寒区隧道保温隔热层的优化设计研究
|
摘要
随着国家西部大开发战略的实施,青藏铁路、西气东输工程以及南水北调西线工程等一些重大建设项目的进行,寒区冻土工程和寒区隧道工程将越来越多。如果这些工程按照一般地区工程修建,那么冻害就在所难免,如天山二号、甘肃七道梁公路隧道以及青藏铁路关角隧道等。为了防止隧道结构冻害,保温隔热层被广泛采用,青藏铁路风火山、昆仑山隧道在隧道衬砌与初支见铺设了5cm的保温材料,西(宁)张(掖)公路大坂山隧道在二衬外铺设了8cm的保温材料。这些铺设的保温层厚度及其导热系数是否最合理,是否既经济又安全等问题,即最优问题也不得而知。为了解决这个问题,就须对保温隔热层进行优化。
为此,本文以青藏铁路风火山隧道和西(宁)—张(掖)公路大坂山隧道为依托,运用寒区隧道温度场计算理论和优化设计基本原理,建立了保温材料优化设计的计算理论,并提出了其求解方法。应用大型有限元软件ANSYS,对多年冻土地区风火山隧道和季节性冻土地区大坂山隧道进行了优化计算分析,得到以下主要成果:
①寒区隧道在不考虑气候变暖和考虑气候变暖情况下,优化结果与验算结果完全一致,最优设计也是在可行域内并且是最优解,因此该优化方法及其结果是可靠的。
②对于风火山隧道,原设计的保温隔热层参数为: H =0.50E-01m和λ=0.30E-01 W.m~(-1).K~(-1),每延米价格为5972.6元。优化结果为:不考虑气候变暖最高价格为7581.3元,考虑气候变暖的情况下最高价格为7581.8元,相应的保温隔热层参数基本相同,均为H =6.64E-02m和λ=0.13025E-01 W.m~(-1).K~(-1);不考虑气候变暖的最低价格为5752.7元,相应的保温隔热层参数为H =4.66E-02m和λ=2.8491E-02 W.m~(-1).K~(-1);考虑气候变暖的最低价格为5812.4,相应的保温隔热层参数为H =5.84E-02m和λ=6.5613E-02 W.m~(-1).K~(-1)。气候变暖是一种趋势,因此为了保证隧道结构周围围岩处于负温,若设置参数为H =6.64E-02m和λ=0.13025E-01 W.m~(-1).K~(-1)的保温隔热层,虽然其价格增加了26.9%,但均可以保证隧道结构周围围岩避免冻融作用的影响,同时说明原设计基本合理。
③对于大坂山隧道,原设计的保温隔热层参数为: H =0.135m和λ=0.341E-01W.m~(-1).K~(-1),每延米价格为12256.8元。优化结果为:不考虑气候变暖最高价格为6787.5元,相应的保温隔热层参数为H =5.51E-02m和λ=1.0323E-02 W.m~(-1).K~(-1);考虑气候变暖的情况下最高价格为7613.0元,相应的保温隔热层参数为H =6.60E-02m和λ=1.0227E-02 W.m~(-1).K~(-1);不考虑气候变暖的最低价格为6030.7元,相应的保温隔热层参数为H =4.52E-02m和λ=1.1027E-02 W.m~(-1).K~(-1);考虑气候变暖的最低价格为6240.0,相应的保温隔热层参数为H =4.77E-02m和λ=1.0226E-02W.m~(-1).K~(-1)。气候变暖是一种趋势,因此为了保证隧道结构周围围岩处于正温,若设置参数为H =6.60E-02m和λ=1.0227E-02 W.m~(-1).K~(-1)的保温隔热层,其价格减少37.9%,因此,在两种条件下,虽然隧道结构周围围岩都处于正温,但大坂山的原设计偏于保守。
④通过对考虑气候变暖和不变暖两种情况计算分析,隧道围岩温度相差较大,而全球气候变暖是不争的事实,因此在寒区隧道工程设计中须考虑气候变暖。
⑤沿隧道纵向,由于平均温度是变化的,因此铺设的保温隔热层的参数也应是不同的,才更加经济合理。
With the national western development strategy for the implementation of the Qinghai-Tibet Railway, the West-East Gas Project, the Water Diversion Project and some other major construction projects are carried out, cold permafrost and cold regions tunnels will be more and more. If those projects are built as the general area of tunnel engineering, the frost is unavoidable, for example, 2th TianShan, QiDaoLiang Highway tunnel in Gansu Province, GuanJiao Tunnel of Qinghai-Tibet Railway and so on. In order to prevent frost from damaging the tunnel structure, thermal insulation layer is widely used in the tunnel engineering,for example, 5cm thermal insulation material has been laid between tunnel lining and the first support in Fenghuoshan tunnel and Kunlun mountain tunnel , Dabanshan tunnel of Xi (ning) Zhang (ye) Highway had used 8cm thermal insulation outside two lining. Whether the thickness and thermal conductivity of insulation layer is reasonable, economic and secure is unknown, Optimization problem is also not known. In order to solve this problem, thermal insulation layer must be optimized and designed.
