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| Study on characterization methods of three-dimensional spatial variability
of frozen soil layer and evolution process of temperature eigenvalue
of freezing curtain |
| WANG Tao1，2，MA Jun2，ZHOU Guoqing1，2，XU Daqing3，JI Yukun1 |
| (1. State Key Laboratory for Geomechanics and Deep Underground Engineering，China University of Mining and Technology，Xuzhou，Jiangsu 221116，China；2. School of Mechanics and Civil Engineering，China University of Mining and
Technology，Xuzhou，Jiangsu 221116，China；3. Anhui Transport Consulting and Design Institute Co.，Ltd.，
Hefei，Anhui 230088，China) |
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Abstract In order to characterize the natural three-dimensional(3D) spatial variability of frozen soil layer and to clarify the evolution process of temperature eigenvalue of freezing curtain，the thermal parameters of frozen soil layer are modeled as 3D random fields，and a new tetrahedral discretization methodology of 3D random field is proposed. An analytical formula and a numerical formula of the covariance for any two tetrahedral random field elements are developed by the volumetric coordinate transformation and gauss integral transformation. A stochastic analysis model for the thermal characteristics of freezing curtain considering the 3D spatial variability of frozen soil layer is established. The dynamic evolution process and statistical law of temperature eigenvalue are obtained，and the influence of the correlation structure of 3D random field on the temperature eigenvalue of the freezing curtain is discussed. The results show that the tetrahedral discretization methodology can be perfectly combined with the tetrahedral finite element method. Also，the corresponding relation is clearer and the computer codes are simpler. The spatial variability of thermal parameters of frozen soil has significant influence on the temperature eigenvalue of freezing curtain，and the spatial variability of thermal conductivity has the greatest influence. The effects of different correlation structure of 3D random field on temperature eigenvalue of freezing curtain are different. The triangle model has the greatest influence，the Gaussian model has the median value，and the exponential model has the least influence.
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| [1] 夏才初，林梓梁，施佳誉，等. 渐冻隧道演化模拟试验系统的研制及初步应用[J]. 岩石力学与工程学报，2021，40(8)：1 525–1 535. (XIA Caichu，LIN Ziliang，SHI Jiayu，et al. Development and preliminary application of a simulation test system for frost penetration tunnel evolution[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(8)：1 525–1 535.(in Chinese))
[2] ALZOUBI M A，NIE-ROUQUETTE A，SASMITO A P. Conjugate heat transfer in artificial ground freezing using enthalpy-porosity method：Experiments and model validation[J]. International Journal of Heat and Mass Transfer，2018，126：740–752.
[3] HU X D，FANG T，ZHANG L Y. Analytical solution to temperature distribution in frozen soil wall with wavy boundaries by single-row and double-row-piped freezing[J]. Cold Regions Science and Technology，2018，145：208–228.
[4] LI T，ZHOU Y，SHI X Y，et al. Analytical solution for the soil freezing process induced by an infinite line sink[J]. International Journal of Thermal Sciences，2018，127：232–241.
[5] HUANG S，GUO Y，LIU Y，et al. Study on the influence of water flow on temperature around freeze pipes and its distribution optimization during artificial ground freezing[J]. Applied Thermal Engineering，2018，135：435–445.
[6] 黄建华，严耿明，杨鹿鸣. 水泥改良土地层联络通道冻结温度场分析[J]. 土木工程学报，2021，54(5)：108–116.(HUANG Jianhua，YAN Gengming，YANG Luming. Analysis of freezing temperature field in connecting passage of cement improved soil layer[J]. China Civil Engineering Journal，2021，54(5)：108–116.(in Chinese))
[7] 胡向东，李忻轶，吴元昊，等. 拱北隧道管幕冻结法管间冻结封水效果实测研究[J]. 岩土工程学报，2019，41(12)：2 207–2 214.(HU Xiangdong，LI Xinyi，WU Yuanhao，et al. Effect of water-proofing in Gongbei tunnel by freeze-sealing pipe roof method with field temperature data[J]. Chinese Journal of Geotechnical Engineering，2019，41(12)：2 207–2 214.(in Chinese))
[8] 张基伟，刘书杰，张 松，等. 富水砂层冻结壁形成过程声场响应特征研究[J]. 岩土工程学报，2020，42(12)：2 230–2 239.(ZHANG Jiwei，LIU Shujie，ZHANG Song，et al. Response characteristics of sound fields of stratum frozen wall of water-rich sand during developing process[J]. Chinese Journal of Geotechnical Engineering，2020，42(12)：2 230–2 239.(in Chinese))
[9] 李健斌，陈 健，程红战，等. 考虑空间变异性的盾构隧道地层力学响应敏感性分析[J]. 岩石力学与工程学报，2019，38(8)：1 667–1 676.(LI Jianbin，CHEN Jian，CHENG Hongzhan，et al. Sensitivity analysis of mechanical parameters to surrounding-soil response induced by shield tunneling considering spatial variability[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(8)：1 667–1 676.(in Chinese))
[10] 蒋水华，刘 贤，黄发明，等. 基于一阶逆可靠度方法的空间变异土坡坡角设计[J]. 岩土工程学报，2021，43(7)：1 245–1 252. (JIANG Shuihua，LIU Xian，HUANG Faming，et al. Reliability-based design of slope angles for spatially varying slopes based on inverse first-order reliability method[J]. Chinese Journal of Geotechnical Engineering，2021，43(7)：1 245–1 252.(in Chinese))
[11] LIU W F，LEUNG Y F，LO M K. Integrated framework for characterization of spatial variability of geological profiles[J]. Canadian Geotechnical Journal，2017，54(1)：47–58.
