Theoretical substantiation of regular system of horizontal drains (a new approach)
The nonlinear problem of regulating the water-physical conditions of over-drained and over-wetted agricultural lands through a regular system of horizontal drains has been formulated and solved by analytical methods. The dynamics of groundwater reserves are analyzed in a generalized manner, rather t...
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Видавничий дім "Академперіодика" НАН України
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Poliakov, V.L. 2025-03-09T15:58:47Z 2023 Theoretical substantiation of regular system of horizontal drains (a new approach) / V.L. Poliakov // Доповіді Національної академії наук України. — 2023. — № 6. — С. 40-48. — Бібліогр.: 15 назв. — англ. 1025-6415 https://nasplib.isofts.kiev.ua/handle/123456789/202248 532.546:628.16 DOI: doi.org/10.15407/dopovidi2023.06.040 The nonlinear problem of regulating the water-physical conditions of over-drained and over-wetted agricultural lands through a regular system of horizontal drains has been formulated and solved by analytical methods. The dynamics of groundwater reserves are analyzed in a generalized manner, rather than locally as done previously. A dependence has been derived to describe the behavior of the water table averaged over the interdrain space, considering a targeted change in head within the drains. Based on this, a formula has been obtained for calculating the optimal drain spacing in both homogeneous and heterogeneous soils, taking into account the requirements for their water-physical state. An assessment was conducted on the uneven distribution of groundwater caused by the local action of horizontal drains. Examples with typical initial data illustrate the decrease in the average water table over time and demonstrate the potential for rarefaction of reclamation drainage using a new methodological approach. This approach will significantly reduce capital costs for its construction and reconstruction. Сформульовано та розв’язано аналітичними методами нелінійну задачу регулювання водного режиму переосушених та перезволожених сільськогосподарських земель регулярною системою горизонтальних дрен. Динаміка запасів ґрунтових вод аналізується узагальнено, а не як раніше локально. Виведено залежність, що описує поведінку середнього за міждренним простором рівня ґрунтових вод при цілеспрямованій зміні напору всередині дрен. На її основі отримано формулу для розрахунку оптимальної відстані між дренами в однорідному і неоднорідному ґрунтах, виходячи з вимог до водного режиму. Виконано оцінку нерівномірності розподілу ґрунтових вод, зумовлену локальною дією горизонтальних дрен. На прикладах із типовими вихідними даними ілюструється зниження осередненого рівня ґрунтових вод з часом, а також показано можливість розрідження меліоративного дренажу завдяки новому методологічному підходу, що дозволить значно економити капітальні витрати на його будівництво та реконструкцію. en Видавничий дім "Академперіодика" НАН України Доповіді НАН України Механіка Theoretical substantiation of regular system of horizontal drains (a new approach) Теоретичне обгрунтування регулярної системи горизонтальних дрен (новий підхід) Article published earlier |
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| title |
Theoretical substantiation of regular system of horizontal drains (a new approach) |
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Theoretical substantiation of regular system of horizontal drains (a new approach) Poliakov, V.L. Механіка |
| title_short |
Theoretical substantiation of regular system of horizontal drains (a new approach) |
| title_full |
Theoretical substantiation of regular system of horizontal drains (a new approach) |
| title_fullStr |
Theoretical substantiation of regular system of horizontal drains (a new approach) |
| title_full_unstemmed |
Theoretical substantiation of regular system of horizontal drains (a new approach) |
| title_sort |
theoretical substantiation of regular system of horizontal drains (a new approach) |
| author |
Poliakov, V.L. |
| author_facet |
Poliakov, V.L. |
| topic |
Механіка |
| topic_facet |
Механіка |
| publishDate |
2023 |
| language |
English |
| container_title |
Доповіді НАН України |
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Видавничий дім "Академперіодика" НАН України |
| format |
Article |
| title_alt |
Теоретичне обгрунтування регулярної системи горизонтальних дрен (новий підхід) |
| description |
The nonlinear problem of regulating the water-physical conditions of over-drained and over-wetted agricultural lands through a regular system of horizontal drains has been formulated and solved by analytical methods. The dynamics of groundwater reserves are analyzed in a generalized manner, rather than locally as done previously. A dependence has been derived to describe the behavior of the water table averaged over the interdrain space, considering a targeted change in head within the drains. Based on this, a formula has been obtained for calculating the optimal drain spacing in both homogeneous and heterogeneous soils, taking into account the requirements for their water-physical state. An assessment was conducted on the uneven distribution of groundwater caused by the local action of horizontal drains. Examples with typical initial data illustrate the decrease in the average water table over time and demonstrate the potential for rarefaction of reclamation drainage using a new methodological approach. This approach will significantly reduce capital costs for its construction and reconstruction.
