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.     

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.     

岩石非理想裂纹圆盘试件动态断裂韧性测试的有限元分析及试验研究

采用中心裂纹圆盘-霍普金森压杆(CCCD-SHPB)试验系统对大理岩中心裂纹圆盘试件进行不同加载速率下的纯Ⅰ型加载试验,研究岩石材料动态断裂韧性的加载速率相关性。考虑到试验中所使用的圆盘试件是带有中心切口的非理想裂纹,结合试件的实际加工情况,提出采用切口尖端形状为小圆弧形的预制裂纹,介绍了试件的制作方法,并利用有限元计算论证了采用这种形状非理想裂纹试件的试验可行性。结果表明,采用圆弧形裂尖、裂纹宽度为1 mm的中心切口非理想裂纹圆盘试件来代替理想裂纹圆盘试件是可行的,误差不超过2.13%。分析试验数据得出：非理想裂纹圆盘试件在纯Ⅰ型加载条件下,其断裂韧度表现出明显的速率相关性,且随着加载速率的增大而增大。     

DEM investigation on fracture mechanism of the CCNSCB specimen under intermediate dynamic loading

The cracked chevron notched semi-circular bending (CCNSCB) method falls into a significant testing category of chevron notched specimens for measuring the mode I fracture toughness, of which the progressive fracture mechanism deserves to be further assessed under intermediate dynamic loading rate (IDLR). In this study, the discrete element method (DEM) is adopted to depict the three-dimensional fracture processes of the CCNSCB specimens subjected to different IDLRs considering different supporting spans. The results demonstrate that the crack front of the CCNSCB specimen with any loading condition is prominently curved, which violates the straight-through crack propagation assumption and may induce some errors in the fracture toughness measurements. For each IDLR, the peak force of the CCNSCB specimen evidently increases with decreased supporting span, and the effect of loading rate on this parameter is more prominent for a smaller supporting span. For a relatively large span, the crack grows restrictively in the notched ligament, which conforms to the ideal assumption of the fracture process and contributes to an accurate measurement of the mode I fracture toughness. Thus, a large supporting span is suggested for the semi-circular bend tests. Additionally, the critical crack length and peak force are found dependent on the loading rate, and they are larger for the higher loading rate. Thus, the critical crack length determined under quasi-static conditions is not strictly suitable for the specimens under different IDLRs, especially for the much higher IDLR. This study calls for more attention on how to accurately determine the fracture toughness via chevron notched samples.     

地震作用下裂隙对岩质边坡稳定性影响分析

在地震作用下岩质边坡内部裂隙可能开裂扩展,对边坡稳定造成不利影响。利用扩展有限元法模拟岩质边坡内部裂隙在地震作用下的开裂扩展,根据扩展后的裂隙分析边坡潜在滑面,采用矢量和法计算边坡在震前、地震过程及震后的安全系数。结果表明：在汶川地震波作用下LLT1与LLT2裂隙均开裂扩展,开裂方向与水平方向夹角近45°,其中LLT1裂隙顶部开裂至边坡面。震前安全系数为1.75,地震过程中最小安全系数为1.01,震后安全系数为1.05。说明了即便是边坡在震前稳定性较好,但由于地震作用使得裂隙扩展贯通至边坡表面,导致滑体抗滑力降低,边坡震后稳定性显著降低。虽然地震过程中边坡并未失稳破坏,若在震后受到其他外部作用则可能失稳破坏,引发次生灾害。     

板裂化模型试样失稳破坏及其裂隙扩展特征的试验研究

锦屏二级水电站深埋隧洞大量岩爆案例表明板裂化围岩的失稳破坏与岩爆之间具有很强的相关性。采用高强石膏配制满足板裂化围岩结构特征的硬脆性模型试样,通过一侧约束条件下的单轴压缩试验研究板裂化模型试样的失稳破坏过程、强度与变形特性及其裂纹扩展特征。研究表明,（1）板裂化模型试样失稳破坏过程表现出应变型岩爆的特征,其典型的破坏过程为预制裂隙尖端张拉裂纹的萌生与扩展-试样劈裂成板-岩板屈曲变形-岩板压折、岩片弹射;（2）与完整试样相比,含1条、2条、3条预制裂隙模型试样的峰值强度、弹性模量均呈现稳定下降的趋势,而峰值轴向应变则是先减小后增大;（3）试样预制裂隙尖端张拉裂纹的产生会造成：相邻预制裂隙尖端横向应变值的突变、试样侧向变形量的突增以及侧向变形速率的显著增大;（4）临空面附近的预制裂隙,其尖端产生的张拉裂纹在很短的时间内便会失稳扩展,并造成试样的失稳破坏。最后,分析试样变形破坏过程中的声发射特性。研究结果对于揭示深埋硬岩隧洞板裂化围岩的失稳破坏规律、岩爆的发生机制具有重要意义。     

