About calculation of some schemes of the filtration from channels and sprinklers

E. N. Bereslavskii ; N. V. Likhacheva

Matematičeskoe modelirovanie, Tome 25 (2013) no. 3, pp. 134-148.

Résumé

We consider several schemes of seepage flows from canals and irrigation canals of irrigation systems through the soil layer, underlain good underlying permeable confined aquifer or water-resistant base. For their study and formulated using the method of P. Y. Kochina-Polubarinova solved multivariable mixed boundary value problems of the theory of analytic functions. On the basis of these models are developed algorithms for calculating the size of the saturated zone in situations when the filter has to evaluate the combined effect of the painting movement of such important factors as seepage back pressure from the underlying confined aquifer or an impermeable base, cross-sectional shape and channel the power supply level of water in it , capillarity of the soil and evaporation from the free surface of groundwater. The results of calculations for all the schemes are compared with the same filtration filter parameters depending on the shape of the channel as a power source (canal or irrigation), and the type of foundation soil layer (strongl permeable confined aquifer or aquitard).

Détail

Keywords: filtering, channel, irrigation, soil capillarity, pressure, evaporation, free surface, the complex flow velocity, method Polubarinova-Kochina, conformal mapping.
Mots-clés : infiltration

Bibliographie

[1] Polubarinova-Kochina P. Ya., Teoriya dvizheniya gruntovykh vod, Gostekhizdat, M., 1952, 656 pp.; 2-е изд., 1977, 664 с.

[2] Aravin V. I., Numerov S. N., Teoriya dvizheniya zhidkostei i gazov v nedeformiruemoi poristoi srede, Gostekhizdat, M., 1953, 616 pp.

[3] Razvitie issledovanii po teorii filtratsii v SSSR (1917–1967), Nauka, M., 1969, 545 pp.

[4] Mikhailov G. K., Nikolaevskii V. N., “Dvizhenie zhidkostei i gazov v poristykh sredakh”, Mekhanika v SSSR za 50 let, v. 2, Nauka, M., 1970, 585–648

[5] Rizenkampf B. K., “Gidravlika gruntovykh vod, 3”, Uch. zapiski Saratovsk. un-ta. Ser. gidravliki, 15:5 (1940), 3–93 | MR

[6] Verigin N. N., “Filtratsiya vody iz orositelya irrigatsionnoi sistemy”, Dokl. AN SSSR, 66:4 (1949), 589–592 | MR

[7] Verigin N. N., “Nekotorye sluchai pod'ema gruntovykh vod pri obschei i mestnoi usilennoi infiltratsii”, Inzh. sb., 2 (1950), 21–34

[8] Numerov S. N., “Ob odnom sposobe resheniya filtratsionnykh zadach”, Izv. AN SSSR, OTN, 1954, no. 4, 133–139 | MR

[9] Numerov S. N., “O filtratsii iz kanalov derivatsionnykh GES i irrigatsionnykh sistem”, Izv. VNIIG, 1947, no. 34, 85–96

[10] Vasilev V. A., “Filtratsiya iz kanalov s maloi glubinoi vody pri uchete kapillyarnosti”, Tr. Sredneaziatsk. un-ta, 83:14 (1958), 43–57

[11] Emikh V. N., “O rezhime gruntovykh vod v oroshaemom pochvennom sloe s nizhelezhaschim silnopronitsaemym napornym gorizontom”, Izv. AN SSSR, MZhG, 1979, no. 2, 168–174

[12] Bereslavskii E. N., Matveev V. V., “Filtratsiya iz kanalov maloi glubiny i orositelei”, Izv. AN SSSR, MZhG, 1989, no. 1, 96–102

[13] Bereslavskii E. N., “O rezhime gruntovykh vod pri filtratsii iz orositelya irrigatsionnoi sistemy”, PMTF, 1989, no. 5, 88–91

[14] Kasimov A. R., Obnosov Yu. V., “Stripfocused phreatic surface flow driven by evaporation: analytical solution by the Riesenkamph function”, Advances in Water Resources, 29 (2006), 1565–1571 | DOI

