季节性寒区隧道围岩温度场与变形特性研究
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摘要
随着振兴东北老工业基地和西部大开发政策的实施，铁路和公路网正从东往西，从南向北发展，而这些地区都属于高纬度或高海拔地区，是季节性冻土区，在这些地方修建隧道将面临着冻害的威胁。本文以新疆玉希莫勒盖隧道为依托，采用现场监测、理论分析、数值模拟以及相似模拟试验等手段相结合，对季节性寒区隧道的温度场与变形进行了一系列的研究，对季节性寒区隧道的建设具有一定的指导意义。
(1)通过在现场监测获得新疆天山玉希莫勒盖隧道的大气及围岩内的温度变化规律，并对大气的监测数据进行拟合分析，为之后的理论计算和数值模拟等相关分析提供基础数据；根据围岩中的温度监测结果可近似得到该隧道的冻结深度，为之后的围岩稳定性分析提供必要的参数，也可对温度场的数值模拟结果进行对比验证；此外通过对隧道不同断面的温度分析得到了现场需要铺设保温层的距离。
(2)基于平面假设，并认为保温层起到良好的保温效果，建立了包括保温层、衬砌和围岩三层介质的寒区隧道温度场的数学模型；采用Laplace积分变换和DenIsger数值反演法对其求解；根据对现场温度监测结果的拟合，对玉希莫勒盖隧道的温度场进行了分析，得到了其相应的变化规律；结果显示现场铺设5cm保温层不足以防止冻害的发生，以衬砌外缘温度大于等于零为判别条件，经过试算确定了在不采取其他防护措施时玉希莫勒盖隧道不发生冻害至少需要19cm厚的保温层；对对流换热系数、年平均气温以及地层温度三个参数进行分析得到：对流换热系数对隧道温度场的影响较小，并分别得到不同的年平均气温或不同地层温度下玉希莫勒盖隧道所需要保温层的厚度。为该地区类似工程的建设提供一定的指导和理论依据。
(3)采用Geo-studio软件中TEMP模块对玉希莫勒盖隧道在未铺设保温层和铺设5cm保温层两种情况下的温度场进行研究；当未铺设保温层时提取与现场相应位置的温度结果，发现两者规律基本一致，验证了所选参数的可靠性；当铺设5cm保温层时，发现虽然保温层能较好的阻止负温的传递，但是该厚度还不足以保证围岩不发生冻结，仍存在0.4m的冻结深度；通过对以上两种情况冻结锋面的移动情况进行整体拟合和分段拟合研究，整体拟合的相关系数虽然较高，但未能较好的包含冻结锋面的所有信息，现对不同材料分别进行线性拟合，得出以下结论：底板是冻结锋面发展最快的位置，拱肩次之，拱脚是发展最慢的位置；冻结锋面在衬砌中扩展的速度是围岩的8~10倍；冻结锋面在第二周期比第一周期扩展的范围要稍大一些。当铺设保温层后拱肩为冻结锋面发展最快、最远的位置，其次是底板。基于以上分析，将拱肩和底板都作为危险位置对玉希莫勒盖隧道所需保温层厚度进行分析，得到在不采取其他措施的情况下，需要铺设21cm厚的保温层方可保证隧道不发生冻害。
(4)将冻胀应变看作为拉应变，并对已有冻结围岩本构方程中的不足进行修正，根据冻胀位移的方向认为存在冻结零位移点，并给出求解方法。基于修正后冻结围岩的本构方程首先求解了不等压条件下寒区隧道围岩应力场，分别分析了衬砌与围岩中在不同的侧压力系数和角度时应力场的规律。其次对静水压力场是围岩中可能出现的三种情况进行了分析，并对塑性半径小于冻结圈时进行了参数分析，从而更好地解释了各相关参数对围岩应力场和塑性区的发生的影响。最后，针对围岩中不发生塑性破坏这种最简单的情况建立冻结围岩融化的弹性模型，考虑冻结围岩融化后体积缩小的现象，得到了冻结融化后围岩应力场。根据以上分析对玉希莫勒盖隧道在冻结和融化时的围岩应力场和变形场的求解。
(5)根据相似理论对季节性寒区隧道的温度场和冻胀力进行了相似模拟试验研究，整个试验装置包括模型主体、边界温度控制系统、大气温度模拟系统、温度控制系统和测试系统组成，分别进行了未铺设保温层和铺设5cm保温层两组试验，虽然试验结果温度的幅值偏低，但是仍然可以得出保温层能较好的阻止负温度传递，平均阻断率达86.5%，未铺设保温层时的冻结深度为2m，铺设保温层时的冻结深度缩小为0.5m。试验中衬砌壁后最大径向和环向冻胀力的平均值为0.29MPa和0.275MPa。通过底板最大的环向应变反算最大冻胀力为0.613MPa，其他三处反算的平均最大冻胀力为0.511MPa，该结果比压力盒的测试结果偏大，主要原因为压力盒厚度达1.1cm导致冻胀力测试结果偏小，另外应变反算的冻胀力是基于圆模型存在一定的偏差。
(6)根据现场的温度监测结果，将其与数值模拟、模型试验和理论计算的结果进行对比分析，并分析其产生偏差的原因；另外，采用数值模拟和理论计算对铺设16cm保温层时衬砌外缘的温度曲线进行对比分析，得出最低温度的大小关系；最后对现场冻胀力和试验测试的冻胀力进行对比分析。
With the revitalization of the northeast industrial base and the implementation of westerndevelopment policy, the railway and road nets are expanding from east to west and from southto north. Yet the regions are almost high latitude or high elevation which belongs to seasonalfrozen soil region. The new challenge, freeze damage, will arise when the tunnel engineeringare built in these areas. This paper takes Yuximolegai tunnel as an example. A series ofresearches on temperature field and the stability analysis of surrounding rocks were carriedout for seasonal cold region using field test, analytical solution, physical test and numericalsimulation. The study can provide some guide significance for the construction of seasonalcold region tunnel.
(1) The temperature laws of air and surrounding rocks of Yuximolegai tunnel areobtained by field measurement. The fitting analysis of temperature data of air can providebasic data for analytical calculation and numerical simulation. The frost depth can beapproximately obtained based on temperature measurement of surrounding rocks, which canprovide the necessary parameters for stability analysis of surrounding rocks. The temperaturemeasurement results can verify the numerical simulation results. The distance with insulationlayer can be determined by analyzing the temperature law of different sections.
