Analytical solutions for one-dimensional consolidation in unsaturated soils considering the non-Darcy law of water flow

Abstract

Analytical solutions were derived for the non-linear, one-dimensional consolidation equations for unsaturated soils. The governing equations with a non-homogeneous mixed-boundary condition were presented, in which the water flow was assumed to be governed by a non-Darcy law, whereas the air flow followed the Darcy law. The non-Darcy law was actually the non-linear, flux-gradients relationship. The consolidation equations were thus present in a strong, non-linear way. In order to analytically solve the equation, a homotopy analysis method (HAM) was introduced in the study, which is an analytical technique for nonlinear problems. Firstly, a governing equation in a dimensionless form was derived for a one-dimensional consolidation under unsaturated soils. The method was then used for a mapping technique to transfer the original nonlinear differential equations to a number of linear differential equations. These differential equations were independent with respect to any small parameters, and were convenient for controlling the convergence region. After this transferring, a series solution to the equations was then obtained using the HAM by selecting the linear operator and the auxiliary parameters. Meanwhile, comparisons between the analytical solutions and the results of the finite-difference method indicate that the analytical solution is more efficient. Furthermore, our solutions indicate that the dissipation of air pressure is much faster than that of water pressure, and the values for the threshold gradient I have obvious effects on the dissipation values of the excess pore-water pressure, but no significant effect on that of the excess pore-air pressure.

Keywords

unsaturated soil;homotopy analysis method;analytical solutions;non-Darcy law;initial and boundary conditions;

Data

Language:	English
Year of publishing:	2014
Typology:	1.01 - Original Scientific Article
Organization:	UM FGPA - Faculty of Civil Engineering, Transportation Engineering and Architecture
UDC:	624.13
COBISS:	281003520
ISSN:	1854-0171
Parent publication:	Acta geotechnica Slovenica
Views:	558
Downloads:	71
Average score:	0 (0 votes)
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Other data

Secondary language:	Slovenian
Secondary title:	Analitične rešitve enodimenzionalne konsolidacije nenasičenih zemljin ob upoštevanju ne-Darcyjevega zakona vodnega toka
Secondary abstract:	Analitične rešitve smo izpeljali za nelinearne enodimenzionalne konsolidacijske enačbe nenasičenih zemljin. Predstavili smo vodilne enačbe z nehomogenim mešanim mejnim stanjem, v katerih je privzeto, da vodni tok sledi ne-Darcyjevemu zakonu, medtem ko sledi zračni tok Darcyjevemu zakonu. Ne-Darcyjev zakon je pravzaprav nelinearno razmerje med tokom in višino. Enačbe za konsolidacijo so torej v nelinearnem načinu. Da bi rešili enačbo analitično, smo v tej študiji uvedli metodo homotopijske analize (HAM), ki je analitična tehnika za nelinearne probleme. Najprej je bila izpeljana vodilna enačba v brezdimenzionalni obliki, za enodimenzionalno konsolidacijo nezasičenih zemljin. Metodo smo potem uporabili za tehniko preslikave za prenos nelinearnih diferencialnih enačb v številne linearne diferencialne enačbe. Te diferencialne enačbe niso bile odvisne od manjših parametrov in so bile primerne za nadzor območja konvergence. Po tem prenosu smo dobili niz rešitev enačb s HAM s selekcijo linearnih operatorjev in dodatnih parametrov. Primerjava med analitičnimi rešitvami in rezultati končne diferencialne metode je pokazala, da je analitična rešitev bolj učinkovita. Naše rešitve so pokazale, da je disipacija zračnega pritiska veliko hitrejša od vodnega pritiska in da imajo vrednosti gradienta I očiten učinek na disipacijske vrednosti presežnega pritiska porne vode, nimajo pa pomembnega učinka na presežni pritisk pornega zraka.
Secondary keywords:	geotehnika;mehanika tal;nenasičena zemljina;analitične rešitve;
URN:	URN:SI:UM:
Type (COBISS):	Scientific work
Pages:	str. 50-60
Volume:	ǂVol. ǂ11
Issue:	ǂ[no.] ǂ1
Chronology:	2014
ID:	10941254