iso-path cracks) are experimentally tested under compressive loading. The same problems are numerically simulated by a modified displacement discontinuity method using higher order displacement discontinuity elements and higher order special crack tip elements for crack tip treatment to increase the accuracy of the Mode I and Mode II stress intensity factors obtained based on linear elastic fracture mechanics theory. The crack propagation and coalescence paths of the inclined crack are estimated by implementing a suitable iteration algorithm of incremental crack length extension in a direction predicted by using the maximum tangential stress criterion. The numerical and analytical crack extension analyses are compared which are in good agreement and show the validity, applicability and accuracy of the present work.     

加载速率对大尺寸试样破裂特性的影响规律

结合当前我国矿井高强度快速推采的现状,系统分析了双轴加载速率对大尺寸岩体破裂的影响规律。以山东能源济宁矿区深部岩体所处的复杂环境为背景,确定了与深部岩体力学特性相似的混合砂浆材料的最优配比。采用自主研发的岩石应力-渗流耦合真三轴试验系统和美国生产的PCI-2声发射系统,分析了双轴加载下加载速率对大尺寸试样破裂的影响规律,揭示了加载过程中单裂隙和双裂隙试样的破裂和声发射行为特征。研究表明:当加载速率为1.5 kN/s时,单裂隙试样在剪切作用下易起裂形成反翼裂隙;试样双裂隙的岩桥倾角越大,越有利于试样的加速破坏,产生的声发射事件数较少,表现出岩体破裂的突变性。      

Use of fracture filling mineral assemblages for characterizing water-rock interactions during exhumation of an accretionary complex: An example from the Shimanto Belt,southern Kyushu Japan

Various fracture filling minerals and secondary minerals in fracture walls were formed by fluid-rock interaction during the exhumation of the Palaeogene Shimanto Belt of Kyushu, Japan, which is located in an accretionary complex. Each mineral formed under favourable geological conditions and can be used to estimate the conditions of accretion and formation of the related rock sequences. Petrographic observations, mineralogical and geochemical analyses were made on fracture filling minerals and secondary minerals from boreholes of ca. 140 m depth, drilled in the Shimanto Belt. Results reveal that the secondary minerals were formed in three major stages distinguished by the sequential textural relationships of the minerals and the interpreted environment of mineral formation. Filling mineral assemblages show that the studied rock formation has been subducted to a depth of several km and the temperature reached was ca. 200–300 °C. After the subduction, the rock formation was uplifted and surface acidic water penetrated up to 80 m beneath the present ground surface. The acid water dissolved calcite fracture filling minerals to form the present groundwater flow-paths, which allowed recent wall rock alteration to occur. The results shown here imply that filling mineral assemblages can be an effective tool to evaluate the environmental changes during exhumation of an accretionary complex.     

Size and Geometry Effects on Rock Fracture Toughness: Mode I Fracture

In this paper, the effects of specimen size and geometry on the apparent mode I fracture toughness (K _c) of an Iranian white marble (Neyriz) are studied. A number of fracture tests were conducted on center-cracked circular disk (CCCD) specimens with different radii to investigate the size effects on K _c. The experimental results demonstrate that the apparent fracture toughness increases in bigger specimens. In order to explain the experimental results, the modified maximum tangential stress (MMTS) criterion is used, where higher order terms of the Williams’ series expansion are included in the maximum tangential stress criterion. It is shown that the MMTS criterion provides good estimates for the apparent fracture toughness of Neyriz marble, obtained from fracture tests of edge-cracked triangular specimens. It is, therefore, concluded that the proposed criterion is able to account for the size and geometry effects on the fracture resistance of rocks simultaneously.     

