土壤孔隙三维构建与特征表达
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摘要
孔隙结构直接影响水分在土表及土体内的迁移途径及方式,决定土壤的持水性、渗透性、导水性等水力性质。研究土壤表土孔隙结构特征对于我国区域土壤的侵蚀防治、环境保护和减少地下水污染等问题均具有重要意义。网络模型是模拟孔隙内部结构最为重要的一种方法。本文以第四纪红粘土母质发育的典型红壤为示例土样,综合应用序列切片法、数字图像处理特别是3S技术分析和识别了不同降雨历时的土壤微形态样本,并在VB 6.0的环境下开发建立孔隙网络模型,提取了孔隙拓扑结构,获取了孔隙空间结构特征定量表达。应用模型统计分析了次降雨过程中表土样本孔隙特征的时空变化规律,初步探讨了土壤表土孔隙特征与土壤侵蚀过程间的关系,结果如下:
(1)应用形态学网络模型理论,结合孔隙空间拓扑结构,通过系统分析和设计,规定了设计约束,确定了适合描述土壤孔隙空间拓扑特征的的网络模型数据结构,采用面向对象的软件开发方法实现了孔隙网络模型的构建。模型研究了提高序列数字图像垂直方向分辨率的关键算法,以及切片水平和垂直方向上像元的连通判断问题,最后在空间拓扑理论的支持下实现了孔隙网络模型的构建。模型测试表明,此模型是孔隙结构特征的直接映射,再现了孔隙三维结构,它较真实反映了孔隙在土壤中的空间分布,能够定量获取孔隙拓扑结构特征。
(2)在对孔隙空间结构拓扑关系研究的基础上,从孔隙结构对土壤中水及溶质的运移的影响作用角度,分析了孔隙的大小、连通性等特性,提出了能够评价孔隙结构特征的定量指标参数:孔隙等效直径、孔隙数量、孔隙度、孔隙有效长度、孔隙倾斜度、扭曲复杂度、孔隙连通度及水力半径,实现了各指标算法的计算。
(3)结合所建孔隙网络模型,利用数值方法对次降雨过程中等效孔径大于50μm红壤孔隙结构变化进行模拟与求解,得到了孔隙结构特征及在次降雨过程中的变化规律。
从孔隙等效孔径来看:在所有降雨时段内,较小孔径孔隙数量较多,孔径为200～400μm的孔隙所占面积比例最大。在次降雨过程中,小孔径孔隙数量增多,大孔径孔隙数量减少,孔隙面积比减小;在各土壤微层次中,平均孔径逐渐增大,表土L1、L2层的土壤孔隙由于受到雨滴的直接打击,变化最为明显。
通过对有效长度大于2.5 mm孔隙的三维指标统计分析可知:示例土壤中孔隙结构各指标都有其分布规律,并随着降雨时间的延续呈规律性变化。由于是扰动后填充的土壤,供试土样中大孔隙较多,大孔隙度为4～7%。土壤中孔隙的结构非常复杂,绝大多数孔隙网络的扭曲复杂度τ在1～2 mm/mm范围内;土壤的连通性较高,平均欧拉数在0.2～0.8范围内,大部分孔隙水力半径在0.05～0.1 mm范围内。孔隙网络倾斜度δ大致在45°以内,表明孔隙在垂直方向上有较好延伸。具有较大有效长度的孔隙各项参数均大于其他孔隙,有效长度30～40mm的孔隙τ值可达到6.5mm/mm,R值可达0.18mm,虽然这部分孔隙数量很少,但对土壤中水及溶质的传导能力影响较短孔隙要大的多。三维指标在降雨过程呈现一定的变化规律,在次降雨前期,孔隙度、水力半径持续减小,孔隙倾斜度、扭曲复杂度、欧拉数增大,表明孔隙连通性、传导性随降雨时间的延续而降低,对水及溶质的传导能力变小,在降雨后期,各指标趋于稳定,此时土壤形成致密层,阻碍了水及溶质的传导。
综上所述,本研究是在对孔隙结构空间数据结构分析的基础上,确定了适合孔隙网络模型计算的土壤孔隙特征指标,建立了能够真实反映孔隙拓扑结构的孔隙网络模型。对模型的应用表明红壤孔隙结构在土壤侵蚀过程中存在一定的变化规律。此研究有利于丰富孔隙拓扑结构的研究理论和进一步拓展土壤侵蚀的研究范围,有助于揭示侵蚀发生发展的动态过程。
The structure of soil pore affects the transmission route and mode of water and solute directly, it also decides the important factors which affect the process of soil erosion, such as water retention, permeability, water transmissibility and so on. To research the properties of pore structure in soil has great practical significance in preventing and curing soil erosion, environment protection, reducing pollution of ground water and so on. The pore-network model is one of the most important methods for modeling porous media pore space. Taking the typical red soil as an example, this paper researches the structure of soil pores larger than 50μm by analyzing soil sample which uses the digital images of the soil slice during rainfall. We analyze and identify the original images by applying the technologies of serial slices, digital image processing especially technology of 3S to pick-up the images of soil. This paper also researches how to quantitatively describe the characteristics of the pore space and a viable pore-network model is built at the platform of Visual Basic 6.0. To study the relationship between pore structure changes and soil erosion process, this paper analyzes the spatial and temporal change rule of top soil pore characteristics. The main results are as follows:
(1) Our research established data structure of network model to describe soil pore space topological characteristics, regulated design restrict by detailed system analysis and design, built pore network model based on the theory of morphologic network model and pore topological characteristics. In the modeling course, we researched the key arithmetic of heightening the vertical resolve, and the judging problem of level and vertical connection, after completed the steps above, base on the theory of space topology to structure the pore network. The result of testing model indicates that, the model can truly describe space distribution and gain topological characteristics of pore in soil.
(2) Based on the research of topological relationship of pore space structure, this paper analysed pore size and connectivity from the aspect of pore affect water and solute to confirm quantitative parameters which can evaluate pore structure characteristics: Equivalent Diameter, Numbers, Porosity, Length, Angel from vertical, Tortuous Complexity, Connectivity and Hydraulic radius, moreover, it realized those arithmetic compute.
(3) By using the pore network model, this paper again the parameters value of pore structure which bigger than 50μm with rainfall by numerical method, and the change rules of parameters.
Pore diameter: majority pore is small, pores belong to 200-400μm have the biggest area. During the process of rainfall, the number of small pores increases, bigger pore decreases and the porosity decreases continually. With the increase in soil depth, the average diameter increases gradually. Pores in soil micro-layer L1, L2 are affected greatly in rainfall.
Statistic the indicators of pores longer than 2.5 mm which play the most important role in affecting water and solute transportation, and the result are: there are regular rules of those parameters. Because the soil is disturb, there are many macropore, porosity is mainly about 4-7%. The pore structure is complex, tortuous Complexityτis mainly 1-2 mm/mm; the connectivity of soil is high, the average of Eluer is about 0.2-0.8, most pores' Hydraulic radius is about 0.05-0.1 mm. Most pore network's Angels from vertical 8 are smaller than 45 degree shows that pore has a good stretch in soil. There are some longer pores' parameters are larger than the others, pores with length is 30-40 mm haveτ6.5 mm/mm, R 0.18 mm. Although these pores with larger parameters are minority, they take more important part in transporting and seeping water and solute than samller pores in soil. The 3-D parameters have rules with rainfall, Porosity, Hydraulic radius decrease, and Angel from vertical, Tortuous Complexity and Euler number increase, indicates the pore connectivity and transmission ability decreases with the increase of rainfall time. In the later of rainfall, the surface layer of soil is compacted and pore structure has no change any more, tending to steady. As a whole, the transmission ability of pore is decreasing with the rainfall.