[12] JIANG S H，HUANG J S，HUANG F M，et al. Modelling of spatial variability of soil undrained shear strength by conditional random fields for slope reliability analysis[J]. Applied Mathematical Modelling，2018，63：374–389.
[13] BONG T H，STUEDLEIN A W. Effect of cone penetration conditioning on random field model parameters and impact of spatial variability on liquefaction-induced differential settlements[J]. Journal of Geotechnical and Geoenvironmental Engineering，2018，144(5)，04018018.
[14] VANMARCKE E. Random fields：analysis and synthesis[M]，Singapore：World Scientific，2010：13–22.
[15] 李健斌，陈 健，罗红星，等. 基于随机场理论的双线盾构隧道地层变形分析[J]. 岩石力学与工程学报，2018，37(7)：1 748–1 765. (LI Jianbin，CHEN Jian，LUO Hongxing，et al. Study on surrounding soil deformation induced by twin shield tunneling based on random field theory[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(7)：1 748–1 765.(in Chinese))
[16] 蒋水华，曾绍慧，潘嘉铭，等. 岩土体参数约束随机场解析模拟方法及边坡可靠度分析[J]. 岩石力学与工程学报，2018，37(3)：642–651.(JIANG Shuihua，ZENG Shaohui，PAN Jiaming，et al. Slope reliability analysis based on analytical simulation of conditional random fields of rock and soil parameters[J]. Chinese Journal of Rock Mechanics and Engineering，2018，37(3)：642–651.(in Chinese))
[17] GHOLAMPOUR A，JOHARI A. Reliability-based analysis of braced excavation in unsaturated soils considering conditional spatial variability[J]. Computers and Geotechnics，2019，115：103163.
[18] EL HAJ A K，SOUBRA A H，FAJOUI J. Probabilistic analysis of an offshore monopile foundation taking into account the soil spatial variability[J]. Computers and Geotechnics，2019，106：205–216.
[19] 刘 勇，李福豪，陈 健，等. 深层搅拌水泥土基底加固层的三维随机有限元分析[J]. 岩土工程学报，2018，40(8)：1 542–1 548.(LIU Yong，LEE FookHou，CHEN Elton J，et al. Three-dimensional random finite element analysis of cement-admixed soil slab for stabilization of foundation pits[J]. Chinese Journal of Geotechnical Engineering，2018，40(8)：1 542–1 548.(in Chinese))
[20] 仉文岗，王 琦，刘汉龙，等. 岩体空间变异性对隧道拱顶失效概率的影响[J]. 岩土力学，2021，42(5)：1 462–1 472.(ZHANG Wengang，WANG Qi，LIU Hanlong，et al. Influence of rock mass spatial variability on probability of tunnel roof wedge failure[J]. Rock and Soil Mechanics，2021，42(5)：1 462–1 472.(in Chinese))
[21] 胡长明，袁一力，梅 源，等. 基于二维随机场在圆弧曲线上局部平均化的边坡可靠度分析[J]. 岩石力学与工程学报，2020，39(2)：251–261.(HU Changming，YUAN Yili，MEI Yuan，et al. Slope reliability analysis based on local averaging of two-dimensional random field on an arc curve[J]. Chinese Journal of Rock Mechanics and Engineering，2020，39(2)：251–261.(in Chinese))
[22] WANG T，ZHOU G Q，CHAO D Y，et al. Influence of hydration heat on stochastic thermal regime of frozen soil foundation considering spatial variability of thermal parameters[J]. Applied Thermal Engineering，2018，142：1–9.
