Influence of Thermal Conductivity on Temporal and Spatial Distributions of Temperature Filed in Cold Region Tunnel
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摘要: 寒区隧道温度场对其抗防冻设计至关重要，围岩和支护结构的导热系数对温度场时空分布具有显著影响. 以寒区公路运营隧道为计算模型，采用理论推导、现场实测、数值仿真等方法对寒区隧道温度场的时空分布受导热系数的影响规律进行了研究. 研究结果表明：在任意时间点，变温圈内各点的温度均随支护结构导热系数的增大而降低，且支护导热系数越大，同位置处的温度降低速率越小；在任意时间点，支护温度随围岩导热系数的增大而升高，围岩温度随其导热系数的变化呈现分区性；可将围岩变温圈分为Ⅰ区和Ⅱ区：Ⅰ区内的各点温度随围岩导热系数的增大而升高；Ⅱ区内的各点温度随围岩导热系数的增大而降低；时间越长，Ⅰ区和Ⅱ区分界线的斜率和截距越大. 研究成果可为寒区隧道的抗防冻设计及选线提供借鉴和参考.Abstract: The temperature field of a tunnel in cold region is crucial to its antifreezing design, and the thermal conductivity of the supporting structure and surrounding rock has a significant effect on the temporal and spatial distributions of the temperature field. Taking a highway tunnel in cold region as the prototype calculation model, methodologies including theoretical derivation, field measurement and numerical simulation are used to study the influence of thermal conductivity on the temporal and spatial distributions of tunnel temperature filed. Results show as follows: At any time the temperature of each point in the variable temperature circle decreases with the growth of thermal conductivity of the supporting structure; and the larger the thermal conductivity of the supporting structure, the smaller the temperature reduction rate at the same position. At any time the temperature of supporting structure increases with the growth of thermal conductivity of surrounding rock, but the temperature variation of surrounding rock is characterized by regionalization. That is, the surrounding rock can be divided into zones Ι and Ⅱ. As the thermal conductivity of the surrounding rock increases, the temperature in zone Ι increases, while the temperature in zone Ⅱ decreases. What’s more, the slope and intercept of the boundaries between zones Ι and Ⅱ are greater at a larger time scale. The research results can provide references for the antifreezing design and route selection of tunnels in cold regions.
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图 1 寒区隧道瞬态热量传递计算简化示意
Figure 1. Simplified sketch for calculation of transient heat transfer in tunnels in cold regions
图 8 隧道拱顶考察点布置图（单位：cm）
Figure 8. Layout map of investigation points in tunnel crown (unit：cm)
图 12 温度随支护结构导热系数变化曲线
Figure 12. Temperature change with thermal conductivity of structure
图 13 温度随围岩导热系数变化曲线
Figure 13. Temperature change with thermal conductivity of surrounding rock
图 14 围岩导热系数的影响分区
Figure 14. Influenced zone by thermal conductivity of surrounding rock
图 15 结构导热系数不同时温度随时间变化曲线
Figure 15. Temperature change with time for different thermal conductivity of structure
图 16 围岩导热系数不同时温度随时间变化曲线
Figure 16. Temperature change with time for different thermal conductivity of surrounding rock
表 1 校验模型的计算参数
Table 1. Parameters of verification model
位置 密度
/（kg•m−3）比热容
/（J•（kg•℃）−1）导热系数
/（W•（m•℃）−1）结构 2 400 960 1.6 围岩 2 025 1 256 2.0 
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表 2 导热系数取值
Table 2. Value of thermal conductivity
W•(m•℃)−1 工况 支护 围岩 1 0.4、0.6、0.8、1.0、1.2、1.4、1.6、1.8、2.0、2.2、2.4、2.6 2.0 2 1.6 0.5、1.0、1.5、2.0、2.5、3.0、3.5、4.0、4.5、5.0、5.5、6.0
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