Сформульовано та розв’язано аналітичними методами нелінійну задачу регулювання водного режиму переосушених та перезволожених сільськогосподарських земель регулярною системою горизонтальних дрен. Динаміка запасів ґрунтових вод аналізується узагальнено, а не як раніше локально. Виведено залежність, що описує поведінку середнього за міждренним простором рівня ґрунтових вод при цілеспрямованій зміні напору всередині дрен. На її основі отримано формулу для розрахунку оптимальної відстані між дренами в однорідному і неоднорідному ґрунтах, виходячи з вимог до водного режиму. Виконано оцінку нерівномірності розподілу ґрунтових вод, зумовлену локальною дією горизонтальних дрен. На прикладах із типовими вихідними даними ілюструється зниження осередненого рівня ґрунтових вод з часом, а також показано можливість розрідження меліоративного дренажу завдяки новому методологічному підходу, що дозволить значно економити капітальні витрати на його будівництво та реконструкцію.
|
| issn |
1025-6415 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/202248 |
| citation_txt |
Theoretical substantiation of regular system of horizontal drains (a new approach) / V.L. Poliakov // Доповіді Національної академії наук України. — 2023. — № 6. — С. 40-48. — Бібліогр.: 15 назв. — англ. |
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2025-11-26T01:45:46Z |
| last_indexed |
2025-11-26T01:45:46Z |
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1850606366760108032 |
| fulltext |
40 ISSN 1025-6415. Dopov. Nac. akad. nauk Ukr. 2023. No 6: 40—48
C i t a t i o n: Poliakov V.L. Th eoretical substantiation of regular system of horizontal drains (a new approach). Dopov. nac.
akad. nauk Ukr. 2023. No. 6. P. 40—48. https://doi.org/10.15407/dopovidi2023.06.040
© Publisher PH «Akademperiodyka» of the NAS of Ukraine, 2023. Th is is an open access article under the CC BY-NC-
ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)
МЕХАНІКА
MECHANICS
https://doi.org/10.15407/dopovidi2023.06.040
UDC 532.546:628.16
V.L. Poliakov
Institute of Hydromechanics of the NAS of Ukraine, Kyiv
E-mail: v.poliakov.ihm@gmail.com
Th eoretical substantiation of regular system
of horizontal drains (a new approach)
Th e nonlinear problem of regulating the water-physical conditions of over-drained and over-wetted agricultural lands
through a regular system of horizontal drains has been formulated and solved by analytical methods. Th e dynamics
of groundwater reserves are analyzed in a generalized manner, rather than locally as done previously. A dependence
has been derived to describe the behavior of the water table averaged over the interdrain space, considering a targeted
change in head within the drains. Based on this, a formula has been obtained for calculating the optimal drain spacing
in both homogeneous and heterogeneous soils, taking into account the requirements for their water-physical state. An
assessment was conducted on the uneven distribution of groundwater caused by the local action of horizontal drains.
Examples with typical initial data illustrate the decrease in the average water table over time and demonstrate the
potential for rarefaction of reclamation drainage using a new methodological approach. Th is approach will signifi cantly
reduce capital costs for its construction and reconstruction.
Keywords: drainage system, water table, regulation, calculation, spacing, saturated-unsaturated fl ow, water loss.
In relation to practical problems of regulating the water resources of agricultural and special-
purpose lands over large areas, regular horizontal subsurface drainage systems have demonstrated
high effi ciency [1, 2]. Depending on the water-physical state of the upper (biologically active) soil
layer and the requirements for water conditions, reclamation drainage, with appropriate techni-
cal support, can serve two functions: drainage (during early spring or aft er heavy precipitation)
or wetting (during dry periods). Th e quality of control of the groundwater fl ow is signifi cantly
reduced, even if the design of the drainage system allows you to quickly raise or lower the water
table (WT), due to the high hydraulic resistance of natural porous media and, as a consequence,
the curvature of the free surface and the uneven distribution of moisture reserves along it. Th us,
water-physical conditions near and away from the drains can diff er signifi cantly. It is obvious that
an objective idea of the total reserves of water available to crops on the territory of the drainage
system is provided by the average, and not the local position of the WT. Th erefore, the primary
objective of this article, and subsequent theoretical studies, is to enhance the methodology for the
41ISSN 1025-6415. Допов. Нац. акад. наук Укр. 2023. № 6
Th eoretical substantiation of regular system of horizontal drains (a new approach)
theoretical substantiation of dual-function drainage based on average characteristics of the regu-
lated water-physical state.
