稀疏裂隙岩体水流传热过程中热应力及位移的半解析计算方法和应用（英文）

A semi-analytical method and its application for calculating the thermal stress and displacement of sparsely fractured rocks with water flow and heat transfer

目的:探索核废料地质处置库近场岩体在热源(核素衰变产生热量)和裂隙水流动影响下的应力和变形规律,为处置库的安全评估提供理论基础。创新点:针对包含内热源和饱和裂隙水流动的岩体,提出一种稀疏裂隙岩体水流传热过程中热应力及位移的半解析计算方法,并将该方法应用于核废物处置库近场裂隙岩体温度、热应力和位移的分布特征分析。方法:首先根据热弹性位移势法建立拉普拉斯变换域内的基本积分方程,然后将裂隙离散化,利用数值积分方法计算不含奇点的裂隙单元积分,采用解析法计算包含奇点的单元积分,再根据拉普拉斯数值逆变换将热弹性位移势转换到时间域中,最后利用中心差分法计算热应力和位移。结论:1.在处置库运营早期,岩石受分布热源影响而产生热膨胀区域的范围(即受压区域)较为有限;2.核素在经过长期的衰变过程后,热流强度大幅降低,使得处置库近场岩石中仅有热源附近的极小部分岩石为受压区域;3.裂隙水的流动传热作用使得处置库下游的温度峰值更高,且裂隙水流速越大,流动传热作用越明显,裂隙水流速对热应力和位移的影响与温度类似;4.过小的热源间距会使不同热源间传热作用叠加,从而导致处置库近场的温度、热应力和位移峰值急剧增大。

Using Goodier＇s thermo-elastic displacement potential and Laplace transform, a semi-analytical method is developed for calculating the displacement and stress induced by heat transfer in sparsely fractured granitic rocks with saturated water flow and distributed heat sources. An integral equation of the thermo-elastic displacement potential is formulated in the Laplace-transformed domain. The fractures are discretized into rectangular elements, and the elemental integrals that involve singularities are calculated analytically. The numerical solutions of the potential are calculated using numerical Laplace inversion, and the temperature-gradient-induced displacements and stresses are calculated using central differences. The method is employed to examine the characteristics of the temperature-gradient-induced displacement and stress for a hypothetical problem that is intended to mimic the near-field environment of deep geological repositories of high-level radioactive wastes. Among other things, the results reveal the following：（1） In early time of operation of the repository, the region of rock under thermal expansion and compressive is limited;（2） As the intensity of the heat source gets smaller with time, only a small portion of the rock expands whereas the remaining portion contracts;（3） Downstream peak temperatures may be higher due to the supply of thermal energy by the water-flow-facilitated heat transfer, and patterns of influences of the water velocities on the thermal stress and displacement are similar;（4） Sufficiently close heat sources would cause superposition of the heating effects and make the near-field temperature increase significantly.