土体冻融特性试验研究现状与思考

doi:10.13722/j.cnki.jrme.2021.0433

摘要
图/表
参考文献
相关文章 (15)

全文: PDF (2452 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要冻融试验是获取冻土物理力学参数、评估冻土工程特性的重要手段。从冻土水热参数、力学参数、冻胀机制和融沉机制4个方面对土体冻融特性试验研究进行综述，对主要水热力参数的试验方法和试验设备进行汇总说明，对理论模型的发展过程及试验验证进行归纳整理。试验装置的变温控制性能是影响冻土试验数据质量的重要因素，但当前高精度冷却液循环控温设备的国产化程度较低，高性能冻融试验系统仍主要依赖进口。因此在开展冻土试验和理论研究的同时，对于试验设备的研发工作同样需引起重视。由神经网络–PID算法和热电制冷模块组成的固态控温系统可以解决试验装置的变温控制问题。固态控温系统的高变温控制性能具备模拟复杂冻结过程的能力。将其与新型传感技术结合，如光纤压力传感技术、线阵CCD扫描成像技术，可以为冻土研究提供新的试验方案，以此促进土体冻融机制研究，为我国寒区工程建设提供参考。

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	周永毅
	张建经
	闫世杰
	牛家永
	谢强

关键词 ：土力学, 冻融试验, 控温技术, 固态制冷, 变温控制, 冻土

Abstract：The freezing-thawing test is vital to obtain the physical parameters and to evaluate the engineering characteristics of frozen soils. In this paper，the experimental study on frozen soils is reviewed from four aspects：hydrothermal parameters，mechanical parameters，frost heaving and thaw settlement mechanisms. The main test methods and equipments of thermal-hydro-mechanical parameters are presented. The development and experimental verification of the theoretical models are summarized. The variable temperature control ability of the equipments is important for the data quality of frozen soil tests. However，the domestic manufacturing level of low temperature coolant circulation pumps with high pecision is immature in China. Freezing-thawing test systems with high performance are still mainly dependent on imports. Therefore，attention should be paid to the research and development of test equipments when the experiment and theoretical researches on frozen soils are carried out. The neural network-PID algorithm combined with the solid-state refrigeration system is capable to solve the problem of variable temperature control of test equipments. The high variable temperature control performance of the solid-state refrigeration system has the ability to simulate the complex freezing process. Combined with new sensing technologies，such as fiber optic pressure sensing technology and linear CCD scanning imaging technology，the solid-state refrigeration system can provide new experimental schemes for the frozen soil research. The improvement of the test technology can promote the research of freezing and thawing mechanism of soils and provide reference for the engineering construction in the cold regions of China.

Key words： soil mechanics freezing and thawing test temperature control technology solid-state refrigeration variable temperature control freezing soil

引用本文:

周永毅，张建经，闫世杰，牛家永，谢强. 土体冻融特性试验研究现状与思考[J]. 岩石力学与工程学报, 2022, 41(6): 1267-1284.
ZHOU Yongyi，ZHANG Jianjing，YAN Shijie，NIU Jiayong，XIE Qiang. Advance and review on the experimental researches of the freezing and thawing characteristics of soils. , 2022, 41(6): 1267-1284.

链接本文:

http://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2021.0433 或 http://rockmech.whrsm.ac.cn/CN/Y2022/V41/I6/1267

[14]	WANG Q，QI J，WANG S，et al. Effect of freeze-thaw on freezing point of a saline loess[J]. Cold Regions Science and Technology，2020，170：102922.
[49]	EVERETT D H. The thermodynamics of frost damage to porous solids[J]. Transactions of the Faraday society，1961，57：1 541–1 551.
[2]	DIMILLIO A F. A quarter century of geotechnical research[R]. Washington：Federal Highway Administration(FHWA)，U. S. Department of Transportation，1998.
