岩石类材料疲劳破坏裂纹扩展分析的数值方法

在进行岩石类材料疲劳断裂破坏的数值分析时,将损伤力学将裂纹形成与裂纹扩展两个过程有机结合在一起。根据裂纹形成阶段的疲劳曲线（S-N）,描述疲劳发展的损伤演变方程,提出了疲劳裂纹扩展的数值计算方法。建立了扩展阶段中裂纹尺寸与载荷循环次数之间的关系,从而将裂纹萌生与扩展这两个独立过程纳入一个统一的理论体系。该方法与断裂力学结合计算出的疲劳寿命与试验值相吻合。     

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。     

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.     

裂缝型HTI介质中的弹性阻抗

在回顾封闭平行硬币状裂缝模型的基础上,将裂缝填充物性质、分布密度与背景介质的横纵波速度比,引入裂缝型水平横向各向同性介质纵波、转换横波弹性阻抗公式,并进行归一化弹性阻抗响应特征模拟。分析表明：裂缝介质弹性阻抗呈现方位各向异性,且随裂缝密度加大而增强;纵波、转换横波弹性阻抗在值域分布规律上具有较大区别;在典型砂岩介质的前提下,弹性阻抗差可以作为裂缝含气、含水指示因子定性地识别裂缝填充物性质。     

基于3D-ILC球体45º三维双内裂纹复合断裂研究

断裂力学是各领域基础科学,材料内裂纹相互作用是断裂力学的重要研究领域,但目前球体内裂纹相互作用研究成果较少。基于三维激光疲劳内裂纹（3D-ILC）技术,在对球体试样表面无任何损伤的情况下,制作三维平行纯内裂纹,开展45o倾角平行双内裂纹单轴压缩试验,对双内裂纹的裂纹扩展过程、应力双折射规律、断口特征、破坏形态、相互作用等多方面开展研究,进行含双内裂纹I-II-III型圆球断裂数值模拟,分析KⅠ、KⅡ、KⅢ分布规律,与试验相符。结果表明：（1）球体双内裂纹在单轴压缩下之间发生屏蔽作用,主裂纹面穿过两预制内裂纹;（2）翼型裂纹光滑区呈现I-II型裂纹断口特征,翼型裂纹侧面撕裂区呈现“矛状”III型裂纹特征;（3）基于M积分计算的KI、KII、KIII分析与基于断裂特征的I、II、III型裂纹类型分析一致。3D-ILC技术可用于球体内裂纹相互作用断裂试验研究,球体内裂纹试验与理论分析为脆性材料内裂纹扩展及相互作用研究提供试验与理论参考。     

DEM analyses of crack propagation in flawed rock mass under uniaxial compressionEI北大核心CSCD

A contact model for rock is established and imbedded into a DEM software by summarizing the bond granule tests. DEM simulation of uniaxial compression test on the pre-cracked Lac du Bonnet granite is performed, and then stress distributions are further analyzed and compared with the theoretical results. Different fracture criteria are employed to predict the crack initiation angles that are compared with theoretical ones. The results show that the failure modes obtained from DEM simulation are similar to experimental results, and stress distributions in DEM simulation are qualitatively similar to theoretical values. When the angle of pre-crack is small, the lateral stresses are compressive and tensile. The compressive strains concentrate at two edges, resulting in the tensile strains in the up-and downward cracks. When the angle of the pre-crack is large enough, the stress concentration is unobvious, leading to a discrepancy between the DEM and theoretical results. The crack extension angle resulting from uniaxial compression measured from DEM tests are in good agreement with those acquired from experimental tests. These angles are consistent with theoretical predictions by the maximum circumferential stress criterion and the maximum energy release rate criterion.     

Modeling soil desiccation cracking by analytical and numerical approaches

An energy approach is proposed as a complement to the stress approach commonly considered for investigating soil desiccation cracking. The elastic strain energies before and after crack initiation are estimated by both numerical and analytical solutions. The energy released by cracking is then compared with the fracture energy to discuss crack initiation conditions. This leads to combined energy and stress conditions for crack initiation following Leguillon's theory. An approximate analytical solution is derived from a variational formulation of the porous elastic body equations. A cohesive zone model and finite element code are used to simulate crack propagation in an unsaturated porous body. This analysis shows that the energy criterion is reached before the stress criterion, and this can explain unstable crack propagation at the beginning. The approximate analytical solution allows predicting correctly the crack depth and opening in its initiation stage.     

