FINDINGS OF RESEARCH INTO PHYSICAL-MECHANICAL PROPERTIES OF MIXTURESOF SEWAGE SLUDGE, SOIL AND PHOSPHOGYPSUM TO BE USED AS LAND RECLAMATION AGENTS

Vestnik MGSU 6/2013
  • Smetanin Vladimir Ivanovich - Moscow State University of Environmental Engineering (MGUP) Doctor of Technical Science, Pro- fessor, Chair, Department of Organization and Building Technology of Environmental Engi- neering Objects, Moscow State University of Environmental Engineering (MGUP), 19 Pryanishnikova st., Moscow, 127550, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zemskov Vladimir Nikolaevich - Moscow State University of Environmental Engineering (MGUP) , Moscow State University of Environmental Engineering (MGUP), 19 Pryanishnikova st., Moscow, 127550, Russian Federation.

Pages 204-113

The authors argue that intensive construction and development operations generate a large number of idle quarries. Now Moscow Metropolitan area has about 2,000 abandoned quarries and in excess of 150 quarries in operation. Most of them were used to develop various minerals, namely, sand, crushed stone, gravel, peat and other materials.Recovery of abandoned quarries and assurance of their safe condition requires a set of actions to be taken. However, mere reclamation cannot resolve all environmental problems arising after the completion of mining operations. Obviously, the use of undisturbed land areas as household waste landfills is not the best idea from the viewpoint of the environment. Therefore, filling idle quarries with specific types of products is an improved method of reclamation of mines and quarries. This method may solve two problems at once: they are land reclamation and safe waste disposal. Sewage sludge generated by households, as well as industrial enterprises, may serve as the solution.In this paper, the authors study the dependence between the permeability ratio, the carrying capacity of different soil mixtures containing sewage sludge to be used as the reclamation agent in the course of restoration of disturbed territories. The authors also consider dependence of concentration of biogases and the phosphogypsum content in biogases.

DOI: 10.22227/1997-0935.2013.6.204-113

References
  1. Smetanin V.I. Rekul’tivatsiya i obustroystvo narushennykh zemel’ [Reclamation and Development of Disturbed Lands]. Moscow, Kolos Publ., 2003, 96 p.
  2. Fosfogips: khranenie i napravlenie ispol’zovaniya kak krupnotonnazhnogo vtorichnogo syr’ya [Phosphogypsum: Storage and Use as Large-tonnage Recycled Material]. Materialy vtoroy Mezhdunarodnoy nauchno-prekticheskoy konferentsii [Materials of the 2nd International Scientific and Practical Conference]. Moscow, OOO «Futuris» Publ., 2010, 192 p.
  3. Mironov V.E., Martynyuk A.A., Kuraev V.N., Kozhenkov L.L. Lesobiologicheskaya rekul’tivatsiya poligonov skladirovaniya fosfogipsa [Forestry Biological Reclamation of Phosphogypsum Landfills]. Moscow, VNIILM Publ., 2006, 120 p.
  4. Metodika rascheta kolichestvennykh kharakteristik vybrosov zagryaznyayushchikh veshchestv v atmosferu ot poligonov tverdykh bytovykh i promyshlennykh otkhodov [Methodology for Analysis of Quantitative Characteristics of Pollutants Emitted into the Atmosphere by Household and Industrial Waste Landfills]. NPP Ekoprom Publ.
  5. Tekhnologicheskiy reglament polucheniya biogaza s poligonov tverdykh bytovykh otkhodov [Process Regulations for Extraction of Biogas at Household Waste Landfills]. Akademiya kommunal’nogo khozyaystva im. K.D. Pamfilova [K.D. Pamfilov Academy of Utility Services]. Moscow, 1989.
  6. Dobycha i utilizatsiya svalochnogo gaza (SG) — samostoyatel’naya otrasl’ mirovoy industrii. [Extraction and Use of Landfill Gas as the Independent Branch of the World Industry]. Ekologicheskie sistemy [Ecological Systems] Company website 2010, no. 5. Available at: http://esco.co.ua. Date of access: 07.06.2013.
  7. Peterson A.E., Speth P.E., Corey R.B., Wright T., Schlecht P.L. Effects of 12 Years of Liquid Digested Sludge Application on the Soil Phosphorus Level. Amer. Soc. Agron. Annu. Meet. 1992, Minneapolis, p. 53.
  8. Water S. A Review of the Agricultural Use of Sewage Sludge: Benefits and Potential Hazards. Korentajer. Agr., 1991, vol. 17, no. 3, pp. 189—196.

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ASYMPTOTICS OF a PARTICLES TRANSPORT PROBLEM

Vestnik MGSU 11/2017 Volume 12
  • Kuzmina Ludmila Ivanovna - National Research University Higher School of Economics Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Applied Mathematics, National Research University Higher School of Economics, 20 Myasnitskaya st., Moscow, 101000, Russian Federation.
  • Osipov Yuri Viktorovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Applied Mathematics, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation.

Pages 1278-1283

Subject: a groundwater filtration affects the strength and stability of underground and hydro-technical constructions. Research objectives: the study of one-dimensional problem of displacement of suspension by the flow of pure water in a porous medium. Materials and methods: when filtering a suspension some particles pass through the porous medium, and some of them are stuck in the pores. It is assumed that size distributions of the solid particles and the pores overlap. In this case, the main mechanism of particle retention is a size-exclusion: the particles pass freely through the large pores and get stuck at the inlet of the tiny pores that are smaller than the particle diameter. The concentrations of suspended and retained particles satisfy two quasi-linear differential equations of the first order. To solve the filtration problem, methods of nonlinear asymptotic analysis are used. Results: in a mathematical model of filtration of suspensions, which takes into account the dependence of the porosity and permeability of the porous medium on concentration of retained particles, the boundary between two phases is moving with variable velocity. The asymptotic solution to the problem is constructed for a small filtration coefficient. The theorem of existence of the asymptotics is proved. Analytical expressions for the principal asymptotic terms are presented for the case of linear coefficients and initial conditions. The asymptotics of the boundary of two phases is given in explicit form. Conclusions: the filtration problem under study can be solved analytically.

