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...     

SV波在饱和土体自由表面的反射

基于饱和两相介质弹性波动方程分析SV波在饱和土体自由表面的反射问题,引入波动方程的势函数解答,求解出二维问题中SV波入射情况下饱和土体自由场的位移、速度、加速度和应力响应。在饱和土体自由场响应解析解基础上,建立SV波入射下饱和土体自由场静、动力有限元模型。建模中考虑了如下几方面因素:(1)在不同分析步,对土体单元赋予不同材料本构。通过*model change命令进行单元生死设定,从而实现在初始应力场平衡的静力状态下采用DuncanChang本构模型,而地震波动输入时采用Davidenkov动力本构模型;(2)采用多孔介质黏弹性人工边界条件,在人工边界上分别施加固相和液相介质的弹簧和阻尼来模拟饱和土体中能量的传播;(3)将地震波转化为作用在人工边界上的等效地震荷载,施加到人工边界节点上;(4)土体单元采用4结点平面应变孔压单元(CPE4P)。有限元计算与解析解比较结果表明:SV波在垂直入射和掠入射时,竖向位移响应为零;在45°左右入射时,水平位移响应最大;60°左右入射时,竖向位移响应最大。这些结论与解析解吻合较好,本文模型为建立土-结构动力相互作用模型打下良好的基础。     

SV波入射下饱和地层浅埋平行隧道动力响应机制

目前城市核心区交叠紧邻的隧道群大量涌现,其抗震安全性问题日益突出,但近邻隧道之间以及与地层的动力相互作用机制尚不清晰.本文针对饱和地层浅埋平行隧道,基于Biot两相介质理论,采用边界积分方程法分别建立了饱和地层水平和竖向双线隧道动力作用分析模型,并与典型算例精确解对比验证了本模型的有效性;在此基础上,研究了SV波入射频...     

饱和土中平面应变波在圆柱体上的散射和折射

采用修改的Biot波动方程,考虑土颗粒压缩和固液两相的粘滞作用,推导出饱和土中平面应变波在圆柱体上的散射和折射问题的理论解答;并求出当圆柱体为空腔、刚性体、单相土介质和流体介质时散射和折射的势函数幅值方程．      

油水两相饱和储层中平面震电波场响应特性

现有的孔隙介质震电理论缺乏针对含油储层震电耦合的数学模型及定量模拟,制约了该方法在含油储层中的推广应用.本文将非饱和孔隙介质中弹性波动理论与含油储层中动电耦合理论及麦克斯韦电磁理论相结合,建立了描述油水两相饱和储层中震电耦合波的数学方法,定量模拟了含油储层中平面震电波场响应特性,并探讨了储层参数对震电波场响应的影响.研究结果表明:油水两相饱和储层中震电耦合产生四种震电耦合波,震电横波、震电纵波P1、P2和P3波;震电波场响应具有频散特性,频率增大,震电纵波P2和P3波传播速度显著增大,震电波衰减常数均增大;相同频率下,震电纵波P2波电场强度及电流密度与固相速度比值的模值相比其它三种震电波的均较大,说明其激发电场和电流能力较强;震电波场响应受到宏观储渗参数的影响,储层孔隙度增大,震电波的传播速度均减小,三种震电纵波的衰减常数均增大,且震电横波和震电纵波P1波的电场强度与固相速度比值的模值均增大,震电纵波P2和P3波的均减小;储层渗透率增大,震电波的传播速度均增大,震电横波的衰减常数、电场强度与固相速度比值的模值亦增大,而三种震电纵波的则相反;含水饱和度增大,震电横波、震电纵波P1(低频时)和P2波的传播速度均减小,衰减常数、电场强度及电流密度与固相速度比值的模值均增大,震电纵波P3波的则相反;震电波响应电场强度及电流密度与固相速度比值的相位在高频时出现频散现象,同样受到储层参数的影响.     

饱和多孔微极介质的波动方程及其势函数方程

土是由一定尺寸大小颗粒所构成的多孔介质,具有明显的颗粒特性,当土颗粒间的孔隙被流体（如水或油）充满时则成为饱和土.利用微极理论和Biot波动理论的研究成果,把饱和土中多孔固体骨架部分近似地视为微极介质,孔隙中的流体部分视为质点介质,获得饱和多孔微极介质的弹性波动方程.借鉴Greetsma理论,建立了饱和多孔微极介质弹性本构方程力学参数与相应单相介质弹性参数的相互关系,使饱和多孔微极介质弹性波动方程中的物理参数具有明确的物理意义,易于在试验中确定.运用场论理论把饱和多孔微极介质的波动方程简化为势函数方程,建立了饱和多孔微极介质中五种弹性波的弥散方程,数值分析了五种简谐体波在无限饱和多孔微极介质中的传播特性. 结果表明,P1波、P2波和剪切S1波的波速弥散曲线与经典饱和多孔介质基本相同,当频率小于临界频率ω0时旋转纵波θ波和横波S2波不存在,当频率大于临界频率ω0时,θ波和S2波的传播速度随频率增加而减小.     

