浅表隧道工程多冷源冻结温度、应力、水分场耦合研究
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摘要
在对人工地层冻结研究现状分析讨论的基础上，本文以上海延安东路隧道地层冻结为背景，应用室内试验、现场实测、理论分析和数值模拟的综合方法，对饱和软土地区的浅表隧道多冷源冻结的温度场、应力场、水分场耦合原理、规律及相关参数进行了较系统的研究，主要研究内容如下：
首先，针对理论研究和冻结工程的实际需要，对上海地区三种饱和软土的起始冻结温度、低温土体未冻水含量、含冰量、冻、融土的比热、土体导热、导温系数、低温土体的无侧限抗压强度、三轴剪切强度、弹性摸量及泊松比等指标进行了室内试验。分析了三种软土的起始冻结温度及冻、融土导热、导温系数的影响因素、低温土体未冻水含量、弹性模量、泊松比与温度的定量关系；研究比较了封闭系统中上海三种软土的冻胀特性；讨论了低温土体无侧限抗压强度、三轴剪切强度的变化规律。
其次，归纳、整理了上海延安东路隧道冻结工程的温度、应力、地表变形和土体分层位移现场实测数据。分析了土体冻结过程中温度场、应力场变化及多冻结管供冷的相互干涉、影响规律，并对水分迁移、孔隙水相变和土体变形与温度场、应力场的耦合规律进行了分析。
第三，在对室内试验和现场实测结果研究的基础上，分析了土体冻结过程中温度场、应力场、水分场耦合原理，并按照冻土体形成发展过程，首先建立了单一冷源冻结轴对称温度、应力、水分场耦合模型；接着利用势场的迭加原理，将单一冷源情况的三场耦合问题推广到多冷源情况的三场耦合；最后根据能量守恒平衡方程、应力平衡方程、质量守恒平衡方程、几何方程、物理方程、初始及边界条件，解出了单一冷源平面轴对称问题的解析解。
最后，在应用Galerkin加权余量法分析的基础上，同时做了一些简化和假设，得到了浅表隧道多冷源冻结情况的温度场、应力场、水分场耦合数值解；利用编制的有限元程序对冻结过程进行了计算机模拟，得到了与现场实测基本一致的结果。
Based on the research achievements of the artificial ground freezing in the past, combined with the ground freezing engineering practice of the tunnel of Yan'an Dong road, Shanghai, and by a series of methods including laboratory tests, site observation, theoretical analysis and numerical simulation, author has systematically studied the coupling mechanism and law of three fields ( temperature, stress, moisture migration) and got some important results about soft soil and freezing process
Firstly, according to the requirement of theoretical study and engineering practice, the physical and mechanical properties of three kinds saturated soft clay in Shanghai area in the frozen and unfrozen conditions have been tested in laboratory. The influencing factors of initial freezing temperature of soft clay which is in natural condition and the thermal conductivity, thermal diffusion ratio of frozen and unfrozen clay are analyzed. The quantitative relationship between the temperature and the unfrozen water content, elastic modulus and Poission's ration are obtained. The frost heave behaviors of the soft clays are also discussed. By means of the unconfined compression test and tri-axial shear test, the strength variation law of frozen clay is studied.
Secondly, by means of the systemizing to the site surveying data of
temperature, stress, surface deformation and soil layers displacement, the variation law of temperature field and stress field and the interference and effect of multi-freezing pipes are analyzed. According to the distribution characteristics of soil layers and installing place and depth of freezing pipes, the coupling properties of temperature, stress, the phase transition of pore water and ground deformation are studied.
Thirdly, according to the development of the frozen soil, the coupling model of single freezing pipe of axial symmetry of temperature field, stress field and moisture migration is put forward firstly. Then, by means of the progressing principle of potential field, the coupling model of temperature field, stress field and moisture migration which is under the condition of the multi-freezing pipes is extended. At last, the energy balance equation, stress balance equation, quality balance equation, geometric equation, physical equation, initial and boundary conditions etc are adopted to give the analytic solution to the problem of plane axial symmetry of single freezing pipe.
At last, based on the analysis of Galerkin finite element method and some simplification and hypothesis, the numerical solution of three fields coupling of shallow tunnel with multi-freezing pipes is obtained. By means of the finite element program for the freezing process in dynamic static, the numerical simulation is made, and the results agree well with the site survey results.
