饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法

本文基于Biot的饱和多孔介质本构方程,考察具有辐射阻尼的外行球面波,推导了饱和多孔介质三维黏弹性人工边界的法向和切向边界方程;在已有的饱和多孔介质二维显式有限元数值计算方法基础上,提出该理论的三维方法,并开发了实现该三维方法的有限元程序.算例表明饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法具有较好的精度和稳定性.     

饱和多孔介质近场波动分析的一种黏弹性人工边界

采用有限模型数值方法求解能量开放系统中的波动问题时,虚拟人工边界的处理方式对计算结果的准确性和精度具有重要的影响.本文针对无限域饱和多孔介质中波传播问题的人工边界处理方式进行了研究,提出了饱和多孔介质近场波动分析的一种黏弹性人工边界处理方法.在考虑多孔介质中固相和液相的相互作用的情况下,通过在人工边界处分别施加反映固相和液相介质波传播效应的弹簧及阻尼来模拟饱和多孔介质中波的能量辐射效应影响.算例表明,本文建议的黏弹性人工边界具有较好的模拟效果.     

流体饱和多孔隙介质弹性波方程边界元解法研究

基于流体饱和多孔隙各向同性介质模型,本文首先推导了流体饱和多孔隙介质中弹性波传播的频率域系统动力方程及边界积分方程,然后给出了流体饱和多孔隙介质弹性波方程的基本解,最后,利用本文给出的边界元方法对流体饱和多孔隙各向同性介质中的弹性波传播进行了数值模拟.结果表明：不论是从固相位移,还是液相位移的地震合成记录都能看到明显的慢速P波,本文提出的流体饱和多孔隙介质弹性波边界元法是有效可行的.     

波在饱和多孔介质与弹性固体介质交界面上的界面效应

本利用Ｂｉｏｔ饱和多孔介质动力学理论及饱和多孔介质和固体介质交界面的连续条件,推导了平面ＰＩ波以任意角饱和多孔介质向弹性固体介质入射时,反射快Ｐ１波,慢ＰＨ波和ＳＶ波和透射Ｐ波、ＳＶ波系数的计算公式,并给出一算例,本不考虑饱和多孔介质中液体渗流的能量耗散。     

流体饱和多孔介质波动方程的有限元解法

讨论了流体饱和多孔介质中波传播问题的有限元解法,首先在Ｂｉｏｔ理论的基础 上,概述了数学问题的提法,然后提出了一种新型简便的人工边界上的无反射边界条件,同时 给出了有人工边界时流体饱和多孔介质波动方程的有限元计算公式．数值试验的结果表明, 本文提出的无反射边界条件和数值方法均很有效．     

流体饱和多孔介质波动方程的有限元解法

讨论了流体饱和多孔介质中波传播问题的有限元解法,首先在Ｂｉｏｔ理论的基础 上,概述了数学问题的提法,然后提出了一种新型简便的人工边界上的无反射边界条件,同时 给出了有人工边界时流体饱和多孔介质波动方程的有限元计算公式．数值试验的结果表明, 本文提出的无反射边界条件和数值方法均很有效．     

黏弹性人工边界在ADINA中的应用

探讨利用ADINA 的弹簧阻尼单元模拟黏弹性人工边界的方法,并进行了均匀半空间算例与成层半空间的计算,验正了采用的黏弹性人工边界具有较高的精度,可以方便的应用于波动问题的模拟解析,从而可以有效地分析结构-地基的动力相互作用问题.     

平面S波在饱和多孔热弹性介质边界的反射问题研究

针对饱和多孔介质中热弹性波的传播特性问题,基于多孔介质理论和广义的热弹性模型,研究平面S波在饱和多孔热弹性介质边界上的反射问题。以考虑流-固耦合的饱和多孔介质波动方程和热-弹耦合的广义热弹性基本方程出发,建立饱和多孔介质的热-流-固耦合弹性波动模型。通过引入势函数并考虑自由透水和绝热的边界条件,经过理论推导最终给出在饱和多孔热弹性介质边界上的四种反射波的振幅反射率的理论表达式。在此基础上进行数值计算,分别讨论平面S波的入射频率、入射角和热膨胀系数等参数对四种反射波的振幅反射率的影响情况。结果表明:各反射波的振幅反射率分别随频率和热膨胀系数的增大而增大,同时也受到平面S波入射角变化的影响。该结论对于土动力学的理论研究及其相关的工程勘探具有一定的指导意义。     

A viscous boundary for transient analyses of saturated porous media

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.     

New artificial boundary condition for saturated soil foundations

A new artificial boundary model based on multi-directional transmitting and viscous-spring artificial boundary theories is proposed to absorb stress waves in a saturated soil foundation in dynamic anal...     

