新型非饱和土稳态渗流试验装置的研制
|
摘要
在岩土工程领域中,经常会遇到各种各样的土体结构,大部分土体处于非饱和状态,因此研究非饱和土对于工程应用有着非常重要的作用。非饱和渗透系数是确定土中水—气运动规律的重要参数,该系数的测量不仅是非饱和土研究领域中的一个重要的课题,而且是研究非饱和土中水分入渗问题的关键。但是非饱和土的渗透系数难以测定,目前还没有测量仪器或者计算方法得到该研究领域的学者的一致认可,测量精度也无法满足工程实际的需要。
本文主要以非饱和土的渗透特性研究为出发点,针对目前研制的非饱和土渗透仪器的不足,对原来的非饱和土稳态渗流试验装置进行了继承和改进,研制出了新型非饱和土稳态渗流试验装置。对原来装置中使用的试样基座的刻槽进行了重新设计,使得压力室的排气功能加强；在气体压力控制系统中,使用微控制器控制气体压力控制阀,实现了智能控制试样室内的气压力值；在新型装置,通过微控制器控制电磁阀,进而实现了试验过程中智能操控试验过程中水的流向。
本文不仅对原来非饱和土稳态渗流试验装置进行了改进和完善,还使用SolidWorks对装置的空间结构进行优化。提出两种结构布局设计方案以满足不同的生产方式需要,把杂散的平铺在试验台上的原来试验装置,变成了现在真正的结构一体化。合理的设计主体框架和内部零部件的工作平台,保证了工作过程中各个零部件之间的干扰最小,做实验时操作变得简单,实验的安全性得到加强,实验数据的可靠性得到了保证。
由于装置目前还处于试验研究阶段,故在保证试验可靠性、安全性、操作性的基础上选择了经济实用的型材设计装置外框,更好的应用到试验中。
In geotechnical engineering domain, there are different kinds of soil structure, which most are in unsaturated status. The research of unsaturated soil is very important to the project. Unsaturated permeability coefficient is one important parameter to the determination of water-air flow in unsaturated soil, the measurement of this parameter not only is a significant issue in unsaturated soil research field but also is a key point to research the water infiltration of the soil. But the measurement of this parameter is so difficult that no measuring device and function can acquire it presicely until now, and cannot satisfy the request of the engineering
This paper, at the start point of the shortage of the current aparatus of water permeability for unsaturated soils, the novel steady flow instrument for unsaturated soils for measurement of unsaturated permeability coefficient has been developed based on the improvement and amendment on original device. In order to enhance the exhaust function of the pressure room, the cutting of the specimen foundation has been redesigned. Also, the air pressure control system has been redesigned,by using the controlling valve of air pressure; For replacing the old manual valves, A new pipeline control system has been designed and the intelligent control of the water-air flow has been achieved.
The device not only be improved and perfected, but also be optimized at space structure by SolidWorks. For changing the condition that all the parts lay on the test bench disorderly into entirety type orderliness, the paper proposes two programs of space structure layout to meet different production. The reasonably design of skeleton frame and parts test bench, can ensure the least interference among parts and easily operation during working. The novel device enhance the security of test and the reliability of experimental result.
