Crack Initiation, Propagation and Coalescence in Rock-Like Material Containing Two Flaws: a Numerical Study Based on Bonded-Particle Model Approach

Cracking and coalescence behavior in a rectangular rock-like specimen containing two parallel (stepped and coplanar) pre-existing open flaws under uniaxial compression load has been numerically studied by a parallel bonded-particle model, which is a type of bonded-particle model. Crack initiation and propagation from two flaws replicate most of the phenomena observed in prior physical experiments, such as the type (tensile/shear) and the initiation stress of the first crack, as well as the coalescence pattern. Eight crack coalescence categories representing different crack types and trajectories are identified. New coalescence categories namely “New 1” and “New 2”, which are first observed in the present simulation, are incorporated into categories 3 and 4, and category 5 previously proposed by the MIT Rock Mechanics Research Group, respectively. The flaw inclination angle (β), the ligament length (L) (spacing between two flaws) and the bridging angle (α) (inclination of a line linking up the inner flaw tips, between two flaws) have different effects on the coalescence patterns, coalescence stresses (before, at or post the peak stress) as well as peak strength of specimens. Some insights on the coalescence processes, such as the initiation of cracks in the intact part of specimens at a distance away from the flaw tips, and coalescence due to the development and linkage of a number of steeply inclined to vertical macro-tensile cracks are revealed by the present numerical study.     

Cracking Processes in Rock-Like Material Containing a Single Flaw Under Uniaxial Compression: A Numerical Study Based on Parallel Bonded-Particle Model Approach

Cracking processes have been extensively studied in brittle rock and rock-like materials. Due to the experimental limitations and the complexity of rock texture, details of the cracking processes could not always be observed and assessed comprehensively. To contribute to this field of research, a numerical approach based on the particle element model was used in present study. It would give us insights into what is happening to crack initiation, propagation and coalescence. Parallel bond model, a type of bonded-particle model, was used to numerically simulate the cracking process in rock-like material containing a single flaw under uniaxial vertical compression. The single flaw’s inclinations varied from 0° to 75° measured from the horizontal. As the uniaxial compression load was increased, multiple new microcracks initiated in the rock, which later propagated and eventually coalesced into longer macrocracks. The inclination of the pre-existing flaw was found to have a strong influence on the crack initiation and propagation patterns. The simulations replicated most of the phenomena observed in the physical experiments, such as the type, the initiation location and the initiate angle of the first cracks, as well as the development of hair-line cracks, which later evolved to macrocracks. Analyses of the parallel bond forces and displacement fields revealed some important mechanisms of the cracking processes. The first cracks typically initiated from the tensile stress concentration regions, in which the tensile stress was partially released after their initiation. The tensile stress concentration regions subsequently shifted outwards close to the propagating tips of the first cracks. The initiation and propagation of the first cracks would not significantly influence the compressive stress singularity at the flaw tips, which was the driving force of the initiation of secondary cracks. The initiation of microcracking zone consisting almost exclusively of micro-tensile cracks, and that of microcracking zone consisting of micro-tensile cracks and mixed micro-tensile and shear cracks, were found to be correlated with two distinct types of displacement fields, namely type I (DF_I) and type II (DF_II), respectively.     

An Experimental Study of Crack Coalescence Behaviour in Rock-Like Materials Containing Multiple Flaws Under Uniaxial Compression

Experiments on man-made flawed rock-like materials are applied extensively to study the mechanical behaviour of rock masses as well as crack initiation modes and crack coalescence types. A large number of experiments on specimens containing two or three pre-existing flaws were previously conducted. In the present work, experiments on rock-like materials (formed from a mixture of sand, plaster, limestone and water at mass ratio of 126:9:9:16) containing multiple flaws subjected to uniaxial compression were conducted to further research the effects of the layout of pre-existing flaws on mechanical properties, crack initiation modes and crack coalescence types. Compared with previous experiments in which only three types of cracks were found, the present experiments on specimens containing multiple flaws under uniaxial compression revealed five types of cracks, including wing cracks, quasi-coplanar secondary cracks, oblique secondary cracks, out-of-plane tensile cracks and out-of-plane shear cracks. Ten types of crack coalescence occurred through linkage among wing cracks, quasi-coplanar secondary cracks, oblique secondary cracks, out-of-plane shear cracks and out-of-plane tensile cracks. Moreover, the effects of the non-overlapping length and flaw angle on the complete stress–strain curves, the stress of crack initiation, the peak strength, the peak strain and the elastic modulus were also investigated in detail.     

