Improvement technology of water regulation and methods of calculating the parameters of modular drainage systems on the lands of the humid zone

The article examines water regulation on drained lands by innovative modular drainage systems with multi-level connection of regulating drains, diagrams of their design parameters are given. The main goal of the article is to demonstrate the results of analytical studies of water regulation by drainage modules under the condition of laying drains at different depths are given. The equations derived in this article allow you to use them to calculate the distance between regulating drains of different installation depths, perfect in terms of the degree and nature of the opening of the aquifer during infiltration water supply within drainage modules. Variants of the application of methods for calculating the parameters of regulatory drainage modules are proposed, which allow predicting groundwater level regimes, establishing watershed lines between perfect shallow-deep drains.


Introduction
Most of the drainage systems operated in Ukraine were built more than 30 years ago.On many of them, the drainage does not work as necessary, and therefore the optimal water regime is not observed.This is due to the physical wear and tear of the elements of the drainage system or violation of the rules of operation of the drainage system or a change in the direction of agricultural use of the drained lands themselves.Another possible reason is the low quality of construction [1,2].Therefore, for the successful use of territories with constructed but defective drainage, it is often necessary to carry out restoration works, which will ensure the optimal water regime of the soil, and, accordingly, agricultural production at the required level.However, approaches to design have changed, new, in certain cases, more effective designs of drainage systems have appeared.Climate change must also be taken into account.So, the current state of water management systems in the humid zone requires new effective approaches to both construction and reconstruction [1][2][3][4], as well as to the design of regulatory drainage networks [5].
In order to effectively regulate the water regime of the soil, we have proposed new innovative designs of closed regulatory drainage networks, which include drainage modules from periodically repeated drains with different laying depths (figure 1).
Conducted experimental studies show that regulatory networks, which include drainage modules, have a greater hydrological effect than their counterparts and allow to unload the upper layers of the soil from excess infiltration water in a faster time, which is especially important Figure 1.Scheme for calculating groundwater levels between shallow and deep drains during infiltration feeding (the deep drain is located on the waterproof layer, the shallow one is above the waterproof layer), the A-point of the water separation between shallow and deep drains.
during critical periods of the operation of drainage networks (the period of spring floods and the period of summer torrential rains).
Equally important for regulating the water regime of the soil is the calculation of the parameters of the adopted drainage schemes.

Materials and methods
If the drainage network is reinforced with additional drains, then in this connection Oleynyk [6,7] proposes a method of filtration calculation of drainage for irrigation arrays.Approximate calculations of such drainage are based on the method of filtration resistances [6].In the case of imperfect drains by the degree of opening of the aquifer (the drains are above the waterproof layer) and imperfect drains by the nature of the opening of the aquifer (the drains are protected by filtering material), a linear equation is used to predict and calculate the position of groundwater levels when constructing the technique of filtration resistances in any intersection of the filtration flow.

Results and discussion
We will calculate the parameters of the regulating drainage module during infiltration water supply of perfect drains of shallow and deep laying (shallow laying drain -perfect according to the degree and nature of the opening of the aquifer, deep -perfect according to the nature of the opening of the aquifer).
Consider the steady, uniform movement of the filtration flow of water in the directions of the deep and shallow drains (from point A, figure 1) of the regulating drainage module in homogeneous soil.
The calculation of the mode groundwater level (for the circuit in figure 1) can be performed on the basis of the Boussinesq's equation, which includes partial derivatives where ε i -vertical infiltration of water, k f -soil filtration coefficient.Since h = h (x), the equation ( 1) includes ordinary derivatives and will be written in the form Dividing the variables of equation ( 2), we find and after integration we get In the case of water infiltration, when ε i > 0, we obtained equation ( 5) -the equation of an ellipse.
Let's determine the constants C 1 and C 2 separately for a deep drain arranged on a waterresistant layer and a shallow hanging drain imperfect in degree and perfect in nature of the opening of the aquifer.
Since when x = 0, h = 0 and when x = l 1 , h = h 0 , then from equation ( 5) we find where Substituting the values of the constants C 1 and C 2 into the equation ( 5), we get After simple transformations in accordance with (figure 1), we make sure that equation (8) defines an ellipse centered on the axis 0x at the point x So, where x is the abscissa of the point of the largest h 0 value for a deep drain.Assuming in equation (10) that x = l 1 , we find where For an imperfect shallow drain when x = l 1 , h = h 0 − m 2 , and when x = l 1 + l 2 , h = m 2 , then from equation (4) we find where Substituting the determined values of the constants into the equation ( 17), we obtain The equation ( 18) is the equation of an ellipse.
The abscissa x is the point of the largest h 0 value for a shallow drain Taking into account the value of A, we get where or After solving the biquadratic equation ( 23), we get Then the total distance (figure 1) between the drains of shallow and deep laying L = l 1 + l 2 .
If in (25) in the root expression , and h 0 = 2t 2 , then l 2 = 0 (if there is a sign before the root (-) and if we take a sign before the root (+)), then The total distance (figure 1) between the drains of shallow and deep laying L The largest value of h = h 0 (figure 1) can be determined at the point with the abscissa L + L .The value of the ordinate h(x) at an arbitrary value x can be determined using (28).
The resulting equations (13), (27) were studied for the possibility of using them to calculate the distance L between perfect regulating drains of shallow-deep laying according to the degree and nature of the opening of the aquifer during infiltration water supply.Equations ( 13), ( 27) and (29) include rather relative, interdependent values of l 1 , l 2 and h 0 .
Analyzing the equation (29), it can be argued that it has an advantage over (8) because it includes only two given values -the distance between the drains L and the hanging height m 2 of an imperfect drain of shallow laying above the waterproof layer.
Thus, the given methods of calculating the parameters of regulating drainage modules operating in the mode of intensive reduction of groundwater level during infiltration water supply in the case of established groundwater filtration allow to predict groundwater level regimes and calculate the distances between drains of shallow-deep laying perfect in terms of the degree and character of the opening of the aquifer.

Conclusions
• According to the results of theoretical and experimental research, generally accepted methods and mathematical models describing the movement of water in the soil have been improved.• Calculations of the parameters of the drainage modules make it possible to predict the groundwater level regimes between perfect and imperfect (material) drains of shallow-deep laying, as well as to obtain the position of the groundwater level in dynamics and in the time during which the groundwater level decrease from the surface of the earth to a depth equal to the drainage rate.• The methods obtained theoretically and experimentally should be used to calculate the distances between perfect and imperfect (material) drains of shallow and deep laying according to the degree and nature of the opening of the aquifer during infiltration water supply.