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1.
This paper is dedicated to study the dynamic response of a thin‐plate resting on a layered poroelastic half‐space under a moving traffic load. Based on the dynamic poroelastic theory of Biot, the general solutions of the homogeneous poroelastic foundation are obtained by Fourier translation. By using the transmission and reflection matrices method in the frequency domain, the equivalent stiffness of the layered poroelastic half‐space is presented. Kirchhoff's hypotheses are applied to obtain the vertical displacement of the thin plate. By using the inverse Fourier transform, the time domain solution is obtained. As an example of three layers, the influences of the load velocity, the material properties of poroelastic layers, and the flexural rigidity of the plate on the response of the pavement system are examined. Analyses show that a soft intermediate layer results in the significant increase of vertical displacement of road pavement. Comparison with the existing work validates the present model. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
2.
为研究空沟对高速列车引起地基振动的隔振效果,在已有研究基础上改进出一种新的解析研究模型。模型中首次运用了饱和半空间模型来研究地基上隔振沟对高速列车的隔振效果;隔振沟则通过在饱和半空间土体上设置3个合适宽度、截面为矩形的弹性层来模拟;中间矩形弹性层为路堤,路堤上方放置了枕木与轨道。枕木与轨道分别通过纵向异性Kirchhoff薄板与Euler梁来模拟,饱和土地基采用Biot多孔饱和介质理论来描述。控制方程通过傅立叶变换与傅立叶级数展开,在变换域中进行求解。研究表明,随着列车运行速度的提高,空沟的隔振效果明显提高;饱和土体固-液相的耦合作用对隔振沟的隔振效果的影响明显,尤其当列车运行速度超过土体表面Rayleigh波速时,随着土体渗透系数的增加,空沟隔振效果显著降低。此外,列车运行速度超过土体表面波速时,饱和土地基上空沟的隔振效果明显优于相应单相弹性地基上空沟的隔振效果。 相似文献
3.
The problem of the dynamic responses of a semi‐infinite unsaturated poroelastic medium subjected to a moving rectangular load is investigated analytical/numerically. The dynamic governing equations are obtained with consideration of the compressibility of solid grain and pore fluid, inertial coupling, and viscous drag as well as capillary pressure in the unsaturated soil, and they can be easily degraded to the complete Biot's theory. Using the Fourier transform, the general solution for the equations is derived in the transformed domain, and then a corresponding boundary value problem is formulated. By introducing fast Fourier transform algorithm, the unsaturated soil vertical displacements, effective stresses, and pore pressures induced by moving load are computed, and some of the calculated results are compared with those for the degenerated solution of saturated soils and confirmed. The influences of the saturation, the load speed, and excitation frequency on the response of the unsaturated half‐space soil are investigated. The numerical results reveal that the effects of these parameters on the dynamic response of the unsaturated soil are significant. 相似文献
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The dynamic responses of an anisotropic poroelastic half-space under an internal point load and fluid source are investigated in the frequency domain in this paper. By virtue of Fourier transform and Stroh formalism, the three-dimensional (3D) general solutions of the anisotropic Biot's coupling dynamics equations are derived in the frequency domain. Considering the two surface conditions, permeable and impermeable, the analytical solutions for displacement fields and pore pressure in half-space under a point source (point load or a fluid source) are obtained. When the material properties are isotropic, the numerical results of the poroelastic half-space are in excellent agreement with the existing analytical solutions. For anisotropic half-space cases, numerical results show the strong dependence of the dynamic Green's functions on the material properties. 相似文献
8.
