岩土多孔介质孔隙结构的分形研究及其应用
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摘要
岩土多孔介质作为一种特殊的工程材料,其工程性质具有复杂性和变化性,而这种复杂性和变化性主要受其微观或细观结构的控制,因而对其微观结构进行研究具有极其重要的意义。岩土多孔介质微观孔隙和颗粒的大小和形状相异,表现出“无序”的特征。大量研究表明它们表现出分形特性,因而分形理论成为岩土介质微观、细观特性研究的有效手段。基于分形理论,本文对岩土介质孔隙结构展开研究工作,目的旨在推动岩土多孔介质的微观结构研究。
论文首先对岩土多孔介质的分形模型进行深入研究,提出了两大类模型。这两类分形模型能将国内外模型统一起来,从而形成了两类统一的模型,有效避免了分形模型的错用。
论文对岩土多孔介质的分形维数进行了系统的归类与定义,并研究它们之间的关系。建立了二维和三维空间分维数之间的联系,从而可以通过二维数字图像技术估算岩土多孔介质在三维空间的分维数。证明了颗粒原状面积(体积)分布分维数与孔隙原状面积(体积)分布分维数在有限尺度范围内能同时存在,并给出了两者之间的关系式。黏性土的微观结构实验数据表明：通过此关系式可有效估算孔隙原状面积分布分维数。建立了土壤黏粒含量与其颗粒质量～粒径分布分维数的关系,大量的实验数据证明了它的有效性。
论文采用土壤切片技术、SEM技术、压汞技术及数字图像技术获得了水泥基环境岩土材料、软黏土的孔隙分布数据,在此基础上研究了取样深度及干湿循环对水泥基环境岩土材料孔隙分布的影响,研究了固结压力对软黏土孔隙分布的影响。
利用软黏土和水泥基环境岩土材料在二维和三维空间内的孔隙实验数据证明了本文提出的分形模型的合理性。
论文探讨了分维数求解方法对岩土多孔介质的孔隙分形特性的影响,结果表明本文提出的分维数求解方法比已有方法更为方便、有效、合理。
论文对孔隙分布的定量化描述进行了深入研究,提出了3种描述孔隙孔径分布的孔隙率模型,并利用黏土和水泥基环境岩土材料在二维和三维空间内的孔隙实验数据研究其适用性,结果表明：三维空间内,第3种孔隙率模型预测值与实测值吻合很好,二维空间内,模型的有效性与相应的孔隙数量-孔径分布分维数大小紧密相关。
利用提出的描述孔隙孔径分布的孔隙率模型,给出了基于土体微观孔隙结构的固结变形计算公式,在低固结压力下压缩应变计算值与实测值相差约0.007；建立了多种非饱和土的土-水特征曲线模型,从形式上包含了现有的土-水特征曲线模型,由于模型中的颗粒原状面积(体积)分布分维数能反映孔隙分布特性,因而建立的土-水特征曲线模型更为合理；最后给出了土体黏聚力及岩土介质体积密度与样本尺寸的关系式,从而验证了黏聚力及体积密度随样本尺寸增大而减小的规律。
As special engineering materials, rock and soil porous media show complicated and diverse engineering properties, which are controlled by their microstructures (or mesostructures), so it is very important to make deep research on their microstructures. The grains and pores in rock and soil porous media vary in shape and size, displaying disordered properties. However, in many other studies it has been shown that they are fractals. Consequently, the fractal theory has become accepted as a valid means to study the microstructures of rock and soil porous media. By using the fractal theory, the study on pore structure of rock and soil porous media was carried out and some valuable conclusions were gained.
At first, two categories of fractal models of rock and soil porous media were established in this study. It was found that previous models can be unified by the two categories of fractal models, so the unified fractal models were formed.
Afterward, the fractal dimensions of rock and soil porous media were classified and defined. A new method was presented to estimate the fractal dimensions in 3D space from the 2D structures of rocks and soils, thus the technique of digital image in 2D can be easily applied to obtain the fractal dimensions in 3D space. This study shows that the grain area (volume) fractal dimension and the pore area (volume) fractal dimension can exist simultaneously on a finite scale. The expression for the relationship between the two fractal dimensions was established. The experimental results of the microstructure of clay indicate that the expression is valid for estimating the pore area fractal dimension. The expression for the relationship between the fractal dimension of grain mass vs particle-size and the clay contents was founded, and its rationality has been verified by many experimental results.
By using soil micromorphology technique, the mercury intrusion technique, the scanning electron microscope (SEM) and image analysis technique, the pore-size distributions of ecotypic revetment material (eco-material) and soft clay were gained. Moreover, the effects of soil depth and wet-dry cycling on the pore property of eco-material and the effects of consolidation pressure on the pore property of soft clay were investigated.
Experimental results of pore distributions of soft clay and eco-material show the fractal models presented by this study are rational.
The relationship between the calculation methods of fractal dimensions and the fractal behaviors of materials was studied. The results show the calculation methods of fractal dimension presented by this study are more effective and rational than previous means.
At last, three new porosity models were developed to describe the pore-size distributions of porous media. Pore-size distributions of soft clay and eco-material in two- and three-dimensional spaces were used to study the applicability of proposed porosity models. The results show that the new porosity models are valid in describing the pore-size distributions of rock and soil samples.
Based on the new porosity models, a new microstructure soil consolidation model was developed and the error of the compression strain prediction was less than 0.007 under low pressure. Several models for soil water retention curve were founded, which in form comprise previous models developed by other researchers, and they may be more accurate than previous models because of the valid mean for determining the fractal dimension. In addition, we obtained an expression for the relationship between soil cohesion and the test specimen size, as well as between the bulk density of rocks and soils and the test specimen size.
