Modelling of anisotropic coal swelling and its impact on permeability behaviour for primary and enhanced coalbed methane recovery

Coal swelling/shrinkage during gas adsorption/desorption is a well-known phenomenon. For some coals the swelling/shrinkage shows strong anisotropy, with more swelling in the direction perpendicular to the bedding than that parallel to the bedding. Experimental measurements performed in this work on an Australian coal found strong anisotropic swelling behaviour in gases including nitrogen, methane and carbon dioxide, with swelling in the direction perpendicular to the bedding almost double that parallel to the bedding. It is proposed here that this anisotropy is caused by anisotropy in the coal's mechanical properties and matrix structure. The Pan and Connell coal swelling model, which applies an energy balance approach where the surface energy change caused by adsorption is equal to the elastic energy change of the coal solid, is further developed to describe the anisotropic swelling behaviour incorporating coal property and structure anisotropy. The developed anisotropic swelling model is able to accurately describe the experimental data mentioned above, with one set of parameters to describe the coal's properties and matrix structure and three gas adsorption isotherms. This developed model is also applied to describe anisotropic swelling measurements from the literature where the model was found to provide excellent agreement with the measurement. The anisotropic coal swelling model is also applied to an anisotropic permeability model to describe permeability behaviour for primary and enhanced coalbed methane recovery. It was found that the permeability calculation applying anisotropic coal swelling differs significantly to the permeability calculated using isotropic volumetric coal swelling strain. This demonstrates that for coals with strong anisotropic swelling, anisotropic swelling and permeability models should be applied to more accurately describe coal permeability behaviour for both primary and enhanced coalbed methane recovery processes.     

Comparison of alternative representations of hydraulic-conductivity anisotropy in folded fractured-sedimentary rock: modeling groundwater flow in the Shenandoah Valley (USA)

A numerical representation that explicitly represents the generalized three-dimensional anisotropy of folded fractured-sedimentary rocks in a groundwater model best reproduces the salient features of the flow system in the Shenandoah Valley, USA. This conclusion results from a comparison of four alternative representations of anisotropy in which the hydraulic-conductivity tensor represents the bedrock structure as (model A) anisotropic with variable strikes and dips, (model B) horizontally anisotropic with a uniform strike, (model C) horizontally anisotropic with variable strikes, and (model D) isotropic. Simulations using the US Geological Survey groundwater flow and transport model SUTRA are based on a representation of hydraulic conductivity that conforms to bedding planes in a three-dimensional structural model of the valley that duplicates the pattern of folded sedimentary rocks. In the most general representation, (model A), the directions of maximum and medium hydraulic conductivity conform to the strike and dip of bedding, respectively, while the minimum hydraulic-conductivity direction is perpendicular to bedding. Model A produced a physically realistic flow system that reflects the underlying bedrock structure, with a flow field that is significantly different from those produced by the other three models.     

层状岩体单轴和双轴压缩蠕变特性的数值试验

以绿片岩和大理岩组成的层状岩体为研究对象,采用FLAC3D对互层状岩体进行了单轴和双轴压缩蠕变试验的数值分析,在数值分析中考虑荷载方向与层理之间的几何关系、大理岩夹层的体积分数、应力水平等的影响。研究结果表明:单轴和双轴压缩条件下,随着夹层倾角由0°增加至90°,轴向和夹层倾斜方向的应变绝对值均呈先增大后减小的变化规律;随着大理岩夹层体积分数的增加,轴向压缩变形和2个侧向方向的膨胀变形量均有所减小。单轴压缩条件下,当轴向荷载方向垂直于层理时,轴向压缩变形均大于轴向荷载方向平行于层理时的轴向压缩变形;双轴压缩条件下,当轴向荷载方向垂直于层理、侧向荷载方向平行于层理时,轴向压缩变形最大,当轴向荷载方向平行于层理、侧向荷载方向垂直于层理时,轴向压缩变形最小。     

Predictions of large stress reversals in true triaxial tests on cross‐anisotropic sand

A rotational kinematic hardening constitutive model with the capability of predicting the behavior of soil during three‐dimensional stress reversals has been developed. An existing elasto‐plastic constitutive model, the Single Hardening Model, utilizing isotropic hardening serves as the basic framework in these formulations. The framework of the kinematic hardening model was discussed in a companion paper. The previously proposed cross‐anisotropic Single Hardening Model is added to the present kinematic hardening mechanism to capture inherent anisotropy of sands in addition to the stress reversals. This model involves 13 parameters, which can be determined from simple laboratory experiments, such as isotropic compression, drained triaxial compression and triaxial extension tests. The results from a series of true triaxial tests with large three‐dimensional stress reversals performed on medium dense cross‐anisotropic Santa Monica Beach sand are employed for comparison with predictions. Copyright © 2008 John Wiley & Sons, Ltd.     

