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The undrained bearing capacity of shallow circular piles in non-homogeneous and anisotropic clay is investigated by the lower bound (LB) finite element limit analysis (FELA) under two-dimensional (2D) axisymmetric condition using second-order cone programming, and the new solution of the problem is presented. Modified from the isotropic von Mises yield criterion, a cross-anisotropic undrained strength criterion of clays under the axisymmetric state of stress requiring three input shear strengths in triaxial compression, direct simple shear, and triaxial extension is employed in the 2D axisymmetric LB FELA. Parametric studies on the effects of pile embedment ratio, dimensionless strength gradient, anisotropic strength ratio, and pile roughness are investigated extensively, while the predicted failure mechanisms associated with these parameters are discussed and compared. Numerical results of undrained end bearing capacity of shallow circular piles are summarized in the form of design tables that are useful for design practice and represent a new contribution to the field of pile capacity considering the combined effects of undrained strength non-homogeneity and anisotropy. 相似文献
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黑色富含有机质页岩由于沉积方式的特殊性,一般具有较强的各向异性。但现有大部分研究是基于各向同性理论开展页岩储层预测工作,这与页岩的实际地质特点不符。文中联合利用实验室岩石力学测试数据以及各向异性参数经验公式计算焦石坝地区页岩的各向异性参数,并进一步探讨了各向异性对页岩岩石速度、储层AVO响应特征以及岩石力学参数计算的影响。结果表明,各向异性对页岩速度、脆性指数预测结果影响较大,在地层倾角较大时进行速度分析及页岩可压性预测时应考虑各向异性参数的影响;同时,AVO正演结果表明地震反射入射角小于40°时,各向异性算法与各向同性算法计算的页岩AVO响应差异较小,利用各向同性叠前反演方法进行页岩储层预测具有可行性。 相似文献
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Most theoretical investigations of seismic wave scattering rely on the assumption that the underlying medium is statistically isotropic. However, deep seismic soundings of the crust as well as geological observations often reveal the existence of elongated or preferentially oriented scattering structures. In this paper, we develop mean field and radiative transfer theories to describe the attenuation and multiple scattering of a scalar wavefield in an anisotropic random medium. The scattering mean free path is found to depend strongly on the propagation direction. We derive a radiative transfer equation for statistically anisotropic random media from the Bethe–Salpeter formalism and propose a Monte Carlo method to solve this equation numerically. At longer times, the energy density is shown to obey a tensorial diffusion equation. The components of the diffusion tensor are obtained in closed form and excellent agreement is found between Monte Carlo simulations and analytical solutions of the diffusion equation. The theory has important potential implications for lithospheric models where scatterers are for example flat structures preferentially aligned along the surface. In this simple geometry, analytical expressions of the Coda Q parameter can be given explicitly in the diffusive regime. Our results suggest that pulse broadening and coda decay are controlled by different parameters, related to the eigenvalues of the diffusion tensor. These eigenvalues can differ by more than one order of magnitude. This theory could be applied to probe the anisotropy of length scales in the lithosphere. 相似文献
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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. 相似文献
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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。 相似文献
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With the aid of integral transform techniques, this paper presents an extended precise integration solution for thermal consolidation problems of a multilayered porous thermo-elastic medium with anisotropic thermal diffusivity and permeability due to a heat source. From the fundamental governing equations, ordinary differential equations are derived by employing Laplace–Hankel transforms. By applying the extended precise integration method, equations in the transformed domain can be solved, and the actual solutions are further obtained by adopting a numerical inverse transformation. The accuracy and feasibility of the proposed theory is demonstrated by contrastive analysis with existing studies. Finally, several examples are carried out to investigate the influence of heat source’s type, axial distance, burial depth of heat source, ratio of thermo-permeability, permeability anisotropy, thermal diffusivity anisotropy and stratification on the thermal consolidation process. 相似文献
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页岩储层通常呈薄层状结构,一般认为其岩石力学参数具有横向各向同性,而其各向异性受围压（CP）、含水率和总有机质含量（TOC）等多种因素的影响。本文对不同围压下的鹰滩（Eagle Ford）页岩进行超声波波速进行测试实验,研究围压对鹰滩页岩波速及岩石力学各向异性的影响。实验结果表明,鹰滩页岩属于弱各向异性多孔介质,并具有横向各向同性、垂向各向异性的性质。纵波（P波）和横波（S波）波速随围压的增大而增大,特别是在低围压范围内增幅显著,同时围压增大会降低纵波和横波的各向异性,纵波各向异性比横波各向异性对围压更敏感。对鹰滩页岩各向异性分析为页岩储层压裂过程中裂缝的起裂和延伸规律研究提供了必要的力学参数。 相似文献