The device is in experimental study point at present, at the base of reliability, security and maintenance this structure is very pithy and cheap, which use the aluminium alloy sections as the basical skeleton frame。
本文主要以非饱和土的渗透特性研究为出发点,针对目前研制的非饱和土渗透仪器的不足,对原来的非饱和土稳态渗流试验装置进行了继承和改进,研制出了新型非饱和土稳态渗流试验装置。对原来装置中使用的试样基座的刻槽进行了重新设计,使得压力室的排气功能加强；在气体压力控制系统中,使用微控制器控制气体压力控制阀,实现了智能控制试样室内的气压力值；在新型装置,通过微控制器控制电磁阀,进而实现了试验过程中智能操控试验过程中水的流向。
本文不仅对原来非饱和土稳态渗流试验装置进行了改进和完善,还使用SolidWorks对装置的空间结构进行优化。提出两种结构布局设计方案以满足不同的生产方式需要,把杂散的平铺在试验台上的原来试验装置,变成了现在真正的结构一体化。合理的设计主体框架和内部零部件的工作平台,保证了工作过程中各个零部件之间的干扰最小,做实验时操作变得简单,实验的安全性得到加强,实验数据的可靠性得到了保证。
由于装置目前还处于试验研究阶段,故在保证试验可靠性、安全性、操作性的基础上选择了经济实用的型材设计装置外框,更好的应用到试验中。
In geotechnical engineering domain, there are different kinds of soil structure, which most are in unsaturated status. The research of unsaturated soil is very important to the project. Unsaturated permeability coefficient is one important parameter to the determination of water-air flow in unsaturated soil, the measurement of this parameter not only is a significant issue in unsaturated soil research field but also is a key point to research the water infiltration of the soil. But the measurement of this parameter is so difficult that no measuring device and function can acquire it presicely until now, and cannot satisfy the request of the engineering
This paper, at the start point of the shortage of the current aparatus of water permeability for unsaturated soils, the novel steady flow instrument for unsaturated soils for measurement of unsaturated permeability coefficient has been developed based on the improvement and amendment on original device. In order to enhance the exhaust function of the pressure room, the cutting of the specimen foundation has been redesigned. Also, the air pressure control system has been redesigned,by using the controlling valve of air pressure; For replacing the old manual valves, A new pipeline control system has been designed and the intelligent control of the water-air flow has been achieved.
The device not only be improved and perfected, but also be optimized at space structure by SolidWorks. For changing the condition that all the parts lay on the test bench disorderly into entirety type orderliness, the paper proposes two programs of space structure layout to meet different production. The reasonably design of skeleton frame and parts test bench, can ensure the least interference among parts and easily operation during working. The novel device enhance the security of test and the reliability of experimental result.
The device is in experimental study point at present, at the base of reliability, security and maintenance this structure is very pithy and cheap, which use the aluminium alloy sections as the basical skeleton frame。
引文
[1]费雷德隆德D G. H拉哈尔佐著.非饱和土土力学.陈仲颐等译.北京：中国建筑工业出版社,1997.
[2]包成纲.非饱和土的性状及膨胀土边坡稳定问题[J].岩土工程学报,2004,Vol.26(1)： 1-15.
[3]谢定义.对非饱和土基本特性的学习和思考.第二届全国非饱和土会议研究讨论会论文集[C].杭州：浙江大学,2005：1-32
[4]蒋彭年.非饱和土工程性质简论[J].岩土工程学报,1989,11(6)pp39-59
[5]Fred Lund D G, Xing A, Huang S G. Predicting the permeability function for unsaturated s-oil using the soil-water characteristic curve. Canadian Geotechnical Journal,1994,31:533-546
[6]Tarantino,A.&M ongiovi, L. Calibration of tensiometer for direct measurement of mat-ricsuc tion [J].Can.Geotech.J.2003,53(1):137-141.
[7]Ridley A M, Dineen K, Burland J B and Vaughan P R. Soil matrix suction:some examples of its measurement and application in geotechnical engineering[J].Geotechnique,2003,53(2):2 41-253.
[8]Leong, E.C., Tripathy, S.&Rahardjo. H. Total suction measurement of unsaturated soils with a device using the chilled-mirror dew-point technique[J].Can.Geotech.J.2003,53(2):173-182.
[9]Fredlund D G. Bringing unsaturated soil mechanics into engineering practice. Proceedings of the 2nd International Conference on Unsaturated soils[C].Vol.2.Inter.Acad.Pub.Beijing.l998, p p1-35.
[10]张在明.地下水与建筑基础工程[M].北京：中国建筑工业出版社,2001.
[11]梁爱民,邵龙潭.非饱和土壤渗透特性及饱和入谂机理试验研究：(博士学位论文).大连：大连理工大学.
[12]刘奉银,谢定义等.非饱和土渗水渗气的机理与参数测试方法的探讨[J].西安公路交通大学报,1996,Vol.16,岩土工程专辑.
[13]刘奉银.非饱和土力学基本试验设备的研制与新有效应力原理的探讨[D].西安理工大学博士学位论文,1999.10.
