Crack Coalescence in Molded Gypsum and Carrara Marble: Part 2—Microscopic Observations and Interpretation

Experimental uniaxial compression loading tests were conducted on molded gypsum and Carrara marble prismatic specimens to study the cracking and coalescence processes between pre-existing artificial flaws. The study showed that material had an influence on the cracking and coalescence processes (see the companion paper in this issue). As reported in the companion paper, one of the pronounced features as observed in the high-speed video recordings was the development of macroscopic white patches prior to the development of observable cracks in marble, but not in gypsum. This paper (part 2) deals with the microscopic aspects of the study. Specifically, the scanning electron microscope (SEM) and the environmental scanning electron microscope (ESEM) imaging techniques were used to study the microscopic development of white patches and their evolution into macroscopic tensile cracks and shear cracks in marble, and the microscopic initiation of hair-line tensile cracks and their evolution into macroscopic tensile cracks in gypsum. The microscopic imaging study in marble showed that the white patches were associated with extensive microcracking zones (process zones), while the extent of process zone development in gypsum was limited. The comparison of the macroscopic and microscopic results indicates that the different extent of microcracking zone development, related to the material textural properties, is a key factor leading to different macroscopic cracking behavior in gypsum and marble.

高温后大理岩动态劈裂拉伸试验研究

为了研究高温处理后的岩石材料在冲击加载速率作用下的动态劈裂拉伸性能,利用大直径分离式霍普金森压杆试验设备对经历不同高温作用冷却后的“大理岩”平台巴西圆盘试样进行不同加载速率作用下的径向冲击试验。研究了高温后大理岩的动态劈裂拉伸强度及动态劈裂破坏形式随温度和冲击加载速率的变化规律。试验结果表明,与静态劈裂拉伸强度相比,经历不同高温作用冷却后,大理岩的动态劈裂拉伸强度有明显的提高,表现出显著的冲击加载速率强化效应,同一冲击加载速率作用下,随着温度的升高,动态劈裂拉伸强度表现出先增大后减小的变化趋势;高温后大理岩的动态劈裂破坏形式受到冲击加载速率和温度的共同影响。     

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.     

Carrara大理岩高温高压变形实验研究

利用高精度的Paterson高温高压流变仪对Carrara大理岩在高温(873~1173K)高压(~300MPa)以及约10-6~10-3s-1应变速率下进行了三轴压缩变形实验。结果表明,在等应变速率条件下,其强度随着温度的升高而降低;在等温和等压条件下,其强度随着应变速率的增加先快速增加而后缓慢增加。在应变速率对差应力的双对数投图中,我们发现随着温度的升高拟合直线的斜率减小,并且在873K和高应变速率时973K温度下Carrara大理岩的流变本构方程服从指数律变化关系;而在高温(1073K和1173K)和973K低应变速率条件下Carrara大理岩的应力指数n为5.3~7.7,且服从幂次律变化关系。因此,Carrara大理岩在本研究的实验条件下主要有两种变形机制,一种是用指数律表示的高应力变形机制;另一种是用幂次律表示的中等应力变形机制。     

花岗岩巴西劈裂渐进破坏特征与能量演化研究

既有的巴西劈裂试验与模拟研究多集中在宏观破坏模式与细观演化规律上,对劈裂渐进过程的能量演化特征的分析较少。结合数字图像相关技术(DIC)与声发射实时监测,开展花岗岩的巴西劈裂实验。首先分析实验过程中,岩石破裂模式与破裂尺度的演化规律。在此基础上,采用颗粒流程序(PFC2D)对劈裂试验过程进行数值模拟,分析实验过程中内部裂纹演化过程的能量特征。试验与数值模拟对比结果表明:加载过程中岩样的损伤变化一共经历了4个阶段,即裂隙压密阶段(Ⅰ)、裂纹萌生阶段(Ⅱ)、裂纹扩展阶段(Ⅲ)、峰后破坏阶段(Ⅳ)。试样在裂隙萌生和裂纹扩展阶段以拉张型微破裂为主,裂纹扩展阶段后期产生剪切型破裂,并在加载直径方向形成大尺度裂纹并贯穿整个圆盘形成宏观破坏;试样在裂隙压密和萌生阶段几乎无耗散能,外力所做功几乎都转为岩体内可释放应变能,在破裂扩展后期应变能快速释放,声发射能量在峰值应力附近时达到最大值,峰后破坏阶段试件的可释放应变能快速减小,能量通过形成大量新裂面被耗散掉。     

Experimental and Numerical Studies on Determination of Indirect Tensile Strength of Rocks