二维粒状材料双轴压缩试验研究

为了研究粒状材料的各向异性力学行为与细观组构演化之间的关系,采用自主研发的双轴压缩试验系统,以圆形和椭圆形截面的金属棒状材料组成的二维堆积体为试验对象,对不同大主应力方向角?（沉积面与大主应力作用面的夹角）的试样进行了各向等压、常侧向压力、等p剪切3种应力路径试验,并通过分析试样在不同变形阶段的数字照片得到了其细观组构演化规律。发现对于椭圆形截面的试样存在一个卓越剪切方向,随剪应变增大,颗粒长轴呈现出向该方向偏转的趋势,并且在大变形条件下沿该方向形成剪切带;卓越剪切方向与沉积面方向关系不大,而与大主应力作用面方向夹角约为45°+ /2, 为残余内摩擦角;随卓越剪切方向与沉降方向夹角的不同,颗粒偏转程度的不同是导致剪胀特性和峰值强度各向异性的主要原因     

Constitutive analysis of the mechanical anisotropy of Opalinus Clay

This paper aims to analyse the anisotropic features of behaviour of Opalinus Clay using the theory of plastic multi-mechanisms. The results of triaxial tests conducted with different load levels and directions showed that the mechanical behaviour of this shale is cross-anisotropic. The stiffer samples are those in which the loading direction is parallel to the bedding plane. This indicates that the preconsolidation stress depends on the orientation of the load with respect to the fabric of Opalinus Clay. It is proposed to interpret the observed cross-anisotropy with an elastoplastic model based on four plastic strain mechanisms that may be successively mobilised depending on the loading direction. The predicted stress–strain responses vary according to the directions of the space as a result of the hardening process, depending on the number of plastic strain mechanisms that have been mobilised. The numerical predictions show overall good agreement with the experimental data in terms of deviatoric stress versus axial strain, demonstrating that multi-mechanism plasticity is a suitable constitutive tool for the interpretation of the mechanical anisotropy of this shale.     

Simulation of yielding and stress–stain behavior of shanghai soft clay

In this paper, a simple bounding surface plasticity model is used to reproduce the yielding and stress–strain behavior of the structured soft clay found at Shanghai of China. A series of undrained triaxial tests and drained stress probe tests under isotropic and anisotropic consolidation modes were performed on undisturbed samples of Shanghai soft clay to study the yielding characteristics. The degradation of the clay structure is modeled with an internal variable that allows the size of the bounding surface to decay with accumulated plastic strain. An anisotropic tensor and rotational hardening law are introduced to reflect the initial anisotropy and the evolution of anisotropy. Combined with the isotropic hardening rule, the rotational hardening rule and the degradation law are incorporated into the bounding surface formulation with an associated flow rule. Validity of the model is verified by the undrained isotropic and anisotropic triaxial test and drained stress probe test results for Shanghai soft clay. The effects of stress anisotropy and loss of structure are well captured by the model.     

各向异性弹黏塑性模型在ABAQUS中的研发

通过将Perzyna过应力理论与临界状态理论相结合,并引入Wheeler旋转硬化法则,提出一个能描述土体初始各向异性及应力诱发各向异性的三维弹黏塑性本构模型。模型考虑流变发生的下限,在三维应力空间,模型存在形状相似的静屈服面及动态加载面。采用缩放形式的幂函数。本构模型数值算法采用回映算法,借助ABAQUS软件UMAT子程序接口实现。并通过对三轴不排水蠕变试验的模拟,确定合适的积分步长。此后,分别对三轴不排水蠕变试验及常应变率三轴不排水剪切试验进行了模拟。模拟中通过设置不同参数值,可将模型退化为各向同性模型,并对这两种模拟结果进行了比较。模拟结果表明：(1) 对于三轴不排水蠕变,在低剪应力水平下,各向同性模型和各向异性模型模拟的结果相差不大,而在高剪应力水平下,各向异性模型模拟结果更接近试验结果;(2) 对于常应变率加载试验的模拟,模型合理反映了土体不排水强度随着加载速率的增大而增大现象。     

