孔径分布函数对水分在非饱和土体中迁移的作用（英文）
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摘要
目的:了解孔径分布函数对水分在非饱和土体中迁移的影响,并提出相关数学模型,量化非饱和土体在不同吸力作用下的渗透系数。创新点:从孔径分布函数出发探讨土体的工程性质,以日常生活中所用的阀门模型解释非饱和土体在不同吸力作用下的渗透系数。提出采用非饱和土渗透系数的实验数据,间接估算土体的孔径分布函数。方法:从物理模型推导相关数学公式,并用实验结果对数学公式进行验证。结论:孔径分布函数主导非饱和土的渗透系数;孔径分布函数是连接土体两大水力特性(包括水土特征曲线和渗流方程)的桥梁。孔径分布函数对水分在土体中迁移的作用可以用日常生活中使用的阀门模型简单描述。基于阀门模型,土体的孔径分布函数也可以由土体的非饱和渗透系数的相关实验数据间接估算得到。
The hydraulic properties of soil(i.e. soil-water characteristic curve(SWCC) and coefficient of permeability) govern the moisture flow in it. Previous research has indicated that the hydraulic properties of soil are dependent on its pore-size distribution. An improved capillary model is now proposed to explain the concept of the pore-size distribution in soil and its relationship to SWCC. A new model, the "valve model", is also proposed as the explanation for water flow in unsaturated soil. The pore-size distribution function is incorporated in the "valve model" and is used to calculate the relative coefficient of permeability for unsaturated soil. In this paper, the role of the pore-size distribution function in the estimation of SWCC and the permeability function are explained. Equations are proposed for estimating the pore-size distribution function from the experimental data of relative coefficient of permeability. The results from the proposed equations agree with the experimental data from laboratory measurement and published data.
The hydraulic properties of soil(i.e. soil-water characteristic curve(SWCC) and coefficient of permeability) govern the moisture flow in it. Previous research has indicated that the hydraulic properties of soil are dependent on its pore-size distribution. An improved capillary model is now proposed to explain the concept of the pore-size distribution in soil and its relationship to SWCC. A new model, the "valve model", is also proposed as the explanation for water flow in unsaturated soil. The pore-size distribution function is incorporated in the "valve model" and is used to calculate the relative coefficient of permeability for unsaturated soil. In this paper, the role of the pore-size distribution function in the estimation of SWCC and the permeability function are explained. Equations are proposed for estimating the pore-size distribution function from the experimental data of relative coefficient of permeability. The results from the proposed equations agree with the experimental data from laboratory measurement and published data.
引文
Brooks RH,Corey AT,1964.Hydraulic Properties of Porous Media.Colorado State University,Fort Collins,CO,USA.
Childs EC,Collis-George N,1950.The permeability of porous materials.Proceedings of the Royal Society A:Mathematical,Physical and Engineering Sciences,201(1066):392-405.https://doi.org/10.1098/rspa.1950.0068
Fredlund DG,Rahardjo H,1993.Soil Mechanics for Unsaturated Soils.Wiley,New York,USA.
Fredlund DG,Xing AQ,1994.Equations for the soil-water characteristic curve.Canadian Geotechnical Journal,31(3):521-532.https://doi.org/10.1139/t94-061
Fredlund DG,Xing AQ,Huang SY,1994.Predicting the permeability function for unsaturated soils using the soilwater characteristic curve.Canadian Geotechnical Journal,31(4):533-546.https://doi.org/10.1139/t94-062
Fredlund DG,Rahardjo H,Fredlund MD,2012.Unsaturated Soil Mechanics in Engineering Practice.Wiley,New York,USA.
Gardner WR,1958.Mathematics of isothermal water conduction in unsaturated soils.Proceedings of the 37th Annual Meeting of the Highway Research Board.
Goh SG,2012.Hysteresis Effects on Mechanical Behavior of Unsaturated Soil.PhD Thesis,Nanyang Technological University,Singapore.
