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A general form of a “fracture function” for isotropic brittle materials is expressed in terms of the three invariants of the stress tensor. The coefficients in the function are determined by use of the small number of experimental data under specific conditions. This function is applicable to an estimate of the fracture condition of brittle rocks under a general stress state i.e., σ1 ≠ σ2 ≠ σ3. The application of this function is attempted for the data of three brittle rocks i.e., Dunham dolomite, Mizuho trachyte, and Westerly granite, reported by previous workers. For the first two, this criterion gives a good estimation of the effect of the intermediate principal stress σ2 on failure. For the last, the fracture strength at high confining pressure is estimated by use of the several data obtained under very low confining pressures, and the agreement with experimental data is also satisfactory. 相似文献
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M. Hohmann 《Astronomy Reports》2018,62(12):890-897
We determine the possible gravitational wave polarizations in two general classes of teleparallel gravity theories, using the metric and symmetric teleparallel geometries. For this purpose we apply the Newman–Penrose formalism, and find that depending on the choice of parameters, the E(2) class of the theories is one of N2,N3, III5, II6, corresponding to two to six polarizations, where all of them include the two tensor polarizations known from general relativity. We also find classes of theories apart from general relativity which yield the same polarizations. 相似文献
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The mixed finite-element approximation to a second-order elliptic PDE results in a saddle-point problem and leads to an indefinite
linear system of equations. The mixed system of equations can be transformed into coupled symmetric positive-definite matrix
equations, or a Schur complement problem, using block Gauss elimination. A preconditioned conjugate-gradient algorithm is
used for solving the Schur complement problem. The mixed finite-element method is closely related to the cell-centered finite
difference scheme for solving second-order elliptic problems with variable coefficients. For the cell-centered finite difference
scheme, a simple multigrid algorithm can be defined and used as a preconditioner. For distorted grids, an additional iteration
is needed. Nested iteration with a multigrid preconditioned conjugate gradient inner iteration results in an effective numerical
solution technique for the mixed system of linear equations arising from a discretization on distorted grids. Numerical results
show that the preconditioned conjugate-gradient inner iteration is robust with respect to grid size and variability in the
hydraulic conductivity tensor. 相似文献
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One of the purposes in this study is to develop a modified micromorphic continuum model for granular materials on the basis of a micromechanics approach. A symmetric curvature tensor is proposed in this model, and a symmetric couple stress tensor is derived conjugating the symmetric curvature tensor. In addition, a correct derivation is presented to obtain the symmetric stress tensor conjugated with the symmetric strain tensor. The modified model provides a complete deformation mode for granular materials by considering the decomposition for motions (displacement and rotation) of particles. Consequently, the macroscopic constitutive relationships and constitutive moduli are derived in expressions of the microstructural information. Furthermore, the balance equations and boundary conditions are obtained for the modified micromorphic model. By considering the extended Drucker-Prager yield criterion, the micromorphic elastoplastic model is developed. Another purpose of this study is to derive the finite element formulation for the developed micromorphic elastoplastic model. Based on the ABAQUS user element (UEL) interface, numerical simulations investigated the load-displacement relationship and the strain localization behavior of granular materials and investigated the influence of microscopic parameters in the micromorphic model on these macroscopic mechanical responses. Numerical results illustrate the presented model's capability of simulating the strain-softening and strain localization behaviors, and the capability of considering the influence of microstructural information on the macroscopic mechanical behaviors of granular materials. 相似文献
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In the methods used for determination of the hydraulic behaviour at large scale of fractured rock masses, based on the simulation of flow in a fracture network, the mean flux and the mean pressure gradient in the network are not rigorously determined. A method is given for deriving these quantities, in a heterogeneous permeable block, from pressure and flux values on the boundary of the block. A block conductivity tensor is then defined, based on the condition of linear variation of the pressure on the boundary of the block. It is shown that this conductivity tensor is symmetric and positive-definite. An example of application to a model of fractured medium is given. To cite this article: A. Pouya, A. Courtois, C. R. Geoscience 334 (2002) 975–979. 相似文献
