土中水膜厚度变化规律及未冻水含量预测方法

doi:10.13866/j.azr.2022.01.14

摘要/Abstract

摘要：

未冻水含量改变直接影响冻土的热力学及变形特性,也是水热数值计算的关键条件。为了探究未冻水含量变化规律,首先采用等效粒径表征土颗粒粒径分布,将土体简化成等效粒径球状堆积体系。其次考虑简单立方堆积和立方最密堆积平均的堆积方式,基于多孔介质预融理论,提出土中未冻水含量的计算方法,并通过试验数据验证其合理性。最后分析了杂质密度以及有效粒径大小对水膜厚度以及未冻水含量的影响。研究结果表明：土颗粒表面电荷密度引发的自由能对水膜厚度的改变极易受杂质浓度的影响,随着浓度增大,土颗粒表面电荷对水膜的影响越来越小。土中液态水含量主要由土颗粒表面水膜厚度变化来决定,当等效颗粒减小时,通过间隙水求解的未冻水体积比例逐渐增大,并且在较低浓度时发挥更大作用。对于较大颗粒土,未冻水含量模型预测效果好。当粉质黏土、黄土、砂土等效粒径分别缩小0.28、0.3、0.36倍时,未冻水体积含量计算结果与试验值吻合较好。

关键词: 预融, 未冻水含量, 等效粒径, 杂质浓度, 表面电荷密度

Abstract:

The variation of unfrozen water content directly influences the thermodynamics and deformation properties of frozen soils, and it is also the key condition for water-heat coupled simulations. In order to study this variation, the distribution of soil particle size was used to an equivalent particle size, and soil was simplified to the equivalent particle size spherical packing system. Based on the premelting theory in porous medium, the calculation method of unfrozen water content in soil was put forward with the considered average packing system of simple cubic packing and cubic close packing, and the accuracy was verified by the experimental data. Moreover, the effect of impurity density and the equivalent particle size on water film thickness and unfrozen water content was analyzed. The results show that the thickness of water film calculated using the surface charge density of soil particles was easily affected by impurity concentration, and the effect of surface charge density on water film was progressively reduced as the impurity concentration increased. The liquid water fraction was mainly determined by the variation of water film thickness on the surface of soil particles, and the contribution of interstitial water to the total liquid fraction increased as the equivalent particle size decreased, especially at low impurity concentrations. Moreover, the model of unfrozen water content produced better predictions in larger particle soils. The calculated values of volumetric unfrozen water were close to the experimental values when the equivalent particle sizes of silty clay, loess, and sand were reduced by 0.28, 0.3, and 0.36, respectively.

Key words: premelting, unfrozen water content, equivalent particle size, impurity density, surface charge density

万旭升,颜梦宇,路建国,晏忠瑞. 土中水膜厚度变化规律及未冻水含量预测方法[J]. 干旱区研究, 2022, 39(1): 135-143.

WAN Xusheng,YAN Mengyu,LU Jianguo,YAN Zhongrui. Variation of water film thickness in soil and prediction method of unfrozen water content[J]. Arid Zone Research, 2022, 39(1): 135-143.

