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ment safely partially covered, a relative area should be over 50 % of that of the grain element. The carcass structure of the foundation of a transportation structure contains technological voids between one shell and the grain element formed as a binder merges with the latter. These technological voids are used to equalize the pressure caused by moist in the pores of the grain element. In the winter season they prevent the shell from breaking apart caused by ice expansion and in the summertime moist turns into vapor.

The use of a polyurethane composite as a binder allows rigid elastic fibres and strong and durable connections at the contact points of the shells of the grain element. Polyurethane composites have a high hydraulic stability, resistance to external environment in different climatic zones, frost-resistance and compatibility with different types of fraction fillers such as crushed stone, gravel, etc.

In order to strengthen a foundation and (or) cover a transportation structure, it is most advisable to utilize a binder based on a two-component polyurethane system. A two-component polyurethane system has a good compatibility with different types of fraction fillers (crushed stone, gravel) (according to the GOST (ГОСТ) 7392-2002). A binder can be modified according to special requirements. All the materials for this two-component polyurethane system are manufactured in Russia, which solves the issue of import and high material costs.

Depending on various usage conditions (temperature, humidity), the optimal viscosity and polymerization rate of a binder allow the filler particles to be covered evenly and strong and durable “connecting bridges” to form at the contact points.

A one-component polyurethane composition whose viscosity is controlled with a mineral filler. A solidified binder of the carcass structure due to no contact of the grain elements allows the use of other materials as grain elements of the carcass structure of the foundation and (or) roadway surfacing, which expands an application range of a structure as different transportation structures are being designed. Fractioned crushed stone, gravel, stone, sifts, artificial crushed stone, fractioned secondary breakage (production of crushing and sifting) of construction materials is used as a grain element. The size of the grain element of the carcass structure of a foundation and (or) roadway surfacing is 5—120 mm.

A transportation structure can contain an upper layer of grain elements with a finer fraction or their sifts with the size of the grain elements of an extra layer being 5—15 mm. This allows the grain elements of medium or small fractions to be used to be used and material and labour costs associated with strengthening soil surfaces due to a wider range of fractions of grain elements to be reduced and more basic pouring tools to be utilized. On top of the structure strengthened with a polymer binder there can be a layer of asphalt or concrete surfacing.

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Polyurethane can be applied for repairing and laying crushed stone counter-corrosive structures made of solid and soft rocks of motorways as well as addressing a number of issues pertaining to strengthening slopes of crushed stone and gravel of different granulometric composition.

The system is polymerized (solidified) under the effect of natural humidity coming in contact with the air. It should be stored in insulated, tightly sealed containers respectively. A technological use time is 20 min [1].

2. Polyurethane binder used for laying and strengthening a transportation structure.

Polyurethane is known to be a heteroceptive polymer material with a macromolecule containing an unprotected and (or) replaced urethane group.

Polyurethane consists of isocyanate and polyol that are obtained using raw oil. As two liquid components ready to be processed that contain different supplementary substances are mixed, there is a chemically responsive mix. Depending on the composition, a range of properties of a resulting polyurethane and rigid, soft, integral, cell (foamed) or monolith material can be obtained that is prone to aging, has a low temperature and a high level of resistance to different environmental effects. Polyurethane is resistant to abrasive wear, most organic dissolvents, ultraviolet radiation and sea water. An advantage is that their elasticity (hardness) is programmed, i.e. it can range widely depending on the proportions of used materials. Polyurethane can be one-, two-, and three-component ones.

Shrinkage of standard samples has exceptionally technological characteristics.