页岩各向异性特征的试验研究

为研究彭水页岩气区块储层的各向异性特征,开展了石柱县龙马溪组页岩的单轴和三轴压缩试验,分析了其力学特性、强度特征和破裂模式的各向异性,并揭示了其破坏机制的各向异性。结果表明：(1) 龙马溪组页岩具有明显的各向异性特征,弹性模量在平行层理方向最大,垂直层理方向最小,且围压的增加使其增加速率不断减小;0°、30°和60°、90°页岩的泊松比随围压的增加呈现出了相反的变化规律,这可能与页岩层理间孔隙和微裂缝的良好发育有关。(2) 相同围压下,0°试样强度最高,90°次之,30°最低,总体上呈现出两边高、中间低的U型变化规律,而不同角度的Hoek-Brown强度准则能较好地反映其强度的各向异性特征。(3) 页岩破裂模式的各向异性是由破坏机制的各向异性引起的,而强度的各向异性是由破坏机制的各向异性控制的。单轴压缩时,0°页岩为沿层理的张拉劈裂破坏,30°为沿层理的剪切滑移破坏,60°为贯穿层理和沿层理的复合剪切破坏,90°为贯穿层理的张拉破坏。三轴压缩时,0°为贯穿层理的共轭剪切破坏,30°为沿层理的剪切滑移破坏,60°和90°为贯穿层理的剪切破坏;页岩地层的层状沉积结构和层理间的弱胶结作用是破坏机制各向异性的根源。研究结果为水平井井壁的稳定性分析和水力压裂施工设计等提供了技术参考。     

复杂应力条件下土体各向异性及其建模思路

由于加荷方式不同,土体在复杂应力状态下在各主应力方向上应力-应变关系表现出显著应力各向异性,在常规三轴试验基础上,采用经典弹塑性理论各向同性土体模型对此不能合理描述。通过真三轴试验,总结应力各向异性柔度矩阵规律,结合试验规律进行相应理论研究,用非线性各向异性弹性矩阵代替弹塑性模型的弹性矩阵,用具有各向异性屈服准则的弹塑性模型描述塑性部分,建立非线性各向异性弹性-塑性模型,可以改善柔度矩阵矩阵形态,反映复杂应力状态下土体应力各向异性特征。     

Laboratory and In Situ Simulation Tests of the Excavation Damaged Zone Around Galleries in Opalinus Clay

In the context of nuclear waste disposal in clay formations, laboratory and in situ simulation experiments were performed to study at reduced scale the excavation damaged zone (EDZ) around tunnels in the indurated Opalinus Clay at Mont Terri, Switzerland. In the laboratory, thick-walled hollow cylindrical specimens were subjected to a mechanical unloading mimicking a gallery excavation. In samples cored parallel to bedding, cracks sub-parallel to the bedding planes open and lead to a buckling failure in two regions that extend from the borehole in the direction normal to bedding. The behaviour is clearly anisotropic. On the other hand, in experiments performed on specimens cored perpendicular to bedding, there is no indication of failure around the hole and the response of the hollow cylinder sample is mainly isotropic. The in situ experiment at Mont Terri which consisted in the overcoring of a resin-injected borehole that follows the bedding strike of the Opalinus Clay showed a striking similarity between the induced damaged zone and the fracture pattern observed in the hollow cylinder tests on samples cored parallel to bedding and such a bedding controlled “Excavation” Damaged Zone is as well consistent with the distinct fracture patterns observed at Mont Terri depending on the orientation of holes/galleries with respect to the bedding planes. Interestingly, the damaged zone observed in the hollow cylinder tests on samples cored parallel to bedding and in situ around URL galleries is found to develop in reverse directions in Boom Clay (Mol) and in Opalinus Clay (Mont Terri). This most probably results from different failure mechanisms, i.e. shear failure along conjugated planes in the plastic Boom Clay, but bedding plane splitting and buckling in the indurated Opalinus Clay.     