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When deriving velocity models by forward modelling or inverting travel time arrivals from seismic refraction data, a heterogeneous but isotropic earth is usually assumed. In regions where the earth is not isotropic at the scale at which it is being sampled, the assumption of isotropy can lead to significant errors in the velocities determined for the crust and the depths calculated to reflecting boundaries. Laboratory velocity measurements on rocks collected from the Haast Schist terrane of South Island, New Zealand, show significant (up to 20%) compressional (P) wave velocity anisotropy. Field data collected parallel and perpendicular to the foliation of the Haast Schist exhibit as much as 11% P-wave velocity anisotropy. We demonstrate, using finite-difference full-wavefield modelling, the types of errors and problems that might be encountered if isotropic methods are used to create velocity models from data collected in anisotropic regions. These reflector depth errors could be as much as 10–15% for a 10-km thick layer with significant (20%) P-wave velocity anisotropy. The implications for South Island, New Zealand, where the problem is compounded by extreme orientations of highly anisotropic rocks (foliation which varies from horizontal to near vertical), are considered. Finally, we discuss how the presence of a significant subsurface anisotropic body might manifest itself in wide-angle reflection/refraction and passive seismic datasets, and suggest ways in which such datasets may be used to determine the presence and extent of such anisotropic bodies. 相似文献
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It has been known that material anisotropy and thermal stresses affect borehole stability significantly. Aiming at the experimental studies associated with borehole stability in anisotropic (transversely isotropic) poroelastic materials subject to non‐isothermal conditions, this paper details and applies an anisotropic porothermoelastic solution to an unjacketed hollow cylinder in a triaxial set‐up. Numerical analyses are presented to demonstrate thermal and material anisotropy effects on the pore pressure and the stress concentrations in and around the geometry of a hollow cylinder subjected to thermal and stress perturbations. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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各向异性对土质心墙坝水力劈裂的影响 总被引：4，自引：2，他引：2
应力诱导各向异性对复杂应力状态下土体的应力-应变规律有重要影响,而建立在各向同性假设基础上的常用土体本构模型并不能反映土体的这种特性,因此需要分析土体各向异性对土质心墙坝水力劈裂的影响。采用各向异性非线性弹性模型,对水荷载作用下粘土心墙坝进行有限元数值分析,并与邓肯模型计算结果比较。结果表明,各向异性模型考虑了蓄水期间从小主应力方向加荷引起的土体应力各向异性,计算得出的小主应力σ3较邓肯模型的大,且相应抗水力劈裂能力亦大,则邓肯E-v模型由于不能模拟蓄水期土体各向异性特性,对于水力劈裂发生的评估可能偏于危险。 相似文献
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Existing solutions to Mandel's problem focus on isotropic, transversely isotropic, and orthotropic materials, the last two of which have one of the material symmetry axes coincide with the vertical loading direction. The classical plane strain condition holds for all these cases. In this work, analytical solution to Mandel's problem with the most general matrix anisotropy is presented. This newly derived analytical solution for fully anisotropic materials has all the three nonzero shear strains. Warping occurs in the cross sections, and a generalized plane strain condition is fulfilled. This solution can be applied to transversely isotropic and orthotropic materials whose material symmetry axes are not aligned with the vertical loading direction. It is the first analytical poroelastic solution considering mechanical general anisotropy of elasticity. The solution captures the effects of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction on the responses of pore pressure, stress, strain, and displacement. It can be used to match, calibrate, and simulate experimental results to estimate anisotropic poromechanical parameters. This generalized solution is capable of reproducing the existing solutions as special cases. As an application, the solution is used to study the responses of transversely isotropic and orthotropic materials whose symmetry axes are not aligned with the vertical loading direction. Examples on anisotropic shale rocks show that the effects of material anisotropy are significant. Mandel-Cryer's effects are highly impacted by the degree of material anisotropy and the deviation of the material symmetry axes from the vertical loading direction. 相似文献
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Egor V. Dontsov 《国际地质力学数值与分析法杂志》2019,43(2):519-529
