Approximate Analytical Solution of Water Movement in Concrete Slabs

doi:10.11908/j.issn.0253-374x.2015.10.012

Home > Archive>Volume 43, Issue 10, 2015 >1528-1535. DOI:10.11908/j.issn.0253-374x.2015.10.012

Approximate Analytical Solution of Water Movement in Concrete Slabs
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                        10.11908/j.issn.0253-374x.2015.10.012
                    
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                        ZHANG XiaoZHANG Xiao
Key Laboratory of Highway Construction and Maintenance Technology in Loess Region, Shanxi Transportation Research Institute, Taiyuan 030006, China;Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai 201804, China
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ZHAO HongduoZHAO Hongduo
Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji University, Shanghai 201804, China
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ZHAO DuijiaZHAO Duijia
Key Laboratory of Highway Construction and Maintenance Technology in Loess Region, Shanxi Transportation Research Institute, Taiyuan 030006, China
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Abstract:

In order to study the development of moisture insider concrete slabs, a one dimension water movement model for early age concrete slabs subjected to external drying was established. Adomian decomposition method (ADM) as an approximate analytical solution to initial boundary value problem (IBVP) of water movement equation for moisture distributions in early age concrete slabs with arbitrary boundary conditions was derived. Comparison between numerical results by Crank Nicolson finite difference scheme and experimental results suggests that the proposed ADM based approximate analytical solution approach converges very fast and is effective for solving nonlinear diffusion equation with arbitrary boundary and initial conditions as well as any diffusivity coefficient function for external drying of concrete slabs.

Key words:road engineering; Portland cement concrete (PCC) pavement; water movement mechanism; Adomian decomposition method

Reference

[1]　魏亚. 水泥混凝土路面板湿度翘曲形成机理及变形计算[J]. 工程力学, 2012, 29(11): 266-271.WEI Ya. Mechanism of Moisture Warping and Deformation Calculations in Concrete Pavements[J].Engineering Mechanics,2012, 29(11): 266-271.

[2]　 BUCH N, ZOLLINGER D G. Preliminary Investigation on Effects of Moisture on Concrete Pavement Strength and Behavior[J]. Transportation Research Record, 1993(1382): 26-31.

[3]　 JANSSEN D J. Moisture in Portland cement concrete[J]. Transportation Research Record 1121, 1987(1121): 40-44.

[4]　 JEONG J, ZOLLINGER D G. Environmental effects on the behavior of jointed plain concrete pavements[J]. Journal of transportation engineering, 2005, 131(2): 140-148.

[5]　 BA?ANT Z P, NAJJAR L J. Nonlinear water diffusion in nonsaturated concrete[J]. Material and Construction, 1972, 5(1): 3-20.

[6]　 KANG S, KIM J, LEE Y, et al. Moisture diffusivity of early age concrete considering temperature and porosity[J]. KSCE Journal of Civil Engineering, 2012, 16(1): 179-188.

[7]　 LI C, LI K, CHEN Z. Numerical Analysis of Moisture Influential Depth in Concrete and Its Application in Durability Design[J]. Tsinghua Science Technology, 2008, 13: 7-12.

[8]　 WEI Y, GAO X, HANSEN W. Influential Depth by Water Absorption and Surface Drying in Concrete Slabs[Z]. 2013: 2342, 76-82.

[9]　 XU Q, RUIZ J M, CHANG G K, et al. Moisture Transport Model for Enhancing FHWA HIPERPAV Predictions[J]. Transportation Research Record: Journal of the Transportation Research Board, 2009, 2113(1): 1-12.

[10]　ZHANG J, QI K, HUANG Y. Calculation of moisture distribution in early-age concrete[J]. Journal of Engineering Mechanics, 2009, 135(8): 871-880.

[11]　晁鹏飞, 郑建岚, 王雪芳. 高性能混凝土水分扩散数值解法[J]. 福州大学学报(自然科学版), 2007, 35(6): 898-903.CHAO Peng-fei, ZHENG Jian-lan, WANG Xue-fang. Numerical Algorithm for Moisture Diffusion in High Performance Concrete [J]. Journal of Fuzhou University(Natural Science), 2007, 35(6): 898-903.

