一种基于弹性应变能的裂隙岩体等效弹性模量评价方法

基于线弹性断裂力学裂隙面张开位移及剪切位移理论公式,考虑裂隙存在常法向和常切向刚度情况,研究了含单个裂隙岩体加载过程中由于裂隙存在而附加的弹性应变能。基于应变能等效方法并假设两种裂隙变形模型--非均匀变形模型和均匀变形模型,研究了二维非贯通裂隙岩体的等效杨氏模量和等效剪切模量解析表达式。研究结果表明,对于贯通裂隙规则分布情况,均匀变形模型得到的解析解与Amadei等的结果一致;对于非贯通裂隙正态分布情况,考虑裂隙相互作用的非均匀变形模型解明显低估裂隙岩体的等效杨氏模量和等效剪切模量,而考虑裂隙相互作用的均匀变形模型解与有限元数值解的偏差在10%以内。得到的解析表达式在一定条件下可以作为裂隙岩体等效弹性模量评价方法之一。     

Propagation of a shear crack in a compressed plane with a circular hole

The problem of the equilibrium of a plane with a circular hole and a shear crack is considered to model failure of an excavation (borehole or circular opening) in rocks weakened by discontinuities (planes of weakness). It is assumed that sliding occurs in a part of the plane of weakness when the Mohr–Coulomb friction criterion is satisfied due to the stress redistribution caused by the excavation. The method of singular integral equations is employed to solve the boundary value problem. Geomechanical problems concerning borehole breakout and rockburst caused by fault-opening interaction are discussed. © 1998 John Wiley & Sons, Ltd.     

Mesoscale numerical study on the evolution of borehole breakout in heterogeneous rocks

Inherent heterogeneity of a rock strongly affects its mechanical behavior. We numerically study the mechanisms governing the initiation, propagation, and ultimate pattern of borehole breakouts in heterogeneous rocks. A two-dimensional finite element model incorporating material heterogeneity is established to systematically examine the effects of several key factors on borehole failure, including borehole diameter, far-field stress, and rock heterogeneity. The inherent heterogeneity of a rock is explicitly characterized by prescribing the rock mechanical properties of mesoscale elements statistically obeying the Weibull distribution. Elastic damage mechanics is used to represent the constitutive law of the mesoscale element. We find that borehole diameter reduction remarkably changes the crack failure from tensile to shear and elevates the critical hydrostatic pressure. Far-field stress anisotropy strongly affects the shape of the borehole breakout. Rock heterogeneity dictates the location of the preferred crack under the hydrostatic stress, which leads to local stress concentration, and determines the types of breakouts around the borehole. Our findings facilitate in-depth understanding of the classic borehole stability problems in heterogeneous rocks.     

Borehole instability in high-porosity Berea sandstone and factors affecting dimensions and shape of fracture-like breakouts

Stress-induced breakouts in vertical boreholes are failure zones caused by excessive compressive stress concentration at the borehole wall along the springline of the least horizontal far-field stress. Wellbores are sometimes drilled into aquifers or oil reservoirs that are weak, poorly consolidated, and highly porous sandstone formations, which are often conducive to breakout formation. Breakouts are an expression of borehole instability and a potential source of sand production. On the other hand, the breakout phenomenon can be used advantageously in obtaining an estimate of the in situ stress condition. The average orientation of breakouts, as identified by borehole geophysical logging, is a reliable indicator of in situ stress directions. It has also been suggested that breakout dimensions could potentially be used as indicators of in situ stress magnitudes. The research reported here has concentrated on the unique type of breakouts observed for the first time in high-porosity Berea sandstone. Drilling experiments in rock blocks subjected to critical far-field true triaxial stress regimes, simulating in situ conditions, induced breakouts that were unlike the ‘dog-ear’ ones previously observed in granites, limestones, and low-porosity sandstones. The newly observed breakouts were thin, tabular, and very long, resembling fractures that counterintuitively extended perpendicular to the maximum principal stress. We found that a narrow zone ahead of a fracture-like breakout tip underwent apparent localized grain debonding and compaction. In the field, such zones have been termed ‘compaction bands’, and are a source of concern because in oil fields and aquifers they constitute curtains of low permeability that can impede the normal flow of oil or water. In order to determine whether a correlation exists between fracture-like breakouts and in situ stress, we conducted several series of tests in which the minimum horizontal and vertical stresses were held constant and the maximum horizontal stress (σ_H) was increased from test to test. These tests showed strong dependence of the breakout length on far-field stress, signaling that potentially the ability to assess fracture-like breakout length in the field could be used to estimate in situ stress magnitudes in conjunction with other indicators. Another series of tests revealed that breakout length increased substantially when borehole diameter was enlarged. This result suggested that in the field, where wellbore size is considerably larger, fracture-like breakout could extend to sizable distances, creating a sand production hazard. Two series of tests, one to evaluate the effect of drill-bit penetration rate, and the other to verify the drilling-fluid flow rate effect on breakout formation and dimensions yielded inconsistent results and showed no unique trends. Remarkably, fracture-like breakouts maintained a consistent narrow width of about 5–10 grain diameters, irrespective of the test conditions. This characteristic supports the suggestion that fracture-like breakouts are emptied compaction bands.     