列车运行时由轨道不平顺引起的地基振动研究 总被引：2，自引：1，他引：1
采用半解析法研究了列车荷载作用下列车-轨道-饱和地基系统的耦合振动问题。研究模型共分为3部分：车体简化为一个多刚体系统,在车轮与钢轨之间引入线性Hertizian弹簧接触模型模拟轮轨动力相互作用、采用离散轨枕支撑的弹性Euler梁来模拟轨道系统、下卧土体采用多孔饱和半空间模型。列车荷载分为轴重和由轨道不平顺引起的轮轨动力相互作用力。采用Fourier变换分别求解各子系统的控制方程,并通过动力子结构法对各子系统进行耦合。土体在时域内的动力响应通过快速Fourier变换求得。在分析了轮轨动力相互作用力的基础上,研究了轮轨动力作用力和列车轴重作用下饱和地基的动力响应,并分析了轨枕间距和土体渗透系数对饱和地基振动响应的影响。研究表明,轮轨动力作用力对地基远场振动有重要贡献,同时枕木间距对轨道与地基振动响应有较大影响。 相似文献
9.
Consolidation of a poroelastic half-space with anisotropic permeability and compressible constituents by axisymmetric surface loading 总被引：1，自引：0，他引：1
The fully coupled Biot quasi-static theory of linear poroelasticity is used to study the consolidation of a poroelastic half-space
caused by axisymmetric surface loads. The fluid and solid constituents of the poroelastic medium are compressible and its
permeability in the vertical direction is different from its permeability in the horizontal direction. An analytical solution
of the governing equations is obtained by taking the displacements and the pore pressure as the basic state variables and
using a combination of the Laplace and Hankel transforms. The problem of an axisymmetric normal load is discussed in detail.
An explicit analytical solution is obtained for normal disc loading. Detailed numerical computations reveal that the anisotropy
in permeability as well as the compressibilities of the fluid and solid constituents of the poroelastic medium have significant
effects on the consolidation of the half-space. The anisotropy in permeability may accelerate the consolidation process and
may lead to a dilution in the theoretical prediction of the Mandel-Cryer effect. The compressibility of the solid constituents
may also accelerate the consolidation process. 相似文献
10.
This paper treats the dynamic response of a multilayered transversely isotropic fluid saturated poroelastic half-space under surface time-harmonic traction. The governing system of partial differential equations is uncoupled with the use of a set of physically meaningful and complete potential functions that decompose different body waves in a saturated poroelastic transversely isotropic medium. After expressing the equations in the Hankel-Fourier domain, a proper algebraic factorization is applied to generate reflection and transmission matrices for decomposed waves. All responses including displacements, stresses, and pore fluid pressure for both general patch load and point load are presented in the form of semi-infinite line integrals. The verification of the method is confirmed with the degeneration of the solutions presented here to the existing solutions for dried both homogeneous and multilayered elastic half-spaces as well as poroelastic half-space. Selected numerical results are depicted to investigate the effects of layering and pore pressure on responses of a transversely isotropic poroelastic medium. The load distribution effects are studied by comparison of the patch and point load responses. Also, resonance notion and effective parameters on this phenomenon such as layering system and anisotropy contrast are discussed. Significant influence of materials and layering configuration on number and amplitude of resonances depicted through the numerical evaluation. 相似文献
