Improvement of the reliability and durability parameters of hydrotechnical structures under conditions of hydrodynamic influence of flows on structural elements

This article concerns the methodological issues of developing principles for increasing the reliability and durability parameters of equipment and auxiliary mechanisms of hydrotechnical structures. An analysis of the conditions ensuring an increase in the accuracy of engineering calculations of the viscosity of disperse systems is carried out. An analytical consideration of the effects of the particle shape on the calculation of the groundwater viscosity using the representations of particles of dispersed media as hydrodynamic dipoles is proposed. An equation for the viscosities of disperse systems is obtained with the determination of the shape factor of solid particles in a liquid. The comparison with the ratios for calculating the viscosity of ideal groundwater consisting of particles of a circular configuration indicates the possibility of reducing errors in calculating the coefficients of permeability of flow rates and pressures of filtration currents in underground horizons under the fluences of hydraulic structures. To improve the reliability of building structural elements operation of spillways without vacuum dams, a method of refined calculation of the dynamic effect of groundwater on the base of spillway dams and dams of the river bed is proposed.


Introduction
The viscosity of inhomogeneous media consisting of solid particles in a liquid is one of the characteristics of groundwaters affecting the parameters of their filtration, which determine the spatial variation of the depression pressure in the underground contours of hydraulic structures. The effect of dispersed phase particles on the viscous flow of groundwater and on the spatial variation of subterranean pressure is due to the fact that those layers of the moving aquatic environment that adjoin directly to the particles move only at the same rate as water [1]. This effect was taken into account for spherical particles in [2]. Taking into account that at a sufficient distance from the surface of the particle the flow has a constant velocity, and the particle itself moves along with the flow, the following relation is obtained for the viscosity of the disperse system: where  is the viscosity of the inhomogeneous medium;  -volume fraction of particles of the disperse phase; 0.5 is the coefficient of the shape of the spherical particles; оо     -relative viscosity.
In the following, the refined dependence of the viscosity with non-spherical particles in filter flows with different intensity of pressure and different orientation of the particles to the direction of flow was considered. As a result, an equation was obtained for the specific viscosity of a dispersive medium showing the increment of viscosity relative to a dispersed medium *  in which the shape of the particles was taken into account through a certain numerical coefficient Ф [3].
  oo * Ф         , where Φ is the empirical coefficient of the shape of the particles with a numerical value exceeding the value Φ = 0.5 and which depends not only on the shape of the particles but also on the gradient of the flow velocity and the orientation of the particles, leading to resistance to flow and pressure losses.
In subsequent work, studies of the viscosity of inhomogeneous media were extended to the case of droplet particles capable of taking a non-spherical shape. Experimental checks of the calculated ratios for the viscosity of inhomogeneous media indicated significant discrepancies with the calculations, especially for media with deformable particles of nonideal form [4]. In fact, there are still no adequate formulas for calculating the viscosity of groundwater with non-ideal solid particles, as applied to project evaluations of the effects of filtration currents on hydraulic plant fluids, although work in this direction does not stop [5; 7; 9]. It remains an open question about how to take into account the change in the tangential viscosity of an inhomogeneous medium with respect to a liquid medium in determining the dynamic interactions of groundwater flows with elements of hydraulic structures.

Viscosity of inhomogeneous medium
Let us turn to the determination of the dependence of the viscosity of porous media such as groundwaters on the conditions of non-ideal-like flow past a liquid medium. We consider the inhomogeneous medium to be a medium composed of two constituents, different in their physicochemical properties of solid particles, distributed in the liquid as individual elements of a volume of a non-ideal form. We represent an inhomogeneous medium in the form of a system of hydrodynamic dipoles. The velocity potential of such dipoles is: 12 We use the values 22 o W,  for calculating the energy, which in the process of filtration currents is converted into the heat of a homogeneous fluid. It is composed of energy losses E  due to a change in the rate of deformation of the flow and from energy losses s Е due to the viscous friction of the liquid against the surface of the particle. Energy It follows from the last equality that the dynamic viscosity coefficient of a disperse medium ()  is determined by the following formula: Formula (3) becomes Einstein's formula for the viscosity of the current inhomogeneous medium with particles of spherical shape at. In fact, for a uniform flow, the flow velocity will coincide with the tangential velocity of the streamlined body. If the body is a streamlined body, then the required velocity will be equal to the velocity at the point of tangency of the sphere lying at the end of the diameter drawn perpendicular to the direction of motion. In this case 12 R R r  , 11 12 22 Substituting these values into the formula for the form factor, we obtain 2 2r S 2    .