Polyurethane items are greatly resistant to sharp atmospheric pressure changes, resistant to beating, industrially durable and have the properties that cannot be achieved for ordinary rubber [13]:

––elasticity (a relative lengthening during breakage is two times as large as that of rubber);

––low wearability (conditional wear resistance is three times as high as that of rubber);

––high strength (is 2.5 times as high as that of rubber);

––high resistance to tear and multiple deformations;

––performance at high pressures (up to 105 МPа);

––acid resistance and stability to a lot of dissolvents;

––extremely high hardness (up to 98 on the Shore scale);

––performance in a temperature range of −50 to +80 °С (during introduction);

––resistance to microorganisms and mould;

––resistance to vibration and oil and fuel;

––elasticity at low temperatures;

––high dielectric properties;

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––resistance to nitrogen;

––resistance to water.

Conclusions

1. The technology for strengthening slopes and dams, cones of bridges and pipelines based on polyurethane. This technology is easy to use and not labour-intensive (only requires staff of 1 or 2 people and no great amount of special machinery). It is also cost-effective due to its long life cycle (12 years) and its maintenance is not financially burdening.

2. This project is designed to strengthen foundations and (or) roadway surfacing, improve shear resistance, prevent migration of certain grain elements due to their varying nature, increase the load-carrying capacity of transportation structures, extension of application ranges of different construction materials and can be employed in construction, repairs, routine maintenance and renovation of transportation structure.

References

1.Belyatskiy V. N., Krivoguz Yu. M. Osobennosti otverzhdeniya poligomernykh produktov iz otkhodov poliuretanov i ikh primenenie na praktike [Features of curing oligomeric products from waste polyurethanes and their application in practice]. Nauka i tekhnika, 2012, no. 2, pp. 68—70.

2.Zadiraka A. A. Preimushchestva primeneniya poliuretanovykh kompozitnykh sostavov pri ukreplenii otkosov nasypey i vyemok v dorozhnom stroitel'stve [Advantages of the use of polyurethane composite compositions in strengthening the slopes of embankments and pits in road construction]. Vestnik Belgorodskogo gosudarstvennogo tekhnologicheskogo universiteta im. V. G. Shukhova, 2017, no. 9, pp. 25—29.

3.Zadiraka A. A. Remont shchebenochnykh konstruktsiy na otkosakh avtomobil'nykh dorog s primeneniem sovremennykh materialov [Repair of crushed stone structures on the slopes of roads with the use of modern materials]. Tekhnicheskoe regulirovanie v transportnom stroitel'stve, 2017, no. 2 (22). Available at: http://trts.esrae.ru/41-247.

4.Zadiraka A. A., Kokodeeva N. E., Bondar' E. S. Fiziko-mekhanicheskie pokazateli i svoystva poliuretana i primenenie poliuretanovykh izdeliy, uvelichivayushchie nadezhnost' transportnykh sooruzheniy v protsesse ekspluatatsii [Physical and mechanical characteristics and properties of polyurethane and the use of polyurethane products that increase the reliability of transport facilities during operation]. Tekhnicheskoe regulirovanie v transportnom stroitel'stve, 2017, no. 6 (26). Available at: http://trts.esrae.ru/46-335.

5.Zadiraka A. A. Primenenie poliuretanovykh kompozitnykh sostavov dlya ustroystva osnovaniy i/ili pokrytiy transportnykh sooruzheniy [Application of polyurethane composite compositions for the construction of bases and / or coatings of transport facilities]. Vestnik Belgorodskogo gosudarstvennogo tekhnologicheskogo universiteta im. V. G. Shukhova, 2017, no. 4, pp. 72—75.

6.Kokodeeva, N. E., Kochetkov A. V., Leont'ev V. Yu. Konstruktsiya pokrytiya transportnogo sooruzheniya

[Construction of the covering of the transport structure]. Patent RF, no. 155397, 2015.

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7.Kokodeeva N. E., Kochetkov A. V., V. Leont'ev Yu. Sposob ustroystva konstruktsii osnovaniya i/ili pokrytiya transportnogo sooruzheniya [Method of construction of the base and / or coating of the transport structure]. Patent RF, no. 2593506, 2016.

