基于双电层模型冻土中未冻水含量理论推演及应用
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摘要
根据冻土中未冻水成因的本质——带负电黏土颗粒表面的扩散层中阳离子溶液特殊分布,依据基于静电场泊松方程与静电荷玻尔兹曼分布的双电层理论,推演出了未冻水含量理论公式,比较分析未冻水含量观测值拟合的经验公式,发现两者形式非常一致,经验公式实质为理论公式的简化。依据此理论,清晰地描述了冻土颗粒表面未冻水的结构特征及成因,定量分析了土壤类型、含盐度、温度对未冻水含量的影响;得出当土壤盐溶液浓度小于某一阈值时,盐渍度变化对未冻水含量的影响可以忽略,即不同类型常规(低含盐度)冻土,双电层结构几近相同,指数形式公式适用于所有常规冻土的未冻水含量;土壤类型通过比表面积影响着未冻水含量,在同等温度下,土壤中黏土颗粒越多,比表面积越大,未冻水含量越多;结合实测资料给出适用于不同类型冻土未冻水含量理论计算的参数值,随后通过两种已有的经验公式对计算结果进行了验证,证实了该理论公式的可行性。
According to the fact that of some water in soil cannot be frozen due to distribution of cationic diffusion layer on the surface of negatively charged clay particles, the theoretical formula of unfrozen water content is obtained by electrical double-layer theory based on Poisson equation of electrostatic field and static charge Boltzmann distribution. the empirical formula of classical unfrozen water content is almost identical to the proposed model. This paper describes the structure and causes of unfrozen water on the surface of soil particles, and quantitatively analyzes the effect of soil type, salinity and temperature on unfrozen water content.When the soil salt concentration is less than a threshold value, changes in salinity negligibly influence the unfrozen water content.This indicated different types of frozen soil texture(low salinity) have analogous structure of electric double layer. the empirical formula of exponential form can describe all unfrozen water content of low salinity frozen soil. The unfrozen water content is dependent on soil types, specific surface area. More clay particles in soil and larger specific surface area resulted in more unfrozen water content. Two existing empirical formulas have been used to verify the theoretical formula. Results prove that the theoretical formula for calculating unfrozen water content in frozen soil is reliable.
According to the fact that of some water in soil cannot be frozen due to distribution of cationic diffusion layer on the surface of negatively charged clay particles, the theoretical formula of unfrozen water content is obtained by electrical double-layer theory based on Poisson equation of electrostatic field and static charge Boltzmann distribution. the empirical formula of classical unfrozen water content is almost identical to the proposed model. This paper describes the structure and causes of unfrozen water on the surface of soil particles, and quantitatively analyzes the effect of soil type, salinity and temperature on unfrozen water content.When the soil salt concentration is less than a threshold value, changes in salinity negligibly influence the unfrozen water content.This indicated different types of frozen soil texture(low salinity) have analogous structure of electric double layer. the empirical formula of exponential form can describe all unfrozen water content of low salinity frozen soil. The unfrozen water content is dependent on soil types, specific surface area. More clay particles in soil and larger specific surface area resulted in more unfrozen water content. Two existing empirical formulas have been used to verify the theoretical formula. Results prove that the theoretical formula for calculating unfrozen water content in frozen soil is reliable.
引文
[1]徐敩祖,王家澄,张立新.冻土物理学[M].北京:科学出版社,2010:1-69.XU Xiao-zu,WANG Jia-cheng,ZHANG Li-xin.Physics of frozen soil[M].Beijing:Science Press,2010:1-69.
[2]霍托维奇.冻土力学[M].张长庆译.北京:科学出版社,1985:19-47.TSYTOVICH N A.The mechanics of frozen soil[M].Translated by ZHANG Chang-qing.Beijing:Science Press,1985:19-47.
[3]DILLON H B,ANDERSLAND O B.Predicting unfrozen water contents in frozen soils[J].Canadian Geotechnical Journal,1966,3(2):53-60.
[4]ANDERSON D M,TICE A R.Predicting unfrozen water contents in frozen soils from surface area measurements[J].Highway Research Record,1972(393):12-18.
[5]ARVIND PHUKAN.Frozen ground engineering[M].[S.l.]:Prentice-Hall Inc.,1985:32-36.
[6]徐敩祖,奥利奋特J L,泰勒A R.土水势、未冻水含量和温度[J].冰川冻土,1985,7(1):1-12.XU Xiao-zu,OLIPHANT J L,TICE A R.Soil-water potential and unfrozen water content and temperature[J].Journal of Glaciology and Geocryology,1985,7(1):1-12.
[7]BRONFENBRENER L,KORIN E.Experimental studies of water crystallization in porous media[J].Chemical Engineering and Processing Process Intensification,2002,41(4):357-363.
[8]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):71-79.
[9]KOZLOWSKI T.A comprehensive method of determining the soil unfrozen water curves:2.stages of the phase change process in frozen soil-water system[J].Cold Regions Science and Technology,2003,36:81-92.
[10]WATANABE K,MIZOGUCHI M.Amount of unfrozen water in frozen porous media saturated with solution[J].Cold Regions Science and Technology,2002,34(2):103-110.