首先，针对理论研究和冻结工程的实际需要，对上海地区三种饱和软土的起始冻结温度、低温土体未冻水含量、含冰量、冻、融土的比热、土体导热、导温系数、低温土体的无侧限抗压强度、三轴剪切强度、弹性摸量及泊松比等指标进行了室内试验。分析了三种软土的起始冻结温度及冻、融土导热、导温系数的影响因素、低温土体未冻水含量、弹性模量、泊松比与温度的定量关系；研究比较了封闭系统中上海三种软土的冻胀特性；讨论了低温土体无侧限抗压强度、三轴剪切强度的变化规律。
其次，归纳、整理了上海延安东路隧道冻结工程的温度、应力、地表变形和土体分层位移现场实测数据。分析了土体冻结过程中温度场、应力场变化及多冻结管供冷的相互干涉、影响规律，并对水分迁移、孔隙水相变和土体变形与温度场、应力场的耦合规律进行了分析。
第三，在对室内试验和现场实测结果研究的基础上，分析了土体冻结过程中温度场、应力场、水分场耦合原理，并按照冻土体形成发展过程，首先建立了单一冷源冻结轴对称温度、应力、水分场耦合模型；接着利用势场的迭加原理，将单一冷源情况的三场耦合问题推广到多冷源情况的三场耦合；最后根据能量守恒平衡方程、应力平衡方程、质量守恒平衡方程、几何方程、物理方程、初始及边界条件，解出了单一冷源平面轴对称问题的解析解。
最后，在应用Galerkin加权余量法分析的基础上，同时做了一些简化和假设，得到了浅表隧道多冷源冻结情况的温度场、应力场、水分场耦合数值解；利用编制的有限元程序对冻结过程进行了计算机模拟，得到了与现场实测基本一致的结果。
Based on the research achievements of the artificial ground freezing in the past, combined with the ground freezing engineering practice of the tunnel of Yan'an Dong road, Shanghai, and by a series of methods including laboratory tests, site observation, theoretical analysis and numerical simulation, author has systematically studied the coupling mechanism and law of three fields ( temperature, stress, moisture migration) and got some important results about soft soil and freezing process
Firstly, according to the requirement of theoretical study and engineering practice, the physical and mechanical properties of three kinds saturated soft clay in Shanghai area in the frozen and unfrozen conditions have been tested in laboratory. The influencing factors of initial freezing temperature of soft clay which is in natural condition and the thermal conductivity, thermal diffusion ratio of frozen and unfrozen clay are analyzed. The quantitative relationship between the temperature and the unfrozen water content, elastic modulus and Poission's ration are obtained. The frost heave behaviors of the soft clays are also discussed. By means of the unconfined compression test and tri-axial shear test, the strength variation law of frozen clay is studied.
Secondly, by means of the systemizing to the site surveying data of
temperature, stress, surface deformation and soil layers displacement, the variation law of temperature field and stress field and the interference and effect of multi-freezing pipes are analyzed. According to the distribution characteristics of soil layers and installing place and depth of freezing pipes, the coupling properties of temperature, stress, the phase transition of pore water and ground deformation are studied.
Thirdly, according to the development of the frozen soil, the coupling model of single freezing pipe of axial symmetry of temperature field, stress field and moisture migration is put forward firstly. Then, by means of the progressing principle of potential field, the coupling model of temperature field, stress field and moisture migration which is under the condition of the multi-freezing pipes is extended. At last, the energy balance equation, stress balance equation, quality balance equation, geometric equation, physical equation, initial and boundary conditions etc are adopted to give the analytic solution to the problem of plane axial symmetry of single freezing pipe.
At last, based on the analysis of Galerkin finite element method and some simplification and hypothesis, the numerical solution of three fields coupling of shallow tunnel with multi-freezing pipes is obtained. By means of the finite element program for the freezing process in dynamic static, the numerical simulation is made, and the results agree well with the site survey results.
引文
1．温家宝．切实加强城乡规划工作推进现代化建设健康发展[N]．人民日报．2000-07-07．
2．赵国隆．关于地下空间----重要的国家资源开发利用问题的思考．探矿王程(岩土钻掘工程)，2001，(1)．
3．徐德新．城市地下空间开发技术的发展趋势．科学时报，2000-06-23．
4．杨林德主编．软土工程施工技术与环境保护．北京：人民交通出版社，2000．
5．陈湘生．人工地层冻结法在岩土工程中的应用．武汉：中国青年学者岩土工程力学讨论会论文集，1994，12．
6．木下诚一著．冻土物理学．王异、张志权译．长春：吉林科学技术出版社，1985
7．程知言等．上海某冻结加固工程试验研究分析．地质与勘探，2002，38(3)
8. Harlan R L. Analysis of coupled heat—fluid transport in partially frozen soil [J] .Water Resources Research, 1973,9(5)
9. Taylor G S, Luthin J N.A model for coupled heat and moisture transfer during soil freezing [J]. Canadian Geotech.,1978,15
