Fatigue Behavior of Granite Subjected to Cyclic Loading Under Triaxial Compression Condition

A series of laboratory tests were performed to examine the fatigue behavior of granite subjected to cyclic loading under triaxial compression condition. In these tests, the influences of volumetric change and residual strain on the deformation modulus of granite under triaxial cyclic compression were investigated. It is shown that the fatigue behavior of granite varies with the tendency for volumetric change in triaxial cyclic compression tests. In the stress–strain space, there are three domains for fatigue behavior of rock subjected to cyclic loading, namely the volumetric compaction, volumetric dilation with strain-hardening behavior, and volumetric dilation with strain-softening behavior domains. In the different domains, the microscopic mechanisms for rock deformation are different. It was also found that the stress level corresponding to the transition from volumetric compaction to volumetric dilation could be considered as the threshold for fatigue failure. The potential of fatigue deformation was compared with that of plastic deformation. The comparison shows that rocks exhibit higher resistances to volumetric deformation under cyclic loading than under plastic loading. The influence of residual strain on the fatigue behavior of rock was also investigated. It was found that the axial residual strain could be a better option to describe the fatigue behavior of rock than the loading cycle number. A constitutive model for the fatigue behavior of rock subjected to cyclic loading is proposed according to the test results and discussion. In the model, the axial residual strain is considered as an internal state variable. The influences of confining pressure and peak deviatoric stress on the deformation modulus are considered in a term named the equivalent stress. Comparison of test results with model predictions shows that the proposed model is capable of describing the prepeak fatigue behavior of rock subjected to cyclic loading.     

颗粒物质在等比例应变加载下的分散性失稳模式

由地下水引起的静力液化可能是边坡失稳的隐含机制之一,松砂在不排水剪切条件下可能发生静力液化,密实的颗粒集合体在特定的应变路径下也会出现相似的现象,即试样整体发生急剧的失稳,应力状态尚处于峰值强度线以内。该种失稳模式称为分散性失稳,是为了强调失稳模式中没有出现应变局部化或者剪切带。采用连续-离散耦合分析方法,研究由不规则形状颗粒组成的密实集合体在等比例应变加载路径下的力学特性。根据Hill的材料失稳理论,当试样的应力增量 和应变增量 对应的2阶功 为负时,试样即发生不可逆的整体失稳破坏。以根据不同等比例应变路径得到 曲线为界,在 平面内将试样的应力状态分为剪缩区、剪胀-稳定区和剪胀-非稳定区,连接不同围压下试样发生分散性失稳时的应力状态形成失稳线发现,峰值强度线高于临界状态线,临界状态线高于失稳线。     

Compaction bands induced by borehole drilling

Drilling experiments in rock blocks subjected to pre-existing true triaxial far-field stresses simulating real in situ conditions often result in localized failure around the created borehole, which brings about the formation of borehole breakouts. In weakly bonded quartz-rich porous sandstones breakouts take the form of narrow tabular (slot-like) openings extending along a plane perpendicular to the maximum applied-stress direction. Scanning electron microscopes images of failed boreholes strongly suggest that these breakouts are compaction bands that have been emptied to different extents. The bands form as a result of the stress concentration accompanying the creation of the borehole. The evacuation of the compaction bands is brought about by the circulating drilling fluid flushing out debonded and often fragmented grains from within these bands (Haimson and co-workers, 2003–2007). The objective of this paper is to predict the conditions under which compaction bands are formed around boreholes. To this end, a new analytical model is formulated that enables prediction of the stress field around emptied and filled compaction bands, the various factors affecting the breakouts lengths, and their final length. Good agreement of the developed analytical model with experimental results obtained by Haimson and co-workers (Haimson and Klaetsch in Rock physics and geomechanics in the study of reservoirs and repositories, vol 284, pp 89–105, 2007; Haimson and Kovachich in Eng Geol 69:219–231, 2003; Klaetsch and Haimson in Mining and tunneling innovation and opportunity, University of Toronto press, pp 1365–1371, 2002; Sheets and Haimson in Proceedings, paper ARMA/NARMS 04-484, 2004) is demonstrated. The presented study is of practical relevance: boreholes are often drilled deep into weak porous sandstone formations for the purpose of extracting oil and gas, and the question of borehole stability is crucial. In addition, borehole breakouts are often used to estimate the state of stress in the Earth’s crust, and our new formulation will help improve these estimates.     

