References
- Aitken, G. W. and Berg, R. L. (1968), Digital solution of modified Berggren equation to calculate depth of freeze or thaw in multilayered systems, Special Report 122, CRREL, pp. 17-18.
- Aldrich, H. P. and Paynter, H. M. (1953), Analytical studies of freezing and thawing in soils, Tech. Report 42. ACFEL., pp. 1-103.
- Aldrich, H. P. and Paynter, H. M. (1966), Depth of frost penetration in non-uniform soil, Special Report 104, CRREL, pp. 1-11.
- Berggren, W. P. (1943), Prediction of temperature-distribution in frozen soils, Transaction of the American Geophysical Union, Vol. 24, Part 3, pp. 71-77. https://doi.org/10.1029/TR024i003p00071
- Braley, W. A. and Zarling, J. P. (1990), MUT1D multilayer user-friendly thermal model in 1 dimension, FHWA-AK-RD-90-02, University of Alaska Fairbanks, Fairbanks, Alaska, USA, pp. 24-27.
- Carslaw, H. S. and Jaeger, J. C. (1959), Conduction of heat in solids, 2th Edition, Oxford University Press, New York, pp. 282-291.
- Comini, G., Del Guidice, S., Lewis, R. W. and Zienkiewicz, O. C. (1974), Finite element solution of non-linear heat conduction problems with special reference of phase change, International Journal of Numerical Methods for Engineering, Vol. 8, Issue 3, pp. 613-624. https://doi.org/10.1002/nme.1620080314
- Donea, J. (1974), On the accuracy of finite element solutions to the transient heat-conduction equation, International Journal of Numerical Methods for Engineering, Vol. 8, Issue 1, pp. 103-110. https://doi.org/10.1002/nme.1620080109
- Hsu, T. R. and Pizey, G. (1981), On the prediction of the fusion rate of ice by finite element analysis, Journal of Heat Transfer, Vol. 103, No. 4, pp. 727-732. https://doi.org/10.1115/1.3244533
- Ingersoll, L. R., Zobel, O. J. and Ingersoll, A. C. (1954), Heat conduction, Rev., Edition, University of Wisconsin Press, Madison, pp. 1-325.
- Kim, Y. S., Kang, J. M., Lee, J. G., Hong, S. S. and Kim, K. J. (2012), Finite element modeling and analysis for artificial ground freezing in egress shafts, KSCE Journal of Civil Engineering, Vol. 16, Issue 6, pp. 925-932 (in Korean). https://doi.org/10.1007/s12205-012-1252-y
- Kreith, F. and Bohn, M. S. (2001), Principles of heat transfer, 6th Edition, Brooks/Cole, California, pp. 133-134.
- Lees, M. (1966), A linear three-level difference scheme for quasilinear parabolic equations, Mathematics of Computation, Vol. 20, No. 96, pp. 516-522. https://doi.org/10.1090/S0025-5718-1966-0207224-5
- Lunardini, V. J. (1980), The neumann solution applied to soil systems, CRREL Report 80-22, Army Cold Regions Research and Engineering Laboratory, New Hampshire, pp. 1-5.
- Matsumaru, T., Kojima, K., Tominaga, M., Maruyama, O. and Ishizuka, M. (2006), Calculation method of frost penetration depth for railway subgrade considering thermal characteristics of multilayer materials, RTRI Resport, Vol. 20, No. 12, pp. 59-61.
- Neumann, F. (1860), Lectures given in the 1980', Riemann-Weber die partiellen differentialgleichungen der mathematischen physik, 5th Edition, 1912, Vol. 2, p. 121.
- Sipola, J. (2011), Tjalintrangning i fyllningsdammars tatkarna i anslutning till betongkonstruktioner, Ph. D. Dissertation, Lulea Tekniska University, Sweden, pp. 128-129.
- Stefan, J. (1889), On the theory of ice formation, particularly ice formation in the artic ocean, S-B Wien Akad, Vol. 98, No. 173, pp. 965-983 (in German).
- Zienkiewicz, O. C. and Taylor, R. L. (2005), The finite element method for solid and structural mechanics, 6th Edition, Elsevier Butterworth-Heinemann, Massachusetts, pp. 37-38.