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.     

Transport model of buoyant metamorphic fluid by hydrofracturing in leaky rock

Abstract Aqueous fluid released in metamorphism is transported upwards from depth to the Earth's surface. I propose a hydrofracturing model for the fluid transport. In the model, fluid is transported by the upward propagation of a two-dimensional vertical fluid-filled crack from a fluid reservoir (e.g. overpressured compartment under a seal) at depth to the Earth's surface; fluid is injected consecutively from the reservoir into the crack at a given (but not necessarily constant) injection rate; some of the injected fluid is lost by infiltration from the crack walls into the surrounding permeable rock. An approximate solution of the crack propagation is obtained using fluid dynamics for turbulent film flow and linear elastic fracture mechanics. The solution shows the transition from a regime in which the excess pressure of the fluid in the reservoir drives the propagation to a regime in which the buoyancy of the fluid in the crack drives the propagation. For example, if the net injection rate of H₂O is 1 m²/s, the regime transition occurs when the vertical crack length becomes 280 m; after the transition, the propagation velocity and average aperture are constant: 21 m/s and 4.8 cm. If the injection rate is lower than a critical value, hydrofracturing cannot be an effective mode for the fluid transport because of the significant fluid loss by infiltration from the crack walls into the surrounding permeable rock. Assuming a fluid-saturated crust with hydrostatic pore fluid pressure, a lower limit can be estimated for the injection rate required to transport H₂O by hydrofracturing without significant fluid loss. For example, the lower limit for transport from a depth of 15 km to the Earth's surface is estimated at 0.2 m²/s if the crustal permeability is 10^-17 m². The lower limit decreases with decreasing crustal permeability.     

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。     

单轴应力下的孔洞–裂隙扩展规律数值模拟

为研究不同孔洞-裂隙（简称"孔-隙"）赋存条件下的裂纹扩展规律,利用RFPA软件,对不同裂纹倾角及不同非均质系数下的岩体破坏进行数值模拟分析,获得其裂纹扩展过程、声发射规律、应力-应变曲线,同时与原试验结果进行对比验证。结果表明:完整试样裂纹沿着剪切方向产生,含孔-隙试样裂纹沿裂隙尖端及孔口侧边产生;翼裂纹贯穿试件的同时,在预制裂纹尖端或孔口侧边产生水平方向的次生裂纹,并产生分叉,非均质系数影响次生裂纹走向;压载前期试样以拉破坏为主,压载后期以拉-剪组合破坏为主,次生裂纹的产生与剪切破坏有关;声发射累计能量与声发射累计数前期缓慢增大,后期迅速增大,预制裂纹倾角越小,非均质系数越大,声发射累计能量越大;不同裂纹倾角及不同非均质系数试件的应力-应变曲线均经历3个阶段:弹性变形阶段、非线性变形阶段及残余变形阶段,孔-隙的存在降低了试样的峰值强度,影响试件的脆性度。研究结果为进一步认识孔-隙相互作用规律提供了参考。      

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。     

大理岩加、卸荷破坏过程的三维颗粒流模拟

从大理岩常规三轴加、卸荷室内试验出发,结合PFC3D颗粒流程序进行分析,在明确室内试验与数值模拟试验卸荷速率对应关系的基础上,对不同卸荷速率下试样破坏过程的力学特性及破坏机制进行探讨。结果表明：加、卸荷路径下整个加载过程中张拉裂纹数量均明显高于剪切裂纹;常规三轴试验损伤应力之后,裂纹围绕某一速率进行扩展,卸荷试验损伤应力之后,裂纹的发展是突发性的;不同应力路径下试样损伤破坏的差异性主要形成于损伤应力至峰值应力这一阶段,直至卸荷速率超过6 MPa/s,试样的损伤程度与破坏形式逐渐趋于一致;随着围压的增大,不同卸荷速率下岩石破坏均呈现出由张拉破坏逐渐向剪切破坏过渡。     

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。     

基于灰关联的微观地质因素与微裂缝发育程度相关性分析

以鄂尔多斯盆地华庆地区长6致密砂岩储层为例,研究了影响致密砂岩储层微裂缝发育程度的复杂微观地质因素。应用灰关联分析法,揭示了微裂缝发育程度与各影响因素的关系。结果表明,灰关联分析法可应用于致密砂岩储层微裂缝成因研究,确定影响致密砂岩储层微裂缝发育程度的主要微观地质因素及其影响程度,与实测结果较吻合,为建立微裂缝发育程度表征参数体系提供了理论依据。     