[15] Baron V. A., “Filtratsiya iz kanala s maloi glubinoi vody pri nalichii khorosho pronitsaemogo sloya na konechnoi glubine isu chetom infiltratsii”, PMTF, 1995, no. 1, 101–105 | MR

[16] Bereslavskii E. N., Panasenko L. A., “Ob opredelenii razmerov zony nasyscheniya prifiltratsii iz kanala s maloi glubinoi vody”, PMTF, 1981, no. 5, 92–94 | MR

[17] Bereslavskii E. N., “K zadache o filtratsii iz orositelya irrigatsionnoi sistemy”, Izv. AN SSSR, MZhG, 1987, no. 2, 105–109

[18] Kasimov A. R., Obnosov Yu. V., Perret J., “Phreatic surface flow frone a near-reservoir saturated tongue”, J. Hydrology, 296 (2004), 271–281 | DOI

[19] Ilinskii N. B., Kasimov A. R., “Obratnaya zadacha filtratsii iz kanala pri nalichii podpora”, Tr. sem. po kraevym zadacham, 20, Izd-vo Kazan. un-ta, Kazan, 1983, 104–115 | MR

[20] Kasimov A. R., “Filtratsionnaya optimizatsiya formy zemlyanogo kanala s uchetom kapillyarnosti”, Vychisl. i prikl. matem., 61, Izd-vo Kievsk. un-ta, Kiev, 1987, 70–74

[21] Bereslavskii E. N., “Modelirovanie filtratsionnykh techenii iz kanalov”, Dokl. RAN, 434:4 (2010), 472–475 | MR

[22] Bereslavskii E. N., Aleksandrova L. A., Zakharenkova N. V., Pesterev E. V., “Modelirovanie filtratsionnykh techenii so svobodnymi granitsami v podzemnoi gidromekhanike”, Sovremennye problemy aerogidrodinamiki, Tez. Dokl. XVI shkoly-seminara pod rukovodstvom akademika RAN G. G. Chernogo, Izd-vo Moskovsk. un-ta, M., 2010, 17–18

[23] Bereslavskii E. N., “Modelirovanie filtratsionnykh techenii iz kanalov”, PMM, 75:4 (2011), 563–571 | MR

[24] Bereslavskii E. N., Aleksandrova L. A., Zakharenkova N. V., Pesterev E. V., “Matematicheskoe modelirovanie filtratsionnykh techenii s neizvestnymi granitsami v podzemnoi gidromekhanike”, X Vserossiiskii S'ezd po fundamentalnym problemam teoreticheskoi i prikladnoi mekhaniki, Vestnik Nizhegorodskogo un-ta im. N. I. Lobachevskogo, no. 4(3), 2011, 644–646 | MR

[25] Bereslavskii E. N., Likhacheva N. V., “O techenii zhidkosti iz orositelei”, Matematicheskoe modelirovanie, 24:2 (2012), 99–108 | MR

[26] Bereslavskii E. N., “O differentsialnykh uravneniyakh klassa Fuksa, svyazannykh s konformnym otobrazheniem krugovykh mnogougolnikov v polyarnykh setkakh”, Differents. uravneniya, 33:3 (1997), 296–301 | MR

[27] Bereslavskii E. N., “Ob integrirovanii v zamknutoi forme nekotorykh differentsialnykh uravnenii klassa Fuksa, vstrechayuschikhsya v gidro- i aeromekhanike”, Dokl. RAN, 428:4 (2009), 439–443 | MR | Zbl

[28] Bereslavskii E. N., “Ob integrirovanii v zamknutoi forme nekotorykh differentsialnykh uravnenii klassa Fuksa, svyazannykh s konformnym otobrazheniem krugovykh pyatiugolnikov s razrezom”, Differents. uravneniya, 46:4 (2010), 459–466 | MR | Zbl

[29] Bereslavskii E. N., “Ob uchete infiltratsii ili ispareniya so svobodnoi poverkhnosti metodom krugovykh mnogougolnikov”, PMM, 74:2 (2010), 239–251 | MR

[30] Bereslavskii E. N., Zakharenkova N. V., “Techeniya v kanalakh pri nalichii ispareniya so svobodnoi poverkhnosti gruntovykh vod i kapillyarnosti grunta”, Matematicheskoe modelirovanie, 22:7 (2010), 22–32