水-力耦合条件下砂岩声发射和能量耗散的颗粒流模拟

对砂岩进行水-力耦合三轴试验和声发射实时监测,得到水-力耦合作用下砂岩应力-应变曲线和声发射数据。根据试验条件和结果建立离散元颗粒流的水-力耦合双轴模型,研究砂岩声发射和能量演化规律。通过定义耗散能,用耗散能增量较好地诠释了声发射的发展规律。利用微破裂源可追踪声发射局域源,得到水-力耦合条件下的声发射空间分布和裂纹类型。研究表明：（1）孔隙水压力对颗粒的拖拽力削弱了颗粒间的平均接触力,从而降低了砂岩整体强度。（2）孔隙水压力反映出对弹性应变能有一定程度的反复“贮存和清空”作用,造成声发射能量相对离散和峰后的应力波动。（3）渗透压的存在提升了总输入能的耗散效率,降低了总输入能和弹性应变能,须综合考虑总输入能（弹性应变能）和耗散效率才能确定累计耗散能。（4）裂纹分布表现为可能出现与主剪切带呈一定夹角的伴生裂隙带,且受水-力梯度影响,进水端比出水端更密集。（5）张拉裂纹与剪切裂纹的比值于峰值强度处显著增加,峰后趋于稳定。     

Stereology-based fabric analysis of microcracks in damaged granite

Crack-related fabric analyses were carried out in terms of crack tensors using Inada granite deformed inelastically in a triaxial vessel up to post-failure, focusing on the fabric changes during brittle failure. Complementarily, numerical simulation tests were conducted to determine the representative volume element (RVE) required for crack surveying. Numerical simulation tests show that the window size for crack surveying should be at least six times the mean trace length in order to obtain a statistically meaningful crack tensor. A larger window is needed to estimate the distribution of crack radii. In quartz, cracks grow preferentially parallel to the major loading axis. Crack tensors in quartz can provide a measure of damage reflecting inelastic deformation under differential stress in past geological events. During the first stage of inelastic deformation, the number density of cracks decreases with a rather sharp increase in crack diameters. This happens because pre-existing cracks in intact rock join together to make longer cracks. However, the density remains almost constant during the second stage of loading from 90% to 100% of the peak stress. The crack diameter gradually increases due to the stable propagation of cracks. When granite is further deformed beyond the peak stress, the number density decreases again while sharp increases in crack diameters appear as a result of the forking and coalescence of cracks. It is also suggested that load-normal grain boundary cracks are generated as a result of the rolling and sliding of disintegrated blocks in the post-failure stage.     

基于CT-CA的天然裂隙岩石受拉破坏特性研究

岩石内部存在的裂隙、孔洞等天然损伤对岩石的力学性能和破坏过程有重要影响,依据细胞自动机理论结合CT无损识别技术实现了含天然裂隙岩石在劈裂条件下裂纹扩展和贯通全过程及其力学性能变化规律的研究。从裂隙砂岩的真实细观结构出发,构建了天然裂隙岩石的数值计算模型,运用CASRock数值计算软件完成了含不同裂隙倾角的砂岩劈裂破坏的数值试验,分析了裂隙倾角对砂岩的力学特性、裂纹扩展过程及能量演化的影响规律。研究表明:(1)天然裂隙砂岩的抗拉强度与裂隙倾角密切相关,随着裂隙倾角的增加,其抗拉强度呈现先减小后增加的趋势;(2)裂隙起裂于天然裂隙尖端,当裂隙倾角0°≤θ<48°时,岩样的破坏是由错开型裂纹引起,裂纹沿着与天然裂隙近垂直方向扩展;当裂隙倾角48°≤θ<94°时,岩样的破坏是由张开型裂纹引起,裂纹沿着与天然裂隙近平行方向扩展;(3)劈裂过程中裂纹尖端应力场存在拉应力区和压应力区,拉应力造成翼裂纹由天然裂隙尖端沿加载端方向萌生扩展,而压应力则引发次生裂纹沿天然裂隙方向扩展;(4)含天然裂隙砂岩劈裂破坏过程能量演化可划分为4个阶段,随裂隙倾角的增大,峰值点处的总能量密度、弹性能密度先缓慢减少再迅速增加,但对岩样耗散能影响不大。     

Fracture-like borehole breakouts in high-porosity sandstone: Are they caused by compaction bands?

