多年冻土地区桩基温度场及其调控效果数值模拟
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摘要
冻土是一种对气候和环境变化极为敏感的不稳定地质体,其物理、化学性质和工程特性除了与土颗粒的矿物成分、密度和含水量等因素有关外,还与土中含冰量和冻土的温度状态密切相关。在气候变化和人为扰动等外界因素影响下,导致一定范围内冻土层的温度场发生变化,进而对冻土地区工程建筑物的稳定性及耐久性产生不可忽视的影响。因此,本文针对冻土温度状况对建筑工程性质的影响,分别对施工扰动和气候条件变化影响下冻土地区桩基温度变化进行了研究,提出了施工期间及后期养护不同的温度调控措施,并对其调控效果及影响因素进行了数值模拟。
文章首先运用有限元模型验证了天然状态下地温状态数值模拟的正确性,得到了天然状态下土体随时间变化的温度分布场。并在此基础上进行了以下几方面的研究：(1)分析了施工扰动对桩基周围冻土温度场的影响,模拟了桩基水化热过程,并着重对通冷冻液人工制冷措施加快桩基周围土体回冻效果进行研究；(2)考虑气候升温变化对冻土桩基温度场的影响,对不同冻土类型、土质参数以及不同升温率对冻土的最大融化深度和地温状况的敏感性进行探讨和分析；(3)针对基于气候变化产生的冻土退化,提出了热棒和人工冻结两种不同的温度调控技术,并利用有限元对其调控效果进行了数值模拟；(4)采用有限元优化分析方法,利用冻土地基实测温度数据对温度场计算中的物理参数——导热系数进行了反演分析。
通过对施工扰动和气候变化影响下的冻土地区桩基温度场进行数值模拟,主要得到以下结论：(1)采用大气实测回归温度和“附面层”原理对天然地基温度场进行有限元数值模拟的方法是可以满足工程计算精度要求；(2)对于冷冻液温度调控措施,在冷冻管横截面积相同情况下,不同布置方案的冷却效果不同,采用多管布设冷却效果较好；(3)不同升温率、冻土类型、土质条件下,冻土的最大融化深度及其对气候变化的敏感性不同；(4)验证热棒技术和人工冷冻技术在冻土地区桩基温度调控中是可行的,且两者的调控效果不同,宜根据施工条件及外部环境因素进行选择；(5)提出了地基土质材料的导热系数反演分析方法,并验证了其可行性和实用性,对冻土地区工程建设有一定的理论实用价值。
Frozen soil is a kind of extremely unsteady geologic body sensitive to climate and environment change. Besides of mineral composition, density and moisture content of soil particle, its physical and chemical features and engineering properties are closely related to the ice content and thermal state of frozen soil. Climate change and human disturbance could also bring about the temperature change within a certain zone of frozen soil. Caused by thermal disturbance, the phase change of water may also lead to frost heaving and thaw deposit problems, and afterward impacting on the stability of engineering structures in frost regions. Thus research on temperature change of frozen soil region pile foundation was conducted in this paper, which in on the basis of the influence to building properties caused by frozen soil thermal state. The paper also proposed temperature control measures during construction period and subsequently maintenance period, and simulations on their controlling effect and influence factors were conducted.
The correctness of numerical simulations of earth temperature in natural state was firstly verified in this paper and then the temperature field of soil varying with time in natural state was obtained. Based on this point, research was conducted at following aspects:refrigerating fluid measure is emphasized to realize the quick refreezing of pile soil while analyzing the effect of construction disturbance and simulating the hydration heat process of pile foundation. In consideration of the influence to temperature field of frozen soil pile foundation caused by climate heating, the sensitivities to the maximum thaw depth and earth thermal state were discussed and analyzed for different frozen soil types, soil conditions and heating rates. On the basis of the degradation of frozen soil due to climate change, this paper also proposed the hot pin technology and artificial freezing technology for the purpose of temperature control, and simulation on their effects were conducted through finite element analysis. In the end, the conductivity factor, which is an important parameter in temperature field computation, was analyzed by optimized inversion computation through the optimization module of finite element analysis.