Coupling multiscale finite element method for consolidation analysis of heterogeneous saturated porous media

The multiscale finite element method is developed for solving the coupling problems of consolidation of heterogeneous saturated porous media under external loading conditions. Two sets of multiscale base functions are constructed, respectively, for the pressure field of fluid flow and the displacement field of solid skeleton. The coupling problems are then solved with a multiscale numerical procedure in space and time domain. The heterogeneities induced by permeabilities and mechanical parameters of the saturated porous media are both taken into account. Numerical experiments are carried out for different cases in comparison with the standard finite element method. The numerical results show that the coupling multiscale finite element method can be successfully used for solving the complicated coupling problems. It reduces greatly the computing effort in both memory and time for transient problems.     

Analysis of Rayleigh waves in saturated porous elastic media by finite element method

A numerical procedure for the analysis of Rayleigh waves in saturated porous elastic media is proposed by use of the finite element method. The layer stiffness matrix, the layer mass matrix and the layer damping matrix in a layered system are presented for the discretized form of the solid-fluid equilibrium equation proposed by Biot. In order to consider the influence of the permeability coefficient on the behavior of Rayleigh waves, attention is focused on the following states: ‘drained’ state, ‘undrained’ state and the states between two extremes of ‘drained’ and ‘undrained’ states. It is found from computed results that the permeability coefficient exerts a significant effect on dispersion curves and displacement distributions of Rayleigh waves in saturated porous media.     

A viscous-spring transmitting boundary for cylindrical wave propagation in saturated poroelastic media

Based on the u–U formulation of Biot equation and the assumption of zero permeability coefficient, a viscous-spring transmitting boundary which is frequency independent is derived to simulate the cylindrical elastic wave propagation in unbounded saturated porous media. By this viscous-spring boundary the effective stress and pore fluid pressure on the truncated boundary of the numerical model are replaced by a set of spring, dashpot and mass elements, and its simplified form is also given. A u–U formulation FEA program is compiled and the proposed transmitting boundaries are incorporated therein. Numerical examples show that the proposed viscous-spring boundary and its simplified form can provide accurate results for cylindrical elastic wave propagation problems with low or intermediate values of permeability or frequency content. For general two dimensional wave propagation problems, spuriously reflected waves can be greatly suppressed and acceptable accuracy can still be achieved by placing the simplified boundary at relatively large distance from the wave source.     

Absorbing boundary conditions for dynamic analysis of fluid-saturated porous media

Based on Biot's two-phase mixture theory and the paraxial approximation, the absorbing boundary conditions in the time domain for u-w, u-U and u-p formulations are presented for the dynamic analysis of fluid-saturated porous media. These absorbing boundaries are equivalent to the viscous boundaries in the fundamental mode. The expressions for the energy ratio and reflection coefficient between the reflected and incident waves along the absorbing boundary are given. The numerical results show that the proposed absorbing boundaries can greatly suppress the spuriously reflected wave and model the far field of the system. These results also dynamic analysis of infinite fluid-saturated porous media. for the transient dynamic analysis of infinite fluid-saturated porous media.     

Wavefield simulation in porous media saturated with two immiscible fluids

Wavefields in porous media saturated by two immiscible fluids are simulated in this paper. Based on the sealed system theory, the medium model considers both the relative motion between the fluids and the solid skeleton and the relaxation mechanisms of porosity and saturation (capillary pressure). So it accurately simulates the numerical attenuation property of the wavefields and is much closer to actual earth media in exploration than the equivalent liquid model and the unsaturated porous medium model on the basis of open system theory. The velocity and attenuation for different wave modes in this medium have been discussed in previous literature but studies of the complete wave-field have not been reported. In our work, wave equations with the relaxation mechanisms of capillary pressure and the porosity are derived. Furthermore, the wavefield and its characteristics are studied using the numerical finite element method. The results show that the slow P3-wave in the non-wetting phase can be observed clearly in the seismic band. The relaxation of capillary pressure and the porosity greatly affect the displacement of the non-wetting phase. More specifically, the displacement decreases with increasing relaxation coefficient.     

Comparison of Galerkin-type discretization techniques for two-phase flow in heterogeneous porous media

A comparison of Standard Galerkin, Petrov-Galerkin, and Fully-Upwind Galerkin methods for the simulation of two-phase flow in heterogeneous porous media is presented. On the basis of the coupled pressure-saturation equations, a generalized formulation for all three finite element methods is derived and analysed. For flow in homogeneous media, the Petrov-Galerkin method gives excellent results. But this method fails miserably for problems with heterogeneous media. This is because it is not able to capture correctly processes that take place at interfaces when, for instance, the capillary pressure-saturation relationship after Brooks and Corey is assumed. The Fully-Upwind Galerkin method is superior to the Petrov-Galerkin approach because it is able to give correct results for flow in homogeneous and heterogeneous media for the two models of van Genuchten and Brooks-Corey. The widely used formulation which is correct for the homogeneous case cannot be used for heterogeneous media. Instead the straightforward approach of gradp_c in combination with a chord-slope technique must be utilized.