In summary, based on the analysis of data structure of soil pore structure, this paper confirmed parameters of pore fit to pore topological structure, modeled pore network model. By using the model, we gained the change rules of red soil pore structure during rainfall. This research helps to enrich the research theory of pore topological characteristics, extend the research extension of soil erosion, open out the dynamic happen and development course of soil erosion.
(1)应用形态学网络模型理论,结合孔隙空间拓扑结构,通过系统分析和设计,规定了设计约束,确定了适合描述土壤孔隙空间拓扑特征的的网络模型数据结构,采用面向对象的软件开发方法实现了孔隙网络模型的构建。模型研究了提高序列数字图像垂直方向分辨率的关键算法,以及切片水平和垂直方向上像元的连通判断问题,最后在空间拓扑理论的支持下实现了孔隙网络模型的构建。模型测试表明,此模型是孔隙结构特征的直接映射,再现了孔隙三维结构,它较真实反映了孔隙在土壤中的空间分布,能够定量获取孔隙拓扑结构特征。
(2)在对孔隙空间结构拓扑关系研究的基础上,从孔隙结构对土壤中水及溶质的运移的影响作用角度,分析了孔隙的大小、连通性等特性,提出了能够评价孔隙结构特征的定量指标参数:孔隙等效直径、孔隙数量、孔隙度、孔隙有效长度、孔隙倾斜度、扭曲复杂度、孔隙连通度及水力半径,实现了各指标算法的计算。
(3)结合所建孔隙网络模型,利用数值方法对次降雨过程中等效孔径大于50μm红壤孔隙结构变化进行模拟与求解,得到了孔隙结构特征及在次降雨过程中的变化规律。
从孔隙等效孔径来看:在所有降雨时段内,较小孔径孔隙数量较多,孔径为200～400μm的孔隙所占面积比例最大。在次降雨过程中,小孔径孔隙数量增多,大孔径孔隙数量减少,孔隙面积比减小;在各土壤微层次中,平均孔径逐渐增大,表土L1、L2层的土壤孔隙由于受到雨滴的直接打击,变化最为明显。
通过对有效长度大于2.5 mm孔隙的三维指标统计分析可知:示例土壤中孔隙结构各指标都有其分布规律,并随着降雨时间的延续呈规律性变化。由于是扰动后填充的土壤,供试土样中大孔隙较多,大孔隙度为4～7%。土壤中孔隙的结构非常复杂,绝大多数孔隙网络的扭曲复杂度τ在1～2 mm/mm范围内;土壤的连通性较高,平均欧拉数在0.2～0.8范围内,大部分孔隙水力半径在0.05～0.1 mm范围内。孔隙网络倾斜度δ大致在45°以内,表明孔隙在垂直方向上有较好延伸。具有较大有效长度的孔隙各项参数均大于其他孔隙,有效长度30～40mm的孔隙τ值可达到6.5mm/mm,R值可达0.18mm,虽然这部分孔隙数量很少,但对土壤中水及溶质的传导能力影响较短孔隙要大的多。三维指标在降雨过程呈现一定的变化规律,在次降雨前期,孔隙度、水力半径持续减小,孔隙倾斜度、扭曲复杂度、欧拉数增大,表明孔隙连通性、传导性随降雨时间的延续而降低,对水及溶质的传导能力变小,在降雨后期,各指标趋于稳定,此时土壤形成致密层,阻碍了水及溶质的传导。
综上所述,本研究是在对孔隙结构空间数据结构分析的基础上,确定了适合孔隙网络模型计算的土壤孔隙特征指标,建立了能够真实反映孔隙拓扑结构的孔隙网络模型。对模型的应用表明红壤孔隙结构在土壤侵蚀过程中存在一定的变化规律。此研究有利于丰富孔隙拓扑结构的研究理论和进一步拓展土壤侵蚀的研究范围,有助于揭示侵蚀发生发展的动态过程。
The structure of soil pore affects the transmission route and mode of water and solute directly, it also decides the important factors which affect the process of soil erosion, such as water retention, permeability, water transmissibility and so on. To research the properties of pore structure in soil has great practical significance in preventing and curing soil erosion, environment protection, reducing pollution of ground water and so on. The pore-network model is one of the most important methods for modeling porous media pore space. Taking the typical red soil as an example, this paper researches the structure of soil pores larger than 50μm by analyzing soil sample which uses the digital images of the soil slice during rainfall. We analyze and identify the original images by applying the technologies of serial slices, digital image processing especially technology of 3S to pick-up the images of soil. This paper also researches how to quantitatively describe the characteristics of the pore space and a viable pore-network model is built at the platform of Visual Basic 6.0. To study the relationship between pore structure changes and soil erosion process, this paper analyzes the spatial and temporal change rule of top soil pore characteristics. The main results are as follows:
(1) Our research established data structure of network model to describe soil pore space topological characteristics, regulated design restrict by detailed system analysis and design, built pore network model based on the theory of morphologic network model and pore topological characteristics. In the modeling course, we researched the key arithmetic of heightening the vertical resolve, and the judging problem of level and vertical connection, after completed the steps above, base on the theory of space topology to structure the pore network. The result of testing model indicates that, the model can truly describe space distribution and gain topological characteristics of pore in soil.