[12]　高原, 张君, 孙伟. 密封养护混凝土内部湿度与收缩的一体化试验与模拟[J]. 建筑材料学报, 2013(02): 203-209.GAO Yuan, ZHANG Jun, SUN Wei. Tests and Simulations of Interior Humidity and Shrinkage of Concrete under Sealed Condition [J]. Journal of Building Materials, 2013(02): 203-209.

[13]　胡昌斌, 王丽娟, 吕恒. 水泥混凝土路面板早龄期湿度场数值模拟研究[J]. 工程力学, 2014, 31(4): 178-188.HU Chang-bin, WANG Li-juan, LV Heng. Numerical Modeling of Cement Concrete Pavements’ Internal Moisture Fields at Early Ages [J]. Engineering Mechanics, 2014, 31(4): 178-188.

[14]　BARRY D A, PARLANGE J Y, LI L, et al. Comment on “Analytical decomposition of the nonlinear unsaturated flow equation” by Sergio E. Serrano[J]. Water Resources Research, 2002, 38(2): 1-7.

[15]　BARRY D A, PARLANGE J Y, SANDER G C, et al. A class of exact solutions for Richards' equation[J]. Journal of Hydrology, 1993, 142(1): 29-46.

[16]　HOGARTH W L, PARLANGE J Y. Application and improvement of a recent approximate analytical solution of Richards' Equation[J]. Water Resources Research, 2000, 36(7): 1965-1968.

[17]　LOCKINGTON D A, PARLANGE J Y, BARRY D A, et al. Drying of porous building materials: hydraulic diffusivity and front propagation[J]. Materials and Structures, 2003, 36(7): 448-452.

[18]　LOCKINGTON D A, PARLANGE J. Anomalous water absorption in porous materials[J]. Journal of Physics D: Applied Physics, 2003, 36(6): 760-767.

[19]　LOCKINGTON D, PARLANGE J Y, DUX P. Sorptivity and the estimation of water penetration into unsaturated concrete[J]. Materials and Structures, 1999, 32(5): 342-347.

[20]　PARLANCE M B, PRASAD S N, PARLANGE J Y, et al. Extension of the Heaslet-Alksne Technique to arbitrary soil water diffusivities[J]. Water Resources Research, 1992, 28(10): 2793-2797.

[21]　PARLANGE J Y. Theory of water-movement in soils: 1. One dimensional absorption[J]. 1971, 111(2): 134-137.

[22]　PARLANGE J Y, BARRY D A, PARLANGE M B, et al. New approximate analytical technique to solve Richards equation for arbitrary surface boundary conditions[J]. WATER RESOURCES RESEARCH, 1997, 33(4): 903-906.

[23]　PARLANGE J Y, BARRY D A, PARLANGE M B, et al. Sorptivity calculation for arbitrary diffusivity[J]. Transport in Porous Media, 1994, 15(3): 197-208.

[24]　PARLANGE J Y, HOGARTH W L, BARRY D A, et al. Analytical approximation to the solutions of Richards' equation with applications to infiltration, ponding, and time compression approximation[J]. Advances in Water Resources, 1999, 23(2): 189-194.

[25]　PARLANGE J Y, HOGARTH W L, PARLANGE M B, et al. Approximate Analytical Solution of the Nonlinear Diffusion Equation for Arbitrary Boundary Conditions[J]. Transport in Porous Media, 1998, 30(1): 45-55.

[26]　PARLANGE J Y, LISLE I G, PRASAD S N, et al. Wetting Front Analysis of the Nonlinear Diffusion Equation[J]. Water Resources Research, 1984, 20(5): 636-638.

[27]　SANDER G C, PARLANGE J, KüHNEL V, et al. Exact nonlinear solution for constant flux infiltration[J]. Journal of Hydrology, 1988, 97(3): 341-346.

[28]　RICHARDS L A. Capillary conduction of liquids through porousmediums[J]. Physics, 1931(1): 318-333.

[29]　KNIGHT J H, PHILIP J R. Exact solutions in nonlinear diffusion[J]. Journal of Engineering Mathematics, 1974, 8(3): 219-227.