DOI: 10.22227/1997-0935.2017.11.1278-1283

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DEPENDENCE OF SUFFOSION STABILITY OF SANDY SOILS OF VARIOUS GENESES ON THE TYPE OF FILTRATE

Vestnik MGSU 5/2012
  • Potapov Ivan Aleksandrovich - Scientific and Research Institute of Emergency Healthcare named after N.V. Sklifosovskiy engineer, Scientific and Research Institute of Emergency Healthcare named after N.V. Sklifosovskiy, ; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Shimenkova Anastasiya Anatol'evna - Moscow State University of Civil Engineering (MGSU) engineer, Department of Engineering Geology and Geoecology, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Potapov Aleksandr Dmitrievich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Head, Department of Engineering Geology and Geoecology, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 79 - 86

Results of calculations and experimental researches of suffosion stability of sandy soils are provided in the article. The authors have assessed the prospects for the application of standard methodologies to demonstrate the need to take account of the filtrate properties in the course of projecting potential suffusion process development patterns typical for sandy soils. The principal attention must be driven to the value of the kinematic viscosity of filtered liquids. Any assessment of filtration-related interaction of the flow of liquid with sandy soils must be backed by the gradation analysis of soils and the analysis of their homogeneity, as well as the mineralogical and morphological analysis. The morphological study of sands of various geneses, performed hereunder, is based on the methodology that takes account of both the shape of sand particles and the structure of their surface.
The proposed methodology makes it possible to assess extensive sand specimen rather than separate sand particles to assure the representative sampling to assure the accuracy of the morphological analysis. The authors provide the data that cover the research of sands of various geneses demonstrating varied granulometric and mineral composition, as well as various morphological peculiarities of correlation with the filtrates that have different values of kinematic viscosity. The methodological research completed by the authors has indicated an urgent need to perform laboratory and field researches of suffosion instability of sandy soils in varied geoecological environments typical for urban lands exposed to anthropogenic pollutions.

DOI: 10.22227/1997-0935.2012.5.79 - 86

References
  1. Rekomendatsii po metodike laboratornykh ispytaniy gruntov na vodopronitsaemost’ i suffozionnuyu ustoychivost’. P 12-83 [Recommendations concerning the Methodology of Laboratory Testing of Waterpermeability and Suffosion Stability of Soils. P 12-83]. Leningrad, VNIIG [Institute Hydroproject], 1983.
  2. Spiridonov V.N. Gidravlicheskie kharakteristiki otkrytogo potoka v pronitsaemom rusle [Hydraulic Characteristics of an Open Stream in a Nontight Channel]. Moscow, Moscow Institute of Civil Engineering, 1985.
  3. Vil’ner Ya.M. Spravochnoe posobie po gidravlike, gidromashinam i gidroprivodam [Handbook of Hydraulics, Hydraulic Machines and Hydraulic Drivers]. Moscow, Mashizdat Publ., 1989.
  4. GOST 25100—95. Grunty. Klassifikatsiya. [All-Russian State Standard 25100—95. Soils. Classification]. Moscow, Gosstroy Publ., 1996.
  5. Potapov A.D. Morfologicheskoe izuchenie peskov razlichnogo genezisa v inzhenernogeologicheskikh tselyakh [Morphological Research of Sands of Various Geneses for Engineering Geology Purposes]. Moscow, PNIIIS [Production, Scientific and Research Institute of Engineering Surveying in Construction], 1982.

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SANDY SOILS: GEO-ECOLOGICAL EVALUATION OF THEIR STRENGTH DEVELOPMENT PROCESS (IN THE CONTEXT OF THE PHYSICAL CHEMICAL THEORY OF EFFECTIVE STRESSES)

Vestnik MGSU 2/2013
  • Potapov Ivan Aleksandrovich - Scientific and Research Institute of Emergency Healthcare named after N.V. Sklifosovskiy engineer, Scientific and Research Institute of Emergency Healthcare named after N.V. Sklifosovskiy, ; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Potapov Aleksandr Dmitrievich - Moscow State University of Civil Engineering (MGSU) Doctor of Technical Sciences, Professor, Head, Department of Engineering Geology and Geoecology, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Shimenkova Anastasiya Anatol’evna - Moscow State University of Civil Engineering (MGSU) engineer, Department of Engineering Geology and Geoecology, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 166-180

The authors consider the strength development of sandy soils in the contest of the physical chemical theory of effective stresses. The authors drive particular attention to the assessment of formation of various types of energy contacts in sandy soils. The article is based on the overview of theories developed by several researchers, on the one hand, and on the findings of the experimental research of sandy soils that have different structural patterns, on the other hand. The experiments include both those that were held a while ago and the most recent projects. The authors have proven that the strength of sandy soils is, to a significant extent, driven by their morphological peculiarities that determine their condition in the context of the assessment of their “densitymoisture”. Strength values of sands are dependent on their moisture content both in terms of their maximal shear stress values obtained in the course of shear testing, or their per-unit penetration resistance, penetration values, as well as the inner friction angle and cohesion. The “strength-moisture” is presented as a curvilinear graph that has two upper limits, one for shear tests and the other one for penetration tests. Maximal strength, according to the shear test, is attained for dry sands, if their moisture content is close to the “optimal” value. As for the penetration tests, maximal per-unit resistance to penetration and penetration values are also close to the “optimal” moisture content value. The authors have identified that moisture content is an important factor of strength of sandy soils that demonstrate various structural characteristics.However, the process of formation of structural peculiarities of sands, namely, their morphological parameters and the nature of the surface of sand particles is influenced by the presence of various films on the surface of sand particles. The article represents a preliminary analysis of the theoretical and experimental findings, therefore, any discussions are welcome.