Indirect tension tests using Brisbane tuff Brazilian disc specimens under standard Brazilian jaws and various loading arcs were performed. The standard Brazilian indirect tensile tests caused catastrophic, crushing failure of the disc specimens, rather than the expected tensile splitting failure initiated by a central crack. This led to an investigation of the fracturing of Brazilian disc specimens and the existing indirect tensile Brazilian test using steel loading arcs with different angles. The results showed that the ultimate failure load increased with increasing loading arc angles. With no international standard for determining indirect tensile strength of rocks under diametral load, numerical modelling and analytical solutions were undertaken. Numerical simulations using RFPA^2D software were conducted with a heterogeneous material model. The results predicted tensile stress in the discs and visually reproduced the progressive fracture process. It was concluded that standard Brazilian jaws cause catastrophic, crushing failure of the disc specimens instead of producing a central splitting crack. The experimental and numerical results showed that 20° and 30° loading arcs result in diametral splitting fractures starting at the disc centre. Moreover, intrinsic material properties (e.g. fracture toughness) may be used to propose the best loading configuration to determine the indirect tensile strength of rocks. Here, by using numerical outcomes and empirical relationships between fracture toughness and tensile strength, the best loading geometry to obtain the most accurate indirect tensile strength of rocks was the 2α?=?30° loading arc.     

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。     

Crack Coalescence in Molded Gypsum and Carrara Marble: Part 1. Macroscopic Observations and Interpretation

Cracking and coalescence behavior has been studied experimentally with prismatic laboratory-molded gypsum and Carrara marble specimens containing two parallel pre-existing open flaws. This was done at both the macroscopic and the microscopic scales, and the results are presented in two separate papers. This paper (the first of two) summarizes the macroscopic experimental results and investigates the influence of the different flaw geometries and material, on the cracking processes. In the companion paper (also in this issue), most of the macroscopic deformation and cracking processes shown in this present paper will be related to the underlying microscopic changes. In the present study, a high speed video system was used, which allowed us to precisely observe the cracking mechanisms. Nine crack coalescence categories with different crack types and trajectories were identified. The flaw inclination angle (β), the ligament length (L), that is, intact rock length between the flaws, and the bridging angle (α), that is, the inclination of a line linking up the inner flaw tips, between two flaws, had different effects on the coalescence patterns. One of the pronounced differences observed between marble and gypsum during the compression loading test was the development of macroscopic white patches prior to the initiation of macroscopic cracks in marble, but not in gypsum. Comparing the cracking and coalescence behaviors in the two tested materials, tensile cracking generally occurred more often in marble than in gypsum for the same flaw pair geometries.

Indirect tensile test assessments for rock materials using 3-D disc-type specimens

Indirect test methods are usually the preferred approach for determining the tensile strength of brittle and quasi-brittle materials such as ceramics, rocks, and concrete. In this paper, the tensile strength of a rock material (Iranian Harsin marble) was obtained indirectly by means of two disc type samples. The test samples were the well-known Brazilian disc and semi-disc specimen under three-point bend loading. Since the existing formula for determining the indirect tensile strength is based on 2-D stress assumption which ignores the effects of specimen thickness, a general 3-D tensile strength formulation was derived for each sample by employing finite element analysis. A series of tensile strength tests were conducted on Harsin white marble using disc and semi-disc specimens with different thicknesses in parallel to finite element analysis. The test results using 3-D formulation showed that the tensile strength of the tested marble depends on the thickness/diameter ratio of the specimen and generally decreases from 11.5 to 7 MPa on increasing the thickness of test samples. The average values of tensile strength were about 8.8 MPa for the Brazilian disc specimen and 9.8 MPa for the semi-disc specimen. The good agreement existing between the results of the two specimens suggests that the semi-disc specimen can also be used for determining the rock tensile strength in addition to using the conventional Brazilian test.     

Experimental Study on the Validity and Rationality of Four Brazilian Disc Tests

The validity and rationality of the Brazilian disc test have attracted much attention since it was proposed. To verify the validity of four Brazilian disc tests, red sandstone and yellow rust granite were employed. In these experiments, uniaxial tensile tests and four Brazilian disc tests were performed. Meanwhile, the typical location of the Brazilian discs was arranged with gages to detect the crack initiation location. By analyzing the rationality of the four Brazilian disc tests from two aspects, the crack initiation location and the difference between indirect tensile strength and direct tensile strength, it was found that the Brazilian disc tests without cushion and the Brazilian disc tests with two small-diameter steer rods are suitable for determining the indirect tensile strength of rock materials. However, the Brazilian disc tests with arc loading jaws should be carefully adopted to measure the indirect tensile strength due to their overestimation of the indirect tensile strength. Additionally, flattened Brazilian disc tests were found to be not suitable for measuring the indirect tensile strength of rock materials.     