温度冲击下煤的微观结构变化与断裂机制

为研究温度冲击下煤的微观结构变化及其损伤断裂机制,以干燥颗粒煤为研究对象,分别开展了煤样的冷冲击和热冷冲击试验。利用扫描电镜（SEM）观测图像结果,分析对比了两种温度冲击前后煤样微观形貌、裂缝分布、开裂和延伸情况,结合断裂力学理论分析了煤样内部微裂缝的开裂机制和扩展方向,并通过ANSYS有限元软件模拟了微裂缝扩展时的应力场和位移场的分布情况,揭示了煤样的断裂机制。研究结果表明,两种温度冲击对煤的结构均造成了不同程度的破坏,温度冲击所形成的热应力最终导致了原始裂纹和新生裂纹的扩展和延伸;温度冲击下所产生的裂纹形式主要有沿晶裂纹、穿晶裂纹、翼型裂纹、交叉裂纹、枝须状裂纹和网状裂纹;分析结果表明,温差愈大,所产生的温度热应力愈大,热冷冲击所产生的裂缝的数量更多、扩展更充分,对煤样的破坏更严重,因此,热冷冲击的破煤效果更好。     

Microcracks in ultrabasic rocks under uniaxial compressive stress

The initiation and propagation of microcracks under stress are highly dependent upon the mineralogical and textural characteristics of the various lithotypes. Detailed observation and quantification of microcracks before and after uniaxial compression test were conducted. A fresh olivine-rich harzburgite and a serpentinized dunite were analyzed, collected from the Pindos and Vourinos ophiolites (northern Greece) respectively, in order to compare their microcrack patterns. Quantitative analysis indicated that during uniaxial compression the intragranular microcracks, which are the dominating crack-type, are gradually transformed or organized into transgranular cracks. Some of the newly formed transgranular cracks may also be a result of the growth of existing grain-boundary cracks. The new intragranular microcracks in the olivine-rich harzburgite are oriented predominantly parallel to the compressive stress direction, while those in the serpentinized dunite show a scattered orientation presumably due to the mesh texture of this rock-type. The new transgranular cracks of both peridotites tend to be subparallel to the compressive stress direction, however, many of them show a random orientation due to the fact that they have been formed as a result of the propagation of grain-boundary cracks. The occurrence of the soft serpentine along fracture surfaces of olivine, when it is in assemblage with orthopyroxene, tends to absorb the applied stress hampering the development of microcracks in olivine. On the other hand in serpentinized peridotites, the microcracks are enhanced in olivine because it is surrounded by large amounts of the much softer and flexible serpentine. Microcracks are usually formed along the cleavage planes of orthopyroxene porphyroclasts, indicating that such crystallographic preferred orientations act as planes of weakness, controlling the direction of the crack paths. Cr-spinel grains likely comprise locations of initiation of microcracks due to their very hard nature and different mechanical behaviour relative to the surrounding silicate phases. Knowledge of the mineralogical and textural characteristics may assist in the prediction of potential development of failure surfaces of an ultrabasic rock in-service.     

赫兹破裂：一种被忽视的构造

赫兹破裂在工程和材料领域一直备受关注,但其在地质学领域的应用还很少,远未像里德尔破裂那样熟知。从微观尺度到露头尺度,从板块尺度到行星尺度,赫兹破裂在自然界都广泛存在。赫兹破裂作为一种点接触破裂区别于常见的里德尔剪切破裂。它们均是自然界中特殊而又普遍发育的破裂形式,代表了不同的边界和应力条件。典型的赫兹破裂属于弹性变形范畴,由于点接触而在三维空间中形成特征的锥形破裂,在平面上则表现为放射状及环状破裂。在剖面上锥形破裂一般会出现一定角度的拐折,下段破裂与接触面的角度变大,是锥形破裂的典型特征之一。在地质学领域,赫兹破裂有着重要的指示意义,可以表征物质的韧性（toughness）、解释环状和放射状构造、解释锥状以及弧形破裂成因与样式、判断冰川以及断层的运动学特征、区分不同破裂机制形成的新月形构造等,也可以应用于恢复沉积环境以及判断成岩过程中或者构造变形过程中的古应力及其方向。板块碰撞过程中,在特定环境下也可形成赫兹破裂,因此该类型破裂将会有助于我们理解一些断层的成因、发展以及大陆的变形,同时为类地行星（卫星）表层的构造提供解释方案。     

Complex replacement patterns in garnets from Bergen Arcs eclogites: A combined EBSD and analytical TEM study

