EPIM FOR THERMAL CONSOLIDATION PROBLEMS OF SATURATED POROUS MEDIA SUBJECTED TO A DECAYING HEAT SOURCE
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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: The thermal consolidation of saturated porous media subjected to a heat source is an important subject in civil engineering and energy engineering. For the complexity of the problem, the porous media are usually treated as homogeneous isotropic media and the heat source is assumed to be a heat source with constant strength in the existing studies. In engineering practice, natural saturated porous media usually show obvious layered characteristics and the heat source is decaying with time. In this case, the extended precise integration method (EPIM) is presented in this study to investigate the thermal consolidation problems of layered saturated porous media subjected to a decaying heat source. The partial differential equations are reduced to ordinary ones by means of the integral transform techniques. Combining the adjacent layer elements and considering the boundary conditions, the EPIM solutions in the transformed domain of the problems are deduced. With the aid of corresponding numerical integral inversion, the temperatures, excess pore pressures and vertical displacements in the physical domain are obtained. A numerical example with the corresponding calculation program is performed to compare with the existing results, which confirm the applicability and validity of the presented method in dealing with the thermal consolidation problems of layered saturated porous media. Finally, numerical examples are carried out to analyse the influence of the heat source's half-life and buried depth, as well as the stratification of medium on the thermal consolidation behaviour. Numerical results show that:the decay period of heat sources has significant influence on the peak values and peak time of temperature and excess pore pressure, the longer the decay period, the greater the peak values and the longer the peak time of temperature and excess pore pressure; burial depths have obvious influence on the variations of excess pore pressure and vertical displacement, the evolutions of vertical displacements against time on both side of the deeply buried heat source are symmetrical, while there is no such phenomenon for the shallow heat source; stratification characteristics of the saturated porous media shows prominent effects on the thermal consolidation.
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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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