DOI: 10.22227/1997-0935.2013.2.166-180

References
  1. Potapov A.D. Nauchno-metodologicheskie osnovy geoekologicheskoy bezopasnosti stroitel’stva [Scientific and Methodological Fundamentals of Geo-ecological Safety of Construction Works]. Moscow, MGSU Publ., 2002, 312 p.
  2. Anan’ev V.P., Potapov A.D. Inzhenernaya geologiya [Engineering Geology]. Moscow, Vyssh. shk. publ., 2008, 346 p.
  3. Potapov A.D. Ekologiya [Ecology]. Moscow, Vyssh. shk. publ., 2005, 328 p.
  4. Platov N.A., Potapov A.D., Lebedeva M.D.. Peschanye grunty [Sandy Soils]. Moscow, ASV Publ., 2008, 186 p.
  5. Potapov A.D., Potapov I.A., Shimenkova A.A. Nekotorye aspekty primenimosti k peschanym gruntam polozheniy fiziko-khimicheskoy teorii effektivnykh napryazheniy [Particular Aspects of Applicability of Provisions of the Physical and Chemical Theory of Effective Stresses to Sandy Soils]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 10, pp. 229—239.
  6. Potapov I.A., Potapov A.D., Shimenkova A.A. Formirovanie raznykh tipov energeticheskikh kontaktov v peschanykh gruntakh v aspekte fiziko-khimicheskoy teorii effektivnykh napryazheniy [Formation of Different Types of Energy Contacts in Sandy Soils in the Framework of the Physicochemical Theory of Effective Stresses]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 11, pp. 210—218.
  7. Potapov I.A., Shimenkova A.A., Potapov A.D. Zavisimost’ suffozionnoy ustoychivosti peschanykh gruntov razlichnogo genezisa ot tipa fil’trata [Dependence of Suffosion Stability of Sandy Soils of Various Geneses on the Type of Filtrate]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 5, pp. 79—86.
  8. Potapov A.D., Potapov I.A., Shimenkova A.A. Rol’ plotnosti — vlazhnosti v peschanykh gruntakh v formirovanii effektivnykh napryazheniyakh s pozitsiy fiziko-khimicheskoy teorii [The Role of the “Density – Moisture” of Sandy Soils in Formation of Efficient Stresses from the Perspective of the Physicochemical Theory]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 12, pp. 104—110.
  9. Senyushchenkova I.M. Teoriya formirovaniya i metody razvitiya urbolandshaftov na ovrazhno-balochnom rel’efe [Theory of Formation and Methods of Development of Urban Landscapes in the Gully Relief]. Moscow, MGSU Publ., 2011, 376 p.
  10. Osipov V.I. Fiziko-khimicheskaya teoriya effektivnykh napryazheniy v gruntakh [Physicochemical Theory of Effective Stresses in Soils]. IGE RAN [Institute of Geo-ecology of the Russian Academy of Sciences]. Moscow, IFZ RAN [Institute of Physics of the Earth (IPE)], 2012, 74 p.
  11. Osipov V.I. Strukturnye svyazi kak osnova otsenki fiziko-mekhanicheskikh svoystv glinistykh porod [Structural Links as the Basis for Assessment of Physical Mechanical Properties of the Glay Rock]. Sovershenstvovanie metodov laboratornykh issledovaniy gruntov pri inzhenernykh izyskaniyakh dlya stroitel’stva : Tezisy dokladov 2 Respublikanskogo soveshchaniya. [Improvement of Methods of Laboratory Testing of Soils as Part of Engineering Surveys for Civil Engineering Purposes. Abstracts of Reports of the 2nd Republican Meeting]. Moscow, Stroyizyskaniya Publ., 1977, pp. 29—40.
  12. Trofimov V.T. Gruntovedenie [Pedology]. Moscow, MGU Publ., Nauka Publ., 2005, 1024 p.
  13. Gol’dshteyn M.N. Mekhanicheskie svoystva gruntov. Osnovnye komponenty grunta I ikh vzaimodeystvie. [Mechanical Properties of Soils. Principal Components of Soil and Their Interaction]. Moscow, Stroyizdat Publ., 1973, 375 p.
  14. Tsytovich N.A. Mekhanika gruntov [Soil Mechanics]. Moscow, Gosstroyizdat Publ., 1963.
  15. Sergeev E.M. Granulometricheskaya klassifikatsiya peskov [Granulometric Classification of Sands]. Vestn. MGU. Ser. biol. i pochv. [Proceedings of Moscow State University. Biology and Soil Series]. 1953, no. 12, pp. 49—56.
  16. Potapov A.D. Morfologicheskoe izuchenie peskov razlichnogo genezisa v inzhenerno-geologicheskikh tselyakh [Morphological Research of Sands of Various Geneses for Engineering Geology Purposes]. Moscow, PNIIIS [Production, Scientific and Research Institute of Engineering Surveying in Construction], 1982.
  17. Rebinder P.A. Strukturno-mekhanicheskie svoystva glinistykh porod i sovremennye predstavleniya fiziko-khimii kolloidov [Structural and Mechanical Properties of Clay Soils and the Present-day Ideas of Physics and Chemistry of Colloids]. Trudy Soveshchaniya po inzhenerno-geologicheskim svoystvam gornykh porod i metodam ikh izucheniya [Collected Works of Geo-engineering Properties of Rocks and Methods of Their Study]. Moscow, AN SSSR Publ., 1956, vol. 1, pp. 31—44.