[12]	马巍，王大雁. 冻土力学[M]. 北京：科学出版社，2014：23–132.(MA Wei，WANG Dayan. Mechanics of frozen soil[M]. Beijing：Science Press，2014：23–132.(in Chinese))
[32]	朱元林. 我国冻土强度与蠕变研究[J]. 冰川冻土，1988，10(3)：332–337.(ZHU Yuanlin. Studies of strength and creep behaviour of frozen soils in china[J]. Journal of Glaciology and Geocryology，1988，10(3)：332–337.(in Chinese))
[10]	TABER S. The mechanics of frost heaving[J]. The Journal of Geology，1930，38(4)：303–317.
[30]	SAYLES F H. Creep of frozen sands[R]. Hanover：U. S. Army Cold Regions Research and Engineering Laboratory，1968.
[80]	MING F，LI D. A model of migration potential for moisture migration during soil freezing[J]. Cold Regions Science and Technology，2016，124：87–94.
[110]	QI J L，YAO X L，YU F，et al. Study on thaw consolidation of permafrost under roadway embankment[J]. Cold Regions Science and Technology，2012，81：48–54.
[28]	ROGGENSACK W D. Geotechnical properties of fine-grained permafrost soils[Ph. D. Thesis][D]. Alberta：University of Alberta，1977.
[68]	KONRAD J M. Frost susceptibility related to soil index properties[J]. Canadian Geotechnical Journal，1999，36(3)：403–417.
[26]	DUNNICLIFF J，GREEN E. Geotechnical instrumentation for monitoring field performance[M]. New York：Wiley，1993：117–163.
[66]	KONRAD J M. Frost heave mechanics[Ph. D. Thesis][D]. Alberta：University of Alberta，1980.
[96]	TSYTOVICH N A. Mechanics of frozen ground[M]. New York：Scripta，McGraw-Hill，1975：126–132.
[27]	KIA M. Measuring pore-water pressure in partially frozen soils[Ph. D. Thesis][D]. Alberta：University of Alberta，2012.
[97]	童长江. 我国冻土融化压缩特性研究[J]. 冰川冻土，1989，10(3)：327–331.(TONG Changjiang. Compression characteristics of thawing permafrost[J]. Journal of Glaciology and Geocryology，1989，10(3)：327–331.(in Chinese))
[55]	MILLER R D. Ice sandwich：functional semipermeable membrane[J]. Science，1970，169(3945)：584–585.
[65]	HILL D W. The influence of temperature and load on moisture transfer in freezing soils[Ph. D. Thesis][D]. Alberta：University of Alberta，1977.
[85]	HOPKE S W. A model for frost heave including overburden[J]. Cold Regions Science and Technology，1980，3(2/3)：111–127.
[3]	程国栋. 青藏高原多年冻土区路基工程地质研究[J]. 第四纪研究，2003，23(2)：134–139.(CHENG Guodong. Research on engineering geology of the roadbed in permafrost regions of Qinghai—Tibet plateau[J]. Quaternary Sciences，2003，23(2)：134–139.(in Chinese))
[5]	陶祥令. 多年冻土区路基纵向裂缝形成机理及演化规律研究[博士学位论文][D]. 徐州：中国矿业大学，2017.(TAO Xiangling. Study of formation machenism and evolution law of longitudinal cracks in permafrost region subgrade[Ph. D. Thesis][D]. Xuzhou：China University of Mining and Technology，2017.(in Chinese))
[7]	周家作，谭龙，韦昌富，等. 土的冻结温度与过冷温度试验研究[J]. 岩土力学，2015，36(3)：777–785.(ZHOU Jiazuo，TAN Long，WEI Changfu，et al. Experimental research on freezing temperature and supercooling temperature of soil[J]. Rock and Soil Mechanics，2015，36(3)：777–785.(in Chinese))
[9]	赵淑萍，朱元林，何平，等. 冻土动力学参数测试研究[J]. 岩石力学与工程学报，2003，22(增2)：2 677–2 681.(ZHAO Shuping，ZHU Yuanlin，HE Ping，et al. Testing study on dynamic mechanics parameters of frozen soil[J]. Chinese Journal of Rock Mechanics and Engineering，2003，22(Supp.2)：2 677–2 681.(in Chinese))
[13]	中华人民共和国国家标准编写组. GB/T50123—2019 土工试验方法标准[S]. 北京：中国计划出版社，2019.(The National Standards Compilation Group of People?s Republic of China. GB/T50123—2019 standard for geotechnical test methods[S]. Beijing：China Planning Press，2019.(in Chinese))
[15]	KOZLOWSKI T. Some factors affecting supercooling and the equilibrium freezing point in soil-water systems[J]. Cold Regions Science and Technology，2009，59(1)：25–33.