Main results obtained through numerical simulation of frozen soil pile foundation under the influence of construction disturbance and climate change are as follows:the finite element analysis of natural foundation by using regression temperature via measured temperatures and boundary layer theory is feasible. For cold fluid control measures, freezing effects varies with different arrangements under the condition of same sectional area and the more pipes, the better the effect will be. The feasibilities of hot pin and artificial cold technology were verified and the option should be determined by construction conditions and environmental factors due to their different controlling effects. The inversion computation method of the conductivity of foundation soils was proposed and its feasibility and practicability were verified, which is significant in some degree for constructions in frozen soil region theoretically and practically.
文章首先运用有限元模型验证了天然状态下地温状态数值模拟的正确性,得到了天然状态下土体随时间变化的温度分布场。并在此基础上进行了以下几方面的研究：(1)分析了施工扰动对桩基周围冻土温度场的影响,模拟了桩基水化热过程,并着重对通冷冻液人工制冷措施加快桩基周围土体回冻效果进行研究；(2)考虑气候升温变化对冻土桩基温度场的影响,对不同冻土类型、土质参数以及不同升温率对冻土的最大融化深度和地温状况的敏感性进行探讨和分析；(3)针对基于气候变化产生的冻土退化,提出了热棒和人工冻结两种不同的温度调控技术,并利用有限元对其调控效果进行了数值模拟；(4)采用有限元优化分析方法,利用冻土地基实测温度数据对温度场计算中的物理参数——导热系数进行了反演分析。
通过对施工扰动和气候变化影响下的冻土地区桩基温度场进行数值模拟,主要得到以下结论：(1)采用大气实测回归温度和“附面层”原理对天然地基温度场进行有限元数值模拟的方法是可以满足工程计算精度要求；(2)对于冷冻液温度调控措施,在冷冻管横截面积相同情况下,不同布置方案的冷却效果不同,采用多管布设冷却效果较好；(3)不同升温率、冻土类型、土质条件下,冻土的最大融化深度及其对气候变化的敏感性不同；(4)验证热棒技术和人工冷冻技术在冻土地区桩基温度调控中是可行的,且两者的调控效果不同,宜根据施工条件及外部环境因素进行选择；(5)提出了地基土质材料的导热系数反演分析方法,并验证了其可行性和实用性,对冻土地区工程建设有一定的理论实用价值。
Frozen soil is a kind of extremely unsteady geologic body sensitive to climate and environment change. Besides of mineral composition, density and moisture content of soil particle, its physical and chemical features and engineering properties are closely related to the ice content and thermal state of frozen soil. Climate change and human disturbance could also bring about the temperature change within a certain zone of frozen soil. Caused by thermal disturbance, the phase change of water may also lead to frost heaving and thaw deposit problems, and afterward impacting on the stability of engineering structures in frost regions. Thus research on temperature change of frozen soil region pile foundation was conducted in this paper, which in on the basis of the influence to building properties caused by frozen soil thermal state. The paper also proposed temperature control measures during construction period and subsequently maintenance period, and simulations on their controlling effect and influence factors were conducted.
The correctness of numerical simulations of earth temperature in natural state was firstly verified in this paper and then the temperature field of soil varying with time in natural state was obtained. Based on this point, research was conducted at following aspects:refrigerating fluid measure is emphasized to realize the quick refreezing of pile soil while analyzing the effect of construction disturbance and simulating the hydration heat process of pile foundation. In consideration of the influence to temperature field of frozen soil pile foundation caused by climate heating, the sensitivities to the maximum thaw depth and earth thermal state were discussed and analyzed for different frozen soil types, soil conditions and heating rates. On the basis of the degradation of frozen soil due to climate change, this paper also proposed the hot pin technology and artificial freezing technology for the purpose of temperature control, and simulation on their effects were conducted through finite element analysis. In the end, the conductivity factor, which is an important parameter in temperature field computation, was analyzed by optimized inversion computation through the optimization module of finite element analysis.
Main results obtained through numerical simulation of frozen soil pile foundation under the influence of construction disturbance and climate change are as follows:the finite element analysis of natural foundation by using regression temperature via measured temperatures and boundary layer theory is feasible. For cold fluid control measures, freezing effects varies with different arrangements under the condition of same sectional area and the more pipes, the better the effect will be. The feasibilities of hot pin and artificial cold technology were verified and the option should be determined by construction conditions and environmental factors due to their different controlling effects. The inversion computation method of the conductivity of foundation soils was proposed and its feasibility and practicability were verified, which is significant in some degree for constructions in frozen soil region theoretically and practically.
