围压对巴西裂纹圆盘应力强度因子影响分析

为了研究围压对巴西裂纹圆盘应力强度因子的影响,使用权函数方法得到了围压作用下巴西裂纹圆盘的应力强度因子,进而得到径向集中荷载与围压共同作用下的应力强度因子的计算公式。在此基础上,从理论上分析了围压对巴西裂纹圆盘应力强度因子的影响,分析结果表明：围压对II型应力强度因子无影响,纯围压作用下裂纹趋于闭合;围压和集中力共同作用下,I型应力强度因子随着围压的增大而减小。对比分析了数值分析与理论结果,分析表明,理论与数值结果吻合良好,从而表明了理论分析的正确性。此外,还研究了围压对纯II型裂纹加载条件的影响,结果表明,纯II型裂纹的临界加载角随着围压增大而减小,直至为0。因此,当围压较大时,加载角为0°左右所发生的断裂不一定全是纯I型断裂。     

水压影响岩石渐进破裂过程的试验研究

岩石的压缩过程伴随着裂纹扩展,在低、中围压条件下扩展的裂纹主要受到张拉作用而产生,张拉破坏是首要的作用机制。研究发现,岩石的渐进破裂过程受岩石的结构和构造影响,比如矿物成分、颗粒大小以及胶结情况等,另外,围压以及开挖扰动等外界因素对岩石的渐进破裂过程也有重要影响。基于试验方法探讨水压对岩石渐进破坏过程的影响,首先,阐述岩石渐进破裂过程各个阶段的特征;然后,对岩石渐进破裂指标--岩石的启裂强度 和损伤强度 的确定方法进行总结;最后,选取细粒的石英砂岩为研究对象,通过试验研究水压对岩石渐进破坏过程的影响。试验结果表明,相同围压条件下,随着岩样两端水压的增大,岩石的 有逐渐增大的趋势,而岩石的 和峰值强度 逐渐变小;随着围压逐渐增大,岩石的启裂强度 、损伤强度 及峰值强度 均逐渐增大。     

平台巴西圆盘复合型加载下T应力计算法

平台巴西圆盘(CFBD)具有避免加载点处应力集中、保证破坏由预制裂纹尖端处起始的优点,成为研究脆性材料断裂性能的常用试件之一。最近的研究发现,T应力也会影响材料断裂性能,但平台巴西圆盘并没有计算T应力的解析公式。使用解析分析与有限元数值分析相结合的方法,对复合型加载条件下平台巴西圆盘试件的T应力进行了计算,并对误差进行了系统的分析。结果表明,在一定载荷分布角内相对裂纹长度 时,不管是纯I、纯II还是复合型加载条件下平台巴西圆盘计算的T应力都可以用中心裂纹巴西圆盘均布载荷下T应力计算公式来计算;T应力相对误差随着相对裂纹长度的增加而增加。     

Effect of Specimen Geometry and Testing Method on Mixed Mode I–II Fracture Toughness of a Limestone Rock from Saudi Arabia

Summary The effect of testing method and specimen geometry such as diameter, thickness, and crack length and type on measured fracture toughness was investigated using specimens collected from a limestone rock formation outcropping in the Central Province of Saudi Arabia. Straight Edge Cracked Round Bar Bend (SECRBB), semicircular disk specimens under three point bending, and Brazilian disk specimens under diametrical compression were used in this investigation. SECRBB specimens were used for the Mode-I study, and notched Brazilian disk and semicircular specimens were used for the mixed Mode I–II study. The results show that specimen diameter and crack type have a substantial influence on the measured fracture toughness; however, loading rate, crack size, and specimen thickness seem to have a negligible effect on the fracture toughness. Mode-I fracture toughness is significantly influenced by specimen diameter and crack type, while their effects on Mode-II fracture toughness are generally negligible. The different specimens (SECRBB, Brazilian disk, and semicircular) can give comparable results only when the proper span to diameter ratio is used. The Brazilian disk with a straight notch was found to be the most convenient geometry to use for fracture toughness determination. A simple method of making a precise notch inside the disk is presented, using the combination of a drilling machine and a wire saw.     

