冲击荷载作用下软土隧道结构热-流-固耦合动力响应分析

爆炸对结构物的作用可以看成是冲击力和热的共同作用结果。基于Biot热弹性波动理论,利用饱和多孔介质热- 流-固耦合动力响应模型,研究了饱和软黏土中隧道结构内受指数衰减热/力冲击荷载作用下的动力响应。利用Flügge薄壳理论,得到隧道结构的运动方程。考虑土-结构接触面上的协调条件并利用热-流-固耦合动力响应模型的通解,得到了热/力冲击荷载作用下应力、位移和孔隙水压力响应在Laplace变换域中的解。利用Laplace数值逆变换技术得到数值计算结果,探讨了冲击荷载和热荷载作用下隧道结构刚度和厚度对应力、位移和孔隙水压力响应的影响。结果表明：在爆炸冲击荷载作用下,隧洞衬砌对周围土体起到很好的屏蔽作用,且衬砌刚度越大,其保护效果越好;衬砌与土体接触面上应力随衬砌刚度增大而减小,并且刚度越大应力衰减越快;衬砌刚度和厚度对热冲击的位移响应有明显影响,而对其温度响应的影响较小。     

简谐线源荷载作用下热流固耦合地基的动力响应

基于Biot波动理论和广义热弹性理论,对简谐线源荷载（力荷载和热荷载）作用下的热-流-固耦合地基的动力响应问题进行了研究。将地基看成是均质各向同性、完全饱和的多孔半空间介质,利用无量纲化和Fourier变换方法对热-流-固耦合控制方程进行简化,得到了变换域内应力分量、位移分量、温度分布及超孔隙水压力的一般解,并利用Fourier逆变换得到了相应的积分形式解答。通过数值计算对按热-流-固耦合理论、饱和多孔弹性理论和热弹性理论得到的结果进行了比较,同时分析了热-流-固耦合条件下热荷载激振频率对竖向应力、竖向位移、温度分布以及超孔隙水压力的影响。     

空心圆柱饱和多孔介质热固结问题的解析解

基于考虑热渗效应和等温热流效应的热-水-力耦合的线性热弹性固结控制方程,建立无限长空心圆柱饱和多孔介质热固结问题的一种理论求解方法。该方法先给出Laplace变换域上的解,然后,利用Stehfest法求其数值逆变换。该理论解考虑了空心圆柱体内、外透水界面随时间变化的外力和温度荷载耦合作用过程。最后,通过一算例分析了饱和多孔介质的热固结特征,给出其温度、孔压、位移和应力的演化规律     

考虑热-水-力耦合效应多孔弹性地基的动力响应

通过对Biot波动方程的修正,得到考虑热-水-力学耦合效应的多孔弹性介质动力响应的控制方程,研究了简谐均布荷载作用下地基土体的热-水-力耦合动力响应问题。利用Fourier变换技术,得到地基中的应力、位移和孔隙水压力积分形式的解答。利用Fourier逆变换得到数值结果,分析了热-水-力学耦合条件下地基土体中温度增量、应力、位移和孔隙水压力响应的分布,并讨论了热源输入的影响, 结果表明：应力、位移和孔隙水压力随 的增大而有一定的减小。     

低渗透煤层气-水流固耦合数学模型及数值模拟

基于有效应力原理,结合弹塑性几何方程、本构方程及平衡方程建立了应力场控制方程。依据流体力学中的质量守恒原理建立了煤层气、水和煤岩体固体颗粒的渗流场方程;以上方程再配以辅助方程和定解条件构成了应力作用下煤层 气-水流固耦合的数学模型,并对简化模型进行了单相流流-固耦合数值模拟分析,得到了压力动态分布曲线,分析了耦合和非耦合情况对压力分布的影响,进一步为煤层气流-固耦合分析提供了一定的理论基础。     

