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1.
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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Transmitting boundary for water-saturated transversely isotropic strata based on the u–U formulation
A new transmitting boundary in a cylindrical coordinate system has been developed for modeling the elastic waves radiating out to an infinite boundary in water-saturated transversely isotropic soil strata over a rigid bedrock. The saturated soil strata are assumed to consist of a porous material and modeled as a transversely isotropic two-phase medium, based on the u−U formulation. The newly developed transmitting boundary is combined with the finite-elements model of the near-field region, using the same u−U formulation, and applied to the study of the dynamics of a rigid circular foundation in porous isotropic or transversely isotropic layered strata, either fully or partly saturated with water. The verification and application examples give valuable insights into new and interesting aspects of the dynamic behavior of rigid circular foundations in fully or partly saturated two-phase ground in terms of permeability, transverse anisotropy, and ground-water table level. 相似文献
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A local time-domain transmitting boundary for simulating cylindrical elastic wave propagation in infinite media 总被引：3，自引：0，他引：3
Finite element simulation of the time-dependent wave propagation in infinite media requires enforcing the transmitting boundary to replace the truncated far-field infinite domain so as to model the effect of the wave radiation towards infinity. This paper proposed a novel local time-domain transmitting boundary for simulating the cylindrical elastic wave radiation problem. This boundary is a mechanical model consisting of the spring, dashpot and mass elements, with the auxiliary degrees of freedom introduced, which is dynamically stable and easily implemented into the commercial finite element codes. Numerical analysis of the cylindrical elastic wave radiation problem indicates that the proposed transmitting boundaries with the order N=3 for cylindrical P and SV waves and with the order N=4 for cylindrical SH wave have very high accuracy, even when the artificial boundary at wave source. The proposed transmitting boundary with order N=0 can be applied approximately to the general two-dimensional infinite elastic wave problems that contain the more complex outgoing wave fields at artificial boundary than the cylindrical waves. The plane-strain Lamb problem is analyzed with the acceptable engineering accuracy achieved. On the other hand, the proposed transmitting boundary with higher order can be a tool to localize the temporal convolution that appears in an exact time-domain transmitting boundary for the general infinite wave problems. This potential applicability is mentioned. 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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The multi-axial perfectly matched layer (M-PML) is a material boundary condition for wave propagation problems in unbounded domains. It is obtained by extending the formulation of the split-field perfectly matched layer to a more general absorptive medium, for which damping profiles are specified along all dimensions of the problem. Under the hypothesis of small damping, it has been demonstrated that the stability of the system of partial differential equations of the M-PML can be related to the ratio of the damping profiles, and stable M-PML terminations for isotropic and orthotropic elastic media have been constructed. In the present work, we use the Routh–Horwitz determinants to demonstrate that the conclusions regarding the stability of M-PML for isotropic media for small damping are in fact valid for the more general case of damping coefficients of any (positive) value. The effectiveness of the M-PML is demonstrated by constructing stable terminations for the abovementioned media. The stability analysis is presented for 2-D in-plane (P-SV) wave propagation in elastic isotropic continua. 相似文献
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Scattering attenuation in short wavelengths has long been interesting to geophysicists. Ultrasonic coda waves, observed as the tail portion of ultrasonic wavetrains in laboratory ultrasonic measurements, are important for such studies where ultrasonic waves interact with small-scale random heterogeneities on a scale of micrometers, but often ignored as noises because of the contamination of boundary reflections from the side ends of a sample core. Numerical simulations with accurate absorbing boundary can provide insight into the effect of boundary reflections on coda waves in laboratory experiments. The simulation of wave propagation in digital and heterogeneous porous cores really challenges numerical techniques by digital image of poroelastic properties, numerical dispersion at high frequency and strong heterogeneity, and accurate absorbing boundary schemes at grazing incidence. To overcome these difficulties, we present a staggered-grid high-order finite-difference (FD) method of Biot’s poroelastic equations, with an arbitrary even-order (2L) accuracy to simulate ultrasonic wave propagation in digital porous cores with strong heterogeneity. An unsplit convolutional perfectly matched layer (CPML) absorbing boundary, which improves conventional PML methods at grazing incidence with less memory and better computational efficiency, is employed in the simulation to investigate the influence of boundary reflections on ultrasonic coda waves. Numerical experiments with saturated poroelastic media demonstrate that the 2L FD scheme with the CPML for ultrasonic wave propagation significantly improves stability conditions at strong heterogeneity and absorbing performance at grazing incidence. The boundary reflections from the artificial boundary surrounding the digital core decay fast with the increase of CPML thicknesses, almost disappearing at the CPML thickness of 15 grids. Comparisons of the resulting ultrasonic coda Q sc values between the numerical and experimental ultrasonic S waveforms for a cylindrical rock sample demonstrate that the boundary reflection may contribute around one-third of the ultrasonic coda attenuation observed in laboratory experiments. 相似文献