  18. Mikhaylov N.V., Rebinder P.A. O strukturno-mekhanicheskikh svoystvakh dispersnykh i vysokomolekulyarnykh sistem [Structural Mechanical Properties of Disperse and High Molecular Systems]. Kolloidnyy zhurnal [Colloid Journal]. 1955, vol. 17, no. 2, pp. 112—119.
  19. Ter-Stepanyan G.I. O vliyanii formy i raspolozheniya chastits na protsess sdviga v gruntakh [Influence of Shape and Position of Partickes onto the Process of Shear of Soils]. Izv. AN ArmSSR [News of the Academy of Sciences of Armenian Soviet Socialist Republic]. 1948, vol. 1, no. 2, pp. 167—185.
  20. Gor’kova I.M. Strukturnye i deformatsionnye osobennosti osadochnykh porod razlichnoy stepeni uplotneniya i litifikatsii [Structural and Deformation-related Peculiarities of Sedimentary Rocks That Have Different Compaction and Lithification Values]. Moscow, Nauka Publ., 1966, 128 p.
  21. Durante V.A. Opyt issledovaniya plotnosti peskov metodom glubinnogo zondirovaniya [Practical Research into the Density of Soils Using Method of Deep Sounding]. Trudy Soveshchaniya po inzhenerno-geologicheskim svoystvam gornykh porod i metodam ikh izucheniya [Works of the Meeting Dedicated to the Geo-engineering Properties of Rocks and Methods of Their Study]. Moscow, AN SSSR Publ., 1956, vol. 1, pp. 249—258.
  22. Lysenko M.P. Sostav i fiziko-mekhanicheskie svoystva gruntov [Composition and Physical Mechanical Properties of Soils]. Moscow, Nedra Publ., 1972.
  23. Dudler I.V. Znachenie ponyatiya «plotnost’ — vlazhnost’» dlya izucheniya i otsenki fiziko-mekhanicheskikh svoystv peschanykh gruntov [Meaning of the “Density-Moisture Content” Notion for the Study and Assessment of Physical Mechanical Properties of Sandy Soils]. Voprosy inzhenernoy geologii [Issues of Engineering Geology]. Moscow, MISI Publ., 1977, 7 p.
  24. Platov N.A., Gor’kova I.M. Strukturno-mekhanicheskie osobennosti melkozernistykh i pylevatykh peskov [Structural and Mechanical Peculiarities of Small-grained and Dusty Sands]. Dokl. AN SSSR. Ser.geol. [Reports of the Academy of Sciences of the Union of Soviet Socialist Republics. Geology Series]. 1972, vol. 206, no. 5, pp. 1204—1206.
  25. Rebinder P.A., Segalova E.E. Novye problemy kolloidnoy khimii mineral’nykh vyazhushchikh materialov [ New Problems of Colloid Chemistry of Mineral Viscous Materials]. Priroda Publ., 1952, no. 12, pp. 22—28.
  26. Gor’kova I.M. Teoreticheskie osnovy otsenki osadochnykh porod v inzhenerno-geologicheskikh tselyakh [Theoretical Fundamentals of Assessment of Sedimentary Rocks for Geo-engineering .Purposes]. Moscow, Nauka Publ., 1966, 136 p.
  27. Gor’kova I.M. Fiziko-khimicheskie issledovaniya dispersnykh osadochnykh porod v stroitel’nykh tselyakh [Physical Chemical Research into Disperse Sedimentary Soils for Construction Purposes]. Moscow, Stroyizdat Publ., 1975, 151 p.
  28. Platov N.A., Gor’kova I.M. O prirode prochnosti melko- i srednezernistykh peschanykh porod razlichnogo geneticheskogo tipa [Character of Strength of Small and Mid-size Sandy Rocks of Different Genetic Origin]. Kolloidnyy zhurnal [Colloid Journal]. 1973, vol. 35, no. 1, pp. 57—62.
  29. Platov N.A., Gor’kova I.M. Tipy deformatsionnogo i reologicheskogo povedeniya peschanykh porod [Type of Deformation-related and Rheological Behavirour of Sandy Rocks]. Dokl. AN SSSR. Ser.geol. [Reports of the Academy of Sciences of the Union of Soviet Socialist Republics. Geology Series]. 1975, vol. 222, no. 2, pp. 456—458.
  30. Tsekhomskiy A.M. O stroenii i sostave plenki na zernakh kvartsevykh peskov [Structure and Composition of the Film Covering Grains of Quartz Sands]. Kora vyvetrivaniya [Residual Soil]. Moscow, 1959, AN SSSR Publ., no. 3, pp. 293—312.
  31. Lemmleyn G.G., Knyazev V.S. Opyt izucheniya oblomochnogo kvartsa [Research into Fragmental Quartz]. AN SSSR Publ., 1951, no. 4, pp. 99—101.
  32. Ziangirov R.S. Ob”emnaya deformiruemost’ glinistykh gruntov [3D Deformability of Clay Soils]. Moscow, Nauka Pbl., 1979, p. 164.
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  35. Baron L.I. Kharakteristika treniya gornykh porod [Characteristic of Rock Friction]. Moscow, Nauka Publ., 1967.
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  37. Kabai J. The Compatibility of Sands and Sandy Gravels. Techn. University Budapest, 1968, vol. 63.