(2) Based on the research of topological relationship of pore space structure, this paper analysed pore size and connectivity from the aspect of pore affect water and solute to confirm quantitative parameters which can evaluate pore structure characteristics: Equivalent Diameter, Numbers, Porosity, Length, Angel from vertical, Tortuous Complexity, Connectivity and Hydraulic radius, moreover, it realized those arithmetic compute.
(3) By using the pore network model, this paper again the parameters value of pore structure which bigger than 50μm with rainfall by numerical method, and the change rules of parameters.
Pore diameter: majority pore is small, pores belong to 200-400μm have the biggest area. During the process of rainfall, the number of small pores increases, bigger pore decreases and the porosity decreases continually. With the increase in soil depth, the average diameter increases gradually. Pores in soil micro-layer L1, L2 are affected greatly in rainfall.
Statistic the indicators of pores longer than 2.5 mm which play the most important role in affecting water and solute transportation, and the result are: there are regular rules of those parameters. Because the soil is disturb, there are many macropore, porosity is mainly about 4-7%. The pore structure is complex, tortuous Complexityτis mainly 1-2 mm/mm; the connectivity of soil is high, the average of Eluer is about 0.2-0.8, most pores' Hydraulic radius is about 0.05-0.1 mm. Most pore network's Angels from vertical 8 are smaller than 45 degree shows that pore has a good stretch in soil. There are some longer pores' parameters are larger than the others, pores with length is 30-40 mm haveτ6.5 mm/mm, R 0.18 mm. Although these pores with larger parameters are minority, they take more important part in transporting and seeping water and solute than samller pores in soil. The 3-D parameters have rules with rainfall, Porosity, Hydraulic radius decrease, and Angel from vertical, Tortuous Complexity and Euler number increase, indicates the pore connectivity and transmission ability decreases with the increase of rainfall time. In the later of rainfall, the surface layer of soil is compacted and pore structure has no change any more, tending to steady. As a whole, the transmission ability of pore is decreasing with the rainfall.
In summary, based on the analysis of data structure of soil pore structure, this paper confirmed parameters of pore fit to pore topological structure, modeled pore network model. By using the model, we gained the change rules of red soil pore structure during rainfall. This research helps to enrich the research theory of pore topological characteristics, extend the research extension of soil erosion, open out the dynamic happen and development course of soil erosion.
引文
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39.Anderson A N,McBratney A B,Fitz Patric E A.Soil mass,surface,and spectral fractal dimensions estimated from thin section photographs.Soil Science Society of America Journal,1996,60(4):962-969
40.Anton W,Jacqueline.Determination of pore networks and water content distributions from 3-D computed tomography images of a clay soil.Bioimaging,1997(5):194-204.
