Estimation amount of snow deposits on the road

Transcription

1 Estimation amount of snow eposits on the roa Olga. Glaysheva oronezh State University of Architecture an Civil Engineering, Russia ABSTRACT The article uner consieration gives the results of the research on quantitative estimation of snow eposits on ifferent parts of roas uring lizzars. The methos of mathematical moeling were use to solve the prolem. There suggeste a mathematical moel giving a general escription of processes of snow accumulation on roas. This moel consiers the asic weather an roa factors, which are necessarily, have to e taken into account. Their list is given in the article. In article the mathematical moels escriing snow transfer an snowring to a site of a roa. The moels take into account the type of cross-section of roa. Data provie y automatic roa meteorological stations can serve as initial ata for calculations. The realization of the moels in the form of computer program is consiere. The example of calculation for the certain roa section is presente. Keywors: roa, mathematical moeling, snow transfer, snowring, amount of snow eposit.. INTRODUCTION For the purpose of proviing roa safety in winter the roa service team carries out a complex of activities. The stanars in force for winter service presuppose timely removal of ice seiments an clearing of the roa surface from snow. The main type of winter slipperiness on most of the territory of Russia is snow coasting. One of the ways of its prevention is a well-time clearing the roas from snow. The technology of work presupposes repeate passing of snow-removal machines. The interval etween passages of machines is etermine y the intensity of snowfall an the requirements of the winter service stanars. The intensity of the snow lockaes epens on large numer of factors, oth weather an roa. The quantitative estimation of those factors is an important prolem, which has not got its solution yet.. THE CALCULATION OF THE SNO TRANSFER AND THE SNOBRIHG ON THE ROAD The amount of snow eposit on the roa epens on the volume of snowring. The metho of summarize transfer suggeste y N.E. Dolgov an D.M. Melnik is use to calculate the volume of the snowring [], []. The metho takes into consieration the intensity of snow transfer, which epens on the win spee an the time uring the snow transfer occurs with particular intensity. The volume of snow transfer in winter perio ( t ) is calculate to the formula: t = t m m i=,( > 5) C i = I с t, () where t is the summary uration of snowstorms for winter perio, hour; m is the numer of measurements of the win spee uring snowstorms (at spees over 5 m/sec); C is an empiric factor, equal to 0,00046 for ensity of snow 0,7 m /m; i is the win spee uring snowstorms, m/seс; I c is the average intensity of snowstorms uring the winter perio, m /m hour. Collecting the ata provie y meteorological stations the wins with the spee less than 5 m/sec are not taken into consieration, ecause their energy is not sufficient to transfer falling an fallen snow. Sirwec 008, Prague, 4-6 May

2 The epenency etween the average intensity of horizontal snow transfer an the win spee at the weathercock height is expresse y the following formula: I = C, () where I is the intensity of horizontal snow transfer, m /m h; C is the factor to proportionality which epens on ensity the snow; is the win spee at the weathercock height, m/seс. The volume of the snowring to a highway at the en of the winter perio from one irection ( s ) is calculate accoring to the formula: = sin( α α ), () s t r i where α r is the irection of the highway, egree ; α i is the irection of the win, egree. The volume of the snowring to one sie of the highway within the winter ( ) is calculate accoring to the formula: 7 = sin ( α α ), s, i д i i = (4) where is the amount of snow rought to one sie of the roa, m /m; s,i is the amount of snow transfer y one compass point, m /m; α i is the azimuth of compass points, egree; α r is roa azimuth, egree. For each irection of the roa the numer of compass point from which snow transfer is calculate equals 7. Counting the amount of snow transfer wins lowing at an angle less than 0 are not taken into consieration. Figure gives the scheme of calculating of irections from which snow is rought to one sie of the roa, irecte northwar. The zone of each irection (at 6 compass points) is calculate y sector with the arc of,5. Snowrin g from irection North 48,75 0,5 0 0,75 0 N N 6,5 0 NN N,5 0 NNE,75 0 NE 56,5 0 ENE left of roa 8,5 0 58,75 0 S 6,5 0 S,75 0 SS 9,5 0 S 68,75 0 SSE SE 46,5 0 E ESE, ,75 0 0,5 0 right of roa Fig.. Scheme of calculation of snowring to the roa irecte on northwar. Sirwec 008, Prague, 4-6 May