10. Gilpin R R.A model for the prediction of ice lensing and frost heave in soil [J]. Water Resour. Research, 1980,16(5)
11. Konrad J M, Duquennoi C. A model for water transport and ice lensing in freezing soils[J].Water Resource Research, 1993,29(9)
12．安维东等著．冻土的温度、水分、应力及其相互作用．兰州：兰州大学出版社，1990
13．李萍、徐学祖、陈峰峰．冻结缘和冻胀模型的研究现状与进展．冰川冻土，2000，22(1)
14．程知言、裘慰伦、张可能、庞荣庆．人工地层冻结水分迁移动力探讨．海峡两岸岩土工程／地工技术交流研讨会论文集．2002，4．上海
15．陈宝明．多孔介质中水平温度梯度和浓度梯度导致的自然对流传热传质．山东建筑工程学院学报，1998，13 (1)
16．崔托维奇著．冻土上的地基与基础(中译本)．北京：中国工业出版社，1985
17. S. L. Huang. Effects of temperature on swelling of coal shell. 5th International Symposium on Ground Freezing. Jones and Holden(eds),1988, Balkema, Rotterdan
18. Development of soil fabric by freeze/thaw cycles—Its effect on Frost heave. Brigitte Van villiet—Lanoe. 5th International Symposium on Ground Freezing, Jones and holden(eds),1988, Balkema, Rotterdan
19. Hareyuk. Yamaguchi. etc. Influence of Freezing—thaw on undrained triaxial compression shear behavior of fibrous peat. 5th International Symposium on Ground Freezing, Jones and Holden(eds), 1988, Balkema, Rotterdan
20. Hideo Younamoto. Keijimatsuoka. Displacement and increment in earth pressure in unfrozen soil by frost heave. 5th International Symposium on Ground Freezing, Jones and Holden(eds),
1988, Balkema, Rotterdan
21. B. Ladany & Mushen. Pressure Variation on a wellbone casing during permafrost thawing. 5th International Symposium on Ground Freezing, Jones and Holden(eds), 1988, Balkema, Rotterdam
22. Holden J.T. Approximate Solution for Miller's Theory of Secondary Heave, Permafrost, 4th International Con..1983
23. Harlan R L. Analysis of Coupled Heated—Fluid transport in partially frozen soil, Water Research, 1973, 9(5)
24．彭万巍．不同掺合料砂砾石的冻胀实验研究．冰川冻土，1988，10(1)
25．陈肖柏．我国土冻胀研究进展．冰川冻土，1988，10(3)
26．童长江．我国冻土融化压缩性研究．冰川冻土，1988．10(3)
27．高维跃、徐学祖．土层冻结期间地下水入流量的现场实测．冰川冻土，1989，11(2)
28. Piper D, Holden J T., Jones R H. A mathematical model of frost heave in granular materials[A]. 5th Int. Conf. on Permafrost[C].Norway: Tapir Pub1. 1988
29. Peng Xuming, Chen Xiaobai and Wang Yaqing. A model coupled heat, moisture and stress field of saturated soil during freezing. Ground Freezing, Yu & Wang(eds), 1991, Balkema, Rotterdam
30．赖远明，吴紫汪，朱元林，朱林楠．寒区隧道温度场、渗流场和应力场耦合问题的非线性分析．岩土工程学报，21(5)
31. Anderson D M, Tice A R, Banin A. The Water-Ice Composition of Clay/Water System. CRREL Research Report, 1974,10
32. Chuvilin E M, Yazynin 0 M. Frozen Soil Macro-and Microtexture Formation. Proceedings of the 5th International Conference on Permafrost, 1988
33. Yoshisuke Nakano. Transport of water through frozen soils. Ground Freezing, Yu & Wang(eds),1991, Balkema, Rotterdam
34. Hadley W. A. and R. Eisenstadt. Thermally actuated moisture migration in granular media. Trans. Amer. Geophysical Union, 1955
35. Hoekstra P. Moisture movement in soils under temperature gradients with the cold side below freezing. Water Resources Res., 1966
36. Hutcheon W.L. Moisture flow induced by thermal gradients within unsaturated soils. Highway Res. Board Special Rep.,1958
37. Takeda K. and Y. Nakano. Quasi-steady problems in freezing soils: Experiment on growth of an ice layer. Cold. Reg. Sci. Technol, 1990
38. S.W. Hopke. A model for frost heave including overburden. Cold Regions Science and technology, 1980(3)
39. Xu xiaozu, Oliphant J.L. and Tice A. R. Experimental study on factors affecting water migration in frozen morin clay. Proceeding of 4th International Symposium on ground freezing, 1985, Vol 1
40．丘国庆，E．张伯伦，I．伊斯坎达．莫玲粘土冻结过程中的离子、水分迁移和冻胀．冰川冻土，1986，8(1)
41. Yoshiuke Nakano. Transport of Water in Frozen Soil[J]. Advance in Water Resource, 1984
42. Yang Daiquan, etc. Modeling fully Coupled Moisture, Air and Heat Transfer in Unsaturated Soils. Chinese Journal of Geotechnical Engineering, 2000,22(3)
43．徐伯孟，卢兴良．粘性土水分状况对冻胀的影响．冰川冻土，1986，8(3)
44．崔托维奇著，张长庆、朱元林译．冻土力学．北京：科学出版社，1985
45．吴紫汪等．土的冻胀性实验研究．中国科学院兰州冰川冻土研究所集刊．北京：科学出版社，1981
46．林世荣，包俊超，兰荣旺．冻融试验研究．岩土工程技术，2001，No3
47．徐学祖．冻土与盐溶液系统中热质迁移及变形过程试验研究．冰川冻土，1992，14(4)
48．楼玲玲，蔡正升，朱玉龙．湿型中水分迁移及其对温度场的影响．铸造，2000，49(1)
49．何平，程国栋，俞祁浩，朱元林、徐学祖．饱和正冻土中的水、热、力场耦合模型．冰川冻土，2000，22 (2)