[17]	KOZLOWSKI T. A comprehensive method of determining the soil unfrozen water curves：1. Application of the term of convolution[J]. Cold Regions Science and Technology，2003，36(1–3)：71–79.
[19]	路建国，张明义，张熙胤，等. 冻融过程中未冻水含量及冻结温度的试验研究[J]. 岩石力学与工程学报，2017，36(7)：1 803–1 812. (LU Jianguo，ZHANG Mingyi，ZHANG Xiyin，et al. Experimental study on the unfrozen water content and the freezing temperatureduring freezing and thawing processes[J]. Chinese Journal of Rock Mechanics and Engineering，2017，36(7)：1 803–1 812. (in Chinese))
[20]	SPAANS E，BAKER J. Examining the use of time domain reflectometry for measuring liquid water content in frozen soil[J]. Water Resources Research，1995，31(12)：2 917–2 925.
[63]	GILPIN R R. A model for the prediction of ice lensing and frost heave in soils[J]. Water Resources Research，1980，16：918–930.
[73]	MIZOGUCHI M. Water heat and salt transport in freezing soil[Ph. D. Thesis][D]. Tokyo：University of Tokyo，1990.
[83]	JAME Y W. Heat and mass transfer in freezing unsaturated soil[Ph. D. Thesis][D]. Saskatchewan：University of Saskatchewan，1977.
[1]	周幼吾，郭东信，邱国庆，等. 中国冻土[M]. 北京：科学出版社，2000：1–2.(ZHOU Youwu，GUO Dongxin，QIU Guoqing，et al. Geocryology in China[M]. Beijing：Science Press，2000：1–2.(in Chinese))
[4]	冯子亮，盛煜，陈继，等. 青海省共和—玉树高速公路沿线典型冻土路基保护多年冻土效果的初步分析[J]. 岩石力学与工程学报，2016，35(3)：638–648.(FENG Ziliang，SHENG Yu，CHEN Ji，et al. A preliminary analysis of protective effect on permafrost of typical embankment along Gonghe—Yushu highway[J]. Chinese Journal of Rock Mechanics and Engineering，2016，35(3)：638–648.(in Chinese))
[6]	董旭光. 多年冻土区新型框架热锚管边坡支护结构的工作机理及试验研究[博士学位论文][D]. 兰州：兰州理工大学，2017.(DONG Xuguang. Research on the working mechanism and experiment of the new frame heat anchor pipe supporting structure for permafrost slope[Ph. D. Thesis][D]. Lanzhou：Lanzhou University of Technology，2017.(in Chinese))
[8]	宋春霞，齐吉琳，刘奉银. 冻融作用对兰州黄土力学性质的影响[J]. 岩土力学，2008，29(4)：1 077–1 086.(SONG Chunxia，QI Jilin，LIU Fengyin. Influence of freeze-thaw on mechanical properties of Lanzhou loess[J]. Rock and Soil Mechanics，2008，29(4)：1 077– 1 086.(in Chinese))
[11]	MILLER R D，LOCH J P G，BRESLER E. Transport of water and heat in a frozen permeameter[J]. Soil Science Society of America Journal，1975，39(6)：1 029–1 036.
[16]	LI G Y，ZHANG J，ZHOU Z，et al. A novel freezing point determination method for oil-contaminated soils based on electrical resistance measurement and its influencing factors[J]. Science of the Total Environment，2020，721：137821.
[21]	刘振亚，刘建坤，李旭，等. 毛细黏聚与冰胶结作用对非饱和粉质黏土冻结强度及变形特性的影响[J]. 岩石力学与工程学报，2018，37(6)：1 551–1 559.(LIU Zhenya，LIU Jiankun，LI Xu，et al. Effect of capillary cohesion and ice cementation on strength and deformation of unsaturated frozen silty clay[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(6)：1 551–1 559.(in Chinese))
[31]	HAYNES F D，KARALIUS J A，KALAFUT J. Strain rate effect on the strength of frozen silt[R]. Hanover：U. S. Army Cold Regions Research and Engineering Laboratory，1975.