An Example of Realistic Modelling of Rock Dynamics Problems: FEM/DEM Simulation of Dynamic Brazilian Test on Barre Granite

The scope of this study is to numerically simulate the behaviour of Brazilian disc specimens as observed in laboratory during dynamic, high-strain rate, indirect tensile tests using an innovative combined finite-discrete element method (FEM/DEM) research code. Laboratory experiments using a split Hopkinson pressure bar (SHPB) apparatus were conducted by the authors and the measured indirect tensile strength values were used to verify the FEM/DEM models. In the models the applied boundary conditions, related to the loading rate of the specimen, were matched with the experimental observations. The results of the numerical simulations, including tensile strength and failure time, are in agreement with the laboratory findings. The main failure mechanisms, i.e. tensile splitting along loading axis and shear failure close to loading platens are captured by the numerical model. A linear relationship between tensile strength and loading rate is found for the range of dynamic strain rates tested and simulated. The simulation results are in good agreement with laboratory observations and demonstrate the potential for using FEM/DEM to realistically model dynamic response of rocks.     

岩石类材料拉伸弹性模量测量方法的对比研究

研究表明岩石材料在拉应力、压应力条件下具有不同的力学行为,因此,岩石材料存在两种弹性模量,分别为拉伸弹性模量和压缩弹性模量。为了甄别出直梁弯折试验和巴西劈裂试验哪一种更加适合测试岩石材料的拉伸弹性模量,以大理岩、花岗岩和砂岩为典型的岩石类型,开展了一系列的单轴压缩、直接拉伸、三点弯折和巴西劈裂试验,测试了岩石材料的拉伸弹性模量;并对测试结果的可靠性、准确性开展了系统的对比研究。最终发现,巴西劈裂试验因为较好的测量精度、制样简便、试验操作简单等因素,可以成为测量岩石材料拉伸弹性模量的推荐方法。     

Static and Dynamic Flexural Strength Anisotropy of Barre Granite

Granite exhibits anisotropy due to pre-existing microcracks under tectonic loadings; and the mechanical property anisotropy such as flexural/tensile strength is vital to many rock engineering applications. In this paper, Barre Granite is studied to understand the flexural strength anisotropy under a wide range of loading rates using newly proposed semi-circular bend tests. Static tests are conducted with a MTS hydraulic servo-control testing machine and dynamic tests with a split Hopkinson pressure bar (SHPB) system. Six samples groups are fabricated with respect to the three principle directions of Barre granite. Pulse shaping technique is used in all dynamic SHPB tests to facilitate dynamic stress equilibrium. Finite element method is utilized to build up equations calculating the flexural tensile strength. For samples in the same orientation group, a loading rate dependence of the flexural tensile strength is observed. The measured flexural tensile strength is higher than the tensile strength measured using Brazilian disc method at given loading rate and this scenario has been rationalized using a non-local failure theory. The flexural tensile strength anisotropy features obvious dependence on the loading rates, the higher the loading rate, the less the anisotropy and this phenomenon may be explained considering the interaction of the preferentially oriented microcracks.     

动态冲击下锦屏大理岩力学响应与能量特性

为了分析锦屏水电站大理岩的动力学响应和能量特性,采用分离式霍普金森压杆对岩样开展了动态压缩试验,并引入分形维数定量表征试样的破碎形态、能耗特性及其与应变率的内在关系。结果表明：动态载荷下大理岩应力-应变曲线初始压密段不明显,当应变率较低时,应力-应变曲线呈现出回弹现象;试样峰值应力随应变率的增大而增加,且动态抗压强度与...     

Stable isotopes and archaeological geology: the Carrara marble,northern Italy

The principal marble quarries of Italy for the past 2000 years have been those of Carrara. In Roman times, the marble was exported all over the ancient world. Renaissance quarries were opened up in Seravezza; both the Seravezza and the Carrara quarries have been exploited until today. The correct identification of Carrara marble has always been a problem because it was traded so widely in Roman times and was later used to fabricate broken or lost pieces of classical statuary. Many types of geochemical analysis have been tried in order to find distinctive signatures for the recognition of classical marbles, including trace elements, ESR spectroscopy of Mn, thermoluminescence, and stable isotopic ratios. To date, the most promising has been isotopic ratio analysis of oxygen and carbon.In this study, stable isotopic signatures were investigated as a means for distinguishing: (1) the principal quarry areas of the Carrara Commune: Fossacava, Miseglia, and Torano, and the Seravezza Commune; (2) or merely the largely classical quarries of Carrara from the Renaissance quarries of Seravezza; (3) and, most important, the Carrara quarries from other quarries of Greece, Turkey, Italy, and Tunisia in the classical marble data base.Discriminant analysis (DA) of the isotopic analyses showed that the three quarry areas of a Carrara could not be told apart but that they could be told easily from Seravezza. In addition, a “mineralized” Carrara quarry at Mandria, with buff to yellow rather than white marble, was also distinctive. DA also suggests that Carrara can be told from those quarries with which it is presently confused: Paros, in the Aegean Sea; Marmara, in Turkey; and Pentelikon, near Athens.Sr isotopic analysis showed a range in the Carrara and other marbles of Hettangian (Lower Jurassic) age from 0.70778 to 0.70810 which is very different from values found in Paros and Pentelikon. This suggests that Sr might make a good third discriminator for classical marble.     

