冻融模型相似性分析及试验验证
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摘要
为提高冻融模型与原型的相似程度,提出冻结指数相似比和实验室修正系数的概念及计算方法。以哈尔滨地区黄土为试验材料,将该地区2010–2012年3年日平均气温进行线性简化,基于含相变热传导的微分方程基础上,采用相似理论,在几何、温度和时间比尺约束下对密度为1.60 g/cm~3、含水率为20%的试样进行冻融循环模型试验,确定实验室修正系数K值为1.13,得到冻结指数相似比CI为1:102.5。对冻融阶段温控历时进行优化,进行冻融循环模型试验。通过对比可知,优化后模型的最大冻深值为21.33 cm,与模型预定值20 cm相差仅6.5%;优化后冻融模型弥补了太阳辐射对冻深的影响,一个冻融周期由108.14 h减少为84.53 h。以实验室修正系数K和冻结指数相似比CI优化冻融过程的各温控阶段历时合理,显著提高了冻融模型的最大冻深和冻融过程在几何比尺和时间比尺上的相似度。
In order to improve the similarity between freeze-thaw model and the prototype, the concept and calculation method of similarity ratio of freezing index and laboratory correction coefficient are put forward. The loess in Harbin is taken as the experimental material; and the average temperature of this area between the year of 2010 and the year of 2012 is linearly simplified. Based on the differential equation with the heat conduction with phase transition, a freeze-thaw cycle model test is carried out for a specimen with a density of 1.60 g/cm3 and a moisture content of 20 % under the constraint of geometry, temperature and time scale by using the similarity theory. The K value of the laboratory correction coefficient is determined as 1.13 and the similarity ratio of the freezing index CI is determined as 1:102.5 so that another freeze-thaw experiment is conducted after an optimization of the temperature control time in the freeze-thaw stage. By comparison, the maximum frozen depth value of the optimized model is 21.33 cm, which is close to the predetermined model value 20 cm and the difference is 6.65 %; and the optimized freeze-thaw period is reduced from 108.14 h to 84.53 h. Therefore, it is reasonable to optimize the duration time of temperature controlled at different temperature controlling stage by using laboratory correction coefficient K and freezing index similarity ratio CI in freezing-thawing model. The ensured that the freeze depth are more similarity to prototype in the geometrical scale and time scale; at the same time reduced the duration time of a freeze-thaw cycle significantly.
In order to improve the similarity between freeze-thaw model and the prototype, the concept and calculation method of similarity ratio of freezing index and laboratory correction coefficient are put forward. The loess in Harbin is taken as the experimental material; and the average temperature of this area between the year of 2010 and the year of 2012 is linearly simplified. Based on the differential equation with the heat conduction with phase transition, a freeze-thaw cycle model test is carried out for a specimen with a density of 1.60 g/cm3 and a moisture content of 20 % under the constraint of geometry, temperature and time scale by using the similarity theory. The K value of the laboratory correction coefficient is determined as 1.13 and the similarity ratio of the freezing index CI is determined as 1:102.5 so that another freeze-thaw experiment is conducted after an optimization of the temperature control time in the freeze-thaw stage. By comparison, the maximum frozen depth value of the optimized model is 21.33 cm, which is close to the predetermined model value 20 cm and the difference is 6.65 %; and the optimized freeze-thaw period is reduced from 108.14 h to 84.53 h. Therefore, it is reasonable to optimize the duration time of temperature controlled at different temperature controlling stage by using laboratory correction coefficient K and freezing index similarity ratio CI in freezing-thawing model. The ensured that the freeze depth are more similarity to prototype in the geometrical scale and time scale; at the same time reduced the duration time of a freeze-thaw cycle significantly.
引文
[1]马巍,王大雁.冻土力学[M].北京:科学出版社,2014.MA Wei,WANG Da-yan.Frozen soil mechanics[M].Beijing:Science Press,2014.
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[4]翁效林.强夯黄土地基震陷性离心试验研究[J].岩土工程学报,2007,29(7):1094-1097.WENG Xiao-lin.Studies on seismic subsidence of loess by centrifugal model tests[J].Chinese Journal of Geotechnical Engineering,2004,29(7):1094-1094.
