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General absorbing boundary conditions based on Biot's two-phase mixture theory and paraxial approximation is presented for the dynamic analysis of fluid-saturated porous media with isotropic, transverse isotropic, and anisotropic properties. For the last two cases, the equivalent Lame's constants, under conditions of uniqueness, are introduced to facilitate the analytical solutions. The numerical results show that the proposed absorbing boundary can greatly suppress spuriously reflected waves and efficiently model the far field of the system with sufficient accuracy. 相似文献
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流体饱和多孔介质黏弹性动力人工边界 总被引：1，自引：0，他引：1
基于Biot流体饱和多孔介质本构方程，采用平面波和远场散射波经验叠加来反映外行波传播，以经验参数反映人工边界外行波动的衰减和多角度透射特性。在人工边界处分别施加反映固相和液相介质传播效应的弹簧及阻尼来模拟人工边界以外的无限域介质对来自有限域的外行波的能量的吸收作用。从而形成一种流体饱和多孔介质的黏弹性动力人工边界。数值算例表明：边界的精度和稳定性高于现有的黏性边界、黏弹性人工边界及一阶透射边界。 相似文献
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Based on the u–p formulation of Biot equation with an assumption of zero permeability coefficient, a high-order transmitting boundary is derived for cylindrical elastic wave propagation in infinite saturated porous media. By this transmitting boundary the total stresses on the truncated boundaries of a numerical model, such as a finite element model, are replaced by a set of spring, dashpot and mass elements, with some additionally introduced auxiliary degrees of freedom. The transmitting boundaries are incorporated into the DIANA SWANDYNE II program and an unconditionally stable implicit time integration algorithm is adopted. Despite the assumption made in the derivation of the transmitting boundary, numerical examples show that it can provide highly accurate results for cylindrical elastic wave propagation problems in infinite saturated porous medium in case the u–p formulation is applicable. Although the direct applications of the proposed transmitting boundary to general two dimensional wave problems in infinite saturated porous media are not highly accurate, acceptable accuracy can still be achieved by placing the transmitting boundary at relatively large distance from the wave source. 相似文献
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An absorbing boundary for saturated porous media is developed that can be used for transient analyses in the time domain. The elastic constitutive equations for the saturated porous media follow Bowen's formulation. The method consists of applying viscous tractions along the artificial boundary. The absorbing boundary behaviour is assumed linear and isotropic. Hadamard's conditions provide the speeds of the dilatational and shear waves that propagate in saturated porous media. Since these expressions are frequency independent, the intensities of the viscous tractions are evaluated in the time domain, and the two dilatational waves are accounted for. The viscous tractions are defined from the drained characteristics, assuming an infinite permeability, at variance with the traditional ‘undrained’ method based on undrained characteristics and a null permeability. Solid media and materials with low permeability are also retrieved as subcases. The results show that, at no additional cost, this ‘drained’ method is more accurate for all permeabilities than the ‘undrained’ method, which disregards the existence of the second dilatational wave. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
