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One‐dimensional consolidation with a threshold gradient: a Stefan problem with rate‐dependent latent heat
Author(s) -
Zhou Yang,
Bu Wankui,
Lu Mengmeng
Publication year - 2013
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.2219
Subject(s) - stefan problem , consolidation (business) , similarity solution , latent heat , matrix similarity , similarity (geometry) , front (military) , mathematics , square root , benchmark (surveying) , boundary (topology) , mechanics , mathematical analysis , computer science , boundary layer , thermodynamics , geometry , geology , physics , artificial intelligence , partial differential equation , meteorology , image (mathematics) , accounting , geodesy , business
SUMMARY During the process of one‐dimensional consolidation with a threshold gradient, the seepage front moves downward gradually, and the problem is indicated as a Stefan problem. The novel feature in this Stefan problem is a latent heat that varies inversely with the rate of the moving boundary. An exact solution for the external load that increases in proportion to the square root of time is constructed using the similarity transformation technique. Computational examples concerning the effect of different parameters on the motion of the seepage front are presented. The exact solution provides a worthwhile benchmark for verifying the accuracy of numerical and approximate methods. Copyright © 2013 John Wiley & Sons, Ltd.