基于裂隙扩展的多级岩质边坡开挖卸荷破坏路径分析

开挖卸荷作用下裂隙岩体边坡的破坏模式与路径分析是边坡工程灾害研究的热点之一,准确识别边坡的潜在破裂路径对工程安全施工和支护优化设计具有重要意义。依据断裂扩展分析方法,将裂隙扩展判别的理论方法开发并应用于数值模拟分析中,通过裂隙尖端应力强度因子计算、裂隙扩展模式识别、裂隙起裂角演算、裂隙扩展交汇等技术实现了岩体中断续裂隙的起裂、扩展与贯通演化过程的快速模拟;以某高速公路沿线裂隙岩体路堑边坡为对象,采用提出的模拟方法分析了多级开挖卸荷作用下坡体裂隙的扩展机制与边坡的破坏路径。结果表明：裂隙岩体边坡从上至下多级开挖过程中,坡肩裂隙首先起裂,并通过拉张型扩展逐渐发展为优势裂隙;随着边坡下挖,优势裂隙沿坡面向下逐步发生拉张/剪切混合型扩展并与既有裂隙交汇,在边坡中上部形成阶梯状扩展破坏路径;裂隙扩展至边坡下部及坡脚后扩展模式由拉张/剪切混合型转化为剪切型,并最终以弧形剪切面从坡脚出露。研究揭示了裂隙岩体边坡多级开挖卸荷作用下上部阶梯状拉张/剪切混合型破裂-下部弧形剪切型破裂的复合破坏模式,可为边坡工程支护设计和施工稳定性控制提供新思路。     

一种改进的光滑粒子动力学法在地震条件下岩质边坡中的验证与应用

开发一种改进损伤框架的粒子流算法,被称为核断裂的光滑粒子流法（kernel-broken smoothed particle hydrodynamics,KBSPH）,用于模拟地震条件下岩质边坡的裂纹扩展和变形破坏过程.在KBSPH中,提出一种改进的损伤框架,通过引入断裂标志来改进损伤粒子的核函数,使损伤粒子的虚拟应力键直接断裂,裂纹在断裂的应力键间生成,从而模拟岩石的裂纹扩展过程.在地震边界上采用了双层边界,将动力输入边界与黏滞边界分离.首先通过薄板振动实验验证KBSPH的动力特性.其次以单裂隙岩体单轴压缩试验验证KBSPH的断裂力学特性.最后模拟地震条件下多节理岩质边坡中裂纹扩展过程和动力响应.薄板振动实验验证了KBSPH的动力特性的准确性.单裂隙岩体单轴压缩试验,证明了KBSPH可以正确模拟预制裂隙尖端的翼型裂纹.通过对比以往数值模拟方法和现场案例,表明KBSPH正确揭示了加速度放大效应以及地震条件下岩质边坡的裂纹扩展过程.KBSPH避免了传统算法的网格畸变,损伤粒子应力分量重新分配的问题,降低了编程难度,提高了运行速率,可为SPH在地震条件下岩石力学中的应用和理解岩石断裂机理提...     

Effective elastic properties of the double‐periodically cracked plates

In this paper, the interaction of double‐periodical cracks is accurately solved based on the isolating analysis procedure, superposition principle, pseudo‐traction method, Chebyshev polynomial expansion and crack‐surface collocation technique. The jump displacement crossing crack faces, the average additional strain and therefore the effective compliance of the double‐periodically cracked plate are directly determined. The numerical results for axial‐symmetrically distributed double‐periodical cracks, general double‐periodical cracks with one collinear direction as well as two sets of double‐periodical cracks with same size and square distribution are given in this paper. And the partial typical numerical results are compared with the previous works. The analysis shows that the anisotropy induced by the general double‐periodical cracks is generally not orthogonal anisotropy. Only when the double‐periodical cracks are axial‐symmetrically distributed, is the anisotropy orthogonal. In this special cases, the effective engineering constants (consist of effective elastic modulus, the effective Poisson's ratio, the effective shear modulus) of cracked plate versus crack spacing, in the plane stress and plane strain conditions, respectively, are analysed. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

