SOLVING THE PROBLEMS OF THE SUBMERGENCE IN URBAN CONSTRUCTION SPHERE

Introduction. The submergence by underground water remains one of the problems in urban construction. It is also associated with the movement of groundwater under buildings and structures. Such processes are non-stationary and their calculation is complex. The paper begins the series of researches on the methodology for solving problems of filtering groundwater while protecting against flooding in urban construction by using an operator method. Oliver Heaviside began the practical application of mathematical operators for solving engineering problems. The operator method with Laplace transformations was used. It was shown how, with the help of the Internet and Maxima program, it is easy to make inverse Laplace transformations.
Methods and materials. The author considered the decision on the submergence of the city road in the presence of a dome watering under asphalt pavement in the dirt road foundation. At the same time, for filtration problems of such type, the author took into account the compaction of the engineering zone of the soil under the road. The paper showed how to solve the complex non-stationary problem of spreading the dome of the flooding under the city road. The technology of the solution is presented not only with all the mathematical details of the operator method, but also provided with new physical representations. Such an original approach, by the author’s opinion, would help better understanding of the flooding process physics in urban construction. Moreover, it would allow solving problems of protection against flooding by a new, more efficient way, taking into account the real non-stationary processes of filtration of groundwater in built-up areas.
Discussion. As a result, the author presents anew statement of the operator method for solving the submergence specific problem in urban construction. First, a specific example demonstrates how to use the Internet and the license-free Maxima program. In this case, the simplest  case is taken, in the form of the electricity and filtration analogy. Then the author considers the filtration spreading of the domed man-made groundwater beneath the city road. Therefore, the paper demonstrates new solutions for non-stationary filtration of groundwater in the engineering zone, which are also compared with the world practice results.
Conclusions. The author presents the methodology for solving unsteady groundwater filtration problems for the submergence protection in urban construction by using the operator method and Laplace transformations. Such decisions make it possible to obtain convenient engineering formulae, by which groundwater levels, substantiate practical solutions and measures for protection against submergence in urban construction could be found. The author intends to further development of such scientific ideas and solutions for submergence protection in the built-up areas.

1. Huggenberger P., Jannis E. Urban Geology. Process-Oriented Concepts for Adaptive and Integrated Resource Management. Springer, Basel, 2011, 233 p. DOI 10.1007/978-3-0348-0185-0.

2. Serikova E., Strelnikova E., Yakovlev V. Mathematical Model of Dangerous Changing the Groundwater Level in Ukrainian Industrial Cities. Journal of Environment Protection and Sustainable Development. Vol. 1, No. 2, 2015, pp. 86–90.

3. Kremez V. S., Buts Y. V., Tsymbal V. A., 2003. Actual issues of modeling flooding territories and other dangerous processes concerned with groundwater regime changes. Environmental Ecology and Life Safety. No. 6, 2003, pp.56–64.

4. Telima S.V., Revyakina N.Y. Model research processes of flooding by groundwater of urban areas in modern conditions. Environmental Safety and Nature Resources. No. 7, 2011, pp. 45–63.

5. Gattinoni P., Pizzarotti E., Scesi L. Engineering Geology for Underground Works. Springer Science+Business Media, Dordrecht, 2014. 312 p. DOI 10.1007/978-94-007-7850-4.

6. Haque Muhammad I. Mechanics of Groundwater in Porous Media. CRC Press, 2017. 280 p. https://www.crcpress.com/Mechanicsof-Groundwater-in-Porous-Media/Haque/p/book/9781138072220

7. Briaud J.L. Geotechnical Engineering: Unsaturated and Saturated Soils. Wiley, 2013. 1024 p.

8. Cushman John H., Tartakovsky Daniel M. The Handbook of Groundwater Engineering. CRC Press, 2016. 1074 p.

9. Nonner J.C.Introduction to Hydrogeology. CRC Press, 2015. 266 p.

10. Eslamian Saeid, Eslamian Faezeh A. Handbook of Drought and Water Scarcity. CRC Press, 2017. 2145 p.

11. Walton C. Principles of Groundwater Engineering. CRC Press, 1990. 568 p.

12. Gray Nicholas. Water Science and Technology: An Introduction. CRC Press, 2017. 680 p.

13. Villholth Karen G. et al. Advances in Groundwater Governance. CRC Press, 2017. 594 p.

14. Ebrahim G. Y. Modelling Groundwater Systems: Understanding and Improving Groundwater Quantity and Quality Management. CRC Press, 2014. 196 p.

15. Kringel R. et al. Mass balance of nitrogen and potassium in urban groundwater in Central Africa Science of the Total Environment, 547 (2016), pp. 382–395. http://dx.doi.org/10.1016/j.scitotenv.2015.12.090. Published by Elsevier B.V.