含交叉裂隙岩体相似材料试件力学性能单轴压缩试验

以相似材料制作含交叉裂隙岩体试件,考虑主裂隙与加载方向之间角度变化及主、次裂隙之间角度变化制作20组试件,对试件进行单轴压缩试验,研究交叉裂隙对岩体破坏模式及力学特性的影响。研究表明,主裂隙与加载方向呈0°及90°时,试件破坏主要为沿次裂隙扩展的剪切型破坏;当主裂隙与加载方向呈30°及45°时,试件破坏主要是沿主裂隙扩展所致的剪切型破坏;主裂隙角度一致情况下,大部分含交叉裂隙岩体破坏强度高于含单向裂隙岩体,含交叉裂隙岩体试件应力-应变曲线峰后下降斜率比含单向裂隙岩体大;主裂隙角度一致情况下,当次裂隙与主裂隙呈45°夹角左右时,岩体试件强度较低,当次裂隙与主裂隙呈30°及90°夹角左右时,岩体试件强度较高。     

Crack propagation trajectories for rocks under mixed mode I-II fracture

Propagation of a crack in engineering materials including rocks can cause failure. Knowledge of the stress state under which a crack can propagate, and the trajectory it may follow during its growth are thus very important for the stability of rock masses/materials and for the safe design of structures in/on rocks. In this paper, the crack initiation angle and subsequent crack propagation path are experimentally investigated for limestone rock specimens. This investigation was conducted under various mixed mode I-II loading conditions, including pure mode-I and pure mode-II.This study includes conducting diametrical compression tests on notched Brazilian disk specimens. Moreover, the effect of confining pressure and temperature on crack initiation and propagation were also studied. The experimental results were compared with theoretical predictions of crack initiation angle. The results showed that limestone behaves in brittle fashion, and the effects of confining pressure and temperature on failure trajectories were not significant. Generally, the crack initiation angle can be predicted by the maximum tangential stress criterion. However, for notched Brazilian disk with high value of crack orientation with respect to loading direction, crack does not propagate from the tip of the crack. This important observation indicated that the tensile-strength failure can become more critical than the fracture-toughness failure.     

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。     

冲击载荷作用下准脆性材料Ⅱ型裂纹扩展研究

冲击载荷作用下准脆性材料的动态断裂一直是关注的热点问题,Ⅱ型裂纹试样受冲击剪切时其裂纹扩展方向同材料力学性质和冲击速度等密切相关。应用岩石动态破裂过程动态分析系统软件,对单边平行双裂缝试样开展了冲击载荷作用下的裂纹动态扩展数值模拟,分别研究了不同材料力学性质、材料均质度、入射应力脉冲幅值和历时对II型裂纹动态扩展的影响。数值模拟结果表明,纯II型裂纹在动荷载作用下的扩展,不仅受到剪切损伤,而且还存在拉伸损伤;准脆性材料的非均匀性导致了主裂缝周围产生大量微裂纹的破坏,影响裂缝的分岔和内部的应力值;应力幅值和应力脉冲历时分别超过某一定值时,主裂缝将出现分叉现象,试样的破坏程度加剧,其研究结果对于深入揭示准脆性材料在动荷载作用下II型裂纹扩展的规律及准脆性材料的损伤断裂机制具有重要的参考价值。     

不同加载速率Ⅰ型预制裂纹花岗岩断裂特征研究

以CCD相机配合高速相机搭建试验变形观测系统,开展不同加载速率下含Ⅰ型预制裂纹花岗岩试件的三点弯试验。利用数字散斑相关方法对试验过程采集的数字散斑图像进行分析,对不同加载速率作用下含Ⅰ型预制裂纹花岗岩试件裂纹扩展过程中的变形演化特征、裂纹扩展速率、裂纹尖端张开位移、裂纹张开角以及初始断裂应力强度因子进行研究,研究结果表明：（1）花岗岩试件初始裂纹扩展速率随着加载速率的增加总体呈线性增加趋势;最大扩展速率随着加载速率增加呈现先较快增加后缓慢增加的变化趋势。（2）不同加载速率作用下,花岗岩试件预制裂纹尖端张开位移均呈现非线性缓慢增长-迅速增长-线性增长的变形趋势,且线性增长阶段曲线斜率随着加载速率的增加而增大。（3）随着加载速率的增加,花岗岩试件初始裂纹张开角先逐渐减小后稳定在0.1o～0.13o。（4）随着加载速率的增加,花岗岩试件初始断裂应力强度因子呈指数增长。     

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.     