50. J. T. Holden. Heat transfer in artificial ground freezing. Ground Freezing, Knutsson(ed.),1997, Balkema, Rotterdam
51．周希圣．隧道冻结工程水、温度、应力、位移场的耦合研究[D]．徐州：中国矿业大学，1998
52. Williams P.J. Properties and Behavior of Freezing Soils Norwegian Geotechnical Institute, Publ. 1967
53．刘宏绪．对土体冻结过程中若干冻胀力学问题的商榷[J]．冰川冻土，1990，12(3)
54．吴紫汪．富冰土的热胀性质[J]．冰川冻土，1990，12(3)
55．高大钊主编．软土地基理论与实践．北京：中国建筑工业出版社、上海：同济大学出版社，1992
56．徐学祖，王家澄，张立新．冻土物理学．北京：科学出版社，2001
57．中国科学院兰州冰川冻土研究所、煤炭工业部特殊凿井公司．冻结凿井冻土壁的工程性质．兰州：兰州大学出版社，1988
58．沈言俐等．土壤水分运动基本参数测定[J]．冰川冻土，1984，6(4)
59. Harlan R. L. Analysis of Couple Heat-Fluid Transport in Partially Frozen Soil. Water Research, 1973, 2
60．徐学祖等．饱水正冻土中水分迁移特征研究．第五届国际冻土学术会议论文集，1988
61．李述讯．冻、融土中的水热输运问题．兰州：兰州大学出版社，1993
62．上海隧道工程股份有限公司，中国矿业大学．盾构隧道冻结加固技术研究，1996
63．上海隧道施工技术研究所，中国矿业大学．上海软土低温特性研究，1995
64．上海隧道施工技术研究所，中国矿业大学．上海软土地层浅覆土盾构隧道冻结加固模拟试验研究，1996
65．中煤特殊工程公司．上海延东隧道复线冻结工程施工总结．1996
66．上海隧道工程股份有限公司．泥水平衡盾构穿越冻结加固区施工技术，1996
67．中国矿业大学．上海延安东路隧道复线冻结工程监测技术及冻土热力参量分析，1996
68．杨平，皮爱如．高流速地下水流地层冻结壁冻结壁形成的研究[J]．岩土工程学报，2001，23(2)
69．白以龙，周恒．迎接新世纪挑战的力学—力学学科21世纪初发展战略的建议[J]．力学与实践，1999．21(1)
70. Ladanyi B. Geotechnique for cold regions. Nerk:McGraw-Hill Book company, 1978
71. Bonacina C, Comini G, Fasano A, etal. Numerical solution of phase-change problems. Int J Heat Mass Transfer, 1973,16(6)
72. Konard J. M., Morgenstern N. R.. The segregation potential of a freezing soil [J]. Can. Geotech. J., 1981,18
73．徐学祖，J．L．奧利丰特，A．R．泰斯．线性温度梯度下非饱和冻结莫玲粘土中的水分迁移．冰川冻土，1985，7 (2)
74. Bathe K. J., Khoshgoftaar M.R., Finite element free surface seepage analysis without mesh iteration. Int. J Numerical Analytical Methods in Geomechanics, 1979,3(1)
75．徐学祖．土水势、未冻水含量和温度．冰川冻土，1985，7(1)
76．盛煜，马巍，侯仲杰．正冻土中水分迁移的迁移势模型．冰川冻土，1993，15(1)
77. G. Lame and B.P. Clapeyron. Ann, Chem. Phys., 1831.
78. H.S. Carslaw and J.C.Jaeger, Conduction of heat in solids, 2nd ed.,Clarendon Press, London, 1959.
79. S. Paterson, Proc. Glasgow Math. Assoc. 1,42-47,1952-53.
80. J. T.Holden. Heat transfer in artificial ground freezing. Ground Freezing, Knutsson(ed), 1997, Balkema, Rotterdam
81. Ershov E. D..Water migration and cryogenic structure in fine grained soils. Moscow: Publishing housing of Moscow State University, 1979
82. Ershov E.D..Physico-chemistry and mechanics of frozen soils. Moscow: Publishing housing of Moscow State University, 1986
83. F.J. Sanger, F.H. Sayles. Thermal and theological computations for artificially frozen ground construction. Engineering Geology, 1979,13
84．蒋斌松，陈伟．立井冻结壁初应力场分析．山东矿业学院学报，1995，14(2)
85．孙家学、刘斌．冻结壁原始冻胀力的分析与计算方法．东北大学学报(自然科学版)，1995，16(3)
86. Beskow G. Soil freezing and frost heaving with special application to roads and railroads [J]. Swedish Geol. Survey Yearbook, 1985,26(3)
87. Everett D.H. The thermodynamics of frost damage to porous solids [J]. Trans. Faraday Soc., 1961,57
88. Miller R.D.. Freezing and heaving of saturated and unsaturated soils [J]. Highway Record, 1972,393
89. Miller R.D.. Lens initiation in secondary frost heaving [R]. Sweden: Int. Symp. On frost
action in soils, 1977
90．崔托维奇著．冻土上的地基与基础(中译本)．北京：中国工业出版社，1985
91．陈传璋，侯宗义，李明忠．积分方程论极其应用．上海：上海科学技术出版社，1987．
92．王云甫．弹性理论(第二版)．北京：科学出版社，1984
93. Zhang Lixin, Pu Yibin, Liao Quanrong, Gu Tongxin. Dynamic investigation of mass transfer in freezing soil with computer tomography. Ground Freezing, Knutsson(ed.), 1997, Balkema, Rotterdam
94. Xu Xiaozu, Deng Yousheng, Gao Weiyue, Wang Fenge. Water and solute migration of freezing soils in closed system under temperature gradients. Ground Freezing, Yu and Wang(eds.), 1991, Balkema, Rotterdam
95. Magean D.W., and N.R. Morgensterm. Observation on moisture migration in frozen soils. Can. Geotech. J. 17
96. Kay B. D. and Perfaet E.. State of the art: Heat and mass transfer in freezing soils. Proceedings of 5th International Symposium on ground freezing, 1988
97. Burr T P., Williams P J..Hydraulic Conductivity Functions of Frozen Soils[J]. Earth Surface Processes, 1976.
98. Black P B., Miller R D.. Hydranlie Conductivity and Unfrozen Water Content of Air-Free Frozen Silt[J]. War. Resour. Res. 1990, 26.
