Two-dimensional unconfined seepage flow toward a highway cut slope

Zerihun, Yebegaeshet T. (author)

The unconfined gravity-flow system near a free-outflow boundary such as a highway cut slope was investigated by using a higher-order numerical model. Unlike the Dupuit–Forchheimer equation, which is applicable mainly to a hydraulic flow problem, the proposed model accounts for the effects of the vertical component of the flow for a full treatment of the problem of plane phreatic flow. The model equations were numerically solved by means of a finite-difference scheme. Their accuracy was then verified using the solutions of the full two-dimensional potential-flow method and rigorous mathematical approaches, revealing that for a face slope flatter than 70º, the differences between the solutions of the model and the earlier approaches for the relative seepage-face height were nearly negligible. The comparison results also demonstrated the substantial effects of the slope of the downstream face on this height and the seepage discharge. Furthermore, the accuracies of the model predictions for the phreatic-surface profile and the distributions of the piezometric head at different vertical sections are much better than the earlier method, which approximates the trapezoidal-shaped aquifer by its equivalent rectangular one. Such a satisfactory performance may be attributed to the model’s higher-order correction factor for the effects of the phreaticsurface curvature and steep slope.

• Language: English
• Keywords: unconfined seepage flow, phreatic surface, artificial cut, seepage discharge, non-hydrostatic groundwater flow, seepage-face height
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FGG - Faculty of Civil and Geodetic Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: Str. 95-109
• Numbering: Vol. 36, no. 65
• PID: 20.500.12556/RUL-163182
• UDC: 556.51
• ISSN on article: 0352-3551
• DOI: 10.15292/acta.hydro.2023.06
• COBISS.SI-ID: 209981187
• Publication date in RUL: 03.10.2024

Record is a part of a journal

• Title: Acta hydrotechnica
• Publisher: Fakulteta za gradbeništvo in geodezijo
• ISSN: 0352-3551
• COBISS.SI-ID: 3664386

Licences

• License: CC BY-NC-SA 4.0, Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Description: A Creative Commons license that bans commercial use and requires the user to release any modified works under this license.

Secondary language

• Language: Slovenian
• Title: Dvodimenzionalni tok podzemne vode s prosto gladino proti avtocestnemu vkopu

Abstract

Z numeričnim modelom višjega reda je bil raziskan gravitacijski tok pri prosti gladini v bližini meje prostega odtoka, kot je na primer vkop avtoceste. Za razliko od Dupuit–Forchheimerjeve enačbe, ki se uporablja predvsem za hidravlični tok, predlagani model upošteva vplive vertikalne komponente toka za celovito obravnavo problema ravninskega toka vode pri prosti gladini. Enačbe modela toka so bile numerično rešene s pomočjo diferenčne sheme. Natančnost rešitve je bila preverjena ob upoštevanju dvodimenzionalnega toka in s strogimi matematičnimi pristopi. Za naklone vkopa, ki je položnejši od 70º, so razlike v višini vode na precejnem robu med rešitvami tega modela in prejšnjimi pristopi skoraj zanemarljive. Primerjava rezultatov je prav tako pokazala na znatne vplive naklona vkopa na višino vode na precejnem robu in odtok. Poleg tega je natančnost modelne napovedi za potek gladine podzemne vode in porazdelitev hidravličnih višin na različnih navpičnih odsekih veliko boljša od prejšnje metode, ki vodonosnik trapezne oblike upošteva kot ekvivalentni pravokotni vodonosnik. Zadovoljivo rešitev je možno pripisati modelnemu korekcijskemu faktorju višjega reda za učinke ukrivljenosti gladine podzemne vode in strmega pobočja.

• Keywords: precejanje pri prosti gladini, gladina podzemne vode, vkop, odtok, nehidrostatsko precejanje, višina vode na precejnem robu