Therefore, this article has taken the Fenghuoshan tunnel Dabanshan tunnel of Xi (ning) Zhang (ye) Highway as examples and established optimal design theory of thermal insulation materials in cold region by means of finite element theory and optimal design theory. Simultaneously, this paper has carried on the optimized computation analysis. Application of large-scale finite element software ANSYS, Fenghuoshan tunnel in Permafrost Regions and Dabanshan tunnel in seasonal frozen soil regions are optimized and calculated, the mainly results as following:
①Without taking into account of climate warming and considering the global warming situation in cold regions tunnel,the optimized result is completely consistent with the checking calculation result,the most optimal r design is also in the feasible territory and is the optimal solution,therefore this optimized method and the results are reliable;
②Regarding to Fenghuoshan tunnel, the original design of the thermal insulation parameters are: H =0.50E-01m,λ=0.30E-01 W.m-1.K-1, the price is 5972.6 yuan per meter. The optimized result is following: when climate is unwarming the highest price is 7581.3 yuan per meter, when climate is warming the highest price is 7581.5 yuan,these parameters are H =6.64E-02m,λ=0.13025E-01 W.m~(-1).K~(-1); when climate is unwarmin the lowest price is 5752.7 yuan , The parameters of thermal insulation are H =4.66E-02m,λ=2.8491E-02 W.m~(-1).K~(-1); when climate is warmin the lowest price is 5812.4 yuan, the parameters are H =5.84E-02m,λ=6.5613E-02 W.m~(-1).K~(-1). Warming is a trend, to ensure the adjacent rock around the tunnel structure at zero temperature,if we established parameters are H =6.64E-02m,λ=0.13025E-01 W.m~(-1).K~(-1), although its price increased 26.9%, all around the surrounding tunnel structure can guarantee to avoid the effect of freezing and thawing, simultaneously, it explained the original design is basically reasonable.
③Regarding to Dabanshan tunnel, the parameter of thermal insulation layer in original designion is H =0.135m andλ=0.341E-01 W.m~(-1).K~(-1), the price is 12256.8 yuan per meter. the optimized results is following: when climate is unwarming the highest price is 6787.5 yuan and the parameters are H =5.51E-02m,λ=1.0323E-02 W.m~(-1).K~(-1);when climate is warming the highest price is 7613.0 yuan and the parameters are H =6.60E-02m,λ=1.0227E-02 W.m~(-1).K~(-1);when climate is unwarming the lowest price is 6030.7 yuan and the parameters are H =4.52E-02m,λ=1.1027E-02 W.m~(-1).K~(-1);when climate is warming the lowest price is 6240.0 yuan and the parameters are H =4.77E-02m,λ=1.0226E-02 W.m~(-1).K~(-1)。Warming is a trend, so in order to ensure that the rock around the tunnel structure is positive, if the parameters of the thermal insulation are H =6.60E-02m,λ=1.0227E-02 W.m~(-1).K~(-1),the price would reduce by 37.9%. Therefore, under the two kinds of conditions, although the temperature of the rock around tunnel structures is positive.The original desig of Dabanshan tunnel is inclined to conservative.