[14]谢定义,陈正汉。非饱和土力学特性的理论与测试[A].。见：土力学机基础工程学会。非饱和土理论与实践学时研讨会文集[C].北京：[S.N.].,1992,227-229
[15]Marshall TJ.A relation between permeability and size distribution of pores[J].J.Soil Sci.,1958, (1):1-8
[16]Milliongton R J, Quirk JP. Permeability of porous media[J].Nature,1959,183(2):387-388
[17]Milliongton R J, Quirk JR. Permeability of Solids[J].Trans.Faraday Soc.,1961,57(10):1200-1 207
[18]陈正汉.非饱和土与特殊土测试技术新进展,第二届全国非饱和土学术研讨会论文集[C],杭州,2005.4,pp77-136.
[19]高永宝.微机控制非饱和土水-气运动联测仪的研制及浸水试验研究：(硕士学位论文).西安：西安理工大学,2006,3.
[20]俞培基,陈愈炯.非饱和土的水-气形态及其与力学性质的关系.水利学报,1965,(1)：16-23.
[21]Corey. A.T. Measurement of water and air permeability in unsaturated soil. Soil Science Soc-iety of America Proceedings,1957,21(1):7-10.
[22]Klute A. Laboratory measurement of hydraulic conductivity of unsaturated soil. In:Black C A, Evans D D, White J L, et al. Methods of Soil Analysis, Madison:American Society of Agronomy,1965:253-261.
[23]Hamilton J M, Daniel D E, Olson R E. Measurement of hydraulic conductivity of partially saturated soils. In:Zimmie T F, Riggs C O. Permeability and Groundwater Contaminant Tra nsport, New York:ASTM Special Technical Publication,1981:182-196
[24]陈正汉.非饱和土固结的混和物理论——数学模型、试验研究、边值问题：(博士学位论文).西安：陕西机械学院,1991.5.
[25]陈正汉,谢定义,王永胜.非饱和土的水气运动规律及其工程性质研究,岩土工程学报1993,15(3)：9-20.
[26]王永胜.非饱和土中水、气运动规律与水、气压力演化特性的研究：(硕士学位论文).西安：西安理工大学,1991,2.
[27]Liu Fengyin and Xie Dingyi. Movement characteristics measurement of pore water-air in unsaturated soils. In:Proceedings of the 2nd International Conference on Unsaturated soils, Beijing, 1998:395-401.
[28]赵敏.非饱和土孔隙流体运动规律的研究：(硕士学位论文).西安：西安理工大学,1999,3.
[29]王文焰,张建丰.在一个水平土柱上同时测定非饱和土壤水各运动参数的试验研究.水利学报,1990,(7)：26-30.
[30]Fleureau J M, Taibi S. Water-air permeabilities of unsaturated soils. In:Proceedings of the 1st International Conference on Unsaturated Soils, Balkema/Rotterdam/Brookfield,1995,2,479-484.
[31]Hamilton J M, Daniel D E, Olson R E. Measurement of hydraulic conductivity of partially saturated soils. In:Zimmie T F, Riggs C O. Permeability and Groundwater Contaminant Transport, New York: ASTM Special Technical Publication,1981:182-196.
[32]Sharma,R.S&Mohamed,M.H.A,Patterns and mechanisms of migration of light non-aqueous phase liquid in an unsaturated sand[J].Can.Geotech.J.2003,53(2):225-239.
[33]Dane,J.H.,Hofstee,C.,and Corey,A.T.Simultaneous measurement of capillary pressure,saturation and effective permeability of immiscible liquids in porous media[J]. Water Resources Research,1998.34(12):3687-3692.
[34]Gan,J.K.M.,and Fredlund,D.G.A new laboratory method for the measurement of unsaturated coefficient of permeability of soils. In unsaturated soils for Asia[C].Edited by H.Rahardjo,D.Toll,and E.C.Leong.A.A.Balkema, Rotterdam,2000.pp.381-386.
[35]Samingan A S.,Leong E C.,and Rahardjo H.A flexible wall permeameter for measurements of water and air coefficients of permeability of residual soils[J].Can.Geotech.J,2003,40:559-574.