(2) The mathematic model of the temperature field of cold region tunnel is establishedbased on plane assumptions, which contains insulation layer, lining and surrounding rocks.The insulation layer is supposed to play a very good role. Then Laplace integral transfer andDenIsger inversion method are used to solve this model. The analysis for temperature field ofYuximolegai tunnel was carried out and the corresponding change law was obtainedaccording to the field measurement. The results show that the5cm thick insulation is notenough to stop frozen damage. The condition that the temperature at the outer edge of liningis greater than equal to zero is as the criterion. According to this criterion, if Yuximolegaitunnel is protected from frozen damage, at least19cm thick insulation layer is laid withoutother protective measures by trail calculation. Besides, the sensitivity analysis for heattransfer coefficient, annual average temperature and formation temperature is carried out andthe following conclusions are obtained: the effect of heat transfer coefficient on temperaturefield of tunnel is small; the thickness needed in Yuximolegai tunnel is determined underdifferent annual average temperature and formation temperature. The study can providecertain guide and theoretical basis.
(3) Temp module in Geo-studio software is selected to calculate temperature field ofYuximolegai tunnel with and without insulation layer. The results of numerical simulation agree with field measurement in the same place when no insulation layer is installed. Thereliability of parameters is verified. When5cm insulation layer is installed, the calculationresults show that the effect of stopping the subzero temperature transfer is good, but thethickness is not enough to clear up frozen damage and the frozen depth is still0.4m. Based onthe whole and piecewise fitting results of freezing front of above two conditions, thecorrelation coefficient of whole fitting is large, but it can not contain all information offreezing front. The piecewise linear fitting is carried out for different materials, respectively.The following conclusions are obtained: the freezing front of the floor expands fastest. Thesecond is spandrel. And the slowest position is arch. The expanding speed of freezing front inlining is faster8~10times than that in surrounding rocks. The freezing range in the secondcycle is a little larger than that in the first cycle. When the insulation layer is installed, theexpanding speed of spandrel is fastest and its range is largest. According to above analysis,the spandrel and floor are both regarded as dangerous section to analyze the insulation layerthickness of Yuximolegai tunnel.21cm insulation layer can stop tunnels from frost damagewithout other measures.