④The results of calculation and analysis indicate that the rock’s temperature have large difference between climate warming and unwarming. The global warming is an indisputable fact, so global warming must to be considered in cold regions tunnel engineering.
⑤Along the tunnel, with the annual average temperature changed inside the tunnel, if the thermal insulation layer is installed with different parameters in different sections, better economic efficiency should be got.
为此,本文以青藏铁路风火山隧道和西(宁)—张(掖)公路大坂山隧道为依托,运用寒区隧道温度场计算理论和优化设计基本原理,建立了保温材料优化设计的计算理论,并提出了其求解方法。应用大型有限元软件ANSYS,对多年冻土地区风火山隧道和季节性冻土地区大坂山隧道进行了优化计算分析,得到以下主要成果:
①寒区隧道在不考虑气候变暖和考虑气候变暖情况下,优化结果与验算结果完全一致,最优设计也是在可行域内并且是最优解,因此该优化方法及其结果是可靠的。
②对于风火山隧道,原设计的保温隔热层参数为: H =0.50E-01m和λ=0.30E-01 W.m~(-1).K~(-1),每延米价格为5972.6元。优化结果为:不考虑气候变暖最高价格为7581.3元,考虑气候变暖的情况下最高价格为7581.8元,相应的保温隔热层参数基本相同,均为H =6.64E-02m和λ=0.13025E-01 W.m~(-1).K~(-1);不考虑气候变暖的最低价格为5752.7元,相应的保温隔热层参数为H =4.66E-02m和λ=2.8491E-02 W.m~(-1).K~(-1);考虑气候变暖的最低价格为5812.4,相应的保温隔热层参数为H =5.84E-02m和λ=6.5613E-02 W.m~(-1).K~(-1)。气候变暖是一种趋势,因此为了保证隧道结构周围围岩处于负温,若设置参数为H =6.64E-02m和λ=0.13025E-01 W.m~(-1).K~(-1)的保温隔热层,虽然其价格增加了26.9%,但均可以保证隧道结构周围围岩避免冻融作用的影响,同时说明原设计基本合理。
③对于大坂山隧道,原设计的保温隔热层参数为: H =0.135m和λ=0.341E-01W.m~(-1).K~(-1),每延米价格为12256.8元。优化结果为:不考虑气候变暖最高价格为6787.5元,相应的保温隔热层参数为H =5.51E-02m和λ=1.0323E-02 W.m~(-1).K~(-1);考虑气候变暖的情况下最高价格为7613.0元,相应的保温隔热层参数为H =6.60E-02m和λ=1.0227E-02 W.m~(-1).K~(-1);不考虑气候变暖的最低价格为6030.7元,相应的保温隔热层参数为H =4.52E-02m和λ=1.1027E-02 W.m~(-1).K~(-1);考虑气候变暖的最低价格为6240.0,相应的保温隔热层参数为H =4.77E-02m和λ=1.0226E-02W.m~(-1).K~(-1)。气候变暖是一种趋势,因此为了保证隧道结构周围围岩处于正温,若设置参数为H =6.60E-02m和λ=1.0227E-02 W.m~(-1).K~(-1)的保温隔热层,其价格减少37.9%,因此,在两种条件下,虽然隧道结构周围围岩都处于正温,但大坂山的原设计偏于保守。
④通过对考虑气候变暖和不变暖两种情况计算分析,隧道围岩温度相差较大,而全球气候变暖是不争的事实,因此在寒区隧道工程设计中须考虑气候变暖。
⑤沿隧道纵向,由于平均温度是变化的,因此铺设的保温隔热层的参数也应是不同的,才更加经济合理。
With the national western development strategy for the implementation of the Qinghai-Tibet Railway, the West-East Gas Project, the Water Diversion Project and some other major construction projects are carried out, cold permafrost and cold regions tunnels will be more and more. If those projects are built as the general area of tunnel engineering, the frost is unavoidable, for example, 2th TianShan, QiDaoLiang Highway tunnel in Gansu Province, GuanJiao Tunnel of Qinghai-Tibet Railway and so on. In order to prevent frost from damaging the tunnel structure, thermal insulation layer is widely used in the tunnel engineering,for example, 5cm thermal insulation material has been laid between tunnel lining and the first support in Fenghuoshan tunnel and Kunlun mountain tunnel , Dabanshan tunnel of Xi (ning) Zhang (ye) Highway had used 8cm thermal insulation outside two lining. Whether the thickness and thermal conductivity of insulation layer is reasonable, economic and secure is unknown, Optimization problem is also not known. In order to solve this problem, thermal insulation layer must be optimized and designed.
