Numerical Analysis for Unsaturated Water Movement in Soil of Changing Bulk Density

Abstract:

With the rapid development of computers and computing techniques, some increasingly complicated computational problems in engineering and science deserve further review and improvement. This work calculated the solution to the problem of Richards partial differential equation with its corresponding initial and boundary condition for one-dimensional unsaturated water movement in soil with changing bulk density by adopting an explicit backward difference method, an implicit forward difference method and an implicit central difference method. Therefore, a temporal-spatial distribution of water content in the process of filtration, evaporation and redistribution of water moisture within the soil column was obtained. Then the computational results were compared and verified, alternatively, by three methods, with a semi-analytical solution. This indicates the methods presented are of high validity, efficiency and accuracy. These methods were used for the first time for the modelling and prediction of the complicated water movement process in soil of changing bulk density. The computations show that the explicit method features a simpler formulation and more capability for complicated modelling, and the authors strongly recommend this method for application in time-related problems. In addition, this work innovatively developed a combination procedure of an implicit difference method and iterative solution method of a large set of linear algebraic equations. It not only avoids solving a large set of linear algebraic equations but also is able to be applied to complicated modelling of soil moisture profiles. Finally, the numerical methods and the technical skills presented in this work can be generalised for two-dimensional or three-dimensional soil moisture movement and more complicated water movement modeling.

• Periodical: Applied Mechanics and Materials (Volume 137)
• Pages: 221-226
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.137.221
• Online since: October 2011
• Authors: Song Bai Cai, Ming An Shao, Dian Qing Lu, Xiao Li Fu, Da Zhi Li
• Keywords: Changing Bulk Density, Finite Difference Method (FDM), Iterative Solution, Soil Water Movement

References

[1] Cabidoche K M. and S Ruya. Field shrinkage curve of a swelling clay soil: analysis of multiple structural swelling and shrinkage phases in the prisms of a Vertisol, Aust J Soil Res. Vol 39, No. 1(2001), pp.143-160.

DOI: 10.1071/sr99132

[2] Crescimanno, Giuseppina. And Provenzano. Givseppe. Soil shrinkage characteristic curve in clay soil: measurement and prediction, Soil Science Soc Am J. Vol 63, No. 1(1999), pp.25-32.

DOI: 10.2136/sssaj1999.03615995006300010005x

[3] Nelder J A. The fitting of a generalization of the logistic curve, Biometrics. Vol 17, No. 1(1961), pp.89-110.

DOI: 10.2307/2527498

[4] McGarry D and K W J Malafant. The analysis of volume change in unconfined unite of soil, Soil Science Soc Am J. Vol. 51, No. 2(1987), pp.290-297.

DOI: 10.2136/sssaj1987.03615995005100020005x

[5] Giraldez J V, G Sposito and C Delgado. A general soil volume change equation: ⅠThe two-parameter model, Soil Sci Soc Am J. Vol 47(1983), pp.419-422.

DOI: 10.2136/sssaj1983.03615995004700030005x

[6] Kim D J, Feyen J and Vereecken H. Prediction of dynamic hydraulic properties in a ripening soil, Geoderma, Vol 57, No 3(1993), pp.231-246.

DOI: 10.1016/0016-7061(93)90007-8

[7] Sobczuk H A and Ryszard T W. Bulk density dependence parameterization of water potential-moisture characteristics of soil, Polish Journal of Soil Science, Vol 29, No 2(1997), pp.81-86.

[8] Smiles D E. Water balance in swelling materials: some comments, Aust J Soil Res. Vol 35, No. 5(1997), pp.1143-1152.

DOI: 10.1071/s97016

[9] Lu D Q and Shao M A. Study on hydraulic parameters and equations of water movement of soil with changing bulk density, Progress in Natural Science, Vol 18, No 7(2008), pp.795-800(in Chinese).

[10] Fu X L and Shao M A. Effect of changing bulk density during SWCC measurement on SWCC parameters, Journal of Soil and Water Conservation, Vol 21, No 3(2007), pp.178-181(in Chinese).

[11] Lu D Q, Shao M A, Horton R. Effect of changing bulk density during water desorption measurement on soil hydraulic properties, Soil sci., Vol 169, No 5(2004), pp.1-11.

DOI: 10.1097/01.ss.0000128017.00021.74

[12] Guo R D, Wu H, Piao F S. A simplified difference method for infiltration equation in saturated soil, Hydrology, Vol 21, No 3(2001), pp.20-22(in Chinese).

[13] Zhang S F, Li X, Gao P L. Natural difference method for ground water seepage, Chinese Journal of Computational Physics, Vol 24, No 3(2007), pp.307-312(in Chinese).

[14] Zhang Z H, Cai H J, Yang R Y, Zhao Y. The water content distribution of trickle source infiltration, Research of Soil and Water Conservation, Vol 11, No 3(2004), pp.91-94. (in Chinese).

[15] Celia M A, E T Bououtas and R L Zarba. A general mass-conservative numerical solution for the unsaturated flow equation, Water Resource Research, Vol 26, No. 7(1990), pp.1483-1496.

DOI: 10.1029/wr026i007p01483

[16] Shao M A, Wang Q J and Huang M B. Soil Physics. Beijing: High Education Press, 2006, pp.80-125. (in Chinese).