This study investigates parametric space of solutions for a planar hydraulic fracture propagating in a homogeneous anisotropic rock. It is assumed that the fracture has an elliptical shape and is driven by a power-law fluid. The purpose of this study is to investigate the influence of anisotropy and power-law fluid rheology on the parametric space of solutions. Rock anisotropy is represented by having two values of fracture toughness, one in the vertical direction and another one in the horizontal direction. Similarly, the effect of elastic anisotropy is approximated by using two different effective elastic moduli in the vertical and horizontal directions. In contrast to the isotropic case, for which there are four limiting solutions, the problem for anisotropic rocks features six different limiting cases. These cases represent competition between toughness and viscosity in the vertical and horizontal directions and competition between fluid storage inside the fracture and fluid leak-off into formation. Approximate expressions for the limiting solutions are obtained using global volume balance and tip asymptotic solutions. Despite the developed solutions rely on a series of approximations, they precisely capture all the scaling laws associated with the problem. Zones of applicability of these limiting solutions are calculated, and their dependence on the problem parameters is investigated. 相似文献
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煤是自然界中一种常见的沉积岩,它具有显著的各向异性特征。然而目前针对煤体渗透特性研究,多数学者为了简化问题,多假设煤体为各向同性材料,提出了相应的各向同性渗透模型。这类模型并不能完全反映含瓦斯煤气-固耦合真实工程和室内试验的实际情况。假设煤体为横观各向同性,推导出以不同方向模量损失率为关键参数的煤体各向异性渗透模型,在此基础上,推导出含瓦斯煤的气-固耦合控制方程,并植入Comsol计算平台,系统研究煤体各向异性对气体扩散和渗透的影响。理论和数值研究结果表明：不同方向的模量损失率 反映出煤体结构各向异性变化程度,若 不同,其煤体各方向渗透特性也不相同;煤体渗透率的改变主要受解吸附效应和有效应力作用双重影响, 反映了这两种效应对于渗透率的影响程度;单轴应变或位移控制边界条件下,水平方向的模量损失率 对于垂直方向的煤体渗透率改变量 的影响程度大于对水平方向的煤体渗透率改变量 的影响程度,垂直方向模量损失率 对 的影响则弱于对于 的影响。 相似文献
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Anisotropy is frequently present in geological structures, but usually neglected when source parameters are determined through waveform inversion. Due to the coupling of propagation and source effects in the seismic waveforms, such neglect of anisotropy will lead to an error in the retrieved source. The distortion of the mechanism of a double-couple point source located in an anisotropic medium is investigated when inverting waveforms using isotropic Green's functions. The anisotropic medium is considered to be transversely isotropic with six levels of anisotropy ranging from a fairly weak to rather strong anisotropy, up to about 24% in P waves and 11% in S waves. Inversions are based on either only direct P waves or both direct P and S waves. Two different algorithms are employed: the direct parametrization (DIRPAR, a nonlinear algorithm) and the indirect parametrization (INPAR, a hybrid scheme including linear and nonlinear steps) of the source. The orientation of the double-couple mechanism appears to be robustly retrieved. The inclination of the resulting nodal planes is very small, within 10° and 20° from the original solution, even for the highest degree of anisotropy. However, the neglect of anisotropy results in the presence of spurious isotropic and compensated linear-vector dipole (CLVD) components in the moment tensor (MT). This questions the reliability of non-double-couple components reported for numerous earthquakes. 相似文献
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The anisotropy of magnetic susceptibility (AMS) of single crystals of biotite, muscovite and chlorite has been measured in order to provide accurate values of the magnetic anisotropy properties for these common rock-forming minerals. The low-field AMS and the high-field paramagnetic susceptibility are defined. For the high-field values, it is necessary to combine the paramagnetic deviatoric tensor obtained from the high-field torque magnetometer with the paramagnetic bulk susceptibility measured from magnetization curves of the crystals. This leads to the full paramagnetic susceptibility ellipsoid due to the anisotropic distribution of iron cations in the silicate lattice. The ellipsoid of paramagnetic susceptibility, which was obtained for the three phyllosilicates, is highly oblate in shape and the minimum susceptibility direction is subparallel to the crystallographic c-axes. The anisotropy of the susceptibility within the basal plane of the biotite has been evaluated and found to be isotropic within the accuracy of the instrumental measurements. The degree of anisotropy of biotite and chlorite is compatible with previously reported values while for muscovite the smaller than previously published values. The shape of the chlorite AMS ellipsoid for all the samples is near-perfect oblate in contrast with a wide distribution of oblate and prolate values reported in earlier studies. Reliable values are important for deriving models of the magnetic anisotropy where it reflects mineral fabrics and deformation of rocks. 相似文献
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Numerical models of ionic diffusion in one and three dimensions: application to dehydration of mantle olivine 总被引：1，自引：0，他引：1