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移动荷载下黏弹性半空间体上双层板的动力响应 总被引：1，自引：0，他引：1
采用黏弹性半空间体上无限大双层板模型模拟路面结构,通过三重Fourier积分变换得到单位脉冲荷载作用下路面动力响应的Green函数。根据线性系统的叠加原理,利用广义Duhamel积分推导出移动荷载作用下路面动力响应的解析解。采用自适应Simpson法编制了计算奇异、振荡函数的广义积分计算程序,完成了路面动力响应从波数-频率域到时间-空间域的转换。结合算例,对移动荷载作用下路面的振动规律进行研究,讨论上、下层板厚度和板材料的弹性模量对路面动力响应的影响,明确了路面结构的振动特性,研究结果可为路面结构的设计、施工提供理论指导。 相似文献
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基于Biot理论,研究了饱和土中带有衬砌的圆形隧洞在移动环形荷载作用下的动力响应。假定衬砌为弹性体,土体为饱和多孔介质,引入两类势函数来表示土体、孔隙水和衬砌的位移,使隧洞的控制方程解耦。结合边界条件及连续条件,通过傅立叶变换得到频率-波数域中衬砌和土体的应力、位移和孔隙水压力解答,最后用傅立叶积分逆变换得到时-空域中的数值解。计算并比较了3种隧洞模型（弹性土体隧洞、饱和土体隧洞和饱和土衬砌隧洞）的动力响应分析。数值分析结果说明：（1）移动荷载速度对3种隧洞动力响应均具有较大影响;（2）弹性土体隧洞和饱和土体隧洞的动力响应具有明显区别,所以在富水地区的隧洞动力响应中土体应该视为饱和土体;（3）衬砌对隧洞动力响应有较大影响,故隧洞的动力分析中不能忽略衬砌作用。 相似文献
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借助于Biot 波动理论和弹性波的传播理论,采用复变函数和多级坐标法,对半空间饱和土中圆形衬砌结构对弹性稳态压缩波的散射问题进行求解和分析。利用一个半径很大的圆弧来逼近半空间直边界,将待解问题转化为稳态弹性压缩波在一个大圆孔和一个弹性衬砌结构的散射问题。通过引入势函数,将饱和土的Biot波动方程和衬砌的弹性波动方程解耦成Helmholtz 方程,借助复变函数级数展开便可以预先写出该组Helmholtz方程的通解。然后,通过引用复变量,把饱和土和衬砌结构中的应力、位移及孔压用设定的势函数表示出来,再利用半空间饱和土和衬砌结构的连续性条件和近似直边界的圆弧边界和衬砌内边界的边界条件求解出该组势函数的特解。最后,利用势函数的特解,得到饱和土中的位移,应力和孔压及衬砌结构的位移和应力;变换不同的参数求解衬砌结构内外边界的动应力和孔压的集中系数,通过对算例结果的分析得出一系列有益的结论。 相似文献
14.
A simplified analytical method is presented for the vertical dynamic analysis of a rigid, massive, cylindrical foundation embedded in a poroelastic soil layer. The foundation is subjected to a time‐harmonic vertical loading and is perfectly bonded to the surrounding soil in the vertical direction. The soil underlying the foundation base is represented by a single‐layered poroelastic soil based on rigid bedrock while the soil at the side of the foundation is modeled as an independent poroelastic layer composed of a series of infinitesimally thin layers. The behavior of the soil is governed by Biot's poroelastodynamic theory and its governing equations are solved by the use of Hankel integral transform. The contact surface between the foundation base and the soil is smooth and fully permeable. The dynamic interaction problem is solved following standard numerical procedures. The accuracy of the present solution is verified by comparisons with the well‐known solutions obtained from other approaches for both the elastodynamic interaction problem and poroelastodynamic interaction problem. Numerical results for the vertical dynamic impedance and response factor of the foundation are presented to demonstrate the influence of nondimensional frequency of excitation, soil layer thickness, poroelastic material parameters, depth ratio and mass ratio on the dynamic response of a rigid foundation embedded in a poroelastic soil layer. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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简谐荷载作用下饱和土体中圆形衬砌隧道三维动力响应分析 总被引：2，自引：0，他引：2
研究了全空间饱和土体中圆形衬砌隧道在径向简谐点荷载作用下的三维动力响应,将衬砌用无限长圆柱壳来模拟,土体用Biot饱和多孔介质模型来模拟,引入两类势函数来表示土骨架的位移和孔隙水压力,并利用修正Bessel方程来求解各势函数,结合边界条件,得到频率-波数域内衬砌和土骨架位移、孔隙水压力的解答,最后进行Fourier逆变换得到时间-空间域内的响应。通过算例分析了荷载振动频率和土体渗透性对土体和衬砌位移响应及土体孔压的影响。结果表明,饱和土体和弹性土体的位移响应具有明显区别。随着荷载频率的增大,土体和隧道位移幅值减小,土体孔压幅值增大;随着土体渗透性增大,土体位移及孔压幅值减小。 相似文献
16.