[41]	STEVENS H W. The response of frozen soils to vibratory loads[R]. Hanover：U. S. Army Cold Regions Research and Engineering Laboratory，1975.
[51]	PENNER E. Heaving pressure is soils during unidirectional freezing. Canadian Geotechnical Journal，1967，4(4)：398–408.
[57]	LOCH J P G，KAY B D. Water redistribution in partially frozen，saturated silt under several temperature gradients and overburden loads[J]. Soil Science Society of America Journal，1978，42(3)：400–406.
[60]	PENNER E，UEDA T. The dependence of frost heaving on load application-preliminary results[C]// Proceedings of the 2nd International Symposium on Frost Action in Soils，University of Lulea，Sweden. Ottawa：the National Research Council of Canada，1977：12–23.
[61]	KONRAD J M，MORGENSTERN N R. The segregation potential of a freezing soil[J]. Canadian Geotechnical Journal，1981，18：482–491.
[67]	KONRAD J M，LEMIEUX N. Influence of fines on frost heave characteristics of a well-graded base-course material[J]. Canadian Geotechnical Journal，2005，42(2)：515–527.
[70]	LI N，CHEN F，SU B，et al. Theoretical frame of the saturated freezing soil[J]. Cold Regions Science and Technology，2002，35(2)：73–80.
[71]	ZHOU G，ZHOU Y，HU K，et al. Separate-ice frost heave model for one-dimensional soil freezing process[J]. Acta Geotechnica，2018，13(1)：207–217.
[75]	PAINTER S L. Three-phase numerical model of water migration in partially frozen geological media：model formulation，validation，and applications[J]. Computational Geosciences，2011，15(1)：69–85.
[77]	徐斅祖，邓友生. 冻土中水分迁移的实验研究[M]. 北京：科学出版社，1991：9–35.(XU Xiaozu，DENG Yousheng. Experimental study on water transport in frozen soil[M]. Beijing：Science Press，1991：9–35.(in Chinese))
[81]	JAME Y W，NORUM D I. Phase composition of a partially frozen soil[M]. Saskatchewan：Agricultural Engineering Department，University of Saskatchewan，1973：1–18.
[91]	MIZOGUCHI M. Water，heat and salt transport in freezing soil[Ph. D. Thesis][D]. Tokyo：University of Tokyo，1990.
[18]	LI Z，CHEN J，SUGIMOTO M. Pulsed NMR measurements of unfrozen water content in partially frozen soil[J]. Journal of Cold Regions Engineering，2020，34(3)：1–10.
[24]	ZHANG H，ZHANG J，ZHANG Z，et al. Variation behavior of pore-water pressure in warm frozen soil under load and its relation to deformation[J]. Acta Geotechnica，2020，15(3)：603–614.
[34]	常丹，刘建坤，李旭，等.冻融循环对青藏粉砂土力学性质影响的试验研究[J]. 岩石力学与工程学报，2014，33(7)：1 496–1 502. (CHANG Dan，LIU Jiankun，LI Xu，et al. Experiment study of effects of freezing-thawing cycles on mechanical properties of Qinghat-Tibet silty sand[J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(7)：1 496–1 502.(in Chinese))
[36]	AL-HUNAIDI M O，CHEN P A，RAINER J H，et al. Shear moduli and damping in frozen and unfrozen clay by resonant column tests[J]. Canadian Geotechnical Journal，1996，33(3)：510–514.
