(1. School of Civil Engineering and Architecture, Xi?an University of Technology, Xi?an, Shaanxi 710048, China; 2. State Key Laboratory of Water Engineering Ecology and Environment in Arid Area, Xi'an University of Technology,
Xi?an, Shaanxi 710048, China; 3. Institute of New Energy Engineering, POWERCHINA Beijing Engineering
Corporation Limited, Beijing 100024, China)
Abstract：Considering the impact of particle non-uniformity on the tortuosity of soil is one approach to enhance the predictive accuracy of soil hydraulic conductivity. In response, a theoretical equation predicting average tortuosity was initially derived based on boundary layer theory and geometric analysis. This equation incorporates ten typical flow paths under varying conditions of particle overlap, selected from the pores of a representative element volume. Additionally, assemblies of square particles with different lengths were numerically simulated using COMSOL Multiphysics software. Several soil column flow tests were conducted under various rainfall intensities. The calculated curves from the proposed equation were then compared with these data, including both previously published simulation and test results. The results indicate that the proposed equation is well-suited to describe the evolution of hydraulic conductivity concerning porosity, as well as the large particle volume fraction and seepage drop relative to flow velocity. Further analysis of the effect of the particle length ratio reveals that soil tortuosity decreases with increasing ratios until this trend stabilizes. Finally, the proposed equation was used to predict the hydraulic conductivity of dam materials in the earth-rock dam with a straight core wall at Nuozhadu Hydropower Station. It was found that the proposed equation outperforms previously published equations due to its consideration of soil particle non-uniformity.
BEAR J. Dynamics of fluids in porous media[M]. New York：Elsevier，1972：13-24.
[2]
饶登宇，白 冰. 溶质运移中多孔介质弥散度影响因素的SPH模拟研究[J]. 水利学报，2019，50(7)：824-834.(RAO Dengyu，BAI Bing. Study on the factors affecting dispersity of porous media by SPH simulation in solute transport[J]. Journal of Hydraulic Engineering，2019，50(7)：824-834.(in Chinese))
[3]
周鸿翔，郑延丰，吴劳生，等. 孔隙尺度多孔介质流动与溶质运移高性能模拟[J]. 水科学进展，2020，31(3)：422-432.(ZHOU Hongxiang，ZHENG Yanfeng，WU Laosheng，et al. Pore-scale simulations of fluid flow and solute transport in porous media by high-performance lattice boltzmann method[J]. Advances In Water Science，2020，31(3)：422-432.(in Chinese))
[4]
刘 杰，崔亦昊，谢定松. 江河大堤均匀砂基渗透破坏机理试验研究[J]. 岩土工程学报，2008，30(5)：642-645.(LIU Jie，CUI Yihao，XIE Dingsong. Failure mechanism of seepage in uniform sand foundation of river levee[J]. Chinese Journal of Geotechnical Engineering，2008，30(5)：642-645.(in Chinese))
[5]
WU L Z，SElVADURAI A P S，ZHANG L M，et al. Poro-mechanical coupling influences on potential for rainfall-induced shallow landslides in unsaturated soils[J]. Advances in Water Resources，2016，98：114-121.
[6]
刘 杰. 土的渗透破坏及控制研究[M]. 北京：中国水利水电出版社，2014：185-195.(LIU Jie. Piping and seepage control of soil[M]. Beijing：China Water Power Press，2014：185-195.(in Chinese))
[7]
毛昶熙. 渗流计算分析与控制[M]. 2版. 北京：中国水利水电出版社，2003：1-10.(MAO Changxi. Analysis and control of seepage calculation[M]. 2 nd ed. Beijing：China Water Power Press，2003：1-10.(in Chinese))
[8]
FU J L，THOMAS H R，LI C F. Tortuosity of porous media：image analysis and physical simulation[J]. Earth-Science Reviews，2021，212：103439.
[9]
郁伯铭. 分形多孔介质输运物理[M]. 北京：科学出版社，2014：55-73.(YU Boming. Transport physics of fractal porous media[M]. Beijing：Science Press，2014：55-73.(in Chinese))
[10]
CHILDS E C. Dynamics of fluids in porous media[J]. Engineering Geology，1973，7(2)：174-175.
[11]
PARLANGE J Y. Porous media：fluid transport and pore structure[J]. Soil Science，1981，132(4)：316-319.
[12]
WYLLIE M R J，GREGORY A R. Fluid flow through unconsolidated porous aggregates[J]. Industrial and Engineering Chemistry，1955，47(7)：1 379-1 388.
[13]
COMITI J，RENAUD M. A new model for determining mean structure parameters of fixed beds from pressure drop measurements：application to beds packed with parallelepipedal particles[J]. Chemical Engineering Science，1989，44(7)：1 539-1 545.
[14]
MOTA M，TEIXEIRA J A，BOWEN W R，et al. Binary spherical particle mixed beds：Porosity and permeability relationship measurement[J]. Filtration Society，2001，1(4)：101-106.