Mode I crack propagation in concrete under fatigue: microscopic observations and modelling

In this study, three‐point bending tests were carried out on notched beams to investigate mode I crack propagation in plain concrete under fatigue. The first part of the study focused on microscopic observations of the crack growth features. Microscopic observations were made using the replica method associated with scanning electron microscopy (SEM). Observations of fatigue crack growth both on the surface and inside the specimens are presented as a comparison between the observed crack lengths and those estimated by the compliance calibration method. In the second part, a finite element model of mode I crack propagation under fatigue is presented. According to the cohesive crack concept, a cohesive force distribution on the crack at various loading stages is assumed, according to both the stress‐crack opening relation worked out by Hordijk (1991; Thesis, Technische Universiteit) and a new proposed relation with hysteresis loop. Finite element computation is used to evaluate the crack extension in the bending beams. Numerical predictions are discussed in comparison with experimental results. Copyright © 2002 John Wiley & Sons, Ltd.     

三轴疲劳-卸围压条件下大理岩力学特性试验研究

为了揭示应力扰动和卸载围压作用下大理岩损伤破裂的物理过程和非线性力学行为,采用GCTS RTR-2000伺服加载岩石力学试验机进行了岩石疲劳卸围压试验,同时对破坏试样进行了压后裂纹形态CT扫描可视化分析。结果表明：周期性的加卸载作用对大理岩起到了主因损伤作用,卸围压的作用对大理岩起到了根本性的破坏作用。岩石疲劳循环形成滞回环,滞回环面积由疏变密,滞回环加载和卸载曲线接近重合,加卸载模量近似相等;岩石经过卸围压作用,岩石的轴向、径向和体积应变表现为不同程度增大,表明应变对围压降低具有强敏感性,敏感程度由高到低依次为体积应变、径向应变和轴向应变;由于疲劳循环的影响,卸围压作用产生的围压降幅随循环次数增多而降低,卸围压时长随循环次数增多而减少;量化宏观应变变形,求得应变损伤指数 、 、 ,疲劳循环次数越多,应变损伤指数越大;岩石破坏后细观CT扫描揭示了疲劳循环损伤对岩石破裂形态影响的内在机制。随疲劳循环次数的增加,裂纹密度和规模显著增加。研究成果可为地下工程疲劳活动规律和开挖卸荷问题提供理论和模型支撑。     

Numerical Observation of Three-Dimensional Wing Cracking of Cracked Chevron Notched Brazilian Disc Rock Specimen Subjected to Mixed Mode Loading

The cracked chevron notched Brazilian disc (CCNBD) specimen has been suggested by International Society for Rock Mechanics for measuring mode I fracture toughness of rocks. Subsequently, this specimen geometry has been widely extended to conduct mixed mode fracture tests on rocks as well. A straight through crack front during the fracturing process upon the root of the chevron notch is assumed in the testing principle, but has never been thoroughly evaluated before. In this study, for the first time, the progressive rock fracture mechanism of the CCNBD rock specimen under mixed mode loading is numerically simulated. Specimens under representative mixed mode loading angles are modelled; and the assumption of the straight through crack front growth is critically assessed. The results show that not only the notch tip but also the saw-cut chevron notch cracks during the experiments, yielding a prominent twisted front, far from being straight. The crack front never grows up to the root of the notch ligament and the straight through crack front assumption is never satisfied in the realistic rock fracture progress of this chevron notched specimen subjected to mixed mode loads. In contrast, the fracture progress features typical three-dimensional wing cracking towards the loading ends. The numerically observed progressive fracture mechanism reveals that the measuring principle of mixed mode fracture tests employing CCNBD specimens is significantly violated and the measures of both modes I and II fracture toughness are uncertain.     