(4) Based on some assumption, the analytical solutions for stress and deformation ofseasonal cold-region tunnel are performed. The frost strain is regarded as tensile strain. Thedeficiencies of constitutive equation are improved. The no displacement position induced byfrost exists according to the direction of frost deformation and its iteration method is given.Firstly, based on the modified constitutive equation of frozen surrounding rocks, the stressfield of cold region tunnel is solved under no equal pressure. The stress fields of lining andsurrounding rocks are analyzed under different lateral pressure coefficients and angles,respectively. Then, the analysis of stress and deformation under hydrostatic pressure field ispreformed, including three possible situations. The sensitivity analysis is carried out whenplastic radius is smaller than frozen radius. The results can explain the influence of parameterson stress field and plastic zone. At last, the elastic melting model of frozen surrounding rocksis established according to the condition where no plastic zone occurs. The melting modelconsiders volume change and then the stress field of surrounding rocks is obtained aftermelting. Based on the above analysis, the stress and deformation of Yuximolegai tunnel aresolved when frost or melting happens.
(5) According to similarity theory, the temperature field and frozen force of seasonalcold region tunnel are studied by physical test. The whole test device contains model body,boundary temperature control system, air temperature simulation system, temperature controlsystem and monitoring system. The tests are divided into two groups,5cm insulation and noinsulation. The temperature amplitude in test is lower than the measurement data, but it is still seen that insulation layer can stop subzero temperature transfer well and the average blockingrate reaches86.5%. When no insulation layer is laid, the frozen depth is about2m.While thefrozen depth is changed to0.5m. In test, the largest radial and circumferential frozen forcesare0.29MPa and0.275MPa, respectively. The largest circumferential strain is used tocalculate the largest frozen force,0.613MPa. The average largest frozen force in otherpositions is0.511MPa. The result is larger than the data monitored by stress tense. It is thereason that the thickness of stress tense reaching1.1cm causes the result to become small.Besides, the results calculated by strain are solved based on the assumption of circle section.
(6) Temperature measured in field is compared with the results of numerical simulation,model test and analytical calculation, and the deviation is analyzed. Besides, the relationshipof the lowest temperature is obtained by analyzing the temperature at the outer edge of liningusing numerical simulation and analytical calculation. At last, the frost force in field iscompared with the result of model test.
(1)通过在现场监测获得新疆天山玉希莫勒盖隧道的大气及围岩内的温度变化规律，并对大气的监测数据进行拟合分析，为之后的理论计算和数值模拟等相关分析提供基础数据；根据围岩中的温度监测结果可近似得到该隧道的冻结深度，为之后的围岩稳定性分析提供必要的参数，也可对温度场的数值模拟结果进行对比验证；此外通过对隧道不同断面的温度分析得到了现场需要铺设保温层的距离。