Goh SG,Rahardjo H,Leong EC,2015.Modification of triaxial apparatus for permeability measurement of unsaturated soils.Soils and Foundations,55(1):63-73.https://doi.org/10.1016/j.sandf.2014.12.005
Kosugi K,1994.Three-parameter lognormal distribution model for soil water retention.Water Resources Research,30(4):891-901.https://doi.org/10.1029/93WR02931
Kunze RJ,Uehara G,Graham K,1968.Factors important in the calculation of hydraulic conductivity.Soil Science Society of America Journal,32(6):760-765.https://doi.org/10.2136/sssaj1968.03615995003200060020x
Lambe TW,1955.The permeability of compacted fine-grained soils.Symposium on Permeability of Soils,ASTM.
Leong EC,Rahardjo H,1997.Review of soil-water characteristic curve equations.Journal of Geotechnical and Geoenvironmental Engineering,123(12):1106-1117.https://doi.org/10.1061/(asce)1090-0241(1997)123:12(1106)
Marshall TJ,1958.A relation between permeability and size distribution of pores.Journal of Soil Science,9(1):1-8.https://doi.org/10.1111/j.1365-2389.1958.tb01892.x
Millington RJ,Quirk JP,1961.Permeability of porous media.Nature,183(4658):387-388.https://doi.org/10.1038/183387a0
Mualem Y,1976.A new model for predicting the hydraulic conductivity of unsaturated porous media.Water Resources Research,12(3):513-522.https://doi.org/10.1029/WR012i003p00513
Pedroso DM,Sheng DC,Zhao JD,2009.The concept of reference curves for constitutive modelling in soil mechanics.Computers and Geotechnics,36(1-2):149-165.https://doi.org/10.1016/j.compgeo.2008.01.009
Priono,2016.Anisotropy in Hydraulic Properties of Unsaturated Soils.PhD Thesis,Nanyang Technological University,Singapore.
Rahimi A,Rahardjo H,2016.New approach to improve soil-water characteristic curve to reduce variation in estimation of unsaturated permeability function.Canadian Geotechnical Journal,53(4):717-725.https://doi.org/10.1139/cgj-2015-0199
Reinson JR,Fredlund DG,Wilson GW,et al.,2005.Unsaturated flow in coarse porous media.Canadian Geotechnical Journal,42(1):252-262.https://doi.org/10.1139/t04-070
Richards LA,1952.Water conducting and retaining properties of soils in relation to irrigation.Proceedings of International Symposium on Desert Research,p.523-546.
Tuli A,Hopmans JW,2004.Effect of degree of fluid saturation on transport coefficients in disturbed soils.European Journal of Soil Science,55(1):147-164.https://doi.org/10.1046/j.1365-2389.2002.00493.x-i1
Tuli A,Hopmans JW,Rolston DE,et al.,2005.Comparison of air and water permeability between disturbed and undisturbed soils.Soil Science Society of America Journal,69(5):1361-1371.https://doi.org/10.2136/sssaj2004.0332
van Genuchten MT,1980.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.Soil Science Society of America Journal,44(5):892-898.https://doi.org/10.2136/sssaj1980.03615995004400050002x
Vogel HJ,1997.Morphological determination of pore connectivity as a function of pore size using serial sections.European Journal of Soil Science,48(3):365-377.https://doi.org/10.1111/j.1365-2389.1997.tb00203.x
Wildenschild D,Hopmans JW,Rivers ML,et al.,2005.Quantitative analysis of flow processes in a sand using synchrotron-based X-ray microtomography.Vadose Zone Journal,4(1):112-126.https://doi.org/10.2136/vzj2005.0112
Zapata CE,1999.Uncertainty in Soil-water Characteristic Curve and Impacts on Unsaturated Shear Strength Predictions.Ph D Thesis,Arizona State University,Tempe,USA.
