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把波函数展开方法用于饱和多孔介质中波的传播的研究中,给出了不同土层界面条件（透水条件和不透水条件）下具有饱和土沉积层的圆弧形沉积河谷场地对平面SV波散射问题的解析解. 其中沉积谷软土场地用饱和多孔介质的Biot动力学理论模拟,半空间场地用单相介质弹性动力理论模拟. 对于入射角大于临界入射角时,产生的面波的波函数用有限Fourier级数展开,这种方法适用于较大的入射波频率范围,这是现存的数值方法所不能比拟的一大优点. 文中算例分析了入射波频率和入射角对地震地面运动的影响. 相似文献
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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。 相似文献
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海域场地地震响应分析是确定海洋工程结构抗震设计地震动输入的重要环节。然而,针对海水、饱和土、基岩之间的流固耦合分析,目前一般通过对3种介质方程进行离散,然后整体求解或分区耦合求解的方式进行,过程复杂而低效。因此,大规模海域场地地震反应分析仍是一个挑战性问题。本文基于流固耦合统一计算框架求解海域近场波动问题,采用透射边界模拟无限域,通过将海水和基岩视为孔隙率分别等于1和0的广义饱和多孔介质,使得海水、饱和土、基岩之间的相互耦合可在统一计算框架中实现,避免不同介质求解器之间的数据交换。采用集中质量显式有限元并行计算,不同进程之间采用MPI进行数据交换,提高计算效率;采用逐元技术,按单元类别存储单元刚度,大大节省了内存,便于大规模计算。通过自编程,输入界面高程数据和材料参数,实现建模-自由场-三维地震动模拟全流程自动化。以东京湾为例,使用该方法和程序在超级计算机上模拟SV波垂直入射时的地震响应,证实了该方法用于三维大规模海域地震波场模拟的高效性和可行性。 相似文献
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基于Biot理论,考虑液相的黏弹性变形和固液相接触面上的相对扭转,提出了含黏滞流体VTI孔隙介质模型.从理论上推导出,在该模型中除存在快P波、慢P波、SV波、SH波以外,还将存在两种新横波－慢SV波和慢SH波.数值模拟分析了6种弹性波的相速度、衰减、液固相振幅比随孔隙度、频率的变化规律以及快P波、快SV波的衰减随流体性质、渗透率、入射角的变化规律.结果表明慢SV波和慢SH波主要在液相中传播,高频高孔隙度时,速度较高;大角度入射时,快P波衰减表现出明显的各向异性,而快SV波的衰减则基本不变;储层纵向和横向渗透率存在差异时,快SV波衰减大的方向渗透率高. 相似文献
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把均匀流体概念引入Biot两相多孔介质动力理论中，用Biot的两相多孔介质模型模拟不完全饱和土层，给出SV波，P波从不完全饱和土层入射到弹性土层时，在土层交界面上反射，透射系数的表达式，结果表明与完全饱和相比，饱和度发生很小的变化就会对交界面上反射，透射系数产生很大的影响。今后应该重视饱和度变化对地震动力响应的影响。 相似文献
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Reflection and transmission of inhomogeneous waves in a composite porous solid saturated by two immiscible fluids 
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下载免费PDF全文 This paper is concerned with reflection and transmission of a plane, elastic, and inhomogeneous wave striking obliquely at some discontinuity inside a porous medium composed of two distinct solids and saturated by two immiscible fluids. It is found that four P‐ and two SV‐waves are reflected, whereas four P‐ and two SV‐waves are transmitted at the interface. All reflected and transmitted waves are inhomogeneous in nature and specified with different directions of propagation and attenuation vectors. An expression for the Umov–Poynting energy flux vector is derived for the system. Continuity of energy flux along normal to the interface gives 12 required boundary conditions. Expressions of amplitude and energy ratios of various reflected and transmitted waves are derived. Variations in amplitude and energy coefficients of reflected and transmitted waves with angle of incidence are numerically studied for a porous matrix composed of shaley sandstone and clay, saturated with water and oil. The effects of change in oil saturation and volume fraction of clay are also observed on amplitude ratios. Numerical simulation reveals that the change in sign in the difference of capillary pressure across the interface causes jump in the values of amplitude ratios of all waves. 相似文献
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基于Biot饱和多孔介质动力学理论,运用Laplace变换和波函数展开法,根据饱和土体与衬砌结构交界面的连续条件和衬砌结构内边界上的应力自由条件,得到饱和土中深埋圆柱形衬砌洞室对瞬态平面P波和SV波散射问题的解答,该解答可以退化成为饱和土中深埋圆柱形空穴或弹性夹塞物的情形,并很容易转换成为对稳态波散射的解.通过与已有的相关问题的解析解答进行对比,验证了该解答的正确性.同时利用Laplace逆变换的数值方法,给出了饱和土和衬砌中应力和位移场在时域内的数值解,通过算例,分析了衬砌厚度、刚度对衬砌内边界处应力集中因子的影响. 