引文
[1]吴青柏,童长江.冻土变化和青藏公路的稳定性问题[J].冰川冻土,1995,17(4)：350-355
[2]温智,盛煜等.青藏铁路路基浅地表热状态动态监测初步分析[J].岩石力学与工程学报,2003,22(增2)：2664-2668
[3]朱德举.多年冻土地区钻孔灌注桩的有限元分析.东北林业大学硕士学位论文.2004.3
[4]青藏公路科研组.昆仑山桩基静荷载试验研究报告之四——水平荷载试验.西安公路学报,1986,218-248
[5]励国良,赵西生,王化卿等.多年冻土地区桩基础试验研究.铁道学报,1980,2(1)
[6]程国栋.用冷却路基的方法修建青藏铁路.中国铁道科学,2003,24(3)：1-4
[7]C.Harley, A.Faghri. Complete transient two-dimensional analysis of two-phase closed thermosyphons including falling condensate film[J].ASME J. Heat Transfer,1994(116)
[8]J.GReed, C.L.Tien Modeling of the two-phase closed thermosyphon [J]. Journal of Heat Transfer,1987(109):722-730
[9]Z.J.ZUO and F.S.Gunnerson, Numerical modeling of the steady-state two-phase closed thermosyphon [J]. Int.J. Heat Mass Transfer,1994,V37(17):2715-2722
[10]陶汉中,张红.采用热管技术加固冻土铁路路基的热影响分析.能源研究与利用,2003,(3)：19-21
[11]吴存真,孙志坚,潘阳.应用热管技术解决寒区地基冻胀问题的理论研究.岩土工程学报,2002,24(3)：347—350
[12]陈鹏,许志健.热管稳定冻土路基的动态传热分析及数值计算.见：第九届全国热管会议论文集.昆明：2003.248-254
[13]李金灵.应用热管技术提高多年冻土地区路基稳定性的数值分析.铁道勘察,2004,(4)：5-8
[14]中铁西北科学研究院.青藏铁路冻土热管的传热分析研究报.2003
[15]汪双杰,陈建兵,黄晓明.热棒路基降温效应的数值模拟.交通运输工程学报,2005,5(3)：41-46
[16]杨永平,魏庆朝,张鲁新等.青藏铁路多年冻土地区热管路基三维数值分析.中国铁道科学,2005,26(2)：20-24
[17]萧岩.城市地下工程冻结法施工技术及其应用.市政技术,2002(3)：20-32
[18]陈湘生.冻结法加固地层的原理与应用.水利水电施工,1997(3)：71-7
[19]马芹永.人工冻结法的理论与施工技术.人民交通出版社,2007
[20]Kavanagh K T, Clough R W. Finite Element application in the characterization of elastic solids, Int. J. Solids Structures,1972, Vol.11-23
[21]Kirsten H A D. Determination of rock mass elastic moduli by back analysis of deformation measurement. In: Proc Symp on Expliration for Rock Eng. Johannesburg, 1976.1154-1160
[22]Maiar G, Jurina. L, Podolak K. On model identification problems in rock mechanics. In: Proc Symp on the Geotechnics of Structurally Complex Formations. Capri, 1977.257-261
[23]Kovari k et al. Integrated measuring technique for rock pressure determination. In: Proc Int Conf on Field Measurements on Rock Mechanics. Zurich,1977.1.533-538
[24]Gioda G. Indirect identification of the average elastic characteristics of rock masses. In: Proc Int Conf on Structural Foundation on Rock. Sydney,1980,1.65-73
[25]Gioda G Some remarks on back analysis and characterization problems. In: Proc 5th Int Conf on Num Meth in Geom. Nagoya,1985,1.47-61