论文首先对岩土多孔介质的分形模型进行深入研究,提出了两大类模型。这两类分形模型能将国内外模型统一起来,从而形成了两类统一的模型,有效避免了分形模型的错用。
论文对岩土多孔介质的分形维数进行了系统的归类与定义,并研究它们之间的关系。建立了二维和三维空间分维数之间的联系,从而可以通过二维数字图像技术估算岩土多孔介质在三维空间的分维数。证明了颗粒原状面积(体积)分布分维数与孔隙原状面积(体积)分布分维数在有限尺度范围内能同时存在,并给出了两者之间的关系式。黏性土的微观结构实验数据表明：通过此关系式可有效估算孔隙原状面积分布分维数。建立了土壤黏粒含量与其颗粒质量～粒径分布分维数的关系,大量的实验数据证明了它的有效性。
论文采用土壤切片技术、SEM技术、压汞技术及数字图像技术获得了水泥基环境岩土材料、软黏土的孔隙分布数据,在此基础上研究了取样深度及干湿循环对水泥基环境岩土材料孔隙分布的影响,研究了固结压力对软黏土孔隙分布的影响。
利用软黏土和水泥基环境岩土材料在二维和三维空间内的孔隙实验数据证明了本文提出的分形模型的合理性。
论文探讨了分维数求解方法对岩土多孔介质的孔隙分形特性的影响,结果表明本文提出的分维数求解方法比已有方法更为方便、有效、合理。
论文对孔隙分布的定量化描述进行了深入研究,提出了3种描述孔隙孔径分布的孔隙率模型,并利用黏土和水泥基环境岩土材料在二维和三维空间内的孔隙实验数据研究其适用性,结果表明：三维空间内,第3种孔隙率模型预测值与实测值吻合很好,二维空间内,模型的有效性与相应的孔隙数量-孔径分布分维数大小紧密相关。
利用提出的描述孔隙孔径分布的孔隙率模型,给出了基于土体微观孔隙结构的固结变形计算公式,在低固结压力下压缩应变计算值与实测值相差约0.007；建立了多种非饱和土的土-水特征曲线模型,从形式上包含了现有的土-水特征曲线模型,由于模型中的颗粒原状面积(体积)分布分维数能反映孔隙分布特性,因而建立的土-水特征曲线模型更为合理；最后给出了土体黏聚力及岩土介质体积密度与样本尺寸的关系式,从而验证了黏聚力及体积密度随样本尺寸增大而减小的规律。
As special engineering materials, rock and soil porous media show complicated and diverse engineering properties, which are controlled by their microstructures (or mesostructures), so it is very important to make deep research on their microstructures. The grains and pores in rock and soil porous media vary in shape and size, displaying disordered properties. However, in many other studies it has been shown that they are fractals. Consequently, the fractal theory has become accepted as a valid means to study the microstructures of rock and soil porous media. By using the fractal theory, the study on pore structure of rock and soil porous media was carried out and some valuable conclusions were gained.
At first, two categories of fractal models of rock and soil porous media were established in this study. It was found that previous models can be unified by the two categories of fractal models, so the unified fractal models were formed.
Afterward, the fractal dimensions of rock and soil porous media were classified and defined. A new method was presented to estimate the fractal dimensions in 3D space from the 2D structures of rocks and soils, thus the technique of digital image in 2D can be easily applied to obtain the fractal dimensions in 3D space. This study shows that the grain area (volume) fractal dimension and the pore area (volume) fractal dimension can exist simultaneously on a finite scale. The expression for the relationship between the two fractal dimensions was established. The experimental results of the microstructure of clay indicate that the expression is valid for estimating the pore area fractal dimension. The expression for the relationship between the fractal dimension of grain mass vs particle-size and the clay contents was founded, and its rationality has been verified by many experimental results.
By using soil micromorphology technique, the mercury intrusion technique, the scanning electron microscope (SEM) and image analysis technique, the pore-size distributions of ecotypic revetment material (eco-material) and soft clay were gained. Moreover, the effects of soil depth and wet-dry cycling on the pore property of eco-material and the effects of consolidation pressure on the pore property of soft clay were investigated.
Experimental results of pore distributions of soft clay and eco-material show the fractal models presented by this study are rational.
The relationship between the calculation methods of fractal dimensions and the fractal behaviors of materials was studied. The results show the calculation methods of fractal dimension presented by this study are more effective and rational than previous means.
At last, three new porosity models were developed to describe the pore-size distributions of porous media. Pore-size distributions of soft clay and eco-material in two- and three-dimensional spaces were used to study the applicability of proposed porosity models. The results show that the new porosity models are valid in describing the pore-size distributions of rock and soil samples.
Based on the new porosity models, a new microstructure soil consolidation model was developed and the error of the compression strain prediction was less than 0.007 under low pressure. Several models for soil water retention curve were founded, which in form comprise previous models developed by other researchers, and they may be more accurate than previous models because of the valid mean for determining the fractal dimension. In addition, we obtained an expression for the relationship between soil cohesion and the test specimen size, as well as between the bulk density of rocks and soils and the test specimen size.
引文
[1]Mandelbrot B B. How long is the coast of Britain, statistical self similarity and fractional dimension[J]. Science,1967,155:636-638.
[2]Perret J, Prasher S O, et al. 3-D visualization of soil macroporosity using x-ray CAT scanning[J]. Can. Agri. Eng.,1997,39 (4):249-261.
[3]李德成,张桃林,B. Velde等.CT分析技术在土壤科学研究中的应用[J].土壤,2002,6：328-332.
[4]Petrovic A M, Siebert J E, Rieke P E. Soil bulk density analysis in three dimensions by computed tomographic scanning[J]. Soil Sci. Soc. Am. J.,1982,46 (3):445-450.
[5]Anderson S H, Gantzer C J, et al. Rapid nondestructive bulk density and soil-water content determination by computed tomography[J]. Soil Sci. Soc. Am. J.,1988,52 (1):35-40.
[6]Zeng Y, Gantzer C J, et al. Fractal dimension and lacunarity of bulk density determined with x-ray computed tomography [J]. Soil Sci. Soc. Am. J.,1996,60 (6):1718-1724.
[7]Hainsworth J M, Aylmore L A G. The use of computer-assisted tomography to determine spatial distribution of soil water content[J]. Aust. J. Soil. Res.,1983,21 (4):435-443
[8]王国梁,周生路,赵其国.土壤颗粒的体积分形维数及其在土地利用中的应用[J].土壤学报,2005,42(4)：545-550.
[9]王清,王剑平.土孔隙的分形几何研究[J].岩土工程学报,2000,22(4)：496-498.
[10]黄丽.饱和软黏土微观孔隙的定量分析及其分形研究[D].武汉：武汉理工大学,2007.
[11]葛世荣,朱华.摩擦学的分形[M].北京：机械工业出版社,2005.
[12]Whitehouse D J. Comparison between stylus and optical methods for measuring surfaces [J]. Annals of the CIPP,1988,37(2):649-653.
[13]曹麟祥,王红.表面粗糙度的现代测量技术[J].测控技术.1992,2：17-20.
[14]Turcotte D L, Harris R A. Relationship between the oceanic geoid and the structure of the oceanic lithosphere[J]. Marine Geophysical Researches,1984,54:1-2.
[15]Matsushita M. Fractal viewpoint of fracture and accretion[J]. J. Phys. Soc. Jpn.,1986; 54: 857-860.
