Thermo-Osmosis Effect in Saturated Porous Medium

In this paper, the thermo-poroelasticity theory is used to investigate the quasi-static response of temperatures, pore pressure, stress, displacement, and fluid flux around a cylindrical borehole subjected to impact thermal and mechanical loadings in an infinite saturated poroelastic medium. It has been reported in literatures that coupled flow known as thermo-osmosis by which flux is driven by temperature gradient, can significantly change the fluid flux in clay, argillaceous and many other porous materials whose permeability coefficients are very small. This study presents a mathematical model to investigate the coupled effect of thermo-osmosis in saturated porous medium. The energy balance equations presented here fulfill local thermal non-equilibrium condition (LTNE) which is different from the local thermal equilibrium transfer theory, accounting for that temperatures of solid and fluid phases are not the same and governed by different heat transfer equations. Analytical solutions of temperatures, pore pressure, stress, displacement, and fluid flux are obtained in Laplace transform space. Numerical results for a typical clay are used to investigate the effect of thermo-osmosis. The effects of LTNE on temperatures, pore pressure, and stress are also studied in this paper.     

热局部非平衡下一维半无限长饱和多孔柱体的温度场分析

对于端部受温度载荷的一维半无限长多孔介质柱体,给出了热局部非平衡下固相和流相温度场在Laplace变换域中的解析表达式.对于冲击温度载荷的情况,获得了温度场在短时间内的Laplace逆变换渐近解析解.数值分析了流、固两相热扩散系数之比以及热交换系数对固相和流相温度场的影响,比较了热局部非平衡下加权温度与热局部平衡下温度之间的差别.     

Response of saturated porous media subjected to local thermal loading on the surface of semi-infinite space

Heat source function method is adopted in the present paper to derive elementary solutions of coupled thermo-hydro-mechanical consolidation for saturated porous media under conjunct actions of instantaneous point heat source, instantaneous point fluid source and constant volume force. By using the so-called fictitious heat source method and images method, the solutions of a semi-infinite saturated porous medium subjected to a local heat source with time-varied intensity on its free surface are developed from elementary solutions. The numerical integral methods for calculating the unsteady temperature, pore pressure and displacement fields are given. The thermomechanical response are analyzed for the case of a circular planar heat source. Besides, the thermal consolidation characteristics of a saturated porous medium subjected to a harmonic thermal loading are also given, and the fluctuation processes of the field variables located below the center of heat source are analyzed. The project supported by the National Natural Science Foundation of China (50578008) The English text was polished byYunming Chen.     

岩土介质非稳态热固结耦合问题的热源函数法

考虑耦合效应的饱和土体热固结问题控制方程,利用Fourier变换、Laplace变换给出其在变换域上的解,将初始温度场分布视为虚拟的热源或者将热源等价为特定的初始温度分布,利用热源函数法给出瞬时线热源非稳态温度场、应力场和位移场的解析求解方法,通过在时间域和空间域上进行积分,给出有初始温度场分布以及有分布内热源存在且热源强度随时间变化条件下的热固结问题计算方法。对一无限大物体内存在有平面矩形域热源情况下周围介质的温度、孔隙水压力以及位移等的变化特征进行分析。研究表明,热源函数法可有效地求解一系列复杂情况下的热固结问题。     

SOLUTIONS FOR CYLINDRICAL CAVITY IN SATURATED THERMOPOROELASTIC MEDIUM

Based on the thermodynamics of irreversible processes, the mass conservation equation and heat energy balance equation are established. The governing equations of thermal consolidation for homogeneous isotropic materials are presented, accounting for the coupling effects of the temperature, stress and displacement fields. The case of a saturated medium with a long cylindrical cavity subjected to a variable thermal loading and a variable hydrostatic pressure （or a variable radial water flux） with time is considered. The analytical solutions are derived in the Laplace transform space. Then, the time domain solutions are obtained by a numerical inversion scheme. The results of a typical example indicate that thermodynamically coupled effects have considerable influences on thermal responses.     

Analytical Solution of Compression,Free Swelling and Electrical Loading of Saturated Charged Porous Media

Analytical solutions are derived for one-dimensional consolidation, free swelling and electrical loading of a saturated charged porous medium. The governing equations describe infinitesimal deformations of linear elastic isotropic charged porous media saturated with a mono-valent ionic solution. From the governing equations a coupled diffusion equation in state space notation is derived for the electro-chemical potentials, which is decoupled introducing a set of normal parameters, being a linear combination of the eigenvectors of the diffusivity matrix. The magnitude of the eigenvalues of the diffusivity matrix correspond to the time scales for Darcy flow, diffusion of ionic constituents and diffusion of electrical potential.     