[36]李永乐,刘翠然,刘海宁等.非饱和土渗透特性试验研究[J].岩石力学与工程学报,2004,23(22)：3861-3865.
[37]徐永福,兰守奇,孙德安等.一种能量测应力状态对非饱和土渗透系数影响德新型试验装置[J].岩石力学与工程学报,2005,24(1)：160-164.
[38]Fredlund DG.Raharjo H.Soil Mechanics for Unsaturated Soils[M].John Wiley&Sons.Inc.1993
[39]Gregson K,Hector DJ,McGowan M.A one-paramerer model for the soil-water characteristic[J].J.Soil Science.1987.38:483-486
[40]Williams J,Perbble R E.Williams W T.etal.The influence of texture.strucure. and clay mineralogy on the soil moisture characteristic[J].Aust.J.Soil Research.1983,21:15-32
[41]Rawls W J, Gish TJ, Brakensiel DL. In:Stewart B A(ed.) Estimating soil water retention from soil physical properties and characteristics[M].Advances in Soil Science.1991.16:213-234. Springer
[42]Wosten J H M. Pedotransfer functions to evaluate soil quality [A].In:Gregorich EG.Carter R.(Ed).Soil Quality for Grop Production and Ecosysrem Health [M].Developments in Soil Science.1997,25:221-245.Amsterdam:Elseier.
[43]Gander W R.Calculation of capillary conductivity from pressure plate outflow data [J].Soil Science,1956,317-320
[44]Vereecken H.Maes J, Feyen J.Estimating unsaturated hydraulic conductivity from easily measured soil properties [J].Soil Science,1990.149:1-12
[45]Campbell G S. A simple model for determining unsarurared hydraulic conductivity from moisture relention data [J]. Soil Science,1974,117:311-314
[46]Van Genuchten M TH. A closed-form equation for predicting the hydraulic conductivity of unsaturated Soils. Soil Science Society of America Journal,1980,44:892-898.
[47]Toledo P G, Novy R A, Davi H T, s et al. Hydraulic conductivity of porous media at low water content. Soil Science Society of America Journal,1990,54:673-679.
[48]Tyler S W, Wheatcraft S W. Fractal process in soil water retention. Water Resources Research,1990, 26:1047-1054.
[49]Mualem Y. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research,1976,12:513-522.
[50]Burdine N T. Relative permeability calculations from size distribution data. Transactions of the American Institute of Mining, Metallurgical and Petroleum Engineers,1953,198:71-78.
[51]Crawford J W. The relationship between structure and the hydraulic conductivity of soil. European Journal of Soil Science,1994,45:493-501.
[52]Fuentes C, Vauclin M, Parlange J I. A note on the soil-water conductivity of a fractal soil. Transport in Porous Media,1996,23:31-36.
[53]Hunt A G, Gee G W. Application of critical path analysis to fractal porous media: comparison with examples from the Hanfordsite. Adv in Water Resources,2002,25: 129-146.
[54]Xu Y F, Dong P. Fractal approach to hydraulic properties in unsaturated porous media. Chaos, Solitons and Fractals,2004,19:327-337.
[55]孙大松,刘鹏,夏小和等.非饱和土的渗透系数.水利学报,2004,(3)：71-75
[56]邵明安,李开元,钟良平.根据土壤水分特征曲线推求土壤的导水参数.水土保持研究,1991,6：26-32.
[57]Xu Y F, Sun D A. A fractal model for soil pores and its application to determination of water permeability. PhysicaA,2002,316 (1-4):56-64.
[58]Xu Y F, Calculation of unsaturated hydraulic conductivity using a fractal model for the pore-size distribution. Computers and Geotechnics,2004,31:37-41.
[59]邵龙潭,韩国城.两相多孔介质力学分析的相互作用原理.见：辽宁省第二届青年学术年会论文集,甲国；大连,1995：232-234.
[60]邵龙潭.孔隙介质力学分析方法及其在土力学中的应用.(博士学位论文).大连：大连理工大学,1996：24-65.