3 . MODEL OF CALCULATING THE AMOUNT OF SNO, DEPOSITED ON THE ROAD AFTER SNOSTORM There is a moe of calculating the amount of snow eposite on the roa surface after snowstorm. There are chosen parameters influencing accumulation of snow on the roa surface. The general moel of quantitative evaluation of snow epenence of roas at the next snowstorm or snowfall is the following: () t r, i = f ( h( t), a( t), t) + (5) where r,i is a quantity of snow eposit on the roa surface; h(t) is parameters of outer factors (meteorological factors) are in the Tale ; a(t) is roa parameters are in the Tale ; t is a time, (t) is the quantity of snow eposits accumulate y the moment of the next snowstorm or snowfall. Components of the vector of weather factors h (t) Name of parameter atmospheric phenomenon (type of precipitation ) Symol of parameter Unit h (t) time of eginning of the phenomenon t n hour h (t) time of finishing of the phenomenon t k hour h 4 (t) win spee m/seс h 5 (t) win irection α в compass point h 6 (t) temperature of air T 0 С h 7 (t) uration of the phenomenon t hour h 8 (t) intensity I m /sec h 9 (t) ensity of snow eposit δ t/m Tale.. Meteorological factors. Components of the vector of Name of parameter Unit roa factors a (t) roa irection compass point a (t) working mark (height of emankment, epth of itch) Н geometrical parameters of cross-section of roa a (t) slopes ramp of itch m a 4 (t) slopes ramp of emankment (itch) m a 5 (t) slopes ramp of cuvette of itch m a 6 (t) with of cuvette l a 7 (t) with of itch shelf l a 8 (t) epth of cuvette h a 9 (t) with of roa shouler а a 0 (t) with of carriageway a (t) with of roa surface В a (t) cross-section slope of carriageway i a (t) cross-section slope of roa shouler i a 4 (t) availaility an type of snow protection - Tale.. Roa factors. Snow accumulate in itches an at slops changes the geometrical parameters of cross-section of roa. For its calculation the parameter of quantity of snow eposit (t) accumulate on roa sie is introuce. alue of the parameter epens on meteorological an roa factors an calculate at precipitations, snow compression at Sirwec 008, Prague, 4-6 May

4 melting an transportation of snow y roa machines at snow cleaning from carriageway. The moel takes into account the type of cross-section of roa. There are moels for low emankments, open an close itches ue to the ifference of their streamlining y winsnow flow.. Moel of quantitative evaluation of snow eposits on emankments For quantitative evaluation of snow eposits on emankments there is solution of the task of streamlining of the wege y the flow of tough uncompressile liqui []. The scheme of calculating takes into account availaility of itches an have seven rate sections (Fig. ). f B i i i i :m y H :m :m l x h Fig.. Scheme of quantitative estimation of snow eposit on the emankments At emankments snow accumulates in winwar sie of the itch of first. Calculation of snow eposit at section I is ase on geometrical parameters of the itch. Maximum quantity of eposit in the winwar itch: Q I. max = h( l + h( m + m )), (6) where h is a epth of the itch, m; l is a with of the itch, m; m, m are a slope ramp of itch. If snow capacity of the winwar itch is more than the quantity of rought snow (Q I.max > ), than the quantity of snow eposit at section I equal the volume snowring (Q I.max = ). If the conition is not oserve than the quantity of snow eposit equals snow capacity of the itch (Q I = Q I.max), an then snow carrie ( ) farther is calculate accoring to the formula: I = Q. (7) At sections II - I calculations of snow eposit are one through snow loss (П) cause y change of spee of winsnow flow: П =, (8) f where f is fiel win spee, m/seс; = (x, y) is the spee of winsnow flow in the point with coorinates x an y over emankment, m/sec. Changes of spee of winsnow flow are calculate accoring to the formula: = f x m. (9) Factor consiering the wege angle is calculate accoring to the formula: Sirwec 008, Prague, 4-6 May 4

