Abstract
It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A mathematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Results show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.
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References
Bear J. Dynamics of fluids in porous media[M]. Li Jingsheng, Chen Chongxi (transls). Beijing: Chinese Architecture Industry Press, 1983, 9–11 (Chinese Version).
Guo Shangping, Liu Ciqun, Yan Qinglai, et al. Recent development of mechanics of fluids in porous media[J]. Mechanics and Engineering, 1981, 13(3):11–16 (in Chinese).
Liu Ciqun, Guo Shangping. Progress in study on flow through multiple-porosity permeability media[J]. Progress in Mechanics, 1982, 12(4):360–364 (in Chinese).
Guo Shangping, Liu Ciqun, Yan Qinglai, et al. Recent development of mechanics of fluids in porous media[J]. Advances in Mechanics, 1986, 16(4):441–454 (in Chinese).
Guo Shangping, Zhang Shengzong, Huan Guanren, et al. Dynamics of study and application of flow in porous media[C]. In: Institute of porous flow and fluid mechanics (ed). Progress in Mechanics of Fluids in Porous Media, Beijing: Petroleum Industry Press, 1996, 1–12 (in Chinese).
Liu Ciqun. Nonliner flow in media with double-porosity[J]. Chinese Science Bulletin, 1980, 17(1):1081–1085 (in Chinese).
Deng Yinger, Liu Ciqun, Huang Runqiu, et al. Advanced theory of mechanics of fluids in porous media and methods[M]. Beijing: Science Press, 2004, 1–15 (in Chinese).
Deng Yinger, Liu Ciqun. Numerical simulation of unsteady flow through porous media with moving boundary[C]. In: Zhang Fenggan (ed). Proceedings of the third international conference on fluid mechanics, Beijing: Beijing Institute of Technology Press, 1998, 759–765.
Scheidegger A E. The physics of flow through porous media[M]. Wang Hongxun (transl). Beijing: Petroleum Industry Press, 1982 (Chinese Version).
Elnaggar H A, Krizek R J, Karadi G M. Effect of non-darcian flow on time rate of consolidation[J]. J Franklin Inst, 1973, 296:323–337.
Schmidt J D, Westmann R A. Consolidation of porous media with non-Darcy flow[J]. J Engng Mech Div Proc Am Soc Civ Eng, 1973, 99:1201–1215.
Pascal F, Pascal H, Murray D W. Consolidation with threshold gradients[J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1981, 5:247–261.
Liu Ciqun. Approximate solutions to consolidation with starting gradient[J]. Chinese Journal of Geotechnical Engineering, 1982, 4(3):107–109 (in Chinese).
Zhuang Lixian, Yin Xieyuan, Ma Huiyang. Fluid mechanics[M]. Hefei: Press of University of Science and Technology of China, 1997, 366–378 (in Chinese).
Du Yanling, Xu Guoan. Finite element method and electric network method of seepage analysis[M]. Beijing: Water Resources and Hydropower Press, 1991, 14–16 (in Chinese).
Yan Qinglai. Mechanics and laws of flow of mono-phase homogeneous liquid at low velocity[C]. In: Chinese Society of Mechanics (ed). Proceedings of the Second Conference on Fluid Mechanics, Beijing: Science Press, 1983, 325–326 (in Chinese).
Deng Yinger, Yan Qinglai, Ma Baoqi, Liu Ciqun. Relationship between interfacial molecular interaction and permeability and its influence on fluid flow[J]. Petroleum Exploration and Development, 1998, 25(2):46–49 (in Chinese).
Xie Heping. Fractal-rock mechanics introduction[M]. Beijing: Science Press, 2005, 1–12 (in Chinese).
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Contributed by XIE He-ping
Project supported by the National Natural Science Foundation of China (Nos. 40202036, 40572163, 50579042); the Youth Science Foundation of Sichuan Province of China (No. 05ZQ026-043); the Science Foundation of State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (No. GZ2004-05); the Postdoctoral Science Foundation of China (No. 35)
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Deng, Ye., Xie, Hp., Huang, Rq. et al. Law of nonlinear flow in saturated clays and radial consolidation. Appl. Math. Mech.-Engl. Ed. 28, 1427–1436 (2007). https://doi.org/10.1007/s10483-007-1102-7
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DOI: https://doi.org/10.1007/s10483-007-1102-7