Zhai Q,Rahardjo H,2012a.Determination of soil-water characteristic curve variables.Computers and Geotechnics,42:37-43.https://doi.org/10.1016/j.compgeo.2011.11.010
Zhai Q,Rahardjo H,2012b.Reply to the discussion by Bellia et al.on“Determination of soil-water characteristic curve variables”.Computers and Geotechnics,45:151-152.https://doi.org/10.1016/j.compgeo.2012.03.008
Zhai Q,Rahardjo H,2015.Estimation of permeability function from the soil-water characteristic curve.Engineering Geology,199:148-156.https://doi.org/10.1016/j.enggeo.2015.11.001
Zhai Q,Rahardjo H,Satyanaga A,et al.,2017a.Effect of bimodal soil-water characteristic curve on the estimation of permeability function.Engineering Geology,230:142-151.https://doi.org/10.1016/j.enggeo.2017.09.025
Zhai Q,Rahardjo H,Satyanaga A,2017b.Effects of residual suction and residual water content on the estimation of permeability function.Geoderma,303:165-177.https://doi.org/10.1016/j.geoderma.2017.05.019
Zhai Q,Rahardjo H,Satyanaga A,2017c.Uncertainty in the estimation of hysteresis of soil-water characteristic curve.Environmental Geotechnics,in press.https://doi.org/10.1680/jenge.17.00008
Zhai Q,Rahardjo H,Satyanaga A,2018a.Estimation of the air permeability function from the soil-water characteristic curve.Canadian Geotechnical Journal,in press.https://doi.org/10.1139/cgj-2017-0579
Zhai Q,Rahardjo H,Satyanaga A,2018b.A pore-size distribution function based method for estimation of hydraulic properties of sandy soils.Engineering Geology,246:288-292.https://doi.org/10.1016/j.enggeo.2018.09.031
Childs EC,Collis-George N,1950.The permeability of porous materials.Proceedings of the Royal Society A:Mathematical,Physical and Engineering Sciences,201(1066):392-405.https://doi.org/10.1098/rspa.1950.0068
Fredlund DG,Rahardjo H,1993.Soil Mechanics for Unsaturated Soils.Wiley,New York,USA.
Fredlund DG,Xing AQ,1994.Equations for the soil-water characteristic curve.Canadian Geotechnical Journal,31(3):521-532.https://doi.org/10.1139/t94-061
Fredlund DG,Xing AQ,Huang SY,1994.Predicting the permeability function for unsaturated soils using the soilwater characteristic curve.Canadian Geotechnical Journal,31(4):533-546.https://doi.org/10.1139/t94-062
Fredlund DG,Rahardjo H,Fredlund MD,2012.Unsaturated Soil Mechanics in Engineering Practice.Wiley,New York,USA.
Gardner WR,1958.Mathematics of isothermal water conduction in unsaturated soils.Proceedings of the 37th Annual Meeting of the Highway Research Board.
Goh SG,2012.Hysteresis Effects on Mechanical Behavior of Unsaturated Soil.PhD Thesis,Nanyang Technological University,Singapore.
Goh SG,Rahardjo H,Leong EC,2015.Modification of triaxial apparatus for permeability measurement of unsaturated soils.Soils and Foundations,55(1):63-73.https://doi.org/10.1016/j.sandf.2014.12.005
Kosugi K,1994.Three-parameter lognormal distribution model for soil water retention.Water Resources Research,30(4):891-901.https://doi.org/10.1029/93WR02931
Kunze RJ,Uehara G,Graham K,1968.Factors important in the calculation of hydraulic conductivity.Soil Science Society of America Journal,32(6):760-765.https://doi.org/10.2136/sssaj1968.03615995003200060020x
Lambe TW,1955.The permeability of compacted fine-grained soils.Symposium on Permeability of Soils,ASTM.
Leong EC,Rahardjo H,1997.Review of soil-water characteristic curve equations.Journal of Geotechnical and Geoenvironmental Engineering,123(12):1106-1117.https://doi.org/10.1061/(asce)1090-0241(1997)123:12(1106)
Marshall TJ,1958.A relation between permeability and size distribution of pores.Journal of Soil Science,9(1):1-8.https://doi.org/10.1111/j.1365-2389.1958.tb01892.x
Millington RJ,Quirk JP,1961.Permeability of porous media.Nature,183(4658):387-388.https://doi.org/10.1038/183387a0
Mualem Y,1976.A new model for predicting the hydraulic conductivity of unsaturated porous media.Water Resources Research,12(3):513-522.https://doi.org/10.1029/WR012i003p00513
Pedroso DM,Sheng DC,Zhao JD,2009.The concept of reference curves for constitutive modelling in soil mechanics.Computers and Geotechnics,36(1-2):149-165.https://doi.org/10.1016/j.compgeo.2008.01.009
Priono,2016.Anisotropy in Hydraulic Properties of Unsaturated Soils.PhD Thesis,Nanyang Technological University,Singapore.
