Determining the optimum length of a bridge opening with a specified reliability level of water runoff

Transcription

1 MATE Web o onerenes 7, 0004 (07) DOI: 0.05/ ateon/ XXVI R-S-P Seinar 07, Theoretial Foundation o ivil Engineering Deterining the optiu length o a bridge opening with a speiied reliability level o water runo Sergey Evdokiov, and Tatiana Doridontova,* Saara State Tehnial University, Institute o Arhiteture and ivil Engineering, 94, Molodogvardeyskaya St., 4400, Saara, Russia Abstrat. urrent trends in onstrution are aied at providing reliability and saety o engineering ailities. Aording to the latest governent regulations or onstrution, the sientii approah to engineering researh, design, onstrution and operation o onstrution projets is a key priority. The reliability o a road depends on a great nuber o ators and harateristis o their statistial opounds (sequential and parallel). A part o a road with suh an-ade strutures as a bridge or a pipe is onsidered as a syste with a sequential eleent onnetion. The overall reliability is the ultipliation o the reliability o these eleents. The paraeters o engineering strutures deined by analytial dependenes are highly volatile beause o the inauray o the deining ators. However eah physial paraeter is statistially unstable that is evaluated by variable oeiient o their values. It auses the lutuation in the paraeters o engineering strutures. Their study ay result in the hanges in general and partiular design rules in order to inrease the reliability. The paper gives the grounds or these hanges by the exaple o a bridge. It allows alulating its optiu length with a speiied reliability level o water runo under the bridge. Introdution At present, saety and reliability o onstrution engineering ailities on roads is a atter o great onern. The paper reports on the reliability o a road that inludes the reliability o its eleents- road suraing, geoetri eleents, an-ade strutures [-7]. The reliability is losely related to the probability o ailures or risks. The reliability o an auto-road and an-ade strutures on it is uh less iportant, less durable and has absolute servieability. The low reliability o a road depends on a large nuber o ators and harateristis o their statistial sequential and parallel opounds. A part o a road with suh an-ade strutures as a bridge or a pipe is onsidered as a syste with a sequential onnetion o eleents. The overall reliability is the ultipliation o the reliability o these eleents. In this regard, the ethodology proposed in this researh work aied at deterining the * orresponding author: adisk6@yandex.ru The Authors, published by EDP Sienes. This is an open aess artile distributed under the ters o the reative oons Attribution iense 4.0 (

2 MATE Web o onerenes 7, 0004 (07) DOI: 0.05/ ateon/ XXVI R-S-P Seinar 07, Theoretial Foundation o ivil Engineering optiu length o the bridge opening with a speiied reliability level o water runo sees to be relevant. Materials and Methods In order to provide the reliability o slopes stabilized with soil, its gradient should orrespond to the alulated shit angle, Forula (): tg ψ Κ tg ϕ p h, () where, assurane oeiient (, as it orresponds to the liit state); angle o internal rition; adhesion; tgϕ p h p h pressure on ground: p h os ϕ h γ r ; os h ground area on the ross-setion o a slope; soil density; r running eter. et s ind the derivatives o the untion ro,, and alulated by the orula () ϕ tg ϕ () p h tgϕ p h γ tgϕ F γ To deterine the reliability o a slope the authors use the existing norative values or the gradient. It should be noted, the reliability is alulated as ollows, Forula (): P ( Ζ) nor nor () To deterine the reliability o superelevation Forula (4) should be used. i superel V /gr M v /gr II (4) Where: V ar speed in superelevation; g aeleration o gravity (g 9,8 /s ); R turning radius (R in 800 or a road o ategory II); M sideway ore oeiient; II oeiient o adhesion o ar wheels with the ground. Then standard or the superelevation gradient should be alulated by (5).

3 MATE Web o onerenes 7, 0004 (07) DOI: 0.05/ ateon/ XXVI R-S-P Seinar 07, Theoretial Foundation o ivil Engineering i V μ V (5) g R Then a bridge apability is alulated. To deterine the probability o exeeding the low through the speiied bridge setion the ollowing orula should be used (6):.5H b (6) Where, H,45V /g head o water; V low veloity under the bridge; g aeleration o gravity (g 9,8 /s ); b width o the bridge. Standard or water low should be alulated by the derivative V, Forula (7). V.5 b (7) V g It should be noted that the reliability o a road and its engineering ailities depends on a nuber o paraeters desribed above. The authors have assessed the statistial harateristis and paraeters o a road and engineering ailities derived ro the statistial distributions [8-0]. The statistial data on the aterial properties, geoetri diensions o road eleents and engineering strutures, and their statistial distribution ated as the initial data. On their basis the distribution o the analyzed paraeters is ade by using standardized ore deoration relationship []. The authors prove this stateent by the exaple providing the ollowing results. Results Aording to statistial researh, variation oeiient or soil density (), angle o internal rition () and adhesion () is V 5%. The average values or, and are: 000 kg/ ; 7,5 and 0,006. Then the standards are ound or,, V γ kg/ γ γ V tgϕ 0.5 tg7.5 0,0 ϕ ϕ V Now the standard gradient, average value and variation oeiient should be ound.