变荷载作用下考虑半透水边界热传导性的一维饱和土热固结特性研究

为了研究温度变化对一维饱和土固结特性的影响,本文基于渗流方程和热传导方程,考虑了顶面边界的半透水性和热传导性,提出了变荷载作用下考虑半透水边界热传导性的一维饱和土热固结的半解析解,并分析了其固结特性。首先,引入Laplace变换分别求解了半透水边界条件下热力耦合模型和非热力耦合模型的一维饱和土热固结方程,推出了有效应力、温差和沉降的半解析解。其次,通过Crump方法进行Laplace数值反演,得到时间域内的解析解。然后,将本文已提出的解分别退化为单边排水条件下的一维饱和土热固结和Terzaghi一维固结的半解析解,结果与已有文献相同,验证了本文研究所推导出解的可靠性。最后通过算例分析了各外荷载作用下半透水边界参数、温度增量、热扩散系数和固结系数对热固结特性的影响。结果表明,半透水边界参数、热扩散系数、固结系数和温度增量对饱和土一维固结特性影响显著。     

饱和多孔介质热-水-力控制方程耦合项的意义及耦合影响分析

基于饱和多孔介质完全耦合条件下热-水-力控制方程的一般形式,对各耦合项的物理意义进行了分析。以等温条件下水-力耦合的Biot渗透固结理论和等压条件下热-力耦合的热弹性理论两种退化形式为基础,给出耦合系数的物理意义及其函数表达式。研究表明,其中一些耦合系数实际上有相同的物理意义和数学形式,因而可使控制方程得到简化。针对不同的介质特性以及热、水、力条件,给出几种特定情形下控制方程的简化形式。以无限大多孔介质中球域热源的热力学响应分析为例,对一些耦合项的影响程度进行了比较研究。     

变荷载作用下考虑半透水边界热传导性的一维饱和土热固结特性研究

为了研究温度变化对一维饱和土固结特性的影响,基于渗流方程和热传导方程,考虑了顶面边界的半透水性和热传导性,提出了变荷载作用下考虑半透水边界热传导性的一维饱和土热固结的半解析解,并分析了其固结特性。首先,引入Laplace变换分别求解了半透水边界条件下热力耦合模型和非热力耦合模型的一维饱和土热固结方程,推出了有效应力、温差和沉降的半解析解;其次,通过Crump方法进行Laplace数值反演,得到时间域内的解析解;然后,将所提解分别退化为单边排水条件下的一维饱和土热固结和Terzaghi一维固结的半解析解,结果与已有文献相同,验证了所推导解的可靠性;最后,通过算例分析了各外荷载作用下半透水边界参数、温度增量、热扩散系数和固结系数对热固结特性的影响。结果表明,半透水边界参数、热扩散系数、固结系数和温度增量对饱和土一维固结特性影响显著。     

冻土路基在地震作用下的动力响应

青藏高原是地震多发区,冻土区的公路、铁路在地震作用下的动力响应必须考虑．将冻土作为黏弹塑性材料,考虑冻土在动力荷载作用下的热力耦合效应,从热传导方程、渗流微分方程和动力平衡方程出发,建立了冻土的动力热一力耦合微分方程．根据相应的有限元列式,对路基在地震荷载作用下的动力响应进行了计算与分析．     

列车荷载下青藏铁路冻土路基动力响应分析

根据带相变瞬态温度场的热量平衡控制微分方程, 采用有限元方法计算分析了青藏铁路路基的瞬态温度场. 随后, 根据温度场的分布特点, 应用Biot动力固结理论推导出的Biot动力固结控制方程, 采用热、力间接耦合方法对青藏铁路路基在列车荷载作用下的瞬态动力问题进行了数值模拟, 并系统的分析了列车荷载作用下铁路路基内的振动孔隙水压力、应力、位移等动力响应特点.     

The fundamental solution of poroelastic plate saturated by fluid and its applications

In this paper, the numerical model of the transverse vibrations of a thin poroelastic plate saturated by a fluid was proposed. Two coupled dynamic equations of equilibrium related to the plate deflection and the equivalent moment were established for an isotropic porous medium with uniform porosity. The fundamental solutions for a porous plate were derived both in the Laplace transform domain and in the time domain. A meshless method was developed and demonstrated in the Laplace transform domain for solving two coupled dynamic equations. Numerical examples demonstrated the accuracy of the method of the fundamental solutions and comparisons were made with analytical solutions. The proposed meshless method was shown to be simple to implement and gave satisfactory results for a poroelastic plate dynamic analysis. Copyright © 2009 John Wiley & Sons, Ltd.     

