共查询到20条相似文献，搜索用时 593 毫秒
1.
In this paper, we consider the upscaling of Hooke's law and its parameters on the fine scale, to a similar law with upscaled parameters on a larger scale. It is assumed that the fine scale material properties of the rock are imperfectly layered. In the governing equations, the deviations from perfect layering introduce a small parameter that can be used in perturbation series expansions for the stress, the strain, and the displacement. In the approximation of order zero the upscaled compliance matrix contains the well-known Backus parameters; this approximation holds exactly for a perfect layering. However, many natural rock types are imperfectly layered and in that case the approximation of order zero may not be sufficiently accurate. Therefore, we consider also the first order corrections. The derivation and results are presented both for the most general case and for the much simpler case in which the fine scale Poisson ratio may be assumed constant. From thermodynamic principles, it follows that the compliance tensor is symmetric on the fine scale. However, it is shown that the argument for symmetry cannot be extended to upscaled rigidities. One of the most important conclusions is that upscaled compliance tensors are nonsymmetric when there are trends in the deviations from perfect layering. 相似文献
2.
The analysis of the wave propagation in layered rocks masses with periodic fractures is tackled via a two-scale approach in order to consider shape and size of the rock inhomogeneities. To match the displacement fields at the two scales, an approximation of the micro-displacement field is assumed that depends on the first and second gradients of the macro-displacement through micro-fluctuation displacement functions obtained by the finite element solution of cell problems derived by the classical asymptotic homogenization. The resulting equations of motion of the equivalent continuum at the macro-scale result to be not local in space, thus a dispersive wave propagation is obtained from the model. The simplifying hypotheses assumed in the multi-scale kinematics limit the validity of the model to the first dispersive branch in the frequency spectrum corresponding to the lowest modes.Although the homogenization procedure is developed to study the macro-scale wave propagation in rock masses with bounded domain, the reliability of the proposed method has been evaluated in the examples by considering unbounded rock masses and by comparing the dispersion curves provided by the rigorous process of Floquet–Bloch with those obtained by the method presented. The accuracy of the method is analyzed for compressional and shear waves propagating in the intact-layered rocks along the orthotropic axes. Therefore, the influence of crack density in the layered rock mass has been analyzed. Vertical cracks have been considered, periodically located in the stiffer layer, and two different crack densities have been analyzed, which are differentiated in the crack spacing. A good agreement is obtained in case of compressional waves travelling along the layering direction and in case of both shear and compressional waves normal to the layering. The comparison between two crack systems with different spacing has shown this aspect to have a remarkable effect on waves travelling along the direction of layering, and limited in the case of waves propagating normal to the layers.The equivalent continuous model obtained through the dynamic homogenization technique here presented may be applied to the computational analysis of non-stationary wave propagation in rock masses of finite size, also consisting of sub-domains with different macro-mechanical characteristics. This avoids the use of computational models represented at the scale of the heterogeneities, which may be too burdensome or even unfeasible. 相似文献
3.
Implementation of a Locally Conservative Numerical Subgrid Upscaling Scheme for Two-Phase Darcy Flow 总被引：1，自引：0，他引：1
Todd Arbogast 《Computational Geosciences》2002,6(3-4):453-481
We present a locally mass conservative scheme for the approximation of two-phase flow in a porous medium that allows us to obtain detailed fine scale solutions on relatively coarse meshes. The permeability is assumed to be resolvable on a fine numerical grid, but limits on computational power require that computations be performed on a coarse grid. We define a two-scale mixed finite element space and resulting method, and describe in detail the solution algorithm. It involves a coarse scale operator coupled to a subgrid scale operator localized in space to each coarse grid element. An influence function (numerical Greens function) technique allows us to solve these subgrid scale problems independently of the coarse grid approximation. The coarse grid problem is modified to take into account the subgrid scale solution and solved as a large linear system of equations posed over a coarse grid. Finally, the coarse scale solution is corrected on the subgrid scale, providing a fine grid representation of the solution. Numerical examples are presented, which show that near-well behavior and even extremely heterogeneous permeability barriers and streaks are upscaled well by the technique. 相似文献
4.
