MODELS FOR DETERMINING MAXIMUM DEGREE FILLING CHANNELS OF CIRCULAR SECTION SHAPE

Objectives The task was to obtain a model for determining the maximum possible degree of filling the circular section channels in the earthen channel based on the condition of ensuring the stability of slopes and the minimum volume of excavation during their construction, as well as finding the optimum degree of filling fortified channels of a closed profile corresponding to maximum throughput.

Method In work analytical methods of differential calculus and the solution of implicit equations are used.

Result The experience of domestic and foreign researchers was taken into account to solve the set tasks, select research methods and criteria for optimizing channel parameters. Two cases of circular-shaped channels are considered: 1) in the earth channel, 2) reinforced with a closed transverse profile. For the case of a hydraulically most advantageous circular channel in the earthchannel channel, equating the first derivative of the equation of a circle with the reciprocal of the allowable embedding coefficient of the slopes obtained an analytical solution for determining the maximum degree of filling from the slope stability condition, which was not dependent on hydraulic flow elements. In the case of non-cohesive soils that form the channel, the circular channel can be filled to a depth not exceeding 20 percent of the channel radius. At the same time, the average flow rate should remain in the range from non-venting to non-blurring. In order to be able to determine the flow rate, analytical expressions are given for finding hydraulic flow elements in a circular channel. When determining the volume of excavation for the construction of the channel, the excess of the channel edge above the maximum water level in the channel was taken into account. For the case of a fortified channel of a closed transverse profile, by taking the derivatives from the Chezy formula, we obtained the optimal values of flow rate and average velocity.

Conclusion A fortified closed circular profile channel has a maximum capacity with a relative degree of filling of 0.938, and the maximum average velocity of a fluid in a pressureless channel is achieved with a degree of filling of 0.815. To determine the maximum permissible relative degree of filling in the case of a circular section channel in the earthen channel, analytical dependences were obtained, before using which, according to the reference literature, it is necessary to take the value of the slope coefficient for this type of channel bed soil. 

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