99. Muhammad Sahimi. Flow and transport in porous media and fractured rock-from classical method to modern approaches [J]. VCH Verlagsgesellschaft MBH, 1995
100. Horiguchi K., Miller R D..Hydraulic Conductivity Functions of Frozen Materials[A]. 4th Int. Conf. on Permafrost[c]. Washington D. C.: National Academy Press, 1983.
101. O'Neill k., Miller R D..Exploration of a Rigid-Ice of Frost Heave[j]. Wat. Resour. Res., 1985, 21.
102. Horiguchi K., Miller R.D.. Hydraulic conductivity function of frozen materials [A]. 4th Int. Conf. on Permafrost [C]. Washington D.C.: National Academy Press. 1983
103．徐学祖，邓右生．冻土中水分迁移的实验研究[M]．北京：科学出版社，1991
104. Witten T A, Sander L M. Diffusion-limited aggregation, a kinetic critical phenomenon[J]. Phys. Rev. Lett., 1981, 47105. Anderson D.M., Tice A.C.. Predicting unfrozen water contents in frozen soils from surface area measuraments [J]. Highway Research Record, 1972,393
105. Anderson D M., Tice A C..Predicting Unfrozen Water Contents in Frozen Soils from Surface Area Measurement[J]. Highway Research Record, 1972.
106．林瑞泰．多孔介质传热传质引论．科学出版社，1995．
107．曾海容，宋惠珍．地下流体场与应力场耦合方程的有限元法．石油勘探与开发，1998，25(4)
108．Kunieda T, Sato T, Ido S. Numerical case studies of ground freezing for the construction of drain pump chambers．In．Ground freezing91. Rotterdam: Balkema. 1991
109．陈宝明．多孔介质中水平温度梯度和浓度梯度导致的自然对流传热传质．山东建筑工程学院学报，1998，13(1)
110．徐曾和，徐小荷．二维应力场下承压地层中渗流的液固耦合问题．岩石力学与工程学报，1999，18(6)
111．余扬政，冯承天，物理学中的几何方法，高等教育出版社、施普林格出版社，1998．
112. N. Wakao and S. Kaguei, Heat and Mass Transfer in Packed Beds, Gordon and Breach, Science Publishers, Inc.,1982.
113. W.M. Kays, Convective Heat and Mass Transfer, McGraw-Hill, New York, 1966.
49 90．舒茨B．F．，数学物理中的几何方法．冯承天等译．上海：科学技术文献出版社，1986
114. W. Pogorzelski, Integral equations and their applications, Vol. 1, Pwn-Polish Scientific Publishers, Warszawa, 1966.
115．Y．S．杜洛金，固体热物理性质导论—理论和测量．奚同庚等译．中国计量出版社，1987
116．卢焕忠．场论极其应用．湖南科学技术出版社，1981．
117．王潼．热势论．科学出版社，1980
118．刘连寿，王正清．数学物理方法．高等教育出版社，1990
119. Kujala K. Factors affecting frost susceptibility and heaving pressure in soils [D]. Finland:University of Oulu, 1991
120. Guymon GL, Luthin JN.A coupled heat and moisture transport model for arctic soils[J]. Wat. Resour. Res.,1974
121. Biermans M B G M, Garg S Z, Pritchett J W. Governing equations for geothermal reservoirs [J].Wat. Resour. Res.,1977,13
122．郭宽良等．计算传热学．合肥：中国科技大学出版社，1988
123．俞昌铭．热传导及其数值分析．北京：清华大学出版社，1982
124．钱壬章，俞昌铭，林文贵．传热分析与计算．北京：高等教育出版社，1987
125．施天谟[美]．计算传热学．北京：科学出版社，1987
126．孔祥谦．有限单元法在传热学中的应用(第三版)．北京：科学出版社，1998
127．张鸣歧．应用泛函分析引论．北京：北京理工大学出版社，1989
128．刘高典．温度场的数值模拟．重庆：重庆大学出版社，1990
2．赵国隆．关于地下空间----重要的国家资源开发利用问题的思考．探矿王程(岩土钻掘工程)，2001，(1)．
3．徐德新．城市地下空间开发技术的发展趋势．科学时报，2000-06-23．
4．杨林德主编．软土工程施工技术与环境保护．北京：人民交通出版社，2000．
5．陈湘生．人工地层冻结法在岩土工程中的应用．武汉：中国青年学者岩土工程力学讨论会论文集，1994，12．
6．木下诚一著．冻土物理学．王异、张志权译．长春：吉林科学技术出版社，1985
7．程知言等．上海某冻结加固工程试验研究分析．地质与勘探，2002，38(3)
8. Harlan R L. Analysis of coupled heat—fluid transport in partially frozen soil [J] .Water Resources Research, 1973,9(5)
9. Taylor G S, Luthin J N.A model for coupled heat and moisture transfer during soil freezing [J]. Canadian Geotech.,1978,15
10. Gilpin R R.A model for the prediction of ice lensing and frost heave in soil [J]. Water Resour. Research, 1980,16(5)
11. Konrad J M, Duquennoi C. A model for water transport and ice lensing in freezing soils[J].Water Resource Research, 1993,29(9)
12．安维东等著．冻土的温度、水分、应力及其相互作用．兰州：兰州大学出版社，1990
13．李萍、徐学祖、陈峰峰．冻结缘和冻胀模型的研究现状与进展．冰川冻土，2000，22(1)
14．程知言、裘慰伦、张可能、庞荣庆．人工地层冻结水分迁移动力探讨．海峡两岸岩土工程／地工技术交流研讨会论文集．2002，4．上海
15．陈宝明．多孔介质中水平温度梯度和浓度梯度导致的自然对流传热传质．山东建筑工程学院学报，1998，13 (1)
16．崔托维奇著．冻土上的地基与基础(中译本)．北京：中国工业出版社，1985