Practical expressions are given for the nine components of the block-scale permeability tensor of a thin block. These expressions are derived from the local-scale continuity equation and Darcy's law in an anisotropic layered porous medium. The flow problem is separated in a bottom-flux problem and a top-flux problem, both of which can be solved in essentially the same way. The bottom-flux problem has been worked out in detail, and has been separated in two parts: a vertical potential difference and a horizontal potential difference part. Each is solved with a different approach specially designed for it. Depth-averaged expressions are obtained first, after which block-scale expressions are obtained by assuming a constant depth-averaged flux. In the zeroth order, this results in the well-known Dupuit approximation in geohydrology, and the vertical equilibrium (VE) approximation in petroleum reservoir engineering. The novelty of the theory presented here stems from the application of a perturbation technique to obtain first-order corrections to these well-known results. The local-scale laws are applied in the coordinate system coinciding with the principal axes of the local-scale permeability tensor. Only in this coordinate system the local-scale permeability tensor has zero off-diagonal components. However, since the porous medium is imperfectly layered, the first-order corrections show that the off-diagonal components of the block-scale permeability tensor are not zero. Furthermore, the block-scale permeability tensor is generally nonsymmetric, which implies that a coordinate system in which the off-diagonal terms disappear does not exist. 相似文献
5.
层状侵入体的一个典型的特征是具有隐导理和韵律层理，分析比较了前人提出的韵律层理形成的各种机制并结合对攀枝花层状侵入体的研究认为，层状侵入体的韵律层理的形成与成岩的压实作用关系密切，细粒韵律层理是由于颗粒大小的微小差别或矿物成分含量的逐渐增加和重复的再平衡所致，矿物成分含量的逐步增加和重复是通过在类似于奥斯特瓦尔德成熟的条件下循环溶解和晶体生长形成的，在影响层理形成的多种因素中，以对流作用，密度，粘度及岩浆房的几何形状等因素的研究较为详细，各研究者也存在较大分歧。 相似文献
6.
Erick R. Burns Larry R. Bentley Rene Therrien Clayton V. Deutsch 《Hydrogeology Journal》2010,18(6):1357-1373
An upscaling algorithm has been developed that generates an irregular coarse grid that preserves flow connectivity by applying a rule-based upscaling algorithm to a fine-scale facies distribution. The algorithm is demonstrated using stochastically generated paleo-fluvial facies distributions. First, an irregular grid honoring the channel facies is created, followed by computation of effective anisotropic parameters for all coarse-grid cells. For the apparent layer-cake geometry of overbank deposits seen in outcrop, two local upscaling methods are compared: (1) the layered system approximation and (2) the mode. To assess upscaling performance, flow simulations for the original and upscaled grids are compared. The horizontal layered approximation (arithmetic mean) performs poorly, over-predicting lateral connectivity where even infrequent disconnection becomes important. Performance of the mode as an upscaling algorithm depends on the probability that a coarse-grid cell will be dominated by a single facies, and it performs surprisingly well because the upscaled grid-generation algorithm honors the channels, informing the upscaling process. Lastly, the irregular coarse grid was compared to a uniform coarse grid, showing superior performance with the irregular grid. The reduction in grid size achieved by irregular-grid generation will be a function of the geometrical complexity of the geologic objects to be honored. 相似文献
7.
