Próba określenia odwodnienia i retencji gleb spękanych

R O C Z N IK I G L E B O Z N A W C Z E , T. X X V , D O D A T E K , W A R S Z A W A 1974

W. O L S Z T A

A N A T T E M P T TO D E T E R M IN E TH E D R A IN A G E A N D R E T E N T IO N OF C R A C K E D SO ILS

Soil Science Laboratory of the Institute for Land Reclam ation and Grassland Farm ing in Lublin

The problem of management of cracked soils, and particularly of their drainage, has not been satisfactorily solved up to now. A need is felt of theoretical elaborations aiming at finding simple solutions for practical purposes.

In the present w ork an attempt is made of deteirmnmg depression curve for cracked organogenic soils and a relationship between this curve and outflow.

D E PR E S S IO N C U RVE

In the considerations which follow there has been assumed that the water flow in cracked soils is running in the network of joined cracks and is governed by the D arcy’s law. The following denotations have been introduced according to the scheme presented in Figs 1 and 2: L— spacing between ditches,

Ъ— filling up a ditch, e— distance between cracks, 5— rainfall.

In the hydraulic scheme of water movement according to the Darcy’s law, the flow volume in the section I-I at the distance x from the starting point of the coordinates’ system (Fig. 1) may be expressed in terms of the simple dependence

1 . - - K Ц - у е

(

1

)

and in the section II-II

3x + d 3x = 3 x + e S dX

provided that the total rainfall (without surface runoff) would go down to ground water.

24 W. Olszta

Fig. 1. A hydraulic scheme of the depression curve during soil

drainage

However, it follows from (1) that

(

2

)

and therefore

(3)

(4)

It is a differential equation of the second order. Upon solving the equation (4) w e obtain

1

where: С and C t — integration constants.

For boundary conditions

X = 0 1 (5)

2

2

1 The equation has been solved by T. Pokora M. Sc. from the Department of Num erical Methods, M. Curie-Skłodowska U niversity in Lublin.

A n attem pt to determine.., ₂₅

hence solution of the equation consists in getting the expression

± ] / - | - X « + [ | > - H - ) + ! £ ] * + H > . (6)

D R A IN A G E A N D W A T E R R E T E N T IO N

W ater retention of uniform soils depends mainly on porosity. In cracked soils water is accumulating also in free spaces of cracks formed in consequence of cracking. The considerations which follow concern determining volume of cracks and their relation to outflow magnitude.

Let us consider two cases of the configuration of cracks:

— the configuration of craoks in a horizontal plane in the shape of a square, at which the crack width W at the depth y is constant (Fig.

2

— the configuration of cradks on a horizontal plane in the shape of a regular hexagon, at which the crack width W at the depth y is constant (Fig. 2b).

a ) Fig. 2. Horizontal section of cracked soil a — craks in the shape of a square, b —

craks in the shape of a re gu la r h exago n

A В С 0 E F G H

/ J И L

M N 0 P

In the former case each square is accumulating water in two ad­ joining cracks: (the square EFJI in the cradks EF and FJ, the square F G K J in the cracks F G and GK , etc. Let us assume that the distance between two opposite cracks (sides) of the square equals e and the crack width is W ; then the length of two cradks w ill be 2e and their area

2

Let us further assume that the depth of cradks with a constant width is y, hence the w ater volume accumulated in the cracks of the cuboid EB y w ill be like in (Molen 2) investigations

2

V = — y (7)

In an infinitely small soil layer the amount of water accumulated in

the cracks will be

2

d V ~

о

(8)

2 M olen W. H. van der — Report about flo w w ater through the cracks soil. Mst. Kampen, Netherlands.

26 W . Olszta

where :

E — length of the soil monolith, В — width of the soil monolith,

у — water depth in craoks, W — crack width,

e — distance between opposite cracks (sides) of the square.

The configuration of cracks in a horizontal plain has the shape of regular hexagon, the crack width W at the depth у being constant.

Let us asume the crack size according to Fig. 2b, at a similar con­ sideration as for the square. Then w e obtain the following formula for the crack volume in an infinitely small layer

d V = 2 E B W •dy (9)

It follows from the above that the system of both squares and regular hexagons would accumulate equal water amounts at the assumption that the square side awould equal to the distance between opposite sides of the hexagon.

In permeable soils between two drains with a free water flow the depression curve is forming. Its shape depends, first of all, on permeability of soils and on feeding by rainfall. It should be reminded that the per­ meability system in the cracked soil profile depends on the shape and width of cracks in the vertical section. Let us then consider two crack shape cases:

a — craks with rectangular section (Fig. 3a).

a) w _{b) r « L}

j/Уу b

>5 \

Fig. 3. V ertical section of cracks craks with rectan gu lar section, b — craks

with trian gu lar section

According to the formula (8) quoted in the work [1], mean permea­ bility coefficient of these soils is constant and may be expressed by the formula

_ W*go 121 3 '//e where :

W — mean width of cracks on the square side length,

e — distance between opposite cracks of the square or hexagon.