To comprehensively assess the consequences of drainage and potential yield reduction due to
uneven groundwater distribution between drains, introducing a specialized dispersion index makes
sense. Th is index would integrally characterize the deviation of optimal water-physical conditions
in drained soil from ideal conditions (strictly corresponding to existing standards). However, it is
necessary to initially correlate the depth of the WT with the yield of the cultivated crop.
Th e balance of water in the saturated zone (limited by the free surface and impervious bar-
rier) is maintained through the balance between the processes of interzone water exchange and
groundwater fl ow infl uenced by nearby drains. In an isotropic uniform (or layered) soil, this bal-
ance is described in the hydraulic approximation by the equation
2
2 ( )e
Uk W h
tx
∂ ∂
=
∂∂
, (1)
where h is the piezometric head (or WT), ek is the (eff ective) hydraulic conductivity, ,W U
characterize the groundwater resource and moisture reserves in the aeration zone. In the case of
hydrodynamic and structural imperfections of drains, jointly taken into account by means of the
hydraulic resistance Φ [3—5], the boundary condition is accepted [6]
0, 2 ( )d
Wx W W m
x
∂
= − Φ =
∂
, (2)
where dm is the head within the drain. Th e change in the head inside the drains is not taken into
account. For a regular drainage system with a drain spacing 2L , the condition is also accepted
, 0.Wx L
x
∂
= =
∂
(3)
In establishing the initial condition, given the typically extreme limitation and even uncer-
tainty of information about the initial position of the water table (WT) and moisture content in
the aeration zone, as well as the diminishing infl uence of groundwater fl ow dependence over time,
it is justifi ed to rely on the primary water reserves in the saturated zone. Th ese reserves in the
humid zone of Ukraine are the closest and main source of moisture available to plants. In general,
they can be characterized by a constant (average) value 0h , so that
00, .t h h= = (4)
To identify the patterns of water exchange between the saturated and unsaturated zones of the
soil, two fundamentally diff erent methodological approaches have traditionally been used. Imple-
menting a thorough approach requires labor-intensive experimental studies, involving complex
nonlinear mathematical models and numerical methods for their solution. It is evident that such
an approach is diffi cult to implement for specifi c water reclamation objects.
In order to determine the value U strictly, it is necessary to solve, in addition to the ground-
water fl ow problem, the complex nonlinear problem of (vertical) moisture transfer. Previously,
we utilized substantially nonlinear soil hydraulic functions (unsaturated conductivity, soil-water
42 ISSN 1025-6415. Dopov. Nac. akad. nauk Ukr. 2023. No 6
V.L. Poliakov
retention) for all types of fi ne-grained mineral soils based on the modern classifi cation, conduct-
ing numerous numerical calculations. As a result, it was found that the intensity of water exchange
between saturated and unsaturated zones depends primarily on the position of the WT and to a
lesser extent on the speed of its movement [7, 8]. Th is implies that it is legitimate to use the second
approach in applications, requiring less initial data, simpler experimental techniques, and allow-
ing the use of analytical methods. Th erefore, in engineering developments to regulate the water-
physical conditions of lands in the humid zone, it is recommended to use a simplifi ed approach,
which is based on the representation
( ) ( )W
hU h h
t t
∂ ∂
≈ μ
∂ ∂
, (5)
where ( )W hμ exactly under conditions of quasi-stationary moisture transfer and approximately
under non-stationary conditions equals U h∂ ∂ and, depending on the functional purpose of the
drainage, characterizes either soil saturation (diff erential water loss) or wetting (lack of satura-
tion). Signifi cant eff orts were made to create an appropriate information base, with special atten-
tion given to diff erential water loss or lack of saturation and their averaged analogues [9, 10].