We induced borehole breakouts in a 25%-porosity Berea sandstone by drilling 23 mm diameter holes into 152×152×229 mm blocks subjected to constant true triaxial far-field stresses. BSen5 consists of large quartz grains (0.5 mm) cemented mainly by sutured grain contacts. Breakouts in BSen5 are demonstratively different from those observed in granite, limestone, and lower porosity sandstones. Rather than the typically short ‘V’-shaped breakouts, BSen5 displays long fracture-like tabular slots, which counterintuitively, develop orthogonally to σ_H. These breakouts originate at the points of highest compressive stress at the borehole wall, along the σ_h spring line. Micrographs of BSen5 breakouts show an apparent compaction band created just ahead of the breakout tip in the form of a narrow layer of grains that are compacted normal to σ_H. The compaction band characteristics are nearly identical to those observed in the field. The mechanism leading to fracture-like breakouts is seen as anti-dilatant, and related directly to grain debonding and porosity reduction accompanying the formation of the compaction band. Some compacted grains at the borehole wall are expelled as a result of the line of tangential loading and the radial expansion of adjacent grains. The circulating drilling fluid flushes out the remaining compacted loose grains at the borehole-rock interface. As the breakout tip advances, the stress concentration ahead of it persists, extending the compaction band, which in turn leads to additional grain removal and breakout lengthening. By extrapolation, this process may continue for considerable distance (at least several times the wellbore diameter) in field situations, leading potentially to substantial sand production.     

含预制单裂隙花岗岩的真三轴单面临空岩爆试验研究

通过开展含预制单裂隙花岗岩的真三轴单面临空岩爆试验,并利用高速摄像系统和声发射（acoustic emission,简称AE）系统监测岩爆过程,探究了不同产状裂隙岩石的破坏模式、强度变形和声发射演化特性,分析了裂隙产状与岩爆过程及弹射动能之间的关系,对比了含裂隙岩石岩爆发生机制与无裂隙完整岩石的差异。有关力学特性的分析表明,随着裂隙倾角的减小,岩样破坏模式大体呈现由“内剪外劈”向“Z型斜剪”变化的趋势,裂隙对岩石强度的削弱作用不断增大。当裂隙倾角小于30°时,岩石峰值应力普遍仅为完整岩样的一半左右;小倾角裂隙的长度越大,岩样岩板劈裂现象变得显著,形成岩爆坑略微变大,且强度折减幅度越大,峰值轴向应变相应变小;裂隙位置向临空面靠近会加剧岩板的劈裂效应,塑性阶段普遍会产生较大变形并萌生大量裂纹,当裂隙已出露且切断临空面将不易形成岩爆坑。有关岩爆过程及弹射动能的分析表明,随着裂隙倾角的减小,岩样弹射动能呈现先显著降低后小幅回升的变化规律,30°倾角为转变拐点;岩样内部裂隙距临空面越近,裂隙岩样的弹射动能越小;树脂填充裂隙使得岩样弹射动能极大提升,而水泥填充的则无明显提升。有关声发射特征的分析表...     

Evolution of Rock Cracks Under Unloading Condition

Underground excavation normally causes instability of the mother rock due to the release and redistribution of stress within the affected zone. For gaining deep insight into the characteristics and mechanism of rock crack evolution during underground excavation, laboratory tests are carried out on 36 man-made rock specimens with single or double cracks under two different unloading conditions. The results show that the strength of rock and the evolution of cracks are clearly influenced by both the inclination angle of individual cracks with reference to the unloading direction and the combination geometry of cracks. The peak strength of rock with a single crack becomes smaller with the inclination angle. Crack propagation progresses intermittently, as evidenced by a sudden increase in deformation and repeated fluctuation of measured stress. The rock with a single crack is found to fail in three modes, i.e., shear, tension–shear, and splitting, while the rock bridge between two cracks is normally failed in shear, tension–shear, and tension. The failure mode in which a crack rock or rock bridge behaves is found to be determined by the inclination angle of the original crack, initial stress state, and unloading condition. Another observation is that the secondary cracks are relatively easily created under high initial stress and quick unloading.     