[5]王玉峰,程谦恭,黄英儒.不同支护模式下黄土高边坡开挖变形离心模型试验研究[J].岩石力学与工程学报,2014,33(5):1032-1046.WANG Yu-feng,CHENG Qian-gong,HUANG Ying-ru.Centriguge tests on excavation of high loess slope with different reinforcement modes[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(5):1032-1046.
[6]龚成明,程谦恭,刘争平.黄土边坡开挖与支护效应的离心模拟试验研究[J].岩土力学,2010,31(11):3481-3486.GONG Cheng-ming,CHENG Qian-gong,LIU Zheng-ping.Centrifuge model tests on excavation and reinforcement effect of loess slope[J].Rock and Soil Mechanics,2010,31(11):3481-3486.
[7]李东庆,朱林楠.荷载作用下冻土模型试验相似分析[J].自然科学进展(国家重点实验室通讯),1994,4(3):323-327.LI Dong-qing,ZHU Lin-nan.Similarity analysis of frozen soil model test under load[J].Advances in Natural Science(State Key Laboratory Newsletter),1994,4(3):323-327.
[8]朱林楠,李东庆,郭兴民.无外荷载作用下冻土模型试验的相似分析[J].冰川冻土,1993,15(1):166-169.ZHU Lin-nan,LI Dong-qing,GUO Xing-min.Simulitude analysis of modeling test for chargeless pressure in the freezing-thawing process of soil[J].Journal of Glaciology and Geocryology,1993,15(1):166-169.
[9]ZHU Y,CARBEE D L.Uniaxial compressive strength of frozen silt under constant deformation rates[J].Journal of Glaciology&Geocryology,1986,9(1):3-15.
[10]马庆宏,朱大勇,雷先顺,等.无黏性土斜坡地基承载力模型试验研究[J].岩土工程学报,2014,36(7):1271-1280.MA Qing-hong,ZHU Da-yong,LEI Xian-shun,et al.Model tests on bearing capacity of footing on sand slopes[J].Chinese Journal of Geotechnical Engineering,2014,36(7):1271-1280
[11]靳德武,牛俊富,陈志新,等.冻土斜坡模型试验相似分析[J].地球科学与环境学报,2004,26(1):29-32.JING De-wu,NIU Fu-jun,CHEN Zhi-xin,et al.Simulation analysis for model experiment of frozen soil slope[J].Journal of Earth Sciences and Environment,2004,26(1):29-32.
[12]汪恩良,刘兴超,常俊德.静冰力学模型试验的相似比尺问题探讨[J].冰川冻土,2015,37(2):417-421.WANG En-liang,LIU Xing-chao,CHANG Jun-de.Discussion on the geometric similar problems in static ice pressure model test[J].Journal of Glaciology and Geocryology,2015,37(2):417-421.
[13]李东阳,刘波,王莉,等.冻结器传热的冷源相似准则[J].岩石力学与工程学报,2015,34(4):814-821.LI Dong-yang,LIU Bo,WANG Li,et al.similarity criterion of freezing pipe as heat sink during heat exchange[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(4):814-821.
[14]KIM N S,LEE J H,CHANG S P.Equivalent multi-phase similitude law for pseudodynamic test on small scale reinforced concrete models[J].Engineering Structures,2009,31(4):834-846.
[15]GAO J,YANG S,WU P,et al.Preliminary study on similitude law in simulative experiment for controlling hydraulic erosion[J].Transactions of the Chinese Society of Agricultural Engineering,2006,22(1):27-31.
[16]张泽,马巍,齐吉琳.冻融循环作用下土体结构演化规律及其工程性质改变机理[J].吉林大学学报(地球科学版),2013,43(6):1904-1914.ZHANG Ze,MA Wei,QI Ji-lin.Structure evolution and mechanism of engineering properties change of soils under effect of freeze-thaw cycle[J].Journal of Jilin University(Earth Science Edition),2013,46(6):1904-1914.
[17]陈继,盛煜,程国栋.从地表能量平衡各分量特点论青藏高原多年冻土工程中的冻土保护措施[J].冰川冻土,2006,28(2):223-228.CHEN Ji,SHENG Yu,CHENG Guo-dong.Discussion on protection measures of permafrost under the action of engineering from the point of earth surface energy[J].Journal of Glaciology and Geocryology,2006,28(2):223-228.