Therefore, this article has taken the Fenghuoshan tunnel Dabanshan tunnel of Xi (ning) Zhang (ye) Highway as examples and established optimal design theory of thermal insulation materials in cold region by means of finite element theory and optimal design theory. Simultaneously, this paper has carried on the optimized computation analysis. Application of large-scale finite element software ANSYS, Fenghuoshan tunnel in Permafrost Regions and Dabanshan tunnel in seasonal frozen soil regions are optimized and calculated, the mainly results as following:
①Without taking into account of climate warming and considering the global warming situation in cold regions tunnel,the optimized result is completely consistent with the checking calculation result,the most optimal r design is also in the feasible territory and is the optimal solution,therefore this optimized method and the results are reliable;
②Regarding to Fenghuoshan tunnel, the original design of the thermal insulation parameters are: H =0.50E-01m,λ=0.30E-01 W.m-1.K-1, the price is 5972.6 yuan per meter. The optimized result is following: when climate is unwarming the highest price is 7581.3 yuan per meter, when climate is warming the highest price is 7581.5 yuan,these parameters are H =6.64E-02m,λ=0.13025E-01 W.m~(-1).K~(-1); when climate is unwarmin the lowest price is 5752.7 yuan , The parameters of thermal insulation are H =4.66E-02m,λ=2.8491E-02 W.m~(-1).K~(-1); when climate is warmin the lowest price is 5812.4 yuan, the parameters are H =5.84E-02m,λ=6.5613E-02 W.m~(-1).K~(-1). Warming is a trend, to ensure the adjacent rock around the tunnel structure at zero temperature,if we established parameters are H =6.64E-02m,λ=0.13025E-01 W.m~(-1).K~(-1), although its price increased 26.9%, all around the surrounding tunnel structure can guarantee to avoid the effect of freezing and thawing, simultaneously, it explained the original design is basically reasonable.
③Regarding to Dabanshan tunnel, the parameter of thermal insulation layer in original designion is H =0.135m andλ=0.341E-01 W.m~(-1).K~(-1), the price is 12256.8 yuan per meter. the optimized results is following: when climate is unwarming the highest price is 6787.5 yuan and the parameters are H =5.51E-02m,λ=1.0323E-02 W.m~(-1).K~(-1);when climate is warming the highest price is 7613.0 yuan and the parameters are H =6.60E-02m,λ=1.0227E-02 W.m~(-1).K~(-1);when climate is unwarming the lowest price is 6030.7 yuan and the parameters are H =4.52E-02m,λ=1.1027E-02 W.m~(-1).K~(-1);when climate is warming the lowest price is 6240.0 yuan and the parameters are H =4.77E-02m,λ=1.0226E-02 W.m~(-1).K~(-1)。Warming is a trend, so in order to ensure that the rock around the tunnel structure is positive, if the parameters of the thermal insulation are H =6.60E-02m,λ=1.0227E-02 W.m~(-1).K~(-1),the price would reduce by 37.9%. Therefore, under the two kinds of conditions, although the temperature of the rock around tunnel structures is positive.The original desig of Dabanshan tunnel is inclined to conservative.