部分饱和孔隙介质中的纵波方程及衰减特性研究（英文）

本文以中观孔隙结构的White模型为基础,构建了部分饱和孔隙介质模型,利用Biot方程的建立思路和Johnson推导的体变模量,推导了部分饱和孔隙介质中的纵波方程,并以平面波为例,求取了方程的衰减系数,分析了地震勘探频带范围内地震波的衰减特性。结果表明:在部分饱和孔隙介质中,地震波在低频段也会发生明显的衰减和频散现象,频率越大,衰减越大;且第二纵波的衰减比第一纵波更为明显;这一结论弥补了Biot理论在描述地震勘探频带范围内波的衰减现象的不足。文中还研究了孔隙度、饱和度和模型内径尺寸对第纵波衰减特性的影响机理,主要表现在在地震勘探频带范围内,波的衰减随孔隙度的增大而增大,随含油气饱和度的增大而减小,当孔隙内径尺寸小于二分之一外径尺寸时,波的衰减随内径尺寸的增大而增大,当内径尺寸大于二分之一外径尺寸时,波的衰减随内径尺寸增大而减小。     

SV波斜入射时双线并行地铁隧道横截面地震响应分析

SV波以大角度斜入射时,场地伴随更大的竖向地震作用,这很可能使得地铁隧道地震响应特点异于小角度斜入射情况。基于粘弹性人工边界理论,采用频域刚度矩阵法计算任意角度斜入射SV波的地震动输入等效节点力,通过ABAQUS有限元软件建立自由场模型,验证了0°、30°、40°和50°斜入射SV波地震动输入的准确性;在此基础上建立任意角度斜入射SV波作用下的地下双线并行圆形地铁隧道地震响应分析数值模型,从场地类别、隧道埋深和双隧道间距等方面分析SV波入射角度对隧道结构横断面地震响应的影响。研究表明:入射角度0°及略大于SV波临界角的入射角度是浅埋圆形地铁隧道结构抗震的最不利角度,尤其对于Ⅱ类场地,若仅在临界角以内研究衬砌结构的地震响应,将显著低估衬砌结构的动力响应;此外,隧道埋深对衬砌动弯矩、动轴力峰值具有显著影响,这种影响与场地类别密切相关;Ⅱ类和Ⅲ类场地中小隧道间距条件下隧道间的动力相互作用对衬砌结构动力响应具有一定的增大效应,而Ⅳ类场地中可忽略隧道间的动力相互作用对衬砌结构动力响应所产生的影响。     

弹性波在横向各向同性弹性土和饱和土界面上的反射与透射.

根据横向各向同性饱和土体的Biot波动方程,推导出qP1波从饱和土入射到弹性介质的反射系数和透射系数的一般算式,数值分析了各向异性,边界透水条件对反射系数和透射系数的影响．本文的推导思路,适用于qSV波、qP2波从饱和土体入射到弹性土体的情形．      

基于Comsol的饱和多孔介质动力方程的数值模拟及应用

两相饱和多孔介质的动力响应问题在地震工程领域具有重要的研究意义,由于涉及到固相和液相的动力耦合,使得该问题的求解尤为复杂。本文利用Comsol在求解多场耦合问题上的优点,针对Biot饱和多孔介质u-U耦合形式下的波动方程特征,经过一系列微分算子运算和矩阵变换得到导数形式下的波动方程,基于Comsol Multiphysics提供的广义偏微分方程模式对变形后的波动方程进行求解,并把改进后的无限元边界应用到无限域动力问题的模拟中。通过与饱和多孔介质动力响应的解析解进行对比,验证模型求解技术的可行性和正确性,并在此基础上讨论饱和土地基中空沟隔振效果与饱和土体参数孔隙率、泊松比的关系。通过研究分析,可以为饱和土地基中空沟隔振设计提供一些有价值的参考。     

饱和土中浅圆弧状埋置基础对平面P波散射解答

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,首次得到饱和土中浅圆弧状埋置基础对平面波散射问题的解答．并利用该解对有埋置基础的饱和土场地地面运动的幅值及其分布进行分析,研究了基础弹性对平面P波作用下饱和土地基与基础动力相互作用的影响。     

Dynamic response of partially sealed circular tunnel in viscoelastic saturated soil

Based on Biot's wave equation, dynamic response of a circular tunnel with partially sealed liner in viscoelastic saturated soil is investigated. By introducing two scalar potential functions, the analytical solutions of stresses, displacements and pore pressure induced by axisymmetric gradually applied step load are derived in Laplace transform domain. Numerical results are obtained by inverting Laplace transform presented by Durbin and used to analyze the influences of partial permeable property of boundary and viscoelastic damping coefficient of soil on dynamic response of the tunnel. It is shown that the attenuation of radial displacement appeared with the increase of viscoelastic damping coefficient of soil, and relative rigidity of liner and soil, and the influence of partial sealing property of boundary on stresses, displacements and pore pressure is remarkable. The available solutions of permeable and impermeable boundary conditions are only two extreme cases of this paper.     

