横观各向同性饱和层状地基的三维稳态动力响应

首先引入状态向量,将直角坐标系下横观各向同性饱和土的Biot波动方程转化为一组状态方程,然后基于双重Fourier变换,求解了状态方程,得到传递矩阵.进而利用传递矩阵,并结合饱和地基的边界条件、排水条件及层间接触和连续条件,求解了横观各向同性饱和层状地基的稳态动力响应问题.     

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY (Ⅱ)—LINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

IntroductionInpart(Ⅰ )ofthework[1],byuseofmixturetheory ,thenonlinearconstitutiveequationsandthefieldequationsofunsaturatedsoilwereconstructed ,andthecompleteequationsforthethermodynamicsystemofunsaturatedsoilwasformed .Inthispart,thelinearconstitutiveequationsandfieldequationsofunsaturatedsoilareobtainedthroughlinearizingnonlinearequations,andthelinearequationsarewrittenintheformssimilartoBiot’sequationsforsaturatedporousmedia .ItisprovedthatDarcy’slawissuitabletodescribethemotionofliquid…     

Wave propagation in fractured porous media

A theory of wave propagation in fractured porous media is presented based on the double-porosity concept. The macroscopic constitutive relations and mass and momentum balance equations are obtained by volume averaging the microscale balance and constitutive equations and assuming small deformations. In microscale, the grains are assumed to be linearly elastic and the fluids are Newtonian. Momentum transfer terms are expressed in terms of intrinsic and relative permeabilities assuming the validity of Darcy's law in fractured porous media. The macroscopic constitutive relations of elastic porous media saturated by one or two fluids and saturated fractured porous media can be obtained from the constitutive relations developed in the paper. In the simplest case, the final set of governing equations reduce to Biot's equations containing the same parameters as of Biot and Willis.Now at Izmir Institute of Technology, Anafartalar Cad. 904, Basmane 35230, Izmir, Turkey.     

海洋地震工程流固耦合问题统一计算框架

海底地震动的模拟以及海洋工程结构的地震反应分析中,涉及到海水、饱和海床、弹性基岩、结构之间的相互耦合.传统的方法分别采用声波方程描述理想流体、Biot方程描述饱和海床、弹性波方程描述基岩和结构,分别考虑相互之间的耦合,十分不便.本文基于理想流体、固体分别为饱和多孔介质的特殊情形(孔隙率分别为1和0),由饱和多孔介质的Biot方程可退化得到理想流体的声波方程和固体的弹性波方程.然后,以饱和多孔介质方程为基础,经集中质量有限元离散,考虑不同孔隙率的饱和多孔介质之间耦合的一般情形,建立了该耦合情形的求解方法.进一步论证了该一般情形的耦合计算方法可分别退化到流体与固体、流体与饱和多孔介质、固体与饱和多孔介质之间的耦合计算,从而将流体、固体、饱和多孔介质间的耦合问题纳入到统一计算框架,并编制了相应的三维并行分析程序.以P-SV波垂直入射时,半无限层状海水-饱和海床、海水-弹性基岩、海水-饱和海床-弹性基岩三种情形的动力分析为例,采用统一计算框架结合透射边界条件进行求解,并与传递矩阵方法得到的解进行对比,验证了该统一计算框架的有效性以及并行计算的可行性.      

CONSTITUTIVE RELATION OF UNSATURATED SOIL BY USE OF THE MIXTURE THEORY (Ⅱ)-LINEAR CONSTITUTIVE EQUATIONS AND FIELD EQUATIONS

The linear constitutive equations and field equations of unsaturated soils were obtained through linearizing the nonlinear equations given in the first part of this work. The linear equations were expressed in the forms similar to Biot’s equations for saturated porous media. The Darcy’s laws of unsaturated soil were proved. It is shown that Biot’s equations of saturated porous media are the simplification of the theory. All these illustrate that constructing constitutive relation of unsaturated soil on the base of mixture theory is rational.     