《Comptes Rendus Geoscience》2015,347(2):66-76
The precise determination and interpretation of anisotropy are relatively difficult because the apparent anisotropy is usually a mixture of intrinsic and extrinsic anisotropy, which might partly hide the true properties of the medium investigated. The artificial anisotropy can be due to the fact that seismic waves do not ‘see’ the real details of a medium, but a ‘filtered’ (or ‘upscaled’) version of the Earth model. This can be due to a bad quality of the data coverage, to limited frequency band effects, or to errors in the approximate theory. With the limitation to layered Earth models, through comparisons of the results of the homogenization method with those of the periodic isotropic two-layered model as an analytical solution, we illustrate that the Backus theory for the long wavelength equivalent effect can be extended to calculate the extrinsic anisotropy, due to upscaling effects at discontinuities for the general isotropic layered model, when its spatial scale is much less than or equal to the seismic wavelength. We find that the extrinsic radial S-wave anisotropy produced by the vertical heterogeneities in the upper mantle of the Earth can be as large as 3% (about 30% extrinsic anisotropy of the 10% radial anisotropy). To better recover information from seismic data, we propose a surface wave phase velocity inversion method based on the first-order perturbation theory. We show that resolution at discontinuities can be improved by adding overtone modes of surface wave data. For more general layered models, the homogenization method could be considered, which can flexibly adapt the scale of the model to seismic wavelengths. However, the periodic isotropic two-layered model can also help to analytically quantify the amount of extrinsic radial, and possibly azimuthal anisotropy produced by the tilted fine layering. 相似文献
8.
9.
The occurrence of foliated rock masses is common in mining environment. Methods employing continuum approximation in describing the deformation of such rock masses possess a clear advantage over methods where each rock layer and each inter‐layer interface (joint) is explicitly modelled. In devising such a continuum model it is imperative that moment (couple) stresses and internal rotations associated with the bending of the rock layers be properly incorporated in the model formulation. Such an approach will lead to a Cosserat‐type theory. In the present model, the behaviour of the intact rock layer is assumed to be linearly elastic and the joints are assumed to be elastic–perfectly plastic. Condition of slip at the interfaces are determined by a Mohr–Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformations. The model is incorporated into the finite element program AFENA and validated against an analytical solution of elementary buckling problems of a layered medium under gravity loading. A design chart suitable for assessing the stability of slopes in foliated rock masses against flexural buckling failure has been developed. The design chart is easy to use and provides a quick estimate of critical loading factors for slopes in foliated rock masses. It is shown that the model based on Euler's buckling theory as proposed by Cavers (Rock Mechanics and Rock Engineering 1981; 14 :87–104) substantially overestimates the critical heights for a vertical slope and underestimates the same for sub‐vertical slopes. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
10.
John S. Myers 《Precambrian Research》1978,6(1):43-64
The development of finely layered gneisses by progressive deformation of a variety of granitoid intrusions, leucogabbroa, anorthosites, and basic and intermediate volcanic rocks is described and illustrated.Gneissose layering developed by the tectonic distortion of: magmatic and volcanic layering; particles such as pillow lavas, igneous crystals, and rock fragments in volcanic and plutonic breccias; patchy igneous textures; and vein networks. The products of extreme deformation during amphibolite facies metamorphism are uniformly layered gneisses. 相似文献
11.
In this paper we study the problem of determining the effective permeability on a coarse scale level of problems with strongly
varying and discontinuous coefficients defined on a fine scale. The upscaled permeability is defined as the solution of an
optimization problem, where the difference between the fine scale and the coarse scale velocity field is minimized. We show
that it is not necessary to solve the fine scale pressure equation in order to minimize the associated cost‐functional. Furthermore,
we derive a simple technique for computing the derivatives of the cost‐functional needed in the fix‐point iteration used to
compute the optimal permeability on the coarse mesh. Finally, the method is illustrated by several analytical examples and
numerical experiments.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
Large scale geomechanical simulations are being increasingly used to model the compaction of stress dependent reservoirs, predict the long term integrity of under‐ground radioactive waste disposals, and analyse the viability of hot‐dry rock geothermal sites. These large scale simulations require the definition of homogenous mechanical properties for each geomechanical cell whereas the rock properties are expected to vary at a smaller scale. Therefore, this paper proposes a new methodology that makes possible to define the equivalent mechanical properties of the geomechanical cells using the fine scale information given in the geological model. This methodology is implemented on a synthetic reservoir case and two upscaling procedures providing the effective elastic properties of the Hooke's law are tested. The first upscaling procedure is an analytical method for perfectly stratified rock mass, whereas the second procedure computes lower and upper bounds of the equivalent properties with no assumption on the small scale heterogeneity distribution. Both procedures are applied to one geomechanical cell extracted from the reservoir structure. The results show that the analytical and numerical upscaling procedures provide accurate estimations of the effective parameters. Furthermore, a large scale simulation using the homogenized properties of each geomechanical cell calculated with the analytical method demonstrates that the overall behaviour of the reservoir structure is well reproduced for two different loading cases. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
13.