[16]Tyler S W, Wheatcraft S W. Fractal scaling of soil particle size distribution:Analysis and limitations[J]. Soil Sci. Soc. Am. J.,1992,56:362-370.
[17]Turcotte D L. Fractals and fragmentation[J]. Journal of Geophysical Research,1986,91 (B2):1921-1926.
[18]张季如,朱瑞赓,祝文化.用粒径的数量分布表征的土壤分形特征[J].水利学报,2004,(4)：67-71,79.
[19]Tyler S W, Wheatcraft S W. Fractal scaling of soil particle-size distribution:Analysis and limitations[J]. Soil Sci. Soc. Am. J.,1992,56 (2):362-369.
[20]杨培岭,罗远培,石元春.用粒径的重量分布表征的土壤分形特征[J].科学通报,1993,38：1896-1899.
[21]李德成,张桃林.中国土壤颗粒组成的分形特征研究[J].土壤与环境,2000,9(4)：263-265.
[22]黄冠华,詹卫华.土壤颗粒的分形特征及其应用[J].土壤学报,2002,39(4)：490-497.
[23]王宝军,·施斌,唐朝生.基于GIS实现黏性土颗粒形态的三维分形研究[J].岩土工程学报,2007,29(2)：309-312
[24]Hurd A J, et al. Surface areas of fractally rough particles studied by scattering[J]. Phys. Rev., 1989, B39:9742-9745.
[25]武生智,魏春玲,马崇武,等.沙粒粗糙度和粒径分布的分形特性[J].兰州大学学报(自然科学版),1999,35(1)：44-47.
[26]Katz A J, Thompson A H. Fractal sandstone pores:implications for conductivity and pore formation[J]. Phys Rev Lett,1985,54(12):1325-1328.
[27]Brakensiek D L, Rwals W J, Logsdond S D, et al. Fractal description of micro-porosity [J]. Soil Sci. Soc. Am.J.,1992,56:1721-1723.
[28]Anderson A N, Mcbratney A B, Fitzpatrick E A. Soil mass, surface, and spectral fractal dimensions estimated from thin section photographs[J]. Soil Sci. Soc. Am. J.,1996,60:962-969.
[29]李向全,胡瑞林,张莉.黏性土固结过程中的微结构效应研究[J].岩土工程技术,1999,3(3)：52-56.
[30]张季如,祝杰,黄丽,等.固结条件下软黏土微观孔隙结构的演化及其分形描述[J].水利学报,2008,39(4)：394-400.
[31]周宇泉,洪宝宁.黏性土压缩过程中的微细结构变化试验研究[J].岩土力学,2005,26(增)：82-86.
[32]王清,王剑平.土孔隙的分形几何研究[J].岩土工程学报,2000,22(4)：496-498.
[33]许勇,张季超,李伍平.饱和软土微结构分形特征的试验研究[J].岩土力学,2007,28(增)：49-52.
[34]Pfeifer P, Avnir D J. "Chemistry in noninteger dimensions between two and three. Ⅰ. Fractal theory of heterogeneous surfaces"[J]. Chem. Phys.,1983,79:3558-3565.
[35]Avnir D, Farin D, Pfeifer P J. Chemistry in noninteger dimensions between two and three. II. Fractal surfaces of adsorbents[J]. Chem. Phys.,1983:3566-3571.
[36]Friesen W I, Mikula R J. Fractal dimensions of coal particles[J]. J of Colloid and Interface, 1987,20(1):263-271.
[37]尹小涛,王水林,党发宁,等.CT实验条件下砂岩破裂分形特性研究[J].岩石力学与工程学报,2008,27(增1)：2721-2726.
[38]Bonala M S, Reddi L N. Fractal representation of soil cohesion[J]. Journal of geotechnical and geoenvironmental engineering,1999,125(10):901-904.
[39]徐永福,龚友平,殷宗泽.非饱和膨胀土强度的分形特征[J].工程力学,1998,15(2)：76-81.
[40]徐永福,傅德明.非饱和土结构强度的研究[J].工程力学,1999,16(4)：73-77.
[41]徐永福.膨胀土地基承载力研究[J].岩石力学与工程学报,2000,19(3)：387-390.
[42]张季如,祝杰,黄文竞.侧限压缩下石英砂砾的颗粒破碎特性及其分形描述[J].岩土工程学报,2008,30(6)：783-789.
[43]卫宏,张玉三,李太任,等.岩石显微空隙粒度分布的分形特征与岩石强度的关系[J].岩石力学与工程学报,2000,19(3)：318-320.
[44]谢和平.分形—岩石力学导论[M].北京：科学出版社,1995.
[45]谢和平,于广明.采动岩体分形裂隙网络研究[J].岩石力学与工程学报,1999,18(2)：147-151.
[46]谢和平,高峰,周宏伟,等.岩石断裂和破碎的分形研究[J].防灾与减灾工程学报,2003,23(4)：1-9.
[47]谢和平,彭瑞东,周宏伟,等.基于断裂力学与损伤力学的岩石强度理论研究进展[J].自然科学进展,2004,14(10)：1086-1092.
[48]涂新斌,王思敬,岳中琦.风化岩石的破碎分形及其工程地质意义[J].岩石力学与工程学报,2005,24(4)：587-595.
[49]王谦源,张清.破碎体颗粒分级的分形分析[C]//中国岩石力学与工程学会第四次学术大会论文集.北京：中国科学技术出版社,1996.8-15.
[50]高峰,谢和平,赵鹏.岩石块度分布的分形性质及细观结构效应[J].岩石力学与工程学报,1994,13(3)：240-246.
[51]廖娜.有机粉状载体表面分形维数与其承载能力关系研究[D].武汉：华中农业大学,2008.
[52]郁伯铭.多孔介质运输性质的分形分析研究进展[J].力学进展,2003,33(3)：333-346.
[53]Shi M H, Cheng Y P. Determination of permeability using fractal method for porous media[J]. Science in China (Series E),2001,44(6):625-630.
[54]Crawford J W. The relationship between structure and the hydraulic conductivity in soil[J]. Geoderma,1994.45(3):493-502.
[55]Gimenez D. Prediction of the satuated hydraulic conductivity-porosity dependence using fractals[J]. Soil Sci. Am. J.,1997,61(5):1284-1290.
[56]Gimenez D, Rawls W J and Lauren J G Scaling properties of saturated conductivity in soil[J]. Geoderma,1999.88:205-220.
[57]Guerrini I, Swartzendruber D. Fractal concepts in relation to soil water diffusivity[J]. Soil Scince,1997,162(11):778-784.