Acoustic viscometer of inhomogeneous medium
To determine the coefficients of viscosity and filtration of inhomogeneous media, acoustic viscometers are practically not used [6]. Meanwhile, they can be a very convenient means of field testing of the filtration characteristics of different media as applied to the refined definition of the parameters of the dynamic effects of groundwater flows on hydro constructions at the stages of preparation and formulation of design specifications [8].
The theory of acoustic viscometers is based on the system of hydrodynamic equations for inhomogeneous media. The system of hydrodynamic equations includes the equations of continuity, motion and state. Concerning the equation of continuity, it is necessary to assume that the entire volume occupied by the inhomogeneous medium is equal to v ; The volume occupied by the inhomogeneities is assumed to be equal to u -the real velocity of the inhomogeneous medium is analogous in sense of the filtration speed in hydrodynamics of porous media [10]. Suppose that this equality holds for any volume and that the number of particles is invariant, then the equation of continuity will look like this: The formula for the viscosity of disperse media allows, according to the usual rule, to form a tensor of viscous stresses and to write the equation of motion of groundwater in the form To solve the hydrodynamic problems of disperse media, the equation of motion is supplemented by the continuity equation and the equation of state Equations (4), (5), (6) are sufficient to solve the acoustic problem and to justify the acoustic viscometer. If we assume that during the transition through the acoustic front the continuity gap is sustained not by the physical-mechanical quantities entering the system of equations of hydrodynamics such as density, pressure and velocity, but only their spacetime derivatives of the first and second order, then the written equations can be applied to the apparatus Hadamard-Predvoditeleva [11]. Using this apparatus, we obtain the following expression for the complex velocity of ultrasound propagation: Here 1 с denotes the real part of the complex velocity, 2    the frequency of the ultrasonic sound. Selecting the imaginary and real parts, we find the following relations for the velocity and the absorption coefficient  : If we assign the obtained absorption coefficient to the absorption coefficient for a medium that does not contain particles, then we have: To evaluate the capabilities of the acoustic viscometer, comparative experiments were conducted to determine the viscosity with traditional Ostwald flow-through capillary viscometers. As a non-uniform medium, two-phase media consisting of particles of lycopodium in salted water were used.
The particle radius was 8 μm, the volume concentration 15%, the water temperature T = 21 ° C, the ratio of the wavelength of the ultrasonic oscillations to the particle radius was determined by the condition that corresponded to the Stokes acoustic dispersion mode with the proportionality of the absorption coefficient to the square of the ultrasound frequency. The ultrasound velocity was measured by the interferometric method, the absorption coefficient by the diffraction method [12]. Data on the absorption coefficient measurements and calculations with viscosity according to formulas with different shape factors are given in Table 1 and in Fig. 1. The value of the form factor Ф, according to formula (1) for the viscosity of two-phase media, corresponds to the assumption of spherically symmetric flow of particles in the process of percolation through the ground. In calculations with a relatively low value of the form factor, it means that in filtration the point at which the flow velocity is equal to the velocity of the incoming flow does not coincide with the surface of the particle. In our case, this point should be outside the particle at a distance of 16 μm from its center. This distance is less than the distance between the particles between the particles, which, for example, with a cubic arrangement of particles is 270 μm. It is not excluded that this circumstance can lead to discrepancies in the measurement data with the use of acoustic viscometers and data obtained by measurements with a flowing capillary viscometer. The performed viscosity measurements in the Ostwald viscometer have shown that the viscosity of the investigated inhomogeneous medium with particles of a non-ideal form has the value 4.7·10 -2 pz, which agrees with the data on an acoustic viscometer, which according to our measurements give a viscosity value of 4.5 · 10 -2 pz. With a shape factor 2 2r S 2  characteristic of ideal spherical particles, the coefficient of viscosity corresponding to our acoustic measurements was 1.12 × 10 -2 pz. Comparison of the measurement data of the viscosity of inhomogeneous media obtained by acoustic and capillary viscometers leads to the conclusion that in non-idealistic movements a non-ideal particle shape corresponding to the Poiseuille character of the flow of a two-phase medium is manifested.
At the same time, there remains the question of the calculation of the form factor independent of acoustic measurements and its solution requires separate consideration. According to Einstein's formula (1), the value of the form factor is determined by the flow conditions of solid particles by the current of the liquid medium in which they are located. The nature of the flow around depends on the concentration of particles in the liquid. An analysis of the results of measuring the absorption coefficient of ultrasound in the twophase medium studied by us (a particle of lycopodium in water) showed that the absorption increases with the concentration of particles linearly. This character of the dependence of (10) The obtained results showed the identity of the measurement data of the acoustic and capillary viscometers in the region of the Stokes dispersion with a quadratic dependence on the frequency of ultrasonic vibrations. On the basis of the results of many experiments carried out with various two-phase media, it is permissible to conclude that in the calculation of the dynamic parameters of groundwater filtration currents, a generalized hydrodynamic formula for the viscosity of two-phase media can be used that takes into account the nature of particles of different configurations flowing through the liquid medium.