海洋地震工程流固耦合问题统一计算框架——————不规则界面情形

海底地震动场及海洋声场的模拟中,需要考虑复杂海床介质及海底地形的影响,涉及到海水、饱和海床、弹性基岩之间的相互耦合.传统的方法分别采用声波方程描述理想流体、Biot方程描述饱和海床、弹性波方程描述基岩,分别进行空间离散和界面耦合, 十分不便.本文基于理想流体、固体分别为饱和多孔介质的特殊情形(孔隙率分别为1和0),由饱和多孔介质的Biot方程可退化得到理想流体的声波方程和固体的弹性波方程.然后, 以饱和多孔介质方程为基础, 经集中质量有限元离散,严格考虑不同孔隙率的饱和多孔介质在不规则界面的耦合条件,通过求解法向和切向界面力的途径,建立了不同孔隙率的饱和多孔介质耦合情形的求解方法,将流体、固体、饱和多孔介质间的耦合问题纳入到统一计算框架,并编制了相应的三维并行分析程序.考虑海水--弹性基岩、海水--饱和海床--弹性基岩体系中凹陷地形情形,采用本文提出的统一计算框架, 结合透射边界条件,分析了P波入射时的动力反应, 并通过结果是否满足界面条件,验证了该统一计算框架的有效性以及并行计算的可行性.      

多孔饱和半空间上刚体垂直振动的轴对称混合边值问题

研究圆柱形刚体在多孔饱和半空间上的垂直振动．首先应用Ｈａｎｋｅｌ变换求解多孔饱和固体的动力基本方程———Ｂｉｏｔ波动方程．然后按混合边值条件建立多孔饱和半空间上刚体垂直振动的对偶积分方程，用Ａｂｅｌ变换化对偶积分方程为第二类Ｆｒｅｄｈｏｌｍ积分方程．文末给出了多孔饱和半空间表面动力柔度系数的计算曲线．     

层状横观各向同性饱和土的非轴对称动力响应

通过方位角的Fourier变换，将圆柱坐标系下横观各向同性饱和土的Biot非轴对称波动方 程转化为一组一阶常微分方程组. 然后基于径向Hankel变换,建立问题的状态方程；求解状态方程后,得到传递矩阵. 进而利用传递矩阵，结合饱和层状地基的边界条件、排水条件及层间接触和连续条件,求解 了任意震源力作用下层状横观各向同性饱和地基频域动力响应问题. 时域解可通过频率的Fourier积分得到.     

3-D DYNAMIC RESPONSE OF TRANSVERSELY ISOTROPIC SATURATED SOILS

Introduction Thedynamicanalysisofsaturatedporoelasticmediaisofbroadmeaninginmanyaspectssuchasseismology,earthquakeengineering,soilmechanicsandgeophysics,etc.Thetransverselyisotropicsaturatedsoilsissolid fluidcoupledtwophasemediainwhichthe soilskeletondisp…     

Body waves in fractured porous media saturated by two immiscible newtonian fluids

A study of body waves in fractured porous media saturated by two fluids is presented. We show the existence of four compressional and one rotational waves. The first and third compressional waves are analogous to the fast and slow compressional waves in Biot's theory. The second compressional wave arises because of fractures, whereas the fourth compressional wave is associated with the pressure difference between the fluid phases in the porous blocks. The effects of fractures on the phase velocity and attenuation coefficient of body waves are numerically investigated for a fractured sandstone saturated by air and water phases. All compressional waves except the first compressional wave are diffusive-type waves, i.e., highly attenuated and do not exist at low frequencies.Now at Izmir Institute of Technology, Faculty of Engineering, Gaziosmanpasa Bulvari, No.16, Cankaya, Izmir, Turkey.     

正交各向异性含液饱和多孔介质中应力波的传播

基于Biot的孔隙介质理论，研究了正交各向异性含液饱和多孔介质中应力波的传播特性．本文引入动态渗透率，导出了整个实频域内应力波传播的复特征方程及其解析解，给出了各种应力波成分的波速和衰减的解析表达武，计算了频散曲线和衰减曲线，并讨论了各类应力波之间的耦合关系及介质的各向异性对应力波传播的影响．     

川藏公路地质环境与整治改建方案的思考

川藏公路由于地质环境复杂、建设标准低、后遗病害多,抗灾能力差,泥石流、滑坡、山崩、雪害、水毁等自然灾害频繁发生,公路阻车断道严重。国家投入巨资进行整治改建,并取得了明显的效果,但由于自然环境特殊、影响因素复杂,许多特大型、大型工程地质病害问题还没有可行、可靠的解决方案。本文通过分析川藏公路沿线的地质环境和灾害特点,总结历年整治改建和经验的教训,提出川藏公路建设的途径、可能达到的目标和应采用的原则。     

Wave propagation with mass-coupling effect in fluid-saturated porous media

This article utilizes the theory of mixtures to formulate a general theory of wave propagation with mass-coupling effect in fluid-saturated porous media. An attempt is made to discuss the physical interpretation and the thermodynamic restriction of the coefficients appearing in the equations obtained. By the comparison it is shown that Biot's classical theory and the present one are essentially consistent. Also, wave velocities in some special cases are calculated, from which it is concluded that mass-coupling and permeability of media greatly affect wave propagation behavior.     