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。     

Strain Rate Dependency of Coarse Crystal Marble Under Uniaxial Compression: Strength,Deformation and Strain Energy

Strain rate during testing, uniaxial or triaxial, has important influence on the measured mechanical properties of rocks. Uniaxial compression tests were performed at nine pre-specified static-to-quasistatic strain rates (ranging from 1 × 10^?5 to 1 × 10^?1 s^?1) on coarse crystal marble. The aim is to gain deep insight into the influence of strain rate on characteristic stresses, deformation properties and conversion of strain energy of such rock. It is found that the strain rate of 5 × 10^?3 s^?1 is the threshold to delineate the failure modes the tested coarse marble behaves in. At a strain rate less than this threshold, single-plane shear and conjugate X-shaped shear are the main failure modes, while beyond this threshold, extensile and splitting failures are dominant. The stress for crack initiation, the critical stress for dilation, the peak stress, and Young’s modulus are all found to increase with strain rate, with an exception that the above stresses and modulus appear relatively low compared to the strain rate in the range of between 1 × 10^?4 and 5 × 10^?3 s^?1. The pre-peak absorbed strain energy, damage strain energy and elastic strain energy are found to increase with strain rate. In addition, the elastic strain energy stored before peak point favors brittle failure of the specimen, as the more stored elastic energy in the specimen, the stronger the fragmenting.     

锦屏二级水电站大理岩复杂加卸载应力路径力学特性研究

地下洞室开挖围岩经历典型径向卸载、环向加载应力路径,由此引起的岩体强度、变形特征和破坏机制也不尽相同。针对锦屏二级水电站高地应力赋存环境,对施工排水洞大理岩开展常规单轴全应变、三轴压缩、卸围压、卸围压-加载轴压等4种不同应力路径力学试验,得到应力-应变全过程曲线、变形破坏特征和极限储能变化规律。试验研究结果表明, （1）锦屏二级水电站大理岩破坏时轴向应变一般较小,为硬脆性材料,卸荷应力路径下该脆性特征更为明显;（2）卸围压同时加载轴压试验峰值强度对应轴向应变、环向应变及体积应变值一般高于单纯的卸围压值,而对应峰值强度则一般低于卸围压值;（3）卸荷速率较大时,变形模量越大,大理岩峰值强度越低。加载速率越大,变形模量越小,峰值强度越高。初始围压越高,变形模量值越低,峰值强度越高;（4）无侧限作用时试件主要为张拉破坏,低侧限作用时为剪切破坏为主,局部存在张拉破坏,较高侧限时,剪切面为典型X或Y型;（5）岩石试件具有极限储能值,该值受多种因素的影响。一般情况下试件破坏对应围压越高,极限储能值越高,卸载速率越大,极限储能值越小。研究结果对于岩爆孕育发生机制解释以及工程实际问题的解决均有参考价值。     

Measurement of Indirect Tensile Strength of Anisotropic Rocks by the Ring Test

Summary This paper presents a new approach, combined with the Boundary Element Method (BEM) analysis and the diametrical compression on a thin disc with a small central hole, referred to as the ring test, for determining the indirect tensile strength of anisotropic rocks. The stress distribution around the hole can be successfully obtained by the proposed single-domain BEM. The complex variable function method was used for conveniently computing the tractions and displacements of a two-dimensional anisotropic body. If we assume that the tensile strength is given by the maximum absolute value of stress in the direction perpendicular to the loaded diameter at the intersection of loaded diameter and the hole, then from the failure load recorded by laboratory testing of ring (disc), the indirect tensile strength of rocks could be obtained. A marble from Hualien (Taiwan) with clearly black-white foliation, which was assumed to be transversely isotropic, was selected to conduct both ring tests and Brazilian tests for evaluating the tensile strength. The variation of the marble tensile strength with the inclination angle of foliation and with the hole size was also investigated. In general, the tensile strength of anisotropic rocks determined by ring test is not a constant, but depends on the elastic properties of rocks, the angle between the planes of rock anisotropy and the loading direction, the diameter of the central hole, and the contact condition of loading.