Impacts of viscous groundwater currents on hydraulic structures
The tasks of non-pressure filtration flow of groundwater are of practical interest in the calculation of dynamic loads of hydraulic origin on various elements of hydraulic structures [13]. When the groundwater is stationary, their free surface is horizontal and the pressure on the structures is determined by the hydrostatic head. During the filtration motion, the free surface changes, decreasing along the flow. The contribution of the high-pressure head of the groundwater, depending on the viscosity of the inhomogeneous medium, creates additional loads on the foundations of the structures. The difficulties in obtaining an exact solution to the problems of non-pressure filtration by the definition of depressive changes in heads are associated with the uncertainty of the shape of the region occupied by the ground flow and the absence of relationships that take into account the influence on the filtration parameters of the head loss due to viscosity. The results presented in the previous sections of the paper on the calculation of the viscosity of inhomogeneous media make it possible to introduce refinements in the solution of the problem of determining the effect of viscous filtration currents on dam-free vacuum weirs of a practical profile. As a design object of the hydraulic engineering structure, the spillway of the waterworks has been chosen. The area of the underground filtration currents under the dam is presented in the diagram of Figure 2. The filtration in the base of the hydro constructions occurs under the action of the head h, equal to the difference in the water levels in the upper pool and the downstream.
h=∇b-∇н. (11) We will assume that the dam's flute, all along including the drain, the water-draining and the water-pipe are waterproof, and the outlet of the filtration flow into the lower tail is carried out through the holes in the apron. The characteristics of the filtration flow in any of its zones of the underground contour of the hydro construction can be determined using a hydrodynamic grid.  The results of calculations of the relative contribution of the velocity head to the total pressure of the non-pressure filtration flow in the underground contour of the hydro structure indicate a significant dependence on the shape of the particles. The relative contribution of the velocity head decreases when passing to filtration through a medium of a containing particle with an ideally spherical configuration (see Fig. 3).
With an increase in the effective viscosity of groundwater, there is a sharp decrease in the force load on the flute of the spillway dam ( Fig. 4 (a)).  The effect of the concentration of groundwater particles on the dynamic effect of filtration flow on the base of the hydro construction is clearly manifested with relatively low values of the particle density ( Fig. 4 (b)). As a percentage of the relative contribution of the velocity head Pu to the total pressure, it reaches values of the order of 20%, mainly for particles of irregular shape, characterized by relatively low values of the shape factor.

Conclusions
Based on the results of an analysis of the dynamic effects of the effective viscosity of inhomogeneous media on elements of hydro constructions, the following conclusion can be drawn. In calculations of groundwater pressures in the case of filtration without pressure on the elements of hydraulic structures, along with hydrostatic effects, take into account the dynamic effects of filtration flows, especially when particles with configurations other than spherical shape and relatively low concentrations are present in an inhomogeneous medium. Errors in assessing the levels of permissible hydraulic loads on the foundations of hydro constructions can reach values of the order of a tenth of a percent. The proposed formulas for determining the effective viscosity of inhomogeneous media and the method for estimating the piezometric loads on hydro structures can be recommended in the practical design of hydrotechnical construction sites.