[38]	徐学燕，仲丛利，陈亚明，等. 冻土的动力特性研究及其参数确定[J]. 岩土工程学报，1998，20(5)：80–84.(XU Xueyan，ZHONG Congli，CHEN Yaming，et al. Research on dynamic characters of frozen soil and determination of its parameters[J]. Chinese Journal of Geotechnical Engineering，1998，20(5)：80–84.(in Chinese))
[44]	陈世杰，马巍，李国玉，等. 与医用CT配合使用的冻土三轴仪的研制与应用[J]. 岩土力学，2017，38(增2)：359–367.(CHEN Shijie，MA Wei，LI Guoyu，et al. Development and application of triaxial apparatus of frozen soil used in conjunction with medical CT[J]. Rock and Soil Mechanics，2017，38(Supp.2)：359–367.(in Chinese))
[46]	凌贤长，徐学燕，邱明国，等. 冻结哈尔滨粉质黏土动三轴试验CT检测研究[J]. 岩石力学与工程学报，2003，22(8)：1 244–1 249. (LING Xianzhang，XU Xueyan，QIU Mingguo，et al. Study on CT scanning of Harbin frozen silt clay before and after dynamic triaxial test[J]. Chinese Journal of Rock Mechanics and Engineering，2003，22(8)：1 244–1 249.(in Chinese))
[48]	赵福堂，常立君，张吾渝. 循环应力比和振动频率对盐渍土微观结构影响分析[J]. 冰川冻土，2020，42(3)：854–864.(ZHAO Futang，CHANG Lijun，ZHANG Wuyu. Analysis on the influence of cyclic stress ratio and vibration frequency on microstructure of saline soil[J]. Journal of Glaciology and Geocryology，2020，42(3)：854–864.(in Chinese))
[54]	MILLER R D. Freezing and heaving of saturated and unsaturated soils[J]. Highway Research Record，1972，393(1)：1–11.
[56]	WATANABE K，OSADA Y. Comparison of hydraulic conductivity in frozen saturated and unfrozen unsaturated soils[J]. Vadose Zone Journal，2016，15(5)：1–7.
[58]	AKAGAWA S. Experimental study of frozen fringe characteristics[J]. Cold Regions Science and Technology，1988，15(3)：209–223.
[64]	BROWN S C，PAYNE D. Frost action in clay soils：2. Ice and water location and suction of unfrozen water in clays below 0℃[J]. Journal of Soil Science，1990，41(4)：547–561.
[74]	LIU Z，YU X. Coupled thermo-hydro-mechanical model for porous materials under frost action：theory and implementation[J]. Acta Geotechnica，2011，6(2)：51–65.
[76]	WU D，LAI Y，ZHANG M. Heat and mass transfer effects of ice growth mechanisms in a fully saturated soil[J]. International Journal of Heat and Mass Transfer，2015，86：699–709.
[84]	PENNER E. Aspects of ice lens growth in soils[J]. Cold regions Science and Technology，1986，13(1)：91–100.
[22]	KONRAD J M. Pore water pressure at an ice lens：its measurement and interpretation[J]. Cold Regions Science and Technology，1989，16(1)：63–74.
[23]	张莲海，马巍，杨成松. 冻融循环过程中土体的孔隙水压力测试研究[J]. 岩土力学，2015，36(7)：1 856–1 864.(ZHANG Lianhai，MA Wei，YANG Chengsong. Pore water pressure measurement for soil subjected to freeze-thaw cycles[J]. Rock and Soil Mechanics，2015，36(7)：1 856–1 864.(in Chinese))
[25]	BARBERIS V. Transmission of pressure states in soils[C]// Proceedings of the 6th International Conference on Soil Mechanics and Foundation Engineering. Montreal，Toronto：University of Toronto Press，1965：8–15.