In this paper, the frequency domain dynamic response of a pile embedded in a porous medium subjected to SH seismic waves is investigated. The surrounding porous medium of the pile is described by Biot’s poro-elastic theory, while the pile embedded in the porous medium is treated as a beam and described by a beam vibration theory. Using the Hankel transformation method, the fundamental solution for a half-space porous medium subjected to a horizontal circular patch load is established. According to the fictitious pile methodology, the second kind of Fredholm integral equation for the pile is established in terms of the obtained fundamental solution and free wave field. The solution of the integral equation yields the dynamic response of the pile to plane SH waves. Numerical results indicate that the parameters of the porous medium, the pile and incident waves have considerable influences on the dynamic response of the pile and the porous medium. 相似文献
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水平简谐荷载作用下层状饱和土体动力响应 总被引：1，自引：0，他引：1
根据Biot波动理论,采用传递、反射矩阵（TRM）方法研究了水平简谐荷载作用下层状饱和土动力响应问题。由Helmholtz矢量分解求出基本解,再利用TRM法推导了层状饱和土动力响应,并由数值Hankel逆变换得到层状土地基位移、应力及孔压在空间域内的解。利用计算结果与已有结果相比较,二者相吻合,验证了算法的正确性。算例分析表明,水平简谐荷载作用在有软弱夹层的层状土体中比均质土中具有更显著的动力响应,尤其是软夹层上下有硬土层时,会引起软弱夹层土体孔隙水压升高、位移幅值增大、土体波动性增强;而荷载作用硬夹层及夹层上下有软土层时,情况则相反。 相似文献
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利用Muki和Sternberg的虚拟桩法,研究了饱和土体地基中排桩对移动荷载引起振动的被动隔振效果。隔振桩作为一维杆,饱和土体满足Biot理论。利用已有的移动荷载作用下的饱和土体的自由波场解及饱和土体内部受竖向圆形分布荷载作用下的基本解,建立了频域内土-桩的第2类Fredholm积分方程。通过Fourier逆变换得到时间域内评价隔振效果的振幅比。与已知文献结果相比较,验证了方法的正确性。数值结果表明,荷载速度对排桩的隔振效果有一定影响,即在相同隔振系统情况下,单排桩对低速荷载引起振动的隔振效果比高速移动荷载效果好。同时,较高速时的最佳桩长比低速时要短。 相似文献
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In this paper, frequency domain dynamic response of a pile embedded in a half‐space porous medium and subjected to P, SV seismic waves is investigated. According to the fictitious pile methodology, the problem is decomposed into an extended poroelastic half‐space and a fictitious pile. The extended porous half‐space is described by Biot's theory, while the fictitious pile is treated as a bar and a beam and described by the conventional 1‐D structure vibration theory. Using the Hankel transformation method, the fundamental solutions for a half‐space porous medium subjected to a vertical or a horizontal circular patch load are established. Based on the obtained fundamental solutions and free wave fields, the second kind of Fredholm integral equations describing the vertical and the horizontal interaction between the pile and the poroelastic half‐space are established. Solution of the integral equations yields the dynamic response of the pile to plane P, SV waves. Numerical results show the parameters of the porous medium, the pile and incident waves have direct influences on the dynamic response of the pile–half‐space system. Significant differences between conventional single‐phase elastic model and the poroelastic model for the surrounding medium of the pile are found. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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A comprehensive analytical solution is developed in this paper to investigate the torsional vibration of an end bearing pile embedded in a homogeneous poroelastic medium and subjected to a time-harmonic torsional loading. The poroelastic medium is modeled using Biot’s two-phased linear theory and the pile using one-dimensional elastic theory. By using the separation of variables technique, the torsional response of the soil layer is solved first. Then based on perfect contact between the pile and soil, the dynamic response of the pile is obtained in a closed form. Numerical results for torsional impedance of the soil layer are presented first to portray the influence of wave modes, slenderness ratio, pile–soil modulus ratio and poroelastic properties. A comparison with the plane strain theory is performed. The selected numerical results are obtained to analyze the influence of the major parameters on the torsional impedance at the level of the pile head. Finally, the dynamic torsional impedance of this study is compared with that for floating pile in elastic soil. 相似文献