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影响孔隙水压力的因素主要包括总平均应力、广义剪应力和应力洛德角。在总结了前人对孔隙水压力系数的研基础上,推导了基于统一硬化模型的孔隙水压力系数,采用变换应力的方法可以使该模型实现三维化,因此,新的孔隙水压力系数能反映上述3因素的变化对孔隙水压力的影响。 相似文献
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We present a new version of the local discontinuous Galerkin method which is capable of dealing with jump conditions along a submanifold ΓLG (i.e., Henry’s Law) in instationary Darcy flow. Our analysis accounts for a spatially and temporally varying, non-linear permeability tensor in all estimates which is also allowed to have a jump at ΓLG and gives a convergence order result for the primary and the flux unknowns. In addition to this, different approximation spaces for the primary and the flux unknowns are investigated. The results imply that the most efficient choice is to choose the degree of the approximation space for the flux unknowns one less than that of the primary unknown. The only stabilization in the proposed scheme is represented by a penalty term in the primary unknown. 相似文献
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We present a new nonlinear monotone finite volume method for diffusion equation and its application to two-phase flow model. We consider full anisotropic discontinuous diffusion or permeability tensors on conformal polyhedral meshes. The approximation of the diffusive flux uses the nonlinear two-point stencil which provides the conventional seven-point stencil for the discrete diffusion operator on cubic meshes. We show that the quality of the discrete flux in a reservoir simulator has great effect on the front behavior and the water breakthrough time. We compare two two-point flux approximations (TPFA), the proposed nonlinear TPFA and the conventional linear TPFA, and multipoint flux approximation (MPFA). The new nonlinear scheme has a number of important advantages over the traditional linear discretizations. Compared to the linear TPFA, the nonlinear TPFA demonstrates low sensitivity to grid distortions and provides appropriate approximation in case of full anisotropic permeability tensor. For nonorthogonal grids or full anisotropic permeability tensors, the conventional linear TPFA provides no approximation, while the nonlinear flux is still first-order accurate. The computational work for the new method is higher than the one for the conventional TPFA, yet it is rather competitive. Compared to MPFA, the new scheme provides sparser algebraic systems and thus is less computational expensive. Moreover, it is monotone which means that the discrete solution preserves the nonnegativity of the differential solution. 相似文献
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Dmitry Kolyukhin Sylvie Schueller Magne S. Espedal Haakon Fossen 《Computational Geosciences》2010,14(2):231-248
Fault damage zones in highly porous reservoirs are dominated by deformation bands that generally have permeability-reducing
properties. Due to an absence of sufficiently detailed measurements and the irregular distribution of deformation bands, a
statistical approach is applied to study their influence on flow. A stochastic model of their distribution is constructed,
and band density, distribution, orientation, and flow properties are chosen based on available field observations. The sensitivity
of these different parameters on the upscaled flow is analyzed. The influence of a heterogeneous permeability distribution
was also studied by assuming the presence of high permeability holes within bands. The fragmentation and position of these
holes affect significantly the block-effective permeability. Results of local upscaling with a diagonal and full upscaled
permeability tensor are compared, and qualitatively similar results for the flow characteristics are obtained. Further, the
procedure of iterative local–global upscaling is applied to the problem. 相似文献
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We developed a three-dimensional(3D) conjugate gradient inversion algorithm for in-verting magnetotelluric impedance tensor measurements.In order to show the importance of including diagonal components of magnetotelluric impedance tensor in 3D inversion,synthetic data were inverted using the 3D conjugate gradient inversion,and the inversion results were compared and analyzed.The results from the 3D inversion of synthetic data indicate that both the off-diagonal and the diagonal components are required in in... 相似文献