Wave-induced dynamic response of saturated multi-layer porous media: Analytical solutions and validity regions of various formulations in non-dimensional parametric space

In this paper, dynamic response of saturated-layered porous media under harmonic waves is evaluated through a semi-analytical solution. The coupled differential equations governing the dynamics of saturated or nearly saturated porous media such as soils containing all the inertial terms of solid and fluid phases are presented for a multi-layer system. Possible simplifications of the equations which are called formulations are introduced based upon the presence of inertial terms associated with the phases. The semi-analytical solutions to the response of multiple layers for all the formulations are presented in terms of pore water pressure and stress variations considering a set of non-dimensional parameters and their respective ratios. Validity of the formulations is presented in a non-dimensional parametric space. The maximum discrepancies in the pore pressure response of the formulations leading to validity regions are illustrated for typical dynamic problems. Subsequently, the effects of layering and drainage conditions on these regions are also presented. The proposed semi-analytical solution may be served as a benchmark one for validating the coupled numerical solutions, which can be used to deal with real scientific and geo-engineering problems in the emerging field of computational geomechanics.     

地震波斜入射下层状场地中地下综合管廊地震响应分析

利用黏弹性人工边界和等效地震荷载时域波动输入方法,结合土层和半空间的精确动力刚度矩阵,实现了地震波斜入射下层状场地地下综合管廊地震反应分析,建立了不同场地条件下地下综合管廊分析模型。计算结果表明:地震波倾斜入射情况下,综合管廊结构地震响应与垂直入射时具有显著差异,一般SV波以30°临界角附近入射时结构地震反应最为剧烈;地下综合管廊动应力集中主要分布在管廊角部、中柱上下端;成层土波速结构变化对地下综合管廊地震反应亦具有显著影响。总体上看:当穿越软夹层时管廊结构地震反应更为剧烈,且覆盖层越厚,管廊结构内力幅值越大。因此地下综合管廊结构抗震设计宜考虑地震波倾斜入射及场地土层性质的影响。     

Kinematic response of single piles to vertically incident P‐waves

Dynamic response of single piles to seismic waves is fundamentally different from the free‐field motion because of the interaction between the pile and the surrounding soil. Considering soil–pile interaction, this paper presents a new displacement model for the steady‐state kinematic response of single piles to vertically incident P‐waves on the basis of a continuum model. The governing equations and boundary conditions of the two undetermined functions in the model are obtained to be coupled by using Hamilton's principle. Then, the two unknown functions are decoupled and solved by an iterative algorithm numerically. A parametric study is performed to investigate the effects of the properties of the soil–pile system on the kinematic response of single piles. It is shown that the effects of the pile–soil modulus ratio, the slenderness ratio of the pile, and the frequency of the incident excitations are very significant. By contrast, the influence of soil damping on the kinematics of the system is slight and can be neglected. Copyright © 2013 John Wiley & Sons, Ltd.     

An indirect boundary element method applied to simulate the seismic response of alluvial valleys for incident P,S and Rayleigh waves

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.     

Dependence of borehole shear‐horizontal‐wave seismoelectric response on soil textures

The phenomenon of acoustic waves inducing electric fields in porous media is called the seismoelectric effect. Earlier investigators proposed the usage of seismoelectric effect for well logging. Soil texture has a strong influence on the coupled wave fields during shallow surface explorations. In this article, we study the borehole pure shear‐horizontal wave and the coupling transverse‐electric field (acoustic–electrical coupling wave fields) in the partially saturated soil. Combined with related theories, we expand the formation parameters to partially saturated forms and discuss the influence of soil texture conditions on the seismoelectric wave fields. The results show that the elastic and electrical properties of porous media are sensitive to water saturation. The compositions of the acoustic and electric fields for different soil textures do not change, but the waveforms differ. We also use the secant integral method to simulate the interface‐converted electromagnetic waves. The results show that interface response strength is greatly influenced by soil texture. In addition, considering the sensitivity of the inducing electric field to fluid salinity, we also simulate the time‐domain waveforms of electric field for different pore fluid salinity levels. The results show that as the salinity increases, the electric field amplitude decreases monotonically. The above conclusions have certain significance for the application of borehole shear wave and its coupled electric fields for resource exploration, saturation assessment and groundwater pollution monitoring.