横观各向同性饱和地基三维瞬态Lamb问题

研究了横观各向同性饱和土地基在地表动力荷载作用下的三维瞬态响应。基于饱和多孔介质的三维Biot波动理论,利用Laplace变换,建立圆柱坐标系下横观各向同性饱和土的波动方程;解耦波动方程后,根据算子理论,并借助Fourier展开和Hankel变换技术,得到瞬态荷载作用下,饱和土介质的土骨架位移和应力、孔隙水相对位移和孔隙水压力的一般解;利用一般解,给出横观各向同性饱和地基在地表集中荷载激励下的瞬态Lamb问题的解答。数值算例结果表明,采用各向同性饱和介质的动力学模型,不能准确描述具有明显各向异性特性的饱和土地基的瞬态动力特性。     

Thermomechanical response of a poroelastic half-space soil medium subjected to time harmonic loads

The thermomechanical responses of a porous elastic medium subjected to time harmonic loads (normal force and thermal source) are investigated analytically in the context of generalised thermoelastic theory with one relaxation time. The material of the foundation, obeying Biot’s dynamic poroelastic theory, is idealised as a uniform, fully saturated poroelastic half-space stratum. The coupled governing equations are established based on Biot’s dynamic poroelastic theory and on generalised thermoelastic theory. Assuming the disturbances to be harmonically time dependent, the general solutions of stress, displacement, temperature distribution and excess pore water pressure are deduced using the Fourier transform, and the transformed solutions are numerically inverted. The differences among the coupled thermo-hydro-mechanical dynamic model (THMD), the hydro-mechanical dynamic model (HMD) and the thermo-elastic dynamic model (TMD) are discussed. In addition, the effects of the thermal loading frequency on the displacement, stress, temperature distribution and excess pore water pressure components are analysed in the numerical results.     

准饱和土中圆柱形衬砌的瞬态动力响应分析

内源瞬态荷载作用下圆柱形孔洞的动力响应解答是土动力学的经典问题之一。已有研究大都假设孔洞周围土体为理想弹性介质或完全饱和多孔介质。然而,实际工程中不存在完全弹性和完全饱和土体。分别视衬砌结构和周围土体为弹性材料和准饱和多孔介质（饱和度 95%）,根据牛顿第二定律、达西定律和Biot波动理论推导出准饱和土体的控制方程。根据边界条件导出衬砌和土体的位移、应力和孔隙压力的Laplace变换空间的解答。利用反Laplace变换数值计算方法,将解答转换为时域解。分析了饱和度对衬砌位移、应力和孔压的影响,结果表明,当95% 99%时,饱和度对径向位移和切向应力的影响较小;99% 100%时,饱和度对径向位移和切向应力的影响较大;但饱和度对孔隙压力的影响远大于对径向位移和切向应力的影响。得出位移、应力和孔压沿径向的衰减规律,当95% 99%时,饱和度对径向位移和切向应力沿径向衰减影响较小,99% 100%时,饱和度对径向位移和切向应力沿径向衰减影响较大,但饱和度对孔压沿径向的衰减影响远大于对径向位移和切向应力沿径向的衰减。     

衬砌隧道中移动轴向激励作用下两相多孔介质动力响应

为了研究衬砌隧道中地铁振动在饱和地层中的传播情况,采用移动轴向激励模拟技术,建立了隧道-衬砌-两相介质的动力分析模型;利用波函数展开法、傅里叶变换法等,推导了频域内衬砌隧道移动轴向激励作用下两相多孔介质动力响应的解析解,并给出了两相多孔介质临界速度的经验公式;通过离散快速傅里叶逆变换得到了时-空域内两相介质的动力响应。结果表明：无衬砌隧道中移动的轴向常激励作用下,两相介质临界速度只与介质的剪切模量和密度有关,且数值接近其剪切波速的1.1倍;对于衬砌隧道,介质的临界速度随着衬砌剪切模量的增大而增大,随着衬砌密度的增大而减小,衬砌对振动向介质中的传播有一定的削弱作用,衬砌剪切模量与介质剪切模量相差越大,削弱越明显;动力响应频率越接近激振频率,其幅值越大,所对应的临界速度越小。     

