Mathematical model for the duration of runoff formation determined from the road surface

Many scientists were engaged in the problems of studying the runoff formation conditions from the water-intake basins area and studying the operation of rainwater drainage systems and its calculations. Among them: Alekseev M. I., Belov М. М., Dykarevskyi V. S., Kurganov А. М., Zhuk V. M., Tkachuk S. G., Salchuk V. L., Tkatchuk O. A., Shevchuk O. V., Dziopak J., James W., Horton R., Huber W., Mays L. W., Rossman L. A., Weitman D. [1–9] and others. The drainage systems calculation is implemented based on empirical or semi-empirical studies for pipes or open water bodies. Unlike the generally accepted conditions for the urban city areas drainage elements calculation, highways have the features of runoff and the formation of maximum runoff. Artificial surfaces of surface runoff are characterized by low water absorption, significant longitudinal and transverse slopes. According to State Building Norms DBN V.2.3–4:2015 «Highways. Part I. Design. Part II. Construction», the largest longitudinal slope for a category I road is 40 %, the carriageway transverse slope on straight sections is 25 %. In the world of engineering practice there is no single generally accepted approach to the construction of hydrographs of rainwater inflow to surface drainage structures. Therefore, the question remains open in terms of establishing the estimated rain duration and the surface runoff volume from the roads surface in particular. To explore and establish the main factors and their parameters for the surface runoff formation from road surfaces. In engineering practice, forecasting the estimated rain duration is defined as the time from its beginning to the time of collection by the drainage system. This research is based on the prediction method and analysis of the factors, which influence the effluents movement on the coating surface of the linear in the plan water-intake basins. Conducting research with the forecasted natural meteorological phenomenon and at the minimum estimated rain intensity values according to climatic conditions of Ukraine. The analysis of known methods for duration of surface runoff formation determining performed. For its determination, it is suggested to take into account the surface wetting duration and the influence of the viscous component of the friction force between the runoff layers. An analytical dependence for the surface runoff formation duration determining for highways with asphalt concrete pavement and variable longitudinal slope in the ra