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This paper has two objectives: to connect directly radiation damping and 1D elastic wave propagation, and to create a simple teaching tool to introduce the subject to students and engineers trained in Structural Dynamics. The first objective is achieved by obtaining the equivalent radiation modal damping using time domain solutions for the fundamental mode in shear of an elastic layer (soil) on flexible rock, for the case in which the rock–soil Impedance Ratio in shear, I=(ρrVr)/(ρsVs)>1, where ρ=mass density and V=shear wave velocity. These time domain solutions are developed for the case of steady-state input sinusoidal shear waves propagating vertically in the rock as well as for horizontal free vibration of the layer. Both derivations result in the same approximate expression for the modal radiation damping in the first mode, ζr1≈2/(πI), which is in turn identical to the approximate equation obtained by Roesset and Whitman [11] using a frequency domain approach. This expression for ζr1 is linked to the fact that, during free vibration, the ratio between two successive positive displacement peaks uso and us1 at the ground surface is us0/us1=[(1+I)/(1−I)]2, associated with two wave reflections at the soil–rock interface. From this ratio, and after applying the standard expression to obtain modal damping from damped free vibration, the same expression for ζr1 is reached again, ζr1≈[1/(2π)] ln(us0/us1)≈[1/(2π)] ln[(1+I)/(1−I)]2≈2/(πI). This finding allows development of the simple teaching tool proposed at the end of the paper. While only a crude approximation lacking in rigor, this teaching tool is physically intuitive, links directly wave propagation and modal damping in a simple way and gives the correct result. 相似文献
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R. Ávila-Carrera F. J. Sánchez-Sesma James H. Spurlin C. Valle-Molina A. Rodríguez-Castellanos 《Pure and Applied Geophysics》2014,171(9):2209-2223
An analytic formulation to understand the scattering, diffraction and attenuation of elastic waves at the neighborhood of fluid filled wells is presented. An important, and not widely exploited, technique to carefully investigate the wave propagation in exploration wells is the logging of sonic waveforms. Fundamental decisions and production planning in petroleum reservoirs are made by interpretation of such recordings. Nowadays, geophysicists and engineers face problems related to the acquisition and interpretation under complex conditions associated with conducting open-hole measurements. A crucial problem that directly affects the response of sonic logs is the eccentricity of the measuring tool with respect to the center of the borehole. Even with the employment of centralizers, this simple variation, dramatically changes the physical conditions on the wave propagation around the well. Recent works in the numerical field reported advanced studies in modeling and simulation of acoustic wave propagation around wells, including complex heterogeneities and anisotropy. However, no analytical efforts have been made to formally understand the wireline sonic logging measurements acquired with borehole-eccentered tools. In this paper, the Graf’s addition theorem was used to describe monopole sources in terms of solutions of the wave equation. The formulation was developed from the three-dimensional discrete wave-number method in the frequency domain. The cylindrical Bessel functions of the third kind and order zero were re-derived to obtain a simplified set of equations projected into a bi-dimensional plane-space for displacements and stresses. This new and condensed analytic formulation allows the straightforward calculation of all converted modes and their visualization in the time domain via Fourier synthesis. The main aim was to obtain spectral surfaces of transfer functions and synthetic seismograms that might be useful to understand the wave motion produced by the eccentricity of the source and explain in detail the new arising borehole propagation modes. Finally, time histories and amplitude spectra for relevant examples are presented and the validation of time traces using the spectral element method is reported. 相似文献
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A first-order formulation to analyze the dynamic response of layered soil profiles is presented as an alternative to the widely used second-order thin-layer method by the direct stiffness approach, including an efficient simulation of the underlaying elastic half-space. In contrast to the thin-layer method where response is expressed through a combination of second-order propagation modes, the proposed procedure uses first-order modal parameters that have the capacity to provide a good approximation in the complete wave number domain k, including the exact stiffness values for k=0 and k→∞, thus justifying its designation of doubly-asymptotic. This feature allows obtaining the exact soil profile response for static loads, while the proposed treatment of the elastic half-space reproduces naturally the radiation condition without a need of artificial damping. The capacity of the proposed formulation to solve elastodynamic problems is assessed by comparing its results with those of exact solutions available in the literature, and numerical solutions of rigid disks supported on the surface of different soil profiles. 相似文献