舰载旋转机械基础冲击响应建模和数值计算

针对舰载旋转机械的水下非接触爆炸冲击动力学响应问题,提出了一种基础冲击转子-轴承系统建模理论.结合牛顿运动定理、动量矩定理和Timoshenko梁理论,推导出了系统动力学微分方程,方程综合考虑了转子的旋转惯性力、剪切力、陀螺效应、轴向力、轴向扭矩以及轴承的油膜力.通过在时间域和空间域分别采用直接积分法和Galerkin...     

衰变热源作用下饱和多孔介质热固结问题的扩展精细积分法

热源作用下饱和多孔介质热固结效应是土木及能源工程领域的一个重要课题.由于问题的复杂性,已有的研究大多将介质假定为均匀各向同性,且将热源假定为恒定强度.实际工程中,天然饱和多孔介质常表现出明显的分层特性,热源强度也存在衰变性,为此本工作采用扩展精细积分法对衰变热源作用下层状饱和多孔介质的热固结问题进行研究.借助于积分变换,将饱和多孔介质热固结问题的偏微分方程转化为变换域内的常微分方程;然后对饱和多孔介质微层元进行合并消元,并结合边界条件,推导出衰变热源作用下层状饱和多孔介质热固结问题在积分变换域内的扩展精细积分解;对所得解答进行相应的数值积分逆变换,可获得所求温度、超静孔压及竖向位移在物理域内的解答.基于上述求解过程,编制相应的计算程序进行数值计算,通过与已有文献对比,验证本文扩展精细积分法在求解层状饱和多孔介质热固结问题中的适应性和正确性;最后通过几组算例,分析热源衰变周期、热源埋深及介质的成层性对热固结效应的影响.结果表明:热源衰变周期对温度和超静孔压的峰值、以及达到峰值的时间均有明显影响,衰变周期越长,二者峰值均越大,且达到峰值所需时间越长;热源埋深对超静孔压及竖向位移变化影响显著,深埋热源作用时热源两侧竖向位移呈对称分布,而浅埋热源两侧则无此现象;饱和多孔介质的分层特性对热固结效应影响明显.     

考虑热渗效应的有限热源固结近似解1）

通过建立考虑热渗效应和热流固耦合效应的饱和土体固结方程,研究了无限长圆柱热固结问题. 利用Fourier 和Laplace 变换及其逆变换,给出了热固结问题的解析解;然后对空间内无限长圆柱形热源问题进行研究,得到非等温条件下柱体周围饱和土体温度、孔隙水压力的近似解,并总结其规律,分析了热渗系数、固结系数对温度作用下土体固结的影响.     

一维流体饱和粘弹性多孔介质层的动力响应

本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论,在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下,建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型,利用Laplace变换,求得了原初边值问题在变换空间中的解析解,并利用Laplace逆变换的Crump数值反演方法,得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应,分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明,与不可压流体饱和弹性多孔介质相同,不可压流体饱和粘弹性多孔介质中亦只存在一个纵波,并且固相骨架的粘性对动力行为有显著的影响。     

多孔介质平板通道强迫对流中热局部非平衡时的热应力

根据微观不可压饱和多孔介质热-力-流相互作用的一般理论,在固相骨架小变形的假定下,考虑固相和流相相互作用的粘性耗散,研究了多孔介质平板通道强迫对流热局部非平衡的热应力问题.建立了问题的热-力数学模型,根据饱和多孔介质的平衡方程,在固相骨架只存在横向位移的假定下,求解了固相骨架的位移和相应的热应力,数值考察了各种物性参数对热应力分布的影响,讨论了热局部平衡模型的适用性.     

On the Hydrodynamics and Heat Convection of an Impinging External Flow Upon a Cylinder with Transpiration and Embedded in a Porous Medium

This paper extends the existing studies of heat convection by an external flow impinging upon a flat porous insert to that on a circular cylinder inside a porous medium. The surface of the cylinder is subject to constant temperature and can include uniform or non-uniform transpiration. These cylindrical configurations are introduced in the analyses of stagnation-point flows in porous media for the first time. The equations governing steady transport of momentum and thermal energy in porous media are reduced to simpler nonlinear differential equations and subsequently solved numerically. This reveals the dimensionless velocity and temperature fields of the stagnation-point flow, as well as the Nusselt number and shear stress on the surface of the cylinder. The results show that transpiration on the surface of the cylinder and Reynolds number of the external flow dominate the fluid dynamics and heat transfer problems. In particular, non-uniform transpiration is shown to significantly affect the thermal and hydrodynamic responses of the system in the circumferential direction. However, the permeability and porosity of the porous medium are found to have relatively smaller influences.     