[58]Mualem Y. A new model for predicting the hydraulic conductivity of unsaturated porous media[J]. Water Res. Res.,1976,12:513-522.
[59]徐永福,黄寅春.分形理论在研究非饱和土力学性质中的应用[J].岩土工程学报,2006,28(5)：635-638.
[60]任强,徐卫亚.裂隙岩体非饱和渗流的分形模型[J].岩土力学,2008,29(10)：2735-2739.
[61]Arya L M, Paris J F. A physicoempirical model to predict the soil moisture characteristic from particel-size distribution and bulk density data[J]. Soil Sci. Soc. Am. J.,1981,45:1023-1030.
[62]Tyler S W, Wheatcraft S W. Application of fractal mathematics to soil water retention estimation[J]. Soil Sci. Soc. Am. J.,1989,53:987-996.
[63]Alexandra Kravchenko, Renduo Zhang. Estimating the soil water retention from particle-size distributions:a fractal approach[J]. Soil Sci.,1998,163(3):171-179.
[64]Rieu M, Sposito G. Fractal fragmentation, soil porosity, and soil water properties:Ⅰ. Theory[J]. Soil Sci. Soc. Am. J.,1991,55:1231-1238.
[65]Rieu M, Sposito G. Fractal fragmentation, soil Porosity, and soil water properties:Ⅱ. applications[J]. Soil Sci. Soc. Am. J.,1991,55:1239-1244.
[66]Perfect E, Mclaughlin N B, Kay B D. An improved fractal equation for the soil water retention curve[J]. Water Resour. Res.,1996,32:281-287.
[67]Perfect E, Mclaughlin N B, Kay B D, et al. Reply[J]. Water Resour. Res.,1998,34(4):933-935
[68]Perrier E, Rieu M, Sposito G, et al. Models of the water retention curve for soils with a fractal pore size distribution[J]. Water Resour. Res.,1996,32:3025-3031.
[69]Bird N R A, Perrier E, Rieu M. The water retention function for a model of soil structure with pore and solid fractal distributions[J]. Eur. J. Soil Sci.,2000,51:55-63.
[70]徐永福,董平.非饱和土的水分特征曲线的分形模型[J].岩土力学,2002,23(4)：400-405.
[71]尹小涛,赵海英,李最雄,等K2SiO3溶液对黏性土孔隙分形特性的影响分析[J].岩土力学,2008,29(10)：2847-2852.
[72]陈慧娥,王清.水泥加固土微观结构的分形[J].哈尔滨工业大学学报,2008,40(2)：307-309.
[73]薛茹,胡瑞林,毛灵涛.软土加固过程中微结构变化的分形研究[J].土木工程学报,2006,39(10)：87-91.
[74]周翠英,林春秀.基于微观结构的软土变形计算模型[J].中山大学学报(自然科学版),2008,47(1)：16-20.
[75]赵明华,陈炳初,苏永华.红层软岩崩解破碎过程的分形分析及数值模拟[J].中南大学学报(自然科学版),2007,38(2)：351-356.
[76]马新仿,张士诚,郎兆新.分形理论在岩石孔隙结构研究中的应用[J].岩石力学与工程学报,22(增1)：2164-2167.
[77]连建发,慎乃齐,张杰坤.分形理论在岩体质量评估中的应用研究[J].岩石力学与工程学报,2001,20(增)：1695-1698.
[78]贺承祖,华明琪.储层孔隙结构的分形几何描述[J].石油与天然气地质,1998,19(1)：15-23.
[79]洪世铎.油藏物理基础[M].北京：石油工业出版社,1987.
[80]王金安,谢和平,田晓燕,等.岩石断裂表面分形测量的尺度效应[J].岩石力学与工程学报,2000,19(1)：11-17.
[81]李廷芥,王耀辉,张梅英.岩石裂纹的分形特性及岩爆机理研究[J].岩石力学与工程学报,2000,19(1)：6-10.
[82]赵安平,王清,李杨.季节冻土区路基土粒度成分的分形特征[J].吉林大学学报(地球科学版),2006,36(4)：583-587,667.
[83]管志勇,路卫卫,戚蓝,等.建筑物地基沉降曲线的分形特征分析[J].岩土力学,2008,29(5)：1415-1418.
[84]Su Y Z, Zhao H L, Zhang T H, el al. Soil degradation process and character in the desertification process of rainfed farmland in horqin sandy land[J]. Journal of Soil and Water Conservation,2002,16(1):25-28.
[85]苏永中,赵哈林.科尔沁沙地农田沙漠化演变中土壤颗粒分形特征[J].生态学报,2004,24(1)：71-74.
[86]谢和平.岩土介质的分形孔隙和分形粒子[J].力学进展,1993,23(2)：145-164.
[87]徐永福,史春乐.用土的分形结构确定土的水份特征曲线[J].岩土力学,1997,18(2)：40-43.
[88]徐永福,林飞.粒状材料的强度与变形[J].岩土力学,2006,27(3)：348-352.
[89]Mandelbrot B B. The Fractal Geometry of Nature[M]. San Francisco:W.H. Freeman,1983.
[90]Yu B M, Li J H. Some fractal characters of porous media[J]. Fractals,2001,9(3):365-372.
[91]Xu Y F, Yin Z Z. Fractal structure of soils—a case study[C]. In:Shen Z J eds. Proceedings of 2nd Int. Conf. on Soft Soil Engineering. Nanjing:Hohai University Press,1996.78-83.
[92]孙霞,吴自勤,黄畇.分形原理及其应用[M].合肥：中国科技技术大学出版社,2003.
[93]陶高梁,张季如.岩土工程中的分形理论及其应用[J].中国科技论文在线,2009,4(7)：493-497.
[94]陶高梁,张季如.表征孔隙及颗粒体积与尺度分布的两类岩土体分形模型[J].科学通报,2009,54(6)：838-846.
[95]胡云锋,刘纪远,庄大方,等.不同土地利用／土地覆盖下土壤粒径分布的分维特征[J].土壤学报,2005,42(2)：336-339.
[96]苏里坦,宋郁东,陶辉.不同风沙土壤颗粒的分形特征[J].土壤通报,2008,39(2)：244 -248.
[97]杨秀春,刘连友,严平.土壤短期吹蚀的粒度分维研究[J].土壤学报,2004,41(2)：176-182.
[98]齐雁冰,常庆瑞,惠泱河.人工植被恢复荒漠化逆转过程中土壤颗粒分形特征[J].土壤学报,2007,44(3)：566-570.