④The results of calculation and analysis indicate that the rock’s temperature have large difference between climate warming and unwarming. The global warming is an indisputable fact, so global warming must to be considered in cold regions tunnel engineering.
⑤Along the tunnel, with the annual average temperature changed inside the tunnel, if the thermal insulation layer is installed with different parameters in different sections, better economic efficiency should be got.
引文
[1]赖远明.寒区隧道温度场、渗流场和应力场耦合问题的非线性分析.兰州.中国科学院兰州冰川冻土研究所博士学位论文.1999.2-3
[2]孙吉堂.青藏铁路关角隧道病害的综合整治.现代隧道技术.2001.38(5).45-49
[3]陈建勋.昝勇杰.寒冷地区公路隧道防冻隔温层效果现场测试与分析.中国公路学报. 2001. 14(4).75-79
[4]北川修三.川上义辉.寒冷地区的隧道变形与围岩冻胀性.隧道译丛.1987.3.14-34
[5]马万一.公路隧道的防水防冻设计.隧道译丛.1990.11.29-33
[6] Bonacina C..Comini C.and Fasano A..et al.Numerical solution of phase-change problems. lnt. J.Heat Mass Transfer. 1973. 16(6). 18521882
[7] Comini C..Guidice S.del and Lewis R. W.et al..Finite element solution of nonlinear heat conduction problems with special reference to phase change. Int. J. for numerical methods in engineering. 1974. 8(6).613624
[8] Guidice S. Comini G.Lewis R W. Finite element simulation of freezing processes in soils. Int. J.numer. Anal .Methods Geomech..1978.2.223-35
[9] Heuer C E. The application of heat pipes on the Trans Alaska pipeline.CRREI Report. 1979.
[10] John P. Zarling P E. Billy C. et al .Air duct system for stabilization over permafrost area.Proceeding of the 4th International conference on Permafrost. Washington.National Academy press. 1983.1463-468
[11] Dennis E. Pufah1 .Frost Action (Section 3 of Roads and Airfields in Cold Rgions.Edited by Teds Vinson). ASCE. 1996.51-85
[12] Goreing D J.Kumar P.Convective heat transfer in railway embankment ballast.Jean-Franqois T. Ground Freezing 2000. Rotterdam.A. A. Balkema. 2000. 31-36
[13] Goering D J.Passively cooled railway embankments for use in permafrost areas .Journal of Coid Regions Engineering. 2003.i 7(3). 119-130
[14] Okada.Lcile prevention by adiatic treatment of tunnel lining. Japanese Railway Engineering. 1985. 26(3).75-80
[15]刘永智.吴青柏.张建明等.高原冻土区冻土地温温度场研究.公路杂志.2000(2)