17. S. L. Huang. Effects of temperature on swelling of coal shell. 5th International Symposium on Ground Freezing. Jones and Holden(eds),1988, Balkema, Rotterdan
18. Development of soil fabric by freeze/thaw cycles—Its effect on Frost heave. Brigitte Van villiet—Lanoe. 5th International Symposium on Ground Freezing, Jones and holden(eds),1988, Balkema, Rotterdan
19. Hareyuk. Yamaguchi. etc. Influence of Freezing—thaw on undrained triaxial compression shear behavior of fibrous peat. 5th International Symposium on Ground Freezing, Jones and Holden(eds), 1988, Balkema, Rotterdan
20. Hideo Younamoto. Keijimatsuoka. Displacement and increment in earth pressure in unfrozen soil by frost heave. 5th International Symposium on Ground Freezing, Jones and Holden(eds),
1988, Balkema, Rotterdan
21. B. Ladany & Mushen. Pressure Variation on a wellbone casing during permafrost thawing. 5th International Symposium on Ground Freezing, Jones and Holden(eds), 1988, Balkema, Rotterdam
22. Holden J.T. Approximate Solution for Miller's Theory of Secondary Heave, Permafrost, 4th International Con..1983
23. Harlan R L. Analysis of Coupled Heated—Fluid transport in partially frozen soil, Water Research, 1973, 9(5)
24．彭万巍．不同掺合料砂砾石的冻胀实验研究．冰川冻土，1988，10(1)
25．陈肖柏．我国土冻胀研究进展．冰川冻土，1988，10(3)
26．童长江．我国冻土融化压缩性研究．冰川冻土，1988．10(3)
27．高维跃、徐学祖．土层冻结期间地下水入流量的现场实测．冰川冻土，1989，11(2)
28. Piper D, Holden J T., Jones R H. A mathematical model of frost heave in granular materials[A]. 5th Int. Conf. on Permafrost[C].Norway: Tapir Pub1. 1988
29. Peng Xuming, Chen Xiaobai and Wang Yaqing. A model coupled heat, moisture and stress field of saturated soil during freezing. Ground Freezing, Yu & Wang(eds), 1991, Balkema, Rotterdam
30．赖远明，吴紫汪，朱元林，朱林楠．寒区隧道温度场、渗流场和应力场耦合问题的非线性分析．岩土工程学报，21(5)
31. Anderson D M, Tice A R, Banin A. The Water-Ice Composition of Clay/Water System. CRREL Research Report, 1974,10
32. Chuvilin E M, Yazynin 0 M. Frozen Soil Macro-and Microtexture Formation. Proceedings of the 5th International Conference on Permafrost, 1988
33. Yoshisuke Nakano. Transport of water through frozen soils. Ground Freezing, Yu & Wang(eds),1991, Balkema, Rotterdam
34. Hadley W. A. and R. Eisenstadt. Thermally actuated moisture migration in granular media. Trans. Amer. Geophysical Union, 1955
35. Hoekstra P. Moisture movement in soils under temperature gradients with the cold side below freezing. Water Resources Res., 1966
36. Hutcheon W.L. Moisture flow induced by thermal gradients within unsaturated soils. Highway Res. Board Special Rep.,1958
37. Takeda K. and Y. Nakano. Quasi-steady problems in freezing soils: Experiment on growth of an ice layer. Cold. Reg. Sci. Technol, 1990
38. S.W. Hopke. A model for frost heave including overburden. Cold Regions Science and technology, 1980(3)
39. Xu xiaozu, Oliphant J.L. and Tice A. R. Experimental study on factors affecting water migration in frozen morin clay. Proceeding of 4th International Symposium on ground freezing, 1985, Vol 1
40．丘国庆，E．张伯伦，I．伊斯坎达．莫玲粘土冻结过程中的离子、水分迁移和冻胀．冰川冻土，1986，8(1)
41. Yoshiuke Nakano. Transport of Water in Frozen Soil[J]. Advance in Water Resource, 1984
42. Yang Daiquan, etc. Modeling fully Coupled Moisture, Air and Heat Transfer in Unsaturated Soils. Chinese Journal of Geotechnical Engineering, 2000,22(3)
43．徐伯孟，卢兴良．粘性土水分状况对冻胀的影响．冰川冻土，1986，8(3)
44．崔托维奇著，张长庆、朱元林译．冻土力学．北京：科学出版社，1985
45．吴紫汪等．土的冻胀性实验研究．中国科学院兰州冰川冻土研究所集刊．北京：科学出版社，1981
46．林世荣，包俊超，兰荣旺．冻融试验研究．岩土工程技术，2001，No3
47．徐学祖．冻土与盐溶液系统中热质迁移及变形过程试验研究．冰川冻土，1992，14(4)
48．楼玲玲，蔡正升，朱玉龙．湿型中水分迁移及其对温度场的影响．铸造，2000，49(1)
49．何平，程国栋，俞祁浩，朱元林、徐学祖．饱和正冻土中的水、热、力场耦合模型．冰川冻土，2000，22 (2)
50. J. T. Holden. Heat transfer in artificial ground freezing. Ground Freezing, Knutsson(ed.),1997, Balkema, Rotterdam