It is crucial to note that errors in the modern techniques arising from the formal simplifi -
cation of diff erential water loss techniques were previously theoretically and experimentally as-
sessed, typically falling within the accuracy of experimental methods. However, the feasibility of
further developing the applied theory of reclamation drainage in a methodological sense seems
evident, considering the scale of land water reclamation and the usual limitation and unreliability
of initial information.
Th e choice of the objective function is fundamentally important when modeling the regula-
tion of the water-physical state against the background of drainage. In view of the close connec-
tion between the WT and humidity conditions on the waterlogged lands, it is suffi cient to take into
account the water-physical conditions and water reserves within the interdrain space, operating,
along with the head h , also with two spatially average values (parameters) ah and aU , namely,
0
1( ) ( , ) ,
L
ah t h x t dx
L
= ∫
0
1( ) ( , ) .
L
aU t U x t dx
L
= ∫ (6)
Moreover, it is proposed to ultimately focus on the characteristics ah , which allows limiting
oneself to a generalized understanding of the main water resource without delving into details at
a distance from drains or in their proximity. Th en the solution to problem (1)—(3) is represented
in the following form
2 2 4( ) ( )
2
a
d
e
dUx Lx LW h W m
k dt
− − Φ
= + . (7)
Applying the operator 1W − to (7), we obtain
2
1 2 4( , ) ( )
2
a
d
e
dUx Lx Lh x t W W m
k dt
− ⎡ ⎤− − Φ
= +⎢ ⎥
⎢ ⎥⎣ ⎦
. (8)
43ISSN 1025-6415. Допов. Нац. акад. наук Укр. 2023. № 6
Th eoretical substantiation of regular system of horizontal drains (a new approach)
Both sides of equality (8) are averaged over x
2
–1
0
1 2 4( ) ( )
2
L
a
a d
e
dUx Lx Lh t W W m dx
L k dt
⎡ ⎤− − Φ
= +⎢ ⎥
⎢ ⎥⎣ ⎦
∫ (9)
and then the operator U is applied. Th e result will be
2
–1 2 4( ) ( )
2
a
d
e
dUx Lx LU h U W W m
k dt
⎧ ⎫⎡ ⎤− − Φ⎪ ⎪= +⎢ ⎥⎨ ⎬
⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭
. (10)
Averaging expression (10) also over the interdrain space gives
2
–1
0
1 2 4( )
2
L
a
a d
e
dUx Lx LU U W W m dx
L k dt
⎧ ⎫⎡ ⎤− − Φ⎪ ⎪= +⎢ ⎥⎨ ⎬
⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭
∫ . (11)
Next, it is formally presented
adUp
dt
=
and both sides of equation (11) are diff erentiated with respect to t . Th us, the following problem
is formulated regarding p
( )d dpp p
dp dt
= Ψ , (12)
00,t p p= = , (13)
where
2
–1
0
1 2 4( ) ( )
2
L
a
d
e
dUx Lx Lp U W W m dx
L k dt
⎧ ⎫⎡ ⎤− − Φ⎪ ⎪Ψ = +⎢ ⎥⎨ ⎬
⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭
∫ ,
0p is determined by selection from equation (9), namely,
2
–1 0
0
0
1 2 4( )
2
L
d
e
x Lx LW W m p dx h
L k
⎡ ⎤− − Φ
+ =⎢ ⎥
⎢ ⎥⎣ ⎦
∫ . (14)
Finally
0
( ) ( )
p
p
d dt p
d
ζ
= Ψ ζ
ζ ζ∫ . (15)
Th e representation ( ) aW h h h= is considered as an example. Th en the expression for h ac-
cording to (8) will be
2 2 4( , ) .
2
a
d
e a
dUx Lx Lh x t m
k h dt
− − Φ
= + (16)
44 ISSN 1025-6415. Dopov. Nac. akad. nauk Ukr. 2023. No 6
V.L. Poliakov
Th is implies
2 2 6( )
2 4 3
d d a
a
e
m m dUL Lh t
k dt
+ Φ
= + − . (17)
By analogy with (11) we obtained
2
0
1 2 4 .