[16]喻文兵.赖远明.牛富俊等.多年冻土区铁路通风路基室内模型试验的温度场特征.冰川冻土.2002.24(5).601-607
[17]喻文兵.赖远明.张学富等.多年冻土区铁路通风路基室内模型试验研究.铁道学报.2002.24 (6).78-83
[18]刘志强.马巍.周国庆等.纵向布管调控冻土路基温度场的模拟试验研究.岩石力学与工程学报.2005.24(11).1827-1831
[19]李国玉.李宁.全晓娟.青藏铁路可调控通风管路基温度场的三维非线性分析.冰川冻土.2005 27(1).128-133
[20]赖远明.吴紫汪.张淑娟.喻文兵.邓友生.寒区隧道保温效果的现场观察研究.铁道学报. 2003. 25(1).81-86
[21]张学富.苏新民.赖远明.喻文兵.寒区隧道三维温度场非线性分析.土木工程学报. 2004. 37(2).47-53
[22]晏启祥.何川.曾东洋.寒区隧道温度场及保温隔热层研究.四川大学学报(工程科学版). 2005. 37(3).24-27
[23]谢红强.何川.李永林.寒区隧道结构抗冻实验研究及仿真分析.公路. 2006.2.184-188
[24]苏磊.付军隆.俞昌铭.王岚.张红.张丽英.保温管道经济评估的优化设计模型.节能技术. 1999. 17(93).18-25
[25]程选生.李慧雯.温度作用下钢筋混凝土矩形贮液池壁厚的优化.特种结构. 2001. 118 (12).49-51
[26]刘晓延.张岁怀.王延勇.低温管道保冷复合结构优化设计.油气田地面工程. 19(6).71-73
[27]黄善波.徐明海.程显刚.赵延茂.双层保温管道总体优化设计.油气储运. 2001. 20(4).20-22
[28]王慧.曾令可.吴建青.管道保温结构的计算机模拟与优化.工业炉. 2002. 24(1). 52-54
[34]徐宝平.管道双层保温材料经济厚度的优化.能源研究与利用. 2002. 3. 43-45
[29]王士永.长距离供汽管道保温优化的研究及应用.炼油设计. 2002. 32(12). 29-33
[30]颜晖.张端.沈锦林.玻璃熔窑多层保温的优化设计方法.材料科学与工程学报. 2005. 23(4). 512-515
[31]李春成.谢禹钧.李世武.武荣华.工业管道保温结构的优化设计及节能分析.辽宁石油化工大学学报. 2006. 26(2). 52-55
[32]柏荣.管道保温的技术经济优化分析.化工设备与管道. 2006. 143(1). 57-61
[33]陈建芳.叶必朝.一种复合保温砌块的结构优化及效果.能源技术. 2007.28(5). 297-299
[34]安维东.吴紫汪等.冻土的温度水分应力及其相互作用.兰州大学出版社.1990.1
[35]吴紫汪等.寒区隧道工程.北京.海洋出版社.2003
[36]中科院寒区旱区环境与工程研究所冻土工程国家重点实验室.高海拔寒冷地区隧道工程冻害防治技术研究.2000.10
[37]苏林军.寒区隧道冻害预测与对策研究.成都.西南交通大学. 2007.6
[38]王余富.寒区公路隧道温度场特征研究.西安.长安大学.2006.5
[39]铁道部第二勘测设计院.铁路隧道设计规范.北京.中国铁道出版社.1999
[2]孙吉堂.青藏铁路关角隧道病害的综合整治.现代隧道技术.2001.38(5).45-49
[3]陈建勋.昝勇杰.寒冷地区公路隧道防冻隔温层效果现场测试与分析.中国公路学报. 2001. 14(4).75-79
[4]北川修三.川上义辉.寒冷地区的隧道变形与围岩冻胀性.隧道译丛.1987.3.14-34
[5]马万一.公路隧道的防水防冻设计.隧道译丛.1990.11.29-33
[6] Bonacina C..Comini C.and Fasano A..et al.Numerical solution of phase-change problems. lnt. J.Heat Mass Transfer. 1973. 16(6). 18521882
[7] Comini C..Guidice S.del and Lewis R. W.et al..Finite element solution of nonlinear heat conduction problems with special reference to phase change. Int. J. for numerical methods in engineering. 1974. 8(6).613624
[8] Guidice S. Comini G.Lewis R W. Finite element simulation of freezing processes in soils. Int. J.numer. Anal .Methods Geomech..1978.2.223-35
[9] Heuer C E. The application of heat pipes on the Trans Alaska pipeline.CRREI Report. 1979.