16. Sologaev V.I. Fil’tratsionnye raschety i komp’yuternoe modelirovanie pri zashchite ot podtopleniya v gorodskom stroitel’stve: Monografiya [Filtrational calculations and computer modeling at flooding protection in city construction]. Omsk: Izd-vo SibADI, 2002. 416 p. (in Russian)

17. Osnovy merzlotnogo prognoza pri inzhenerno-geologicheskikh issledovaniyakh [Bases of the cryosolic forecast at engineeringgeological researches]. V.A. Kudryavtsev, L.S. Garagulya, K.A. Kondrat’eva, V.G. Melamed. M.: Izd-vo MGU, 1974. 432 p. (in Russian)

18. Abzhalimov R.Sh. Ispol’zovanie sezonno promerzayushchikh puchinistykh gruntov v kachestve osnovanii dlya fundamentov maloetazhnykh zdanii i podzemnykh sooruzhenii v inzhenernoi praktike: Monografiya [Use of the soil which is seasonally freezing through the puchinistykh as the bases for the bases of low buildings and underground constructions in engineering practice]. Omsk: Omskblankizdat, 2013. 442 p. (in Russian)

19. Kuranov N.P. Lineinye modeli gidrodinamicheskoi teorii fil’tratsii [Linear models of the hydrodynamic theory of filtering]. Doklady Akademii nauk SSSR. Moscow, Nauka, 1984. Tom 278, no 2. pp. 309–313. (in Russian).

20. Kuranov N.P. O svyazi gidrodinamicheskoi i gidravlicheskoi teorii fil’tratsii i sposobakh ikh linearizatsii pri issledovanii voprosov podtopleniya territorii gruntovymi vodami [About communication of hydrodynamic and hydraulic theories of filtering and ways of their linearization at a research of issues of flooding of territories by subsoil waters]. Inzhenernaya zashchita territorii, Moscow, VNII VODGEO, 1982. pp. 5–20. (in Russian).

21. Ditkin V.A., Prudnikov A.P. Integral’nye preobrazovaniya i operatsionnoe ischislenie [Integrated conversions and operational calculation]. Moscow, Nauka, 1974. 544 p. (in Russian).

22. Ditkin V.A., Prudnikov A.P. Spravochnik po operatsionnomu ischisleniyu [Reference book on operational calculation]. Moscow, Vysshaya shkola, 1965. 467 p. (in Russian).

23. Karslou Kh., Eger D. Operatsionnye metody v prikladnoi matematike [Operational methods in applied mathematics]. Moscow, Gosudarstvennoe izdatel’stvo inostrannoi literatury, 1948. 292 p. (in Russian).

24. Karslou G., Eger D. Teploprovodnost’ tverdykh tel [Teploprovodnost of solid bodies]. Moscow, Nauka, 1964. 487 p. (in Russian).

25. Kartashov E.M. Analiticheskie metody v teorii teploprovodnosti tverdykh tel [Analytical methods in the theory of heat conductivity of solid bodies]. Moscow, Vysshaya shkola, 1985. 480 p. (in Russian).

26. Korn G., Korn T. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov [The reference book on mathematics for scientists and engineers]. Moscow Nauka, 1984. 832 p. (in Russian).

27. Lykov A.V., Mikhailov Yu.A. Teoriya teplo- i massoperenosa [Theory warm and mass transfer]. M.-L.: Gosenergoizdat, 1963. 536 p. (in Russian).

28. Kamke E. Spravochnik po obyknovennym differentsial’nym uravneniyam [Reference book on ordinary differential equations]. Moscow, Nauka, 1976. 576 p. (in Russian)

29. Polubarinova-Kochina P.Ya. Teoriya dvizheniya gruntovykh vod [Theory of the subsoil waters movement]. Moscow, Gostekhteorizdat, 1952. 676 p. (in Russian).

30. Polubarinova-Kochina P.Ya. Teoriya dvizheniya gruntovykh vod [Theory of the subsoil waters movement]. Moscow, Nauka, 1977. 664 p. (in Russian).

31. Polubarinova-Kochina P.Ya., Pryazhinskaya V.G., Emikh V.N. Matematicheskie metody v voprosakh orosheniya [Mathematical methods in questions of irrigation]. M.: Nauka, 1969. 416 p. (in Russian).

32. Prognozy podtopleniya i raschyot drenazhnyh sistem na zastraivaemyh i zastroennyh territoriyah / VNII VODGEO. [Forecasts of flooding and calculation of drainage systems on the built-up and built up VODGEO’S territories] Moscow, Strojizdat, 1991. 272p. Avt.: A.ZH. Muftahov, I.V. Korinchenko, N.M. Grigor’eva, A.P. SHevchik, V.I. Sologaev. (in Russian).