图/表 11

图1

图2

图3

图4

图5

图6

图7

图8

图9

图10

图11

参考文献 35

[1]	徐敩祖, 王家澄, 张立新, 等. 冻土物理学[M]. 北京: 科学出版社, 2010.
	[Xu Xiaozhu, Wang Jiacheng, Zhang Lixin, et al. Frozen Soil Physics[M]. Beijing: Science Press, 2010. ]
[2]	徐敩祖, 王家澄, 张立新, 等. 土体的冻胀和盐胀机理[M]. 北京: 科学出版社, 1995.
	[Xu Xiaozhu, Wang Jiacheng, Zhang Lixin, et al. Mechanisms of Frost Heave and Soil Expansion of Soils[M]. Beijing: Science Press, 1995. ]
[3]	Kurylyk B L, Watanabe K. The mathematical representation of freezing and thawing processes in variably-saturated, non-deformable soils[J]. Advances in Water Resources, 2013, 60: 160-177. doi: 10.1016/j.advwatres.2013.07.016
[4]	Zhou J Z, Wei C F, Lai Y M. et al. Application of the generalized clapeyron equation to freezing point depression and unfrozen water content[J]. Water Resources Research, 2018, 54(11): 9412-9431. doi: 10.1029/2018WR023221
[5]	乌艺恒, 赵鹏武, 周梅, 等. 季节性冻土区土体冻融过程及其对水热因子的响应[J]. 干旱区研究, 2019, 36(6): 1568-1575.
	[Wu Yiheng, Zhao Pengwu, Zhou Mei, et al. Freezing-thawing process of seasonal frozen soil and its response to moisture and temperature[J]. Arid Zone Research, 2019, 36(6): 1568-1575. ]
[6]	Kleinberg R L, Griffin D D. NMR measurement of permafrost: Unfrozen water assay, pore-scale distribution of ice, and hydraulic permeability of sediments[J]. Cold Regions and Technology, 2005, 42(1): 63-77.
[7]	裴万胜. 冻土水-热-力相互作用过程及数值模拟研究[D]. 北京: 中国科学院大学, 2015.
	[Pei Wansheng. Study of the Hydro-thermal-mechanical Interaction Process of Frozen Soil and Its Numerical Simulation[D]. Beijing: University of Chinese Academy of Sciences, 2015. ]
[8]	Kruse A M, Darrow M M, Akagawa S. Improvements in measuring unfrozen water in frozen soils using the pulsed nuclear magnetic resonance method[J]. Journal of Cold Regions Engineering, 2018, 32(1): 04017016. https://doi.10.1061/(ASCE)CR.1943-5495.0000141.
[9]	吴芹芹, 莫淑红, 程圣东, 等. 黄土区冻融期不同土地利用土壤水分与温度的关系[J]. 干旱区研究, 2020, 37(3): 627-635.
	[Wu Qinqin, Mo Shuhong, Cheng Shengdong, et al. Study on the correlation between soil moisture and temperature of different land uses in the loess area during a freezing-thawing period[J]. Arid Zone Research, 2020, 37(3): 627-635. ]
[10]	Anderson D M, Tice A R. Predicting unfrozen water content in frozen soils from surface area measurements[J]. Highway Research Record, 1972, 393: 12-18.
[11]	McKenzie J M, Voss C I, Siegel D I. Groundwater flow with energy transport and water-ice phase change: Numerical simulations, benchmarks, and application to freezing in peat bogs[J]. Advanced Water Resources, 2007, 30(4): 966-983. doi: 10.1016/j.advwatres.2006.08.008
[12]	Kong L M, Wang Y S, Sun W J, et al. Influence of plasticity on unfrozen water content of frozen soils as determined by nuclear magnetic resonance[J]. Cold Regions Science and Technology, 2020, 172:102993.https://doi.org/10.1016/j.coldregions.2020.102993.
[13]	Daanen R P, Nieber J L. Model for coupled liquid water flow and heat transport with phase change in a snowpack[J]. Journal of Cold Regions Engineering, 2009, 23(2): 43-68. doi: 10.1061/(ASCE)0887-381X(2009)23:2(43)
[14]	Painter S L, Karra S. Constitutive model for unfrozen water content in subfreezing unsaturated soils[J]. Vadose Zone Journal, 2014, 13(4): 334-338.
[15]	Chai M T, Zhang J M, Zhang H, et al. A method for calculating unfrozen water content of silty clay with consideration of freezing point[J]. Applied Clay Science, 2018, 161: 474-481. doi: 10.1016/j.clay.2018.05.015
[16]	Shoop S, Bigl S. Moisture migration during freeze and thaw of unsaturated soils: Modeling and large scale experiments[J]. Cold Regions Science and Technology, 1997, 25: 33-45. doi: 10.1016/S0165-232X(96)00015-8
[17]	Zhang X, Sun S, Xue Y. Development and testing of a frozen soil parameterization for cold region studies[J]. Journal of Hydrometeorology, 2007, 8: 690-701. doi: 10.1175/JHM605.1