含裂隙岩体单轴压缩裂纹扩展机制离散元分析

将由室内试验总结得到的岩石微观胶结模型嵌入离散元软件,对Lac du Bonnet花岗岩石进行预制单裂隙单轴压缩试验DEM数值模拟,分析了压缩过程中裂隙试样中应力的分布,并与理论计算结果进行对比分析,同时对各种断裂判据中裂纹起裂角的预测值进行了适用性的对比分析。结果表明,离散元模拟试样破坏形态与试验结果相近;离散元分析得到的应力分布与理论解在定性上相似;当预制角度较小时,侧向应力都处于拉压状态;由于裂隙左右两端压应变的集中造成了裂隙上下面拉应变的产生,造成了裂隙周围特殊的应力分布;当裂隙角度较大时,应力集中现象已不明显,因而,理论值与试验值有偏差;在断裂判据中最大周应力准则和最大能量释放率准则得到的裂纹扩展角与室内试验与DEM结果中的数值较为吻合。     

含预制裂纹巴西盘试样破裂模式的数值模拟

利用岩石破裂过程分析系统（RFPA）软件, 进行了岩石含中心裂纹的巴西盘在单轴压缩荷载作用下破裂过程的数值模拟。数值模拟再现了含不同预制裂纹角度时巴西盘试样所表现出不同的破裂模式以及主裂纹的产生、扩展、贯通、次生裂纹的产生等过程,得到的破裂模式结果与有关文献中的实验结果十分吻合。除此以外,数值试验还能够给出在物理实验中不能观察到的应力场信息及岩石的破裂机制。     

剪应力作用下Ⅱ型平行节理扩展模式的分叉研究

利用伪力法考虑了剪应力作用下Ⅱ型平行节理之间的相互作用,提出利用节理的长度和间距之比, ,来确定平行裂纹发生分叉的条件。从理论上研究了2条,3条和任意多条平行节理在剪应力作用下的分叉。对于2条平行节理,当节理的长度和间距之比 大于0.816 497 5时,节理的扩展模式要发生分叉;对于3条平行节理,当节理的长度和间距之比 大于0.717 572 8时,节理的扩展模式要发生分叉;对于无穷多条平行节理,当节理的长度和间距之比 大于0.636 638 5时,节理的扩展模式要发生分叉。计算了2条到150条平行节理的分叉问题,结果表明节理数越大,节理发生分叉时节理的长度和间距之比越小。     

Crack propagation analysis with Galerkin boundary element method

This paper describes the application of symmetric Galerkin boundary element methods (SGBEM) for the analysis of a 2D crack propagation problem. The sub-domain SGBEM for crack problem is derived. The coefficient matrix is completely symmetric. Cohesive crack model is used to simulate crack propagation. The increment control method for crack propagation and the method for unknown crack propagation path have been derived for high-order element. Two-stage interpolation method called the ‘quasi-higher order element method’ (QHOEM) is then proposed to solve the double integrals. In the initial stage, it uses higher order elements to interpolate the field variables, and for the numerical integration involved, it further uses interpolation functions to decompose the higher order elements into lower order elements so that the existing analytical integration can be applied. A finite rectangular plate containing a centre crack growth and four-points bending beam problem have been analysed to check the accuracy of the proposed method. For actual application, a dam buttress with an edge crack has been analysed and the results are found to be in agreement with the other numerical and experimental results. Copyright © 2004 John Wiley & Sons, Ltd.     

裂隙含流体、气体各向异性介质波场数值模拟

由目前普遍被勘探地震工作者承认的Ｈｕｄｓｏｎ本构方程出发，首先讨论了裂隙含流体、气体各向异性介质一维二、三分量波动方程，然后用有限元方法进行了波场数值模拟。该研究有益于加深对地震波在裂隙含流体、气体各向异性介质中传播规律的认识。     

裂土裂隙演化过程试验研究

裂土的裂隙是影响其工程性质的重要因素。为研究土体裂隙在外界环境变化条件下的演化过程,设计了一套精确控制湿度的试验装置,再现了裂土在脱湿情况下裂隙产生、传播、扩展的过程。对试验结果进行了理论分析,总结了试验中裂土裂隙出现、传播、扩展的规律。研究结果有助于加深对土体裂隙变化物理过程的认识,为处理工程问题提供思路。     

底板导水裂隙带中含承压水裂隙的力学特性

华北煤田煤系地层的底部为含水丰富的奥陶系灰岩,该层灰岩与地表水系和煤系地层含水层存在着密切的水力联系。许多大型突水是采掘空间与含水层之间形成突水通道引起的。因此,分析开采工过程中底板岩体中含承压水裂隙的断裂力学特性具有重要意义。本文采用作者提出的数值方法分析了含高压水裂隙在开采过程中的断裂力学特性。假设裂隙面上作用着均匀水压力,考虑地应力的影响,采用断裂力学的叠加原理,分析了采煤工作面推进过程中含承压水裂隙的断裂力学特性,讨论了开采过程中底板承压水导升。结果表明:在工作面推进过程中,位于底板岩层且与含承压水岩层连通的裂隙,会在承压水水压力和扰动应力的共同作用下,产生破坏,导水裂隙带的高度会增加;这就增加了底板突水的危险性。     

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.     