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Cosserat extension of the Gauss stress-strain inversion method and multiple-slip method (MSM) are used to analyse 18 examples of natural wedge faulting observed in Slovenia. Based on additional numerical tests we show that kinematic incompatibility of slip along intersecting faults (wedges) has a significant effect on the state of stress in the Earth's crust. The slip direction along intersecting faults (wedges) can only be subparallel to the intersection direction between the faults. The normal stress on the wedges is then equal to the intermediate principal stress (eigenvalue) of the symmetric part of the stress tensor. This equality is very fundamental and could potentially be interpreted as a new law of faulting along tectonic wedges and non-planar faults. In the Cosserat theory of wedge faulting we also define two stress criteria, these are the weak and the strong stress conditions. The weak stress condition is related to the frictional reactivation of the wedges. It defines two limit values of the stress parameter and intermediate principal stress of the symmetric part of the stress tensor. The strong stress condition is related to the brittle faulting along tectonic wedges. It relates the angle of internal friction to the value of the stress parameter and the intermediate principal stress of the symmetric part of the stress tensor. For the value of the angle of internal friction larger than zero, the stress parameter is less than 0.5, which is in agreement with numerical and empirical observations described in this paper. 相似文献
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在裂隙岩体二维柔度张量数值试验的基础上,建立了裂隙岩体三维柔度张量及其表征单元体积（REV）尺度研究的简化数值试验方法。首先根据岩体裂隙的统计参数及分布规律,运用蒙特卡罗方法在研究域内获得与实际岩体裂隙同分布的三维随机裂隙网络,提取位于不同方位的岩体试件,运用二维柔度张量的数值试验方法求出各个平面方向上的二维柔度张量,然后根据二维与三维柔度张量的拓扑关系,用数学方法求解裂隙岩体的三维柔度张量。对于含3组正交全贯通裂隙的岩体,通过数值试验获得的柔度张量与理论解相比,其主对角线上各参数的误差在5%以内,表明该数值试验方法较为可靠。最后将此方法运用到小湾水电站工程中,确定左岸坝区裂隙岩体的应力REV为11 m×11 m×11 m,并获得该区域裂隙岩体的三维柔度张量。 相似文献
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Soil–structure interaction problems are commonly encountered in geotechnical practice and remarkably characterized with significant material stiffness contrast. When solving the soil–structure interaction problems, the employed Krylov subspace iterative method may converge slowly or even fail, indicating that the adopted preconditioning method may not suit for such problems. The inexact block diagonal preconditioners proposed recently have been shown effective for the soil–structure interaction problems; however, they haven't been exploited to full capabilities. By using the same partition strategy according to the structure elements and soil elements, the partitioned block symmetric successive over‐relaxation preconditioners or partitioned block constraint preconditioners are proposed. Based on two pile‐group foundation problems and a tunnel problem, the proposed preconditioners are evaluated and compared with the available preconditioners for the consolidation analysis and the drained analysis, respectively. In spite of one additional solve associated with the structure block and multiplications with off‐diagonal blocks in the preconditioning step, numerical results reveal that the proposed preconditioners obviously possess better performance than the recently developed inexact block preconditioners. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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In this paper the second order characteristic (discontinuous bifurcation) condition is derived for the granular flow (fully plastic) equations. This second order bifurcation equation is shown to be formally identical to the first order localization requirement during steady elastoplastic deformation provided the elastic compliance tensor is substituted for the product of the plastic multiplier with the flow Hessian. For isotropic yield and flow functions the invariant form of the characteristic condition is given in detail, as well as an alternative expression in adapted co‐ordinates. The characteristic condition can be regarded as defining a hardening function which is maximized to identify the critical angles. When the method is applied to 3D Coulomb flow, Mohr's 3D fracture plane conditions are obtained uniquely. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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Nancy L. Chabot Andrew J. Campbell David S. Draper Munir Humayun Elizabeth Cottrell 《Geochimica et cosmochimica acta》2008,72(16):4146-4158
Earth’s core may contain C, and it has been suggested that C in the core could stabilize the formation of a solid inner core composed of Fe3C. We experimentally examined the Fe-C system at a pressure of 5 GPa and determined the Fe-C phase diagram at this pressure. In addition, we measured solid metal/liquid metal partition coefficients for 17 trace elements and examined the partitioning behavior between Fe3C and liquid metal for 14 trace elements. Solid metal/liquid metal partition coefficients are similar to those found in one atmosphere studies, indicating that the effect of pressure to 5 GPa is negligible. All measured Fe3C/liquid metal partition coefficients investigated are less than one, such that all trace elements prefer the C-rich liquid to Fe3C. Fe3C/liquid metal partition coefficients tend to decrease with decreasing atomic radii within a given period. Of particular interest, our 5 GPa Fe-C phase diagram does not show any evidence that the Fe-Fe3C eutectic composition shifts to lower C contents with increasing pressure, which is central to the previous reasoning that the inner core may be composed of Fe3C. 相似文献
17.