[61]邵龙潭.相间相互作用原理与土壤水动力学基本方程.水科学进展,2002,13(2)：24-65.
[62]杨金忠等.多孔介质中水分及溶质运移的随机理论[M],科学出版社,2000.
[63]雷志栋,杨诗秀,谢森传.土壤水动力学[M],清华大学出版社,1988.
[64]Richards L A. Capillary conduction of liquids in porous mediums. Journal of Physics,1931, (1):30-33.
[65]Kostiakov A N.On the dynamics of the coeffient of water percolation in soils and on the necessity of studying it from a dynamic point of view for purposes of amelioration. Journal of Soil Science. 1932,97(1):17-21.
[66]Childs E C,N Collis-George. The permeability of porous materials. Proceedings of Royal Society of London,1950,201:392-405.
[67]钱家欢,殷宗泽.土工原理与计算.北京：中国水利水电出版社,1996.
[68](日)雨宫好文.控制用电机入门.科学工业出版社.2000.
[69]土工试验规程.中华人民共和国行业标准(SL237-1999).北京：中国水利水电出版社,1999：19-27.
[2]包成纲.非饱和土的性状及膨胀土边坡稳定问题[J].岩土工程学报,2004,Vol.26(1)： 1-15.
[3]谢定义.对非饱和土基本特性的学习和思考.第二届全国非饱和土会议研究讨论会论文集[C].杭州：浙江大学,2005：1-32
[4]蒋彭年.非饱和土工程性质简论[J].岩土工程学报,1989,11(6)pp39-59
[5]Fred Lund D G, Xing A, Huang S G. Predicting the permeability function for unsaturated s-oil using the soil-water characteristic curve. Canadian Geotechnical Journal,1994,31:533-546
[6]Tarantino,A.&M ongiovi, L. Calibration of tensiometer for direct measurement of mat-ricsuc tion [J].Can.Geotech.J.2003,53(1):137-141.
[7]Ridley A M, Dineen K, Burland J B and Vaughan P R. Soil matrix suction:some examples of its measurement and application in geotechnical engineering[J].Geotechnique,2003,53(2):2 41-253.
[8]Leong, E.C., Tripathy, S.&Rahardjo. H. Total suction measurement of unsaturated soils with a device using the chilled-mirror dew-point technique[J].Can.Geotech.J.2003,53(2):173-182.
[9]Fredlund D G. Bringing unsaturated soil mechanics into engineering practice. Proceedings of the 2nd International Conference on Unsaturated soils[C].Vol.2.Inter.Acad.Pub.Beijing.l998, p p1-35.
[10]张在明.地下水与建筑基础工程[M].北京：中国建筑工业出版社,2001.
[11]梁爱民,邵龙潭.非饱和土壤渗透特性及饱和入谂机理试验研究：(博士学位论文).大连：大连理工大学.
[12]刘奉银,谢定义等.非饱和土渗水渗气的机理与参数测试方法的探讨[J].西安公路交通大学报,1996,Vol.16,岩土工程专辑.
[13]刘奉银.非饱和土力学基本试验设备的研制与新有效应力原理的探讨[D].西安理工大学博士学位论文,1999.10.
[14]谢定义,陈正汉。非饱和土力学特性的理论与测试[A].。见：土力学机基础工程学会。非饱和土理论与实践学时研讨会文集[C].北京：[S.N.].,1992,227-229
[15]Marshall TJ.A relation between permeability and size distribution of pores[J].J.Soil Sci.,1958, (1):1-8
[16]Milliongton R J, Quirk JP. Permeability of porous media[J].Nature,1959,183(2):387-388
[17]Milliongton R J, Quirk JR. Permeability of Solids[J].Trans.Faraday Soc.,1961,57(10):1200-1 207
[18]陈正汉.非饱和土与特殊土测试技术新进展,第二届全国非饱和土学术研讨会论文集[C],杭州,2005.4,pp77-136.
[19]高永宝.微机控制非饱和土水-气运动联测仪的研制及浸水试验研究：(硕士学位论文).西安：西安理工大学,2006,3.
[20]俞培基,陈愈炯.非饱和土的水-气形态及其与力学性质的关系.水利学报,1965,(1)：16-23.
