Study on Multi-Factor Coupling Analysis of Temperature Field and Freezing Radius Prediction for Cold-Region Tunnels
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摘要:
为明确自然风与列车活塞风共同作用下寒区隧道围岩温度场演化及冻结半径变化规律，提高冻害风险快速评估能力，以果拉山隧道为工程背景开展数值模拟与机器学习联合研究. 基于现场参数建立空气、初期支护、二次衬砌和围岩组成的三维瞬态传热模型，采用非等温流动耦合空气流动与衬砌围岩传热过程，并以等效风速法表征列车活塞风及余风作用；通过控制变量法分析自然风风速、风温、风向、隧道断面尺寸、初始岩温、列车速度和运行频次7类因素，提取纵向、径向温度分布及90 d冻结半径，并基于658组正交样本建立随机森林、支持向量机和XGBoost预测模型. 结果表明：洞口段调温圈随冷空气作用时间增加而扩大，围岩纵向温度呈快速上升和稳定增长两阶段特征，径向温度逐渐趋近初始岩温；自然风风温、风向和初始岩温为主导因素，敏感性系数分别为0.22、0.21和0.21；XGBoost模型预测精度最优，均方根误差为0.118，工程算例冻结半径预测值为1.85 m，相对误差为1.1%. 外界低温空气条件和围岩初始热状态是寒区隧道冻害风险控制的关键因素，所建模型可为冻结半径快速估算和防冻设计参数优化提供依据.
Abstract:To clarify the evolution laws of surrounding-rock temperature field and freezing radius in cold-region tunnels under the combined action of natural wind and train piston wind, and to improve the capability of rapid frost-damage risk assessment, a joint study of numerical simulation and machine learning was conducted using the Guolashan Tunnel as an engineering background. Based on field parameters, a three-dimensional transient heat transfer model consisting of air, primary support, secondary lining, and surrounding rock was established. Non-isothermal flow was used to couple the airflow with the heat transfer process of the lining and surrounding rock, and an equivalent wind speed method was adopted to characterize the effects of train piston wind and residual wind. Seven types of factors, including natural wind speed, natural wind temperature, natural wind direction, tunnel cross-section size, initial rock temperature, train speed, and train operation frequency, were analyzed through the control variable method. The longitudinal and radial temperature distributions and the freezing radius after 90 days were extracted, and random forest, support vector machine, and XGBoost prediction models were established based on 658 sets of orthogonal samples. The results indicate that the temperature-adjustment zone at the tunnel portal expands with the increase of cold-air action time; the longitudinal temperature of the surrounding rock presents two-stage characteristics of rapid rise and stable growth, and the radial temperature gradually approaches the initial rock temperature. Natural wind temperature, natural wind direction, and initial rock temperature are the dominant factors, with sensitivity coefficients of 0.22, 0.21, and 0.21, respectively. The XGBoost model has the optimal prediction accuracy with a root mean square error of 0.118; the predicted freezing radius for the engineering case is 1.85 m, with a relative error of 1.1%. External low-temperature air conditions and the initial thermal state of the surrounding rock are the key factors for frost-damage risk control in cold-region tunnels. The established models can provide a basis for rapid estimation of the freezing radius and optimization of anti-freezing design parameters.
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Key words:
- cold-region tunnel /
- temperature field /
- multi-factor coupling /
- freezing radius /
- machine learning
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图 5 隧道二衬温度纵向变化云图
Figure 5. Cloud map of longitudinal temperature variation in tunnel secondary lining
图 6 不同自然风因素对围岩温度影响对比
Figure 6. Comparison of effects of different natural wind factors on surrounding-rock temperature
图 7 隧道断面对围岩温度影响对比
Figure 7. Comparison of effects of tunnel cross-section on surrounding-rock temperature
图 8 初始岩温对围岩温度影响对比
Figure 8. Comparison of effects of initial rock temperature on surrounding-rock temperature
图 9 活塞风对围岩温度影响对比
Figure 9. Comparison of effects of piston wind on surrounding-rock temperature
图 10 不同影响因素的指标值变化曲线
Figure 10. Variation curves of index values under different influencing factors
图 11 不同影响因素敏感因子排序
Figure 11. Ranking chart of sensitivity factors under different influencing factors
图 12 不同模型目标值与预测值对比图
Figure 12. Comparison chart between target values and predicted values of different models
图 13 不同模型随迭代次数增加误差变化图
Figure 13. Variation chart of errors of different models with increasing iterations
表 1 模型材料热力学参数
Table 1. Thermodynamic parameters of model materials
材料 导热系数/
（W•m−1•K−1）比热容/
（J•kg−1•K−1）密度/
（kg•m−3）动力粘度/
（Pa•s）空气 0.026 1005 ρa（T） μa（T） 初支 1.801 900 2450 二砌 1.742 920 2450 围岩 1.911 800 2500 
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表 2 计算工况
Table 2. Calculation case settings
工况 1 2 3 4 5 6 7 自然风
风速/（m•s−1）自然风
风温/℃自然风
风向/°隧道断面
大小/m2围岩
岩温/℃列车运行
速度/（km•h−1）列车运行
频次/min1 −5 0 60 （单线） 5 80 10 2 −10 30 10 140 20 3 −15 60 97 （双线） 15 200 30 4 −20 90 20 250 40 注：加粗数字表示该影响因素的基准值.
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表 3 不同列车速度下计算工况
Table 3. Calculation case settings under different train speeds
列车运行速度/（km•h−1） 活塞风作用时间/s 活塞风峰值速度/（m•s−1） 余风作用时间/s 列车频次/min 80 45 12.8 300 30 140 26 22.1 316 200 18 31.4 324 250 15 39.4 327
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表 4 不同模型结果评价参数
Table 4. Evaluation parameters for results of different models
模型 RF SVM Xgboost MSE 0.580 0.018 0.014 RMSE 0.762 0.155 0.118 MAE 0.602 0.108 0.086 R2 0.757 0.903 0.973
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