真三轴应力条件下钻孔围岩塑性区及增透半径研究

深部岩体处于三维应力场中受开挖扰动影响钻孔、巷道围岩处于明显的真三轴应力状态。钻孔抽采技术是煤矿广泛用于瓦斯治理的重要措施,钻孔周围塑性区是瓦斯流动的优质通道,研究钻孔围岩塑性区特性对于抽采钻孔的优化布置至关重要。为研究钻孔围岩的塑性区特性,基于广义平面应变理论分析围岩应力分布,比较几种常用强度准则（MC、Mises、D-P、MLC、SMP）的适用性和精确性,对比试验结果表明,MLC准则能较好地表征岩石的真三轴强度特性。基于MLC准则推导了围岩塑性区半径公式,分析偏应力、中间主应力、岩石内摩擦角、岩石黏聚力和钻孔半径对增透半径的影响,结果表明,增透半径随着偏应力的增大而增大,随中间主应力的增加先减小后增大,随岩石内摩擦角、岩石黏聚力的增加而逐渐减小,随钻孔半径的增加而线性增大。研究结果可为实际工程中巷道支护、煤层瓦斯抽采等技术的参数设计等提供重要参考。     

软泥岩井眼弹塑性变形的拉格朗日元法计算

首次将大变形原理引入井眼及其围岩弹塑性变形计算,应用拉格朗日元法对塑性泥页岩地层的井眼缩径问题进行分析求解。拉格朗日元法能够计算材料非线性和几何非线性问题,采用常用的摩尔-库仑强度准则对所选择的计算模型进行拉格朗日元分析计算,求解出井眼的收缩变形、井眼围岩位移场分布以及井眼围岩塑性区的分布规律。      

Mechanical properties and permeability evolution of gas-bearing coal under phased variable speed loading and unloading

It is of great significance for the analysis and prediction of coal-gas outburst disasters to understand the mechanical properties and permeability evolution of coal and rock under conditions of stope stress evolution. In this study, mechanical tests were conducted on gas-bearing coal under four stress paths, including conventional triaxial compression (CTC), phased variable speed triaxial compression (PVSTC), unloading confining pressure (UCP), and phased variable speed unloading confining pressure (PVSUCP), simultaneously measuring the permeability in mechanical tests. The mechanical properties and permeability evolutions in gas-bearing coal under four different stress paths were compared. The obtained results show that the deviatoric stress-strain curves of gas-bearing coal under four stress paths could be divided into five stages: compaction, linear elasticity, plastic deformation, stress drop, and residual stress stage. The permeability-strain curves under four stress paths could also be divided into five stages: fast drop, slow decrease, slow increase, sharp increase, and slowed growth. Compared to the CTC conditions, the peak strain and strength of coal under PVSTC conditions increased. Furthermore, the stress drop and energy release under PVSTC were more intense at the moment of instability failure. Compared to both loading paths, the coal was damaged more rapidly under unloading paths and the damage was stronger. Additionally, among both unloading paths, the time required for the failure of coal under PVSUCP was shorter than that under UCP, while the damage under PVSUCP was stronger. The strength characteristics of the gas-bearing coal under PVSTC and PVSUCP still met the Mohr–Coulomb criterion. This preliminary study has guiding significance for the understanding of the co-occurrence mechanisms of coal-gas outburst disasters.     

高静载条件下受频繁动力扰动时蛇纹岩动力学特性研究

基于改进的分离式霍普金森压杆（SHPB）岩石动静组合加载试验系统,进行了在不同静力轴压条件下受频繁动力扰动作用的动力学试验,研究蛇纹岩在高静载下受频繁冲击扰动过程中的动态变形特性、动态峰值应力和应变、能量变化规律和岩石破坏模式等动力学特性。研究结果表明：高静载条件下受频繁冲击扰动作用时,在动态峰值应力前,动态应力与应变呈正相关关系,而在动态峰值应力后,出现变形回弹和不回弹两种现象;随着动力扰动次数的增加,岩石动态峰值应力减小、动态峰值应变增大、动态变形模量减小、岩石由释放能量向吸收能量方向转化;随着预加静力轴压的增大,单次冲击过程中岩石损伤加剧,岩石破坏需要的扰动冲击次数减少,同时岩石由拉伸破坏模式向压剪破坏模式转变,破坏块度由小变大、均匀度降低。试验结果对揭示深部岩体承受高地应力和频繁开挖爆破等动力扰动作用下的破坏机制具有重要意义,同时为工程实际中通过调整围岩静应力状态和爆破以提高围岩长期稳定性的可行性提供了室内试验支持。     