5 β m =, (0) β where β is the angle of wege opening. The angle of wege opening is calculate through geometrical position of rate section: y sin β =. () x + y Formulas of calculation of snow quantity eposite on emankments an of snow quantity carrie farther for sections II I are given in Tale. Section numer of istance etween the point of rise of streams an rate section of height of rate section Calculation formulae of quantity of snow eposit at rate section of quantity of snow carrie past II x = m y y = H (0,5B i + i ) Q II = П = Q II III x = y = i Q III = П = Q III I x = 0,5B y = 0,5B i Q I = П 4 = Q I x = 0,5B y = 0,5B i Q = 4 П 5 = 4 Q I x = y = i Q I = 5 П 6 = 5 Q I Tale.. Formulas of calculation of snow quantity eposite on the roa surface. At section II on leewar sie slope an in itch quantity of snow eposit is calculate accoring to their geometrical parameters, total snow capacity of the slope an the itch is calculate. Total snow capacity of slope is limite y location of snow surface :8 an can e calculate accoring to the formula:. max = h ( l + h ( m + m )) + H 4 m. () Q II Analysis of snow lockaes of leewar sie itch is one similarly to win war itch, an the quantity of snow carrie farther ( 7 ) is calculate accoring to the formula: II 7 = 6 Q. () Quantity of snow eposit on the roa surface of emankments (Q ) is calculate accoring to the formula: III I I Q = Q + Q + Q + Q. (4). Moel of the quantitative evaluation of snow eposit in open itches At snowstorms into slopes of open itches there are eposits of snow ue to change of spee of winsnow flow. In calculation scheme (Fig.) there are six characteristic sections at which change spee correlation (/ f ) occurs. To calculate epenence of share of snow fallen from winsnow flow (n) on slopes ramp (m) formula of A.K. Djunin is use [4]: f = h, п + y hп y erf + erf ax ax (5) Sirwec 008, Prague, 4-6 May 5

6 where h n is epth of lowering of surface of slope, m; a is factor of turulence (at natural conitions accepte a = 0,06); x is ascissa counte from the top point of the threshol, m; y is height of the point uner consieration, m; erf (h n + y) is error integral of Gauss. f :m II H III I h I :m :m l l h :m B l c L l c I Fig.. Calculating scheme of quantitative evaluation of snow rifting of open itches. Thus knowing the volume of snowring ( ) quantity of snow eposite at the consiere section of itch can e calculate accoring to the formula: Q = П, (6) where П is snow loss cause y change of spee of winsnow flow, accoring to the formula Eq. (8). An the volume of snow carrie farther ( i ) is calculate accoring to the formula: i = Q. (7) Formulae of calculation of quantity of snow at consiere sections are the same as the formulas for emankments given in Tale. Quantity of snow eposit on the roa surface of open itches (Q ) is calculate accoring to the formula: III I Q = Q + Q. (8) For practical calculations the moel of efinition of quantity of snow in the opene itches is simplifie. As snow accumulates like equal layer in the opene itches at lizzars the relation of spees winsnow flow can e efine only for section I uner the formula Eq. (5) [5]. Quantity of snow eposite at the consiere section of itch can e calculate accoring to the formula Eq. (6). Average height of snow eposite is consiere uner the formula: I Q h = a, L (9) where L is length of a surface of slopes, cuvettes an of roa surface of the opene itches, m. Quantity of snow eposite on the roa surface of open itches (Q ) is calculate accoring to the formula: Q = h B, (0) a where B is with of roa surface. Sirwec 008, Prague, 4-6 May 6