[26]Maier G, Gioda G Optimization methods for parametric identification of geotechnical system. In: Maitins J B ed. Num Methods in Geom. Boston,1980.431-436
[27]Gioda G, Maier G. Direct, search solution of an inverse problem in elasto-plasticity, identification of cohesion, friction angle and in-situ stress by pressure tunnel tests. Int J Num Methods in Eng,1980,15:1823-1834
[28]Gioda G, Pandolfi A. A comparative evaluation of some back analysis algorithms and their application to in-situ load tests. In: Proc 2nd Int Symp on Field Measurement in Geom,1987.1131-1144
[29]Arai R. An inverse problem approach to the prediction of Multi-dimensional consolidation behavior. Soil and Foundations,1984,24(1):95-108
[30]Sakurai S, Abe S. A design approach to dimensioning underground openings. In: Proc 3rd Int Conf Numerical Methods in Geomechanics. Aachen,1979.649-661
[31]杨志法,王思敬,冯紫良.岩土工程反分析理论及应用[M].北京：地震出版社,2002
[32]杨林德.岩土工程问题的反演理论与工程试验[M].北京：科学出版社,1996
[33]吴凯华.隧洞围岩原始应力与弹性常数的反分析[J].土木工程学报,1988
[34]王芝银,李云鹏.地下工程位移反分析法及程序[M].西安：陕西科学技术出版社,1993
[35]吕爱钟,蒋斌松.岩石力学反问题[M].北京：煤炭工业出版社,1998
[36]冯夏庭.智能岩石力学导论[M].北京：科学出版社,2000
[37]Kavanagh K. And R. W. Clough, Finite Element application in the characterization of elastic solids, Int. J. Solids Structure,1971, Vol.11-23
[38]Sakurai, Back analysis of measured displacements in shallow tunnel excavated in sandy materials, Proc Int Symp on Underground Engineering, Vol,1983
[39]刘允芳.弹性介质岩体中非圆形洞室位移反分析计算[J].岩石力学和工程学报,1986(5)：43-46
[40]薛琳,杨志法.确定流变岩体的参数及地应力的位移反分析[J].地质科学,1986(4)：5-8
[41]Gioda, Sakurai, Back analysis Ptocedure for the Interpretation of Field Measurements in Geomechanics, Int. J. for Num. and Analy Methods in Geomech, Vol.11,1987:555-583
[42]王芝银,李云鹏.地下工程围岩粘弹塑性参数反分析[J].水利学报,1990(9)：31-34
[43]Maier, International Journal For Numerical and Analytical Methods in Geo-mechanics, Vol.8,1983
[44]袁勇.围岩弹塑性参数反算的极大似然法[J].工程勘察,Vol.5,1991
[45]邹海,王桂梁,桂和荣,陈兆炎.岩体力学参数的损伤—反分析优化性研究[J].长春科技大学学报,1999,29(2)：167-170
[46]王华宁,吕爱钟.巷道裂隙岩体的损伤参数辨识[J].岩土工程学报,2001,23(5)：593-597
[47]李兴高,高延法.采场底板岩层破坏与损伤分析[J].岩石力学与工程学报,2003,22(1)：35-39
[48]郭继伟.分型粗糙面散射的边界元法及参数反演[J].复旦大学硕士学位论文,2008
[49]蔡志杰,郭志伟.用边界元法反演分形粗糙面[J].复旦学报(自然科学版),2010,49：395-403