Subsurface flows are affected by geological variability over a range of length scales. The modeling of well singularity in
heterogeneous formations is important for simulating flow in aquifers and petroleum reservoirs. In this paper, two approaches
in calculating the upscaled well index to capture the effects of fine scale heterogeneity in near-well regions are presented
and applied. We first develop a flow-based near-well upscaling procedure for geometrically flexible grids. This approach entails
solving local well-driven flows and requires the treatment of geometric effects due to the nonalignment between fine and coarse
scale grids. An approximate coarse scale well model based on a well singularity analysis is also proposed. This model, referred
to as near-well arithmetic averaging, uses only the fine scale permeabilities at well locations to compute the coarse scale
well index; it does not require solving any flow problems. These two methods are systematically tested on three-dimensional
models with a variety of permeability distributions. It is shown that both approaches provide considerable improvement over
a simple (arithmetic) averaging approach to compute the coarse scale well index. The flow-based approach shows close agreement
to the fine scale reference model, and the near-well arithmetic averaging also offers accuracy for an appropriate range of
parameters. The interaction between global flow and near-well upscaling is also investigated through the use of global fine
scale solutions in near-well scale-up calculations. 相似文献
14.
Layered rock masses can be modelled either as standard, orthotropic continua if the layer bending can be neglected or as Cosserat continua if the influence of layer bending is essential. This paper presents a finite element smeared joint model based on the Cosserat theory. The layers are assumed to be elastic with equal thickness and equal mechanical properties. All the cosserat parameters are expressed through the elastic properties of layers, layer thickness and joint stiffness. Plastic-slip as well as tensile-opening of layer interface (joint) are accounted for in a manner similar to the conventional non-associative plasticity theory. As an application, the behaviour of an excavation in a layered rock mass is examined. The displacement and stress fields given by smeared joint models based on the Cosserat continuum and the conventional anisotropic continuum approaches are compared with those obtained from the discrete joint model. The conventional anisotropic continuum model is found to break-down completely when the effective shear modulus in the direction parallel to layering is low in comparison to the shear modulus of the intact layer, whereas the Cosserat model is found to be capable of accurately reproducing complex load–deflection patterns irrespective of the differences in shear moduli. © 1998 John Wiley & Sons, Ltd. 相似文献
15.
16.
宜兴抽水蓄能电站试验洞的反分析研究 总被引：4，自引：2，他引：4
结合江苏宜兴抽水蓄能电站地下厂房试验洞量测资料的分析,研究了成层各向异性岩体中洞室工程问题的反分析方法。采用分层均质模型进行反分析计算。计算区域的各层岩层均被分别视为均质各向同性体,初始地应力假设呈线性分布。有限元分析中,对倾斜成层的岩层、软弱夹层及断层节理等分别划分了单元,据以模拟成层岩体的各向异性特征。为使计算过程简化,对离洞室较远的岩层拟按地质资料对材料特性参数赋值,反分析计算的目标未知数为初始地应力和试验洞相邻围岩的弹性模量。结果表明,与工程实践符合较好。 相似文献
17.