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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This paper presents an analytical solution for two-dimensional scattering and diffraction of plane P waves by circular-arc alluvial valleys with shallow saturated soil deposits. The solution is based on Biot's dynamic theory for saturated porous media, and derived by employing Fourier–Bessel series expansion technique. In this analysis, soil deposits in the circular-arc valley are modeled as saturated porous media based on Biot's dynamic theory, and the circular-arc valley is assumed to be imbedded in an infinite half-space, filled with elastic single-phase media. Numerical results from this solution show that the amplitudes of displacement at the surface of an alluvial valley are mainly relative to the angle of incidence, the dimensionless frequency of incident P wave, the degree of saturation and porosity of soil deposits, and the stiffness and Poisson's ratio of the solid skeleton of the soil deposits. Furthermore, the proposed solution is compared with the previous solution, in which the soil deposit was modeled as an elastic single-phase solid. 相似文献
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A simple theoretical model for soil–structure interaction in water saturated poroelastic soils is presented, developed to explore if the apparent building–foundation–soil system frequency changes due to water saturation. The model consists of a shear wall supported by a rigid circular foundation embedded in a homogenous, isotropic poroelastic half-space, fully saturated by a compressible and inviscid fluid, and excited by in-plane wave motion. The motion in the soil is governed by Biot's theory of wave propagation in fluid saturated porous media. Helmholtz decomposition and wave function expansion of the two P-wave and the S-wave potentials is used to represent the motion in the soil. The boundary conditions along the contact surface between the soil and the foundation are perfect bond (i.e. welded contact) for the skeleton, and either drained or undrained hydraulic condition for the fluid (i.e. pervious or impervious foundation). For the purpose of this exploratory analysis, the zero stress condition at the free surface is relaxed in the derivation of the foundation stiffness matrix, which enables a closed form solution. The implications of this assumption are discussed, based on published comparisons for the elastic case. Also, a closed form representation is derived for the foundation driving forces for incident plane (fast) P-wave or SV wave. Numerical results and comparison with the full-scale measurements are presented in the companion paper, published in this issue. 相似文献
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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。 相似文献
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基于Biot多孔介质波动模型,研究了非均匀饱和土层对平面P-SV波入射时的动力响应.考虑饱和土地基的物理力学特性沿厚度方向连续变化,利用亥姆霍兹矢量分解原理和动力刚度法,分析了平面入射P-SV波在非均匀饱和土层中的反射和透射,并给出了基岩表面和自由表面处反射系数和透射系数的计算表达式.基于理论推导结果,数值分析了平面SV波入射下非均匀饱和土自由场地的动力响应,其中假设饱和土地基的物理力学性质沿土层深度按幂律梯度变化.数值结果表明,平面SV波入射所引起的地面位移与基岩位移之比均随土层厚度和土体的非均匀程度、波的入射角和入射频率的增加而减小,且其竖向位移比的减小更为显著,厚土层对地震波的耗散作用尤为明显. 相似文献
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Based on the solutions of the Green’s function for a saturated porous medium obtained by the authors,and using transformation of axisymmetric coordinates,Sommerfeld integrals and superposition of the influence field on a free surface,the authors have obtained displacement solutions of a saturated porous medium subjected to a torsional force in a half-space.The relationship curves of the displacement solutions and various parameters(permeability,frequency,etc.)under action of a unit of torque are also given in this paper.The results are consistent with previous Reissner’s solutions,where a two-phase medium decays to a single-phase medium.The solution is useful in solving relevant dynamic problems of a twophase saturated medium in engineering. 相似文献