煤岩两体模型变形破坏数值模拟

采用拉格朗日元法,在弹性岩石与弹性-应变软化煤体所构成的平面应变两体模型的上、下端面上不存在水平方向摩擦力条件下,模拟了模型的破坏过程、岩石高度对模型及煤体全程应力-应变曲线、煤体变形速率、煤体破坏模式及剪切应变增量分布的影响。结果表明,当模型的全程应力-应变曲线达到峰值时煤体内部的剪切带图案已经十分明显,在模型的应变硬化阶段,煤体中的应变局部化可视为模型失稳破坏的前兆,随岩石高度的增加,模型应力-应变曲线的软化段变得陡峭,这与单轴压缩条件下的解析解在定性上是一致的;煤体应力-应变曲线的软化段变得平缓,煤体消耗能量的能力增强;弹性阶段煤体的变形速率降低;煤体内部的剪切应变增量增加。煤体应力-应变曲线的软化段的斜率、弹性阶段煤体的变形速率、煤体内部的剪切应变增量及塑性耗散能都受岩石高度的影响,说明了岩石几何尺寸对煤体的影响(煤岩相互作用)是不容忽视的。     

冻融循环作用下泥质白云岩力学特性及损伤演化规律研究

针对饱水状态下的泥质白云岩,采用BCD–218 C低温数控恒温箱、WDW3100型微机控制电子万能试验机进行不同冻融循环状态下的单轴压缩试验,对其在单轴状态下应力-应变曲线变化特征以及抗压强度、峰值应变、弹性模量、泊松比的变化规律进行了分析。在现有的损伤力学理论基础上,引入斜率增大趋势系数,建立了以冻融循环次数和应变为控制变量的本构模型。结果表明,在冻融循环过程中,单轴抗压强度、峰值应变、弹性模量参数呈指数下降趋势,泊松比呈线性增加的趋势;受冻融循环的影响,应力-应变全过程曲线在第一阶段后出现短暂的线形平缓阶段,具有岩石局部滑移现象;岩石破坏形态从脆性向延性转化,具有峰前塑性硬化和峰后应变软化等行为特征。理论本构模型与试验结果相符合。     

Formation stability after hydraulic fracturing

This paper investigates stress changes resulting from fracturing in a weak formation and estimates the reduced risk of formation failure. The analysis is based on fracture propagation and closure of a plane strain elasto–plastic fracture. It is shown that during fracture propagation the area near the fracture tip undergoes plastic deformation, with the result that the in situ stresses there are significantly reduced from the original compressive state. The stress relief is driven by the reduction of the minimum in situ stress and the consistency condition which requires the stress state to remain on the yield or failure envelope. After fracture closure, due to permanent deformation the stress state does not return to its original state, as in the case of elastic material. The risk of formation failure, which is quantified with the introduction of a yield factor, is significantly reduced after fracturing and closure. The residual width from plastic deformation results in a non-uniform closure stress on proppant with higher values near the tip and lower value near the wellbore which is detrimental to the stability of proppant. The closure stress becomes more uniform with increasing fracture length. Copyright © 1999 John Wiley & Sons, Ltd.     

A fully implicit and consistent finite element framework for modeling reservoir compaction with large deformation and nonlinear flow model. Part I: theory and formulation

Reservoir depletion results in rock failure, wellbore instability, hydrocarbon production loss, oil sand production, and ground surface subsidence. Specifically, the compaction of carbonate reservoirs with soft rocks often induces large plastic deformation due to rock pore collapse. On the other hand, following the compaction of reservoirs and failure of rock formations, the porosity and permeability of formations will, in general, decrease. These bring a challenge for reservoir simulations because of high nonlinearity of coupled geomechanics and fluid flow fields. In this work, we present a fully implicit, fully coupled, and fully consistent finite element formulation for coupled geomechanics and fluid flow problems with finite deformation and nonlinear flow models. The Pelessone smooth cap plasticity model, an important material model to capture rock compaction behavior and a challenging material model for implicit numerical formulations, is incorporated in the proposed formulation. Furthermore, a stress-dependent permeability model is taken into account in the formulation. A co-rotational framework is adopted for finite deformation, and an implicit material integrator for cap plasticity models is consistently derived. Furthermore, the coupled field equations are consistently linearized including nonlinear flow models. The physical theories, nonlinear material and flow models, and numerical formulations are the focus of part I of this work. In part II, we verify the proposed numerical framework and demonstrate the performance of our numerical formulation using several numerical examples including a field reservoir with soft rocks undergoing serious compaction.     

The Various Stress Paths Causing Deformation and Failure in Rocks

The rock deformation and failure tests are performed along various stress paths under true triaxial stress state. The experimental results have shown that the change of three principal stresses (the increase of the maximum principal stress, the decrease of the minimum principal stress, the decrease of the confining pressure and the increase or decrease of the intermediate principal stress ) can lead to deformation and failure in rocks. The strength, the deformability and the failure precursors of rocks are related with stress paths. Based on the results of the study, the problems of the stress path in rock engineering are discussed.     