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采用规则网格有限差分方法对二维平面弹性波动方程进行差分离散,得到相应的弹性波动方程的有限差分方程,再将弹性波动方程的差分格式与吸收边界、自由边界的离散形式结合形成弹性波动方程有限差分方程解决问题的主体,将其应用于含方形凹陷半无限非均匀介质的模型中进行数值模拟,得到此离散化模型中不同时刻不同节点的位移值。针对具体算例,运用上述方法结合科学计算软件MATLAB和结果后处理软件DIFEM ISOLINE PLOTER得到不同时刻的水平方向位移等值线图与接收器测量点处的合成位移记录,讨论非均匀介质、吸收边界、方形凹陷等对波动特性的影响。 相似文献
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Mahdi Taiebat Boris Jeremić Yannis F. Dafalias Amir M. Kaynia Zhao Cheng 《Soil Dynamics and Earthquake Engineering》2010
To predict the earthquake response of saturated porous media it is essential to correctly simulate the generation, redistribution, and dissipation of excess pore water pressure during and after earthquake shaking. To this end, a reliable numerical tool requires a dynamic, fully coupled formulation for solid–fluid interaction and a versatile constitutive model. Presented in this paper is a 3D finite element framework that has been developed and utilized for this purpose. The framework employs fully coupled dynamic field equations with a u–p–U formulation for simulation of pore fluid and solid skeleton interaction and a SANISAND constitutive model for response of solid skeleton. After a detailed verification and validation of the formulation and implementation of the developed numerical tool, it is employed in the seismic response of saturated porous media. The study includes examination of the mechanism of propagation of the earthquake-induced shear waves and liquefaction phenomenon in uniform and layered profiles of saturated sand deposits. 相似文献
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3D viscous-spring artificial boundary in time domain 总被引：8，自引：1，他引：7
After a brief review of studies on artificial boundaries in dynamic soil-structure interaction, a three-dimensional viscous-spring artificial boundary （VSAB） in the time domain is developed in this paper. First, the 3D VSAB equations in the normal and tangential directions are derived based on the elastic wave motion theory. Secondly, a numerical simulation technique of wave motion equations along with the VSAB condition in the time domain is studied. Finally, numerical examples of some classical elastic wave motion problems are presented and the results are compared with the associated theoretical solutions, demonstrating that high precision and adequate stability can be achieved by using the proposed 3D VSAB. The proposed 3D VSAB can be conveniently incorporated in the general finite element program, which is commonly used to study dynamic soil-structure interaction problems. 相似文献
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本文分析了具有有限大小的柱状声源下充流体的裸眼井中弹性波的传播,给出了弹性波场的解析结果,表明在某些条件下可发生共振,提出了所谓“频率-功率测井”及“频率测井”的设想。 相似文献
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The phenomenon of wave dispersion in dry sand is studied both by purely analytical studies and by analytical–numerical experiments on the basis of gradient elastic and viscoelastic material models. These material models are employed in order to simulate the microstructural characteristics of dry sand. The analytical studies treat the material body as a one-dimensional (for the viscoelastic case) and three-dimensional (for the gradient elastic case) and for both material models provide explicit expressions for the velocity of propagation of harmonic compressional (P) and shear (S) waves. These velocities are found to be functions of frequency, i.e., dispersive. The analytical–numerical studies treat the material as a one-dimensional one and try to simulate P and S wave propagation along the axial direction of cylindrical dry sand specimens. Thus, a sinusoidal pulse with a specific frequency is applied at one end of the specimen and the response is determined at some other point by solving a transient dynamic boundary value problem with the aid of a numerical Laplace transform. This analytical–numerical experiment is repeated for various frequencies. Thus, one determines the velocities of P and S waves as functions of frequency, thereby proving again that wave propagation in dry sand is dispersive. 相似文献
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本文发展了建立在地层参考状态为各向同性介质假定下的现行井孔声弹性理论,就井外为横向各向同性面与井轴垂直的、具有9个独立三阶弹性模量的横向各向同性介质(VTI井况),水平面内受双轴应力作用下给出了一个简洁的与井内压力、应力差、应力和以及多极源偏振方位角有关的井孔弯曲波声弹公式,并且导出了平面纵、横波速度的声弹公式.数值考察了弯曲波速度之改变量的灵敏系数随频率的变化、受井外水平双轴应力作用时两种偏振的偶极弯曲波频散曲线以及对应不同方位径向偏振的横波速度.研究结果表明弯曲波声弹公式与5个二阶弹性系数以及7个独立的三阶弹性模量有关;而且由内压引起的井孔弯曲波声弹性公式中的三阶弹性模量仅与6个独立的弹性模量有关.横向各向同性介质井孔弯曲波速度的交叉现象仍是判断地应力存在的标志;一个重要的认识是受双轴应力作用的弯曲波速度变化在低频区主要与c144和c155两个三阶弹性模量有关,而且此认识与径向偏振的平面横波一致.在缺乏足够实验条件情况下,对VTI情况,以c144,c155和c123三个独立的量进行测量,然后可暂不考虑三阶弹性模量的各向异性,建立简化的应力反演公式.反之,如果已知地层的地应力信息,由简化的声弹公式可以反演三阶弹性模量c144,c155和c123. 相似文献
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A boundary integral formulation is presented and applied to model the ground motion on alluvial valleys under incident P, S and Rayleigh waves. It is based on integral representations for the diffracted and the refracted elastic waves using single-layer boundary sources. This approach is called indirect BEM in the literature as the sources' strengths should be obtained as an intermediate step. Boundary conditions lead to a system of integral equations for boundary sources. A discretization scheme based on the numerical and analytical integration of exact Green's functions for displacements and tractions is used. Various examples are given for two-dimensional problems of diffraction of elastic waves by soft elastic inclusion models of alluvial deposits in an elastic half-space. Results are displayed in both frequency and time domains. These results show the significant influence of locally generated surface waves in seismic response and suggest approximations of practical interest. For shallow alluvial valleys the response and its resonant frequencies are controlled by a coupling mechanism that involves both the simple one-dimensional shear beam model and the propagation of surface waves. 相似文献