Eclogite-facies rocks within the Bergen Arcs, western Norway, have formed from granulites along shear zones and fluid pathways. Garnets that were inherited from granulite facies protoliths show different types of replacement patterns due to an incomplete eclogitisation process including concentric rim zoning, zoning along vein fillings and inclusion trails, and zoning bands without inclusions. The interfacial part between the granulitic core and the eclogitic rim of garnet as well as the microstructure of other relevant minerals (omphacite, plagioclase) has been analysed using analytical transmission electron microscopy (ATEM). In garnet, the interface is characterised by gradual changes in composition from X_alm=0.31, X_pyr=0.50 to X_alm=0.54, and X_pyr=0.25 within ≈20 μm and exhibits no distinct change in microstructure. Granulitic plagioclase shows exsolution lamellae of the Bøggild intergrowth. In omphacite, anti-phase domains (APDs) which potentially record the temperature of cation ordering after mineral growth have been observed and their size suggest eclogitisation at 600–700 °C. The electron backscatter diffraction (EBSD) analysis revealed that the lattice orientation of the granulitic feldspar is basically unrelated to tectonic axes whereas newly formed eclogitic minerals omphacite and kyanite show a crystallographic relation to the foliation. In garnet, no change in the basic crystallographic orientation between the eclogitic and granulitic garnet composition was confirmed. However, misorientation analysis suggests a cellular microstructure not more than 1° misorientation in the core of the garnets, which is missing in the eclogitic rim indicating textural equilibration of the latter. The heterogeneous replacement patterns are characteristic for dissolution and re-precipitation reactions in an open system limited to fluid availability. The appearance of the compositional profile in garnet is interpreted as a diffusional re-equilibration step after the time-limited, fluid-mediated eclogitisation event that apparently obscured the initially sharp interface within the further retrograde metamorphic history.     

Effects of Grain Size on the Initiation and Propagation Thresholds of Stress-induced Brittle Fractures

Summary The microstructure of rock is known to influence its strength and deformation characteristics. This paper presents the results of a laboratory investigation into the effects of grain size on the initiation and propagation thresholds of stress-induced brittle fracturing in crystalline rocks with similar mineralogical compositions, but with three different grain sizes. Strain gauge and acoustic emission measurements were used to aid in the identification and characterization of the different stages of crack development in uniaxial compression. Results indicate that grain size had only a minor effect on the stress at which new cracks initiated. Crack initiation thresholds were found to be more dependent on the strength of the constituent minerals. Grain size did have a significant effect, however, in controlling the behaviour of the cracks once they began to propagate. The evidence suggests that longer grain boundaries and larger intergranular cracks, resulting from increased grain size, provide longer paths of weakness for growing cracks to propagate along. This promoted degradation of material strength once the longer cracks began to coalesce and interact. Thus, rock strength was found to decrease with increasing grain size, not by inducing crack initiation at lower stresses, but through a process where longer cracks propagating along longer planes of weakness coalesced at lower stresses.     

循环荷载作用下盐岩微观结构变化及经验疲劳模型

为研究盐岩在循环荷载作用下的疲劳特性和微观结构变化,对盐岩试件展开了不同上限应力下的单轴疲劳试验;同时,利用SEM和NMR设备观测了盐岩试验前后的微观结构。结果表明：循环荷载作用下,盐岩内部裂纹发育以晶间裂纹的生成为主,且裂纹数量随上限应力比（上限应力与单轴抗压强度的比值）增大而增加。循环荷载作用后（12 000次循环）,盐岩内部大孔隙和总孔隙数量增加,小孔隙数量减少,且大孔隙和总孔隙增加的数量及小孔隙减少的数量均随上限应力比增大而增加。上限应力比为0.40且荷载循环次数N≤2 000次时,盐岩内部小孔隙、大孔隙和总孔隙数量均随荷载循环次数增加而增加;但小孔隙数量的增长速率大于大孔隙,此时盐岩孔隙结构变化以小孔隙萌生为主。上限应力比为0.40且荷载循环次数N >2 000次时,盐岩内部大孔隙和总孔隙数量仍随荷载循环次数增加而增加,而小孔隙数量不断减少,此时盐岩孔隙结构变化以大孔隙生成为主。通过求解S形函数反函数的方法,建立了一个形式简单、参数少,且能够描述盐岩累计不可逆变形发展全过程的经验疲劳模型,并利用盐岩疲劳试验结果验证了模型的合理性。     