[10] John P. Zarling P E. Billy C. et al .Air duct system for stabilization over permafrost area.Proceeding of the 4th International conference on Permafrost. Washington.National Academy press. 1983.1463-468
[11] Dennis E. Pufah1 .Frost Action (Section 3 of Roads and Airfields in Cold Rgions.Edited by Teds Vinson). ASCE. 1996.51-85
[12] Goreing D J.Kumar P.Convective heat transfer in railway embankment ballast.Jean-Franqois T. Ground Freezing 2000. Rotterdam.A. A. Balkema. 2000. 31-36
[13] Goering D J.Passively cooled railway embankments for use in permafrost areas .Journal of Coid Regions Engineering. 2003.i 7(3). 119-130
[14] Okada.Lcile prevention by adiatic treatment of tunnel lining. Japanese Railway Engineering. 1985. 26(3).75-80
[15]刘永智.吴青柏.张建明等.高原冻土区冻土地温温度场研究.公路杂志.2000(2)
[16]喻文兵.赖远明.牛富俊等.多年冻土区铁路通风路基室内模型试验的温度场特征.冰川冻土.2002.24(5).601-607
[17]喻文兵.赖远明.张学富等.多年冻土区铁路通风路基室内模型试验研究.铁道学报.2002.24 (6).78-83
[18]刘志强.马巍.周国庆等.纵向布管调控冻土路基温度场的模拟试验研究.岩石力学与工程学报.2005.24(11).1827-1831
[19]李国玉.李宁.全晓娟.青藏铁路可调控通风管路基温度场的三维非线性分析.冰川冻土.2005 27(1).128-133
[20]赖远明.吴紫汪.张淑娟.喻文兵.邓友生.寒区隧道保温效果的现场观察研究.铁道学报. 2003. 25(1).81-86
[21]张学富.苏新民.赖远明.喻文兵.寒区隧道三维温度场非线性分析.土木工程学报. 2004. 37(2).47-53
[22]晏启祥.何川.曾东洋.寒区隧道温度场及保温隔热层研究.四川大学学报(工程科学版). 2005. 37(3).24-27
[23]谢红强.何川.李永林.寒区隧道结构抗冻实验研究及仿真分析.公路. 2006.2.184-188
[24]苏磊.付军隆.俞昌铭.王岚.张红.张丽英.保温管道经济评估的优化设计模型.节能技术. 1999. 17(93).18-25
[25]程选生.李慧雯.温度作用下钢筋混凝土矩形贮液池壁厚的优化.特种结构. 2001. 118 (12).49-51
[26]刘晓延.张岁怀.王延勇.低温管道保冷复合结构优化设计.油气田地面工程. 19(6).71-73
[27]黄善波.徐明海.程显刚.赵延茂.双层保温管道总体优化设计.油气储运. 2001. 20(4).20-22
[28]王慧.曾令可.吴建青.管道保温结构的计算机模拟与优化.工业炉. 2002. 24(1). 52-54
[34]徐宝平.管道双层保温材料经济厚度的优化.能源研究与利用. 2002. 3. 43-45
[29]王士永.长距离供汽管道保温优化的研究及应用.炼油设计. 2002. 32(12). 29-33
[30]颜晖.张端.沈锦林.玻璃熔窑多层保温的优化设计方法.材料科学与工程学报. 2005. 23(4). 512-515
[31]李春成.谢禹钧.李世武.武荣华.工业管道保温结构的优化设计及节能分析.辽宁石油化工大学学报. 2006. 26(2). 52-55
[32]柏荣.管道保温的技术经济优化分析.化工设备与管道. 2006. 143(1). 57-61
[33]陈建芳.叶必朝.一种复合保温砌块的结构优化及效果.能源技术. 2007.28(5). 297-299
[34]安维东.吴紫汪等.冻土的温度水分应力及其相互作用.兰州大学出版社.1990.1
[35]吴紫汪等.寒区隧道工程.北京.海洋出版社.2003
[36]中科院寒区旱区环境与工程研究所冻土工程国家重点实验室.高海拔寒冷地区隧道工程冻害防治技术研究.2000.10
[37]苏林军.寒区隧道冻害预测与对策研究.成都.西南交通大学. 2007.6
[38]王余富.寒区公路隧道温度场特征研究.西安.长安大学.2006.5
[39]铁道部第二勘测设计院.铁路隧道设计规范.北京.中国铁道出版社.1999