[50]李仲奎,莫兴华,王爱民,徐千军.地下洞室松动区模型及其在反馈分析中的应用[J].水利水电技术,1999,30(5)：49-51
[51]江权,冯夏庭,苏国韶,陈国庆.基于松动圈-位移增量监测信息的高地应力下洞室群岩体力学参数的智能反分析[J].岩石力学与工程学报,2007,26：2654-2692
[52]陈秋红,李仲奎,张志增.松动圈分区模型及其在地下工程反馈分析中的应用[J].岩石 力学与工程学报,2010,29：3216-3220
[53]Harlan,R.L Analysis of Coupled Heat-fluid Transport in Partially Frozen Soil[J]. Water Resource Research 1973 Vol 9(3)
[54]郭兰波等.竖井冻结壁温度场的有限元分析.中国矿业学院学报,1981(3)：31-35
[55]王铁行,胡长顺等.考虑多种因素的冻土路基温度场有限元方法.中国公路学报.长安大学.2000,13(4)：8-11
[56]吴亚平,苏强,朱元林.冻土区桥梁群桩基础地基回冻过程的非线性分析[J].土木工程学报,2006
[57]汤懋苍,程国栋,林振耀.青藏高原近代气候变化及对环境的影响[M].广东科技出版社,1998
[58]郭余良.青藏铁路多年冻土区的地温特征及影响因素[J].铁道勘察,2007
[59]金会军,孙立平.青藏高原中、东部局地因素对地温的双重影响[J].冰川冻土,2008
[60]王绍令.青藏高原局地因素对近地表层地温的影响[J].高原气象,2002
[61]中国科学院兰州冰川冻土研究所.冻土的温度水分应力及其相互作用[M].兰州大学出版社,1989
[62]李黎明.ANSYS有限元分析实用教程[M].清华大学出版社,2005
[63]中国科学院兰州冰川冻土研究所青藏公路冻土路基研究组.冻土路基工程[M].兰州大学出版社,1988
[64]朱林楠.高原冻土区不同下垫面的附面层研究[J].冰川冻土,1988,10(1)：8～14
[65]徐学祖,王家澄,张立新.冻土物理学[M].科学出版社.2001.4
[66]朱伯芳,王同生,丁宝瑛,郭之章.水工混凝土结构的温度应力与温度控制.北京：水利电力出版社,1976
[67]蔡正咏.混凝土性能.北京：中国建筑工业出版社,1979
[68]中华人民共和国电力工业部.水工混凝土结构设计规范.北京：中国电力出版社,1996
[69]贾晓云,李文江.多年冻土区灌注桩混凝土水化热影响分析.2003
[70]郭宽良等.计算传热学[M].安徽：中国科技大学出版社,1988.68～69
[71]吴青柏,董献付,刘永智.青藏公路沿线多年冻土对气候变化和工程影响的响应分析[J].冰川冻土,2005,27(1)：50-54
[72]徐冰魁.多年冻土区热棒路基设计计算[J].硕士论文,2005
[73]汪双杰.多年冻土地区公路修筑技术[M].人民交通出版社,2008
[74]陈鹏,许志键.热管稳定冻土路基的动态传热分析及数值计算[A].第九届全国热管会议论文集[C].昆明：中国工程热物理学会热管专业组,2003
[75]张恒运,葛新石.两相闭式热虹吸管的集总参数模型研究[J].中国科学技术大学学报,1997
[76]汪双杰.高原多年冻土区公路路基稳定及预测技术研究[J].博士论文,2005
[77]王彦飞.反演问题的计算方法及其应用[M].北京：高等教育出版社,2007
[78]刘家琦.数学物理方程反问题的分类及不适定问题求解[J].计算数学和应用数学,1983,(4)：43-64
[79]黄光远,刘维倩,刘小军.反问题与计算力学[J].计算结构力学及其应用,1993,(8)
[80]谭贤君,褚以悼,陈卫忠,戴永浩,陈培帅.考虑冻融影响的岩土类材料导热系数计算新方法[J].岩土力学,2010,11：70-74
[81]龚晓南.反分析去确定固结过程中土的力学参数[J].浙江大学学报,1989(6)：841-848
[82]张兴武.白山拱坝坝基分区弹模的敏度反分析方法[M].岩土力学数值方法的工程应用.上海：同济大学出版社,1990：786-796
[83]王芝银.空间轴对称蠕变位移反分析.第二届全国岩石力学数值计算与模型实验学术研讨会论文集[C].上海：同济大学出版社,1990
[84]陈卫忠,伍国军,贾善坡等.ABAQUS在隧道及地下工程中的应用[M].中国水利水电出版社,2010
[85]沈永飞.边坡位移反分析及其工程应用研究[J].重庆大学硕士学位论文,2010
[86]武晓晖,宋宏伟.地下工程围岩力学参数反分析的ANSYS方法[J].山西建筑,2005：52-53
[87]李宁,陈波,陈飞熊.寒区复合地基的温度场、水分场与变形场三场耦合模型[J].土木工程学报,2003
[88]王秉纲,毛雪松,李宁.冻土路基水热迁移问题的理论模型及数值模拟[J].中外公路,2006
[89]李宁,康佳梅,全晓娟.高温冻土区一种新型路基护坡的冷却机理研究[J].岩土工程学报,2007