基于3D-ILC含内裂纹孔口脆性固体断裂特性试验

孔口问题为力学领域中经典问题之一,也是岩土如隧洞、巷道等工程领域重要的问题之一。随断裂力学的发展,对含裂纹孔口问题的研究也不断深入。但是,以往研究多集中在二维问题或者含表面裂纹的孔口问题,含纯内裂纹的孔口问题研究报道较少。基于3D-ILC技术（对表面无任何影响的情况下,凭空生成任意参数的深埋内裂纹）,在含有孔口的脆性材料中生成内裂纹,开展单轴压缩试验,与无裂纹完整孔口试样试验结果及已有文献进行对比,并开展理论与数值模拟研究。结果表明：（1）3D-ILC与传统方法相比,裂纹特征更为真实,为解决断裂力学中的三维内裂纹问题奠定了基础;（2）完整孔口试样裂纹形态主要有主裂纹与八字形裂纹;（3）含内裂纹试样裂纹形态以内裂纹扩展为主,主要有翼裂纹、次生裂纹、反翼裂纹、反向次生裂纹、竖向扭曲裂纹与主裂纹6种;（4）含裂纹孔口试样最终的破坏荷载比无裂纹孔口试样平均低76.49%,起裂应力较无裂纹孔口试样平均低96.72%;（5）通过数值模拟对完整孔口试样、含主裂纹孔口试样、含内裂纹孔口试样的裂纹扩展进行定性分析,与试验结论一致。该研究结果为含三维内裂纹的孔口脆性材料的断裂理论研究提供了物理试验基础。     

不同级配珊瑚砂水泥胶结体的破坏行为分析

为探究不同级配的珊瑚砂水泥胶结体在静、动荷载下的破坏行为,利用落锤冲击试验机对不同级配的珊瑚砂水泥胶结体试样进行了一系列冲击试验,并结合静力压缩试验,综合分析了珊瑚砂水泥胶结体的力学行为及破坏形态。试验结果表明：珊瑚砂的级配区间越广,其水泥试块的抗压强度越大、抗冲击性能越强、受冲击破坏程度越小且破碎角逐渐递减;珊瑚砂水泥试块在不同种类的荷载作用下展现出不一样的破坏形态,区别于混凝土试块。在此基础上,建立了三维离散元模型,以模拟的应力-应变曲线与静力试验结果相吻合作为PFC细观参数的选取原则,并利用该细观参数对试块冲击试验进行数值重现。通过细观分析可以看出：从裂隙分布角度分析,随着级配区间越广、平均粒径的增大,均匀且分散的冲击微裂隙会越来越集中往某个方向发展,使得试块的裂缝数量减小、破损程度减轻。从系统黏结力角度分析,级配区间范围窄的试块内部黏结力较小且分布均匀,级配区间范围广的试块内部黏结力较大且分布不均匀。     

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.     

定面射孔新工艺对水力裂缝扩展影响研究

定面射孔技术是为了提高体积压裂改造效果而提出的一种新的射孔方案。根据岩石力学及流-固耦合理论,建立了定面射孔地层的三维弹塑性流固-耦合地应力模型,采用数值方法进行求解,结合最大拉应力准则,研究了定面射孔水力裂缝的起裂规律。经过大量计算发现：定面射孔条件下,裂缝首先在射孔面内的射孔眼起裂,然后射孔眼相互贯通而形成扇形裂缝面,增大了水力裂缝的波及体积及井筒的连通性;同一平面内两侧孔眼在中间孔眼上产生的附加应力降低了Y方向主应力而增大了X方向和Z方向主应力,导致正断层采用定面射孔时,起裂压力较大,起裂压力随射孔方位角的增大而降低,只有当射孔方位角大于60°时,定面射孔起裂压力低于螺旋射孔起裂压力;对于逆断层,射孔方位角越小,起裂压力越低,且均低于螺旋射孔起裂压力;减小射孔间夹角、增大射孔直径及深度均可降低起裂压力。     

堆石料单轴流变试验的颗粒流模拟

岩石断裂力学的亚临界裂缝扩展理论认为微裂缝扩展可导致岩石破碎,即岩石颗粒破碎具有时间效应。根据亚临界裂缝扩展理论,提出了考虑微裂缝扩展导致堆石颗粒破碎时间效应的数值流变模拟新方法,并进行了考虑颗粒不同典型破碎模式的单轴流变颗粒流数值试验。在对比数值与室内流变试验曲线的基础上,分析了数值流变过程中颗粒破碎情况与颗粒体内部结构发展过程等。研究成果表明,两种试验手段得到的堆石流变的发展趋势基本一致,由微裂缝扩展引起的颗粒延时破碎是堆石流变的主要原因之一,深化了对堆石料变形机制的认识。