竖向荷载作用下半透水边界固结问题解

本文基于Biot固结理论,采用积分变换的方法,获得了竖向点荷载、环形荷载作用下半透水边界固结问题基本解,并求得圆形分布荷载作用下的固结解,计算分析了圆形分布荷载作用下的竖向位移、总应力和孔压的时间效应。     

Thermal Responses of Saturated Silty Clay During Repeated Heating–Cooling Processes

The thermal responses of the saturated silty clay to repeated heating–cooling are studied in laboratory. Results show that the pore pressure induced by undrained heating increases with increasing temperature, but the peak pore pressure appears a degradation trend with increasing temperature cycles. During the consolidation process at an elevated temperature, the specimen contracts due to the dissipation of the pore pressure; however, the thermally induced pore pressure is under no conditions fully dissipated to zero, therefore, there always exists a residual pore pressure in the specimens once a thermal loading higher than the ambient temperature is applied. During the undrained cooling, pore pressure continues to decline and eventually falls below zero. During the isothermal consolidation at the original temperature, the specimen begins to expand due to water absorption caused by the negative pore pressure, and eventually reaches a steady value. In addition, the consolidation volumetric strain generated during the drainage process at 50°C is greater than that during the water absorption process at 25°C, the difference seems to be most obvious for the first three cycles, and begins to diminish gradually thereafter.     

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.     

饱和多孔介质大变形分析的一种有限元-有限体积混合方法

建立了饱和多孔介质大变形分析的一种有限元-有限体积混合计算方法.将饱和多孔介质视为由固体骨架和孔隙水组成的两相体,其基本方程包括动力平衡方程和渗流连续方程.基于u-p假定和更新的Lagrange方法,饱和多孔介质的动力平衡方程在空间域内采用有限元方法进行离散,而渗流连续方程在空阃域内则采用有限体积法进行离散.通过两个数值算例,一维有限弹性固结和动力荷载作用下堤坝动力响应的计算,验证了该方法的有效性.     

层状饱和土Biot固结问题状态空间法

针对饱和多孔介质空间非轴对Biot固结问题，引入状态变量，构造了两组相比独立的状态变量方程，利用Fourier级数和Laplace-Hankel变换，将状态变量方程转换为两组一阶常微分方程组，提出了均质饱和多孔介质空间非轴对称Biot固结问题的传递矩阵，得到以状态变量和传递矩阵乘积的形式表示的均质饱和多孔介质空间非轴对称Biot固结问题的解，利用层间完全接触的条件，可得到N层饱和多孔介质空间非轴对称Biot固结问题的一般解析表达式，文中考虑几种不同的边界条件，分析了两个算例，数值结果表明该方法具有较高的计算精度和良好的计算稳定性。     

Short-Term Damage Micromechanics of Laminated Fibrous Composites Under Thermal Actions

A microdamage theory is constructed for laminated fibrous materials with transversely isotropic fibers and a porous isotropic matrix under thermal actions. Microdamages in the matrix are simulated by pores, empty or filled with particles of the damaged material that resist compression. The fracture criterion for a microvolume of the matrix is assumed to have the Nadai–Schleicher form, which takes into account the difference between the tensile and compressive ultimate loads, with the ultimate strength being a random function of coordinates with a power or Weibull distribution. The stress–strain state and the effective properties of the material are determined from the thermoelastic equations for laminated fibrous materials with a porous matrix. The deformation and microdamage equations are closed by the porosity balance equations corrected for the thermal effect. For various types of loading, nonlinear relations are derived for the coupled processes of deformation of a laminated fibrous material and microdamage of the matrix due to the thermal macrostrain. The effect of physical and geometrical parameters on these processes is studied.     

Natural convection on one side of a vertical wall embedded in a Brinkman-porous medium coupled with film condensation on the other side

A theoretical study of conjugate natural convection and film condensation in porous media is reported. The natural convection phenomenon takes place along one side of a vertical impermeable wall and the condensation phenomenon along the other side. This wall constitutes the interface between two spaces filled with fluid-saturated porous media. The flow in both porous spaces is modelled on the basis of the Brinkman-modified Darcy momentum equation which satisfies the condition of zero velocity on a solid boundary. The temperature and flow fields in the porous medium are completely determined in the natural convection side as well as in the condensation side of the wall. In addition, the dependence of the wall heat flux and temperature distributions on height and on a number of dimensionless groups relevant to the problem is thoroughly documented. Important results pertinent to the impact of the problem parameters on the overall heat leak from the condensation space to the natural convection space are also reported. These results are presented with the help of the Nusselt number. Finally, the effect of the wall thermal resistance on the heat and fluid flow characteristics of the system is determined.     

拉─扭复合加载下不锈钢的弹塑性本构关系─I．实验

讨论了１Ｃｒ１８Ｎｉ９Ｔｉ不锈钢薄壁圆管试件沿三段折线、不同曲率的圆形和椭圆应变路径承受拉－扭复合载荷的实验．在塑性应变空间中，观察加载路径的内蕴几何参数对应力矢量大小、方向影响的规律．结果表明：响应的延迟角、瞬时软化和重新强化性质与路径的内蕴几何学密切相关；Ｌｅｎｓｋｙ的“局部确定性”假设不完全符合事实；变形历史和应变分量相互间的耦合效应对响应存在显著的影响．初步的电镜实验表明，材料中的位错组态和塑性应变历史密切相关