41. Bakke S, Oren P E. 3D pore-scale modeling of sanstones and flow simulations in the pore networks. SPE, 1997:35-49
42. Bertuzzi P, Garcia-Sanchez L, Chadoeuf J, et al . Modeling surface-roughness by a Boolean approach. European Journal of Soil Science, 1995, 46: 215-220
43. Beven K. Germann P. Macropores and water flow in soils. Water Resour Res, 1982, 18 (5): 1311-1325
44. Blunt M J, Jackson M D. Piri M, Valvatne P H. Detailed physics predictive capabilities and macroscopic consequences for pore-network models of multiphase flow.Advances in Water Resources, 2002a, 25(1): 1069-1089
45. Blunt M J, King P. Macroscopic parameters from simulations of pore scale flow. Physical Review, 2002b, 42(8): 4780-4787
46. Blunt M J, King P. Relative permeability from two- and three-dimensional pore-scale modeling. Transport in Porous Media, 1991, 6(8): 407-433
47. Bouma J, Jongerius A. Boersma O H. The function of different types of macropores during saturated flow through four swelling soil horizons. Soil Science Society of America Journal, 1977, 41:945-950
48. Bryant S. Blunt M. Prediction of relative permeability in simple porous-media Physical Review. 1992, 46(4): 2004-2011
49. Chandler B, Koplik J, Lerman K. Capillary displacement and percolation in porous media. Journal of Fluid Mechanics, 1982, 119: 249-267
50. Chatzis 1, Dullien F A L. Modeling porestructure by 2D and 3D networks with application to sandstone. Journal of Canadian Ptroleum Technology, 1977, 16: 97-108
51. Christos D, Tsakiroglou, Alkiviades C. Payatakes. Characterization of the pore structure of reservoir rocks with the aid of serial sectioning analysis, mercury porosimetry and network simulation, 2000, 23: 773-789
52. Edwards, Norton L D. Redmond-Characterizing macropores that affect infiltration into nontilled soil. Soil Science Society of America Journal, 1988, 52(2): 483-487
53. Fatt I. The network model of porous media I. Capillary characteristics. Petroleum Transactions, AIME, 1956,207: 144-159
54. Fox D M, Bryan R B, Fox C A. Changes in pore characteristics with depth for structure crust. Geoderma, 2004, 120: 109-120
55. Fox D M, Bryan R B, Fox C A. Changes in pore characteristics with depth for structural crusts. Geoderma, 2004, 120: 109-120
56. German P F, Edwards W M, Owens L B. Profile of bromide and increased soil moisture after infiltration into soils with macropores. Soil Science Society of America Journal, 1984, 48: 237-244
57. Gonzales R C, Woods, R E. Digtial image processing. Addison-Wesley Publishing Company, New York, 1992
58. Goulard, Chadoeuf J, Bertuzzi P. Random Boolean functions nonparametric -estimation of the intensity-application to soil surface-roughness. Statistics, 1994,25: 123-136
59. Graham W, Horgan. A rewiew of soil pore models. Biomathematics and Statistics Scotland, 1996, 10: 1-15
60. Greenland, D J. Soil management and soil degradation.Journal of Soil Science. 1997, 32:301-322
61. Hall. An amended functional leaching model applicable to structured soils model description. Soil Science Society of America Journal, 1993, 44: 579-588
62. Hallaire V. Description of microcrack rientation in a clayey soil using image analysis. Proceedings of In-ternational Agricultural Mechanization Conference, 1994. 549-557
63. Jackson M D, Valvatne P H. Blunt M. J. Prediction of wettability variation and its impact on waterflooding using pore-to-reservoir-scale simulation. SPE, 2002: 577-585
64. Johan Perret, Prasher S O. Three-Dimensional Quantification of Macropore Networks in Undisturbed Soil Cores. Soil Science Society of America Journal, 1999:1530-1543
65. Liang Z, Ioannidis M A, Chatzis I. Pemeability and electrical conductivity of porous media from 3D stochastic replicas of the microstructure. [J]. Chem Eng Sci, 2000,55: 5247-5262