层状岩体由于层理面或者结构面的存在,在力学上具有横观各向同性的特点,现有的各向同性蠕变模型难以全面反映横观各向同性岩体的蠕变力学特性。为构建能够反映横观各向同性岩体的三维蠕变模型,以能反映瞬时应变、减速蠕变和稳态蠕变特征的黏弹性Burgers模型为基础,基于常泊松比假定,在三维各向同性蠕变本构方程的基础上,按照算子替换的方法,将横观各向同性柔度矩阵代替各向同性柔度矩阵,并考虑了平行和垂直层理方向岩体蠕变力学行为的差异性,推导了横观各向同性岩体的三维蠕变本构方程。根据本构方程的特点,提出了根据平行和垂直方向岩体蠕变试验结果进行三维蠕变本构模型中蠕变参数的辨识方法。将提出的模型应用于三轴蠕变试验参数辨识,从而获得了一套完整的三维蠕变参数,并与试验结果进行对比分析,从而验证了所提模型与方法的合理性和有效性。进一步,指出了传统蠕变试验设计方案的局限性,给出了横观各向同性材料蠕变试验设计建议。研究成果为研究岩体三维蠕变机制提供了新思路,可对岩体蠕变试验设计提供相应的科研支撑。 相似文献
18.
裂隙网络模拟与REV尺度研究 总被引：4，自引：2，他引：2
研究了利用平面四边形模拟节理岩体三维裂隙网络的方法。在生成裂隙网络时,同时考虑结构面几何参数和力学参数的随机性。利用裂隙网络研究了确定岩体REV尺度的指标。在此基础上,编制了岩体裂隙网络模拟程序、裂隙网络图形输出程序和岩体REV尺度指标分析程序。通过算例分析,验证了研究成果及程序的合理性,并得出了岩体REV尺度约为各组裂隙中最大迹长期望值3~4倍的结论。研究成果为后续计算岩体等效力学参数奠定了基础。 相似文献
19.
降雨入渗条件下软岩边坡稳定性分析 总被引：7，自引：0，他引：7
降雨条件下软岩边坡的失稳模式是进行边坡处治的基本依据之一。为研究软岩边坡在降雨条件下的稳定性,提出了一种既能考虑渗流场对边坡稳定性的影响,又能体现岩石软化效应对边坡失稳所带来的不利作用的新方法。运用二维渗流数值计算方法,对降雨条件下的边坡孔隙水压力大小及暂态饱和区面积在空间及时间上的分布进行了模拟。并将渗流场计算结果与暂态饱和区岩石软化试验所得岩石物理力学参数随时间的取值相结合,采用强度折减法分析软岩边坡在降雨入渗条件下的稳定性。对算例边坡的研究表明：降雨入渗条件下软岩边坡的失稳在降雨初期表现为边坡表层局部分层垮塌。随着降雨历时的增长,失稳形式则表现为局部分层垮塌与整体滑移相结合。降雨停止后,边坡负孔隙水压力的消散,对软岩边坡安全系数的继续降低具有一定的延缓作用。 相似文献
20.
This paper presents a novel dynamical model to analyze the long‐term response of a percussive drilling system. This departs from existing approaches that usually consider a single activation and bit/rock interaction cycle for the analysis of the process performance. The proposed model integrates the axial dynamics of an elastic piston and an elastic drill bit, a motion‐dependent pressure law to drive the piston, and a generalized bit/rock interaction law representative of the dynamic indentation taking place at the bit/rock interface. It applies to down‐the‐hole percussive drilling as well as top‐hole, with minor modifications. The model does not account for the angular motion or the hole cleaning, however. The model is first formulated mathematically; then, a finite‐dimensional approximation is proposed for computations. Numerical analyses of the model response, for a low‐size down‐the‐hole percussive system, follow. The period‐1 stationary response for the reference configuration is studied in detail, and parametric analyses assessing the influence on the rate of penetration of the bit/rock interaction parameters, the feed force, and the percussive activation parameters are conducted. These analyses reveal that the multiscale nature of the process is well captured by the model and recover expected trends for the influence of the parameters. They also suggest that a significant increase of the penetration rate can be achieved by increasing the percussive frequency. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献