[18]	Dall’Amico M, Endrizzi S, Gruber S, et al. A robust and energy-conserving model of freezing variably-saturated soil[J]. The Cryosphere, 2011, 5: 469-484. doi: 10.5194/tc-5-469-2011
[19]	Watanabe K, Kito T, Wake T, et al. Freezing experiments on unsaturated sand, loam and silt loam[J]. Annals of Glaciology, 2011, 52: 37-43. doi: 10.3189/172756411797252220
[20]	Sheshukov A Y, Niber J L. One dimensional freezing of nonheaving unsaturated soils: Model formulation and similarity solution[J]. Water Resources Research, 2011, 47(11): 11519. https://doi:10.1029/2011WR010512.
[21]	Wang C, Lai Y M, Zhang M Y. Estimating soil freezing characteristic curve based on pore-size distribution[J]. Applied Thermal Engineering, 2017, 124: 1049-1060. doi: 10.1016/j.applthermaleng.2017.06.006
[22]	Xiao Z A, Lai Y M, Zhang J. A thermodynamic model for calculating the unfrozen water content of frozen soil[J]. Cold Regions Science and Technology, 2020, 172: 103011. https://doi.org/10.1016/j.coldregions.2020.103011.
[23]	Hitchcock I, Holt E M, Lowe J P, et al. Studies of freezing-melting hysteresis in cryoporometry scanning loop experiments using NMR diffusometry and relaxometry[J]. Chemical Engineering Science, 2011, 66(4): 582-592. doi: 10.1016/j.ces.2010.10.027
[24]	Cash J W, Dash J G, Fu H Y. Theory of ice premelting in monosized powders[J]. Journal of Crystal Growth, 1992, 123: 101-108. doi: 10.1016/0022-0248(92)90014-A
[25]	Wettlaufer J S. Impurity effects in the premelting of ice[J]. Physical Review Letters, 1999, 82: 2516. https://doi.org/10.1103/PhysRevLett.82.2516.
[26]	Hendrik H G, Wettlaufer J S. Theory of ice premelting in porous media[J]. Physical Review E, 2010, 81: 031604: 1-13.
[27]	Dash J G, Rempel A W, Wettlaufer J S. The physics of premelted ice and its geophysical consequences[J]. Review of Modern Physics, 2006, 78: 695-741. doi: 10.1103/RevModPhys.78.695
[28]	Tang L Y, Wang K, Jin L, et al. A resistivity model for testing unfrozen water content of frozen soil[J]. Cold Regions Science and Technology, 2018, 153: 55-63. doi: 10.1016/j.coldregions.2018.05.003
[29]	Qiu E X, Wan X S, Qu M F, et al. Estimating unfrozen water content in frozen soils based on soil particle distribution[J]. Journal of Cold Regions Engineering, 2020, 34(2): 04020002, doi: 10.1061/(ASCE)CR.1943-5495.0000208. doi: 10.1061/(ASCE)CR.1943-5495.0000208
[30]	靳潇, 杨文, 孟宪红, 等. 基于双电层模型冻土中未冻水含量理论推演及应用[J]. 岩土力学, 2019, 40(4): 1449-1456.
	[Jin Xiao, Yang Wen, Meng Xianhong, et al. Deduction and application of unfrozen water content in soil based on electrical double-layer theory[J]. Rock and Soil Mechanics, 2019, 40(4): 1449-1456. ]
[31]	Wen Z, Ma W, Feng W J, et al. Experimental study on unfrozen water content and soil matric potential of Qinghai-Tibet silty clay[J]. Environmental Earth Science, 2012, 66(5): 1467-1476. doi: 10.1007/s12665-011-1386-0
[32]	Wan X S, Lai Y M, Wang C. Experimental Study on the Freezing Temperatures of Saline Silty Soils[J]. Permafrost and Periglacial Processes, 2015, 26(2): 175-187. doi: 10.1002/ppp.v26.2
[33]	Lu J G, Pei W S, Zhang X Y, et al. Evaluation of calculation models for the unfrozen water content of freezing soils[J]. Journal of Hydrology, 2019, 575: 976-985. doi: 10.1016/j.jhydrol.2019.05.031
[34]	冷毅飞, 张喜发, 杨凤学, 等. 冻土未冻水含量的量热法试验研究[J]. 岩土力学, 2010, 31(12): 3758-3764.
	[Leng Yifei, Zhang Xifa, Yang Fengxue, et al. Experimental research on unfrozen water content of frozen soils by calorimetry[J]. Rock and Soil Mechanics, 2010, 31(12): 3758-3764. ]
[35]	李述训, 程国栋, 刘继民, 等. 兰州黄土在冻融过程中水热输运实验研究[J]. 冰川冻土, 1996, 18(4): 319-324.
	[Li Shuxun, Cheng Guodong, Liu Jimin, et al. Experimental study on heat moisture transfer in lanzhou loess during freezing-thawing processes[J]. Journal of Glaciology and Geocryology, 1996, 18(4): 319-324. ]