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

Current trends in construction are aimed at providing reliability and safety of engineering facilities. According to the latest government regulations for construction, the scientific approach to engineering research, design, construction and operation of construction projects is a key priority. The reliability of a road depends on a great number of factors and characteristics of their statistical compounds (sequential and parallel). A part of a road with such man-made structures as a bridge or a pipe is considered as a system with a sequential element connection. The overall reliability is the multiplication of the reliability of these elements. The parameters of engineering structures defined by analytical dependences are highly volatile because of the inaccuracy of the defining factors. However each physical parameter is statistically unstable that is evaluated by variable coefficient of their values. It causes the fluctuation in the parameters of engineering structures. Their study may result in the changes in general and particular design rules in order to increase the reliability. The paper gives the grounds for these changes by the example of a bridge. It allows calculating its optimum length with a specified reliability level of water runoff under the bridge.


Introduction
At present, safety and reliability of construction engineering facilities on roads is a matter of great concern. The paper reports on the reliability of a road that includes the reliability of its elements-road surfacing, geometric elements, man-made structures [1][2][3][4][5][6][7].
The reliability is closely related to the probability of failures or risks. The reliability of an auto-road and man-made structures on it is much less important, less durable and has absolute serviceability.
The low reliability of a road depends on a large number of factors and characteristics of their statistical sequential and parallel compounds. A part of a road with such man-made structures as a bridge or a pipe is considered as a system with a sequential connection of elements. The overall reliability is the multiplication of the reliability of these elements. In this regard, the methodology proposed in this research work aimed at determining the optimum length of the bridge opening with a specified reliability level of water runoff seems to be relevant.

Materials and Methods
In order to provide the reliability of slopes stabilized with soil, its gradient m should correspond to the calculated shift angle ȥ, Formula (1): where, Ʉ Ɂ -assurance coefficient (Ʉ Ɂ = 1, as it corresponds to the limit state); ĳ -angle of internal friction; ɫ -adhesion; It should be noted, the reliability is calculated as follows, Formula (3): To determine the reliability of superelevation Formula (4) should be used.
Where: V -car speed in superelevation; g -acceleration of gravity (g = 9,81 m/s 2 ); Rturning radius (R min =800 m for a road of Category II); M -sideway force coefficient; C IIcoefficient of adhesion of car wheels with the ground. Then standard for the superelevation gradient should be calculated by (5).
Then a bridge capability is calculated. To determine the probability of exceeding the flow through the specified bridge section the following formula should be used (6) . 1 (6) Where, H = 1,45V C /g -head of water; V C -flow velocity under the bridge; g -acceleration of gravity (g = 9,81 m/s 2 ); b -width of the bridge.
Standard for water flow should be calculated by the derivative V C, Formula (7).
It should be noted that the reliability of a road and its engineering facilities depends on a number of parameters described above. The authors have assessed the statistical characteristics and parameters of a road and engineering facilities derived from the statistical distributions [8][9][10]. The statistical data on the material properties, geometric dimensions of road elements and engineering structures, and their statistical distribution acted as the initial data. On their basics the distribution of the analyzed parameters is made by using standardized force deformation relationship [11]. The authors prove this statement by the example providing the following results.
Then the standards are found for Ȗ, ĳ, c Then the reliability is determined by the following: Then the reliability of a bridge capability is calculated, Formula (6).
The distribution of statistical characteristics [12][13][14][15] should be used to determine the reliability of engineering facilities.

Discussion
To determine the failure of a bridge, you must subtract one distribution from another, that is Q ɋ -Q L , Fig.1. The difference in these distributions will give the characteristic presence of zero on the abscissa axis, which divides the area below the distribution line into two parts, the risk is on the left while the reliability is on the right [16][17].
To determine zero it is necessary to find the value of Z. At that we find Z for Q L average and ı Ʌ with probability value hour ɚ 1,2,3 ɢ 4%, (8), It is evident that the specified bridge opening b=10m is not able to provide the passage of the storm drain L Q with the necessary probability degree of failure even if the probability value hour ɚ is 4%. Therefore for the given exceedance interval hour ɚ and L Q it is necessary to calculate the required bridge length by using a pick method. It has been confirmed by the latest calculation studies.

Conclusions
The reliability of each of the components of roads and engineering structures on them is a great task. The reliability of the road is different depending upon the season. Thus it should be determined for spring-summer and autumn-winter periods. These estimates are independent. For solving it you should: -know the factors that make up the parameters of roads and engineering facilities; -make sequential and parallel connections; -determine the statistical factors; -evaluate the reliability of each factor. The calculations got in the research make it possible to calculate the optimum length of a bridge opening with a specified reliability level of water runoff under the bridge.