岩石节理倾角和间距对隧道掘进机破岩特性影响的试验研究

为了研究岩体节理参数（节理间距和节理倾角）对全断面岩石掘进机（TBM）盘形滚刀破岩效果的影响,对实际条件进行简化,在改进的试验装置上进行压头作用下相似材料的变形、破坏试验。采集整个加载过程中压头的侵入深度和荷载数据,并采用相机实时拍摄,获得试件表面破坏的发展过程以及最终破坏形态。试验结果表明,当节理倾角一定时,随着节理间距增大,达到跃进点的贯入荷载值增加,侵入功以及主裂纹扩展能量也都呈增大趋势,当 =0°、90°时,抗侵入系数基本一致,当 = 30°、60°时,抗侵入系数逐渐增大。当节理间距一定时,随着 角度的增加,跃进点荷载、抗侵入系数、侵入功以及主裂纹扩展能量都呈现先减小后增大趋势,在 =30°时,各值都为最小值。根据试件破坏后形态分析发现,节理的空间特征对裂纹扩展模式有明显的控制作用,对破坏区域的形成也有明显的限制。     

Specimen-apparatus interaction during stick-slip in a tri axial compression machine: A decoupled two-degree-of-freedom model

The stick-slip of frictional sliding depends not only on material properties but also on the elastic and inertial properties of the loading system. To compare data from different testing machines or to apply them to the problem of natural seismogenic faulting, one must account for the differences in stiffness and mass. We develop a simple mechanical model to describe the stick-slip oscillation during frictional sliding in a triaxial-compression machine. The experimental system, the loading frame and rock specimen with precut sliding surface, is divided into two subsystems across this surface. The model is based upon two key assumptions: the kinetic friction is constant regardless of the relative motion of the subsystems, and the elastic restoring force is uniform throughout each subsystem. The first assumption leads to the decoupling of the subsystems, and the behavior of each becomes mathematically analogous to that of a simple spring/mass/slider-block model, owing to the second assumption. The theory agrees well with the experimental data from the dynamic measurements of stick-slip. The displacement-time function is of cosine form, the rise time of stick-slip is constant, and the relation between force drop and average displacement rate is linear. From this model we argue that the differences in the frictional behavior of experimental fault-gouges may indeed be ascribed to differences in the material properties of their specimens because the elastic and inertial properties of a particular testing machine are little influenced by the specimen itself, so long as all specimens are of about the same size. However, interlaboratory correlations may well be invalid unless machine effects are properly accounted for.     

基于颗粒离散元模型的不同加载速率下花岗岩数值试验研究

不同加载速率条件下岩石的力学特性,对于其动载下破裂内在机制的研究具有积极的意义。基于颗粒流理论,通过黏结颗粒模型（bonded particle model,简称BPM）虚拟实现不同加载速率0.001～0.500 m/s下花岗岩单轴压缩和巴西劈裂试验,定量分析加载速率对应力-应变、破裂形态、应变能率及声发射的影响。结果表明：单轴抗压强度和抗拉强度及其对应峰值应变随加载速率增加而非线性增长;单轴压缩作用下,随加载速率增加,试样由单一斜截面破坏向多斜截面破坏转变,且主控裂隙带宽度急剧增大,由裂纹数量及水平向高应变率区域变化规律可明显看出,试样破坏程度随着加载速率增加而逐渐加剧;巴西劈裂作用下试样从一条主控裂隙向多条主控裂隙转变,且裂纹向圆盘试样两侧边缘部分延伸,破坏程度加剧;单轴压缩和巴西劈裂作用下,声发射事件及应变能率均随加载速率增加而呈现出非线性增长趋势。     

Investigation of crack formation during loading of brittle rock

Conclusions The response of elastic/brittle targets to loading by conical-, wedge-and hemispherical-indenter shapes representing jackhammer bit tips was analyzed. Theoretical predictions of crack extent and direction are based on values of the maximum principal strains and the associated extension strain criterion in the target assuming a semi-infinite, homogeneous and isotropic solid.Corresponding static experiments using an MTS machine and dynamic percussive tests involving an encased circular target disk of Sierra granite have been conducted. The damage pattern consisting of a crater, a crushed zone, a region of multiple minor cracks as well a some longer fissures has been delineated. Comparison with theoretical predictions indicate that cracks are produced by maximum tensile strain, with their directions predicted well by the present theory. The upper bound predictions of the crack extent are also in reasonable accord. Deviations are due to the presence of inhomogeneities and anisotropies in the tests specimens.