[90]张子明,宋智通,石端学.混凝土绝热温升新理论及在龙滩工程中的应用[J].红水河,2005
[2]温智,盛煜等.青藏铁路路基浅地表热状态动态监测初步分析[J].岩石力学与工程学报,2003,22(增2)：2664-2668
[3]朱德举.多年冻土地区钻孔灌注桩的有限元分析.东北林业大学硕士学位论文.2004.3
[4]青藏公路科研组.昆仑山桩基静荷载试验研究报告之四——水平荷载试验.西安公路学报,1986,218-248
[5]励国良,赵西生,王化卿等.多年冻土地区桩基础试验研究.铁道学报,1980,2(1)
[6]程国栋.用冷却路基的方法修建青藏铁路.中国铁道科学,2003,24(3)：1-4
[7]C.Harley, A.Faghri. Complete transient two-dimensional analysis of two-phase closed thermosyphons including falling condensate film[J].ASME J. Heat Transfer,1994(116)
[8]J.GReed, C.L.Tien Modeling of the two-phase closed thermosyphon [J]. Journal of Heat Transfer,1987(109):722-730
[9]Z.J.ZUO and F.S.Gunnerson, Numerical modeling of the steady-state two-phase closed thermosyphon [J]. Int.J. Heat Mass Transfer,1994,V37(17):2715-2722
[10]陶汉中,张红.采用热管技术加固冻土铁路路基的热影响分析.能源研究与利用,2003,(3)：19-21
[11]吴存真,孙志坚,潘阳.应用热管技术解决寒区地基冻胀问题的理论研究.岩土工程学报,2002,24(3)：347—350
[12]陈鹏,许志健.热管稳定冻土路基的动态传热分析及数值计算.见：第九届全国热管会议论文集.昆明：2003.248-254
[13]李金灵.应用热管技术提高多年冻土地区路基稳定性的数值分析.铁道勘察,2004,(4)：5-8
[14]中铁西北科学研究院.青藏铁路冻土热管的传热分析研究报.2003
[15]汪双杰,陈建兵,黄晓明.热棒路基降温效应的数值模拟.交通运输工程学报,2005,5(3)：41-46
[16]杨永平,魏庆朝,张鲁新等.青藏铁路多年冻土地区热管路基三维数值分析.中国铁道科学,2005,26(2)：20-24
[17]萧岩.城市地下工程冻结法施工技术及其应用.市政技术,2002(3)：20-32
[18]陈湘生.冻结法加固地层的原理与应用.水利水电施工,1997(3)：71-7
[19]马芹永.人工冻结法的理论与施工技术.人民交通出版社,2007
[20]Kavanagh K T, Clough R W. Finite Element application in the characterization of elastic solids, Int. J. Solids Structures,1972, Vol.11-23
[21]Kirsten H A D. Determination of rock mass elastic moduli by back analysis of deformation measurement. In: Proc Symp on Expliration for Rock Eng. Johannesburg, 1976.1154-1160
[22]Maiar G, Jurina. L, Podolak K. On model identification problems in rock mechanics. In: Proc Symp on the Geotechnics of Structurally Complex Formations. Capri, 1977.257-261
[23]Kovari k et al. Integrated measuring technique for rock pressure determination. In: Proc Int Conf on Field Measurements on Rock Mechanics. Zurich,1977.1.533-538
[24]Gioda G. Indirect identification of the average elastic characteristics of rock masses. In: Proc Int Conf on Structural Foundation on Rock. Sydney,1980,1.65-73
[25]Gioda G Some remarks on back analysis and characterization problems. In: Proc 5th Int Conf on Num Meth in Geom. Nagoya,1985,1.47-61