含双裂隙岩石裂纹演化机理的离散元数值分析

采用离散单元法探讨了预制双裂隙岩石的裂纹演化机理。用近期从试验资料提取的无胶结厚度含抗转动能力的岩石微观力学模型和相应的离散单元法商业软件,模拟了含不同预制倾角的双裂隙岩石试样在单轴压缩作用下裂纹的扩展与贯通规律,揭示了裂纹演化的宏微观机理。同时,将离散元法DEM岩石试样的裂纹的扩展和贯通规律以及强度特性与室内试验结果进行了比较分析。结果表明,预制裂隙之间以及端点处的拉应力集中是导致裂隙岩石破坏的主要原因,且DEM数值试验得到裂纹的演化规律与室内试验结果较为一致。含30°的预制裂隙的岩石试样最容易起裂,含75°的预制裂隙的岩石试样最困难起裂,造成此种现象的原因可能是裂纹在垂直于主应力方向上的长度不同导致试样受拉区域大小不同。     

Morphological aspects of crack growth in rock materials with various flaws

Crack evolution is initiated by the occurrence of tensile wing cracks and is then further promoted due to the crack coalescence caused by the extension of a central tensile crack segment between two relatively adjacent flaws. To understand such progressive failures in rock, a parallelized peridynamics coupled with a finite element method is utilized. Through this method, the initiation position of tensile wing cracks is observed with respect to varying inclination angles of a flaw, and then its corresponding shifting mechanism is investigated. In addition, the phenomenon of the position shifting being sensitive to various flaw shapes is discussed. Moreover, it is observed that the inclination angle of a central flaw affects the initiation position of other flaws; therefore, the initiation positions of tensile wing crack emanating from other neighboring flaws are analyzed with their angles. Following tensile wing cracks, a central tensile crack segment occurs in the bridging region between a central flaw and other neighboring flaws; the developmental patterns caused by the crack segment are discussed as well. Finally, the role a central tensile crack segment plays in the formation of crack coalescence and specimen failure is investigated in detail. The numerical results in this paper demonstrate good fidelity with established physical test results and complement them, thereby expanding the understanding of fracturing morphology in rock specimens with various flaws.     

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。     

单轴压缩条件下含三叉裂隙类岩石试样力学特性的细观研究

三叉裂隙是自然界普遍存在的一种岩体缺陷形式,其对岩体的力学特性有重要影响。对含预制三叉裂隙的水泥砂浆试样进行室内单轴压缩试验,配合使用摄像机拍摄裂纹的起裂、扩展、贯通过程,通过数字图像技术处理获取试样的应变场云图,并结合PFC2D程序研究不同?、? 条件下试样的强度特征、裂纹模式和裂纹演化扩展规律。研究表明：三叉裂隙对试样单轴抗压强度有明显的削弱作用。当? 恒定为120°时,试样在? = 30°时达到最大抗压强度;当? 恒定为90°时,随?增大,试样抗压强度呈先减小后增大的趋势,且当? = 45°时达到最大抗压强度。试样产生的裂纹可分为3类,分别是张拉型裂纹(Ⅰ型裂纹)、剪切型裂纹(Ⅱ型裂纹)、混合型裂纹(Ⅲ型裂纹)。这3类裂纹通常从裂隙尖端开始产生,并且Ⅰ型裂纹沿加载方向扩展,通常未扩展至试样边界;Ⅱ型和Ⅲ型裂纹通常与加载方向呈一定角度扩展至试样边界。通过对裂纹的几何形态和组成宏观裂纹的微裂纹成分的分析,得知导致含三叉裂隙试样在单轴压缩条件下失效的是张拉破坏。数字图像技术得到的应变云图表明,当载荷达到一定阶段,裂隙尖端出现应力集中,微破裂开始发育并聚集成微破裂区,微破裂区扩大产生宏观裂纹。通过对主应变和剪应变云图分析,发现导致试样失效的是张拉破坏,剪应变在裂纹扩展过程中的影响较小。     