A n attempt to determine... ₂₇

Hence the depression curve equation for cracked soils assumes accord­ ing to (6) the following shape

y = x 2 + 2 C x H-2C, (11)

Referring to the system presented in Fig. 1 w e can assume in the formula (7) the value of В = 1 and E = dx.

Then we obtain

2 W

d V = - - - y d x (12)

A t substitution of the value (11) into the formula (12) w e get

2 W i /

121

3

d V — ---- 1 / " _TV73 X 2 + 2C x + 2 C t • dx (13)

e w W óap 1

e W W sgg Let us denote the constant value at x 2 by D

D ттгЗ

12] 3 ijeS W*gë~~

Upon integrating the formula (13) within the limits from 0 to w e obtain the water volume between drains per the drain length unit

L 2 ______________________________

2

W hile assuming that at maximal ground w ater level V = V max and mean V = V śr, the water volume which could be accumulated by the profile in cracks in the rainfall period could be

A V = V max — V śr

b— cracks of the triangular section — Fig. 3b. According to Fig. 3b the width of crack at the depth y w ill change after the formula

w v = ” w (15)

where :

W y — crack width depending on y, W — crack width on the soil surface,

28 W . Olszta

y — water level in cracks, a — crack depth.

Upon substituting the expression for W y into the formula (10) we obtain

W zgq

K 12|/3qea* У (16)

W e denote the constant values by C2, hence

К = C 2y* (17)

where :

W zgQ

Co = --- (18)

121

3

rjea0

y

’

It follows from the above that the permeability coefficient К for cracks with triangular section constitutes a function of filling up cradks with water y.

Hence, according to the formula (4) the depression curve equation will assume the shape of

d2y , l dy \ 2 , S

+ U + c ^ ~ ° (19)

£

and assuming that = T we get

+ т = о

(2o)

The methods of analytical solution of the above equations are known, nevertheless we obtain in this case the solution in an implicit form, and for this reason its calculation has been omitted. On the other hand, this equation can be solved relatively easily on the computer while obtaining the solution in tabular form.

Let us go now to the calculation of water volume iin cracks. According to the formula (8) w e obtain

2 E B W у d V ^ - - - ~- dy

Upon substituting the expression (15) for W y we obtain 2 E B W

dV — - ea •y d y

A n attempt to determine... ₂₉

Upon substitution in (21) the value determined by the equation (20) for y we would obtain the expression determining the water volume V, which can be accumulated by the profile between drains.

The above formulae concerning the depression curve shape as well as the crack volume should be regarded as hypothetical one. To precise the developed dependences or to verify further the assumed theses a num bsr of observation material would be necessary.

REFERENCES

[1] S e g e r e n W. A., O l s z t a W.: An attempt to determine the perm eability coefficient of cracked soils. Polish Journal of Soil Sei. 1, 1968, 2.

в. О Л Ь Ш Т А П О П Ы Т К А О П РЕ Д Е Л Е Н И Я О С У Ш Е Н И Я И В Л А Г О З А Д Е Р Ж А Т Е Л Ь Н О Й С П О С О Б Н О С ТИ Т Р Е Щ И Н О В А Т Ы Х П О Ч В Лаборатория мелиоративного почвоведения Института мелиорации и луговодства в Лю блине Р е з ю м е В труде предпринята попытка определения уравнения кривой зеркала грз'нтовой воды ’между канавами в трещ иноватых органогенных почвах при принятии, что движение воды в этих почвах происходит исклю чительно в сети соединенных трещин и подчиняется закону Дарси — ф орм улы (6), (11), (20). П редлагаю тся такж е ф орм улы для определения объема воды V накоплен­ ной в трещ инах как функции формы кривой депрессии. Рассматриваются два случая распределения трещин: — распределение трещин в горизонтальной плоскости в форме квадрата (рис. 2а, ф орм ула (8)), — распределение трещин в форме регулярного ш естиугольника (рис. 26, ф орм ула (9)). Д ля вы ш еуказанны х распределений трещин вы делены два случая верти­ кальн ого сечения трещин, в частности: — трещины с прямоугольным сечением (рис. За, ф ормула 14)), — трещины с треугольны м сечением (рис. 36, ф орм ула (21)), П редлож енны е ф орм улы д ля объе’ма трещин и формы кривой зеркала грун­ товой воды д ля трещ иноватых почв следует рассматривать как гипотетические. С целью уточнения установленны х зависимостей или дальнейш ей проверки приняты х положений, необходимо больш ое количество наблю дательского ма­ териала.

30 W . Olszta W. OLSZTA

E S S A IS DE L A D É T E R M IN A T IO N DU D R A IN A G E ET DE L A R E T E N T IO N DES SO LS CREVASSÉS

Laboratoire de la Pédologie am eliorative

de rin stitu t d’Hydraulique agricole et des Herbages à Lublin R é s u m é

Dans cet ouvrage on a fa it un essais de la détermination d’une equation de la courbe du m iroir d’eau entre des fosses dans des sols crevassés organogéniques en admettant que l’écoulement de l ’eau dans ces sols parcourt seulement par le réseau de crevasses reliées et il est soumis au droit Darcy — form ules (6), (11), (20).