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Studying the filtration mode of large dams’ foundations on mathematical models

Vestnik MGSU 10/2014
  • Aniskin Nikolay Alekseevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Engineering, Professor, Director of Institute of Hydrotechnical and Energy Construction, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Antonov Anton Sergeevich - Moscow State University of Civil Engineering (MGSU) postgraduate Student, Department of Hydraulic Engineering Structures, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Mgalobelov Yuriy Borisovich - JSC “Institute Hydroproject” Doctor of Technical Sciences, Academician, Academy of Water Sciences, Professor, Head, Department of Calculating Substantiation, JSC “Institute Hydroproject”, 2 Volokolamskoe shosse, Moscow, 125993, Russian Federation; +7 (495) 940-54-57; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Deyneko Andrey Viktorovich - JSC “Institute Hydroproject” Candidate of Technical Sciences, Assosiate Professor, Deputy Head, Department of Calculating Substantiation, JSC “Institute Hydroproject”, 2 Volokolamskoe shosse, Moscow, 125993, Russian Federation; +7 (495) 926-38-22; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 114-131

The essential issue of engineering safety of high dams is substantiation of the seepage conditions of the dam - foundation system. In most cases, a violation of the filtration mode leads to disruption of the hydraulic structure. The authors analyzed the methods of mathematical simulation of a filtration mode for large dams’ foundations basing on finite element method. Up-to-date computational capability permits solving seepage problems in 3D transient formulation. The possible reasons for filtration mode disturbance in foundations of large dams are observed, as well as the corresponding methods of analytical forecasting for the parameters of inappropriate development of filtration processes. Application of the universal industrial-strength software complexes makes it possible to combine on a single software platform the seepage modeling with other methods of design-basis validation of hydraulic structures, such as computations of stress-strain state, strength and stability of the dam - foundation system. The analysis results should be further used in the calculation of the stress strain state of the structures.

DOI: 10.22227/1997-0935.2014.10.114-131

References
  1. Losleben T.R. Pilot Study of Horizontal Roughing Filtration in Northern Ghana as Pretreatment for Highly Turbid Dugout Water. Master of Engineering thesis. USA Massachussets Institute of Technology, 2008, 149 p.
  2. Rasskazov L.N., Aniskin N.A., Sainov M.P. Analiz sostoyaniya gruntovoy plotiny Kolymskoy GES [State Analysis of Soil Kolyma Hydroelectric Power Station Dam]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2009, special issue no. 2, pp. 111—118.
  3. Loginov V.A., Shabanov V.A. Issledovanie fil'tratsionnykh techeniy v verkhovom kline gruntovoy plotiny [The Study of Filtration Flows in the Upper Wedge of Soil Dam]. Gidrotekhnicheskoe stroitel'stvo [Hydraulic Engineering]. 2011, no. 7, pp. 52—55.
  4. Anakhaev K.N., Shogenova Zh.Kh., Amshokov B.Kh. Raschet fil'tratsii cherez zemlyanye plotiny na pronitsaemom osnovanii raznoy moshchnosti [Calculation of the Filtration through the Earthen Dam on Permeable Foundation of Different Capacity]. Gidrotekhnicheskoe stroitel'stvo [Hydraulic Engineering]. 2011, no. 2. pp. 29—33.
  5. Bukhartsev V.N., Petrichenko M.R. Reshenie zadachi o fil'tratsii v odnorodnom pryamougol'nom gruntovom massive na osnove variatsionnykh printsipov [The Solution of the Problem of Filtering in a Homogeneous Rectangular Earthen Array Basing on Variation Principles]. Gidrotekhnicheskoe stroitel'stvo [Hydraulic Engineering]. 2012, no. 3. pp. 32—37.
  6. Bereslavskiy E.N., Aleksandrova L.A., Pesterev E.V. Matematicheskoe modelirovanie fil'tratsionnykh techeniy pod gidrotekhnicheskimi sooruzheniyami [Mathematical Modeling of Filtration Flows under Hydraulic Structures]. Nauchnye vedomosti Belgorodskogo gosudarstvennogo universiteta. Seriya: Matematika. Fizika [Proceedings of Belgorod State University Series: Mathematics. Phisics]. 2009, no. 16, vol. 5, pp. 32—46.
  7. Polubarinova-Kochina P.Ya. Razvitie issledovaniy po teorii fil'tratsii v SSSR (1917—1967) [The Development of Investigations on Filtration Theory in the USSR (1917—1967)]. Moscow, Nauka Publ.,1969, 545 p.
  8. Belkova I.N., Glagovsy V.B., Pavlovskaya L.N., Radchenko V.G. Otsenka fil'tratsionnoy prochnosti gruntovoy plotiny na primere Irganayskoy GES [Estimation of Seepage Strength of Earth Dam by the Example of Irganaiskaya HPP]. Izvestiya VNIIG imeni B.E. Vedeneeva [News of the All-Union Scientific and Research Institute of Hydraulic Engineering named after B.E. Vedeneev]. 2011, vol. 264, pp. 3—12.