Mode of a spherical cavity’s thermo-elastodynamic response in a saturated porous medium for non-torsional loads

The thermo-hydro-elastodynamic model (THED), in which the thermo-osmosis and thermal-filtration phenomenon in a two-phase porous thermoelastic medium can be considered, was previously presented by the authors [Ganbin Liu, Kanghe Xie, Rongyue Zheng. Model of nonlinear coupled thermo-hydro-elastodynamics response for a saturated poroelastic medium. Sci China (Ser E) 2009;52(8):2373–83] and is used in this paper to investigate the thermo-elastodynamic response of a spherical cavity in a saturated poroelastic medium when subjected to a time-dependent non-torsional thermal/mechanical source. The Separated Variable Method is introduced, and the non-zero displacement potentials are expanded in terms of the Legendre polynomial. Solutions for the displacement, temperature increment, pore pressure and stress are obtained in the domain of the Laplace transform. Numerical results are also performed for different modes and are compared with the results of the thermoelastic model (TED) to ascertain the validity and the difference between these two models.     

Linear coupled analysis of desiccation shrinkage in a double‐layer partially saturated medium: semi‐explicit solutions

Solutions are presented for the problem of isothermal dessiccation shrinkage in a double‐layer porous partially saturated medium. The rheological model taken into account is linear poroelastic. Hence the analysis is mainly focused on hydromechanical coupling effects and contrasts of mechanical and hydraulic properties between two materials: a low thickness skin comprised between the outer boundary and the reference porous material. Three one‐dimensional ideal structures are taken into account: a wall of finite thickness (cartesian geometry), a thick cylinder and a thick sphere. The solution of the time‐dependent problem is arrived at by applying Laplace transforms to the field variables. Exact solutions are obtained in Laplace transform space using Mathematica^© to solve the field equations whilst taking into account the continuity equations at the interface and the boundary conditions. The Talbot's modified algorithm has been performed to invert the Laplace transform solutions. A bibliographical and numerical study shows that this method is remarkably precise, stable and close to the analytical inversion. Results are presented using poroelastic data representative of a concrete material and involve a strong coupling effect between hydraulical and mechanical behaviours. A first approach elastic modelling of degradation process have been presented using a thin outer layer. Apart from emphasising the semi‐explicit solution utility due to accurate speed calculation, this paper deals with more complex problems than those which can be solved using purely analytical solutions. Copyright © 2001 John Wiley & Sons, Ltd.     

Transient response of a circular cavity in a poroelastic medium

This paper considers the transient response of a pressurized long cylindrical cavity in an infinite poroelastic medium. To obtain transient solutions, Biot's equations for poroelastodynamics are specialized for this problem. A set of exact general solutions for radial displacement, stresses, pore pressure and discharge are derived in the Laplace transform space by using analytical techniques. Solutions are presented for three different types of prescribed transient radial pressures acting on the surface of a permeable as well as an impermeable cavity surface. Time domain solutions are obtained by inverting Laplace domain solutions using a reliable numerical scheme. A detailed parametric study is presented to illustrate the influence of poroelastic material parameters and hydraulic boundary conditions on the response of the medium. Comparisons are also presented with the corresponding ideal elastic solutions to portray the poroelastic effects. It is noted that the maximum radial displacement and hoop stress at the cavity surface are substantially higher than the classical static solutions and differ considerably from the transient elastic solutions. Time histories and radial variations of displacement, hoop stress, pore pressure and fluid discharge corresponding to a cavity in two representative poroelastic materials are also presented.