8.Leont'ev, V. Yu., Kochetkov A. V., Yankovskiy L. V. e. a. Metodika rascheta ugla osypaniya sklonov metodom izlishnikh figur pri proektirovanii zashchitnykh shchebenochno-poliuretanovykh sloev [The method of calculation of the angle of slope shedding by the method of excessive figures in the design of protective crushed stone-polyurethane layers]. Dorogi i mosty, 2016, no. 2. Available at: http://rosdornii.ru/files/dorogi-i- mosti/36/4.pdf.

9.Leont'ev V. Yu., Kokodeeva N. E. Metody remonta shchebenochnykh konstruktsiy, armirovannykh ob"emnymi georeshetkami na konusakh mostovykh sooruzheniy i otkosakh avtomobil'nykh dorog [Repair methods crushed stone constructions, reinforced surround geogrid on cones of bridges and the road slopes]. Dorogi. Innovatsii v stroitel'stve, 2015, no. 43, pp. 74—78.

10.Leont'ev V. Yu. Poliuretanovye pokrytiya [Polyurethane coating]. Avtomobil'nye dorogi, 2016, no. 5, pp. 78—83.

11.Leont'ev V. Yu. Primenenie vyazhushchego materiala na osnove poliuretana dlya ukrepleniya i remonta zashchitnykh pokrytiy transportnykh sooruzheniy [Application of polyurethane-based binder for strengthening and repair of protective coatings of transport facilities]. Transportnoe stroitel'stvo, 2016, no. 1, pp. 7—10.

12.Leont'ev V. Yu., Kochetkov A. V., Kokodeeva N. E., Zadiraka A. A. Primenenie poliuretanovogo vyazhushchego v transportnom stroitel'stve [Use a polyurethane binder in road building]. Saratov, RATA Publ., 2017. 240 p.

13.Leont'ev V. Yu. Ukreplenie otkosov zemlyanykh sooruzheniy. Vyazhushchiy material na osnove dvukhkomponentnoy poliuretanovoy sistemy DOROLIT [Strengthening of slopes of earthen structures. Astringent material on the basis of two-component polyurethane system DOROLIT]. Novye tekhnologii v stroitel'stve, 2016, no. 1, pp. 14—31.

14.Kochetkov A. V., Leont'ev V. Yu. e.a. STO 88902325-01. Material vyazhushchiy na osnove poliuretana dlya avtomobil'nykh dorog. Tekhnicheskie usloviya [STO 88902325-01. Astringent material based on polyurethane for roads. Technical conditions]. Moscow, OrgsintezResurs Publ., 2014. 23 p.

15.Hoffmann A., Ebert H., Klesczewski B. Method for Producing Mineral-Bearing Cover Layers for Floor Coverings. German Patent, no. EP2007/000234, 2012.

16.Hoffmann A., Udo M., Hans-Guido W., Kleiner T., Busch R., Torsten E. Process for the Production of Ballast. German Patent, no. US9297121B2, 2014.

17.Mohmeyer N., Reese O., Eisenhardt A., Leberfinger M., Mohmeyer H. German. Patent WO2009037205A1 Process for the Production of Ballast. German Patent, no. EP2008/062180, 2009.

18.Moisture-Curing Pavement Material: Japanese Patent, no. JP2001000318045, 2003.

19.Opferkuch R., Hartenburg R., Heinz S. Method of Manufacturing Water Permeable Surface from Mineral Aggregate Bonded with Organic Adhesive. German Patent, no. DE19733588A, 1999.