[11]WATANABE K,WAKE T.Measurement of unfrozen water content and relative permittivity of frozen unsaturated soil using NMR and TDR[J].Cold Regions Science and Technology,2009,59(1):34-41.
[12]WEN Z,MA W,FENG W,et al.Experimental study on unfrozen water content and soil matric potential of Qinghai-Tibetan silty clay[J].Environmental Earth Sciences,2012,66(5):1467-1476.
[13]陶高梁,柏亮,袁波,等.土-水特征曲线与核磁共振曲线的关系[J].岩土力学,2018,39(3):943-948.TAO Gao-liang,BAI Liang,YUAN Bo,et al.Study of relationship between soil-water characteristic curve and NMR curve[J].Rock and Soil Mechanics,2018,39(3):943-948.
[14]谭龙,韦昌富,田慧会,等.冻土未冻水含量的低场核磁共振试验研究[J].岩土力学,2015,36(6):1566-1572.TAN Long,WEI Chang-fu,TIAN Hui-hui,et al.Experimental study of unfrozen water content of frozen soils by low-field nuclear magnetic resonance[J].Rock and Soil Mechanics,2015,36(6):1566-1572.
[15]YOSHIKAWA K,OVERDUIN P P.Comparing unfrozen water content measurements of frozen soil using recently developed commercial sensors[J].Cold Regions Science and Technology,2005,42(3):250-256.
[16]ZHOU X,ZHOU J,KINZELBACH W,et al.Simultaneous measurement of unfrozen water content and ice content in frozen soil using gamma ray attenuation and TDR[J].Water Resources Research,2015,50(12):9630-9655.
[17]张立新,徐敩祖,张招祥,等.冻土未冻水含量与压力关系的实验研究[J].冰川冻土,1998,20(2):124-127.ZHANG Li-xin,XU Xiao-zu,ZHANG Zhao-xiang,et al.Experimental study of the relationship between the unfrozen water content of frozen soil and pressure[J].Journal of Glaciology and Geocryology,1998,20(2):124-127.
[18]LAI Y,LIAO M,KAI H.A constitutive model of frozen saline sandy soil based on energy dissipation theory[J].International Journal of Plasticity,2015,78:84-113.
[19]马敏,邴慧,李国玉.硫酸钠盐渍土未冻水含量的实验研究[J].冰川冻土,2016,38(4):963-969.MA Min,BING Hui,LI Guo-yu.Experimental research on unfrozen water content of sodium sulphate saline soil[J].Journal of Glaciology and Geocryology,2016,38(4):963-969.
[20]马田田,韦昌富,夏晓龙,等.NaCl溶液对土体冻结特征影响的试验研究[J].岩土力学,2017,38(7):1919-1925.MA Tian-tian,WEI Chang-fu,XIA Xiao-long,et al.Experimental study of effect of NaCl solution on soil freezing characteristic[J].Rock and Soil Mechanics,2017,38(7):1919-1925.
[21]VAN OLPHEN H.Introduction to clay colloid chemistry[M].[S.l.]:Interscience Publishers Inc,1964:228-239.
[22]DOBSON M C,ULABY F T,HALLIKAINEN M T,et al.Microwave dielectric behavior of wet soil-part II:dielectric mixing models[J].IEEE Transactions on Geoscience and Remote Sensing,1985,23(1):35-46.
[23]BABCOCK K.Theory of the chemical properties of soil colloidal systems at equilibrium[J].California Agriculture,1963,34(11):417-542.
[24]BANIN A,ANDERSON D M.Effects of salt concentration changes during freezing on the unfrozen water content of porous materials[J].Water Resources Research,1974,10(1):124-128.
[25]SHIRAZI M A,BOERSMA L.A unifying quantitative analysis of soil texture[J].Soil Science Society of America Journal,1984,48(1):142-147.
[26]SEPASKHAH ALI REZA,TAFTEH ARASH.Pedotransfer function for estimation of soil-specific surface area using soil fractal dimension of improved particle-size distribution[J].Archives of Agronomy and Soil Science,2013,59(1):93-103.
[27]孙美玲.兰州地区黄土的比表面积分析[D].兰州:兰州大学,2014:28-37.SUN Mei-ling.Analysis of the specific surface area of loess in Lanzhou[D].Lanzhou:Lanzhou University,2014:28-37.
[2]霍托维奇.冻土力学[M].张长庆译.北京:科学出版社,1985:19-47.TSYTOVICH N A.The mechanics of frozen soil[M].Translated by ZHANG Chang-qing.Beijing:Science Press,1985:19-47.
[3]DILLON H B,ANDERSLAND O B.Predicting unfrozen water contents in frozen soils[J].Canadian Geotechnical Journal,1966,3(2):53-60.
[4]ANDERSON D M,TICE A R.Predicting unfrozen water contents in frozen soils from surface area measurements[J].Highway Research Record,1972(393):12-18.
[5]ARVIND PHUKAN.Frozen ground engineering[M].[S.l.]:Prentice-Hall Inc.,1985:32-36.