  9. Mishin D.V. Programmnaya arkhitektura i interaktivnaya sreda konechno-elementnogo raschetnogo kompleksa DISK-Geomekhanika [Program Arcgitecture and Interactive Environment of DISK-Geomechanics Finite Element Computation Set]. Izvestiya VNIIG imeni B.E. Vedeneeva [News of the All-Union Scientific and Research Institute of Hydraulic Engineering named after B.E. Vedeneev]. 2002, vol. 241, pp. 193—196.
  10. Belov A.N., Gorokhov E.N. Trekhmernoe matematicheskoe modelirovanie temperaturnogo rezhima gruntovykh plotin v kriolitozone [3D Thermal Modeling of Soil Dams in Cryolithic Zone]. Privolzhskiy nauchnyy zhurnal [Privolzhsky Scientific Review]. 2010, no. 1, pp. 65—71.
  11. Panov C.I., Buryakov O.A., Pryamitskiy A.V., Bichkov E.A. Vliyanie granichnykh i nachal'nykh usloviy na rezul'taty raschetov temperaturnogo sostoyaniya gruntovykh plotin na severe [Influence of Boundary and Initial Conditions on the Calculation Results of Thermal State of Earth Dams in the North]. Izvestiya VNIIG imeni B.E. Vedeneeva [News of the All-Union Scientific and Research Institute of Hydraulic Engineering named after B.E. Vedeneev]. 2012, vol. 266, pp. 44—54.
  12. Aniskin N.A. Temperaturno-fil’tratsionnyy rezhim osnovaniya i plotiny Kureyskoy GES vo vtorom pravoberezhnom ponizhenii [Thermal and Filtration Behaviour of Dam Base and Structure of Kureyskaya Hydro-electric Power Plant at the Second Reduced Level of the Right Bank]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2006, no. 2, pp. 43—52.
  13. Gorokhov E.N. Temperaturnyy rezhim gruntov levoberezhnogo primykaniya Vilyuyskoy GES-3 [Thermal Mode of Soils of the Left-bank Abutment of Vilyuyskaya-3 Hydroelectric Power Plant]. Gidrotekhnicheskoe stroitel’stvo [Hydraulic Engineering]. 2003, no. 2, pp. 12—15.
  14. Gorokhov E.N. Teoriya i metod rascheta temperaturno-kriogennogo rezhima plotin iz kamennoy nabroski v kriolitozone [Theory and Method of Analysis of Thermal and Cryogenic Mode of Rock-mound Dams in the Permafrost Zone]. Izvestiya vuzov. Stroitel’stvo [News of Institutions of Higher Education. Construction]. 2005, no. 9, pp. 32—39.
  15. Markhilevich O.K. Primenenie metodov modelirovaniya geofil'tratsii pri proektirovanii gidrotekhnicheskikh sooruzheniy [Application of modeling techniques of geofiltration when designing hydraulic structures]. Gidrotekhnicheskoe stroitel'stvo [Hydro Review]. 2009, no. 4, pp. 61—72.
  16. Suntsov N.N. Metody analogiy v aerogidrodinamike [Analog Method in Aerohydrodynamics]. Moscow, Fizmatlit Publ., 1958, 324 p.
  17. Aniskin N.A. Temperaturno-fil’tratsionnyy rezhim prigrebnevoy zony gruntovoy plotiny v surovykh klimaticheskikh usloviyakh [Thermal and Filtration Behaviour of the Earth Dam Crest Area in Severe Climatic Conditions]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 4, pp. 129—137.
  18. Sheng-Hong C. Adaptive FEM Analysis for Two-dimensional Unconfined Seepage Problems. Journal of Hydrodynamics. 1996, Ser. B, vol. 8, no. 1, pp. 60—66.
  19. Basov K.A. ANSYS: spravochnik pol'zovatelya [ANSYS. The User's Guide]. Moscow, DMK Press Publ., 2011, 640 p.
  20. Zhao Xiao-xi, Zhang Bao-lei, Wang Zong-ming. Stability Analysis of Seepage Flow through Earth Dam of Huangbizhuang. Reservoir Based on ANSYS/APDL Rock and Soil Mechanics. 2005. Available at: http://en.cnki.com.cn/Article_en/CJFDTotal-YTLX2005S2053.htm. Date of access: 24.08.2014.
  21. Kaplun A.B., Morozov E.M., Olfer'eva M.A. ANSYS v rukakh inzhenera. Prakticheskoe rukovodstvo [ANSYS in the Hands of an Engineer. Practical Guide.]. Moscow, Librokom Publ., 2014, 272 p.
  22. Locke M., Indraratna B., Adikari G. Time-Dependent Particle Transport through Granular Filters. Journal of Geotechnical and Geoenvironmental Engineering. 2001, vol. 127, no. 6, pp. 521—528.
  23. Mgalobelov Yu.B., Deyneko A.V. Raschetnoe obosnovanie bezopasnosti sovremennykh gidrotekhnicheskikh sooruzheniy i osobennosti ucheta vozdeystviy ot tekhnologicheskogo oborudovaniya pri zemletryasenii [Justifying Calculations of Modern Waterworks Safety and Peculiarities of Account for the Process Equipment Impact in Case of Earthquakes]. Gidrotekhnicheskoe stroitel'stvo [Hydraulic Engineering]. 2010, no. 7, pp. 46—51.
  24. Evstigneev N.M. Uskorenie raschetov inzhenernykh zadach, privodimykh k ellipticheskim operatoram, s ispol'zovaniem graficheskogo protsessora tekhnologii CUDA [Acceleration of Engineering Problems Calculation, which are Reduced to Elliptic Operators with GPU Technology CUDA]. Stroitel'noe proektirovanie [Construction Design]. 2009, no. 2, pp. 55—60.