地震条件下黏性土挡土墙土压力分析 总被引：1，自引：0，他引：1
Mononobe-Okabe理论是现阶段计算地震土压力的常用方法,但Mononobe-Okabe理论的诸多假设使其具有一定的局限性。针对Mononobe-Okabe理论的不足,考虑到地震作用下挡土墙偏转对土压力的影响,采用斜向条分法推导了复杂条件下黏性土地震土压力强度分布、土压力合力及其作用点位置公式,并利用图解法给出了临界破裂角的解析解。研究表明：填土黏聚力和地震系数对土压力影响显著;忽略黏性填土表面开裂与地震作用对均布超载及开裂填土等效超载的影响将使主动土压力计算结果偏小,其误差随着填土黏聚力和均布超载的增大而增大;在不同水平地震系数下土压力沿墙高呈非线性分布;所提公式适用范围更广,有效完善了Mononobe-Okabe理论。 相似文献
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A new anisotropic poroelastic damage model is proposed for saturated brittle porous materials. The model is formulated in the framework of the continuum damage mechanics. A second‐rank symmetric tensor is used to characterize material damage due to oriented microcracks. The classic Biot poroelastic theory is then extended to include poroelastic damage coupling. Both the deterioration of elastic properties and poroelastic coefficients is taken into account. A suitable procedure for determination of model parameters from standard laboratory tests is presented. The validity of the model is tested through comparison between numerical predictions and experimental data in various loading conditions. The overall performance of the model is evaluated. The choice of relevant effective stress for the microcrack propagation criterion in saturated cohesive geomaterials is discussed. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
19.
以位场数据处理中的傅里叶变换为出发点,推导出由重力异常计算梯度张量的余弦谱变换公式,进而通过离散余弦变换实现梯度张量的数值计算。对不同贮油厚度的三度体球冠模型梯度张量的研究表明:当油气含量较小时,其梯度张量与均匀三度体球冠模型所表现出的特征相似,Vxx、Vyy呈“两高夹一低”的对称特征;Vxy总体上呈现出向中心变小的趋势,在4个边缘的中部分别有4个呈两两对称的相对较高值;Vzz四周低,中间高;Vzx、Vzy呈现出西低东高和南低北高的特征。而当贮油厚度逐渐增大时,Vxx、Vyy的形态则渐变为“两低夹一高”;Vxy在四周有相对低值,中部有极大值;Vzz四周高,中间低,变化更加尖锐;Vzx及Vzy呈西高东低和南高北低的特征。对三度体球冠模型重力梯度张量的研究,可以为寻找储油背斜构造提供理论依据。 相似文献
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A simple method called anisotropic transformed stress (ATS) method is proposed to develop failure criteria and constitutive models for anisotropic soils. In this method, stress components in different directions are modified differently in order to reflect the effect of anisotropy. It includes two steps of mapping of stress. First, a modified stress tensor is introduced, which is a symmetric multiplication of stress tensor and fabric tensor. In the modified stress space, anisotropic soils can be treated to be isotropic. Second, a TS tensor is derived from the modified stress tensor for the convenience of developing anisotropic constitutive models to account for the effect of intermediate principal stress. By replacing the ordinary stress tensor with the TS tensor directly, the unified hardening model is extended to model the anisotropic deformation of soils. Anisotropic Lade's criterion is adopted for shear yield and shear failure in the model. The form of the original model formulations remains unchanged, and the model parameters are independent of the loading direction. Good agreement between the experimental results and predictions of the anisotropic unified hardening model is observed. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献