[29]	晏长根，王婷，贾海梁，等. 冻融过程中未冻水含量对非饱和粉土抗剪强度的影响[J]. 岩石力学与工程学报，2019，38(6)：1 252–1 260.(YAN Changgen，WANG Ting，JIA Hailiang，et al. Influence of the unfrozen water content on the shear strength of unsaturated silt during freezing and thawing[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(6)：1 252–1 260.(in Chinese))
[33]	马巍，徐学祖，张立新. 冻融循环对石灰粉土剪切强度特性的影响[J]. 岩土工程学报，1999，21(2)：158–160.(MA Wei，XU Xuezu，ZHANG Lixin. Influence of frost and thaw cycles on shear strength of lime silt[J]. Chinese Journal of Geotechnical Engineering，1999，21(2)：158–160.(in Chinese))
[35]	王大雁，马巍，常小晓，等. 冻融循环作用对青藏黏土物理力学性质的影响[J]. 岩石力学与工程学报，2005，24(23)：4 313– 4 319.(WANG Dayan，MA Wei，CHANG Xiaoxiao，et al. Physico-mechanical properties changes of Qinghai—Tibet clay due to cyclic freezing and thawing[J]. Chinese Journal of Rock Mechanics and Engineering，2005，24(23)：4 313–4 319.(in Chinese))
[37]	郭妍，王大雁，马巍，等. 冻土空心圆柱仪的研发与应用[J]. 哈尔滨工业大学学报，2016，48(12)：114–120.(GUO Yan，WANG Dayan，MA Wei，et al. Development and application of frozen hollow cylinder apparatus[J]. Journal of Harbin Institute of Technology，2016，48(12)：114–120.(in Chinese))
[39]	LING X Z，LI Q L，WANG L，et al. Stiffness and damping radio evolution of frozen clays under long-term low-level repeated cyclic loading：experimental evidence and evolution model[J]. Cold Regions Science and Technology，2013，86：45–54.
[40]	赵福堂，常立君，张吾渝. 温度变化条件下路基盐渍土动应力-动应变响应规律研究[J]. 铁道标准设计，2019，63(5)：54–59. (ZHAO Futang，CHANG Lijun，ZHANG Wuyu. Study on the dynamic stress-strain response of subgrade saline soil under temperature change condition[J]. Railway Standard Design，2019，63(5)：54–59.(in Chinese))
[43]	CHEN D，WANG D，MA W，et al. A strength criterion for frozen clay considering the influence of stress Lode angle[J]. Canadian Geotechnical Journal，2019，56(11)：1 557–1 572.
[45]	刘增利，李洪升，朱元林，等. 冻土初始与附加细观损伤的CT识别模型[J]. 冰川冻土，2002，24(5)：676–680.(LIU Zengli，LI Hongsheng，ZHU Yuanlin，et al. Distinguish model for initial and additional micro-damages on frozen soil[J]. Journal of Glaciology and Geocryology，2002，24(5)：676–680.(in Chinese))
[47]	薛珂，温智，马小涵，等. 冻结作用对青藏红黏土及兰州粉土微观结构的影响分析[J]. 冰川冻土，2019，41(5)：1 122–1 129. (XUE Ke，WEN Zhi，MA Xiaohan，et al. Effect of freezing on the microstructure of Qinghai—Tibet red clay and Lanzhou silt[J]. Journal of Glaciology and Geocryology，2019，41(5)：1 122–1 129.(in Chinese))
[50]	VIGNES M，DIJKEMA K M. A model for the freezing of water in a dispersed medium[J]. Journal of Colloid and Interface Science，1974，49(2)：165–172.
[53]	HARLAN R L. Analysis of coupled heat-fluid transport in partially frozen soil[J]. Water Resources Research，1973，9(5)：1 314–1 323.
[42]	于啸波，孙锐，袁晓铭，等. 负温对土动剪切模量阻尼比的影响规律[J]. 岩石力学与工程学报，2016，35(7)：1 452–1 465. (YU Xiaobo，SUN Rui，YUAN Xiaoming，et al. Influence of negative temperature on dynamic shear modulus and damping ratio of soil[J]. Chinese Journal of Rock Mechanics and Engineering，2016，35(7)：1 452–1 465.(in Chinese))
[52]	LOCH J P G，MILLER R D. Tests of the concept of secondary frost heaving[J]. Soil Science Society of America Journal，1975，39(6)：1 036–1 041.
[62]	SHENG D，AXELSSON K，KNUTSSON S. Frost heave due to ice lens formation in freezing soils：2. Field application[J]. Hydrology Research，1995，26(2)：147–168.