2
L
a
a d
e a
dUx Lx LU U m dx
L k h dt
⎛ ⎞− − Φ
= +⎜ ⎟⎜ ⎟
⎝ ⎠
∫ (18)
Th e dependence ( )t p has the form (15), where
2 2 4( )
2 ( )d
e a
x Lx Lp U m p
k h p
⎛ ⎞− − Φ
Ψ = +⎜ ⎟⎜ ⎟
⎝ ⎠
,
0 0
0 2
( )
3
6
d
e
h h m
p k
L L
−
= −
+ Φ
. (19)
Th e calculation scheme is implemented as follows: for a given parameter p , it is sequentially
calculated 0p from (19), t and ah from (15) and (17), respectively. If necessary, the WT is calcu-
lated in accordance with (16).
Th e main design parameter is determined from the condition [11, 12]
* *, at t h M S= = − , (20)
where M is the thickness of the soil horizon (from the impervious barrier to the soil surface),
*S is the depth to which it is necessary to lower the WT in time *t . Great number of works are
dedicated to the theoretical substantiation of the drain spacing [13—15]. Th e indicated values
* *,t S and the required spacing correspond to the parameter *p , which is expressed in the fol-
lowing way:
2
* *
* 2
( ) ( )
( ) 3
6
d
e
M S m M S
p L k
L L
− − −
= −
+ Φ
. (21)
Expressions (19), (21) are substituted into (15) and, thus, an equation is derived for L
*
0
( )
*
( )
( , )
p L
p L
d dL t
d
ζ
Ψ ζ =
ζ ζ∫ . (22)
Th e fundamental diff erence in the previously used and new approaches to solving the basic
problems of reclamation drainage lies in the interpretation of ah . While previously, the parameter
ah played an auxiliary role, and its approximate value was established in advance based on drain-
age conditions and requirements for the favorable water-physical conditions, now this value is
initially unknown, and ultimately serves as the main (generalized) indicator of the water-physical
state of the soil. Based on the ah dynamics, the optimal values of the most important design (2 )L
and technological (head within the drain for wetting) parameters are then justifi ed.
45ISSN 1025-6415. Допов. Нац. акад. наук Укр. 2023. № 6
Th eoretical substantiation of regular system of horizontal drains (a new approach)
It is possible to signifi cantly simplify the calculation expressions without seriously reducing
their accuracy if the water exchange between the saturated and unsaturated zones is approximate-
ly described in accordance with (5) as follows
( )a a
W a
U hh
t t
∂ ∂
≈ μ
∂ ∂
. (23)
Th us, it is assumed that the rate of water exchange mentioned above remains constant
throughout the entire interdrain space and only changes due to the average movement of the
water table (WT).
Th e system of equations involving , ,ah p t (15), (17) plays a key role in calculating the eff ect
of regular drainage. In the case of the simplifi ed representation (23), which is traditional for the
applied theory of reclamation drainage, the specifi ed system is reduced to a dependence of ah on
t in the form of the following inverse function
02
2
( )( 4 )
3
a
h
W
e dh
L Lt d
k m
μ ζ+ Φ
= ζ
ζ − ζ∫ . (24)
With the known dynamics of the average WT, its actual change between the drains according
to (8) is described by the formula
2
2
3( , ) ( 2 4 )[ ( ) ].
2( 4 )d a dh x t m x Lx L h t m
L L
= − − − Φ −
+ Φ
(25)
Th en, for a given standard regulation period *( )t and rate *( )S , it is proposed to calculate the
optimal spacing L using the formula
0
*
2*
2
3 9 3
( )
e
h
W
dM S
k tL
m−
= + Φ − Φ
μ ζ
ζ − ζ∫
. (26)
If we operate with a constant value Waμ (but varying depending on ah ), then expressions
(24)—(26) are signifi cantly simplifi ed. Th us, function (24) reduces to this form
2 0
0
( )( 4 ) ( )
ln
3 ( )
Wa a a a d
e d a a d
h L L h h m
t
k m h h m
μ + Φ −
=
−
. (27)
Th en the drain spacing should be found using the formula
2*
0
*
* 0
*
3 9 3
( )
( )ln
( )( )
e d
a d
Wa
a d
k m tL
h M S m
M S
h m M S
= + Φ − Φ
− −
μ −
− −
. (28)
46 ISSN 1025-6415. Dopov. Nac. akad. nauk Ukr. 2023. No 6
V.L. Poliakov
Due to the localization of the infl uence of drains, the question naturally arises about the con-
sequences of the inevitable and possibly noticeable diff erence in the depth of the WT for water
consumption of crops. A primary representation can be obtained by calculating the total deviation
of the WT from its average (optimal) position between the drains. It is proposed to calculate the
corresponding dispersion index LSΔ in relation to drain system as follows:
*
*0
1( ) [ ( ) ( , )] [ ( , ) ( )]
x L
L a a
x
S t h t h x t dx h x t h t dx
L
⎧ ⎫⎪ ⎪Δ = − + −⎨ ⎬
⎪ ⎪⎩ ⎭
∫ ∫ . (29)
where *x is from the condition *( , ) ( )ah x t h t= . In this case, the coordinate *x does not depend
on time and will be
*
11
3
x L⎛ ⎞
= −⎜ ⎟
⎝ ⎠
. (30)
Th en, taking into account the expression for ( , )h x t (25), the pattern of reduction of LSΔ over
time follows from (29)
( ) 0,075 [ ( ) ].