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。     

Microcracks in granite cores from the EPS-1 geothermal drill hole, Soultz-sous-Forêts (France): paleostress directions, paleofluids and crack-related Vp-anisotropies

For the modelling of Hot Dry Rock systems the interactions between macrofractures, prominent microcrack sets and the in situ stress field is of fundamental importance. In this study complete 3D analyses of microcrack orientations were carried out on granitoid samples from the Soultz geothermal borehole (EPS-1). The crack population is dominated by healed cracks in quartz forming three orthogonal sets (I, II, III) with strong preferred orientation, which probably result from superposition of internal thermal stresses during cooling and external tectonic stresses. The inferred orientation of paleo-σ_H is NE–SW. Based on the microthermometry of secondary fluid inclusions it can be assumed that cyclic crack/healing events occurred at P/T conditions roughly ranging between 1 and 2?kbar and 200–400?°C. A younger generation of open cracks in quartz which coincide with macroscopic fractures can be correlated with the Tertiary N–S direction of σ_H. The distribution of P-wave velocities (Vp) was measured by using the pulse transmission technique in 132 propagation directions at confining pressures up to 200?MPa. These Vp data and their variation with confining pressure are a suitable tool for detecting prominent crack patterns and to estimate the crack-controlled in situ properties. The observed bulk Vp anisotropy roughly reflects the composite microcrack fabric and the relative importance of individual sets. It can be assumed that the prominent crack sets represent planes of weakness and hence may cause a mechanically anisotropic behaviour dependent on their orientation with respect to the recent in situ stresses.     

Inference of in situ stress from thermoporoelastic borehole breakouts based on artificial neural network

The determination of in situ stresses is very important in petroleum engineering. Hydraulic fracturing is a widely accepted technique for the determination of in situ stresses nowadays. Unfortunately, the hydraulic fracturing test is time-consuming and expensive. Taking advantage of the shape of borehole breakouts measured from widely available caliper and image logs to determine in situ stress in petroleum engineering is highly attractive. By finite element modeling of borehole breakouts considering thermoporoelasticity, the authors simulate the process of borehole breakouts in terms of initiation, development, and stabilization under Mogi-Coulomb criterion and end up with the shape of borehole breakouts. Artificial neural network provides such a tool to establish the relationship between in situ stress and shape of borehole breakouts, which can be used to determine in situ stress based on different shape of borehole breakouts by inverse analysis. In this paper, two steps are taken to determine in situ stress by inverse analysis. First, sets of finite element modeling provide sets of data on in situ stress and borehole breakout measures considering the influence of drilling fluid temperature and pore pressure, which will be used to train an artificial neural network that can eventually represent the relationship between the in situ stress and borehole breakout measures. Second, for a given measure of borehole breakouts in a certain drilling fluid temperature, the trained artificial neural network will be used to predict the corresponding in situ stress. Results of numerical experiments show that the inverse analysis based on finite element modeling of borehole breakouts and artificial neural network is a promising method to determine in situ stress.     

Formation of drying crack patterns in soils: a deterministic approach

Soils, as well as most of deformable multiphase porous materials, are likely to suffer from desiccation cracking, leading to the formation of regular crack patterns affecting their permeability. The ensuing crack spacing has often been related to a concept sometimes called “sequential infilling”: it is assumed that desiccation cracks are formed by successive generations. However, such a concept does not consider the pattern of a simultaneous crack formation at a given moment. Using our desiccation cracking test results and their numerical simulation, we propose a consistent explanation for the formation of desiccation crack patterns in soils. We show that the “sequential infilling” concept is suitable only when the position of the crack(s) clearly stems from the stress field. To derive an estimate of the desiccation crack spacing, the overall energy of the system needs to be considered. Statistical variability should be superimposed on the mean deterministic conditions discussed here.     