(2)基于平面假设，并认为保温层起到良好的保温效果，建立了包括保温层、衬砌和围岩三层介质的寒区隧道温度场的数学模型；采用Laplace积分变换和DenIsger数值反演法对其求解；根据对现场温度监测结果的拟合，对玉希莫勒盖隧道的温度场进行了分析，得到了其相应的变化规律；结果显示现场铺设5cm保温层不足以防止冻害的发生，以衬砌外缘温度大于等于零为判别条件，经过试算确定了在不采取其他防护措施时玉希莫勒盖隧道不发生冻害至少需要19cm厚的保温层；对对流换热系数、年平均气温以及地层温度三个参数进行分析得到：对流换热系数对隧道温度场的影响较小，并分别得到不同的年平均气温或不同地层温度下玉希莫勒盖隧道所需要保温层的厚度。为该地区类似工程的建设提供一定的指导和理论依据。
(3)采用Geo-studio软件中TEMP模块对玉希莫勒盖隧道在未铺设保温层和铺设5cm保温层两种情况下的温度场进行研究；当未铺设保温层时提取与现场相应位置的温度结果，发现两者规律基本一致，验证了所选参数的可靠性；当铺设5cm保温层时，发现虽然保温层能较好的阻止负温的传递，但是该厚度还不足以保证围岩不发生冻结，仍存在0.4m的冻结深度；通过对以上两种情况冻结锋面的移动情况进行整体拟合和分段拟合研究，整体拟合的相关系数虽然较高，但未能较好的包含冻结锋面的所有信息，现对不同材料分别进行线性拟合，得出以下结论：底板是冻结锋面发展最快的位置，拱肩次之，拱脚是发展最慢的位置；冻结锋面在衬砌中扩展的速度是围岩的8~10倍；冻结锋面在第二周期比第一周期扩展的范围要稍大一些。当铺设保温层后拱肩为冻结锋面发展最快、最远的位置，其次是底板。基于以上分析，将拱肩和底板都作为危险位置对玉希莫勒盖隧道所需保温层厚度进行分析，得到在不采取其他措施的情况下，需要铺设21cm厚的保温层方可保证隧道不发生冻害。
(4)将冻胀应变看作为拉应变，并对已有冻结围岩本构方程中的不足进行修正，根据冻胀位移的方向认为存在冻结零位移点，并给出求解方法。基于修正后冻结围岩的本构方程首先求解了不等压条件下寒区隧道围岩应力场，分别分析了衬砌与围岩中在不同的侧压力系数和角度时应力场的规律。其次对静水压力场是围岩中可能出现的三种情况进行了分析，并对塑性半径小于冻结圈时进行了参数分析，从而更好地解释了各相关参数对围岩应力场和塑性区的发生的影响。最后，针对围岩中不发生塑性破坏这种最简单的情况建立冻结围岩融化的弹性模型，考虑冻结围岩融化后体积缩小的现象，得到了冻结融化后围岩应力场。根据以上分析对玉希莫勒盖隧道在冻结和融化时的围岩应力场和变形场的求解。
(5)根据相似理论对季节性寒区隧道的温度场和冻胀力进行了相似模拟试验研究，整个试验装置包括模型主体、边界温度控制系统、大气温度模拟系统、温度控制系统和测试系统组成，分别进行了未铺设保温层和铺设5cm保温层两组试验，虽然试验结果温度的幅值偏低，但是仍然可以得出保温层能较好的阻止负温度传递，平均阻断率达86.5%，未铺设保温层时的冻结深度为2m，铺设保温层时的冻结深度缩小为0.5m。试验中衬砌壁后最大径向和环向冻胀力的平均值为0.29MPa和0.275MPa。通过底板最大的环向应变反算最大冻胀力为0.613MPa，其他三处反算的平均最大冻胀力为0.511MPa，该结果比压力盒的测试结果偏大，主要原因为压力盒厚度达1.1cm导致冻胀力测试结果偏小，另外应变反算的冻胀力是基于圆模型存在一定的偏差。
(6)根据现场的温度监测结果，将其与数值模拟、模型试验和理论计算的结果进行对比分析，并分析其产生偏差的原因；另外，采用数值模拟和理论计算对铺设16cm保温层时衬砌外缘的温度曲线进行对比分析，得出最低温度的大小关系；最后对现场冻胀力和试验测试的冻胀力进行对比分析。
With the revitalization of the northeast industrial base and the implementation of westerndevelopment policy, the railway and road nets are expanding from east to west and from southto north. Yet the regions are almost high latitude or high elevation which belongs to seasonalfrozen soil region. The new challenge, freeze damage, will arise when the tunnel engineeringare built in these areas. This paper takes Yuximolegai tunnel as an example. A series ofresearches on temperature field and the stability analysis of surrounding rocks were carriedout for seasonal cold region using field test, analytical solution, physical test and numericalsimulation. The study can provide some guide significance for the construction of seasonalcold region tunnel.
(1) The temperature laws of air and surrounding rocks of Yuximolegai tunnel areobtained by field measurement. The fitting analysis of temperature data of air can providebasic data for analytical calculation and numerical simulation. The frost depth can beapproximately obtained based on temperature measurement of surrounding rocks, which canprovide the necessary parameters for stability analysis of surrounding rocks. The temperaturemeasurement results can verify the numerical simulation results. The distance with insulationlayer can be determined by analyzing the temperature law of different sections.