[18]程地会,曲绍平,谢可夫.北方地区基土标准冻深的预报[J].黑龙江工程学院学报,2003,17(4):62-64.CHENG Di-hui,QU Shao-ping,XIE Ke-fu.The prediction of standard frost of foundation soil in northern area[J].Journal of Heilongjiang Institute of Technology,2003,17(4):62-64.
[19]南京水利科学研究院.GB/T 50123–1999土工试验规程[S].北京:中国计划出版社1999.Nanjing Hydraulic Research Instittute.GB/T 50123-1999Speciffcation of soil test[S].Beijing:China Planning Press 1999.
[20]宁夏水利科学研究院.DB 60T811–2012灌溉渠道衬砌工程技术规范[S].宁夏:阳光出版社,2012.Ningxia Hydraulic Research Institute.DB 60T811-2012.supervision bureau technical specification for irrigation channel lining engineering[S].Ningxia:Yangguang Press,2012.
[21]阳艳红,王柏林,雷勇.百叶箱与通风防辐射罩的温度对比观测结果分析[J].气象水文海洋仪器,2014,31(4):21-25.YANG Yan-hong,WANG Bo-lin,LEI Yong.Comparative analysis on thermometer screens and ventilation radiation shield[J].Meteorological,Hydrological and Marine Instrumrnts,2014,31(4):21-25.
[22]丁德文,罗学波.冻土热工的模型理论基础[J].科学通报,1979,8(8):360-364.DING De-wen,LUO Xue-bo.Theoretical basis of thermal soil model of permafrost[J].Chinese Science Bulletin,1979,8(8):360-364.
[23]魏先祥,赖远明.相似方法的原理及应用[M].兰州:兰州大学出版社,2001.WEI Xian-yuan,LAI Yuan-ming.Principle and application of similar methods[J].Lanzhou:Lanzhou University Press,2001.
[24]汪恩良,张安琪,包天鹅,等.寒区不同材质垂直埋管土壤冻结深度测量差异性分析[J].水利学报,2017,48(1):86-95.WANG En-liang,ZHANG An-qi,BAO Tian-e,et al.Variability analysis of freezing depth mode of vertical buries pipes with different materials in coil area[J].Journal of Hydraulic Engineering,2017,48(1):86-95.
[25]陈志国,王哲人.季节性冻土地区公路路面抗冻设计方法[J].中国公路学报,2009,22(5):34-40.CHEN Zhi-guo,WANG Zhe-ren.Anti-frost design method for highway pavement in seasonal frost region[J].China Journal of Highway and Transport,2009,22(5):34-40.
[26]黑龙江水利水电勘测设计研究院.SL 23–2006渠系工程抗冻设计规范[S].北京:水利电力出版社,1991.Heilongjiang Water Conservancy and Hydropower Survey and Design Institute.SL 23-2006 Code of design for frost resistance of water conservancy department and canal system[S].Beijing:Water Resources and Electric Power Press,1991.
[27]谭志伟,杨革.水工建筑物冻害防治技术[M].郑州:黄河水利出版社,2008.TAN Zhi-wei,YANG Ge.Frost damage prevention and cure technology for hydraulic structures[M].Zhengzhou:Yellow River Water Conservancy Press,2008.
[28]汪恩良,姜海强,崔恩彤,等.冻融对重塑黏土导热系数影响的试验研究[J].工程热物理学报,2018,39(4):871-879.WANG En-liang,JIANG Hai-qiang,CUI En-tong,et al.Study on the effect of freezing and thawing on thermal conductivity of remolded clay[J].Journal of Engineering Thermophysics,2018,29(4):871-879.
[2]齐鄂荣,曾玉红.工程流体学[M].武汉:武汉大学出版社,2005:420-435.QI E-rong,ZENG Yu-hong.Engineering fluid science[M].Wuhan:Wuhan University Press,2005:420-435.
[3]沈泰.地质力学模型试验技术的进展[J].长江科学院学报,2001,18(5):32-36.SHEN Tai.Development of geomechanic model experiment techniques[J].Journal of Yangtze River Scientific Research Institute,2001,18(5):32-36.