The hydrogen content of nominally anhydrous minerals is of great interest, because it can influence many physical and mechanical properties of mantle rocks. Moreover, the hydrogen diffusion profiles can be used to constrain timescales related to magma eruptions. Here, we report models of ionic diffusion for trace elements in anisotropic crystals and apply them to hydrogen diffusing out of mantle-derived olivine. We first compare and discuss the characteristics of 1D and 3D models and show that only 3D anisotropic diffusion models can lead to diffusion profiles exhibiting non-equilibrium plateau at the center of the solid along the slowest axis, as measured in natural samples. In a second part, we discuss the differences between hydration and dehydration of olivine for diffusion that is linked to two different atomic sites involved in hydrogen mobility. Finally, we apply our 3D anisotropic model to previous results on mantle-derived olivine from Pali-aike to better characterize diffusion coefficients and their anisotropy that could be relevant for dehydration of olivine. Our results show that dehydration has to be strongly anisotropic, with a fast [100] axis and a significantly slower [001] axis. 相似文献
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We rederive and present the complete closed-form solutions of the displacements and stresses subjected to a point load in a transversely isotropic elastic half-space. The half-space is bounded by a horizontal surface, and the plane of transverse isotropy of the medium is parallel to the horizontal surface. The solutions are obtained by superposing the solutions of two infinite spaces, one acting a point load in its interior and the other being free loading. The Fourier and Hankel transforms in a cylindrical co-ordinate system are employed for deriving the analytical solutions. These solutions are identical with the Mindlin and Boussinesq solutions if the half-space is homogeneous, linear elastic, and isotropic. Also, the Lekhnitskii solution for a transversely isotropic half-space subjected to a vertical point load on its horizontal surface is one of these solutions. Furthermore, an illustrative example is given to show the effect of degree of rock anisotropy on the vertical surface displacement and vertical stress that are induced by a single vertical concentrated force acting on the surface. The results indicate that the displacement and stress accounted for rock anisotropy are quite different for the displacement and stress calculated from isotropic solutions. © 1998 John Wiley & Sons, Ltd. 相似文献
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Cliff S. J. Shaw 《Contributions to Mineralogy and Petrology》2012,164(5):839-857
Quartz dissolution in melts in the KCAS and KCMAS systems results in the formation of a silica- and potassium-enriched boundary layer next to the dissolving crystals. The presence of potassium in CAS melts has no discernible effect on dissolution rate compared with that in K-free melts with otherwise similar composition despite a small decrease in the diffusivity of silica in the potassium-bearing melts. The decrease in silica diffusivity is offset by an increase in the solubility of silica in the K-bearing melts. Addition of potassium to CMAS melts results in a large decrease in the dissolution rate of quartz. Even though the solubility of silica is enhanced, the addition of potassium leads to large changes in the structure of the melt in the boundary layer (as measured by NBO/T), which results in a large decrease in the diffusivity of silica and thus slower dissolution. There is significant diffusive coupling of Al2O3, CaO and MgO during dissolution, which leads to local uphill diffusion of these components. K2O is decoupled from the other components, as shown by its much thicker diffusion zone. Potassium moves through the boundary layer as a result of two homogeneous reactions: uphill diffusion in which potassium diffuses into the silica-enriched melt adjacent to the dissolving quartz crystal and downhill diffusion in the region furthest from the crystal–melt interface where SiO2 and K2O diffuse away from the interface together. 相似文献
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Richard Giot Sylvie Granet Maxime Faivre Nadia Massoussi Julie Huang 《Geomechanics and Geoengineering》2018,13(4):246-263
A transversely isotropic thermo-poroelastic constitutive law is developed and implemented in the finite element code Code_Aster (EDF, France). It is then validated using an analytic solution for an inclined borehole in a transversely isotropic medium. A strategy for identifying the parameters of the transversely isotropic thermo-poroelastic model based on an inverse method is proposed on the basis of different laboratory tests. To demonstrate the efficiency and applicability of the model, it is then applied in a three-dimensional numerical model of an underground structure in a parameter sensitivity study. The results of the modelling highlight the importance of accounting for anisotropic phenomena when determining the dimensions of underground facilities. The whole approach is presented in the paper, from model development to application to 3D numerical modelling to an engineering case study. 相似文献