单轴循环荷载下含天然裂隙脆性页岩变形及破裂特征试验研究

利用RMT–150C岩石力学测试系统,对重庆彭水含天然裂隙脆性页岩在单轴循环荷载作用下的变形及破裂特征进行了试验研究。研究结果表明：（1）在循环加卸载和裂隙的共同影响下页岩所含天然裂隙使页岩性质局部劣化、加剧裂隙扩展和破坏提前,导致屈服应力、破裂压力和峰值强度等减小,其中峰值强度降低了13.7%～58.3%;（2）轴向应变形成封闭的“尖叶”状滞回环,并呈疏-密-疏排列,而横向应变形成上开口“8”字形滞回环,并呈密-疏排列,横向应变-循环次数曲线可分为初始变形阶段、小速率等速变形阶段、大速率等速变形阶段和失稳破坏阶段等四阶段演化规律,前期横向应变突变现象可作为天然裂隙和新裂隙扩展、交汇完成,进入大速率等速变形阶段的标志,后期突变可作为整体失稳破坏的前兆;（3）含天然裂隙页岩的破坏模式主要呈拉剪贯通模式和拉贯通模式,两种贯通模式均至少包含一条贯通天然裂隙的拉裂隙;（4）在弹性阶段,有效弹性模量与损伤面积系数呈线性关系,损伤面积系数越大,有效弹性模量越小;（5）在低应力水平内循环,不可逆变形缓慢增加,轴向应变-循环次数曲线始终处于初始变形阶段,试样不发生破坏;在高应力水平内循环,经历3个变形阶段后试样发生破坏;在接近峰值应力的应力水平内循环,曲线直接进入加速变形阶段,几次循环后试样发生破坏。该研究为认清页岩的裂隙扩展形成复杂裂隙网的发展机制提供了有益参考。     

含充填节理岩体相似材料试件单轴压缩试验及断裂损伤研究

研究了单轴压缩条件下裂隙含充填与否对节理岩体力学性能的影响。以相似材料模拟脆性岩石材料制作含预置裂隙试件,在刚性试验机上对试件进行单轴压缩试验,研究了裂隙充填与否对节理岩体强度峰值及峰后塑性变形能力的影响;用有限元软件ABAQUS对试件进行断裂及损伤分析,研究了裂隙充填与否对节理岩体应力强度因子及损伤因子的影响。研究表明,在单轴压缩情况下,裂隙中含充填与不含充填相比,裂隙含充填岩体峰值强度提高、峰后塑性变形能力增强、总应变能释放率Gc降低,增大了节理岩体抵抗开裂的能力;裂隙含充填岩体环向拉应力场从分布区域及峰值都小于无充填裂隙试件;在同样外荷载作用下,裂隙含充填岩体损伤度小于无充填岩体。     

基于Weibull分布的黄土状土的单轴损伤模型

通过扫描电镜和偏光显微镜对不同方向切面试样的观察,分析了损伤前后黄土状土微观结构的变化。分析结果表明:受力前黄土状土呈粒状架空接触结构,石英、长石、伊利石及高岭石等矿物在试样中分布杂乱无定向性。黄土状土的单轴压缩过程分为3个阶段:第一阶段为压密阶段,此阶段土体中微裂隙闭合,大孔隙变成为微孔隙; 第二阶段为峰值应力前开始损伤阶段,此阶段土体微结构转为镶嵌微孔微胶结结构,颗粒之间产生滑移,原有和新生的小裂隙变宽、变长; 第三阶段峰值应力后损伤快速发展,孔洞、裂隙连通,矿物发生明显定向。在此基础上,利用黄土状土微元强度服从Weibull随机分布的特点,运用统计损伤理论,并考虑到黄土状土的含水率、损伤门槛的影响,建立了考虑损伤门槛的损伤本构方程。以黄土状土的单轴压缩试验结果作为实例,进行了验证。理论计算结果与试验结果对比表明,该模型能够较好地描述黄土状土的变形破坏全应力-应变试验曲线。     