[21]Corey. A.T. Measurement of water and air permeability in unsaturated soil. Soil Science Soc-iety of America Proceedings,1957,21(1):7-10.
[22]Klute A. Laboratory measurement of hydraulic conductivity of unsaturated soil. In:Black C A, Evans D D, White J L, et al. Methods of Soil Analysis, Madison:American Society of Agronomy,1965:253-261.
[23]Hamilton J M, Daniel D E, Olson R E. Measurement of hydraulic conductivity of partially saturated soils. In:Zimmie T F, Riggs C O. Permeability and Groundwater Contaminant Tra nsport, New York:ASTM Special Technical Publication,1981:182-196
[24]陈正汉.非饱和土固结的混和物理论——数学模型、试验研究、边值问题：(博士学位论文).西安：陕西机械学院,1991.5.
[25]陈正汉,谢定义,王永胜.非饱和土的水气运动规律及其工程性质研究,岩土工程学报1993,15(3)：9-20.
[26]王永胜.非饱和土中水、气运动规律与水、气压力演化特性的研究：(硕士学位论文).西安：西安理工大学,1991,2.
[27]Liu Fengyin and Xie Dingyi. Movement characteristics measurement of pore water-air in unsaturated soils. In:Proceedings of the 2nd International Conference on Unsaturated soils, Beijing, 1998:395-401.
[28]赵敏.非饱和土孔隙流体运动规律的研究：(硕士学位论文).西安：西安理工大学,1999,3.
[29]王文焰,张建丰.在一个水平土柱上同时测定非饱和土壤水各运动参数的试验研究.水利学报,1990,(7)：26-30.
[30]Fleureau J M, Taibi S. Water-air permeabilities of unsaturated soils. In:Proceedings of the 1st International Conference on Unsaturated Soils, Balkema/Rotterdam/Brookfield,1995,2,479-484.
[31]Hamilton J M, Daniel D E, Olson R E. Measurement of hydraulic conductivity of partially saturated soils. In:Zimmie T F, Riggs C O. Permeability and Groundwater Contaminant Transport, New York: ASTM Special Technical Publication,1981:182-196.
[32]Sharma,R.S&Mohamed,M.H.A,Patterns and mechanisms of migration of light non-aqueous phase liquid in an unsaturated sand[J].Can.Geotech.J.2003,53(2):225-239.
[33]Dane,J.H.,Hofstee,C.,and Corey,A.T.Simultaneous measurement of capillary pressure,saturation and effective permeability of immiscible liquids in porous media[J]. Water Resources Research,1998.34(12):3687-3692.
[34]Gan,J.K.M.,and Fredlund,D.G.A new laboratory method for the measurement of unsaturated coefficient of permeability of soils. In unsaturated soils for Asia[C].Edited by H.Rahardjo,D.Toll,and E.C.Leong.A.A.Balkema, Rotterdam,2000.pp.381-386.
[35]Samingan A S.,Leong E C.,and Rahardjo H.A flexible wall permeameter for measurements of water and air coefficients of permeability of residual soils[J].Can.Geotech.J,2003,40:559-574.
[36]李永乐,刘翠然,刘海宁等.非饱和土渗透特性试验研究[J].岩石力学与工程学报,2004,23(22)：3861-3865.
[37]徐永福,兰守奇,孙德安等.一种能量测应力状态对非饱和土渗透系数影响德新型试验装置[J].岩石力学与工程学报,2005,24(1)：160-164.
[38]Fredlund DG.Raharjo H.Soil Mechanics for Unsaturated Soils[M].John Wiley&Sons.Inc.1993
[39]Gregson K,Hector DJ,McGowan M.A one-paramerer model for the soil-water characteristic[J].J.Soil Science.1987.38:483-486
[40]Williams J,Perbble R E.Williams W T.etal.The influence of texture.strucure. and clay mineralogy on the soil moisture characteristic[J].Aust.J.Soil Research.1983,21:15-32
[41]Rawls W J, Gish TJ, Brakensiel DL. In:Stewart B A(ed.) Estimating soil water retention from soil physical properties and characteristics[M].Advances in Soil Science.1991.16:213-234. Springer
[42]Wosten J H M. Pedotransfer functions to evaluate soil quality [A].In:Gregorich EG.Carter R.(Ed).Soil Quality for Grop Production and Ecosysrem Health [M].Developments in Soil Science.1997,25:221-245.Amsterdam:Elseier.