51．周希圣．隧道冻结工程水、温度、应力、位移场的耦合研究[D]．徐州：中国矿业大学，1998
52. Williams P.J. Properties and Behavior of Freezing Soils Norwegian Geotechnical Institute, Publ. 1967
53．刘宏绪．对土体冻结过程中若干冻胀力学问题的商榷[J]．冰川冻土，1990，12(3)
54．吴紫汪．富冰土的热胀性质[J]．冰川冻土，1990，12(3)
55．高大钊主编．软土地基理论与实践．北京：中国建筑工业出版社、上海：同济大学出版社，1992
56．徐学祖，王家澄，张立新．冻土物理学．北京：科学出版社，2001
57．中国科学院兰州冰川冻土研究所、煤炭工业部特殊凿井公司．冻结凿井冻土壁的工程性质．兰州：兰州大学出版社，1988
58．沈言俐等．土壤水分运动基本参数测定[J]．冰川冻土，1984，6(4)
59. Harlan R. L. Analysis of Couple Heat-Fluid Transport in Partially Frozen Soil. Water Research, 1973, 2
60．徐学祖等．饱水正冻土中水分迁移特征研究．第五届国际冻土学术会议论文集，1988
61．李述讯．冻、融土中的水热输运问题．兰州：兰州大学出版社，1993
62．上海隧道工程股份有限公司，中国矿业大学．盾构隧道冻结加固技术研究，1996
63．上海隧道施工技术研究所，中国矿业大学．上海软土低温特性研究，1995
64．上海隧道施工技术研究所，中国矿业大学．上海软土地层浅覆土盾构隧道冻结加固模拟试验研究，1996
65．中煤特殊工程公司．上海延东隧道复线冻结工程施工总结．1996
66．上海隧道工程股份有限公司．泥水平衡盾构穿越冻结加固区施工技术，1996
67．中国矿业大学．上海延安东路隧道复线冻结工程监测技术及冻土热力参量分析，1996
68．杨平，皮爱如．高流速地下水流地层冻结壁冻结壁形成的研究[J]．岩土工程学报，2001，23(2)
69．白以龙，周恒．迎接新世纪挑战的力学—力学学科21世纪初发展战略的建议[J]．力学与实践，1999．21(1)
70. Ladanyi B. Geotechnique for cold regions. Nerk:McGraw-Hill Book company, 1978
71. Bonacina C, Comini G, Fasano A, etal. Numerical solution of phase-change problems. Int J Heat Mass Transfer, 1973,16(6)
72. Konard J. M., Morgenstern N. R.. The segregation potential of a freezing soil [J]. Can. Geotech. J., 1981,18
73．徐学祖，J．L．奧利丰特，A．R．泰斯．线性温度梯度下非饱和冻结莫玲粘土中的水分迁移．冰川冻土，1985，7 (2)
74. Bathe K. J., Khoshgoftaar M.R., Finite element free surface seepage analysis without mesh iteration. Int. J Numerical Analytical Methods in Geomechanics, 1979,3(1)
75．徐学祖．土水势、未冻水含量和温度．冰川冻土，1985，7(1)
76．盛煜，马巍，侯仲杰．正冻土中水分迁移的迁移势模型．冰川冻土，1993，15(1)
77. G. Lame and B.P. Clapeyron. Ann, Chem. Phys., 1831.
78. H.S. Carslaw and J.C.Jaeger, Conduction of heat in solids, 2nd ed.,Clarendon Press, London, 1959.
79. S. Paterson, Proc. Glasgow Math. Assoc. 1,42-47,1952-53.
80. J. T.Holden. Heat transfer in artificial ground freezing. Ground Freezing, Knutsson(ed), 1997, Balkema, Rotterdam
81. Ershov E. D..Water migration and cryogenic structure in fine grained soils. Moscow: Publishing housing of Moscow State University, 1979
82. Ershov E.D..Physico-chemistry and mechanics of frozen soils. Moscow: Publishing housing of Moscow State University, 1986
83. F.J. Sanger, F.H. Sayles. Thermal and theological computations for artificially frozen ground construction. Engineering Geology, 1979,13
84．蒋斌松，陈伟．立井冻结壁初应力场分析．山东矿业学院学报，1995，14(2)
85．孙家学、刘斌．冻结壁原始冻胀力的分析与计算方法．东北大学学报(自然科学版)，1995，16(3)
86. Beskow G. Soil freezing and frost heaving with special application to roads and railroads [J]. Swedish Geol. Survey Yearbook, 1985,26(3)
87. Everett D.H. The thermodynamics of frost damage to porous solids [J]. Trans. Faraday Soc., 1961,57
88. Miller R.D.. Freezing and heaving of saturated and unsaturated soils [J]. Highway Record, 1972,393
89. Miller R.D.. Lens initiation in secondary frost heaving [R]. Sweden: Int. Symp. On frost
action in soils, 1977
90．崔托维奇著．冻土上的地基与基础(中译本)．北京：中国工业出版社，1985
91．陈传璋，侯宗义，李明忠．积分方程论极其应用．上海：上海科学技术出版社，1987．
92．王云甫．弹性理论(第二版)．北京：科学出版社，1984
93. Zhang Lixin, Pu Yibin, Liao Quanrong, Gu Tongxin. Dynamic investigation of mass transfer in freezing soil with computer tomography. Ground Freezing, Knutsson(ed.), 1997, Balkema, Rotterdam
94. Xu Xiaozu, Deng Yousheng, Gao Weiyue, Wang Fenge. Water and solute migration of freezing soils in closed system under temperature gradients. Ground Freezing, Yu and Wang(eds.), 1991, Balkema, Rotterdam
95. Magean D.W., and N.R. Morgensterm. Observation on moisture migration in frozen soils. Can. Geotech. J. 17
96. Kay B. D. and Perfaet E.. State of the art: Heat and mass transfer in freezing soils. Proceedings of 5th International Symposium on ground freezing, 1988