[23] 陈朝晖，黄凯华. 土质边坡可靠性分析的分层非平稳随机场模型[J]. 岩土工程学报，2020，42(7)：1 247–1 256.(CHEN Zhaohui，HUANG Kaihua. Non-homogeneous random field model for reliability analysis of slopes[J]. Chinese Journal of Geotechnical Engineering，2020，42(7)：1 247–1 256.(in Chinese))
[24] LIU Y，HU J，XIAO H W，et al. Effects of material and drilling uncertainties on artificial ground freezing of cement-admixed soils [J]. Canadian Geotechnical Journal，2017，54：1 659–1 671.
[25] HU J，LIU Y，WEI H，et al. Finite-element analysis of heat transfer of horizontal ground-freezing method in shield-driven tunneling[J]. International Journal of Geomechanic，2017，17(10)：04017080.
[26] YANG Z，CHING J. Simulation of three-dimensional random field conditioning on incomplete site data[J]. Engineering Geology，2021，281(2)：105987.
[27] LI D Q，XIAO T，ZHANG L M，et al. Stepwise covariance matrix decomposition for efficient simulation of multivariate large-scale three-dimensional random fields[J]. Applied Mathematical Modelling，2019，68：169–181.
[28] LIU Y，ZHANG W G，ZHANG L，et al. Probabilistic stability analyses of undrained slopes by 3D random fields and finite element methods[J]. Geoscience Frontiers，2018，9：1 657–1 664.
[29] ZHU B，HIRAISHI T，MASE H，et al. A 3-D numerical study of the random wave-induced response in a spatially heterogenous seabed[J]. Computers and Geotechnics，2021，135：104159.
[30] LI D Q，JIANG S H，CAO Z J，et al. A multiple response- surface method for slope reliability analysis considering spatial variability of soil properties[J]. Engineering Geology，2015，187：60–72.
[31] LIU Z Q，YANG W H，WEI J. Analysis of random temperature field for freeway with wide subgrade in cold regions[J]. Cold Regions Science and Technology，2014，106–107：22–27.
[32] LIU Y，HU J，XIAO H W，et al. Effects of material and drilling uncertainties on artificial ground freezing of cement-admixed soils[J]. Canadian Geotechnical Journal，2017，54：1 659–1 671.
[33] WANG T，ZHOU G Q，WANG J Z，et al. Stochastic analysis of uncertain thermal parameters for random thermal regime of frozen soil around a single freezing pipe[J]. Heat and Mass Transfer，2018，54(9)：2 845–2 852.
[34] WANG T，LIU Y，ZHOU G Q，et al. Effect of uncertain hydrothermal properties and freezing temperature on the thermal process of frozen soil around a single freezing pipe[J]. International Communications in Heat and Mass Transfer，2021，124：105267.
[35] LI KQ，LI DQ，LIU Y. Meso-scale investigations on the effective thermal conductivity of multi-phase materials using the finite element method[J]. International Journal of Heat and Mass Transfer，2020，151：119383.
[36] ZHOU G Q，WANG T，WANG J Z，et al. Stochastic analysis of uncertain temperature characteristics for expressway with wide subgrade in cold regions[J]. Cold Regions Science and Technology，2015，114：36–43.
[37] ZHU H，ZHANG L M，XIAO T，et al. Generation of multivariate cross-correlated geotechnical random fields[J]. Computers and Geotechnics，2017，86：95–107.
[38] WANG T，ZHOU G Q，JIANG X，et al. Assessment for the spatial variation characteristics of uncertain thermal parameters for warm frozen soil[J]. Applied Thermal Engineering，2018，134：484–489.
[39] ZHANG X Y，ZHANG M Y，LU J G，et al. Effect of hydro- thermal behavior on the frost heave of a saturated silty clay under different applied pressures[J]. Applied Thermal Engineering，2017，117：462–467.
[40] LI S Y，NIU F J，LAI Y M，et al. Optimal design of thermal insulation layer of a tunnel in permafrost regions based on coupled heat-water simulation[J]. Applied Thermal Engineering，2017，110：1 264–1 273.
[41] LEWIS R W，MORGAN K，THOMAS H R，et al. The finite element method in heat transfer analysis[M]. [S.l.]：Wiley，1996：66–78.
[42] WANG T，ZHOU G Q，XU D Q，et al. Field experiment and stochastic model of uncertain thermal processes of artificial frozen wall around multi-circle freezing pipe[J]. International Journal of Thermal Sciences，2021，160：106658.
[43] 杨 平，张 婷. 城市地下工程人工冻结法理论与实践[M]. 北京：科学出版社，2015：9–10.(YANG Ping，ZHANG Ting. Theory andpractice of artificial freezing method for urban underground engineering[M]. Beijing：Science Press，2015：9–10.(in Chinese))
[44] CHAI M T，ZHANG J M，MA W，et al. Thermal influences of stabilization on warm and ice-rich permafrost with cement：Field observation and numerical simulation[J]. Applied Thermal Engineering，2019，148：536–543. |
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2022, Vol. 41 