[4]翁效林.强夯黄土地基震陷性离心试验研究[J].岩土工程学报,2007,29(7):1094-1097.WENG Xiao-lin.Studies on seismic subsidence of loess by centrifugal model tests[J].Chinese Journal of Geotechnical Engineering,2004,29(7):1094-1094.
[5]王玉峰,程谦恭,黄英儒.不同支护模式下黄土高边坡开挖变形离心模型试验研究[J].岩石力学与工程学报,2014,33(5):1032-1046.WANG Yu-feng,CHENG Qian-gong,HUANG Ying-ru.Centriguge tests on excavation of high loess slope with different reinforcement modes[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(5):1032-1046.
[6]龚成明,程谦恭,刘争平.黄土边坡开挖与支护效应的离心模拟试验研究[J].岩土力学,2010,31(11):3481-3486.GONG Cheng-ming,CHENG Qian-gong,LIU Zheng-ping.Centrifuge model tests on excavation and reinforcement effect of loess slope[J].Rock and Soil Mechanics,2010,31(11):3481-3486.
[7]李东庆,朱林楠.荷载作用下冻土模型试验相似分析[J].自然科学进展(国家重点实验室通讯),1994,4(3):323-327.LI Dong-qing,ZHU Lin-nan.Similarity analysis of frozen soil model test under load[J].Advances in Natural Science(State Key Laboratory Newsletter),1994,4(3):323-327.
[8]朱林楠,李东庆,郭兴民.无外荷载作用下冻土模型试验的相似分析[J].冰川冻土,1993,15(1):166-169.ZHU Lin-nan,LI Dong-qing,GUO Xing-min.Simulitude analysis of modeling test for chargeless pressure in the freezing-thawing process of soil[J].Journal of Glaciology and Geocryology,1993,15(1):166-169.
[9]ZHU Y,CARBEE D L.Uniaxial compressive strength of frozen silt under constant deformation rates[J].Journal of Glaciology&Geocryology,1986,9(1):3-15.
[10]马庆宏,朱大勇,雷先顺,等.无黏性土斜坡地基承载力模型试验研究[J].岩土工程学报,2014,36(7):1271-1280.MA Qing-hong,ZHU Da-yong,LEI Xian-shun,et al.Model tests on bearing capacity of footing on sand slopes[J].Chinese Journal of Geotechnical Engineering,2014,36(7):1271-1280
[11]靳德武,牛俊富,陈志新,等.冻土斜坡模型试验相似分析[J].地球科学与环境学报,2004,26(1):29-32.JING De-wu,NIU Fu-jun,CHEN Zhi-xin,et al.Simulation analysis for model experiment of frozen soil slope[J].Journal of Earth Sciences and Environment,2004,26(1):29-32.
[12]汪恩良,刘兴超,常俊德.静冰力学模型试验的相似比尺问题探讨[J].冰川冻土,2015,37(2):417-421.WANG En-liang,LIU Xing-chao,CHANG Jun-de.Discussion on the geometric similar problems in static ice pressure model test[J].Journal of Glaciology and Geocryology,2015,37(2):417-421.
[13]李东阳,刘波,王莉,等.冻结器传热的冷源相似准则[J].岩石力学与工程学报,2015,34(4):814-821.LI Dong-yang,LIU Bo,WANG Li,et al.similarity criterion of freezing pipe as heat sink during heat exchange[J].Chinese Journal of Rock Mechanics and Engineering,2015,34(4):814-821.
[14]KIM N S,LEE J H,CHANG S P.Equivalent multi-phase similitude law for pseudodynamic test on small scale reinforced concrete models[J].Engineering Structures,2009,31(4):834-846.
[15]GAO J,YANG S,WU P,et al.Preliminary study on similitude law in simulative experiment for controlling hydraulic erosion[J].Transactions of the Chinese Society of Agricultural Engineering,2006,22(1):27-31.
[16]张泽,马巍,齐吉琳.冻融循环作用下土体结构演化规律及其工程性质改变机理[J].吉林大学学报(地球科学版),2013,43(6):1904-1914.ZHANG Ze,MA Wei,QI Ji-lin.Structure evolution and mechanism of engineering properties change of soils under effect of freeze-thaw cycle[J].Journal of Jilin University(Earth Science Edition),2013,46(6):1904-1914.