Poro‐elasto‐plastic response of an unconsolidated formation confined with stiff seal rocks under radial injection

In this article, we evaluate geomechanics of fluid injection from a fully penetrating vertical well into an unconsolidated formation confined with stiff seal rocks. The coupled behavior of an isotropic, homogeneous sand layer is studied under injection pressures that are high enough to induce plasticity yet not fracturing. Propagation of the significant influence zone surrounding the injection borehole, quantified by the extent of the plastic domain in the elasto‐plastic model, is examined for the first time. First, a new fully coupled axisymmetric numerical model is developed. A comprehensive assessment is performed on pore pressures, stresses/strains, and failure planes during the entire transient period of an injection cycle. Results anticipate existence of five distinctive zones in terms of plasticity state: liquefaction at wellbore; two inner plastic domains surrounding the wellbore, where failure occurs along two planes and major principal stress is in vertical direction; remaining of the plastic domain, where formation fails along one plane and major principal stress is in radial direction; and a non‐plastic region. Failure mechanism at the wellbore is found to be shear followed by liquefaction. Next, a novel methodology is proposed based on which new weakly coupled poro‐elasto‐plastic analytical solutions are derived for all three stress/strain components. Unlike previous studies, extension of the plastic zone is obtained as a function of injection pressure, incorporating plasticity effects on the subsequent elastic domain. Solutions, proven to be a good approximation of numerical simulations, offer a huge advantage as the run time of coupled numerical simulations is considerably long. Copyright © 2016 John Wiley & Sons, Ltd.     

岩体变形和破坏的各种应力途径

在真三轴应力状态下进行了各种应力途径的岩石变形和破坏实验。实验表明,三个主应力的变化(最大主应力的增加,最小主应力的减小,围压的减小以及中间主应力的增加或减小)都能引起岩石变形和破坏。而且岩石的强度、延性和脆性、体积变化和破坏前兆等都与应力途径有关。据根试验结果探讨了岩体工程中的应力途径问题。     

Deformation Behavior of Chalk Studied Close to In Situ Reservoir Conditions

A laboratory test program, which simulated reservoir conditions of pressure and temperature, was conducted on outcrop and reservoir chalk samples of various porosities. All the samples experienced a stress path following uniaxial strain condition K ₀ that led to compaction failure, i.e. pore collapse. The experiments were loaded by depletion of pore pressure conducted under load controlled conditions. This depletion phase was followed by a creep period, where time-dependent deformation was monitored. The intention of creating such reservoir condition in these laboratory experiments was to gain knowledge of the nature of chalk compaction. Chalk is an important reservoir rock for the oil and gas industry with unique storage capability with porosities up toward 50%. However, this rock is also very weak which has resulted in significant reservoir compaction and in turn severe seabed subsidence and casing failure. Mapping of the mechanical behavior of chalk in terms of deformation is thus decisive for a proper understanding of these reservoirs. The results of this study show that chalk is indeed a rate-dependent material under laboratory loading conditions as time effects were revealed as the loading rate was varied. However, the results raise uncertainty about the importance of rate dependency for chalk under completely drained conditions. Further, such high-porosity chalk suffers for substantial plastic strains and obvious strain hardening. Indeed, a relation between deformation/porosity and hardening is proposed by the introduction of real-time modulus values. Time-dependent deformation, also called creep was influenced by the depletion phase, as consolidation or transient creep influenced the deformation response for as much as 175 h after a change in load. This indicates that transient creep is dependent on the stress history. However, observations suggest the existence of a universal mechanism for steady state creep, governed by neither the initial porosity nor the stress history or chalk type, which thus seems to be an independent strain contributor. Finally, time dependence is found on the K ₀ development for chalk tested at typically laboratory rates, which has been discussed as a reflection of the nature of the grain re-arrangement during failure and plastic deformation. Ultimately, such time dependence of the K ₀ may contribute to the understanding of stress path data deduced from field data.     

The relationship between the deformation mechanism and permeability on brittle rock

In order to study the relationship between the deformation mechanism and permeability on brittle rock, the curves of stress–strain and permeability–strain of brittle rock were analyzed, the results indicated that the permeability of brittle rock increased rapidly at the critical failure point due to the microstructure changed seriously during the compaction, elastic deformation, and progressive failure process. When the rock bridges or asperities on the internal structural plane were ruptured partly or completely after the peak stress, a sudden decrease in rock strength occurred and the peak permeability could be the maximum. The strain at the critical point and turning point on the stress–strain curve corresponded to that at the rapid increase point and the peak point on the permeability–strain curve according to the renormalization theory and curves of stress–strain and permeability–strain. In addition, the ratios could be described by mathematical expressions. The conclusions could be proved reasonably by the experimental studies and examples of statistical analysis.     