[26]Maier G, Gioda G Optimization methods for parametric identification of geotechnical system. In: Maitins J B ed. Num Methods in Geom. Boston,1980.431-436
[27]Gioda G, Maier G. Direct, search solution of an inverse problem in elasto-plasticity, identification of cohesion, friction angle and in-situ stress by pressure tunnel tests. Int J Num Methods in Eng,1980,15:1823-1834
[28]Gioda G, Pandolfi A. A comparative evaluation of some back analysis algorithms and their application to in-situ load tests. In: Proc 2nd Int Symp on Field Measurement in Geom,1987.1131-1144
[29]Arai R. An inverse problem approach to the prediction of Multi-dimensional consolidation behavior. Soil and Foundations,1984,24(1):95-108
[30]Sakurai S, Abe S. A design approach to dimensioning underground openings. In: Proc 3rd Int Conf Numerical Methods in Geomechanics. Aachen,1979.649-661
[31]杨志法,王思敬,冯紫良.岩土工程反分析理论及应用[M].北京：地震出版社,2002
[32]杨林德.岩土工程问题的反演理论与工程试验[M].北京：科学出版社,1996
[33]吴凯华.隧洞围岩原始应力与弹性常数的反分析[J].土木工程学报,1988
[34]王芝银,李云鹏.地下工程位移反分析法及程序[M].西安：陕西科学技术出版社,1993
[35]吕爱钟,蒋斌松.岩石力学反问题[M].北京：煤炭工业出版社,1998
[36]冯夏庭.智能岩石力学导论[M].北京：科学出版社,2000
[37]Kavanagh K. And R. W. Clough, Finite Element application in the characterization of elastic solids, Int. J. Solids Structure,1971, Vol.11-23
[38]Sakurai, Back analysis of measured displacements in shallow tunnel excavated in sandy materials, Proc Int Symp on Underground Engineering, Vol,1983
[39]刘允芳.弹性介质岩体中非圆形洞室位移反分析计算[J].岩石力学和工程学报,1986(5)：43-46
[40]薛琳,杨志法.确定流变岩体的参数及地应力的位移反分析[J].地质科学,1986(4)：5-8
[41]Gioda, Sakurai, Back analysis Ptocedure for the Interpretation of Field Measurements in Geomechanics, Int. J. for Num. and Analy Methods in Geomech, Vol.11,1987:555-583
[42]王芝银,李云鹏.地下工程围岩粘弹塑性参数反分析[J].水利学报,1990(9)：31-34
[43]Maier, International Journal For Numerical and Analytical Methods in Geo-mechanics, Vol.8,1983
[44]袁勇.围岩弹塑性参数反算的极大似然法[J].工程勘察,Vol.5,1991
[45]邹海,王桂梁,桂和荣,陈兆炎.岩体力学参数的损伤—反分析优化性研究[J].长春科技大学学报,1999,29(2)：167-170
[46]王华宁,吕爱钟.巷道裂隙岩体的损伤参数辨识[J].岩土工程学报,2001,23(5)：593-597
[47]李兴高,高延法.采场底板岩层破坏与损伤分析[J].岩石力学与工程学报,2003,22(1)：35-39
[48]郭继伟.分型粗糙面散射的边界元法及参数反演[J].复旦大学硕士学位论文,2008
[49]蔡志杰,郭志伟.用边界元法反演分形粗糙面[J].复旦学报(自然科学版),2010,49：395-403