Evolution of anisotropy with saturation and its implications for the elastoplastic responses of clay rocks

Many clay rocks have distinct bedding planes. Experimental studies have shown that their mechanical properties evolve with the degree of saturation (DOS), often with higher stiffness and strength after drying. For transversely isotropic rocks, the effects of saturation can differ between the bed-normal (BN) and bed-parallel (BP) directions, which gives rise to saturation-dependent stiffness and strength anisotropy. Accurate prediction of the mechanical behavior of clay rocks under partially saturated conditions requires numerical models that can capture the evolving elastic and plastic anisotropy with DOS. In this study, we present an anisotropy framework for coupled solid deformation-fluid flow in unsaturated elastoplastic media. We incorporate saturation-dependent strength anisotropy into an anisotropic modified Cam-Clay (MCC) model and consider the evolving anisotropy in both the elastic and plastic responses. The model was calibrated using experimental data from triaxial tests to demonstrate its capability in capturing strength anisotropy at various levels of saturation. Through numerical simulations, we demonstrate the role of evolving stiffness and strength anisotropy in the mechanical behavior of clay rocks. Plane strain simulations of triaxial compression tests were also conducted to demonstrate the impacts of material anisotropy and DOS on the mechanical and fluid flow responses.     

Study of the Anisotropic Properties of Argillite Under Moisture and Mechanical Loads

Due to various factors, such as sedimentation, layered morphology of clay minerals, in situ stress, etc., argillite rocks often exhibit anisotropic behavior. In order to study the anisotropic properties of the Callovo-Oxfordian (COx) argillite of the Meuse–Haute-Marne site in France considered as a possible host rock for high-level radioactive nuclear waste repository, a series of tests including uniaxial compression and dehydration and hydration at different constant applied stress levels are carried out. In this study, a specific setup combining moisture and mechanical loading with optical observation is used and it allows to continuously capture surface images from which the full-field strains are determined by using Digital Image Correlation techniques. The results show evidence of the mechanical and hydric anisotropy of the material. The anisotropy parameters are identified, assuming the studied argillite as transversely isotropic. The shrinkage and swelling depend on the applied stress and the angle with respect to the vertical direction of the mechanical load and the stratification plane, and this dependence is quantified. The non-linearity and the hysteresis observed during dehydration and hydration cycles are discussed.     

初始组构各向异性对砂土力学特性及临界状态的影响

采用离散元方法,利用半径扩展法和重力沉积法分别生成具有初始各向同性和各向异性内结构的试样,并开展三轴不排水压缩和拉伸试验,研究不同制样方法产生的初始各向异性对砂土宏微观力学特性及其临界状态的影响。运用组构张量对砂土的各向异性进行量化,分析不同初始组构各向异性对组构张量演化的影响并确定了组构张量的临界值。试验结果表明：初始组构各向异性对试样的剪胀性有重要影响,由于受重力影响形成初始各向异性,其各向异性程度越大、组构方向与加载方向越一致,剪胀性越显著;初始组构各向异性对试样的临界状态没有影响,砂土的组构张量具有唯一的临界状态值。     

从各向异性的角度解释和模拟土的非共轴特性

从发挥面的角度出发,分析论证各向异性是引起岩土材料出现非共轴现象的根本原因,得到与材料力学一致的结论。当共轭的两发挥面与沉积面的夹角不相等时,主应力面上将出现塑性应变增量的切向分量,所以塑性应变增量的主方向与应力的主方向非共轴。按照这一结论,对非共轴的数值模拟,也应当根据各向异性本构模型进行。为考虑各向异性影响新近提出的各向异性变换应力法,改变了各应力分量的相对大小,得到的各向异性变换应力张量与真实应力张量的主方向不一致,因此也能反映非共轴。利用各向异性变换应力法,能够在现有的弹塑性本构模型的框架下,描述土的非共轴现象。以各向异性UH模型为例,预测各种加载条件下的非共轴变形,验证了该方法的有效性。     

The influence of anisotropy on compaction bands: The case of coaxiality between stress and fabric anisotropy tensors

Compaction bands are localized failure patterns that appear in highly porous rock material under the effect of relatively high confining pressure. Being affected mainly by volumetric compression, these bands appear to be almost perpendicular to the most compressive principal stress of a stress state at the so-called “cap” of the yield surface (YS). In this study, we focus on the mechanism that leads to the onset of compaction bands by using a viscoplasticity model able to describe the post-localization response of these materials. The proposed constitutive framework is based on the overstress theory of Perzyna (1966) and the anisotropic clay plasticity model of Dafalias (1986), which provides not only the necessary “cap” of the YS, but introduces a rotational hardening (RH) mechanism, thus, accounting for the effect of fabric anisotropy. Following the analysis of Veveakis and Regenauer-Lieb (2015), we identify the compaction bands as “static” cnoidal wave formations in the medium that occur at a post-yield regime, and we study the effect of rotational and isotropic hardening on their onset. Moreover, we determine a theoretical range of confining pressures in triaxial compression tests for the compaction bands to develop. Under the assumption of coaxiality between stress and anisotropy tensors, the results show that the isotropic hardening promotes compaction localization, whereas the RH has a slightly negative effect on the onset of compaction localization.     

