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Analytical solution for 1D consolidation under haversine cyclic loading
Author(s) -
Razouki Sabah S.,
Bonnier Paul,
Datcheva Maria,
Schanz Tom
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.2188
Subject(s) - consolidation (business) , dimensionless quantity , pore water pressure , effective stress , partial differential equation , geotechnical engineering , mechanics , finite element method , materials science , structural engineering , mathematics , geology , engineering , physics , mathematical analysis , accounting , business
SUMMARY Presented and discussed in this paper is an exact analytical solution of the nonhomogeneous partial differential equation governing the conventional one‐dimensional consolidation under haversine repeated loading. The derived analytical solution to the 1D consolidation equation is compared with the numerical solution of the same consolidation problem via FEM. The series solution takes into account the frequency of repeated loading through a dimensionless time factor T 0 . The paper reveals that an increase in the frequency of imposed repeated haversine loading (a decrease in period of repeated loading) causes an increase in the number of cycles required to achieve the steady state, whereas the effect of frequency on the maximum excess pore water pressure at the bottom of a clay layer with permeable top and impermeable bottom for the range of frequencies studied is generally insignificant. The effective stress at the bottom of the clay deposit with permeable top and impermeable bottom increases with time but with some fluctuations without changing the sign. These fluctuations become more pronounced for increasing values of T 0 . An increase in T 0 also causes an increase in maximum effective stress. Copyright © 2013 John Wiley & Sons, Ltd.