20.500.12556/DKUM-70816 Analytical solutions for one-dimensional consolidation in unsaturated soils considering the non-Darcy law of water flow Analitične rešitve enodimenzionalne konsolidacije nenasičenih zemljin ob upoštevanju ne-Darcyjevega zakona vodnega toka 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. 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. unsaturated soil homotopy analysis method analytical solutions non-Darcy law initial and boundary conditions geotehnika mehanika tal nenasičena zemljina analitične rešitve nenasičena zemljina metoda homotipijske analize ne-Darcyjev zakon začetni pogoji mejni pogoji true false true Angleški jezik Slovenski jezik Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo Univerze v Mariboru Znanstveno delo 2018-06-14 11:33:21 2018-06-14 11:34:26 2022-08-01 19:51:38 2019-07-11 18:20:47 2014 0 0 str. 51-60 št. 1 Letn. 11 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 1854-0171 624.13 215987712 281003520 1854-0171 URN:SI:UM:DK:4XCPUR8M Acta_geotechnica_Slovenica_2014_Li,_Wang_Analytical_solutions_for_one-dimensional_consolidation_in_unsaturated_soils_considering_the_non.pdf Acta_geotechnica_Slovenica_2014_Li,_Wang_Analytical_solutions_for_one-dimensional_consolidation_in_unsaturated_soils_considering_the_non.pdf 1 9A52D0E66B4BDF680543F8A156198171 66f1ec75bbb2ed1af3ea1bd93efcf0b7c7312ade406c8e2b8672579199492e22 08840cf3-7c10-11eb-bb7a-00155d0001ca 20.500.12556/dkum/99ea5c02-852c-4a24-baad-2b6885778123 https://dk.um.si/Dokument.php?lang=slv&id=125672 http://fgserver3.fg.um.si/journal-ags/2014-1/article-5.asp 1 https://dk.um.si/Dokument.php?lang=slv&id=125673 Fakulteta za gradbeništvo, prometno inženirstvo in arhitekturo Acta geotechnica Slovenica 0 0 0