砂岩的I/III复合型断裂试验研究

为了了解砂岩的I/III复合型断裂力学性能,采用含有裂纹面垂直于底面但倾斜于正背面的三点弯曲（TPB）试件实现面外断裂。使用Abaqus通过有限元法研究了不同裂纹面倾斜角下沿着试件厚度的I型、II型与III型无量纲应力强度因子。通过讨论可知,在靠近试件厚度中点处I型与III型无量纲应力强度因子取得较大值,而II型无量纲应力强度因子取得接近于0的可以忽略的极小值,且靠近自由面处的应力强度因子不作考虑。故该种试件可用于测量材料的I/III复合型断裂性能。数值计算结果与常规TPB试件的解析公式及倾斜裂纹面TPB试件的近似计算公式的结果进行对比,证明了数值模拟结果的准确性并讨论了近似公式存在的问题。使用7组共28个该种三点弯曲试件,研究砂岩的I/III复合型断裂特性,结果表明：砂岩的I型与III型临界应力强度因子随着裂纹面倾斜角的增大先增大后减小,但其变化趋势不同;砂岩的I/III复合型等效断裂韧度随着裂纹面倾斜角的增大先增大后减小,在倾斜角接近20°时取得最大值。裂纹扩展时裂纹面将发生扭转,倾斜角θ越大则扭转角度越大。     

Modeling crack propagation path of anisotropic rocks using boundary element method

In a cracked material, the stress intensity factors (SIFs) at the crack tips, which govern the crack propagation and are associated with the strength of the material, are strongly affected by the crack inclination angle and the orientation with respect to the principal direction of anisotropy. In this paper, a formulation of the boundary element method (BEM), based on the relative displacements of the crack tip, is used to determine the mixed‐mode SIFs of isotropic and anisotropic rocks. Numerical examples of the application of the formulation for different crack inclination angles, crack lengths, and degree of material anisotropy are presented. Furthermore, the BEM formulation combined with the maximum circumferential stress criterion is adopted to predict the crack initiation angles and simulate the crack propagation paths. The propagation path in cracked straight through Brazilian disc specimen is numerically predicted and the results of numerical and experimental data compared with the actual laboratory observations. Good agreement is found between the two approaches. The proposed BEM formulation is therefore suitable to simulate the process of crack propagation. Copyright © 2008 John Wiley & Sons, Ltd.     

基于颗粒流的直切槽式巴西圆盘裂纹扩展分析

利用颗粒流程序（PFC) 对直切槽式圆盘试样进行巴西试验模拟,分析了不同的裂隙倾角和裂隙长度对直切槽式圆盘试样裂纹扩展规律的影响。根据起裂位置的不同,主裂纹可分为从裂隙尖端萌生的Ⅰ型主裂纹和从裂隙尖端一定距离处萌生的Ⅱ型主裂纹;次生裂纹可分为从加载点附近萌生的Ⅰ型次生裂纹和从远离加载点的一侧萌生的Ⅱ型次生裂纹。当裂隙长度保持不变而增大裂隙倾角时,主裂纹从Ⅰ型过渡为Ⅱ型,次生裂纹则从Ⅰ型转变为Ⅰ型和Ⅱ型共存,最后又变为Ⅰ型。当裂隙角度保持不变而增大裂隙长度时,主裂纹保持不变,次生裂纹则由Ⅰ型逐渐过渡为Ⅰ型和Ⅱ型共存。另外,当径向应力达到峰值应力之后,试样内会有大量的微裂纹萌生、扩展,造成了圆盘试样的破坏。从力链和能量角度来看,巴西圆盘试样的破裂过程是试样内部拉应力集中产生的颗粒间黏结破裂以及应变能释放的过程。     