不同围压时含孔洞模型裂缝扩展的 连续—非连续数值模拟

为了有效地模拟连续介质向非连续介质的转化,发展了一种拉格朗日元方法、变形体离散元方法及虚拟裂纹模型耦合且考虑四边形单元沿对角线开裂的连续—非连续方法。利用该方法,模拟了不同围压时含孔洞模型的变形—开裂过程,统计了拉裂缝及剪裂缝区段数目,监测了一些单元的最大主应力。研究结果表明:当围压较小时,初始拉裂缝首先出现在孔洞的顶、底部,然后向模型的上、下端扩展,在初始拉裂缝的左、右两侧的拉应力集中区中产生远场拉裂缝,随后在孔洞的左、右两侧出现剪裂缝,最后,剪裂缝贯穿模型;当围压较大时,远场拉裂缝数量较少,未充分发展,远场拉裂缝与剪裂缝的发展阶段的界限不分明。含孔洞模型的最大承载力的下降是由于孔洞左、右两侧的剪裂缝向外扩展造成的。随着围压的增加,开始出现初始拉裂缝的时步数目增大,初始拉裂缝两侧的远场拉裂缝数目变少、出现变晚。      

切槽对TBM刀具破岩机制的影响研究

高压水射流与机械滚刀相联合破岩技术的出现,改变了传统隧道掘进机（tunnel boring machine,简称TBM）的作业方式。以高压水射流在滚刀两侧岩体切槽的破岩模式为研究对象,开展常截面滚刀压头贯入不同预切槽深度白砂岩板状试样的试验和数值模拟计算分析,对破裂后图像进行DIC分析,研究发现：切槽的存在,阻断了刀具贯入裂纹的拓展,使能量能够更加集中于压头下方的局部岩石块体,有利于形成“八”字形贯通裂纹,促进岩石的破碎;随着槽深增加,压头下方岩石内部的应力状态和力学响应分区逐渐过渡改变。槽深较大时,压头下方的力学响应区域在原有裂纹扩展区、弹性区之间增加了破坏过渡区,该区域内微裂纹被压密,区域内岩石存在较大变形,但未出现明显破坏;切槽后,滚刀压头下方的岩体破坏机制由无切槽试样挤压剪切为主导的径向裂纹拓展,演变为由刀具和切槽共同控制作用—拉伸剪切为主导的主裂纹扩展。     

A numerical method for the study of shear band propagation in soft rocks

This paper investigates the possibility of interpreting progressive shear failure in hard soils and soft rocks as the result of shear propagation of a pre‐existing natural defect. This is done through the application of the principles of fracture mechanics, a slip‐weakening model (SWM) being used to simulate the non‐linear zone at the tips of the discontinuity. A numerical implementation of the SWM in a computation method based on the boundary element technique of the displacement discontinuity method (DDM) is presented. The crack and the non‐linear zone at the advancing tip are represented through a set of elements, where the displacement discontinuity (DD) in the tangential direction is determined on the basis of a friction law. A residual friction angle is assumed on the crack elements. Shear resistance decreases on elements in the non‐linear zone from a peak value at the tip, which is characteristic of intact material, to the residual value. The simulation of a uniaxial compressive test in plane strain conditions is carried out to exemplify the numerical methodology. The results emphasize the role played by the critical DD on the mechanical behaviour of the specimen. A validation of the model is shown through the back analysis of some experimental observations. The results of this back analysis show that a non‐linear fracture mechanics approach seems very promising to simulate experimental results, in particular with regards to the shear band evolution pattern. Copyright © 2009 John Wiley & Sons, Ltd.     

压剪作用下裂隙扩展过程渗流与应力耦合模型研究

裂隙的剪胀特性及扩展演化规律对岩体的渗流特性具有重要影响。为揭示裂隙剪胀及扩展演化对岩体渗流的影响,基于残余强度提出了一种能较好描述岩石硬化-软化特性的全剪切本构关系;结合剪切变形与裂隙开度的关系,利用最小势能原理和立方定律,建立了压剪作用下考虑裂隙剪胀特性的渗流应力耦合模型;假定压剪作用下裂隙发生Ⅰ型扩展,提出了伴有翼型裂纹的渗流模型,该模型不仅考虑了岩石的剪胀特性,更反映了裂隙扩展过程渗流的演化规律。对不同裂隙粗糙度的剪切应力-位移曲线进行分析,全剪切本构模型表现出较高的拟合精度。在剪切应力-位移关系基础上,通过剪切渗流试验数据对压剪作用下渗流模型进行验证,结果表明,该模型能较好地描述岩体剪胀阶段渗透性演化规律。利用等效裂隙简化裂隙网络,并通过试验数据进行验证,证实了裂隙扩展过程渗流-应力耦合模型的准确性与适用性。     