[72]	周扬，周国庆，王义江. 饱和土水热耦合分离冰冻胀模型研究[J]. 岩土工程学报，2010，32(11)：1 746–1 751.(ZHOU Yang，ZHOU Guoqing，WANG Yijiang. Separate ice frost heave model for coupled moisture and heat transfer in saturated soils[J]. Chinese Journal of Geotechnical Engineering，2010，32(11)：1 746–1 751. (in Chinese))
[78]	何平，程国栋，俞祁浩，等. 饱和正冻土中的水、热、力场耦合模型[J]. 冰川冻土，2000，22(2)：135–138.(HE Ping，CHENG Guodong，YU Qihao，et al. A couple model of heat，water and stress fields of saturated soil during freezing[J]. Journal of Glaciology and Geocryology，2000，22(2)：135–138.(in Chinese))
[82]	TAYLOR G S，LUTHIN J N. A model for coupled heat and moisture transfer during soil freezing[J]. Canadian Geotechnical Journal，1978，15(4)：548–555.
[86]	RIEKE R D. The role of specific surface area and related index properties in the frost susceptibility of soils[M. S. Thesis][D]. Oregon：Oregon State University，1982.
[88]	KONRAD J M. Sixteenth Canadian geotechnical colloquium：frost heave in soils：concepts and engineering[J]. Canadian Geotechnical Journal，1994，31(2)：223–245.
[92]	HE Z，TENG J，YANG Z，et al. An analysis of vapour transfer in unsaturated freezing soils[J]. Cold Regions Science and Technology，2020，169：102914.
[94]	ZHANG Y，MICHALOWSKI R L. Thermal-hydro-mechanical analysis of frost heave and thaw settlement[J]. Journal of geotechnical and geoenvironmental engineering，2015，141(7)：325–329.
[98]	张喜发，陈继，张冬青. 融沉系数在季冻区高速公路路基冻害研究中的应用[J]. 冰川冻土，2003，24(5)：634–638.(ZHANG Xifa，CHEN Ji，ZHANG Dongqing. Application of thawing settlement coefficient to the research on the roadbed frost damage of freeway in seasonal frost region[J]. Journal of Glaciology and Geocryology，2003，24(5)：634–638.(in Chinese))
[101]	中华人民共和国行业标准编写组. JGJ118—98 冻土地区建筑地基基础设计规范[S]. 北京：中国建筑工业出版社，1999.(The Professional Standards Compilation Group of People?s Republic of China. JGJ118—98 The designing criterion of the foundations in permafrost regions[S]. Beijing：China Architecture and Building Press，1999.(in Chinese))
[102]	祁长青，吴青柏，施斌. 基于遗传算法的冻土路基融沉可靠性分析[J]. 岩土力学，2006，27(8)：1 429–1 432.(QI Changqing，WU Qingbai，SHI Bin. Reliability analysis of thawing settlement of permafrost subgrade based on genetic algorithm[J]. Rock and Soil Mechanics，2006，27(8)：1 429–1 432.(in Chinese))
[104]	FREMOND M，GHIDOUCHE H，POINT N. Freezing of a porous medium with water supply coupled Stefan problem[J]. Journal of mathematical analysis and applications，1985，108(2)：371–402.
[59]	HOEKSTRA P. Moisture movement in soils under temperature gradients with the cold-side temperature below freezing[J]. Water Resources Research，1966，2(2)：241–250.
[69]	KONRAD J M. Influence of overconsolidation on the freezing characteristics of a clayey silt[J]. Canadian Geotechnical Journal，1989，26(1)：9–21.
[79]	周金生，周国庆，马巍，等. 间歇冻结控制人工冻土冻胀的试验研究[J]. 中国矿业大学学报，2006，35(6)：708–712.(ZHOU Jinsheng，ZHOU Guoqing，MA Wei，et al. Experimental research on controlling frost heave of artificial frozen soil with intermission freezing method[J]. Journal of China University of Mining and Technology，2006，35(6)：708–712.(in Chinese))
[89]	KONRAD J M. Estimation of the segregation potential of fine-grained soils using the frost heave response of two reference soils[J]. Canadian Geotechnical Journal，2005，42(1)：38–50.
[99]	何平，程国栋，杨成松，等. 冻土融沉系数的评价方法[J]. 冰川冻土，2003，25(6)：608–613.(HE Ping，CHEN Guodong，YANG Chengsong，et al. The evaluation of thawing-settlement coefficient of frozen soils[J]. Journal of Glaciology and Geocryology，2003，25(6)：608–613.(in Chinese))
[106]	MORGENSTER N R，SMITH L B. Thaw-consolidation tests on remoulded clays[J]. Canadian Geotechnical Journal，1973，10(1)：25–40.