[6]徐敩祖,奥利奋特J L,泰勒A R.土水势、未冻水含量和温度[J].冰川冻土,1985,7(1):1-12.XU Xiao-zu,OLIPHANT J L,TICE A R.Soil-water potential and unfrozen water content and temperature[J].Journal of Glaciology and Geocryology,1985,7(1):1-12.
[7]BRONFENBRENER L,KORIN E.Experimental studies of water crystallization in porous media[J].Chemical Engineering and Processing Process Intensification,2002,41(4):357-363.
[8]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):71-79.
[9]KOZLOWSKI T.A comprehensive method of determining the soil unfrozen water curves:2.stages of the phase change process in frozen soil-water system[J].Cold Regions Science and Technology,2003,36:81-92.
[10]WATANABE K,MIZOGUCHI M.Amount of unfrozen water in frozen porous media saturated with solution[J].Cold Regions Science and Technology,2002,34(2):103-110.
[11]WATANABE K,WAKE T.Measurement of unfrozen water content and relative permittivity of frozen unsaturated soil using NMR and TDR[J].Cold Regions Science and Technology,2009,59(1):34-41.
[12]WEN Z,MA W,FENG W,et al.Experimental study on unfrozen water content and soil matric potential of Qinghai-Tibetan silty clay[J].Environmental Earth Sciences,2012,66(5):1467-1476.
[13]陶高梁,柏亮,袁波,等.土-水特征曲线与核磁共振曲线的关系[J].岩土力学,2018,39(3):943-948.TAO Gao-liang,BAI Liang,YUAN Bo,et al.Study of relationship between soil-water characteristic curve and NMR curve[J].Rock and Soil Mechanics,2018,39(3):943-948.
[14]谭龙,韦昌富,田慧会,等.冻土未冻水含量的低场核磁共振试验研究[J].岩土力学,2015,36(6):1566-1572.TAN Long,WEI Chang-fu,TIAN Hui-hui,et al.Experimental study of unfrozen water content of frozen soils by low-field nuclear magnetic resonance[J].Rock and Soil Mechanics,2015,36(6):1566-1572.
[15]YOSHIKAWA K,OVERDUIN P P.Comparing unfrozen water content measurements of frozen soil using recently developed commercial sensors[J].Cold Regions Science and Technology,2005,42(3):250-256.
[16]ZHOU X,ZHOU J,KINZELBACH W,et al.Simultaneous measurement of unfrozen water content and ice content in frozen soil using gamma ray attenuation and TDR[J].Water Resources Research,2015,50(12):9630-9655.
[17]张立新,徐敩祖,张招祥,等.冻土未冻水含量与压力关系的实验研究[J].冰川冻土,1998,20(2):124-127.ZHANG Li-xin,XU Xiao-zu,ZHANG Zhao-xiang,et al.Experimental study of the relationship between the unfrozen water content of frozen soil and pressure[J].Journal of Glaciology and Geocryology,1998,20(2):124-127.
[18]LAI Y,LIAO M,KAI H.A constitutive model of frozen saline sandy soil based on energy dissipation theory[J].International Journal of Plasticity,2015,78:84-113.
[19]马敏,邴慧,李国玉.硫酸钠盐渍土未冻水含量的实验研究[J].冰川冻土,2016,38(4):963-969.MA Min,BING Hui,LI Guo-yu.Experimental research on unfrozen water content of sodium sulphate saline soil[J].Journal of Glaciology and Geocryology,2016,38(4):963-969.
[20]马田田,韦昌富,夏晓龙,等.NaCl溶液对土体冻结特征影响的试验研究[J].岩土力学,2017,38(7):1919-1925.MA Tian-tian,WEI Chang-fu,XIA Xiao-long,et al.Experimental study of effect of NaCl solution on soil freezing characteristic[J].Rock and Soil Mechanics,2017,38(7):1919-1925.
[21]VAN OLPHEN H.Introduction to clay colloid chemistry[M].[S.l.]:Interscience Publishers Inc,1964:228-239.
[22]DOBSON M C,ULABY F T,HALLIKAINEN M T,et al.Microwave dielectric behavior of wet soil-part II:dielectric mixing models[J].IEEE Transactions on Geoscience and Remote Sensing,1985,23(1):35-46.
[23]BABCOCK K.Theory of the chemical properties of soil colloidal systems at equilibrium[J].California Agriculture,1963,34(11):417-542.
[24]BANIN A,ANDERSON D M.Effects of salt concentration changes during freezing on the unfrozen water content of porous materials[J].Water Resources Research,1974,10(1):124-128.
[25]SHIRAZI M A,BOERSMA L.A unifying quantitative analysis of soil texture[J].Soil Science Society of America Journal,1984,48(1):142-147.
[26]SEPASKHAH ALI REZA,TAFTEH ARASH.Pedotransfer function for estimation of soil-specific surface area using soil fractal dimension of improved particle-size distribution[J].Archives of Agronomy and Soil Science,2013,59(1):93-103.
[27]孙美玲.兰州地区黄土的比表面积分析[D].兰州:兰州大学,2014:28-37.SUN Mei-ling.Analysis of the specific surface area of loess in Lanzhou[D].Lanzhou:Lanzhou University,2014:28-37.