页岩水力压裂过程的态型近场动力学模拟研究

水力压裂技术广泛使用于页岩气开采工程中。为了分析压裂过程中多裂缝扩展形成复杂裂缝网的机制,尝试将态型近场动力学理论引入页岩水平井水力压裂过程的力学建模与数值仿真,在物质点间相互作用力模型中加入等效水压力项以实现在新生裂缝面上跟踪施加水压力,建立了水力压裂过程的近场动力学分析模型。通过模拟页岩储层的水力压裂过程,可得到复杂的裂缝扩展路径、裂缝网络的形成过程以及裂缝扩展受射孔间距及页岩天然裂缝和层理的影响。研究结果表明:射孔间距过小会造成起裂干扰,使中心射孔的裂缝扩展受到抑制;在压裂压力一定的情况下适当增大射孔间距,可以显著增强页岩压裂形成裂缝网的能力;压裂过程中水平层理面可能张开形成水平裂缝,且天然裂缝会诱导形成更复杂的垂直裂缝。模型和方法可为页岩水力压裂过程和机制研究及工程实践提供参考。     

岩石剪切细观开裂演化与贯通机制分析

利用自主研发的煤岩剪切细观试验装置,以砂岩为研究对象,开展了不同饱和度数条件下的岩石剪切细观开裂演化与贯通机制试验研究,分析了砂岩剪切细观开裂演化过程和贯通机制,探讨了饱水系数对细观开裂和裂纹形态特征的影响。研究结果表明：剪切过程中,伴随着应力降,裂纹一般首先出现在剪切面中部,几条裂纹间断分布,距离较近的裂纹相互连通形成大裂纹,在应力继续下降的一瞬间,各裂纹连通形成贯通面;水的弱化作用影响了岩石的强度,使得试件底部出现较大的次级裂纹;饱水系数越大,分叉裂纹越多,使得试件的表面裂纹形态更加复杂,断裂面弯折段的数目越多,下端部次级裂纹越发育,整体损伤范围越大;细观上,局部独立裂纹贯通过程伴随着胶结颗粒岩桥的梁式旋转和弯曲折断,水的弱化作用,使得岩桥内部和外部微裂纹增多;随着饱水系数的增加,岩石剪切过程中出现的独立和次级裂纹的数目均呈增加趋势。     

A fully coupled element‐free Galerkin model for hydro‐mechanical analysis of advancement of fluid‐driven fractures in porous media

Hydraulic fracturing (HF) of underground formations has widely been used in different fields of engineering. Despite the technological advances in techniques of in situ HF, the industry uses semi‐analytical tools to design HF treatment. This is due to the complex interaction among various mechanisms involved in this process, so that for thorough simulations of HF operations a fully coupled numerical model is required. In this study, using element‐free Galerkin (EFG) mesh‐less method, a new formulation for numerical modeling of hydraulic fracture propagation in porous media is developed. This numerical approach, which is based on the simultaneous solution of equilibrium and continuity equations, considers the hydro‐mechanical coupling between the crack and its surrounding porous medium. Therefore, the developed EFG model is capable of simulating fluid leak‐off and fluid lag phenomena. To create the discrete equation system, the Galerkin technique is applied, and the essential boundary conditions are imposed via penalty method. Then, the resultant constrained integral equations are discretized in space using EFG shape functions. For temporal discretization, a fully implicit scheme is employed. The final set of algebraic equations that forms a non‐linear equation system is solved using the direct iterative procedure. Modeling of cracks is performed on the basis of linear elastic fracture mechanics, and for this purpose, the so‐called diffraction method is employed. For verification of the model, a number of problems are solved. According to the obtained results, the developed EFG computer program can successfully be applied for simulating the complex process of hydraulic fracture propagation in porous media. Copyright © 2016 John Wiley & Sons, Ltd.     

锚固的贯通节理岩体剪切破坏特性分析

为了研究节理对锚固岩体力学特征和失稳损伤演化的影响,采用对锚固贯通节理岩体进行室内剪切试验和PFC2D数值模拟的方法,研究不同节理倾角下锚固贯通节理岩体剪切性能的作用机制和破坏模式,研究结果表明:（1）随着节理倾角变化,贯通节理岩体呈现出不同的破坏形式,锚固贯通节理岩体的抗剪强度与剪切位移曲线并不是呈线性增长,而是呈"双驼峰"趋势。（2）锚固体系在剪切试验的过程中,节理面颗粒的接触方位角会发生一定程度的改变,主要集中在锚杆和节理倾角附近。（3）锚固体系在剪切试验的过程中,会因为颗粒间黏结键的断裂生成裂纹,裂纹数生成的越少,其抗剪强度越高,裂纹分为张拉裂纹和剪切裂纹,并且张拉裂纹的数量要远远大于剪切裂纹的数量。研究结论可用于实际工程破坏模式的预测和岩体工程稳定性评价。