[99]Su Y Z, Zhao H, Zhao W, et al. Fractal features of soil particle size distribution and the implication for indicating desertification[J]. Geoderma,2004,122:43-49.
[100]张季如,黄丽,祝杰,等.微观尺度上土壤孔隙及其分维数的SEM分析[J].土壤学报,2008,45(2)：22-30.
[101]Ferreiro E A, De Bussetti S G, Helmy A K. Determination of surface area of soil by adsorption methods[J]. Eur. J. Soil Sci.,2002,53:475-480.
[102]陶高梁,张季如,黄丽,等.岩土介质分维数求解方法[J].华中科技大学学报(自然科学版),2010,38(8)：103-106.
[103]赵来,吕成文.土壤分形特征与土壤肥力关系研究—以皖南地区水稻土为例[J].土壤肥料,2005,(6)：7-11.
[104]郭冬梅,白英,郭炜.表层风蚀土壤粒径分布的分形特征研究[J].内蒙古农业大学学报,2005,26(1)：82-86.
[105]程先富,史学正,王洪杰.红壤丘陵区耕层土壤颗粒的分形特征[J].地理科学,2003,23(5)：617-621.
[106]Skopp J. Comment on "micro, meso, and macroposity of soil" [J]. Soil Sci. Soc. Am. J., 1981,45:1246.
[107]Beven K, Germann P. Macropores and water flow in soils[J]. Water Resour. Res.,1982,18 (5):1311-1325.
[108]Singh P, Rameshwar K S, Thompson M L. Measurement and characterization of macropores by using AUTOCAD and automatic image analysis[J]. J. Envi. Ron. Qual., 1991,20:289-294.
[109]Luxmoore R J, Jardine P M, Wilson G V, et al. Physical and chemical controls of preferred path flow through a forested hillslope[J]. Geoderma,1990,46:139-154.
[110]Warner G S, Nieber J L, More I D, et al. Characerizing macropores in soil by computed tomography[J]. Soil Sci. Soc. Am. J.,1989,53:653-660.
[111]Vermeul V R, Istok J D, Flint A L, et al. An improved method for quantifying soil macroporosity[J]. Soil Sci. Soc. Am. J.,1993,57:809-816.
[112]Hall D G M, Reeve M J, Thomasson, A J, et al. Water retention, porosity, and density of field soils[J]. Soil Survey Technical Monograph, No.9, Harpenden, UK.1977,77.
[113]唐衡楚,朱海之.制作松散岩石及土样薄片的新方法[J].科学通报,1963,8：65-66.
[114]中国科学院南京土壤研究所土壤微形态实验室.用不饱和聚醋树脂制备土壤薄片的 方法[J].土壤,1976,5-6：329-333.
[115]中国科学院南京土壤研究所土壤微形态实验室.制备黏质致密土壤薄片的方法[J].土壤,1977,4：213-215.
[116]曹升赓.土壤和非固结物质薄片的系统制备方法[J].土壤专报,1989,43：83-90.
[117]贺秀斌.土壤薄片的甲基丙烯酸甲酯固结方法[J].土壤通报,1998,2：97.
[118]李德成,Velde B, Delerue J F,等.利用土壤切片及数字图像研究低丘缓坡不同部位土壤的孔隙结构特征[J].土壤通报,2002,33(1)：6-8.
[119]何毓蓉,黄成敏,周红艺.成都平原水耕人为土诊断层的微形态特征与土壤基层分类[J].山地学报,2002,20(2)：157-163.
[121]Donald H G, Robbin B S. Biotechnical stablization of highway cut slope[J]. Journal of Geotechnical Engineering,1992,118:1395-1409.
[122]陶高梁,张季如,黄丽,等.多孔材料孔隙特性的分形描述[J].建筑材料学报,2010,13(5)：678-681.
[123]喻乐华,欧辉,段庆普.掺珍珠岩水泥石孔分形维数及其与孔结构、强度的关系[J].材料科学与工程学报,2007,25(2)：201-204,224.
[124]刘松玉,张继文.土中孔隙分布的分形特征研究[J].东南大学学报,1997,27(3)：127-130.
[125]Perfect E, Kenst A B, Diaz-Zorita M, et al. Fractal analysis of soil water desorption data collected on disturbed samples with water activity meters[J]. Soil Sci. Soc. Am. J.,2004, 68:1177-1184.
[126]Roberts J N. Comment about fractal sandstone pores[J]. Phys. Rev. Lett,1986,56:2111.
[127]Feder J. Fractals[M]. New York:Plenum Press,1988.
[128]Yu B M. Comments on "fractal fragmentation, soil porosity, and soil water properties I. Theory"[J]. Soil Sci. Soc. Am. J.,2007,71:632.
[129]Sposito G. Response to "comments on'fractal fragmentation, soil porosity, and soil water properties:Ⅰ. Theory"[J]. Soil Sci. Soc. Am. J.,2007,71:633.
[130]Garga K V. Effect of sample size on shear strength of basaltic residual soils[J]. Can. Geotech. J,1988,25:478-487.
[131]Lo K Y. The operational strength of fissured clays[J]. Geotechnique,1970,20:57-64.
[132]Tsur-lavie Y, Denkamp S A. Comparison of size effect for different types of strength tests[J]. Rock Mech,1982,15:243-254.
[133]张季如,陶高梁,黄丽,等.表征孔隙孔径分布的岩土体孔隙率模型及其应用.科学通报,2010,55(27-28)：2761-2770.
[2]Perret J, Prasher S O, et al. 3-D visualization of soil macroporosity using x-ray CAT scanning[J]. Can. Agri. Eng.,1997,39 (4):249-261.
[3]李德成,张桃林,B. Velde等.CT分析技术在土壤科学研究中的应用[J].土壤,2002,6：328-332.
[4]Petrovic A M, Siebert J E, Rieke P E. Soil bulk density analysis in three dimensions by computed tomographic scanning[J]. Soil Sci. Soc. Am. J.,1982,46 (3):445-450.
[5]Anderson S H, Gantzer C J, et al. Rapid nondestructive bulk density and soil-water content determination by computed tomography[J]. Soil Sci. Soc. Am. J.,1988,52 (1):35-40.
[6]Zeng Y, Gantzer C J, et al. Fractal dimension and lacunarity of bulk density determined with x-ray computed tomography [J]. Soil Sci. Soc. Am. J.,1996,60 (6):1718-1724.