Rahimi A,Rahardjo H,2016.New approach to improve soil-water characteristic curve to reduce variation in estimation of unsaturated permeability function.Canadian Geotechnical Journal,53(4):717-725.https://doi.org/10.1139/cgj-2015-0199
Reinson JR,Fredlund DG,Wilson GW,et al.,2005.Unsaturated flow in coarse porous media.Canadian Geotechnical Journal,42(1):252-262.https://doi.org/10.1139/t04-070
Richards LA,1952.Water conducting and retaining properties of soils in relation to irrigation.Proceedings of International Symposium on Desert Research,p.523-546.
Tuli A,Hopmans JW,2004.Effect of degree of fluid saturation on transport coefficients in disturbed soils.European Journal of Soil Science,55(1):147-164.https://doi.org/10.1046/j.1365-2389.2002.00493.x-i1
Tuli A,Hopmans JW,Rolston DE,et al.,2005.Comparison of air and water permeability between disturbed and undisturbed soils.Soil Science Society of America Journal,69(5):1361-1371.https://doi.org/10.2136/sssaj2004.0332
van Genuchten MT,1980.A closed-form equation for predicting the hydraulic conductivity of unsaturated soils.Soil Science Society of America Journal,44(5):892-898.https://doi.org/10.2136/sssaj1980.03615995004400050002x
Vogel HJ,1997.Morphological determination of pore connectivity as a function of pore size using serial sections.European Journal of Soil Science,48(3):365-377.https://doi.org/10.1111/j.1365-2389.1997.tb00203.x
Wildenschild D,Hopmans JW,Rivers ML,et al.,2005.Quantitative analysis of flow processes in a sand using synchrotron-based X-ray microtomography.Vadose Zone Journal,4(1):112-126.https://doi.org/10.2136/vzj2005.0112
Zapata CE,1999.Uncertainty in Soil-water Characteristic Curve and Impacts on Unsaturated Shear Strength Predictions.Ph D Thesis,Arizona State University,Tempe,USA.
Zhai Q,Rahardjo H,2012a.Determination of soil-water characteristic curve variables.Computers and Geotechnics,42:37-43.https://doi.org/10.1016/j.compgeo.2011.11.010
Zhai Q,Rahardjo H,2012b.Reply to the discussion by Bellia et al.on“Determination of soil-water characteristic curve variables”.Computers and Geotechnics,45:151-152.https://doi.org/10.1016/j.compgeo.2012.03.008
Zhai Q,Rahardjo H,2015.Estimation of permeability function from the soil-water characteristic curve.Engineering Geology,199:148-156.https://doi.org/10.1016/j.enggeo.2015.11.001
Zhai Q,Rahardjo H,Satyanaga A,et al.,2017a.Effect of bimodal soil-water characteristic curve on the estimation of permeability function.Engineering Geology,230:142-151.https://doi.org/10.1016/j.enggeo.2017.09.025
Zhai Q,Rahardjo H,Satyanaga A,2017b.Effects of residual suction and residual water content on the estimation of permeability function.Geoderma,303:165-177.https://doi.org/10.1016/j.geoderma.2017.05.019
Zhai Q,Rahardjo H,Satyanaga A,2017c.Uncertainty in the estimation of hysteresis of soil-water characteristic curve.Environmental Geotechnics,in press.https://doi.org/10.1680/jenge.17.00008
Zhai Q,Rahardjo H,Satyanaga A,2018a.Estimation of the air permeability function from the soil-water characteristic curve.Canadian Geotechnical Journal,in press.https://doi.org/10.1139/cgj-2017-0579
Zhai Q,Rahardjo H,Satyanaga A,2018b.A pore-size distribution function based method for estimation of hydraulic properties of sandy soils.Engineering Geology,246:288-292.https://doi.org/10.1016/j.enggeo.2018.09.031