Law of Nonlinear Flow in Saturated Clays and Radial Consolidation

DENG Ying-er; XIE He-ping; HUANG Run-qiu; LIU Ci-qun

Volume 28 Issue 11

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(11): 1272-1280

DENG Ying-er, XIE He-ping, HUANG Run-qiu, LIU Ci-qun. Law of Nonlinear Flow in Saturated Clays and Radial Consolidation[J]. Applied Mathematics and Mechanics, 2007, 28(11): 1272-1280.

Citation:

DENG Ying-er, XIE He-ping, HUANG Run-qiu, LIU Ci-qun. Law of Nonlinear Flow in Saturated Clays and Radial Consolidation[J]. Applied Mathematics and Mechanics, 2007, 28(11): 1272-1280.

Citation:

DENG Ying-er, XIE He-ping, HUANG Run-qiu, LIU Ci-qun. Law of Nonlinear Flow in Saturated Clays and Radial Consolidation[J]. Applied Mathematics and Mechanics, 2007, 28(11): 1272-1280.

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Law of Nonlinear Flow in Saturated Clays and Radial Consolidation

1.
State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, P. R. China;
Institute of Engineering Science and Hazard Mechanics, Sichuan University, Chengdu 610064, P. R. China;

Received Date: 2006-09-08
Rev Recd Date: 2007-09-05
Publish Date: 2007-11-15

Abstract

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 the square root of 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 instead 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 Darcy flow are a special case of that of the nonlinear flow.
- saturated clay,
- nonlinear flow law,
- consolidation,
- average degree of consolidation,
- moving boundary

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References(18)

References

[1]	贝尔 J.多孔介质流体动力学[M].李竟生，陈崇希译.北京：中国建筑业出版社，1983,9-11.
[2]	郭尚平，刘慈群，阎庆来,等.渗流力学的近况和展望[J].力学与实践，1981，13(3)：11-16.
[3]	刘慈群，郭尚平.多重介质渗流研究进展[J].力学进展，1982，12(4)，360-364.
[4]	郭尚平，刘慈群，阎庆来，等.渗流力学的新发展[J].力学进展，1986，16(4)：441-454.
[5]	郭尚平，张盛宗，桓冠仁，等.渗流研究和应用的一些动态[A].见：渗流所主编.渗流力学进展[C].北京：石油工业出版社，1996：1-12.
[6]	刘慈群. 双重介质非线性渗流[J].科学通报，1981，17(1)：1081-1085
[7]	邓英尔，刘慈群，黄润秋，等.高等渗流理论与方法[M].北京：科学出版社，2004,1-15.
[8]	DENG Ying-er, LIU Ci-qun.Numerical simulation of unsteady flow through porous media with moving boundary[A].In: ZHANG Feng-gan,Ed.Proceedings of the Third International Conference on Fluid Mechanics[C].Beijing: Beijing Institute of Technology Press，1998: 759-765
[9]	薛定谔 A E. 多孔介质中的渗流物理[M].王鸿勋，张朝琛，孙书琛译. 北京：石油工业出版社，1982.
[10]	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(5):323-337. doi: 10.1016/0016-0032(73)90212-3
[11]	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(3):1201-1215.
[12]	Pascal F, Pascal H,Murray D W. Consolidation with threshold gradients[J].International Journal for Numerical and Analytical Methods in Geomechanics，1981,5(1):247-261. doi: 10.1002/nag.1610050303
[13]	刘慈群.有起始比降固结问题的近似解[J].岩土工程学报，1982，4(3)：107-109.
[14]	庄礼贤，尹协远，马晖扬.流体力学[M].合肥：中国科技大学出版社，1997,366-378.
[15]	杜延龄，许国安.渗流分析的有限元法和电网络法[M].北京：水利电力出版社，1991,14-16.
[16]	阎庆来. 单相均质液体低速渗流机理及流动规律[A].见：中国力学学会主编. 第二届全国流体力学会议论文集[C].北京：科学出版社，1983,325-326.
[17]	邓英尔，阎庆来，马宝歧，等.界面分子力作用与渗透率的关系及其对渗流的影响[J].石油勘探与开发，1998，25(2)：46-49.
[18]	谢和平. 分形-岩石力学导论[M].北京：科学出版社，2005,1-12.

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