Strength,fragmentation and fractal properties of mixed flaws

Experiments on Portland cement samples containing mixed flaws are conducted to investigate the strength, fragmentation and fractal properties. Flaw geometry is a new combination of two edge-notched flaws and an imbedded flaw, which is different from those in the previous studies, where parallel or coplanar flaws are used. The physical implications of the shear-box test applied to result to rock slopes are studied. The physical and analytical fragmentation characteristics of preflawed samples are analyzed through the sieve test and fractal theory, respectively. Three different patterns of tensile cracks and shear cracks are observed. A sliding crack model is presented to elucidate the brittle failure flaws. In all of the cases of the shear-box tests, the coalescence is produced by the linkage of shear cracks, and two types of coalescence (Type C1 and Type C2) have been classified, which tend to confirm the observations from the numerical model and field of jointed rock slopes. The shear strength is a function of the flaw geometry and the shear–normal stress ratio. The result of sieve tests indicates that the fragment size distribution of fragments has the fractal property, providing a physical understanding of the fragmentation mechanism. The fragments under the shear-box test have fractal dimensions between 2.2 and 2.6, which are larger than those under the compression test but similar to those in the fault cores. The fragmentation in the case of Type C2 has a smaller fractal dimension, corresponding to a larger shear strength.     

Fracture Initiation and Propagation in a Brazilian Disc with a Plane Interface: a Numerical Study

In the present study, fracture initiation and propagation from a pre-existing plane interface in a Brazilian disc is investigated using a finite-discrete element combined method. Different fracture patterns, depending on the frictional resistance of the pre-existing crack or interface, are observed from the numerical simulation. It is found that when there is no or very little frictional resistance on the surfaces of the pre-existing crack, the primary fractures (wing cracks), which are tensile in nature and are at roughly right angles to the pre-existing crack, start from the tips of the pre-existing crack. As the friction coefficient increases, the wing cracks’ initiation locations deviate from the crack tips and move toward the disc center. Secondary fractures, which are also tensile in nature, initiate from the disc boundary and occur only when the length of the pre-existing crack is sufficiently long. The secondary fractures are roughly sub-parallel to the pre-existing crack. The failure load is found to be influenced by the friction coefficient of the pre-existing crack. A 38 % failure load increase can result when the friction coefficient changes from 0 to 1. A good understanding of the fracture initiation and propagation in the forms of primary and secondary fractures provides insight into explaining some fracture patterns observed underground.     

Influence of single flaw on the failure process and energy mechanics of rock-like material

This paper investigates the influence of a flaw on crack initiation, the failure mode, deformation field and energy mechanism of the rock-like material under uniaxial compression. The results of laboratory test and numerical simulation demonstrate the flaw inclination effect can be classified into three groups: 0–30°, 30–60° and 75–90°. The characteristic stresses increase as the flaw angle increases. The tensile cracks initiate from gentle flaws (α ⩽ 30°) and shear cracks appear at tips of steep flaws (α ⩾ 45°). The input energy, strain energy and dissipation energy of a specimen show approximate increasing trends as the flaw angle increases.     

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.     