7 . Moel of quantitative evaluation of snow eposit in close itches. Analysis of streamlining of close itch y winsnow flow allows making the conclusion that quantity of snow eposite on roa can e calculate asing on geometrical calculations. Two calculation schemes shoul e use to calculate snow rifting of close itches epening on correlation etween volumes of snowring an snow capacity of itches (Fig.4). The first scheme is use to calculate of snow eposite on the roa surface when volume of snowring excees the snow capacity of itches. In this case the area of snow eposit on slope an in cuvette of itch is limite y shae polygon in the scheme. f A :m :8 B C :0,5 H h L l G :m F l D :m E Fig. 4. Calculating scheme of quantitative evaluation of snow rifting of close itches. Base on geometrical calculations maximum quantity of snow eposit on the winwar slope of itch per linear meter can e calculate accoring to the formula: H m l + h( m + m ) 0,5H Q sl., cuv = + l H + H + () l + h( m + m ) + h L, The secon calculation scheme is use when the quantity of snowring oes not excee snow capacity of itch. An the top surface of snow eposit is limite y the line AС with the ase of slope towars the axis of roa :8 [6]. Maximum quantity of snow eposit on the winwar slope of itch per one linear meter, in this case, can e calculate accoring to the formula: Q sl., cuv l + H m = + h ( m + m ) + l l H + h 0,065 + h ( m + m ) 0,5H ( H m + l + l + h( m + m ) 0,5H ) L, H + () Knowing the volume of snowring uring the winter or uring a single snowstorm ( ) quantity of snow eposit on the roa (Q ) is calculate accoring to the formula: Q = Q sl,cuv. () 4. APPLICATION OF MODEL OF THE QUANTITATIE EALUATION OF SNO ON THE ROAD Moels are realize in the form of the computer program. The results of calculations are the registration of snow-oun parts an quantity of snow to e cleare after snowstorm on each snow-oun part of roa, quantity of snow to e cleare after snowfall on a separate part of roa an on the whole roa. All coming out parameters can e calculate for any ay uring winter perio. The example of calculation for a site of roa is presente on Figure 5. Sirwec 008, Prague, 4-6 May 7

8 a) Quantity of snow eposit on the roa, m L, m ) -,9 -,55 -,56 -,0,9-0,98 0,6,97 olume of snowring, m / m Technical class of roa Roa irection Type of cross-section Stake 8 II SSE Close itch Opene itch Emankment Fig. 5. Graphic presentation of results of calculations: a) iagram of change of quantity of snowstorm eposits on the roa surface; ) initial ata for calculation quantity of snowstorm eposits on the roa surface. Calculations have een one for test parts. During experimental work aequateness of the moels was teste accoring to the snow measurements. Data receive from meteorological stations for corresponing winter perios were use to calculate the volume of snowring. Coincience of calculate an actual ata of quantity of snow eposits on average was 88 percent. At the experiment the volume of snow transporte into itches an onto slopes uring snow-removal was not taken into consieration. Analysis of receive results shows that with availaility of such ata coincience will increase. Therefore the conclusion can e mae aout the possiility of application of the moel for solution of the task of winter roa maintenance. 5. REFERENCES [] Dolgov, N.E.95. Organic laws snow transport an their application to calculation of a egree snow lockaes ifferent parts of roa an to calculation of portale an constant snow protection. Meeting concerning snow-rift control. Ekatirinoslav, [] Melnik, D.M. 95. Aout laws of snow transport an their use in snow-rift control. Technics of railways, :6-. [] Schlichting, H Bounary-layer theory. Pulishing house «Science», Moscow, 58. [4] Djunin, A.K Roa winter maintenance. Pulishing house «Transport», Moscow, 44. [5] Kungurcev, A.A. 96. Designing snow protective actions on roas. Pulishing house «Autotransizat», Moscow, 08. [6] asiliev, A.P Designing of highways in view of influence of a climate on conitions of traffic. Pulishing house «Transport», Moscow, 48. Sirwec 008, Prague, 4-6 May 8