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Russian Journal of Building Construction and Architecture

DOI 10.25987/VSTU.2018.41.1.009

UDC 124.131.63 : 631.616

A. I. Tsaplin1, М. Ye. Zhalko2

MATHEMATICAL ANALYSIS OF HUMIDITY URE TRANSFER OF UNDERGROUND WATER IN THE SUBBASE OF ROAD SURFACING

AND PREDICTING THE PARAMETERS OF A DRAINAGE SYSTEM

Perm National Research Polytechnic University

Russia, Perm

1D. Sc. in Engineering, Prof., Honored Worker of the Higher School of Russia Lysva Branch of the Perm National Research Polytechnic University Russia, Lysva

2Researcher, tel.: 8-34-249-5-46-13, e-mail: mihailz-49@mail.ru

Statement of the problem. The problems of searching for an accelerated solution of the problem of calculating the parameters of drainage systems are studied by means of mathematical modeling of water transfer in a porous subbase of a road.

Results. Based on an exact solution of a humidity ure transport equation in porous soils, a technique for investigating vertical filtration has been developed. It is shown that the rate of a rise in water levels along the height of the soil layer is unstable and changes as a maximum value of the height of a subbase is reached.

Conclusions. The technique sufficiently describes the transfer of humidity ure in a porous soil and is useful for accelerated analysis of the parameters of drainage systems in the subbase of a road. An example of the application of the procedure is given for a new scheme of water removal from under the roadway, which reduces the negative effects of frost heaving.

Keywords: road surfacing, destruction, soil freezing, filtration, fluid migration, mathematical modeling.

Introduction. Motorway foundations are water-resistant media, the water filtration rate for a single pumping gradient changes from several hundreds of m/day (for pebbles and gravel with coarse sand) to a one tenth proportion m/day (for weakly penetrated loam, sandy loam) [9, 14]. The height of a capillary lift over a mirror of underground water in sand can be 1 m and more and it can be 8 m in clays [14], the porosity of sandy soils varies in the range of 0.55…0.80 [4].

© Tsaplin А. I., Zhalko М. Ye., 2019

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Low deposition of underground waters causes porous water to come into the upper part of a base foundation. For negative Celsius temperatures this water freezes and it goes from liquid to solid accompanied by forces of frosty swelling [15] that result in the failure of roadway surfacing.

In order to dry water-saturated soil, the upper part of a drowned slope is drained using highporous sand and gravel drains [5] and anti-filtration screens [13], oil waste hydrophobisators, preventing water migration in the freezing zone [15]. In [12] there is a suggestion for water drainage systems using draining pipes.

A high-speed solution for calculating the parameters of drainage systems is achieved by mathematical modeling of water transfer in a porous motorway foundation. There are also papers that deal with modeling in porous media [1, 9, 11, 17]. In [16] a mathematical modeling describing an improbable imbalanced heat and thermal transfer in a three-dimensional porous medium is set forth.

There are methods of mathematical modeling of filtration in soils considering film humidity transfer [6], evaporation from its free surface [2], horizontal filtration increasing as does the depth of underground water [19], non-stationary vertical filtration based on the Fokker-Planck equation [18] based on vertical capillary cylinders [20].

In the present paper a mathematical model is suggested that allows only for vertical filtration and major typical porosity of soils, an accurate solution for the equation of the humidity transfer and the way it could be applied for calculating a drainage system.

1. Statement of the problem. The Figure presents a scheme of a road foundation that is a porous medium. The humidity ure transfer of underground water is presented which is a porous medium. The humidity ure transfer of underground water in the vertical direction occurs under the effect of capillary forces and gravity.

Fig. Scheme for calculating humidity ure transfer of underground water in a motorway foundation:

1 is underground water;

2 is a soil foundation;

3 is a draining layer;

4 is roadway surfacing

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In this case a differential equation of humidity ure transfer, which is a particular case of the movement equation presented in [16] takes the following form:

where m=Vpor/V is the porosity of the soil; k is the coefficient of the penetrability of the soil that has a dimensional area; x is the coordinate calculated from the vertical up to the underground water level; u is a projection of the water lifting rate up to the axis x; ν is a kinematic viscosity of water; g is the free fall acceleration. In engineering calculations of water penetrability of soils the filtration coefficient is employed

characterizing the filtration rate related to a dimensionless pumping gradient [3]. We transform the equation (1):

(4)

we get an accurate solution:

where uσ and ug are the humidity transfer rates in a porous soil only under the effect of capillary forces and gravity.