径向压缩下圆环砂岩样的力学特性研究

为了研究径向压缩下圆环试样孔壁处的应力特征,利用厚度为34 mm,外径为50 mm的完整圆盘及不同内径（8～30 mm）的圆环砂岩试样,在巴西劈裂试验中测量孔壁的应变变化,分析试样的力学特性。试验结果表明：圆环试样的峰值载荷随着内径的增大而逐渐减少。圆盘和内径较小的圆环试样达到峰值载荷时出现了失稳破坏,载荷迅速跌落：当内径大于 16 mm,圆环试样达到峰值载荷后,载荷略有下降,但是试样并没有出现失稳破坏,而是持续压缩一定时间后才破裂。圆环最弱部位拉应力不是材料参数,而是一个结构参数,且随圆环内径而变化,基于弹性理论的Hobbs公式不能用于计算岩石抗拉强度。孔壁岩石的破裂只能是达到拉伸变形极限才会破裂,不能以拉伸应力作为破坏指标。研究结果为理解岩石在压拉组合下的力学特征提供了参考。     

中国大陆科学钻主孔现今地应力状态

用钻孔崩落法确定了中国大陆科学钻探主钻孔5 047 m深度以上的现今地应力状态.由钻孔声波成像测井资料发现, 科学钻主钻孔在1 200 m深度以下出现了钻孔崩落现象.我们从1 216~5 047 m的深度范围内采集了143个钻孔成像测井图象资料, 对钻孔崩落椭圆长轴方位进行了统计, 结果表明崩落椭圆长轴平均方位为319.5°±3.5°, 最大水平主应力方位平均为49.5°±3.5°.利用崩落形状要素(崩落深度和崩落宽度) 以及岩石的内聚力和内摩擦角, 估算了1 269 m至5 047 m范围内52个深度上的最大和最小水平主应力的大小.结果表明, 在浅处1 216 m深度, 最大水平主应力为42 MPa, 最小水平主应力为30.3 MPa; 在深处5 000 mm深度, 最大水平主应力为160.5 MPa, 最小水平主应力为120 MPa; 地应力随深度近于线性增加.据岩石密度测井资料计算了各个深度上静负载应力.3个主应力的大小和方向反映出科学钻主孔位置的应力场处于走滑应力状态, 与临近地区地震震源机制解和其他方法得到的应力场一致.利用声发射法对岩心试件进行了声发射测量, 得到了最大水平主应力幅值, 并与崩落法测量结果进行了对比, 两者十分一致.      

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.     

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.     

类节理岩石直剪试验力学特性的数值模拟研究

节理岩体的剪切特性是主导岩体工程稳定性的关键因素。基于PFC2D离散元颗粒流程序,结合室内试验结果对比分析,选取合理的细观参数进行数值模拟,分别从细观角度研究了节理岩石的裂纹发展、能量转化及声发射现象等特性,从宏观角度研究了节理岩石的强度模型和破坏形态。结果表明：节理岩体主要呈现磨损和剪断两种破坏形态,不同的破坏形态对应不同的强度模型;随着剪切变形增加,岩体沿节理面发生破坏,弹性阶段以法向裂纹为主,而塑性阶段切向裂纹起主导作用,滑移区R、P裂纹贯通形成破碎带,节理面产生较大滑移;在应力达到峰值强度前,边界能主要转化为应变能,法向裂纹生成较多;越过峰值强度后,摩擦能快速增长,并伴随大量切向裂纹产生。与室内试验结果相比,PFC2D较好地模拟了节理岩体剪切力学特性,弥补了室内试验中无法进行细观特性研究的缺陷,对于节理岩体后期研究提供了一些参考。     

Simulation of drilling‐induced compaction bands using discrete element method

Rock failure is observed around boreholes often with certain types of failure zones, which are called breakouts. Laboratory‐scale drilling tests in some high‐porosity quartz‐rich sandstone have shown breakouts in the form of narrow localized compacted zones in the minimum horizontal stress direction. They are called fracture‐like breakouts. Such compaction bands may affect hydrocarbon extraction by forming barriers that inhibit fluid flow and may also be a source of sand production. This paper presents the results of numerical simulations of borehole breakouts using 3D discrete element method to investigate the mechanism of the fracture‐like breakouts and to identify the role of far‐field stresses on the breakout dimensions. The numerical tool was first verified against analytical solutions. It was then utilized to investigate the failure mechanism and breakout geometry for drilled cubic rock samples of Castlegate sandstone subjected to different pre‐existing far‐field stresses. Results show that failure occurs in the zones of the highest concentration of tangential stress around the borehole. It is concluded that fracture‐like breakout develops as a result of a nondilatant failure mechanism consisting of localized grain debonding and repacking and grain crushing that lead to the formation of a compaction band in the minimum horizontal stress direction. In addition, it is found that the length of fracture‐like breakouts depends on both the mean stress and stress anisotropy. However, the width of the breakout is not significantly changed by the far‐field stresses. Copyright © 2013 John Wiley & Sons, Ltd.