层理面特性对砂岩断裂力学行为的影响研究

层理弱面对层状岩石的力学特性影响较显著，为了研究层理面特性对岩石断裂力学特性的影响，开展了具有不同层理方向的砂岩试样三点弯试验，探讨了砂岩断裂韧度及断裂模式的各向异性。之后基于有限元中的黏聚单元建立了数值模型，采用数值模拟方法研究了层理面强度对各层理角度试样断裂力学行为的影响规律。结果表明：层理方向影响下砂岩的断裂韧度及模式存在各向异性；同一层理方向试样的断裂韧度随层理面强度的增大而增大，且试样的层理面与加载方向夹角越小，断裂韧度受层理面强度变化影响越明显；试样的断裂模式不仅与层理面强度有关，还受层理倾角的控制，层理面与加载方向夹角θ = 0o试样断裂模式基本不受层理面强度影响，θ = 30o试样主要沿层理面张拉或剪切破坏，且沿层理面的破裂长度随层理面强度的降低逐渐增大；层理面强度较大时，θ = 45o试样主要沿层理面张拉破坏，θ = 60o～90o试样主要以贯穿层理的张拉破坏为主；层理面强度较小时，θ = 45o～90o试样均以沿层理面的剪切破坏为主，其中θ = 45o试样沿层理剪切长度最大。另外，通过数值模拟结果分析了层理面强度及方向对试样的起裂角及裂纹扩展路径产生的影响。该研究成果可作为层状岩石断裂力学理论的有益补充。     

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。     

基于巴西劈裂试验的页岩强度与破坏模式研究

为了研究页岩横观各向同性性质对劈裂强度及破坏模式的影响,对7组不同倾角下的试样进行了巴西劈裂和声发射测试。研究表明：层理的方向对试样的劈裂强度和最终破坏模式有着重要的影响。随着层面倾角 的增加,页岩试样的劈裂强度逐渐减小。在不同倾角下的破坏模式可分为直线形（ 0°、90°）、月牙形（ 15°）和曲弧形（ 30°、45°、60°、75°）。通过分析不同倾角下圆盘中心点沿层理分解得到的正应力和剪应力,当 0°时,试样的破坏方式为基质的拉伸破坏;当 90°时,试样的破坏方式为层理的拉伸破坏,当15° 75°时,试样的破坏为复合型破坏。观察声发射空间累计定位演化分布情况,直线型的声发射点较均匀地分布在试样中轴线的两侧;曲弧型的声发射点在圆盘的一端较密而另一端较稀疏;月牙型则在试样的中部和一端都累积了部分声发射点;分布特征与宏观破坏方式具有相似性。分形维数D可以较好地反映试样的破坏模式,从倒V形的变化趋势可知,直线形试样D值接近于2,而月牙形和曲弧形试样D值介于2.2～2.7。因此,D值越大,说明裂纹的曲率半径越大;相反D值越小,裂纹越趋于一条直线,破裂形态也就越简单。     

Slope failure analysis considering anisotropic characteristics of foliated rock masses

Weak planes affect the strength and deformational behaviors of rock slopes, and the anisotropic characteristics of rock mass should be considered in slope stability analysis. Effects of joint plane orientations on failure mechanism and strength response of inherently anisotropic rock samples were firstly investigated. The specimens with various orientations of joints were evaluated under uniaxial compression, Brazilian tensile, and direct shear tests. By treating the foliated rock as transversely isotropic materials, the relevant elastic constants and strength parameters were obtained from experimental results. The slope damage zone was then investigated using Comsol Multiphysics code based on Hoffman criterion. It is indicated that the failure mechanism and strength response depend highly on the inclination of specimens with respect to the loading direction. For disks with the same inclination angle, the value of tensile strength has an increasing trend with the total fracture length. Numerical results show that partial slope mass failed in single slope and no large-scale landslide occurred. The failure pattern in numerical results agrees well with the field observations. The cooperation between the experimental results and the numerical results allows an in-depth analysis of the experimental results and thus better understanding the dominant effect of joints on the deformation and failure of rock mass.     

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.

     

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。     

Determination of Fracture Toughness of Anisotropic Rocks by Boundary Element Method

Summary  This paper presents a systematic procedure for determining fracture toughness of an anisotropic marble using the diametral compression test (Brazilian test) with a central crack on the discs. Additionally, a novel formulation to increase the accuracy in Stress Intensity Factor (SIF) calculations using Boundary Element Method (BEM) is applied to determine the stress intensity factors and the fracture toughness of anisotropic rocks under mixed-mode loading. The numerical results show that the SIFs for both isotropic and anisotropic problems are in good agreement with those reported by previous authors. The marble with clear white-black foliation from Hualien (in eastern Taiwan), was selected for the Brazilian tests. Diametral loading was conducted on the Cracked Straight Through Brazilian Disc (CSTBD) specimens to evaluate their fracture toughness. In addition, a new fracture criterion was developed to predict pure mode I, pure mode II or mixed mode (I–II) fracture toughness of the anisotropic marble. The new fracture criterion is based on the examination of mode I, mode II and mixed mode (I–II) fracture toughness for different crack angles and anisotropic orientation. Authors’ address: Associate Professor Chao-Shi Chen, Department of Resources Engineering, National Cheng Kung University, No. 1 Dasyue Rd., East District, Tainan 701, Taiwan     

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.     