An extremum study of the function (5) shows that the rate of water lifting along the height of the soil level is not stable and changes from zero to the underground water level up to the maximum at

x 2gk 2 m2 2 ,

and then drops down to zero. The maximum and average length in the range of a layer with the thickness δ of the rate is given by the ratios

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For a multi-layer structure of a motorway foundation along the height the local rates at the contact boundaries are equal. Therefore the distribution of the water lifting rate in the i-th layer is determined with the formula:

where i is the number of the layer, i = 1, 2, …, n; n is the number of the layers of the thickness δi with homogeneous porosity along the height of a motorway foundation.

The complete water consumption ρ in any layer of a motorway foundation for one running meter of a motorway with the halfwidth B (Fig.) is given by the formula

(9) 2. The results of the calculation analysis. Let us look at the example of calculating humidity transfer for three types of homogeneous subbase foundation with varying penetrability for fixed halfwidths of a roadway B = 10 m and thermal and physical properties of water: ν = 10−6 m2/sec; ρ = 103 kg/m3.

The tables shows that the maximum water filtration rate (6) is the same as the filtration coefficient, which proves that the calculation analysis based on the solution of the movement equation is viable (1).

3. Calculation of the parameters of a new drainage system. In [12] a new scheme for road drainage in areas with high humidity humidity is suggested which is effective for small deposits of underground water for constantly flooded areas as well as those with a great amount of

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rainfall and where water is accumulated and coming from the surface submerges roadways. In a drainage layer of a subbase foundation with the filtration coefficient of no less than 1 m/day there are perforated plastic pipes with the diameter d = 70—110 mm filled with coarse crushed stone. The pipes are positioned along the entirety of the road.

If a draining level is not too thick, pipes are positioned horizontally with the distance L between them. These intervals then have to be identified using the conditions of equal water consumption in a subbase foundation and drainage pipes.

The water consumption in a subbase foundation of sand and sandy loam for one running meter of a roadway with the halfwidth B is given by the formula (9):

The mass water consumption per second along a pipe with the diameter d = 0.1 m filled with coarse crushed stone and sand is determined only with capillary forces thus

The distance between the drainage pipes is

Conclusions

1.The developed method considering only vertical filtration and the major characteristics of the porosity of soil yields the accurate solution for the humidity transfer equation. The water lifting rate along the height of a soil layer is shown to be unstable and changeable as a maximum is reached along the height of a subbase foundation.

2.The method provides an accurate description of humidity transfer in porous soil and is instrumental in high-speed calculation analysis of the parameters of drainage systems in roadway subbase foundations.

3.The example is provided of the use of the method of evaluating a distance between drainage pipes in a new drainage system from under a roadway foundation that mitigates the negative effects of swelling.

References

1. Barenblatt G. I., Entov V. M., Ryzhik V. M. Dvizhenie zhidkostey i gazov v prirodnykh plastakh [Movement of liquids and gases in natural layers]. Moscow, Nedra Publ., 1984. 212 p.

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2.Bereslavskiy E. N., Aleksandrova L. A., Zakharenkova N. V., Pesterev E. V. Matematicheskoe modelirovanie fil'tratsionnykh techeniy s neizvestnymi granitsami v podzemnoy gidromekhanike [Mathematical modeling of seepage flows with unknown boundaries in an underground fluid mechanics]. Mekhanika zhidkosti i gaza. Vestnik Nizhegorodskogo universiteta im. N. I. Lobachevskogo, 2011, no. 4 (3), pp. 644—646.

3.Boldyrev G. G., Malyshev M. V. Mekhanika gruntov. Osnovaniya i fundamenty (v voprosakh i otvetakh). 4-e izd., pererab. i dop. [Soil mechanics. Bases and foundations (in questions and answers). 4th ed.]. Penza, PGUAS Publ., 2009. 412 p.