(2) The mathematic model of the temperature field of cold region tunnel is establishedbased on plane assumptions, which contains insulation layer, lining and surrounding rocks.The insulation layer is supposed to play a very good role. Then Laplace integral transfer andDenIsger inversion method are used to solve this model. The analysis for temperature field ofYuximolegai tunnel was carried out and the corresponding change law was obtainedaccording to the field measurement. The results show that the5cm thick insulation is notenough to stop frozen damage. The condition that the temperature at the outer edge of liningis greater than equal to zero is as the criterion. According to this criterion, if Yuximolegaitunnel is protected from frozen damage, at least19cm thick insulation layer is laid withoutother protective measures by trail calculation. Besides, the sensitivity analysis for heattransfer coefficient, annual average temperature and formation temperature is carried out andthe following conclusions are obtained: the effect of heat transfer coefficient on temperaturefield of tunnel is small; the thickness needed in Yuximolegai tunnel is determined underdifferent annual average temperature and formation temperature. The study can providecertain guide and theoretical basis.
(3) Temp module in Geo-studio software is selected to calculate temperature field ofYuximolegai tunnel with and without insulation layer. The results of numerical simulation agree with field measurement in the same place when no insulation layer is installed. Thereliability of parameters is verified. When5cm insulation layer is installed, the calculationresults show that the effect of stopping the subzero temperature transfer is good, but thethickness is not enough to clear up frozen damage and the frozen depth is still0.4m. Based onthe whole and piecewise fitting results of freezing front of above two conditions, thecorrelation coefficient of whole fitting is large, but it can not contain all information offreezing front. The piecewise linear fitting is carried out for different materials, respectively.The following conclusions are obtained: the freezing front of the floor expands fastest. Thesecond is spandrel. And the slowest position is arch. The expanding speed of freezing front inlining is faster8~10times than that in surrounding rocks. The freezing range in the secondcycle is a little larger than that in the first cycle. When the insulation layer is installed, theexpanding speed of spandrel is fastest and its range is largest. According to above analysis,the spandrel and floor are both regarded as dangerous section to analyze the insulation layerthickness of Yuximolegai tunnel.21cm insulation layer can stop tunnels from frost damagewithout other measures.
(4) Based on some assumption, the analytical solutions for stress and deformation ofseasonal cold-region tunnel are performed. The frost strain is regarded as tensile strain. Thedeficiencies of constitutive equation are improved. The no displacement position induced byfrost exists according to the direction of frost deformation and its iteration method is given.Firstly, based on the modified constitutive equation of frozen surrounding rocks, the stressfield of cold region tunnel is solved under no equal pressure. The stress fields of lining andsurrounding rocks are analyzed under different lateral pressure coefficients and angles,respectively. Then, the analysis of stress and deformation under hydrostatic pressure field ispreformed, including three possible situations. The sensitivity analysis is carried out whenplastic radius is smaller than frozen radius. The results can explain the influence of parameterson stress field and plastic zone. At last, the elastic melting model of frozen surrounding rocksis established according to the condition where no plastic zone occurs. The melting modelconsiders volume change and then the stress field of surrounding rocks is obtained aftermelting. Based on the above analysis, the stress and deformation of Yuximolegai tunnel aresolved when frost or melting happens.
(5) According to similarity theory, the temperature field and frozen force of seasonalcold region tunnel are studied by physical test. The whole test device contains model body,boundary temperature control system, air temperature simulation system, temperature controlsystem and monitoring system. The tests are divided into two groups,5cm insulation and noinsulation. The temperature amplitude in test is lower than the measurement data, but it is still seen that insulation layer can stop subzero temperature transfer well and the average blockingrate reaches86.5%. When no insulation layer is laid, the frozen depth is about2m.While thefrozen depth is changed to0.5m. In test, the largest radial and circumferential frozen forcesare0.29MPa and0.275MPa, respectively. The largest circumferential strain is used tocalculate the largest frozen force,0.613MPa. The average largest frozen force in otherpositions is0.511MPa. The result is larger than the data monitored by stress tense. It is thereason that the thickness of stress tense reaching1.1cm causes the result to become small.Besides, the results calculated by strain are solved based on the assumption of circle section.
(6) Temperature measured in field is compared with the results of numerical simulation,model test and analytical calculation, and the deviation is analyzed. Besides, the relationshipof the lowest temperature is obtained by analyzing the temperature at the outer edge of liningusing numerical simulation and analytical calculation. At last, the frost force in field iscompared with the result of model test.
引文
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