[108]	GIBSON R E，SCHIFFMAN R L，CARGILL K W. The theory of one-dimensional consolidation of saturated clays. II. Finite nonlinear consolidation of thick homogeneous layers[J]. Canadian Geotechnical Journal，1981，18(2)：280–293.
[109]	YAO X L，QI J L，WU W. Three dimensional analysis of large strain thaw consolidation in permafrost[J]. Acta Geotechnica，2012，7(3)：193–202.
[112]	周永毅，张建经. 一种新型冻土可视化试验系统及其在冻融试验中的应用[J]. 岩石力学与工程学报，2020，39(8)：1 671–1 681. (ZHOU Yongyi，ZHANG Jianjing. A novel visualization apparatus for freezing soils and its application in freezing-thawing test[J]. Chinese Journal of Rock Mechanics and Engineering，2020，39(8)：1 671– 1 681.(in Chinese))
[114]	牛家永，周永毅，张建经，等. 基于新型拉伸装置的根–土复合体抗拉强度研究[J]. 西南交通大学学报，2021，DOI：10.3969/j.issn.0258–2724. 20200077.(NIU Jiayong，ZHOU Yongyi，ZHANG Jianjing，et al. Experimental study on tensile strength of root and soil composite based on new tensile apparatus[J]. Journal of Southwest Jiaotong University，2021，DOI：10.3969/j.issn.0258–2724.20200077.(in Chinese))
[87]	KONRAD J M，MORGENSTERN N R. Effects of applied pressure on freezing soils[J]. Canadian Geotechnical Journal，1982，19(4)：494–505.
[90]	NAKANO Y. Quasi-steady problems in freezing soils：1. Analysis on the steady growth of an ice layer[J]. Cold Regions Science and Technology，1990，17(3)：207–226.
[95]	WATSON G H，SLUSARCHUK W A，ROWLEY R K. Determination of some frozen and thawed properties of permafrost soils[J]. Canadian Geotechnical Journal，1973，10(4)：592–606.
[100]	陈肖柏，刘建坤，刘鸿绪，等. 土的冻结作用与地基[M]. 北京：科学出版社，2006：297–327.(CHEN Xiaobai，LIU Jiankun，LIU Hongxu，et al. Frost action of soil and foundation engineering[M]. Beijing：Science Press，2006：297–327.(in Chinese))
[105]	MORGENSTERN N R，NIXON J F. One-dimensional consolidation of thawing soils[J]. Canadian Geotechnical Journal，1971，8(4)：558–565.
[107]	FORIERO A，LADANYI B. FEM assessment of large-strain thaw consolidation[J]. Journal of Geotechnical Engineering，1995，121(2)：126–138.
[115]	MOLLON G，ZHAO J. Fourier-Voronoi-based generation of realistic samples for discrete modelling of granular materials[J]. Granular Matter，2012，14(5)：621–638.
[93]	FUKUDA M，KIM H S，KIM Y C. Preliminary results of frost heave experiments using standard test sample provided by TC8[C]// Proceedings of the Ground Freezing 97：Frost Action in Soils Lulea，Sweden：[s. n.]，1997：25–30.
[103]	姚晓亮，齐吉琳. 融沉系数的人工神经网络预测方法[J]. 冰川冻土，2011，33(4)：891–896.(YAO Xiaoliang，QI Jilin. Artificial neural net work forecasting method for thaw-settlement coefficient[J]. Journal of Glaciology and Geocryology，2011，33(4)：891–896.(in Chinese))
[113]	周永毅，张建经，牛家永，等. 超声诱导成核技术在冻结温度试验中的应用[J]. 岩石力学与工程学报，2021，40(增2)：3 052–3 062. (ZHOU Yongyi，ZHANG Jianjing，NIU Jiayong. Application of ultrasonic-induced nucleation technology in the freezing point test[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(Supp.2)：3 052–3 062.(in Chinese))
[111]	YAO X L，QI J L，LIU M，et al. Pore water pressure distribution and dissipation during thaw consolidation[J]. Transport in Porous Media，2017，116(2)：435–451.