[43]Gander W R.Calculation of capillary conductivity from pressure plate outflow data [J].Soil Science,1956,317-320
[44]Vereecken H.Maes J, Feyen J.Estimating unsaturated hydraulic conductivity from easily measured soil properties [J].Soil Science,1990.149:1-12
[45]Campbell G S. A simple model for determining unsarurared hydraulic conductivity from moisture relention data [J]. Soil Science,1974,117:311-314
[46]Van Genuchten M TH. A closed-form equation for predicting the hydraulic conductivity of unsaturated Soils. Soil Science Society of America Journal,1980,44:892-898.
[47]Toledo P G, Novy R A, Davi H T, s et al. Hydraulic conductivity of porous media at low water content. Soil Science Society of America Journal,1990,54:673-679.
[48]Tyler S W, Wheatcraft S W. Fractal process in soil water retention. Water Resources Research,1990, 26:1047-1054.
[49]Mualem Y. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research,1976,12:513-522.
[50]Burdine N T. Relative permeability calculations from size distribution data. Transactions of the American Institute of Mining, Metallurgical and Petroleum Engineers,1953,198:71-78.
[51]Crawford J W. The relationship between structure and the hydraulic conductivity of soil. European Journal of Soil Science,1994,45:493-501.
[52]Fuentes C, Vauclin M, Parlange J I. A note on the soil-water conductivity of a fractal soil. Transport in Porous Media,1996,23:31-36.
[53]Hunt A G, Gee G W. Application of critical path analysis to fractal porous media: comparison with examples from the Hanfordsite. Adv in Water Resources,2002,25: 129-146.
[54]Xu Y F, Dong P. Fractal approach to hydraulic properties in unsaturated porous media. Chaos, Solitons and Fractals,2004,19:327-337.
[55]孙大松,刘鹏,夏小和等.非饱和土的渗透系数.水利学报,2004,(3)：71-75
[56]邵明安,李开元,钟良平.根据土壤水分特征曲线推求土壤的导水参数.水土保持研究,1991,6：26-32.
[57]Xu Y F, Sun D A. A fractal model for soil pores and its application to determination of water permeability. PhysicaA,2002,316 (1-4):56-64.
[58]Xu Y F, Calculation of unsaturated hydraulic conductivity using a fractal model for the pore-size distribution. Computers and Geotechnics,2004,31:37-41.
[59]邵龙潭,韩国城.两相多孔介质力学分析的相互作用原理.见：辽宁省第二届青年学术年会论文集,甲国；大连,1995：232-234.
[60]邵龙潭.孔隙介质力学分析方法及其在土力学中的应用.(博士学位论文).大连：大连理工大学,1996：24-65.
[61]邵龙潭.相间相互作用原理与土壤水动力学基本方程.水科学进展,2002,13(2)：24-65.
[62]杨金忠等.多孔介质中水分及溶质运移的随机理论[M],科学出版社,2000.
[63]雷志栋,杨诗秀,谢森传.土壤水动力学[M],清华大学出版社,1988.
[64]Richards L A. Capillary conduction of liquids in porous mediums. Journal of Physics,1931, (1):30-33.
[65]Kostiakov A N.On the dynamics of the coeffient of water percolation in soils and on the necessity of studying it from a dynamic point of view for purposes of amelioration. Journal of Soil Science. 1932,97(1):17-21.
[66]Childs E C,N Collis-George. The permeability of porous materials. Proceedings of Royal Society of London,1950,201:392-405.
[67]钱家欢,殷宗泽.土工原理与计算.北京：中国水利水电出版社,1996.
[68](日)雨宫好文.控制用电机入门.科学工业出版社.2000.
[69]土工试验规程.中华人民共和国行业标准(SL237-1999).北京：中国水利水电出版社,1999：19-27.