Heat transfer characteristics for temperature of simple harmonic quantity in the cold-region tunnel and sensitivity of influencing factors
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摘要: 为探究寒区隧道温度场的时空演化规律, 以波的视角从时间尺度和空间尺度建立了寒区隧道温度简谐波径向传热模型, 基于傅里叶传热定律推导了寒区隧道温度简谐波径向传热表达式; 依托兴安岭公路隧道温度测试结果, 验证了温度简谐波径向传热表达式的可行性, 分析了温度简谐波沿隧道径向深度的分布特征与随冻融周期的变化规律; 采用系统稳定分析法, 研究了温度简谐波对各影响因素归一化的敏感度因子。研究结果表明: 沿隧道径向深度0.00~4.00 m, 温度振幅呈负指数函数形式衰减, 变化范围为11.67℃~0.45℃; 温度相位移呈正比例函数形式增大, 变化范围为0.00~75.24 d; 年平均温度呈线性升高的趋势, 变化范围为-0.62℃~1.98℃; 受隧道区气温逐年变暖趋势的影响, 隧道进口端壁面年平均温度从2016~2019年升高了约0.75℃, 年平均温度随冻融周期逐年增大, 2.00 m深度内年平均温度受冻融周期影响较大, 超过2.00 m年平均温度受冻融周期影响相对较小; 隧道进口端壁面温度振辐从2016~2019年衰减了1.48℃, 温度振幅随冻融周期逐年衰减, 2.00 m深度内温度振幅衰减较快, 超过2.00 m温度振幅衰减较慢; 隧道进口端壁面日相位从2016~2019年延迟了7.20 d, 日相位随冻融周期逐年增大。温度简谐波对各影响因素的敏感性由高到低依次为壁面温度振幅、壁面年平均温度、围岩含冰率、围岩含水率、围岩孔隙率、骨架颗粒的质量热容量与导热系数。Abstract: In order to investigate the spatial-temporal changing laws of temperature field in cold-region tunnels, a radial heat transfer model was established of temperature of simple harmonic quantity in the cold-region tunnel according to the time and space scales from the perspective of waves. Moreover, the radial heat transfer expression of temperature of simple harmonic quantity in the cold-region tunnel was deduced based on Fourier's laws of heat transfer. Based on the temperature test results of Xing'anling Highway Tunnel, the feasibility of the radial heat transfer expression of temperature of simple harmonic quantity was verified. Distribution characteristics of temperature of simple harmonic quantity in radial depth and its variation with freeze-thaw cycles were analyzed. The sensitivity factor for this temperature was normalized to each influence factor using the system stability analysis method. Analysis result shows that within the tunnel radial depth of 0.00-4.00 m, the temperature amplitude has a range of 11.67 ℃-0.45 ℃ and it decays as a negative exponential function. The temperature phase shift has a range of 0.00-75.24 d and it increases as a proportional function. The average annual temperature increases linearly and has a range of-0.62 ℃-1.98 ℃. Affected by the annual warming trend of temperature at the tunnel site, the average annual temperature on the tunnel wall at the entrance increases by approximately 0.75 ℃ from 2016 to 2019, which increasing every year with the freeze-thaw cycles. The average annual temperature is greatly affected by the freeze-thaw cycles within a depth of 2.00 m, but less affected at depths beyond 2.00 m. The temperature amplitude on the tunnel wall at the entrance decreases by 1.48 ℃ from 2016 to 2019, and that attenuates every year with the freeze-thaw cycles. The temperature amplitude decays faster below the depth of 2.00 m, but slower above 2.00 m. The day phase on the tunnel wall at the entrance is delayed by 7.20 d from 2016 to 2019, which continues to rise every year within freeze-thaw cycles. The sensitivities of temperature of simple harmonic quantity to each influence factor from high to low are temperature amplitude and average annual temperature of tunnel wall, ice content, water content and porosity of surrounding rock, specific heat capacity and thermal conductivity of skeleton particles.
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图 1 温度简谐波径向传热模型
Figure 1. Radial heat transfer model of temperature of simple harmonic quantity
图 2 兴安岭公路隧道测试断面与温度传感器布置
Figure 2. Test sections and temperature sensors arrangement in Xing'anling Highway Tunnel
图 3 不同径向深度处隧道温度拟合曲线
Figure 3. Fitted curves of tunnel temperature at different radial depths
图 7 温度简谐波径向传热特征随冻融周期的变化规律
Figure 7. Variation law of radial heat transfer characteristics for temperature of simple harmonic quantity with freeze-thaw cycles
图 8 温度简谐波的实测值与计算值
Figure 8. Measured and calculated values for temperature of simple harmonic quantity
表 1 围岩年平均温度的拟合参数
Table 1. Fitting parameters of average annual temperature of surrounding rock
隧道名称 z/m γ/(℃·m-1) R2 林场隧道 0.00~3.60 1.29 0.906 3 无名隧道 0.00~1.24 1.97 0.997 8 祁连山隧道 0.00~4.00 0.06 0.993 2 鹧鸪山隊道 0.00~3.50 0.56 0.991 4 绥阳隧道 0.00~12.60 0.11 0.689 8 昆仑山隧道 0.00~5.00 0.07~0.09 0.998 4 风火山隧道 0.00~5.00 0.09~0.17 0.997 6 玉希莫勒盖隧道 0.00~1.90 1.80 0.785 8 
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表 2 兴安岭公路隧道相关参数取值
Table 2. Related parameters in the Xing'anling Highway Tunnel
序号 参数 取值 1 λs/[W·(m·K)-1] 2.50~3.20 2 λw/ [W·(m·K)-1] 0.608 0 3 λi/ [W·(m·K)-1] 2.22 4 λg/ [W·(m·K)-1] 0.022 4 5 cs/ [kJ·(kg·K)-1] 0.84~1.17 6 cw/ [kJ·(kg·K)-1] 4.18 7 ci/ [kJ·(kg·K)-1] 2.09 8 ρdr/ (kg·m-3) 2 354~2 550 9 ρw/ (kg·m-3) 1 000 10 ρi/ (kg·m-3) 900 11 Gs/(-) 2.40~2.60 12 n/% 1.83~33.20 13 w/% 0.80~30.00 14 wi/% 0.70~27.90 15 T0a/℃ -0.91~1.55 16 A0/℃ 3.83~11.67 17 φ0/℃ 125.00~148.00
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表 3 温度简谐波对主要影响参数的敏感度
Table 3. Sensitivity of temperatures of simple harmonic quantity to main influencing factors
参数 A0 T0a λs Cs w wi n 0.30 0.30 0.30 0.30 0.30 0.30 0.30 0.849 7 0.119 6 0.004 0 0.009 2 0.013 0 0.024 7 0.009 3 S′k 0.825 4 0.116 2 0.003 9 0.008 9 0.012 6 0.024 0 0.009 0
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