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Experience and problems of earth dam construction and exploitation in severe climatic conditions in Russia

Vestnik MGSU 7/2014
  • Aniskin Nikolay Alekseevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Engineering, Professor, Director of Institute of Hydrotechnical and Energy Construction, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Antonov Anton Sergeevich - Moscow State University of Civil Engineering (MGSU) postgraduate Student, Department of Hydraulic Engineering Structures, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 133-146

Hydraulic engineering constructions or dams are necessary constructive elements for river development. In severe climatic conditions (deep-frozen soil, low temperatures, high amplitudes of temperature fluctuations) the most expedient type of water retaining constructions are soil dams. In our paper we have examined economic conditions of the region with severe climate, available water resources and their development. We made the conclusions concerning preference for building reservoirs on the territory of Siberia. A two-century period, beginning with the first soil dams in the end of the 18th century, was considered for the building analysis. Our attention has been mainly focused on structures, engineering decisions and causes of accidents, which took place in operating cycle period. The results showed the importance of investigation of filtration and temperature regimes, as well as their collaboration in hydro technical structures design and operation.

DOI: 10.22227/1997-0935.2014.7.133-146

References
  1. Rogers J.R., Brown G.O., Garbrecht J.D. Water Resources and Environmental History. ASCE — American Society of Civil Engineers. New York, 2004, 285 p. DOI: http://dx.doi.org/10.1061/9780784406502.
  2. Andersland O.B., Ladanyi B. Introduction to Frozen Ground Engineering. Chapman&Hall, New York, USA, ASCE & John Wiley & Sons, 2003, 363 p.
  3. Kuperman V.L., Myznikov Yu.N., Toropov L.N. Gidroenergeticheskoe stroitel'stvo na Severe [Hydropower Construction in the North]. Moscow, Energoatomizdat Publ., 1987, 303 p.
  4. Gol'din A.L., Rasskazov L.N. Proektirovanie gruntovykh plotin [Design of Soil Dams]. Moscow, ASV Publ., 2001, 375 p.
  5. Kogodovskiy O.A., Frishter Yu.I. Gidroenergetika kraynego Severo-Vostoka [Hydropower Engineering in Far Noth-East]. Moscow, Energoatomizdat Publ., 1996, pp. 201—205.
  6. Pekhtin V.A. O bezopasnosti plotin v severnoy stroitel'no-klimaticheskoy zone [On the Safety of Dams in the Northern Construction-Climatic Zone]. Gidrotekhnicheskoye stroitel'stvo [Hydraulic Engineering]. 2004, no. 10, pp. 6—9.
  7. Rasskazov L.N., Aniskin N.A., Sainov M.P. Analiz sostoyaniya gruntovoy plotiny Kolymskoy GES [Analysis of Soil Dam Condition of Kolyma HPP]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2009, no. 2, pp. 111—118.
  8. Aniskin N.A. Temperaturnofil'tratsionnyy rezhim prigrebnevoy zony gruntovoy plotiny v surovykh klimaticheskikh usloviyakh [Temperature-Filtration Mode of the Crestal Zone of Embankment Dam in Severe Climatic Conditions]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2013, no. 4, pp. 129—137.
  9. Aniskin N.A. Temperaturnofil'tratsionnyy rezhim osnovaniya i plotiny Kureyskoy GES vo vtorom pravoberezhnom primykanii [Temperature-Filtration Mode Regime of Kureyskaya HPP Dam Base in Second Right Bank Abutment]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2006, no. 2, pp. 43—52.
  10. Foster M., Fell R., Spannagle M. The Statistics of Embankment Dam Failures and Accidents. Canadian Geotechnical Journal. 2000, vol. 37 (5), pp. 1000—1024. DOI: http://dx.doi.org/10.1139/t00-030.
  11. Sherard J.L. Hydraulic Fracturing in Embankment Dams. Seepage and Leakage from Dams and Impoundments. R.I. ASCE. New York, 1985, pp. 115—141.
  12. Belov A.N., Gorokhov E.N. Trekhmernoe matematicheskoe modelirovanie temperaturnogo rezhima gruntovykh plotin v kriolitozone [3D Thermal Modeling of Soil Dams in Cryolithic Zone]. Privolzhskiy nauchnyy zhurnal [Privolzhsky Scientific Review]. 2010, no. 1, pp. 65—71.
  13. Sobol' S.V., Gorokhov E.N., Sobol' I.S., Ezhkov A.N. Issledovanie dlya obosnovaniya proektov malykh vodokhranilishch v kriolitozone [Design Consideration of Small Reservoirs in Cryolithic Zone]. Izvestiya vuzov. Stroitel'stvo [News of Higher Educational Institutions. Construction]. 2005, no. 9, pp. 29—31.
  14. Gorokhov E.N. Temperaturnyy rezhim gruntov levoberezhnogo primykaniya Vilyuyskoy GES-3 [The Temperature Regime of Left Bank Abutment Soils of Vilyuiskaya HPP-3]. Gidrotekhnicheskoye stroitel'stvo [Hydraulic Engineering]. 2003, no. 2, pp. 12—15.
  15. Sheng-Hong C. Adaptive FEM Analysis for Two-Dimensional Unconfined Seepage Problems. Journal of Hydrodynamics. 1996, Ser. B., vol. 8, no. 1, pp. 60—66.

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Operational analysis of the tailings bund wall drainage system at mirny ore mining and processing enterprise

Vestnik MGSU 12/2016
  • Aniskin Nikolay Alekseevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Doctor of Engineering, Professor, Director of Institute of Hydrotechnical and Energy Construction, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Malakhanov Vyacheslav Vasilyevich - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Engineering, Associate Professor of Hydraulics and Hydraulic Engineering Construction, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Antonov Anton Sergeevich - Moscow State University of Civil Engineering (National Research University) (MGSU) postgraduate student of Department of Hydraulics and Hydrotechnical engineering, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoye shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 91-102

Issues of environmental safety of tailings of ore mining and processing enterprises are considered; parameters of drainage of bund walls are of great significance for the environmental safety. Description of the bund wall of Mirny ore mining and processing enterprise and the tailings filling layouts are given. Results of field observation and model study of the tailings bund wall drainage system at Mirny ore mining and processing enterprise are presented. The drainage system rebuilding project analysis was performed. Proposals for its improvement were set forward.

DOI: 10.22227/1997-0935.2016.12.91-102

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Mathematical model of the filtration process in suspended floc layer of the contact mass with account for its horizontal size limit