On a proposé aussi form ules pour l ’établissement du volum e d’eau ramassée dans des crevasser comme fonction de la form e de dépression courbe.

Dans ces reflexions on a pris deux cas de la dispersion des crevasses:

— arrangem ent des crevasses dans une plaine horizontale en form e d’un carré (dess. 2a, form ule (8))

— arrangem ent des crevasses en form e d’un hexagone régulier (dess. 2ô, form ule (9)).

Pour les arrangements ci-dessus on a distingué deux cas de la coupe verticale des crevasses:

— crevasses à la coupe rectangulaire (dess. 3a, form ule (14)), — crevasses à la coupe triangulaire (dess. 3b, form ule (21)).

Il faut traiter comme hypothétiques les form ules proposées concernant le volu m e des crevasses et la form e de la courbe du m iroir d’eau pour les sols crevassés.

Pour rendre plus précises les dépendances déduites ou pour v é rifie r des p rin ci­ pes adoptés, on aura besoin d’une grande quantité de m atériel d’observation.

w . OLSZTA

P R O B E DER E R M IT T L U N G DER E N T W Ä S S E R U N G UND W A S S E R H A L T E F Ä H IG K E IT V O N R IE S S IG E N BÖDEN

Laboratorium fü r M eliorations-Bodenkunde

des Institutes für M eliorationswesen und Grünland-forschung in Lublin

Z u s a m m e n f a s s u n g

In der verliegenden A rb e it w ird eine Probe unternommen, die Gleichung der G rundwassespiegelkurve zwischen den Gräben in riessigen organogenen Böden zu ermitteln, unter der Annahme, dass der Wasserdurchfluss in diesen Böden durch einen N etz der vereinigten Ritzen erfo lg t und unter das Darcy — Gesetz fä llt (Form eln (6), (11), (20)).

Es wurden auch die Form eln zur Erm ittlung des in den Ritzen angespeicherten W asservolumens V als den Faktor der Depressionskurveform vorgeschlagen. In den Erwägungen sind zw ei Ritzenanordnungsfälle angenommen, und zw ar:

— die Ritzenanordnung in einer Horizontalebene in der Quadratform (abb. 2ö, Form el (8)),

A n attempt to determine... ₃₁

— die Ritzenanordnung in der Form eines regelm ässigen Sechsecks (Abb. 2b, Form el (9)).

Für beide obigen Anordnungen sind zw ei F ä lle eines veritkalen Ritzeschnittes abgesondert worden:

— die Ritzen m it einem rechteckigen Schnitt (Abb. 3a, F orm el (14)), — die Ritzen m it einem dreieckigen Schnitt (Abb. 3b, Form el (21)).

Die vorgeschlagenen Form eln für das Ritzevolum en und die W asserspiegelkurve für riessige Böden dürfen als hypothetisch betrachtet werden. Um die erm ittelten Zusammenhänge zu präzisieren bzw. w eitere Nachprüfungen der angenommenen Voraussetzungen zu machen, w erdtti grosse Mengen des Beobachtungsmaterials nötig.

w. O L S Z T A

P R Ó B A O K R E Ś L E N IA O D W O D N IE N IA I R E TE N C JI G LE B S P Ę K A N Y C H

Pracow nia Gleboznawstwa M elioracyjnego IM U Z w Lublinie

S t r e s z c z e n i e

W pracy podjęto próbę określenia równania k rzyw ej zw ierciadła w ody m iędzy row am i w spękanych glebach organogenicznych przyjm ując, że p rzepływ wody w tych glebach przebiega tylko siecią połączonych szczelin i podlega prawu Darcy — w zory (6), (11), (20).

Zaproponowano rów nież w zory do ustalenia objętości w ody V zgrom adzonej w szczelinach jako fu n kcji kształtu k rzyw ej depresji. W rozważaniach przyjęto dwa przypadki układu szczelin:

— układ szczelin w płaszczyźnie poziom ej w kształcie kwadratu (rys. 2a, w zór (8)),

— układ szczelin w kształcie sześcioboku forem nego (rys. 2b, w zór (9)). Dla tych układów w yróżniono dwa przypadki pionowego przekroju szczelin: — szczeliny o przekroju prostokątnym (rys. За, w zór (14),

— szczeliny o przekroju trójkątnym (rys. 3b, w zór (21)).

Zaproponowane w zory dotyczące objętości szczelin i kształtu krzyw ej z w ie r­ ciadła w ody dla gleb spękanych należy traktow ać jako hipotetyczne. W celu uściś­ lenia w yprow adzonych zależności lub dalszej w ery fik a cji przyjętych założeń n ie­ zbędne będą duże ilości m ateriału obserwacyjnego.

D r inź. W e n a n t y Olszta P r a c o w n i a G l e b o z n a w s t w a M e l i o r a c y j n e g o I M U Z L u b l i n.ul. P K W N 29