Mixed mode crack propagation in low brittle rock-like materials

Mixed mode fracture is quite common in rock structures. Numerous investigators have used the Brazilian disk specimens with a central crack for investigating modes I, II, and mixed fracture toughness in brittle materials. In this study, analytical, experimental, and numerical investigations were planned and performed on Central Straight Through Crack Brazilian Disk (CSCBD) specimens. Ranking of geometrical parameters effective on the value of stress intensity factors (SIFs) of CSCBD specimens were obtained using stochastic analysis. Furthermore, experimental tests were undertaken in order to evaluate the crack propagation in rock-like material of low brittleness. Finally, numerical modeling was performed to assess the effect of crack length on the failure mode of CSCBD specimens. Analytical analyses revealed that the inclination angle of the crack with respect to the diametrical load has the most important impact on the SIFs among the geometrical parameters of CSCBD specimen. Performed experimental and numerical analyses also confirmed the effect of inclination angle and crack length and their impact on the mode of failure of the tested specimen.     

修正应变能密度因子准则及岩石裂纹扩展研究

由应变能密度因子理论得出裂纹沿着形状改变比能密度因子最小的方向扩展,但理论中所使用的应力强度因子是在拉应力作用下计算得出的,而自然界中的岩体通常处于压应力场中。因此,在修正的应变能密度因子理论的基础上,结合压缩荷载作用下的裂纹尖端应力强度因子,并考虑裂纹面之间的摩擦作用得出了针对压缩荷载作用下的岩石裂纹扩展的应变能密度因子理论,并运用该理论分析了裂纹倾角、围压以及裂面摩擦力对破裂角的影响,将分析结果与已有的试验和数值分析结果进行比较,取得了良好的一致性。分析得出,在单轴压缩荷载作用下临界破裂荷载随着裂纹倾角的增大而先减小、后增大,并且一个裂纹倾角对应多个破裂角,即裂纹朝多个方向发展;在三轴压缩荷载作用下,破裂角与围压大小有关。此研究成果可为压应力场中岩石裂纹扩展的数值模拟提供参考。     

一种测量岩石压缩裂纹扩展过程声波波速的连续测量方法

中低围压或单轴压缩荷载条件下,可以将脆性岩石材料的裂纹扩展过程划分为原生裂纹压密、新生裂纹起裂并稳定扩展、不稳定裂纹扩展和交互贯通以及峰后5个主要发展阶段。含预制裂纹试样的直接观测法、应变监测、声发射（AE）监测、声波波速测试、CT（computerized tomography）扫描、微电镜观察等间接监测方法被用来研究裂纹起裂和扩展过程。本文基于在中、低围压以及单轴压缩荷载条件下,脆性岩石材料首先产生张拉裂纹,并优先沿加载方向发育的规律,提出采用声波波速连续测量方法进行岩石加载过程波速的连续观测,有助于分析裂纹扩展过程中声波波速的变化,为研究裂纹扩展过程提供一种间接测量手段。     

The Brazilian Disc Test for Rock Mechanics Applications: Review and New Insights

The development of the Brazilian disc test for determining indirect tensile strength and its applications in rock mechanics are reviewed herein. Based on the history of research on the Brazilian test by analytical, experimental, and numerical approaches, three research stages can be identified. Most of the early studies focused on the tensile stress distribution in Brazilian disc specimens, while ignoring the tensile strain distribution. The observation of different crack initiation positions in the Brazilian disc has drawn a lot of research interest from the rock mechanics community. A simple extension strain criterion was put forward by Stacey (Int J Rock Mech Min Sci Geomech Abstr 18(6):469–474, 1981) to account for extension crack initiation and propagation in rocks, although this is not widely used. In the present study, a linear elastic numerical model is constructed to study crack initiation in a 50-mm-diameter Brazilian disc using FLAC^3D. The maximum tensile stress and the maximum tensile strain are both found to occur about 5 mm away from the two loading points along the compressed diameter of the disc, instead of at the center of the disc surface. Therefore, the crack initiation point of the Brazilian test for rocks may be located near the loading point when the tensile strain meets the maximum extension strain criterion, but at the surface center when the tensile stress meets the maximum tensile strength criterion.     