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.     

三轴压缩条件下单裂隙岩石的破坏特性研究

通过在高强硅粉砂浆材料模型中预制特定倾角和特定尺寸的单裂隙,以常规三轴压缩试验为手段,研究单裂隙试样的破坏特性。试验中观察到3类典型的裂纹,即拉伸型裂纹（Ⅰ型）、滑移型裂纹（Ⅱ型）和撕开型裂纹（Ⅲ型）,其中Ⅱ型、Ⅲ型裂纹在三维试验中普遍存在,Ⅰ型裂纹仅在部分试件中观察到;三轴压缩条件下试样的破裂模式有3种,即拉剪复合破坏、“X”型的剪切破坏和沿裂隙面的剪切破坏。试验结果表明：三轴压缩条件下的单裂隙试样的裂隙扩展规律与预制裂隙关系密切,围压是试样宏观破裂模式的主要影响因素,预制裂隙长度主要影响裂隙扩展的规模,预制裂隙倾角则是新裂隙起裂的诱因。     

孔槽式圆盘破坏特性与裂纹扩展机制颗粒流分析

基于室内岩石类脆性材料圆盘试样巴西试验结果,利用颗粒流程序（PFC）,获得一组能够反映其力学特征的细观参数。在此基础上,对孔槽式圆盘试样进行巴西试验模拟,分析了裂隙倾角和半径比变化对孔槽式圆盘试样力学参数和裂纹扩展规律的影响。孔槽式圆盘试样力学参数显著低于完整圆盘试样,降幅与孔槽几何参数密切相关。劈裂荷载随裂隙倾角的增大呈非线性变化,而随着半径比的增大呈近似线性减小规律。通过分析认为,在试验模拟范围内保持半径比不变,当裂隙倾角较小时,孔洞是主裂纹起裂的主要诱因;裂隙倾角较大时,裂隙成为主裂纹起裂的主要诱因。保持裂隙倾角不变,当半径比较小时,裂隙是主裂纹起裂的主要诱因;半径比较大时,孔洞成为主裂纹起裂的主要诱因。最后,从细观层面探讨了孔槽式圆盘试样裂纹扩展机制。     

Location of the Crack Initiation Points in the Brazilian Disc Test

To study the location of crack initiation and its failure mode in the Brazilian test, the analytical location of the crack initiation under different failure modes was first discussed with the stress formulas of the Brazilian test. Then, by using the numerical simulation technique of fast Lagrangian analysis of continua to simulate the ideal Brazilian test, we found that: (a) when the crack was a tensile fracture, the crack initiation point was found to be around the maximum tension stress point; (b) when the crack was a shear failure, the crack initiation point, which was only related to the internal friction angle, was found between the maximum tension stress point and the tensile critical point; and c. the numerical conclusion well verified the correctness of the theoretical analysis and was in good agreement with the results of other papers.     

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。     

基于P-CCNBD试样的岩石动态断裂韧度测试方法

预裂的人字形切槽巴西圆盘(Pre-cracked chevron notched Brazilian disc,简称P-CCNBD)是将人字形切槽巴西圆盘(cracked chevron notched Brazilian disc,简称CCNBD)的切槽尖端再稍加切削制成直裂纹前沿的试样。利用霍普金森压杆对P-CCNBD砂岩试样进行径向冲击,完成I型动态断裂试验后再做数值分析得到岩石的动态断裂韧度。为了验证数值模拟的可靠性,先进行了无限平面中一条有限尺寸裂纹表面受冲击拉伸作用的动态有限元分析,结果表明,数值模拟的结果与Shi得到的结果非常吻合。将试验-数值法和他人的准静态法分别确定的砂岩的动态起裂韧度进行对比,两种方法得到的结果有一定的差异。采用试验-数值法,将比较成熟的直裂纹巴西圆盘(cracked straight-through Brazilian disc,简称CSTBD)和P-CCNBD两种试样测得的结果进行对比,两者吻合较好。得到的动态起裂韧度都有随着加载率的增加而增大的加载率效应。分析了准静态法的缺陷,认为试验-数值法得到的结果更为合理。     

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。     

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.