双轴循环荷载条件下含预制裂纹类玄武岩岩桥贯通模式

揭示双轴循环荷载条件下类玄武岩内裂纹起裂、扩展及岩桥贯通模式。配制类玄武岩相似材料,预制裂纹倾角=30、裂纹长度2a=20mm、裂纹厚度l=0.3mm的双裂纹,设计不同岩桥长度L、岩桥倾角试样,采用双轴压缩、双轴循环加卸载方式,研究裂纹扩展及岩桥贯通模式。试验结果表明:(1)双轴循环加卸载条件下,裂纹扩展-岩桥贯通过程可分为翼裂纹起裂、翼裂纹扩展和次生裂纹起裂及扩展、岩桥贯通3个阶段;(2)岩桥贯通类型可分为剪性贯通、张剪复合贯通和张性贯通3类。双轴压缩条件下,岩桥贯通模式可进一步划分为9种模式,双轴循环加卸载条件下,岩桥贯通模式可分为8种模式;(3)双轴循环加卸载试验比双轴压缩试验更易发生剪性贯通,且在部分试样岩桥处出现局部压碎隆起现象;(4)岩桥倾角和岩桥长度L对岩桥贯通模式影响显著,随着岩桥倾角的增大,岩桥贯通模式逐渐转变为剪性或张剪性贯通。双轴压缩条件下,岩桥长度增加,贯通模式由张剪复合贯通过渡为剪性贯通,而双轴循环加卸载试验则恰恰相反。     

Crack Initiation and Coalescence Behavior of Two Non-parallel Flaws

Crack initiation and coalescence behavior of rock or rock-like specimens containing artificial flaws under uniaxial compression have been subjects of intensive investigation in the past. Most of these investigations however focused on crack initiation and coalescence between two or more parallel flaws. Although there have been few experimental studies on non-parallel flaws, these studies did not address the influence of geometrical factors such as ligament length and ligament angle on the crack initiation and coalescence behavior of non-parallel flaws. To investigate whether the individual geometrical factors have similar effects on the crack initiation and coalescence behavior of both parallel and non-parallel flaws, we conducted uniaxial compression tests to investigate crack cracking and coalescence processes in rock like material containing two non-parallel flaws. The paper presents the influence of individual geometrical factors on the crack initiation process and coalescence pattern of non-parallel flaws. Initiation of primary first cracks from all the tips of the two flaws did not occur simultaneously in all the flaw configurations. The flaw configuration of the non-parallel flaws influences the crack initiation, crack trajectories and coalescence behavior. The crack coalescence pattern changes with an increasing ligament angle from indirect to shear crack or mixed tensile-shear crack to tensile crack coalescence. The chance of direct coalescence is reduced with an increase in ligament length. In conclusion, the crack initiation and coalescence behavior of prismatic rock-like specimens with non-parallel flaws, as influenced by the geometrical factors, are analogous to the cracking and coalescence pattern observed in specimens with parallel flaws.     

三轴压缩条件下冻融单裂隙岩样裂缝贯通机制

采用岩石力学伺服试验机,对预制单裂隙模型试样进行冻融循环后的三轴压缩试验,基于冻融循环试验对裂隙岩体的冻融损伤劣化模式进行研究,探讨经历不同冻融循环次数后的裂隙岩样在三轴压缩条件下裂缝的贯通机制。试验发现：裂隙岩体的冻融损伤劣化模式有颗粒散落模式、龟裂模式和沿预制裂隙断裂模式3种;在三轴加载条件下,冻融裂隙岩样的贯通模式呈现拉贯通、剪贯通、压贯通和混合贯通4种;贯通模式和冻融循环次数、围压的大小以及裂隙倾角有关,随着冻融循环次数的增加和围压的升高,岩样表面的破裂线越来越多,导致裂纹的贯通模式由单一贯通转换为混合贯通,在围压为2、6 MPa时,岩样的破坏模式为拉-压贯通,而围压为4 MPa时,岩样主要呈现拉贯通,裂隙倾角为30°的岩样主要贯通模式为拉贯通,裂隙倾角为60°的岩样主要贯通模式为剪贯通。     

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.