4.Trofimov V. T., ed. Gruntovedenie. 6-e izd., dop. i pererab. [Soil science. 6th ed.]. Moscow, Izd-vo MGU, 2005. 1024 p.

5.Dolzhik K., Khmelevska I. Raschetnaya otsenka fil'tratsii nesvyaznykh gruntov [Calculation evaluation of non-cohesive soil filtration]. Osnovaniya, fundamenty i mekhanika gruntov, 2014, no. 5, pp. 2—5.

6.Kashchenko N. M., Malakhovskiy V. S., Semenov V. I., Gritsenko V. A. Matematicheskoe modelirovanie protsessov fil'tratsii vlagi v tyazhelykh gruntakh [Mathematical modeling of moisture filtration processes in heavy soils]. Matematicheskoe modelirovanie. Vestnik Baltiyskogo federal'nogo universiteta im. I. Kanta, 2012, vol. 10, pp. 50—53.

7.Kashchenko N. M., Malakhovskiy V. S., Semenov V. I., Gritsenko V. A. Matematicheskoe modelirovanie protsessov fil'tratsii vlagi v tyazhelykh gruntakh [Mathematical modeling of moisture filtration processes in heavy soils]. Matematicheskoe modelirovanie. Vestnik Baltiyskogo federal'nogo universiteta im. I. Kanta, 2012, vol. 10, pp. 50—53.

8.Kim Khyun Chol. Sovershenstvovanie metodov rascheta glubiny sezonnogo promerzaniya puchinistykh

gruntov zemlyanogo polotna zheleznodorozhnogo puti. Avtoref. diss. kand. tekhn. nauk [Improvement of methods for calculating the depth of seasonal freezing of heaving soils of the railroad tracks. Abstract of diss.]. Novosibirsk, 2013. 24 p.

9.Korolev V. A. [Soil water permeability]. Rossiyskaya geologicheskaya entsiklopediya: v 3 t. T. 1 (A—I) [Russian geological encyclopedia: in 3 vol. Vol. 1 (A––I)]. Saint-Petersburg, VSEGEI Publ., 2010. 211 p.

10.Leybenzon L. S. Dvizhenie prirodnykh zhidkostey i gazov v poristoy srede [Movement of natural liquids and gases in a porous medium]. Leningrad, OGIZ-Gostekhizdat Publ., 1947. 244 p.

11.Masket M. Techenie odnorodnykh zhidkostey v poristoy srede [Flow of homogeneous liquids in a porous medium]. Moscow –– Izhevsk, NITs “Regulyarnaya i khaoticheskaya dinamika”, 2004. 628 p.

12.Trefilov V. A., Zhalko M. E. Ustroystvo vodootvedeniya iz-pod dorozhnogo polotna [Device drainage under the roadway]. Patent RF, no. 151370, 2015.

13.Semashkin K. V., Shestakov V. N. Obosnovanie sposoba obespecheniya ustoychivosti v protsesse ekspluatatsii podtoplennykh dorozhnykh nasypey [Justification of the method of ensuring stability during operation of flooded road embankments]. Vestnik TGASU, 2013, no. 4, pp. 280—290.

14.Sugak V. G., Ovchinkin O. A., Silaev Yu. S., Sugak A. V. Georadarnyy metod obnaruzheniya vodonasyshchennykh sloev grunta s otsenkoy ikh ob"emnoy vlazhnosti [GPR method for detection of watersaturated soil layers with assessment of their volume humidity]. Geofizicheskiy zhurnal, 2014, vol. 36, no. 2, pp. 127—137.

15.Khabibullina I. N., Beshenov M. E., Geleverya T. I. Ispol'zovanie ukreplennykh gruntov dlya ustroystva protivopuchinistykh sloev na avtomobil'nykh dorogakh [The use of reinforced soils for the device of anti-fouling

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