[17]陈继,盛煜,程国栋.从地表能量平衡各分量特点论青藏高原多年冻土工程中的冻土保护措施[J].冰川冻土,2006,28(2):223-228.CHEN Ji,SHENG Yu,CHENG Guo-dong.Discussion on protection measures of permafrost under the action of engineering from the point of earth surface energy[J].Journal of Glaciology and Geocryology,2006,28(2):223-228.
[18]程地会,曲绍平,谢可夫.北方地区基土标准冻深的预报[J].黑龙江工程学院学报,2003,17(4):62-64.CHENG Di-hui,QU Shao-ping,XIE Ke-fu.The prediction of standard frost of foundation soil in northern area[J].Journal of Heilongjiang Institute of Technology,2003,17(4):62-64.
[19]南京水利科学研究院.GB/T 50123–1999土工试验规程[S].北京:中国计划出版社1999.Nanjing Hydraulic Research Instittute.GB/T 50123-1999Speciffcation of soil test[S].Beijing:China Planning Press 1999.
[20]宁夏水利科学研究院.DB 60T811–2012灌溉渠道衬砌工程技术规范[S].宁夏:阳光出版社,2012.Ningxia Hydraulic Research Institute.DB 60T811-2012.supervision bureau technical specification for irrigation channel lining engineering[S].Ningxia:Yangguang Press,2012.
[21]阳艳红,王柏林,雷勇.百叶箱与通风防辐射罩的温度对比观测结果分析[J].气象水文海洋仪器,2014,31(4):21-25.YANG Yan-hong,WANG Bo-lin,LEI Yong.Comparative analysis on thermometer screens and ventilation radiation shield[J].Meteorological,Hydrological and Marine Instrumrnts,2014,31(4):21-25.
[22]丁德文,罗学波.冻土热工的模型理论基础[J].科学通报,1979,8(8):360-364.DING De-wen,LUO Xue-bo.Theoretical basis of thermal soil model of permafrost[J].Chinese Science Bulletin,1979,8(8):360-364.
[23]魏先祥,赖远明.相似方法的原理及应用[M].兰州:兰州大学出版社,2001.WEI Xian-yuan,LAI Yuan-ming.Principle and application of similar methods[J].Lanzhou:Lanzhou University Press,2001.
[24]汪恩良,张安琪,包天鹅,等.寒区不同材质垂直埋管土壤冻结深度测量差异性分析[J].水利学报,2017,48(1):86-95.WANG En-liang,ZHANG An-qi,BAO Tian-e,et al.Variability analysis of freezing depth mode of vertical buries pipes with different materials in coil area[J].Journal of Hydraulic Engineering,2017,48(1):86-95.
[25]陈志国,王哲人.季节性冻土地区公路路面抗冻设计方法[J].中国公路学报,2009,22(5):34-40.CHEN Zhi-guo,WANG Zhe-ren.Anti-frost design method for highway pavement in seasonal frost region[J].China Journal of Highway and Transport,2009,22(5):34-40.
[26]黑龙江水利水电勘测设计研究院.SL 23–2006渠系工程抗冻设计规范[S].北京:水利电力出版社,1991.Heilongjiang Water Conservancy and Hydropower Survey and Design Institute.SL 23-2006 Code of design for frost resistance of water conservancy department and canal system[S].Beijing:Water Resources and Electric Power Press,1991.
[27]谭志伟,杨革.水工建筑物冻害防治技术[M].郑州:黄河水利出版社,2008.TAN Zhi-wei,YANG Ge.Frost damage prevention and cure technology for hydraulic structures[M].Zhengzhou:Yellow River Water Conservancy Press,2008.
[28]汪恩良,姜海强,崔恩彤,等.冻融对重塑黏土导热系数影响的试验研究[J].工程热物理学报,2018,39(4):871-879.WANG En-liang,JIANG Hai-qiang,CUI En-tong,et al.Study on the effect of freezing and thawing on thermal conductivity of remolded clay[J].Journal of Engineering Thermophysics,2018,29(4):871-879.
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