A relationship between tensile strength and loading stress governing the onset of mode I crack propagation obtained via numerical investigations using a bonded particle model

Numerical models based on the discrete element method are used to study the fracturing process in brittle rock‐like materials under direct and indirect tension. The results demonstrate the capacity of the model to capture the essential characteristics of fracture including the onset of crack propagation, stable and unstable crack growth, arrest and reinitiation of fracturing, and crack branching. Simulations of Brazilian indirect tension tests serve to calibrate the numerical model, relating macroscopic tensile strength of specimens to their micromechanical breakage parameters. A second suite of simulations reveals a linear relationship between the tensile strength of specimens and the loading stress for which mode I tensile crack propagation ensues. Based on these results, a crack initiation criterion for brittle materials is proposed, prescribing the stressing conditions required to induce tensile failure. Such a criterion, if broadly applicable, provides a practical means to rapidly assess the failure potential of brittle materials under tensile loads.     

复合型加载条件下锈岩断裂韧度试验研究

岩石断裂韧度表征其抵抗裂纹起裂和扩展的能力,作为其力学性能的一个重要指标,在岩石力学理论研究与岩体工程应用中有着不可替代的作用。由于岩石结构的复杂性,其破坏形式大多呈现为复合型断裂破坏,研究复合型加载条件下岩石断裂韧度具有重要的意义。为了研究锈岩的断裂力学性能,以便其在建筑工业中得到更为广泛的应用,通过18个中心裂纹圆盘（CSTBD）试件径向受压试验,进行了复合型加载条件下锈岩断裂韧度的试验研究。测得了锈岩在纯I型,纯II型以及复合型加载时的断裂韧度,并将试验结果与基于广义最大周向应力（GMTS）准则的理论值进行了对比分析,结果表明：锈岩的纯I型断裂韧度为1.01 MPa?m0.5,而纯II型断裂韧度为1.51 MPa?m0.5,是纯I型断裂韧度的1.49倍,这与基于GMTS准则的理论值1.34非常接近,而比基于最大周向应力（MTS）准则的理论值0.87大很多。裂纹尖端附近的T应力及断裂过程区裂纹尖端的临界距离rc对岩石类材料的开裂路径以及复合型断裂韧度都有较大的影响。考虑了T应力的广义最大周向应力（GMTS）准则能很好的预测试验结果。     

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.     

Influence of crack surface friction on crack initiation and propagation: A numerical investigation based on extended finite element method

Rock strengths are directly influenced by the open or closed flaws widely distributed in rock masses. Extensive studies have been conducted on the propagations of open flaws in rocks. However, few concerns are paid on the propagation of closed flaws, the influence of the surface friction on the initiation and propagation of closed flaws should be investigated systematically. In present article, the crack initiation and propagation in rock like material subjected to compressive loads have been investigated. The effects of crack surface friction on crack initiation and propagation have been quantified with the help from extended finite element method which is efficient and accurate. Based on the analysis on stress distribution and propagation patterns, following results are obtained: Firstly, minor effects are exerted by crack surface friction on the stress distribution around the flaws when the flaws inclination angle is 30° and 45°. However, as the inclination angle increases to 60°, the effects are much more significant. Secondly, as the inclination angle ranges from 30° to 60°, the most favorable angle for crack propagation is 45°. Thirdly, the initiation location and angle of the wing cracks will not be influenced by the frictions. However, the propagation length will be greatly influenced by the friction and the inclination angle.     

Three-dimensional numerical study on the failure characteristics of intermittent fissures under compressive-shear loads

A 3-D conjugated bond-pair-based peridynamic model is developed to comprehensively investigate failure characteristics of rock-like materials with intermittent fissures in the compressive-shear loading tests. Rock-like specimens containing one single central fissure are first simulated. Numerical results indicate that the 3-D conjugated bond-pair-based peridynamic model can faithfully reproduce failure characteristics of rock-like materials under compressive-shear loads. Then, the failure characteristics of rock-like specimens containing two parallel central intermittent fissures are numerically investigated. Effects of fissure inclination angle, fissure ligament length and rock bridge angle on fracturing behaviors, such as crack coalescence patterns, are also studied as well as crack initiation stress and coalescence stress.