干湿交替作用后砂岩破裂过程实时观测与分析

采用岩石破裂全过程的细观力学试验系统进行了天然状态及干湿交替作用后的完整和含预制圆孔砂岩试件的单轴压缩破裂试验。利用显微镜观察了砂岩裂纹萌生、扩展以及试件的失稳破坏过程。经过干湿交替作用后岩样更容易在较低的应力状态下发生裂纹的扩展,并且裂纹扩展的初始阶段一般表现为拉破裂。完整试件的裂纹是随机性的三维扩展,而有预制圆孔试件一般是从预制圆孔周边开始扩展。天然状态下的预制圆孔试件在起裂时从圆孔的压应力集中区产生剪切裂纹;而干湿交替作用后,起裂时可能先从拉应力集中区产生拉裂纹,并且裂纹演化过程更为复杂一些,破裂形式多样化。与天然状态相比,经过干湿循环作用后的砂岩破坏脆性降低,强度等力学参数也随干湿交替次数增加而逐渐降低。     

裂隙充填影响巴西圆盘抗拉力学特性试验研究

裂隙是影响岩石力学特性和破裂模式最重要的因素之一,通过试验、数字照相技术和声发射监测对完整和含不同裂隙倾角 单裂隙、不同岩桥与裂隙夹角 双裂隙充填与非充填类岩石材料巴西圆盘的抗拉强度和破裂模式进行研究,探讨了随着 、 的不断变化和裂隙充填与否对试样最终破坏机制的影响。试验结果表明：（1）随着裂隙倾角 不断增大,单裂隙试样的抗拉强度先减小后增大,然后又减小;预制裂隙尖端萌生的翼裂纹贯通造成试样破坏;（2）双裂隙试样的抗拉强度随着 的增大先减小后增大;预制裂隙尖端萌生的翼裂纹和远场裂纹的扩展导致试样破坏;（3）在 、 相同的情况下,充填试样抗拉强度明显要高于非充填试样;预制裂隙充填与否对试样裂纹扩展的时间和裂纹数目影响较大;（4）加载初期,声发射较为平稳;宏观裂纹出现或者抗拉强度跌落时声发射将会变的异常活跃;在 、 相同的情况下充填试样声发射的起伏变化更为剧烈。     

Propagation and coalescence of quasi-static cracks in Brazilian disks: an insight from a phase field model

The phase field model represents sharp cracks by diffusive mushy-zone and can simulate crack propagation automatically. Propagation and coalescence of quasi-static cracks in Brazilian disks are investigated by a phase field model. The phase field modeling is implemented in Comsol Multiphysics and initially verified by a benchmark of three-point bending test. The Brazilian disk specimens containing no initial crack, a single and two pre-existing cracks subjected to compression are then tested by the phase field model. Crack propagation patterns along with the load–displacement curves are fully discussed. Meanwhile, the effects of length scale parameter and critical energy release rate on crack propagation are evaluated. In addition, the effect of crack inclination angle on the pre-cracked Brazilian disk specimens is also investigated. The numerical results obtained by the phase field model are in good agreement with previous experimental and numerical results.

     

Modeling of Crack Initiation, Propagation and Coalescence in Uniaxial Compression

Summary ?Cracks that initiate from pre-existing discontinuities can link with other cracks or with other discontinuities and produce failure in a rock mass. The Displacement Discontinuity Method (DDM), FROCK, is used in this investigation to model experimental observations on pre-cracked specimens of gypsum. In these experiments two fractures, which were either both open or closed, were placed through the thickness of the specimens, and detailed observations of the cracking process were performed as the specimens were loaded in uniaxial compression. The following aspects are studied for both open and closed fractures: 1) crack initiation stress; 2) direction and propagation of the new cracks; 3) type of coalescence and stress at which it occurs. Modeling is done considering the actual size of the specimens. Relations between the direction of initiation for each type of crack, the orientation of the initial fractures, and the type and coalescence are established. In addition, comparisons between results from experiments and predictions from the model are presented. The numerical results are in agreement with the experiments.     

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。