Mixture modeling of jointed fluidsaturated porous media

The quasi-static equations of motion are studied for bi-laminated fluid-saturated porous media within the framework of non-phenomenological mixture theories. The flow-deformation coupled behavior of the media is governed by Biot's theory for which all constituents are considered compressible. The asymptotic analysis for a periodic microstructure with multiple scales, developed by Hegemier and Murakami, is adopted to obtain the equations of equilibrium and mass conservation in a binary saturated porous medium. The multiscale analysis appears to be advantageous for dealing with consolidation phenomena because it is capable of transforming a coupled, transient problem into two decoupled, steady-state ones. Various models with different degrees of approximation are generated, and among them a theory for saturated rocks with a single joint system is described. Mixture properties are expressed explicitly in terms of characteristics of intact and joint material. The most distinctive feature of this model comes from the fact that some cross terms, that have not been included in previous models, appear in the constitutive equations for fluid mass change and fluid flux. These cross terms are physically understood because they simply take into account effects occurring on the local level: the deformation-flow coupled phenomenon, the stress continuity and displacement compatibility conditions. These novel results may have far-reaching consequences for future theoretical modeling and experimental programs in two-phase fluid-filled porous media.     

横观各向同性液体饱和多孔介质中平面波的传播

基于孔隙介质的Ｂｉｏｔ理论１，研究了横观各向同性液体饱和多孔介质中平面波的传播特性。首先导出了波传播的特征方程并给出了其解析解，结果显示：有４种不同波速的平面体波传播；第一准纵波，第二准纵波，准横波和反平面横波。文中给出了波速和衰减的解析表达式，数值计算了频散曲线和衰减曲线，并讨论了各类准体波位移之间的耦合关系。     

半空间饱和土内置点载荷作用下的热弹性波动

基于Biot波动理论及热弹性动力理论,利用已建立的饱和多孔弹性介质热流固耦合控制方程,研究半无限地基在内置点热力源作用下的动力响应问题. 求解过程引用Hankel变换技术,得到了热力源作用下土体中温度增量、应力、位移和孔隙水压力的积分形式解答.利用Hankel数值逆变换得到计算结果,分析了热流固耦合条件下激振频率对竖向位移和孔隙水压力响应的影响. 对热流固耦合、热弹性和多孔弹性模型计算结果进行了比较.      

液饱和多孔介质中三维应力波的传播

为了深入研究液饱和多孔介质中应力波的传播，提出了三维两相细观计算模型．基于此模型。应用Galerkin余量法并计及流-固耦合界面的耦合效应，利用直接耦合的技术，开发了三维流-固混合显式动力有限元计算程序．在此基础上对冲击载荷作用下液饱和多孔介质中三维应力波的传播现象进行了数值模拟，并详细讨论了孔隙率，孔隙形状等因素对应力波传播主导波形的影响．     

不可压饱和粘弹性多孔介质的变分原理及其无网格模拟

基于饱和多孔介质理论,在固相和液相微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,建立了流体饱和粘弹性多孔介质动力响应的若干Gurtin型变分原理,包括Hu-Washizu变分原理.利用所建立的变分原理,导出了流体饱和粘弹性多孔介质动力响应无网格数值模拟的离散控制方程,此方程是一个关于时间的对称微分方程组,便于分析计算.作为数值例子,研究了流体饱和粘弹性多孔柱体的一维动力响应,数值结果揭示了流体饱和粘弹性多孔柱体中波的传播特性以及固相粘性的影响.     

AN ANALYTICAL SOLUTION FOR THREE-DIMENSIONAL DIFFRACTION OF PLANE P-WAVES BY A HEMISPHERICAL ALLUVIAL VALLEY WITH SATURATED SOIL DEPOSITS

An analytical solution for the three-dimensional scattering and diffraction of plane P-waves by a hemispherical alluvial valley with saturated soil deposits is developed by employing Fourier-Bessel series expansion technique. Unlike previous studies, in which the saturated soil deposits were simulated with the single-phase elastic theory, in this paper, they are simulated with Biot's dynamic theory for saturated porous media, and the half space is assumed as a single-phase elastic medium. The effects of the dimensionless frequency, the incidence angle of P-wave and the porosity of soil deposits on the surface displacement magnifications of the hemispherical alluvial valley are investigated. Numerical results show that the existence of a saturated hemispherical alluvial valley has much influence on the surface displacement magnifications. It is more reasonable to simulate soil deposits with Biot's dynamic theory when evaluating the displacement responses of a hemispherical alluvial valley with an incidence of P-waves.