[50]李仲奎,莫兴华,王爱民,徐千军.地下洞室松动区模型及其在反馈分析中的应用[J].水利水电技术,1999,30(5)：49-51
[51]江权,冯夏庭,苏国韶,陈国庆.基于松动圈-位移增量监测信息的高地应力下洞室群岩体力学参数的智能反分析[J].岩石力学与工程学报,2007,26：2654-2692
[52]陈秋红,李仲奎,张志增.松动圈分区模型及其在地下工程反馈分析中的应用[J].岩石 力学与工程学报,2010,29：3216-3220
[53]Harlan,R.L Analysis of Coupled Heat-fluid Transport in Partially Frozen Soil[J]. Water Resource Research 1973 Vol 9(3)
[54]郭兰波等.竖井冻结壁温度场的有限元分析.中国矿业学院学报,1981(3)：31-35
[55]王铁行,胡长顺等.考虑多种因素的冻土路基温度场有限元方法.中国公路学报.长安大学.2000,13(4)：8-11
[56]吴亚平,苏强,朱元林.冻土区桥梁群桩基础地基回冻过程的非线性分析[J].土木工程学报,2006
[57]汤懋苍,程国栋,林振耀.青藏高原近代气候变化及对环境的影响[M].广东科技出版社,1998
[58]郭余良.青藏铁路多年冻土区的地温特征及影响因素[J].铁道勘察,2007
[59]金会军,孙立平.青藏高原中、东部局地因素对地温的双重影响[J].冰川冻土,2008
[60]王绍令.青藏高原局地因素对近地表层地温的影响[J].高原气象,2002
[61]中国科学院兰州冰川冻土研究所.冻土的温度水分应力及其相互作用[M].兰州大学出版社,1989
[62]李黎明.ANSYS有限元分析实用教程[M].清华大学出版社,2005
[63]中国科学院兰州冰川冻土研究所青藏公路冻土路基研究组.冻土路基工程[M].兰州大学出版社,1988
[64]朱林楠.高原冻土区不同下垫面的附面层研究[J].冰川冻土,1988,10(1)：8～14
[65]徐学祖,王家澄,张立新.冻土物理学[M].科学出版社.2001.4
[66]朱伯芳,王同生,丁宝瑛,郭之章.水工混凝土结构的温度应力与温度控制.北京：水利电力出版社,1976
[67]蔡正咏.混凝土性能.北京：中国建筑工业出版社,1979
[68]中华人民共和国电力工业部.水工混凝土结构设计规范.北京：中国电力出版社,1996
[69]贾晓云,李文江.多年冻土区灌注桩混凝土水化热影响分析.2003
[70]郭宽良等.计算传热学[M].安徽：中国科技大学出版社,1988.68～69
[71]吴青柏,董献付,刘永智.青藏公路沿线多年冻土对气候变化和工程影响的响应分析[J].冰川冻土,2005,27(1)：50-54
[72]徐冰魁.多年冻土区热棒路基设计计算[J].硕士论文,2005
[73]汪双杰.多年冻土地区公路修筑技术[M].人民交通出版社,2008
[74]陈鹏,许志键.热管稳定冻土路基的动态传热分析及数值计算[A].第九届全国热管会议论文集[C].昆明：中国工程热物理学会热管专业组,2003
[75]张恒运,葛新石.两相闭式热虹吸管的集总参数模型研究[J].中国科学技术大学学报,1997
[76]汪双杰.高原多年冻土区公路路基稳定及预测技术研究[J].博士论文,2005
[77]王彦飞.反演问题的计算方法及其应用[M].北京：高等教育出版社,2007
[78]刘家琦.数学物理方程反问题的分类及不适定问题求解[J].计算数学和应用数学,1983,(4)：43-64
[79]黄光远,刘维倩,刘小军.反问题与计算力学[J].计算结构力学及其应用,1993,(8)
[80]谭贤君,褚以悼,陈卫忠,戴永浩,陈培帅.考虑冻融影响的岩土类材料导热系数计算新方法[J].岩土力学,2010,11：70-74
[81]龚晓南.反分析去确定固结过程中土的力学参数[J].浙江大学学报,1989(6)：841-848
[82]张兴武.白山拱坝坝基分区弹模的敏度反分析方法[M].岩土力学数值方法的工程应用.上海：同济大学出版社,1990：786-796
[83]王芝银.空间轴对称蠕变位移反分析.第二届全国岩石力学数值计算与模型实验学术研讨会论文集[C].上海：同济大学出版社,1990
[84]陈卫忠,伍国军,贾善坡等.ABAQUS在隧道及地下工程中的应用[M].中国水利水电出版社,2010
[85]沈永飞.边坡位移反分析及其工程应用研究[J].重庆大学硕士学位论文,2010
[86]武晓晖,宋宏伟.地下工程围岩力学参数反分析的ANSYS方法[J].山西建筑,2005：52-53
[87]李宁,陈波,陈飞熊.寒区复合地基的温度场、水分场与变形场三场耦合模型[J].土木工程学报,2003
[88]王秉纲,毛雪松,李宁.冻土路基水热迁移问题的理论模型及数值模拟[J].中外公路,2006
[89]李宁,康佳梅,全晓娟.高温冻土区一种新型路基护坡的冷却机理研究[J].岩土工程学报,2007
[90]张子明,宋智通,石端学.混凝土绝热温升新理论及在龙滩工程中的应用[J].红水河,2005