含折线型裂隙砂岩试件翼型裂纹起裂与扩展机制研究

岩体内部赋存的裂隙很多表现为折线型,为探究这类岩体的断裂机制,制备含折线型裂隙砂岩试件并对其进行单轴压缩试验。采用数字图像相关(DIC)方法计算加载过程中的变形场演化,根据新生裂纹两侧的位移差异识别裂纹类型;运用扩展有限元法(XFEM)模拟断裂过程,根据应力分布特征解释翼型裂纹起裂与扩展机制。DIC计算结果表明,新生裂纹处出现应变局部化带,裂纹两侧发生相对分离;含直线型和折线型裂隙砂岩试件的翼型裂纹分别萌生于预制裂隙端部以及折角处,这是因为裂隙几何形态会改变拉应力集中位置;含折线型裂隙砂岩试件的起裂应力小于含直线型裂隙砂岩试件,这是因为相同加载条件下前者的最大拉应力值更大;这2类试件的裂纹扩展均是由于裂纹尖端集中的拉应力引起的,裂纹依然呈张开状态;裂隙几何形态未改变试件的最终破坏模式,均表现为对角剪切破坏。     

岩石剪切细观开裂演化与贯通机制分析

利用自主研发的煤岩剪切细观试验装置,以砂岩为研究对象,开展了不同饱和度数条件下的岩石剪切细观开裂演化与贯通机制试验研究,分析了砂岩剪切细观开裂演化过程和贯通机制,探讨了饱水系数对细观开裂和裂纹形态特征的影响。研究结果表明：剪切过程中,伴随着应力降,裂纹一般首先出现在剪切面中部,几条裂纹间断分布,距离较近的裂纹相互连通形成大裂纹,在应力继续下降的一瞬间,各裂纹连通形成贯通面;水的弱化作用影响了岩石的强度,使得试件底部出现较大的次级裂纹;饱水系数越大,分叉裂纹越多,使得试件的表面裂纹形态更加复杂,断裂面弯折段的数目越多,下端部次级裂纹越发育,整体损伤范围越大;细观上,局部独立裂纹贯通过程伴随着胶结颗粒岩桥的梁式旋转和弯曲折断,水的弱化作用,使得岩桥内部和外部微裂纹增多;随着饱水系数的增加,岩石剪切过程中出现的独立和次级裂纹的数目均呈增加趋势。     

Stress-dependent morphological features on fracture surfaces of quartz and glass

Stress dependent morphological features have been found on tensile fracture surfaces of natural Brazilian quartz and synthetic quartz specimens which were flexed in air at room temperature. These features are similar to stress dependent morphological features found on fracture surfaces of pyrex, soda-lime and lead glass when deformed in similar experiments. For glass, the relevant morphological feature is the fracture “mirror”, a planar region surrounding the initial flaw. Stress dependent index features chosen for measurement in quartz depend upon the crystallographic orientation on the fracture surface. Their development is related to the crack-system energy but, in contrast to glass, the features are not directly related to crack branching. The experimental results follow an equation of the form: where σ_f is the fracture stress, r* is the size of a particular morphological feature (e.g. the “mirror” radius in the case of glass) and A* is a constant.From the magnitudes of A* and the fracture toughness determined in these experiments we conclude that the natural Brazilian quartz used in this study has significantly higher resistance to fracture than synthetic quartz.     