[7]Hainsworth J M, Aylmore L A G. The use of computer-assisted tomography to determine spatial distribution of soil water content[J]. Aust. J. Soil. Res.,1983,21 (4):435-443
[8]王国梁,周生路,赵其国.土壤颗粒的体积分形维数及其在土地利用中的应用[J].土壤学报,2005,42(4)：545-550.
[9]王清,王剑平.土孔隙的分形几何研究[J].岩土工程学报,2000,22(4)：496-498.
[10]黄丽.饱和软黏土微观孔隙的定量分析及其分形研究[D].武汉：武汉理工大学,2007.
[11]葛世荣,朱华.摩擦学的分形[M].北京：机械工业出版社,2005.
[12]Whitehouse D J. Comparison between stylus and optical methods for measuring surfaces [J]. Annals of the CIPP,1988,37(2):649-653.
[13]曹麟祥,王红.表面粗糙度的现代测量技术[J].测控技术.1992,2：17-20.
[14]Turcotte D L, Harris R A. Relationship between the oceanic geoid and the structure of the oceanic lithosphere[J]. Marine Geophysical Researches,1984,54:1-2.
[15]Matsushita M. Fractal viewpoint of fracture and accretion[J]. J. Phys. Soc. Jpn.,1986; 54: 857-860.
[16]Tyler S W, Wheatcraft S W. Fractal scaling of soil particle size distribution:Analysis and limitations[J]. Soil Sci. Soc. Am. J.,1992,56:362-370.
[17]Turcotte D L. Fractals and fragmentation[J]. Journal of Geophysical Research,1986,91 (B2):1921-1926.
[18]张季如,朱瑞赓,祝文化.用粒径的数量分布表征的土壤分形特征[J].水利学报,2004,(4)：67-71,79.
[19]Tyler S W, Wheatcraft S W. Fractal scaling of soil particle-size distribution:Analysis and limitations[J]. Soil Sci. Soc. Am. J.,1992,56 (2):362-369.
[20]杨培岭,罗远培,石元春.用粒径的重量分布表征的土壤分形特征[J].科学通报,1993,38：1896-1899.
[21]李德成,张桃林.中国土壤颗粒组成的分形特征研究[J].土壤与环境,2000,9(4)：263-265.
[22]黄冠华,詹卫华.土壤颗粒的分形特征及其应用[J].土壤学报,2002,39(4)：490-497.
[23]王宝军,·施斌,唐朝生.基于GIS实现黏性土颗粒形态的三维分形研究[J].岩土工程学报,2007,29(2)：309-312
[24]Hurd A J, et al. Surface areas of fractally rough particles studied by scattering[J]. Phys. Rev., 1989, B39:9742-9745.
[25]武生智,魏春玲,马崇武,等.沙粒粗糙度和粒径分布的分形特性[J].兰州大学学报(自然科学版),1999,35(1)：44-47.
[26]Katz A J, Thompson A H. Fractal sandstone pores:implications for conductivity and pore formation[J]. Phys Rev Lett,1985,54(12):1325-1328.
[27]Brakensiek D L, Rwals W J, Logsdond S D, et al. Fractal description of micro-porosity [J]. Soil Sci. Soc. Am.J.,1992,56:1721-1723.
[28]Anderson A N, Mcbratney A B, Fitzpatrick E A. Soil mass, surface, and spectral fractal dimensions estimated from thin section photographs[J]. Soil Sci. Soc. Am. J.,1996,60:962-969.
[29]李向全,胡瑞林,张莉.黏性土固结过程中的微结构效应研究[J].岩土工程技术,1999,3(3)：52-56.
[30]张季如,祝杰,黄丽,等.固结条件下软黏土微观孔隙结构的演化及其分形描述[J].水利学报,2008,39(4)：394-400.
[31]周宇泉,洪宝宁.黏性土压缩过程中的微细结构变化试验研究[J].岩土力学,2005,26(增)：82-86.
[32]王清,王剑平.土孔隙的分形几何研究[J].岩土工程学报,2000,22(4)：496-498.
[33]许勇,张季超,李伍平.饱和软土微结构分形特征的试验研究[J].岩土力学,2007,28(增)：49-52.
[34]Pfeifer P, Avnir D J. "Chemistry in noninteger dimensions between two and three. Ⅰ. Fractal theory of heterogeneous surfaces"[J]. Chem. Phys.,1983,79:3558-3565.
[35]Avnir D, Farin D, Pfeifer P J. Chemistry in noninteger dimensions between two and three. II. Fractal surfaces of adsorbents[J]. Chem. Phys.,1983:3566-3571.
[36]Friesen W I, Mikula R J. Fractal dimensions of coal particles[J]. J of Colloid and Interface, 1987,20(1):263-271.
[37]尹小涛,王水林,党发宁,等.CT实验条件下砂岩破裂分形特性研究[J].岩石力学与工程学报,2008,27(增1)：2721-2726.
[38]Bonala M S, Reddi L N. Fractal representation of soil cohesion[J]. Journal of geotechnical and geoenvironmental engineering,1999,125(10):901-904.
[39]徐永福,龚友平,殷宗泽.非饱和膨胀土强度的分形特征[J].工程力学,1998,15(2)：76-81.
[40]徐永福,傅德明.非饱和土结构强度的研究[J].工程力学,1999,16(4)：73-77.
[41]徐永福.膨胀土地基承载力研究[J].岩石力学与工程学报,2000,19(3)：387-390.
[42]张季如,祝杰,黄文竞.侧限压缩下石英砂砾的颗粒破碎特性及其分形描述[J].岩土工程学报,2008,30(6)：783-789.
[43]卫宏,张玉三,李太任,等.岩石显微空隙粒度分布的分形特征与岩石强度的关系[J].岩石力学与工程学报,2000,19(3)：318-320.
[44]谢和平.分形—岩石力学导论[M].北京：科学出版社,1995.
[45]谢和平,于广明.采动岩体分形裂隙网络研究[J].岩石力学与工程学报,1999,18(2)：147-151.
[46]谢和平,高峰,周宏伟,等.岩石断裂和破碎的分形研究[J].防灾与减灾工程学报,2003,23(4)：1-9.
[47]谢和平,彭瑞东,周宏伟,等.基于断裂力学与损伤力学的岩石强度理论研究进展[J].自然科学进展,2004,14(10)：1086-1092.
[48]涂新斌,王思敬,岳中琦.风化岩石的破碎分形及其工程地质意义[J].岩石力学与工程学报,2005,24(4)：587-595.
[49]王谦源,张清.破碎体颗粒分级的分形分析[C]//中国岩石力学与工程学会第四次学术大会论文集.北京：中国科学技术出版社,1996.8-15.
