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

发布时间：2018-07-27 16:48

【摘要】：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.
[Abstract]:Thermal consolidation of saturated porous media under heat source is an important subject in civil engineering and energy engineering. Due to the complexity of the problem, most of the previous studies assume that the medium is homogeneous isotropic and the heat source is assumed to be constant intensity. In practical engineering, natural saturated porous media often shows obvious delamination, and the heat source strength also has decay. In this paper, the thermal consolidation of layered saturated porous media under the action of decay heat source is studied by using extended fine integration method. By means of integral transformation, the partial differential equations for thermal consolidation of saturated porous media are transformed into ordinary differential equations in the transform domain, and then the microlayer elements of saturated porous media are combined with the boundary conditions. The extended precise integral solution of the thermal consolidation problem of layered saturated porous media under the action of decay heat source in the domain of integral transformation is derived, and the corresponding numerical integral inverse transformation is carried out to obtain the obtained temperature. Solutions of excess pore pressure and vertical displacement in physical domain. Based on the above solution process, a corresponding calculation program is compiled to carry out numerical calculation. By comparing with the existing literatures, the adaptability and correctness of the extended fine integration method in solving the thermal consolidation problem of layered saturated porous media are verified. Finally, the effects of decay period of heat source, buried depth of heat source and stratification of medium on thermal consolidation effect are analyzed by several examples. The results show that the decay period of heat source has an obvious effect on the temperature, the peak value of the superstatic pore pressure and the time to reach the peak value. The longer the decay period, the larger the peak value and the longer the time required to reach the peak value. The influence of buried depth of heat source on the variation of superstatic pore pressure and vertical displacement is significant. The vertical displacement of both sides of the heat source is symmetrically distributed under the action of deep buried heat source, but there is no such phenomenon on both sides of shallow buried heat source, and the stratification characteristic of saturated porous media has an obvious effect on the thermal consolidation effect.
【作者单位】：同济大学地下建筑与工程系岩土及地下工程教育部重点实验室;浙江大学岩土工程研究所软弱土与环境土工教育部重点实验室;
【基金】：国家自然科学基金资助项目(50578121,41672275)
【分类号】：O551.3

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