6L a d
LS t h t m
L
Δ = −
+ Φ
(31)
If it is possible to link LSΔ to a decrease in crop productivity due to unfavorable water-physi-
cal conditions, it becomes feasible to evaluate the decrease in yield resulting from the peculiarities
of groundwater fl ow against the background of regular horizontal drainage.
To illustrate the calculation dependencies derived above and, crucially, to clarify potential sav-
ings in capital costs due to transitioning from a local assessment of reclamation drainage effi ciency
to a generalized assessment, serial calculations were performed. Th eir subject was the reduction of
the WT on average ( )ah and in the middle between drains ( )Lh , as well as a key design parameter
( )L . Initially, the coeffi cient ek (1 m day , the structure of the soil horizon was not detailed) was
fi xed; diff erential water loss according to available experimental data (Institute of Water Problems
and Land Reclamation) was taken in linear form, namely, ( ) 0,15( )W h M hμ = − , and its averaged
analogue ( ) 0,075( )Wa h M hμ = − . Th e thickness of the soil horizon varied discretely (1, 2, 4 m).
Th e depth of the drains, that were constructively perfect, at was given 1 and 1,2 m, respectively.
Th us, in the fi rst case, the drainage was hydraulically perfect, and in the second and third cases,
it was hydrodynamically imperfect. Th e corresponding values of Φ were calculated according to
the recommendations of [4] and amounted to 1 and 3,5 m.
Th e dynamics of WT were characterized by its decrease in values ah and Lh . Th e correspond-
ing graphs were calculated at 4, 2,8 mdM m= = and shown in Fig. 1. At each calculation step,
the value ah (or Lh ) was specifi ed, and then the corresponding value of t was determined in
four ways. In this case, the appropriate values of Φ and Waμ were previously calculated. From a
formal point of view, the solution obtained by averaging the supply of the groundwater fl ow over
the interdrain space seems more reliable. Widely practiced in theoretical developments on recla-
mation drainage, the identifi cation of diff erential water loss (or lack of saturation) ( )W hμ with
subsequent reference to the critical section of the groundwater fl ow, and in the case under consid-
47ISSN 1025-6415. Допов. Нац. акад. наук Укр. 2023. № 6
Th eoretical substantiation of regular system of horizontal drains (a new approach)
eration, also with its similar averaging and, fi nally, additional dynamic averaging (corresponding
to ( )W Lhμ , ( )W ahμ , ( )Wa ahμ ) cause an increase in calculating errors. Th erefore, the fi rst, two-
parameter solution is justifi ed to be considered as the basis for subsequent comparative analysis.
Th e feasibility of such an analysis and the revealing nature of its results follow from methodologi-
cal considerations. Th e low position of curve 4 and its slight deviation from the other curves is
natural due to the relatively small curvature of the free surface. Such curves are in close proximity
to each other and diverge minimally only during prolonged drainage. Particularly noteworthy is
the proximity and the intersection of curves 1 and 2 precisely at groundwater depths that provide
water-physical conditions favorable for agricultural production in the aeration zone. Th erefore,
judging by the results of calculations of the drainage eff ect, it can be recommended to use, along
with a two-parameter solution, a signifi cantly simpler solution, which involves dynamic averaging
of diff erential water loss and is expressed by dependencies (23), (24) and formula (25).
In the second series of calculations, the parameter L was calculated as a function of time *t .