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模拟弹性波在孔隙介质中传播，需要稳定有效的吸收边界来消除或尽可能的减小由人工边界引起的虚假反射. 本文在前人工作基础上，首次建立了弹性孔隙介质情况下完全匹配层吸收边界的高阶速度-应力交错网格有限差分算法，并详细讨论了完全匹配层的构建及其有限差分算法实现. 首先，本文通过均匀孔隙模型的数值解与解析解的对比，验证所提出的数值方法的正确性；然后，本文考察了完全匹配层对不同入射角度入射波和自由表面上的瑞利波的吸收性能，将完全匹配层与廖氏和阻尼吸收边界进行了对比，研究了这三种吸收边界在不同吸收厚度情况下对弹性波吸收能力. 数值结果表明，在孔隙介质中，完全匹配层作为吸收边界能十分有效地吸收衰减外行波，无论对体波还是面波，是一种高效边界吸收算法. 相似文献
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Amongst different existing techniques developed for absorbing boundaries in transient dynamic analysis, the paraxial approximation represents an elegant framework. This approach is extended to the case of saturated porous media, which is of vital interest in many earthquake engineering problems. With respect to the frequency content of the dynamic process, several formulations exist for modelling the two-phase behaviou of soil or rock materials. The existence of a shear wave and two dilatational waves, which are standard features of porous media, is verified for the adopted formulation. The paraxial approximation is presented in the case of the u – p Biot two-phase dynamic formulation, suitable for seismic analyses and implemented by using a finite element approach. The efficiency of these boundaries is further verified through same numerical examples. 相似文献
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基于ABAQUS软件平台,应用自行开发的流固耦合动力模型孔压单元模拟场地土体,并通过黏弹性人工边界方法实现地震动的输入,对饱和土体场地中的双孔隧道结构在地震荷载作用下的动力反应进行研究。计算结果表明:在地震反应结束时刻,场地土体位移幅值在两隧道之间以及两隧道的附近区域较大,而远离隧道的区域则较小;场地底部区域土体的孔压幅值较大,而场地顶部区域土体则较小;隧道左右两侧拱腰部位的衬砌的应力较大,而拱顶部位则较小。计算结果同时表明了流固耦合动力模型孔压单元在饱和土体-隧道体系地震反应研究中的适用性。 相似文献
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本文基于Biot理论,推导出Zoeppritz形式的双相介质分界面上弹性波的反射与透射公式,对单相Zoeppritz公式与双相反射系数公式进行了比较,对双相介质含油、水、气不同流体时的反射规律以及孔隙度、渗透率、饱和度等储层参数对纵波反射的影响进行了研究.数值模拟分析表明,双相与单相反射公式的主要差异在于双相介质反射公式中考虑了液相、固液耦合相弹性模量的影响;油砂、水砂、气砂岩的慢P波反射差异明显;快P波反射对孔隙度的变化敏感,饱和度次之,对渗透率和频率的变化不敏感. 相似文献
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二相介质饱和土中群桩动力阻抗分析 总被引：4，自引：0，他引：4
用流体饱和多孔介质材料描述土体，由饱和土和群桩及承台系统的位移协调条件和力平衡条件建立饱和土和群桩及承台系统动力相互作用的控制方程，分析饱和土中群桩动力阻抗。结果表明：孔隙流体对饱和土中桩基础动力阻抗有一定的影响；在饱和土具有不同的流体渗透系数时，饱和土中群桩动力阻抗也有一定差别。在地基上与基础结构动力相互作用研究中应该考虑地基土中孔隙流体的影响。 相似文献
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《Advances in water resources》1998,21(3):203-215
Transport of inert solutes in two-dimensional bounded heterogeneous porous media is investigated in a stochastic framework. After adopting a first-order approximation of the flow equations, analytical expressions are derived for the velocity covariances. Effects of the boundary conditions and aquifer size upon the statistical moments are analyzed. While the size of the domain is shown to have small influence on the covariances in most cases, the solutions are considerably modified by the boundaries. The results are compared with analytical solutions on infinite domains, and several discrepancies are demonstrated. For example, while the velocity variances on infinite domains are homogeneous, the present results are strongly non-stationary. Finally, the problem is solved numerically by the Monte Carlo simulation method. The results, including the behavior near the boundaries, are shown to be in close agreement with analytical solutions. 相似文献
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Seyyed M. Hasheminejad Reza Avazmohammadi 《Soil Dynamics and Earthquake Engineering》2007,27(1):29-41