66. Lowry M I, Miller C T. Pore-scale modeling of nonwetting-phase residual in porous media.Water Resources Research, 1995, 31(3): 455-473
67. Luk S H, Abrahams A D, Parsons A J. A simple rainfall simulator and trickle system for hydro-geomorphic experiments. Physical Geography, 1986, 7: 344-356
68. Macdonald I F, Kaufmann P. Dullien. Quantitative image analysis of finite porous media: I. Development of genus and pore map software. J. Microscopy, 1986, 144: 277-296
69. Meyer F. Mathematical morphology: from two dimensions to three dimensions. Journal of Microscopy, 1992, 165: 5-28
70. Moreau E, Velde B, Terribile F. Comparison of 2Dand 3D images of fractures in a vertisol. Geoderma, 1999, 92: 55-72
71. Oren P E, Bakke S. Process based reconstruction of sandstones and predictions of transport properties. Transport on Porous Media, 2002, 46(2): 311-343
72. Pagliai M, La Marca M, Lucamante G. Micro-morphometric and micro-morphological investigations of a clay loam soil in viticulture under zero and conventional tillage. [J]. Soil Science Society of America Journal, 1983, 34:391 -403
73. Panini T, Torri D, Pellegrini S. A theoretical approach to soil porosity and sealing development using simulated rainstorms. Catena, 1997, 31:199-218
74. Pierret, Capowiez Y. 3D reconstruction and quantification of macropores using X-ray computed tomography and image analysis. Geoderma, 2002, 106: 247-271
75. Poesen, Ingelmo J, Sanchez. Runoff and sediment yield from topsoils with different porosity as affected by rock fragment cover and position. Catena, 1992, 19: 451-474
76. Serra J. Image Analysis and mathematical Morphology. Academic Press, London. 1992
77. Thomas G W, Phillips R E. Consequences of water movement in marcopores J. Environ. Qual, 1979,(8): 149-152.
78. Toledo, Novy P G, Davis R A, Scriven L E. Hydraulic conductivity of porous media atlowwater content. Soil Science Society of America Journal, 1990, 54: 673-679
79. Tovey K. A digital computer technique for ori-entation analysis of micrograhs of soil fabric. Journal of Microscopy. 1990, 102: 303-315
80. Velde B, Moreau E, Terribile F. Pore networks in an Italian Vertisol: quantitative characterisation by two dimensional image analysis. Geoderma. 1996 (72): 271-285
81. Vogel H J. Kretzschmar A. Topological characterization of pore space in soil sample preparation and digital image-processing. Geoderma, 1996, 73: 23-28
82. Vogel H J, Roth K. A new approach for determining effective soil hydraulic functions. European Journal of Soil Science, 1998, 49: 547-556
83. Vogel H J, Roth K. Quantitative morphology and network representation of soil pore structure. Advances in Water Resources, 2001, (24): 233-242
84. Vogel H J. Morphological determination of pore connectivity as a function of pore size using serial sections. European Journal of Soil Science, 1997, 9(48): 365-377
85. Wise, W R. A new insight on pore structure and permeability. Water Resources Research, 1992, 28: 189-198
86. Yang A, Miller C T, Turcoliver L D. Simulation of correlated and uncorrelated packing of random size spheres [J]. Physical Review E. 1996. 53: 1516-1524
2.曹海峰,王晨光,孔亮.血管连续切片图像的计算机三维重建.东北农业大学学报.2003,34(1):10-14
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37.周明耀,余长洪,钱晓晴.基于孔隙分形维数的土壤大孔隙流水力特征参数研究.中国农业工程学会.2005年学术年会论文集.2005:315-319
38.Adiler P M,Jacquin C G,Thovert J F.The formation factor of reconstructed porous media.Water Resources Research,1992,28(6):1571-1576
39.Anderson A N,McBratney A B,Fitz Patric E A.Soil mass,surface,and spectral fractal dimensions estimated from thin section photographs.Soil Science Society of America Journal,1996,60(4):962-969
40.Anton W,Jacqueline.Determination of pore networks and water content distributions from 3-D computed tomography images of a clay soil.Bioimaging,1997(5):194-204.