In this case, formulas, were based on new ( )L and traditional 0( )L approaches, were used to assess
assessing the drainage resource of drain system, respectively (22), (24) and from [6]. Th e results
of calculations of this value are presented in Fig. 2 in graphic form. Th e curves of the dependence
*( )L tΔ , where 0 0( )L L L LΔ = − , clearly demonstrate the feasibility of correcting the drain spac-
ing determined from the results of the analysis of the water-physical state in the middle between
the drains. If we focus exclusively on the total water reserves in both zones and their even distribu-
tion between the drains, then a noticeable rarefaction of drainage and, as a consequence, a corre-
sponding reduction in the cost of its design are possible. Th e indicated savings turn out to be more
signifi cant for thin soil horizons and longer drainage time. Th e value LΔ reached a maximum
value of 0,23 in the case of 1M = and * 8 days.t =
Th erefore, the new approach is more conceptual in terms of information since it takes into
account the water-physical state, although in general, of the entire of drained (wetting) land.
M-ha, L
1 2 3 40.6
0.4
0.2
0 1.5 3.0 4.5 6.0 t, day
ΔL 1
2
3
4
0.20
0.15
0.10
0.05
0
2 4 6 t, day
Fig. 1. Decrease in WT on average and in the middle
between drains over time: 1—3 — aM h− , 4 — LM h− ;
1 — at ( )Wa ahμ using (27); 2 — using (15), (17); 3 — at
( )W ahμ using (24); 4 — at ( )Wa Lhμ according to [6]
Fig. 2. Dependence *( )L tΔ : 1, 2, 4 — at 0( )Wa M Sμ − ,
L using (28), 0L according to [6]; 3 — at 0( )W M Sμ − ,
L using (26), 0L according to [6]
48 ISSN 1025-6415. Dopov. Nac. akad. nauk Ukr. 2023. No 6
V.L. Poliakov
REFERENCES
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Russian).
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270.
3. Lennoz-Gratin, Ch. (1989). Effect of envelopes on flow pattern near drain pipe. J. Irrig. Drain. Engrg., ASCE,
115, No. 4, pp. 626-641. https://doi.org/10.1061/(ASCE)0733-9437(1989)115:4(626)
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105, No. 4, pp. 367-373. https://doi.org/10.1061/JRCEA4.0001274
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zones of light fine soils. Gidrotehnicheskoe stroitelstvo, No. 2, pp.191-199.
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of saturation. Land reclamation and water management, 19, pp.134-142.
11. Ivitsky, A. I. (1988). Foundations of design and calculations of drainage and drainage-wetting systems. Minsk:
Nauka and Tehnika (in Russian).
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Agropromizdat (in Russian).
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15. Wenyan, W., Bing, S. & Zhilu, L. (1994). Drain-spacing calculation considering influence of evaporation. J.
Irrig. Drain. Engrg., ASCE, 120, No. 3, pp. 563-572. https://doi.org/10.1061/(ASCE)0733-9437(1994)120:3(563)
Received 18.10.2023
В.Л. Поляков
Інститут гідромеханіки НАН України, Київ
E-mail: v.poliakov.ihm@gmail.com
ТЕОРЕТИЧНЕ ОБГРУНТУВАННЯ РЕГУЛЯРНОЇ
СИСТЕМИ ГОРИЗОНТАЛЬНИХ ДРЕН (НОВИЙ ПІДХІД)
Сформульовано та розв’язано аналітичними методами нелінійну задачу регулювання водного режиму пе-
реосушених та перезволожених сільськогосподарських земель регулярною системою горизонтальних
дрен. Динаміка запасів ґрунтових вод аналізується узагальнено, а не як раніше локально. Виведено залеж-
ність, що описує поведінку середнього за міждренним простором рівня ґрунтових вод при цілеспрямова-
ній зміні напору всередині дрен. На її основі отримано формулу для розрахунку оптимальної відстані між
дренами в однорідному і неоднорідному ґрунтах, виходячи з вимог до водного режиму. Виконано оцінку
нерівномірності розподілу ґрунтових вод, зумовлену локальною дією горизонтальних дрен. На прикладах
із типовими вихідними даними ілюструється зниження осередненого рівня ґрунтових вод з часом, а також
показано можливість розрідження меліоративного дренажу завдяки новому методологічному підходу, що
дозволить значно економити капітальні витрати на його будівництво та реконструкцію.
Ключові слова: система дрен, рівень грунтових вод, регулювання, розрахунок, відстань, насичено-ненасиче-
ний потік, водовіддача.
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