[30]　PHILIP J R. General method of exact solution of the concentration-dependent diffusion equation[J]. Australian Journal of Physics, 1960, 13(1): 1-12.

[31]　NASSERI M, SHAGHAGHIAN M R, DANESHBOD Y, et al. An analytic solution of water transport in unsaturated porous media[J]. JOURNAL OF POROUS MEDIA, 2008, 11(6): 591-601.

[32]　WARRICK A W. Analytical solutions to the one-dimensional linearized moisture flow equation for arbitrary input[J]. Soil Science, 1975, 120(2): 79-84.

[33]　SERRANO S E. Modeling infiltration with approximate solutions to Richard's equation[J]. Journal of Hydrologic Engineering, 2004, 9(5): 421-432.

[34]　SERRANO S E, ADOMIAN G. New contributions to the solution of transport equations in porous media[J]. Mathematical and Computer Modelling, 1996, 24(4): 15-25.

[35]　SERRANO S E. Analytical decomposition of the nonlinear unsaturated flow equation[J]. Water Resources Research, 1998, 34(3): 397-407.

[36]　RASHIDI M M, DOMAIRRY G, DINARVAND S. Approximate solutions for the Burger and regularized long wave equations by means of the homotopy analysis method[J]. Communications in Nonlinear Science and Numerical Simulation, 2009, 14(3): 708-717.

[37]　PAMUK S. Solution of the porous media equation by Adomian's decomposition method[J]. Physics Letters A, 2005, 344(2): 184-188.

[38]　ASGARI A, BAGHERIPOUR M H, MOLLAZADEH M. A generalized analytical solution for a nonlinear infiltration equation using the exp-function method[J]. Scientia Iranica, 2011, 18(1): 28-35.

[39]　李春秋. 干湿交替下表层混凝土中水分与离子传输过程研究[Z]. 清华大学, 2009.LI Chun-qiu. Study on Water and Ionic Transport Processes in Cover Concrete Under Drying-wetting Cycles[D].Beijing, Tsinghua University,2009.

[40]　ABBAOUI K, CHERRUAULT Y. Convergence of Adomian's method applied to differential equations[J]. Computers Mathematics with Applications, 1994, 28(5): 103-109.

[41]　ADOMIAN G. A review of the decomposition method and some recent results for nonlinear equations[J]. Computers Mathematics with Applications, 1991, 21(5): 101-127.

[42]　ADOMIAN G, RACH R. Analytic Solution of Nonlinear Boundary-Value Problems in Several Dimensions by Decomposition[J]. Journal of Mathematical Analysis and Applications, 1993, 174(1): 118-137.

[43]　ADOMIAN G. Solving Frontier Problems of Physics: The Decomposition Method[M]. Springer Netherlands, 1994.

[44]　CHEN W, LU Z. An algorithm for Adomian decomposition method[J]. Applied Mathematics and Computation, 2004, 159(1): 221-235.

[45]　DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multiobjective genetic algorithm: NSGA-II[J]. Evolutionary Computation, IEEE Transactions on, 2002, 6(2): 182-197.

[46]　AKITA H, FUJIWARA T, OZAKA Y. A practical procedure for the analysis of moisture transfer within concrete due to drying[J]. Magazine of Concrete Research, 1997, 49(179): 129-137.

[47]　WONG S F, WEE T H, SWADDIWUDHIPONG S, et al. Study of water movement in concrete[Z]. 2001: 53, 205-220.

[48]　MARQUARDT D W. An algorithm for least-squares estimation of nonlinear parameters[J]. Journal of the Society for Industrial Applied Mathematics, 1963, 11(2): 431-441.

[49]　LEVENBERG K. A method for the solution of certain non-linear problems in least squares[J]. Quarterly Journal of Applied Mathmatics, 1944, 11(2): 164-168.

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ZHANG Xiao, ZHAO Hongduo, ZHAO Duijia. Approximate Analytical Solution of Water Movement in Concrete Slabs[J].同济大学学报(自然科学版),2015,43(10):1528~1535

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Received:January 13,2015
Revised:July 30,2015
Adopted:June 17,2015
Online: October 26,2015
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