Vestnik MGSU 10/2013
  • Skolubovich Yuriy Leonidovich - The Novosibirsk State University of Architecture and Civil Engineering (NGASU) Doctor of Technical Sciences, Professor, Rector, The Novosibirsk State University of Architecture and Civil Engineering (NGASU), 113 Leningradskaya street, Novosibirsk, 630008, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Boyko Ol'ga Aleksandrovna - The Novosibirsk State University of Architecture and Civil Engineering (NGASU) Senior Lecturer, Department of Information tehnology, The Novosibirsk State University of Architecture and Civil Engineering (NGASU), 113 Leningradskaya street, Novosibirsk, 630008, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Zerkal' Sergey Mikhaylovich - The Novosibirsk State University of Architecture and Civil Engineering (NGASU) Doctor of Technical Sciences, Professor, Department of Applied Mathematics, The Novosibirsk State University of Architecture and Civil Engineering (NGASU), 113 Leningradskaya street, Novosibirsk, 630008, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Rogazinskiy Sergey Valentinovich - The Novosibirsk State University of Architecture and Civil Engineering (NGASU) Doctor of Technical Sciences, Professor, Department of Applied Mathematics, The Novosibirsk State University of Architecture and Civil Engineering (NGASU), 113 Leningradskaya street, Novosibirsk, 630008, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Sineeva Natal'ya Valer'evna - The Novosibirsk State University of Architecture and Civil Engineering (NGASU) Candidate of Technical Sciences, Dean, Faculty of Engineering and Ecology, The Novosibirsk State University of Architecture and Civil Engineering (NGASU), 113 Leningradskaya street, Novosibirsk, 630008, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 309-316

The problem of filtration in the conditions of suspended contact mass appears not only in the process of water purification, but also in other spheres of human activity.New theory on foreign particle motion inside suspended floc layer is observed (only their upward motion). The influence of horizontal limit of the suspended floc layer on foreign particle motion is considered. The co-authors present equations for calculating new space coordinates of a foreign particle.Therefore, the authors form mathematical model of the water purifying filter reactor functioning, which can be used in the process of studying the peculiarities of filtration and in prospect can be taken as the basis for experiment planning. Further specification of this model may be made in case of developing the method of calculating the free path length in space case.

DOI: 10.22227/1997-0935.2013.10.309-316

References
  1. Nikiforov A.I., Nikan'shin D.P. Perenos chastits dvukhfaznym fil'tratsionnym potokom [Transportation of Particles in Two-phase Filtration Flow]. Matematicheskoe modelirovanie [Mathematical Modeling]. 1998, vol. 10, no. 6, pp. 42—52.
  2. Pirumov U.G., Gidaspov V.Yu., Danielyan A.A., Ivanov I.E., Kryukov I.A., Muslaev A.V. Chislennyy analiz dvukhfaznogo techeniya v gazodinamicheskom fil'tre [Numerical Analysis of Two-Phase Flow in Gasdynamic Filter]. Matematicheskoe modelirovanie [Mathematical Modeling]. 1998, vol. 10, no. 11, pp. 19—28.
  3. Voytov E.L., Skolubovich Yu.L. Podgotovka pit'evoy vody iz poverkhnostnykh istochnikov s povyshennym prirodnym i antropogennym zagryazneniem: monografiya [Advancing of Drinking Water from Surface Sources with Elevated Natural and Man-made Pollution]. Novosibirsk, NGASU (Sibstrin) Publ., 2010, 217 p.
  4. Skolubovich Yu.L., Boyko O.A., Zerkal' S.M., Rogazinskiy S.V., Voytov E.L., Skolubovich A.Yu. Chislennoe modelirovanie protsessa ochistki vodnykh rastvorov v psevdoozhizhennom sloe kontaktnoy massy [Numerical Modelling of the Aqueous Solution Purification Process in Fluidized Contact Mass Layer]. Izvestiya vuzov. Stroitel'stvo [News of Institutions of Higher Education. Engineering]. 2012, no. 7—8, pp. 38—44.
  5. Skolubovich Yu.L., Boyko O.A., Zerkal' S.M., Rogazinskiy S.V., Voytov E.L., Skolubovich A.Yu. Chislennoe issledovanie vliyaniya oshibok izmereniya fizicheskikh parametrov reaktora-osvetlitelya na ustoychivost' ego statisticheskoy modeli [Numerical Investigation of the Influence of Physical Measurements Errors of the Clarifying Reactor on its Statistical Model Stability]. Izvestiya vuzov. Stroitel'stvo [News of Institutions of Higher Education. Engineering]. 2012, no. 9, pp. 60—65.

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Asymptotic solution of the filtration equation

Vestnik MGSU 2/2016
  • Kuzmina Ludmila Ivanovna - Higher School of Economics Department of Applied Mathematics, Moscow Institute of Electronics and Mathematics, Higher School of Economics, 20 Myasnitskaya str., Moscow, 101000, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .
  • Osipov Yuri Viktorovich - Moscow State University of Civil Engineering (National Research University) (MGSU) Candidate of Physical and Mathematical Sciences, Associate Professor, Department of Computer Science and Applied Mathematics, Moscow State University of Civil Engineering (National Research University) (MGSU), 26 Yaroslavskoe Shosse, Moscow, 129337, Russian Federation; This e-mail address is being protected from spambots. You need JavaScript enabled to view it .

Pages 49-61

The problem of filtering a suspension of tiny solid particles in a porous medium is considered. The suspension with constant concentration of suspended particles at the filter inlet moves through the empty filter at a constant speed. There are no particles ahead of the front; behind the front of the fluid flow solid particles interact with the porous medium. The geometric model of filtration without effects caused by viscosity and electrostatic forces is considered. Solid particles in the suspension pass freely through large pores together with the fluid flow and are stuck in the pores that are smaller than the size of the particles. It is considered that one particle can clog only one small pore and vice versa. The precipitated particles form a fixed deposit increasing over time. The filtration problem is formed by the system of two quasi-linear differential equations in partial derivatives with respect to the concentrations of suspended and retained particles. The boundary conditions are set at the filter inlet and at the initial moment. At the concentration front the solution of the problem is discontinuous. By the method of potential the system of equations of the filtration problem is reduced to one equation with respect to the concentration of deposit with a boundary condition in integral form. An asymptotic solution of the filtration equation is constructed near the concentration front. The terms of the asymptotic expansions satisfy linear ordinary differential equations of the first order and are determined successively in an explicit form. For verification of the asymptotics the comparison with the known exact solutions is performed.

DOI: 10.22227/1997-0935.2016.2.49-61

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