This study investigates the dynamic interaction of time harmonic plane waves with a pair of parallel circular cylindrical cavities of infinite length buried in a boundless porous elastic fluid-saturated medium. The novel features of Biot dynamic theory of poroelasticity along with the appropriate wave field expansions, the pertinent boundary conditions, and the translational addition theorems for cylindrical wave functions are employed to develop a closed-form solution in the form of infinite series. The analytical results are illustrated with numerical examples in which two empty cavities are insonified by a fast compressional or a shear wave at end-on incidence. The basic dynamic field quantities such as the hoop stress amplitude and the radial displacement of the elastic frame are evaluated and discussed for representative values of the parameters characterizing the system. The effects of the proximity of the two cavities, the incident wave frequency and type are examined. Particular attention has been focused on multiple scattering interactions in addition to the slow wave coupling effects which is known to be the primary distinction of the scattering phenomenon in poroelasticity from the classical elastic case. Limiting case involving two empty cylindrical cavities in an elastic solid is considered and excellent agreement with a well-known solution is established. 相似文献
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平面SV波在饱和土半空间中圆柱形孔洞周边的散射 总被引：3，自引：1，他引：2
在Biot饱和多孔介质动力学理论的基础上,利用Fourier—Bessel级数展开法,得到SV波在饱和土半空间中圆柱形孔洞周边的散射问题的解析解答。与已有相关问题的解析解答进行对比,验证了此解的正确性,并给出算例,分析了入射频率对柱面上的应力集中因子的影响。 相似文献
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We derive a governing second-order acoustic wave equation in the time domain with a perfectly matched layer absorbing boundary condition for general inhomogeneous media. Besides, a new scheme to solve the perfectly matched layer equation for absorbing reflections from the model boundaries based on the rapid expansion method is proposed. The suggested scheme can be easily applied to a wide class of wave equations and numerical methods for seismic modelling. The absorbing boundary condition method is formulated based on the split perfectly matched layer method and we employ the rapid expansion method to solve the derived new perfectly matched layer equation. The use of the rapid expansion method allows us to extrapolate wavefields with a time step larger than the ones commonly used by traditional finite-difference schemes in a stable way and free of dispersion noise. Furthermore, in order to demonstrate the efficiency and applicability of the proposed perfectly matched layer scheme, numerical modelling examples are also presented. The numerical results obtained with the put forward perfectly matched layer scheme are compared with results from traditional attenuation absorbing boundary conditions and enlarged models as well. The analysis of the numerical results indicates that the proposed perfectly matched layer scheme is significantly effective and more efficient in absorbing spurious reflections from the model boundaries. 相似文献
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应用高精度人工边界条件可有效提升近场波动数值模拟计算效率.完美匹配层是吸收层形式高精度人工边界条件,匹配层内场方程和界面条件通常分别采用复坐标延伸技术变换强形式无限域内波动方程和界面条件得到,亦曾将无限域界面条件当作匹配层界面条件.场方程和界面条件构建过程相互独立,可能出现匹配不合理而引发数值失稳、计算精度低下等问题.本文提出采用复坐标延伸技术变换弱形式无限域波动方程以构建完美匹配层的方法.弱形式波动方程耦合了波动方程及界面条件,进而规避了变换后所得场方程与界面条件之间的匹配不合理问题.新方法可直接建立弱形式匹配层,在此基础上亦可给出强形式匹配层.弱形式便于有限元离散,强形式便于有限差分离散.基于弱形式完美匹配层,结合勒让德谱元建立了弹性介质近场波动谱元模拟方案.利用算例验证了新方案的精度及数值稳定性.本文工作可直接推广至多相耦合介质近场波动数值模拟. 相似文献
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基于双相各向异性介质模型,首先推导了双相各向异性介质中弹性波传播的动力学方程及其Galerkin变分方程和有限元运动方程,然后给出了孔隙弹性波方程的有限元数值解法以及二维双相PTL介质中波场模拟的人为吸收边界条件. 最后,利用本文给出的有限元方法对双相PTL介质和双相各向同性介质中的弹性波传播进行了数值模拟. 结果表明:有限元方法和吸收边界条件有效、可行,在理想相界条件下,不论是从固体位移,还是从流体位移的波场快照都能看到明显的慢速拟P波;在黏滞相界情况下,能否观察到慢速拟P波,与含流体地层介质的耗散性质有关.对实际含流体介质,从流体位移分量的波场快照比从固体位移波场快照更容易观察到慢速拟P波. 相似文献