基于梯度塑性本构理论的岩样侧向变形分析(Ⅰ):基本理论及本构参数对侧向变形的影响

研究了岩样在单轴压缩条件下轴向应力．侧向或环向变形的全程曲线特征。基于考虑峰值剪切强度后微小结构之间相互影响和作用的梯度塑性理论，得到了由于剪切局部化而引起的侧向塑性变形。利用虎克定律描述了试件的弹性变形，得到了轴向应力．侧向变形全程曲线的解析解。在软化阶段，试件中部侧向变形及对靠近试件上端或下端部位的侧向变形并不相同。与轴向应力．应变曲线可能出现的回跳现象类似。试件中部轴向应力．侧向应变曲线也可能出现回跳现象。在应变软化阶段，与应力．侧向应变曲线相比，应力．环向应变曲线不容易发生回跳现象。若在试件内部出现多条剪切带，则应该以等效剪切带宽度替代本文中的剪切带宽度。随着剪切带倾角、内部长度参数的降低、剪切模量的增加及弹性模量的降低，轴向应力．侧向应变曲线越陡；甚至能出现弹性回跳。     

Material stability analysis of rock joints

For prediction of rockfalls, the failure of rock joints is studied. Considering these failures as constitutive instabilities, a second‐order work criterion is used because it explains all divergence instabilities (flutter instabilities are excluded). The bifurcation domain and the loading directions of instabilities, which fulfill the criterion, are determined for any piecewise linear constitutive relation. The instability of rock joints appears to be ruled by coupling features of the behavior (e.g., dilatancy). Depending on the loading parameters, instabilities can lead to failure, even before the plastic limit criterion. Results for two given constitutive relations illustrate the approach. Some given loading paths are especially considered. Constant volume (undrained) shear and τ‐constant paths are stable or not depending on the link between the deviatoric stress and strain along undrained paths, as found for soils. Some unstable loading paths are illustrated. Along these paths, failure before the plastic limit criterion is possible. The corresponding failure rules are determined. Copyright © 2012 John Wiley & Sons, Ltd.     

A model of strain localization in porous sandstone as a function of tectonic setting,burial and material properties; new insight from Provence (southern France)

The analysis of three cataclastic band sets from Provence (France) reveals that the band density, their conjugate angles, their ratio of shear displacement to compaction, and the amount of cataclasis within the bands differ and can be expressed as functions of tectonic setting and petrophysical properties. We identify (1) a dense and closely spaced network of shear-enhanced (reverse) compaction bands; (2) a regularly spaced less dense network of reverse compactional shear bands; and (3) a localized network of normal shear bands. The field data show that strain localization is favored in an extensional regime and is characterized by shear bands with a large shear to compaction ratio and a small conjugate band angle. In contrast, distributed strain is favored in a contractional regime and is characterized by compactional bands with a low ratio of shear to compaction and a large conjugate band angle. To explain the mechanical origin of this strain localization, we quantify the yield strength and the stress evolution in extensional and contractional regimes in a frictional porous granular material. We propose a model of strain localization in porous sands as a function of tectonic stresses, burial depth, material properties, strain hardening and fluid pressure. Our model suggests that stress reduction, inherent to extensional regime, favors strain localization as shear bands, whereas stress increase during contraction favors development of compactional bands.     

砂岩三轴循环加卸载条件下的渗透率研究

渗透率是地下工程的流-固耦合分析中的一个关键因素。对多孔红砂岩进行了三轴压缩试验,在不同变形阶段实施了轴向应力循环加卸载,并在试验全过程中测量轴向渗透率,得到了试样破坏全过程的渗透率演化规律。从平均应力和循环加卸载对渗透率的影响等两方面进行了深入分析,结果表明,（1）随着轴向变形的增加,初始压密阶段和弹性变形试样渗透率均匀减小;进入塑性变形阶段,渗透率与轴向变形的曲线逐渐趋于水平,低围压条件下渗透率略有增加。（2）轴向加载使骨架颗粒被压缩,引起孔隙减小,造成渗透率减小;采用经验公式定量描述了渗透率和平均应力之间的关系。（3）轴向应力循环加卸载过程中,骨架颗粒的不可恢复变形引起渗透率产生不可恢复现象。（4）峰值后渗透率只发生少许突跳,说明对于多孔砂岩,孔隙和裂隙对渗透率的影响相当,且渗透率的突跳程度随着围压的升高而降低。