寒区浅埋隧道围岩非稳态温度场解析研究  

Analytical research on unsteady temperature field of shallow buried tunnel surrounding rock in cold regions

作　　者：余俊[1] 姜岸 李东凯 YU Jun;JIANG An;LI Dongkai(School of Civil Engineering,Central South University,Changsha 410075,China;College of Civil Engineering and Architecture,Zhejiang University,Hangzhou 310000,China)

机构地区：[1]中南大学土木工程学院,湖南长沙410075 [2]浙江大学建筑工程学院,浙江杭州310000

出　　处：《冰川冻土》2025年第2期441-452,共12页Journal of Glaciology and Geocryology

基　　金：国家自然科学基金项目(52078496,52478427)资助。

摘　　要：寒区围岩冻融循环等地质灾害对隧道结构稳定性的影响不可忽略,因此,对寒区浅埋隧道围岩非稳态温度场进行了解析研究。运用保角变换将隧道围岩区域转换为圆环区域,基于叠加原理将非稳态热传导方程分解为一个稳态热传导方程和一个非稳态热传导方程,运用分离变量法和变量代换得到了隧道围岩非稳态温度场的解析解。将解析解与有限元数值模拟的结果及已有文献进行对比,发现解析结果与二者均吻合较好,验证了解析解的正确性。对解析解进行参数分析,发现围岩热扩散率的增大及隧道半径的增加均会加快围岩的导热过程,隧道埋深的增加则会减慢拱顶导热过程;对隧道衬砌法向的非稳态温度场进行对比分析,发现随着所分析法线段的平缓,与隧道衬砌距离相同的点趋于稳态时的温度变化增加,距隧道衬砌越远的点稳态时的变温幅度越高,隧道围岩温度的角向分布呈现弱对称性;对隧道拱顶温度场非稳态分量进行分析,发现越靠近隧道拱顶,且热传导所经时间越短,隧道拱顶温度场中非稳态分量在温度场解析解中占比越大。该研究对寒区隧道结构的温度响应预测有一定参考意义。The impact of geological hazards on tunnel structural stability in cold regions,such as freeze-thaw cy⁃cles in surrounding rock,cannot be ignored.Thus,unsteady temperature field of the shallow buried tunnel sur⁃rounding rock in cold regions is studied analytically.After the conversion of the shallow buried circular tunnel surrounding rock region into an annular region by conformal transformation,the equation is decomposed into a steady heat transfer equation and an unsteady heat transfer equation linearly based on superposition principle com⁃bined with temperature boundary conditions.Finally,the explicit analytical solution for the unsteady tempera⁃ture field of the tunnel envelope is derived by variable separation method and variable substitution.Comparisons among results of this analytical solution,finite element data and existing article data show a reasonable similari⁃ty,which verifies the correctness of this analytical solution,demonstrating a higher operational efficiency com⁃pared to numerical methods.Parametric analysis of the analytical solution shows both the increase in thermal dif⁃fusivity rate of the surrounding rock and tunnel radius will accelerate the unsteady heat conduction process of the surrounding rock,while the increase in tunnel depth will slow down the heat conduction process above the vault;The unsteady temperature fields of the normal lines at different angles from the tunnel lining are compared and analyzed,which shows that as the normal line becomes more horizontal,the temperature of the points with the same distance from the tunnel lining varies more in steady state,and the more distant those points from the tun⁃nel lining is,the more the temperature varies at steady state,and the angular distribution of the tunnel surround⁃ing rock temperature field shows weak symmetry;The analysis of unsteady component of temperature field above the tunnel vault shows that the shorter the distance to the tunnel vault and the time elapsed for heat conduc⁃tion are,the larger the pr

关 键 词：浅埋圆形隧道 非稳态温度场 保角变换 分离变量法 变量代换 解析解 

分 类 号：U451.2[建筑科学—桥梁与隧道工程]