基于3D-ILC含偏心内裂纹半圆弯拉断裂特性研究

断裂力学是各行业的基础学科之一。半圆弯拉(SCB)试验为该领域经典试验,目前含裂纹的SCB研究多为底部切口等表面裂纹或穿透型裂纹研究。内裂纹和内部类裂纹缺陷是材料的固有属性,但是对于SCB内裂纹扩展规律研究较少。基于3D-ILC（三维激光疲劳内裂纹）技术,分析了表面无任何影响的情况下凭空生成任意参数的纯内裂纹,在SCB试样中生成内裂纹,对含内裂纹试样进行SCB试验,分析了裂纹生长过程、应力双折射规律、I-II-III型裂纹扩展面、破坏形态、宏微观断口特征,开展数值模拟,得到裂纹尖端应力强度因子分布规律及扩展路径,与物理试验一致。结果表明：（1）基于3D-ILC的SCB内裂纹及I-II-III型扩展断裂规律明显,3D-ILC为断裂力学中的内裂纹问题研究提供了有力工具;（2）应力云纹在内裂纹处显示应力集中,SCB整体云纹在内裂纹处发生明显变异;（3）SCB试样从预制裂纹处发生压剪型起裂,发生I-II-III型裂纹扩展,分为光滑区和撕裂区,持续生长转变为动态断裂进而破坏,动态断口存在裂纹分叉出现雾化区、羽毛区特征;（4）根据M积分和最大周向应力准则,对试样进行了数值模拟,得到了试样内裂纹尖端应力强度因子分布规律及扩展路径,与试验结果一致。结论与成果对断裂力学领域的SCB试验、内裂纹、I-II-III型断裂问题、裂纹扩展路径模拟问题的研究,具有重要意义。     

大理岩加、卸荷破坏过程的三维颗粒流模拟

从大理岩常规三轴加、卸荷室内试验出发,结合PFC3D颗粒流程序进行分析,在明确室内试验与数值模拟试验卸荷速率对应关系的基础上,对不同卸荷速率下试样破坏过程的力学特性及破坏机制进行探讨。结果表明：加、卸荷路径下整个加载过程中张拉裂纹数量均明显高于剪切裂纹;常规三轴试验损伤应力之后,裂纹围绕某一速率进行扩展,卸荷试验损伤应力之后,裂纹的发展是突发性的;不同应力路径下试样损伤破坏的差异性主要形成于损伤应力至峰值应力这一阶段,直至卸荷速率超过6 MPa/s,试样的损伤程度与破坏形式逐渐趋于一致;随着围压的增大,不同卸荷速率下岩石破坏均呈现出由张拉破坏逐渐向剪切破坏过渡。     

Stress Analysis for Rock Mass Failure with Offset Joints

Two-dimensional finite element model was created in this work to investigate the stress distribution within rock-like samples with offset open non-persistent joints under uniaxial loading. The results of this study have explained the fracture mechanisms observed in tests on rock-like material with open non-persistent offset joints (Mughieda and Alzo’ubi, Geotech Geol Eng J 22:545–562, 2004). Finite element code SAP2000 was used to study the stresses distribution within the specimens. Four-noded isoperimetric plain strain element with two degrees of freedom per node, and the three-noded constant strain triangular element with two degree of freedom per node were used in the present study. The results of the present study showed that the tensile stress in the bridge area caused coalescence for specimens with overlapped preexisting cracks (joints) while the coalescence of the secondary cracks, due to shear stress, caused the failure of specimens with non-overlapping cracks.     

Polygonal grain‐based distinct element modeling for mechanical behavior of brittle rock

The microstructure of rock was numerically reproduced by a polygonal grain‐based model, and its mechanical behavior was examined by performing the uniaxial compression test and Brazilian tests via the Universal Distinct Element Code. The numerical results of the model demonstrated good agreement with the experimental results obtained with rock specimens in terms of the stress–strain behavior, strength characteristics, and brittle fracture phenomenon. An encouraging result is that the grain‐based model‐Universal Distinct Element Code model can reproduce a low ratio of tensile to compressive strength of 1/20 to 1/10 without the need for an additional process. This finding is ascribed to the fact that the geometrical features of polygons can effectively capture the effects of angularity, finite rotation, and interlocking of grains that exist in reality. A numerical methodology to monitor the evolution of micro‐cracks was developed, which enabled us to examine the progressive process of the failure and distinguish the contribution of tensile cracking to the process from that of shear cracking. From the observations of the micro‐cracking process in reference to the stress–strain relation, crack initiation stress, and crack damage stress, it can be concluded that the failure process of the model closely resembles the microscopic observations of rock. We also carried out a parametric study to examine the relationships between the microscopic properties and the macroscopic behavior of the model. Depending on the micro‐properties, the model exhibited a variety of responses to the external load in terms of the strength and deformation characteristics, the evolution of micro‐cracks, and the post‐peak behavior. Copyright © 2016 John Wiley & Sons, Ltd.