4 MATE Web o onerenes 7, 0004 (07) DOI: 0.05/ ateon/ XXVI R-S-P Seinar 07, Theoretial Foundation o ivil Engineering tgϕ Ο ( tg7.5 ) p h Ο 0. os ψ γ tgϕ tgϕ os p ϕ γ h tgϕ 0. os ϕ h γ v To deterine the reliability o the slope the norative values or the slope should be used. For loa the slightest slope is :.5 V is 0%, thus: V The reliability is alulated by the Forula (): V P (.5) 0. 9 The reliability o the superelevation an be alulated by the Forula (4) ollowing the stateent o the researh that provides the best onditions or ar passage along the urve when μ0.05h0.. Then the value o μ and the average values o μ and μ are alulated. μ μ ( ) ( ) 0.05 ν μ For speed V we take variation oeiient V 0., while the average value is V 0 k/h. We get: 4

5 MATE Web o onerenes 7, 0004 (07) DOI: 0.05/ ateon/ XXVI R-S-P Seinar 07, Theoretial Foundation o ivil Engineering V ν k h V V / Then the standard or the superelevation gradient is alulated by the Forula (5). i % i V (0 /.6) g R i 0.06 i 0.5 i For ategory II road with the turning radius ro 000 to 000 the superelevation gradient is 00 0 / 00. V take 0 %, thus: V V i 0 0. Then the reliability is deterined by the ollowing: 0 / ( ) nor P Ζ 6 nor (,) Then the reliability o a bridge apability is alulated, Forula (6)..45 V.5 g V b.7 g b In the given orula only the low veloity under the bridge is variable. The average value o low veloity, standard and its variation oeiient are the ollowing. 5 7 V 6 / s ( 6 5) ( 6 7).4/ s V v V Standard or water low is deterined by the Forula (7). V 6.5 b V / s g 9.8 V 6.7 b / s g 9.8 5

6 MATE Web o onerenes 7, 0004 (07) DOI: 0.05/ ateon/ XXVI R-S-P Seinar 07, Theoretial Foundation o ivil Engineering vv V The distribution o statistial harateristis [-5] should be used to deterine the reliability o engineering ailities. 4 Disussion To deterine the ailure o a bridge, you ust subtrat one distribution ro another, that is, Fig.. ( ) ( ) Fig.. Distribution o bridge ailures. The dierene in these distributions will give the harateristi presene o zero on the absissa axis, whih divides the area below the distribution line into two parts, the risk is on the let while the reliability is on the right [6-7]. To deterine zero it is neessary to ind the value o Z. At that we ind Z or average and with probability value hour,, 4%, (8), Fig.. (8) Z R P Fig.. Total bridge ailure distribution. 0 6

7 MATE Web o onerenes 7, 0004 (07) DOI: 0.05/ ateon/ XXVI R-S-P Seinar 07, Theoretial Foundation o ivil Engineering 4% % % % R R P ( ) R ,7 ( 0.697) , R ( 0.58) ( 0.47 ) R ( ) The probability o exeeding hour under the bridge or the ategory II road is %. The bridge ailure should be 0.0 or %, thus the reliability is V 6.5 b V / s g 9.8 V 6.7 b / s g 9.8 R P R ( ).07 (.5 ) It is evident that the speiied bridge opening b0 is not able to provide the passage o the stor drain with the neessary probability degree o ailure even i the probability value hour is 4%. Thereore or the given exeedane interval hour and it is neessary to alulate the required bridge length by using a pik ethod. It has been onired by the latest alulation studies. 5 onlusions The reliability o eah o the oponents o roads and engineering strutures on the is a great task. The reliability o the road is dierent depending upon the season. Thus it should 7

8 MATE Web o onerenes 7, 0004 (07) DOI: 0.05/ ateon/ XXVI R-S-P Seinar 07, Theoretial Foundation o ivil Engineering be deterined or spring-suer and autun-winter periods. These estiates are independent. For solving it you should: - know the ators that ake up the paraeters o roads and engineering ailities; - ake sequential and parallel onnetions; - deterine the statistial ators; - evaluate the reliability o eah ator. The alulations got in the researh ake it possible to alulate the optiu length o a bridge opening with a speiied reliability level o water runo under the bridge. Reerenes..G. Gordovskaya, Urban onstrution and Arhiteture, 7-80 (05) doi:0.767/vestnik A.N. Davydov, Tradition and Innovation in Building and Arhiteture, 6-65 (05). A.N. Davydov, Tradition and Innovation in Building and Arhiteture, 6-0 (06). 4. T.V Doridontova, Monograph, Sibak, 5 (05) 5. T.V. Doridontova, Internet journal Naukovedenie, (05) 6. T.V. Doridontova, Patent to Useul Model 6045 (06) 7. S.V. Evdokiov, Sientii Survey, 0-07 (05) 8. B.G. Ivanov, Ways o Iproving the uality o Roads, 07- (05) 9. B.G. Ivanov, Tradition and Innovation in Building and Arhiteture, 6-7 (0) 0. B.G. Ivanov, Tradition and Innovation in Building and Arhiteture, 47 (0). E.I. Marinin, Urban onstrution and Arhiteture 4, (04) doi:0.767/vestnik V.A. Pavlova, Ways o Iproving the uality o Roads, (05). V.A. Pavlova, Tradition and Innovation in Building and Arhiteture, 56-6 (05) 4..V. Pavlova, Urban onstrution and Arhiteture, 96-0 (06) doi:0.767/vestnik V. Pavlova, Ways o Iproving the uality o Roads, (05) 6. A.V. Filatova Ways o Iproving the uality o Roads, 06- (05) 7. A.V. Filatova, Sientii Survey 7, 5-56 (05) 8