97. Burr T P., Williams P J..Hydraulic Conductivity Functions of Frozen Soils[J]. Earth Surface Processes, 1976.
98. Black P B., Miller R D.. Hydranlie Conductivity and Unfrozen Water Content of Air-Free Frozen Silt[J]. War. Resour. Res. 1990, 26.
99. Muhammad Sahimi. Flow and transport in porous media and fractured rock-from classical method to modern approaches [J]. VCH Verlagsgesellschaft MBH, 1995
100. Horiguchi K., Miller R D..Hydraulic Conductivity Functions of Frozen Materials[A]. 4th Int. Conf. on Permafrost[c]. Washington D. C.: National Academy Press, 1983.
101. O'Neill k., Miller R D..Exploration of a Rigid-Ice of Frost Heave[j]. Wat. Resour. Res., 1985, 21.
102. Horiguchi K., Miller R.D.. Hydraulic conductivity function of frozen materials [A]. 4th Int. Conf. on Permafrost [C]. Washington D.C.: National Academy Press. 1983
103．徐学祖，邓右生．冻土中水分迁移的实验研究[M]．北京：科学出版社，1991
104. Witten T A, Sander L M. Diffusion-limited aggregation, a kinetic critical phenomenon[J]. Phys. Rev. Lett., 1981, 47105. Anderson D.M., Tice A.C.. Predicting unfrozen water contents in frozen soils from surface area measuraments [J]. Highway Research Record, 1972,393
105. Anderson D M., Tice A C..Predicting Unfrozen Water Contents in Frozen Soils from Surface Area Measurement[J]. Highway Research Record, 1972.
106．林瑞泰．多孔介质传热传质引论．科学出版社，1995．
107．曾海容，宋惠珍．地下流体场与应力场耦合方程的有限元法．石油勘探与开发，1998，25(4)
108．Kunieda T, Sato T, Ido S. Numerical case studies of ground freezing for the construction of drain pump chambers．In．Ground freezing91. Rotterdam: Balkema. 1991
109．陈宝明．多孔介质中水平温度梯度和浓度梯度导致的自然对流传热传质．山东建筑工程学院学报，1998，13(1)
110．徐曾和，徐小荷．二维应力场下承压地层中渗流的液固耦合问题．岩石力学与工程学报，1999，18(6)
111．余扬政，冯承天，物理学中的几何方法，高等教育出版社、施普林格出版社，1998．
112. N. Wakao and S. Kaguei, Heat and Mass Transfer in Packed Beds, Gordon and Breach, Science Publishers, Inc.,1982.
113. W.M. Kays, Convective Heat and Mass Transfer, McGraw-Hill, New York, 1966.
49 90．舒茨B．F．，数学物理中的几何方法．冯承天等译．上海：科学技术文献出版社，1986
114. W. Pogorzelski, Integral equations and their applications, Vol. 1, Pwn-Polish Scientific Publishers, Warszawa, 1966.
115．Y．S．杜洛金，固体热物理性质导论—理论和测量．奚同庚等译．中国计量出版社，1987
116．卢焕忠．场论极其应用．湖南科学技术出版社，1981．
117．王潼．热势论．科学出版社，1980
118．刘连寿，王正清．数学物理方法．高等教育出版社，1990
119. Kujala K. Factors affecting frost susceptibility and heaving pressure in soils [D]. Finland:University of Oulu, 1991
120. Guymon GL, Luthin JN.A coupled heat and moisture transport model for arctic soils[J]. Wat. Resour. Res.,1974
121. Biermans M B G M, Garg S Z, Pritchett J W. Governing equations for geothermal reservoirs [J].Wat. Resour. Res.,1977,13
122．郭宽良等．计算传热学．合肥：中国科技大学出版社，1988
123．俞昌铭．热传导及其数值分析．北京：清华大学出版社，1982
124．钱壬章，俞昌铭，林文贵．传热分析与计算．北京：高等教育出版社，1987
125．施天谟[美]．计算传热学．北京：科学出版社，1987
126．孔祥谦．有限单元法在传热学中的应用(第三版)．北京：科学出版社，1998
127．张鸣歧．应用泛函分析引论．北京：北京理工大学出版社，1989
128．刘高典．温度场的数值模拟．重庆：重庆大学出版社，1990