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Published on 02 February 2021

# MATHEMATICAL MODELING OF WATER WAVE MOTION IN A RESERVOIR CAUSED BY THE INTRUSION OF A LANDSLIDE ARRAY

## I. D. Muzaev, V. G. Sozanov

The construction of dams and reservoirs in mountainous and foothill areas poses a number of urgent tasks for designers and researchers related to the wave movement of water in a reservoir with a complex geometric configuration. The collapse of significant masses of rock into the reservoir basin as a result of a landslide phenomenon provokes high surface waves, leading to catastrophic natural disasters in the form of victims and destruction. Designers, construction organizations and maintenance services are required to assess the expected wave increase in water level through the dam crest, as well as the zone and degree of flooding of the area in the reservoir bays and along the river gorge, depending on the geometric, kinematic and dynamic characteristics of potentially possible landslide massifs, mudslides and avalanche flows. In this way, you can predict and then prevent or mitigate the consequences and damage that can cause the formation of destructive waves. In addition to the above problem, this article develops a mathematical model of the wave movement of water in a reservoir, when the movement is caused by the intrusion of a landslide rock mass or a high-speed mudflow into its bowl. The model is the initial boundary value problem of hydrodynamics and hydraulics of gravitational waves. In contrast to previous works, the developed mathematical model takes into account the planned non-prismatic configuration of the reservoir and changes in the water depth in the longitudinal direction of the reservoir. Taking these factors into account significantly clarifies the numerical values of the amplitude of the wave formed, as well as the values of the flow rate, speed and volume of water poured over the dam crest. In the General initial-boundary value problem, the coefficients of the main differential equation are variables that depend on the spatial coordinate. In the General formulation, this creates great difficulties in the analytical solution of the problem and has not been solved by anyone in the whole world to date. In this article was found and applied original and effective substitution, i.e. replacing a variable that in two special cases based on the coefficients from the spatial coordinates that led basic differential equation initial-boundary value problem to the equation with constant coefficients, and thus substantially easier way of solving the initial-boundary value problem. In the above-mentioned special cases, the initial-boundary value problem is solved by strict analytical methods of mathematical physics. For each case, a set of calculation formulas is obtained for calculating the amplitude of the waves formed, as well as for the flow rate and volume of water poured over the dam crest.

 City Vladikavkaz Country Russia UDC 532 (075.8) Issue 2020, № 4 (Т. 12) Key words Displacement wave, initial boundary value problem, Fourier method, dam relief, slope safety margin, geotechnical characteristics of slopes, landslide array.
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Tags: волна вытеснения, начальнокраевая задача, метод Фурье, бьеф плотины, запас устойчивости откоса, геотехнические характеристики откосов, обвально-оползневый массив.

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ISSN 1998-4502 (Print)                                                            ISSN 2499-975Х (Online)