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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

王路君 艾智勇

王路君, 艾智勇. 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[J]. 力学学报, 2017, 49(2): 324-334. doi: 10.6052/0459-1879-16-272
引用本文: 王路君, 艾智勇. 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[J]. 力学学报, 2017, 49(2): 324-334. doi: 10.6052/0459-1879-16-272
Wang Lujun, Ai Zhiyong. EPIM FOR THERMAL CONSOLIDATION PROBLEMS OF SATURATED POROUS MEDIA SUBJECTED TO A DECAYING HEAT SOURCE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 324-334. doi: 10.6052/0459-1879-16-272
Citation: Wang Lujun, Ai Zhiyong. EPIM FOR THERMAL CONSOLIDATION PROBLEMS OF SATURATED POROUS MEDIA SUBJECTED TO A DECAYING HEAT SOURCE[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 324-334. doi: 10.6052/0459-1879-16-272

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

doi: 10.6052/0459-1879-16-272
基金项目: 

国家自然科学基金资助项目 50578121

国家自然科学基金资助项目 41672275

详细信息
    通讯作者:

    2) 王路君, 博士, 主要研究方向:岩土工程及地下工程.E-mail:wanglujun007@163.com

    3) 艾智勇, 教授, 主要研究方向:岩土工程及地下工程.E-mail:zhiyongai@tongji.edu.cn

  • 中图分类号: O302

EPIM FOR THERMAL CONSOLIDATION PROBLEMS OF SATURATED POROUS MEDIA SUBJECTED TO A DECAYING HEAT SOURCE

  • 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.

     

  • 图  1  微层元示意图

    Figure  1.  Diagram of an arbitrary layer element

    图  2  相邻微层元的合并

    Figure  2.  Combination of adjacent layer elements

    图  3  层状体系的三个层块

    Figure  3.  Three blocks of a layered system

    图  4  点热源作用时超静孔压随时间变化

    Figure  4.  Variation of excess pore pressure with time due to a point heat source

    图  5  衰变周期对热固结效应的影响

    Figure  5.  Effect of the heat source's half-life on thermal consolidation

    图  6  热源埋深对超静孔压及竖向位移的影响

    Figure  6.  Effect of the heat source's buried depth on the variation of excess pore pressure and vertical displacement

    图  7  不同埋深条件下竖向位移随时间的变化曲线

    Figure  7.  Evolutions of vertical displacement against time with different conditions of buried depths

    图  8  不同时刻多层介质超静孔压沿深度分布

    Figure  8.  Distribution of excess pore pressure along depth of multilayered medium at different time

    表  1  多层饱和半空间计算参数

    Table  1.   Parameters of the multilayered half-space

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  • 收稿日期:  2016-09-28
  • 网络出版日期:  2017-01-09
  • 刊出日期:  2017-03-18

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