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Diffraction of plane SV waves by a shallow circular-arc canyon in a saturated poroelastic half-space 总被引：7，自引：0，他引：7
Jianwen Liang Zhenning Ba Vincent W. Lee 《Soil Dynamics and Earthquake Engineering》2006,26(6-7):582-610
An analytical solution for the scattering and diffraction of incident plane SV waves by a shallow circular-arc canyon in a saturated poroelastic half-space is derived by the wave function expansion method. The solution is utilized to analyze the dependence of the computed surface motions on the incident frequencies, incident angles, porosity, boundary drainage and Poisson's ratio. It is shown that, depending on the incident angles, the surface displacement amplitudes around a canyon in a dry poroelastic half-space and saturated poroelastic half-space can be very different. The surface displacement amplitudes of an undrained saturated poroelastic half-space are close to those of a drained saturated poroelastic half-space. For low porosity, the surface displacement amplitudes of a saturated poroelastic half-space are almost identical to those of a dry poroelastic half-space, and drainage condition has little influence on the surface displacement amplitudes. But for high porosity, the effect of drainage condition becomes significant, and for the same porosity, the displacement amplitudes of an undrained saturated half-space will be larger than those of a drained saturated half-space. Poisson's ratio is also an important factor affecting the surface displacement amplitudes around the canyon, both in drained and undrained conditions, but leads to larger effects for an undrained saturated half-space than for a drained saturated half-space. Large pore pressures are found around the canyon and their amplitudes depend on the incident angles and frequencies. Below the surface, the amplitudes of pore pressures are less than they are at the surface, especially for high frequencies. 相似文献
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基于孔隙介质的Biot理论,首先利用Laplace变换,给出圆柱坐标系下横观各向同性饱和弹性多孔介质在变换域上的波动方程;将波动方程解耦后,根据方位角的Fourier展开和径向Hankel变换,求解了Biot波动方程,得到以土骨架位移、孔隙水压力和土介质总应力分量的积分形式的一般解;借助一般解,建立了有限厚度饱和土层和饱和半空间的精确动力刚度矩阵,并由土层的层间界面连续条件建立三维非轴对称层状饱和地基的总刚度方程;在此基础上,系统研究了横观各向同性饱和半空间体在内部集中荷载激励下的动力响应,并给出了问题的瞬态解答.该研究为运用边界元法求解饱和地基动力响应奠定了理论基础. 相似文献
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A general solution of Biot's field equations governing small motions of a porous solid saturated by viscous liquid is employed to study the reflection and refraction at the interface between an elastic solid and a liquid-saturated porous solid. The incident wave is assumed to be plane and homogeneous, propagating through the isotropic elastic solid. The poroelastic solid is considered to be a dissipative one. Amplitude and energy ratios are computed numerically for a particular model. With first-order corrections for the porosity of solid and viscosity of liquid, the limiting cases of low and high frequencies are computed. 相似文献
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饱和土半空间中地下圆形衬砌洞室对平面SV波的散射 总被引：2，自引：0，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,通过对舍有衬砌洞室的局部场地进行波场分析,得到饱和土半空间中圆柱形衬砌洞室对平面SV波的散射问题的解析解。经验证,本文得到的解可以退化为半空间单相介质的情况。通过与已有的单相弹性介质半空间中圆柱形衬砌洞室对平面SV波散射问题的解析解的对比,验证了此解的正确性。在解析解的基础上,数值计算给出洞口动应力集中放大系数,分析了入射频率和孔洞埋深对柱面上的应力集中因子的影响。 相似文献
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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,P1波、P2波和剪切S1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ω0时旋转纵波θ波和横波S2波不存在,当频率大于临界频率ω0时,θ波和S2波的传播速度随频率增加而减小. 相似文献