41. Bakke S, Oren P E. 3D pore-scale modeling of sanstones and flow simulations in the pore networks. SPE, 1997:35-49
42. Bertuzzi P, Garcia-Sanchez L, Chadoeuf J, et al . Modeling surface-roughness by a Boolean approach. European Journal of Soil Science, 1995, 46: 215-220
43. Beven K. Germann P. Macropores and water flow in soils. Water Resour Res, 1982, 18 (5): 1311-1325
44. Blunt M J, Jackson M D. Piri M, Valvatne P H. Detailed physics predictive capabilities and macroscopic consequences for pore-network models of multiphase flow.Advances in Water Resources, 2002a, 25(1): 1069-1089
45. Blunt M J, King P. Macroscopic parameters from simulations of pore scale flow. Physical Review, 2002b, 42(8): 4780-4787
46. Blunt M J, King P. Relative permeability from two- and three-dimensional pore-scale modeling. Transport in Porous Media, 1991, 6(8): 407-433
47. Bouma J, Jongerius A. Boersma O H. The function of different types of macropores during saturated flow through four swelling soil horizons. Soil Science Society of America Journal, 1977, 41:945-950
48. Bryant S. Blunt M. Prediction of relative permeability in simple porous-media Physical Review. 1992, 46(4): 2004-2011
49. Chandler B, Koplik J, Lerman K. Capillary displacement and percolation in porous media. Journal of Fluid Mechanics, 1982, 119: 249-267
50. Chatzis 1, Dullien F A L. Modeling porestructure by 2D and 3D networks with application to sandstone. Journal of Canadian Ptroleum Technology, 1977, 16: 97-108
51. Christos D, Tsakiroglou, Alkiviades C. Payatakes. Characterization of the pore structure of reservoir rocks with the aid of serial sectioning analysis, mercury porosimetry and network simulation, 2000, 23: 773-789
52. Edwards, Norton L D. Redmond-Characterizing macropores that affect infiltration into nontilled soil. Soil Science Society of America Journal, 1988, 52(2): 483-487
53. Fatt I. The network model of porous media I. Capillary characteristics. Petroleum Transactions, AIME, 1956,207: 144-159
54. Fox D M, Bryan R B, Fox C A. Changes in pore characteristics with depth for structure crust. Geoderma, 2004, 120: 109-120
55. Fox D M, Bryan R B, Fox C A. Changes in pore characteristics with depth for structural crusts. Geoderma, 2004, 120: 109-120
56. German P F, Edwards W M, Owens L B. Profile of bromide and increased soil moisture after infiltration into soils with macropores. Soil Science Society of America Journal, 1984, 48: 237-244
57. Gonzales R C, Woods, R E. Digtial image processing. Addison-Wesley Publishing Company, New York, 1992
58. Goulard, Chadoeuf J, Bertuzzi P. Random Boolean functions nonparametric -estimation of the intensity-application to soil surface-roughness. Statistics, 1994,25: 123-136
59. Graham W, Horgan. A rewiew of soil pore models. Biomathematics and Statistics Scotland, 1996, 10: 1-15
60. Greenland, D J. Soil management and soil degradation.Journal of Soil Science. 1997, 32:301-322
61. Hall. An amended functional leaching model applicable to structured soils model description. Soil Science Society of America Journal, 1993, 44: 579-588
62. Hallaire V. Description of microcrack rientation in a clayey soil using image analysis. Proceedings of In-ternational Agricultural Mechanization Conference, 1994. 549-557
63. Jackson M D, Valvatne P H. Blunt M. J. Prediction of wettability variation and its impact on waterflooding using pore-to-reservoir-scale simulation. SPE, 2002: 577-585