[50]高峰,谢和平,赵鹏.岩石块度分布的分形性质及细观结构效应[J].岩石力学与工程学报,1994,13(3)：240-246.
[51]廖娜.有机粉状载体表面分形维数与其承载能力关系研究[D].武汉：华中农业大学,2008.
[52]郁伯铭.多孔介质运输性质的分形分析研究进展[J].力学进展,2003,33(3)：333-346.
[53]Shi M H, Cheng Y P. Determination of permeability using fractal method for porous media[J]. Science in China (Series E),2001,44(6):625-630.
[54]Crawford J W. The relationship between structure and the hydraulic conductivity in soil[J]. Geoderma,1994.45(3):493-502.
[55]Gimenez D. Prediction of the satuated hydraulic conductivity-porosity dependence using fractals[J]. Soil Sci. Am. J.,1997,61(5):1284-1290.
[56]Gimenez D, Rawls W J and Lauren J G Scaling properties of saturated conductivity in soil[J]. Geoderma,1999.88:205-220.
[57]Guerrini I, Swartzendruber D. Fractal concepts in relation to soil water diffusivity[J]. Soil Scince,1997,162(11):778-784.
[58]Mualem Y. A new model for predicting the hydraulic conductivity of unsaturated porous media[J]. Water Res. Res.,1976,12:513-522.
[59]徐永福,黄寅春.分形理论在研究非饱和土力学性质中的应用[J].岩土工程学报,2006,28(5)：635-638.
[60]任强,徐卫亚.裂隙岩体非饱和渗流的分形模型[J].岩土力学,2008,29(10)：2735-2739.
[61]Arya L M, Paris J F. A physicoempirical model to predict the soil moisture characteristic from particel-size distribution and bulk density data[J]. Soil Sci. Soc. Am. J.,1981,45:1023-1030.
[62]Tyler S W, Wheatcraft S W. Application of fractal mathematics to soil water retention estimation[J]. Soil Sci. Soc. Am. J.,1989,53:987-996.
[63]Alexandra Kravchenko, Renduo Zhang. Estimating the soil water retention from particle-size distributions:a fractal approach[J]. Soil Sci.,1998,163(3):171-179.
[64]Rieu M, Sposito G. Fractal fragmentation, soil porosity, and soil water properties:Ⅰ. Theory[J]. Soil Sci. Soc. Am. J.,1991,55:1231-1238.
[65]Rieu M, Sposito G. Fractal fragmentation, soil Porosity, and soil water properties:Ⅱ. applications[J]. Soil Sci. Soc. Am. J.,1991,55:1239-1244.
[66]Perfect E, Mclaughlin N B, Kay B D. An improved fractal equation for the soil water retention curve[J]. Water Resour. Res.,1996,32:281-287.
[67]Perfect E, Mclaughlin N B, Kay B D, et al. Reply[J]. Water Resour. Res.,1998,34(4):933-935
[68]Perrier E, Rieu M, Sposito G, et al. Models of the water retention curve for soils with a fractal pore size distribution[J]. Water Resour. Res.,1996,32:3025-3031.
[69]Bird N R A, Perrier E, Rieu M. The water retention function for a model of soil structure with pore and solid fractal distributions[J]. Eur. J. Soil Sci.,2000,51:55-63.
[70]徐永福,董平.非饱和土的水分特征曲线的分形模型[J].岩土力学,2002,23(4)：400-405.
[71]尹小涛,赵海英,李最雄,等K2SiO3溶液对黏性土孔隙分形特性的影响分析[J].岩土力学,2008,29(10)：2847-2852.
[72]陈慧娥,王清.水泥加固土微观结构的分形[J].哈尔滨工业大学学报,2008,40(2)：307-309.
[73]薛茹,胡瑞林,毛灵涛.软土加固过程中微结构变化的分形研究[J].土木工程学报,2006,39(10)：87-91.
[74]周翠英,林春秀.基于微观结构的软土变形计算模型[J].中山大学学报(自然科学版),2008,47(1)：16-20.
[75]赵明华,陈炳初,苏永华.红层软岩崩解破碎过程的分形分析及数值模拟[J].中南大学学报(自然科学版),2007,38(2)：351-356.
[76]马新仿,张士诚,郎兆新.分形理论在岩石孔隙结构研究中的应用[J].岩石力学与工程学报,22(增1)：2164-2167.
[77]连建发,慎乃齐,张杰坤.分形理论在岩体质量评估中的应用研究[J].岩石力学与工程学报,2001,20(增)：1695-1698.
[78]贺承祖,华明琪.储层孔隙结构的分形几何描述[J].石油与天然气地质,1998,19(1)：15-23.
[79]洪世铎.油藏物理基础[M].北京：石油工业出版社,1987.
[80]王金安,谢和平,田晓燕,等.岩石断裂表面分形测量的尺度效应[J].岩石力学与工程学报,2000,19(1)：11-17.
[81]李廷芥,王耀辉,张梅英.岩石裂纹的分形特性及岩爆机理研究[J].岩石力学与工程学报,2000,19(1)：6-10.
[82]赵安平,王清,李杨.季节冻土区路基土粒度成分的分形特征[J].吉林大学学报(地球科学版),2006,36(4)：583-587,667.
[83]管志勇,路卫卫,戚蓝,等.建筑物地基沉降曲线的分形特征分析[J].岩土力学,2008,29(5)：1415-1418.
[84]Su Y Z, Zhao H L, Zhang T H, el al. Soil degradation process and character in the desertification process of rainfed farmland in horqin sandy land[J]. Journal of Soil and Water Conservation,2002,16(1):25-28.
[85]苏永中,赵哈林.科尔沁沙地农田沙漠化演变中土壤颗粒分形特征[J].生态学报,2004,24(1)：71-74.
[86]谢和平.岩土介质的分形孔隙和分形粒子[J].力学进展,1993,23(2)：145-164.
[87]徐永福,史春乐.用土的分形结构确定土的水份特征曲线[J].岩土力学,1997,18(2)：40-43.
[88]徐永福,林飞.粒状材料的强度与变形[J].岩土力学,2006,27(3)：348-352.
[89]Mandelbrot B B. The Fractal Geometry of Nature[M]. San Francisco:W.H. Freeman,1983.
[90]Yu B M, Li J H. Some fractal characters of porous media[J]. Fractals,2001,9(3):365-372.
[91]Xu Y F, Yin Z Z. Fractal structure of soils—a case study[C]. In:Shen Z J eds. Proceedings of 2nd Int. Conf. on Soft Soil Engineering. Nanjing:Hohai University Press,1996.78-83.
