Relative Permeability Coefficient Model of Unsaturated Soil with Multiphase Flow Based on Fractal Theory

CAO Shuai; NING Jin-cheng; YANG Qing-guo

doi:10.11988/ckyyb.20201141

PDF(1225 KB)

Journal of Changjiang River Scientific Research Institute ›› 2022, Vol. 39 ›› Issue (4) : 135-139. DOI: 10.11988/ckyyb.20201141

ROCK SOIL ENGINEERING

Relative Permeability Coefficient Model of Unsaturated Soil with Multiphase Flow Based on Fractal Theory

CAO Shuai¹, NING Jin-cheng¹, YANG Qing-guo²

Author information +

History +

Abstract

Relative permeability coefficient is a crucial parameter describing the hydraulic characteristics of unsaturated soil. In researches of traditional relative permeability model for unsaturated soil, the seepage characteristic model of wet phase rather than non-wet phase received much focus. To study the multiphase flow transport model of unsaturated soil, we at first simplified the soil pores into a group of tortuous capillaries obeying the fractal law; by establishing the transport characteristic model of liquid and gas phase in porous media, we obtained the model of relative permeability coefficient of both liquid and gas phase of unsaturated soil in association with the Young-Laplace equation and the Buckingham-Darcy’s law. The model only contains two parameters, with clear physical meanings and can be measured by experiments. Eight groups of test data validated the rationality and applicability of the present model. We hence conclude that the model better describes the multiphase seepage characteristics of unsaturated soil.

Key words

unsaturated soil / relative permeability coefficient model / multiphase flow / fractal theory / pore distribution

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

CAO Shuai, NING Jin-cheng, YANG Qing-guo. Relative Permeability Coefficient Model of Unsaturated Soil with Multiphase Flow Based on Fractal Theory[J]. Journal of Changjiang River Scientific Research Institute. 2022, 39(4): 135-139 https://doi.org/10.11988/ckyyb.20201141

References

[1] HU R, CHEN Y F, ZHOU C B. Modeling of Coupled Deformation, Water Flow and Gas Transport in Soil Slopes Subjected to Rain Infiltration[J]. Science China Technological Sciences, 2011, 54(10): 2561-2575.
[2] 韦秉旭, 陈亮胜, 肖罗明, 等. 基于多场耦合的膨胀土边坡非饱和降雨入渗分析[J]. 长江科学院院报, 2021, 38(3): 90-96.
[3] BURDINE N T. Relative Permeability Calculations from Pore Size Distribution Data[J]. Transactions of the American Institute of Mining, Metallurgical, and Petroleum Engineers, 1953, 98(3):71-78.
[4] 彭子茂, 黄震. 模拟非饱和流的新型相对渗透系数模型[J].长江科学院院报,2020,37(7):115-119.
[5] MUALEM Y. A New Model for Predicting the Hydraulic Conductivity of Unsaturated Porous Media[J]. Water Resources Research, 1976, 12(3): 513-522.
[6] BURDINE N T. Relative Permeability Calculations from Pore Size Distribution Data[J]. Journal of Petroleum Technology, 1953, 5(3): 71-78.
[7] MUALEM Y. Modified Approach to Capillary Hysteresis Based on a Similarity Hypothesis[J]. Water Resources Research, 1973, 9(5): 1324-1331.
[8] GENUCHTEN M T V. A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils[J]. Soil Science Society of America Journal,1980,44:892-898.
[9] YANG Z, MOHANTY B P. Effective Parameterizations of Three Nonwetting Phase Relative Permeability Models[J]. Water Resources Research, 2015, 51(8): 6520-6531.
[10] KOSUGI K. General Model for Unsaturated Hydraulic Conductivity for Soils with Lognormal Pore-size Distribution[J]. Soil Science Society of America Journal, 1999, 63(2): 270-277.
[11] ALEXANDER L,SKAGGS R W.Predicting Unsaturated Hydraulic Conductivity from the Soil Water Characteristic[J]. Transactions of the ASAE, 1986, 29(1): 176-184.
[12] SKAGGS T H. Assessment of Critical Path Analyses of the Relationship Between Permeability and Electrical Conductivity of Pore Networks[J]. Advances in water resources, 2011, 34(10): 1335-1342.
[13] 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.
[14] 陶高梁, 孔令伟. 基于微观孔隙通道的饱和/非饱和土渗透系数模型及其应用[J]. 水利学报, 2017, 48(6): 702-709.
[15] 李毅. 岩石裂隙的非饱和渗透特性及其演化规律研究[J].岩土力学,2016,37(8):2254-2262.
[16] YOUNG T. An Essay on the Cohesion of Fluids[J]. Philosophical Transactions of the Royal Society of London,1805, 95: 65-87.
[17] 郁伯铭. 多孔介质输运性质的分形分析研究进展[J]. 力学进展, 2003, 33(3):333-346.
[18] YU B. Analysis of Flow in Fractal Porous Media[J]. Applied Mechanics Reviews, 2008, 61(5):1239-1249.
[19] BEAR J. Dynamics of Fluids in Porous Media[M]. New York: Elsevier, 1988.
[20] BUCKINGHAM E. Studies on the Movement of Soil Moisture[R]. Washington: Bulletin 38 of US Government Print Office, 1907.
[21] ASSOULINE S.A Model for Soil Relative Hydraulic Conductivity Based on the Water Retention Characteristic Curve[J].Water Resources Research,2001,37(2):265-271.
[22] FISCHER U, KULLI B, FLÜHLER H. Constitutive Relationships and Pore Structure of Undisturbed Fracture Zone Samples with Cohesionless Fault Gouge Layers[J]. Water Resources Research, 1998, 34(7): 1695-1701.
[23] DURY O, FISCHER U, SCHULIN R. A Comparison of Relative Nonwetting-Phase Permeability Models[J]. Water Resources Research, 1999, 35(5): 1481-1493.