64. Johan Perret, Prasher S O. Three-Dimensional Quantification of Macropore Networks in Undisturbed Soil Cores. Soil Science Society of America Journal, 1999:1530-1543
65. Liang Z, Ioannidis M A, Chatzis I. Pemeability and electrical conductivity of porous media from 3D stochastic replicas of the microstructure. [J]. Chem Eng Sci, 2000,55: 5247-5262
66. Lowry M I, Miller C T. Pore-scale modeling of nonwetting-phase residual in porous media.Water Resources Research, 1995, 31(3): 455-473
67. Luk S H, Abrahams A D, Parsons A J. A simple rainfall simulator and trickle system for hydro-geomorphic experiments. Physical Geography, 1986, 7: 344-356
68. Macdonald I F, Kaufmann P. Dullien. Quantitative image analysis of finite porous media: I. Development of genus and pore map software. J. Microscopy, 1986, 144: 277-296
69. Meyer F. Mathematical morphology: from two dimensions to three dimensions. Journal of Microscopy, 1992, 165: 5-28
70. Moreau E, Velde B, Terribile F. Comparison of 2Dand 3D images of fractures in a vertisol. Geoderma, 1999, 92: 55-72
71. Oren P E, Bakke S. Process based reconstruction of sandstones and predictions of transport properties. Transport on Porous Media, 2002, 46(2): 311-343
72. Pagliai M, La Marca M, Lucamante G. Micro-morphometric and micro-morphological investigations of a clay loam soil in viticulture under zero and conventional tillage. [J]. Soil Science Society of America Journal, 1983, 34:391 -403
73. Panini T, Torri D, Pellegrini S. A theoretical approach to soil porosity and sealing development using simulated rainstorms. Catena, 1997, 31:199-218
74. Pierret, Capowiez Y. 3D reconstruction and quantification of macropores using X-ray computed tomography and image analysis. Geoderma, 2002, 106: 247-271
75. Poesen, Ingelmo J, Sanchez. Runoff and sediment yield from topsoils with different porosity as affected by rock fragment cover and position. Catena, 1992, 19: 451-474
76. Serra J. Image Analysis and mathematical Morphology. Academic Press, London. 1992
77. Thomas G W, Phillips R E. Consequences of water movement in marcopores J. Environ. Qual, 1979,(8): 149-152.
78. Toledo, Novy P G, Davis R A, Scriven L E. Hydraulic conductivity of porous media atlowwater content. Soil Science Society of America Journal, 1990, 54: 673-679
79. Tovey K. A digital computer technique for ori-entation analysis of micrograhs of soil fabric. Journal of Microscopy. 1990, 102: 303-315
80. Velde B, Moreau E, Terribile F. Pore networks in an Italian Vertisol: quantitative characterisation by two dimensional image analysis. Geoderma. 1996 (72): 271-285
81. Vogel H J. Kretzschmar A. Topological characterization of pore space in soil sample preparation and digital image-processing. Geoderma, 1996, 73: 23-28
82. Vogel H J, Roth K. A new approach for determining effective soil hydraulic functions. European Journal of Soil Science, 1998, 49: 547-556
83. Vogel H J, Roth K. Quantitative morphology and network representation of soil pore structure. Advances in Water Resources, 2001, (24): 233-242
84. Vogel H J. Morphological determination of pore connectivity as a function of pore size using serial sections. European Journal of Soil Science, 1997, 9(48): 365-377
85. Wise, W R. A new insight on pore structure and permeability. Water Resources Research, 1992, 28: 189-198
86. Yang A, Miller C T, Turcoliver L D. Simulation of correlated and uncorrelated packing of random size spheres [J]. Physical Review E. 1996. 53: 1516-1524