Anisotropic behavior of the Bushehr carbonate sand in the Persian Gulf

The anisotropy effect is exhibited more prominently in sedimentary depositions, and it relates the soil’s mechanical specifications to the directions of imposed loads. Even though this phenomenon has been comprehensively explored in silica sands, few research has been conducted for studying the anisotropic behavior of marine carbonate sands. To bridge this gap, the present study investigates the anisotropy effect on the mechanical behavior of Bushehr carbonate sand acquired from the north shelf of the Persian Gulf in Iran. Toward this end, some undrained principal stress rotation tests are conducted using a hollow cylinder shear torsional apparatus in such a manner that the direction of the applied principal stresses are fixed along a desired orientation and the total mean stress and intermediate principal stress ratio are kept constant. Furthermore, prior to shearing, the samples are consolidated under three confining pressures and two isotropic and anisotropic states. The results show that dilative behavior is observed in all loading directions after initial contraction; this contradicts the response observed in silica sands. The anisotropy response of soil follows two different trends in the contractive and dilative phases. The relation of soil’s mechanical properties shows a descending trend with the angle of maximum principal stress in the contractive phase; on the other hand, the anisotropy behavior shows a dominant parabola trend in the dilative phase, where the maximum ultimate pore pressure and minimum soil strength occur in the stress direction with an angle of α?=?30°. By increasing the confining pressure in the soil element, the intensity of the anisotropy in some mechanical properties except the soil deformation is reduced. Furthermore, the deviatoric-to-effective mean stress ratio in the phase transformation state from contraction to dilation is independent of the loading direction and consolidation stress state, and it is considered one of the intrinsic properties of sand.     

Three‐dimensional shakedown solutions for anisotropic cohesive‐frictional materials under moving surface loads

Previous work on three‐dimensional shakedown analysis of cohesive‐frictional materials under moving surface loads has been entirely for isotropic materials. As a result, the effects of anisotropy, both elastic and plastic, of soil and pavement materials are ignored. This paper will, for the first time, develop three‐dimensional shakedown solutions to allow for the variation of elastic and plastic material properties with direction. Melan's lower‐bound shakedown theorem is used to derive shakedown solutions. In particular, a generalised, anisotropic Mohr–Coulomb yield criterion and cross‐anisotropic elastic stress fields are utilised to develop anisotropic shakedown solutions. It is found that shakedown solutions for anisotropic materials are dominated by Young's modulus ratio for the cases of subsurface failure and by shear modulus ratio for the cases of surface failure. Plastic anisotropy is mainly controlled by material cohesion ratio, the rise of which increases the shakedown limit until a maximum value is reached. The anisotropic shakedown limit varies with frictional coefficient, and the peak value may not occur for the case of normal loading only. Copyright © 2013 John Wiley & Sons, Ltd.     

Three‐dimensional elasto‐plastic model for unsaturated compacted soils with different initial densities

This paper presents an elasto‐plastic model for unsaturated compacted soils and experimental results obtained from a series of suction‐controlled triaxial tests on unsaturated compacted clay with different initial densities. The initial density dependency of the compacted soil behaviour is modelled by establishing experimental relationships between the initial density and the corresponding yield stress and thereby between the initial density and the location and slope of normal compression line. The model is generalized to three‐dimensional stress states by assuming that the shapes of the failure surface and the yield surface in the deviatoric plane are given by the extended SMP criterion. A considerable number of the isotropic compression, triaxial compression and extension tests on unsaturated compacted clay with different initial densities were performed using a suction‐controllable triaxial apparatus, to measure the stress–strain–volume change in different stress paths and wetting paths. The model has well‐predicting capabilities to reproduce the mechanical behaviour of specimens compacted under different conditions not only in isotropic compression but also in triaxial compression and triaxial extension. Copyright © 2003 John Wiley & Sons, Ltd.