     

模拟岩石中裂纹扩展连接的近场动力学方法

脆性岩石材料在压应力作用下常出现两类裂纹：翼型张拉裂纹和次生剪切裂纹。近场动力学是一种新型的无网格数值计算方法。在近场动力学理论中,采用积分形式的控制方程代替微分形式的控制方程使得该数值算法在断裂问题上具有独特的优势。将Mohr-Coulomb准则和最大主应力准则引入非普通“态”基近场动力学理论中,分别用于模拟材料常见的压剪和张拉破坏。这种扩展的非普通“态”基近场动力学可以有效地模拟脆性岩石材料在多种受力状态下的裂纹起裂、扩展和连接问题。通过5个不同的数值算例说明该数值算法在处理脆性岩石材料断裂问题的有效性和准确性。首先,通过模拟含圆孔的弹性板拉伸数值试验说明该数值算法的有效性和准确性。其次,数值模拟了简单三点弯曲试验以及不使用其他外部准则条件下动荷载作用下裂纹的分叉试验,所得结果与其他试验结果或数值结果相吻合,从而验证了该理论的有效性。然后,模拟了包含斜裂纹的巴西圆盘试验,裂纹扩展路径和计算所得的断裂韧度同样吻合于试验结果。最后,模拟了单轴压缩状态下,预制裂纹试样的裂纹扩展和连接问题。将该数值算法与试验结果对比表明,所提出的数值方法可以模拟和预测岩石类材料的张拉和压剪裂纹的起裂、扩展和连接行为。     

Mapping the state of fracture around cavities

The state of stress around cavities is heterogeneous. Consequently, the state of fracture may also vary from point to point. Under compressive loading, cavity may be in one of four possible states: pre-fracture (pre-microfracture initiation), microfracture propagation (initiation to the onset of dilata dilatancy to failure) and post-failure. These four states are separated by the crack initiation stress, the crack damage stress and the failure stress. fracture events with confining pressure is examined with reference to three intact rocks: a brittle granite, a semi-brittle limestone and a ductile sal

The maximum principal stress (σ₁) at crack initiation, crack damage (onset of dilatancy), yielding and failure are established as a function stress (σ₃). For a single intact rock, all four fracture events can be represented using one function (the Rocker function) with a single fac various fracture states.

The proposed fracture criteria, based on the experimental data, are combined with the existing state of stress to prepare a fracture map around an elli intact Lac du Bonnet granite. The state of stability is expressed through a newly defined stability factor, the unconfined strength ratio (USR), wh to the traditional safety factor. In contrast to the conventional safety factor in rock mechanics (SFstrength/σ₁), which is σ₃ 3–σ₁, space of the stability diagram.     

炭质页岩巴西劈裂载荷下破坏过程的时空特征研究

页岩在加载过程中的破裂时机及其空间位置研究对于页岩气探测及储层评价具有重要意义,为此开展了不同层理倾角条件下页岩的巴西圆盘劈裂载荷下的破坏过程试验,采用数字图像相关技术（DIC）,全程跟踪页岩裂纹萌生、扩展和贯通全过程的变形场实时演化特征,同时记录力-位移曲线,利用扫描电镜获得炭质页岩的破裂面特征及微观结构,采用宏、细观相结合的手段,研究不同层理方向炭质页岩微裂缝起裂时间、空间位置和扩展规律及其破裂机制。结果表明：页岩的巴西劈裂强度随层理方向与加载方向角度的增大而逐渐增大;随加载方向与层理面夹角的增加,裂缝萌生的时间逐渐增加,而裂缝从萌生、扩展到贯通所用时间逐渐减少。所有角度试件基本从试件端部萌生裂缝并沿层理面扩展,除90°试件外,不同层理倾角试样主裂缝破裂的位置逐渐偏离中心位置而向试件外侧发展。各角度试件主破坏类型存在一定差异性,除90°试件竖向主裂缝为张拉破坏外,随加载方向与层理面夹角的增加,各加载角度试件的主破裂模式从张拉剪切破坏逐渐过渡为剪切滑移破坏。     