[92]孙霞,吴自勤,黄畇.分形原理及其应用[M].合肥：中国科技技术大学出版社,2003.
[93]陶高梁,张季如.岩土工程中的分形理论及其应用[J].中国科技论文在线,2009,4(7)：493-497.
[94]陶高梁,张季如.表征孔隙及颗粒体积与尺度分布的两类岩土体分形模型[J].科学通报,2009,54(6)：838-846.
[95]胡云锋,刘纪远,庄大方,等.不同土地利用／土地覆盖下土壤粒径分布的分维特征[J].土壤学报,2005,42(2)：336-339.
[96]苏里坦,宋郁东,陶辉.不同风沙土壤颗粒的分形特征[J].土壤通报,2008,39(2)：244 -248.
[97]杨秀春,刘连友,严平.土壤短期吹蚀的粒度分维研究[J].土壤学报,2004,41(2)：176-182.
[98]齐雁冰,常庆瑞,惠泱河.人工植被恢复荒漠化逆转过程中土壤颗粒分形特征[J].土壤学报,2007,44(3)：566-570.
[99]Su Y Z, Zhao H, Zhao W, et al. Fractal features of soil particle size distribution and the implication for indicating desertification[J]. Geoderma,2004,122:43-49.
[100]张季如,黄丽,祝杰,等.微观尺度上土壤孔隙及其分维数的SEM分析[J].土壤学报,2008,45(2)：22-30.
[101]Ferreiro E A, De Bussetti S G, Helmy A K. Determination of surface area of soil by adsorption methods[J]. Eur. J. Soil Sci.,2002,53:475-480.
[102]陶高梁,张季如,黄丽,等.岩土介质分维数求解方法[J].华中科技大学学报(自然科学版),2010,38(8)：103-106.
[103]赵来,吕成文.土壤分形特征与土壤肥力关系研究—以皖南地区水稻土为例[J].土壤肥料,2005,(6)：7-11.
[104]郭冬梅,白英,郭炜.表层风蚀土壤粒径分布的分形特征研究[J].内蒙古农业大学学报,2005,26(1)：82-86.
[105]程先富,史学正,王洪杰.红壤丘陵区耕层土壤颗粒的分形特征[J].地理科学,2003,23(5)：617-621.
[106]Skopp J. Comment on "micro, meso, and macroposity of soil" [J]. Soil Sci. Soc. Am. J., 1981,45:1246.
[107]Beven K, Germann P. Macropores and water flow in soils[J]. Water Resour. Res.,1982,18 (5):1311-1325.
[108]Singh P, Rameshwar K S, Thompson M L. Measurement and characterization of macropores by using AUTOCAD and automatic image analysis[J]. J. Envi. Ron. Qual., 1991,20:289-294.
[109]Luxmoore R J, Jardine P M, Wilson G V, et al. Physical and chemical controls of preferred path flow through a forested hillslope[J]. Geoderma,1990,46:139-154.
[110]Warner G S, Nieber J L, More I D, et al. Characerizing macropores in soil by computed tomography[J]. Soil Sci. Soc. Am. J.,1989,53:653-660.
[111]Vermeul V R, Istok J D, Flint A L, et al. An improved method for quantifying soil macroporosity[J]. Soil Sci. Soc. Am. J.,1993,57:809-816.
[112]Hall D G M, Reeve M J, Thomasson, A J, et al. Water retention, porosity, and density of field soils[J]. Soil Survey Technical Monograph, No.9, Harpenden, UK.1977,77.
[113]唐衡楚,朱海之.制作松散岩石及土样薄片的新方法[J].科学通报,1963,8：65-66.
[114]中国科学院南京土壤研究所土壤微形态实验室.用不饱和聚醋树脂制备土壤薄片的 方法[J].土壤,1976,5-6：329-333.
[115]中国科学院南京土壤研究所土壤微形态实验室.制备黏质致密土壤薄片的方法[J].土壤,1977,4：213-215.
[116]曹升赓.土壤和非固结物质薄片的系统制备方法[J].土壤专报,1989,43：83-90.
[117]贺秀斌.土壤薄片的甲基丙烯酸甲酯固结方法[J].土壤通报,1998,2：97.
[118]李德成,Velde B, Delerue J F,等.利用土壤切片及数字图像研究低丘缓坡不同部位土壤的孔隙结构特征[J].土壤通报,2002,33(1)：6-8.
[119]何毓蓉,黄成敏,周红艺.成都平原水耕人为土诊断层的微形态特征与土壤基层分类[J].山地学报,2002,20(2)：157-163.
[121]Donald H G, Robbin B S. Biotechnical stablization of highway cut slope[J]. Journal of Geotechnical Engineering,1992,118:1395-1409.
[122]陶高梁,张季如,黄丽,等.多孔材料孔隙特性的分形描述[J].建筑材料学报,2010,13(5)：678-681.
[123]喻乐华,欧辉,段庆普.掺珍珠岩水泥石孔分形维数及其与孔结构、强度的关系[J].材料科学与工程学报,2007,25(2)：201-204,224.
[124]刘松玉,张继文.土中孔隙分布的分形特征研究[J].东南大学学报,1997,27(3)：127-130.
[125]Perfect E, Kenst A B, Diaz-Zorita M, et al. Fractal analysis of soil water desorption data collected on disturbed samples with water activity meters[J]. Soil Sci. Soc. Am. J.,2004, 68:1177-1184.
[126]Roberts J N. Comment about fractal sandstone pores[J]. Phys. Rev. Lett,1986,56:2111.
[127]Feder J. Fractals[M]. New York:Plenum Press,1988.
[128]Yu B M. Comments on "fractal fragmentation, soil porosity, and soil water properties I. Theory"[J]. Soil Sci. Soc. Am. J.,2007,71:632.
[129]Sposito G. Response to "comments on'fractal fragmentation, soil porosity, and soil water properties:Ⅰ. Theory"[J]. Soil Sci. Soc. Am. J.,2007,71:633.
[130]Garga K V. Effect of sample size on shear strength of basaltic residual soils[J]. Can. Geotech. J,1988,25:478-487.
[131]Lo K Y. The operational strength of fissured clays[J]. Geotechnique,1970,20:57-64.
[132]Tsur-lavie Y, Denkamp S A. Comparison of size effect for different types of strength tests[J]. Rock Mech,1982,15:243-254.
[133]张季如,陶高梁,黄丽,等.表征孔隙孔径分布的岩土体孔隙率模型及其应用.科学通报,2010,55(27-28)：2761-2770.