[15]
KOPONEN A，KATAIA M，TIMONEN J. Tortuous flow in porous media[J]. Physical Review E，1996，54(1)：406-410.
[16]
KOPONEN A，KATAIA M，TIMONEN J. Permeability and effective porosity of porous media[J]. Physical Review E，1997，56(3)： 3 319-3 325.
[17]
LI J H，YU B M. Tortuosity of flow paths through a sierpinski carpet[J]. Chinese Physics Letters，2011，28(3)：34 701-34 703.
[18]
YU B M，LI J H. A geometry model for tortuosity of flow path in porous media[J]. Chinese Physics Letters，2004，21(8)：1 569-1 571.
[19]
ZHANG S，YAN H，TENG J D，et al. A mathematical model of tortuosity in soil considering particle arrangement[J]. Vadose Zone Journal，2020，19(1)：e20004.
[20]
WHITE F M. Viscous fluid flow[M]. 3rd ed，New York：McGraw-Hill，2006：153-227.
[21]
齐俊修，赵晓菊，刘 艳，等. 不均匀系数 的无黏性土的渗透变形类型统计分析研究[J]. 岩石力学与工程学报，2014，33(12)：2 554-2 562.(QI Junxiu，ZHAO Xiaoju，LIU Yan，et al. A statistical analysis of seepage deformation type of noncohesive soil with uniformity coefficient [J]. Chinese Journal of Rock Mechanics and Engineering，2014，33(12)：2 554-2 562.(in Chinese))
[22]
刘飞禹，林 旭，王 军. 砂土颗粒级配对筋土界面抗剪特性的影响[J]. 岩石力学与工程学报，2013，32(12)：2 575-2 582.(LIU Feiyu，LIN Xu，WANG Jun. Influence of particle-size gradation on shear behavior of geosynthetics and sand interface[J]. Chinese Journal of Rock Mechanics and Engineering，2013，32(12)：2 575-2 582.(in Chinese))
[23]
祝良玉. 表征水在均质土中流动特性的理论模型与试验研究[硕士学位论文][D]. 西安：西安理工大学，2023.(ZHU Liangyu. Theoretical model and experimental study on characterization of water flow in homogeneous soil[M. S. Thesis][D]. Xi¢an：Xi¢an University of Technology，2023.(in Chinese))
[24]
马路兴. 高压下应力路径对饱和砂土力学特性的影响研究[硕士学位论文][D]. 徐州：中国矿业大学，2014.(MA Luxing. Influence of stress paths on mechanical characteristics of saturated sand at high pressures[M. S. Thesis][D]. Xuzhou：China University of Mining and Technology，2014.(in Chinese))
[25]
苏立君，张宜健，王铁行. 不同粒径级砂土渗透特性试验研究[J]. 岩土力学，2014，35(5)：1 289-1 294.(SU Lijun，ZHANG Yijian，WANG Tiexing. Investigation on permeability of sands with different particle sizes[J]. Rock and Soil Mechanics，2014，35(5)：1 289- 1 294.(in Chinese))
[26]
王淑云，鲁晓兵，时忠民. 颗粒级配和结构对粉砂力学性质的影响[J]. 岩土力学，2005，26(7)：1 029-1 032.(WANG Shuyun，LU Xiaobing，SHI Zhongmin. Effects of grain size distribution and structure on mechanical behavior of silty sands[J]. Rock and Soil Mechanics，2005，26(7)：1 029-1 032.(in Chinese))
[27]
陈逸方. 桂林市砂土渗透破坏规律研究[硕士学位论文][D]. 桂林：桂林理工大学，2017.(CHEN Yifang. Study on the permeability law of deformation and failure of Guilin sand[M. S. Thesis][D]. Guilin：Guilin University of Technology，2017.(in Chinese))
[28]
钱 琨，王新志，陈剑文，等. 南海岛礁吹填钙质砂渗透特性试验研究[J]. 岩土力学，2017，38(6)：1 557-1 564.(QIAN Kun，WANG Xinzhi，CHEN Jianwen，et al. Experimental study on permeability of calcareous sand for islands in the South China Sea[J]. Rock and Soil Mechanics，2017，38(6)：1 557-1 564.(in Chinese))
[29]
CHI S C，NI S S，LIU Z P. Back analysis of the permeability coefficient of a high core rockfill dam based on a RBF neural network optimized using the PSO algorithm[J]. Mathematical Problems in Engineering，2015，124042：1-15.
[30]
FENG S，VARDANEGA P J，IBRAAIM E，et al. Permeability assessment of some granular mixtures[J]. Géotechnique，2019，69(7)：646-654.
[31]
INDRARATNA B，DILEMA E L G，VAFAI F. Experimental study of the filtration of a lateritic clay slurry by sand filters[J]. Geotechnical Engineering，1996，119(2)：75-83.
2025, Vol. 44 