节理岩石卸载损伤破坏过程CT实时检测

在国内外首次利用CT专用岩石三轴试验加载设备,完成了单一裂纹岩石卸围压应力作用下损伤破坏全过程CT实时监测试验,得到了非常清晰的节理岩石卸围压破坏全过程中从裂纹发展、贯通到破坏等各个阶段的CT图像。结果表明,节理岩石的卸载破坏具有突发性。     

Influence of inclination angles and confining pressures on mechanical behavior of rock materials containing a preexisting crack

To deeply understand the cracking mechanical behavior of brittle rock materials, numerical simulations of a rock specimen containing a single preexisting crack were carried out by the expanded distinct element method (EDEM). Based on the analysis of crack tips and a comparison between stress- and strain-based methods, the strain strength criterion was adopted in the numerical models to simulate the crack initiation and propagation processes under uniaxial and biaxial compression. The simulation results indicated that the crack inclination angle and confining pressure had a great influence on the tensile and shear properties, peak strength, and failure behaviors, which also showed a good agreement with the experimental results. If the specimen was under uniaxial compression, it was found that the initiation stress and peak strength first decreased and then increased with an increasing inclination angle α. Regardless of the size of α, tensile cracks initiated prior to shear cracks. If α was small (such as α ≤ 30°), the tensile cracks dominated the specimen failure, the wing cracks propagated towards the direction of uniaxial compression, and the propagation of shear cracks was inhibited by the high concentration of tensile stress. In contrast, if α was large (such as α ≥ 45°), mixed cracks dominated the specimen failure, and the external loading favored the further propagation of shear cracks. Analyzing the numerical results of the specimen with a 45° inclination angle under biaxial compression, it was revealed that lateral confinement had a significant influence on the initiation sequence and the mechanical properties of new cracks.     

A three-dimensional numerical investigation of the fracture of rock specimens containing a pre-existing surface flaw

Three-dimensional surface crack initiation and propagation in two kinds of heterogeneous rocks were numerically investigated via parallel finite element analysis using a supercomputer. Numerically simulated rock specimens containing a pre-existing flaw were subjected to uniaxial compression until failure. The initiation and propagation of wing cracks, anti-wing cracks, and shell-like cracks were reproduced by numerical simulations. The numerically simulated results demonstrate that the further propagation of wing cracks and shell-like cracks stop due to their wrapping (curving) behavior in three-dimensional spaces, even if the applied loads continue to increase. Furthermore, rock heterogeneity could significantly influence crack propagation patterns and the peak uniaxial compressive strengths of rock specimens. Moreover, anti-wing cracks only appeared in relatively heterogeneous rocks, and the peak uniaxial compressive strengths of the specimens were observed to depend on the inclination of the pre-existing flaw. Finally, the mechanism of surface crack propagation is discussed in the context of numerically simulated anti-plane loading tests, wherein it was identified that Mode III loading (anti-plane loading) does not lead to Mode III fracture in rocks due to their high ratio of uniaxial compressive strength to tensile strength. This finding could explain the lateral growth of an existing flaw in its own plane, which is a phenomenon that has not been observed in laboratory experiments.     

Mechanical Behaviour of Reservoir Rock Under Brine Saturation

Acoustic emissions (AE) and stress–strain curve analysis are well accepted ways of analysing crack propagation and monitoring the various failure stages (such as crack closure, crack initiation level during rock failure under compression) of rocks and rock-like materials. This paper presents details and results of experimental investigations conducted for characterizing the brittle failure processes induced in a rock due to monocyclic uniaxial compression on loading of two types of sandstone core samples saturated in NaCl brines of varying concentration (0, 2, 5, 10 and 15 % NaCl by weight). The two types of sandstone samples were saturated under vacuum for more than 45 days with the respective pore fluid to allow them to interact with the rocks. It was observed that the uniaxial compressive strength and stress–strain behaviour of the rock specimens changed with increasing NaCl concentration in the saturating fluid. The acoustic emission patterns also varied considerably for increasing ionic strength of the saturating brines. These observations can be attributed to the deposition of NaCl crystals in the rock’s pore spaces as well some minor geo-chemical interactions between the rock minerals and the brine. The AE pattern variations could also be partly related to the higher conductivity of the ionic strength of the high-NaCl concentration brine as it is able to transfer more acoustic energy from the cracks to the AE sensors.