J. Hydrol. Hydromech., 50, 2002, 1, 3-19

INFILTRATION INTO A SWELLING. CRACKED CLAY SOLVILIAM NOVAK, NRi SWTCWEK, MARTINUS TH. VAN GENUCHTEN
Transient infiltration into a swelling, cracked fine-textured soil was
calculated using the originally designed FRACTURE submodel (version B)of the HYDRUS-ET simulation model. The model permits changes in thedimensions of the cracks during the infiltration process. Modeling results
obtained with the new model were compared with those from FRACTURE
submodel (version A) assuming a stable crack system. It is shown that
deforming cracks lead to higher rates of infiltration during precipitation
events as compared with stable cracks. A difference of about 20 percent wasestimated in our illustrative example.

KEY WORDS: Swelling Soils, Soil Cracks, Water Infiltration,
Mathematical Modeling.

Viliam Noviik, Jifi Simfrnek and Martinus Th. van Genuchten:
INFILTRAC,IA DO NAPUEIAVAJUCEJ PODY S PUKLINAMI. J.
Hydrol. HyJromech., 50,2002,1; l8lit.,5 obr.
Pr6ca obsahuje vjsledky matematick6ho modelovania infiltr6cie vody
do p6dy s puklinami, meniacimi svoje rozmery podas procesu, (verzia B) v
ziivislosti na vlhkosti p6dy, ktor6 sf porovnan6 s vlisledkami, zfskanjmi

pomocou modelu s konitantnymi rozmermi pukiin (verzia A) podas
infiltr6cie zrhlok. Submodel FRACTURE - yerzia B, ktor6 kvantifikuje
infiltr6ciu vody do p6dy s deformujricimi sa puklinami je sridast'ou modelu
HYDRUS-ET. Porovnanie vjsledkov modelovania pomocou oboch
submodelov uk6zalo, Ze podas zrilkovej udalosti v tomto ilustrativnom
priklade rychlost' infiltr6cie do p6dy s deformujircimi sa puklinamije asi o
20 Y" vdllia ako do p6dy so stabilnj'mi puklinami. Treba poznarnenat,2e
meranie charakteristik infiltr6cie vody do p6dy s puklinami a sfdasn6
meranie deform6cii siete puklin nie je v prirode prakticky moZn6, preto
matematick6 modely mdZu byt'pouZit6 aj ako n6stroje vedeck6ho vj,skumu
v numerickych experimentoch.

Ing. Viliam Nov6k, DrSc, Ustav hydrol6gie SAV, Radianska 75, P.O.B. 94, 838 11 Bratislava 38. Slovenskd reoublika.

Jiii Siminek, phO., fr4.m. van Genuchten, George E. Brown, Jr., Salinity Laboratory,
450 W. Big Springs Road, Riverside,CA9250'7- 4617, USA.

V. Novdk, J. Simrinek, M. Th. van Genuchten

KLUCOVE SLOVA: napudiavajfce p6dy, p6dne pukliny, infiltr6cia vody,matematick6 modelovanie.

Introduction

infiltration of water into fine-textured, low-permeable soils is a slow

process, in which precipitation and/or irrigation water enters the soil at a low
rate, which in turn often causes surface runoff. The presence of drying cracks ina soil can increase the infiltration rate and increase the soil water content.

Negative features often associated with crack infiltration are a) solutes
penetrating faster into deeper soil layers and thus contributing to soil andgroundwater pollution, and b) nutrients moving out of the range of plant root
extraction.

Infiltration rates calculated using classical flow models deviatesignificantly from those observed in the field for swelling, fine-textured soils.
Accurate simulation of infiltration into initially dry, cracked, clay soils remains
a weak point of many SWAP (soil-water-atmosphere-plant) models. Such
infiltration is usually modeled using the classical Richards' equation forvariably saturated flow in a homogeneous soil. Lack of good procedures
describing infiltration of water into soil cracks in the SWAP models generally
leads to underestimation of infiltration and overestimation of water
accumulation at the soil surface, overestimation of runoff, and consequently tounrealistic soil water regime predictions.
A variety of models describing the movement of water and dissolved
solutes in soils containing cracks have been developed, most of them based onschematic representation of crack network (V a n G e n u c h t e n 1991, M aand Selim 1998,Van Genuchten and Sudicky 1999).Results
obtained with these models are relatively poor, in parl because of conceptual
weakness of the models, and in part because of difficulties in accurately
estimating crack input parameters. Flow in structured porous media isfrequently also described using dual-permeability models (P r u e s s andWang 1986,Gerke and Van Genuchten 7993,1 arvis 1994,
1998). Approaches of this type assume that the soil consists of two regions, one
associated with the macropores (cracks) and the other with the less permeable
matrix region. The difficulty in applying this approach to cracked soil is thatflow in both regions is described using the Richards' equation, an assumption
probably not valid for large drying cracks.
Another class of models uses statistical properties of cracks (e. g., depth
and width). Such models do not require detailed knowledge of the crack system
and/orthespatialdistributionof macropores (S lawi n ski etal. 1996,Van

4

Infiltration into a swelling, cracked clay soil

D a m et al.1997, N o v 6 k et al.2000). An advantage ofthese types ofmodels is a more realistic description of the physics involved and easierassessment of input data. As an example, the latest version of SWATRE ( V a n
D a m etal. 1997) adds a source term to the Richards' equation to allow for the

infiltration of water from the crack. Lateral infiltration is as to be constant in
time, with the infiltration rate changing only as a function of active crack area.
In this study we describe the FRACTURE submodel that quantitatively
describes the infiltration of rain water into an initially relatively dry, cracked
soil. Variably-saturated flow in the soil matrix is described using the Richards'
equation. Excess water at the soil surface that cannot infiltrate because of a
relatively low infiltration capacity of the soil, is removed by surface runoff, or
allowed to fill the soil cracks from where it can infiltrate laterally into the soil
matrix. Lateral infiltration is described using the Green-Ampt approach.
The basic feature of the first version of the FRACTURE submodel (referredto here as version A), as described in N o v il k et al. (2000), is that crack
dimensions are constant during the infiltration. This approach makes thecalculations relatively simple and saves CPU time. In reality, soil cracks usuallychange their dimensions depending upon the actual soil water content during theinfiltration process. The new FRACTURE submodel (version B) quantitatively
describes infiltration of rain into a clay soil containing cracks that can change
their dimensions during the infiltration process. The goal of this paper is toevaluate the potential effects of changes in the crack geometry on infiltration
using both submodels (versions A and B).
In the previous version of the FRACTURE submodel (Nov6k et al., 2000),
we assumed that the vertical distribution of the crack porosity, P", is a functionof the vertical distribution of the soil water content, w, at the beginning of the
precipitation (irrigation) event. The P. distribution was estimated from the
known soil water content vertical distribution, w(z), before precipitation started,and the relationship between crack porosity and the soil water content, P,(w).
The dimensions of the soil cracks were assumed to be stable during theinfiltration event, i. e., we calculated the infiltration of water into the soil
assuming constant crack parameters. This assumption was based on fieldobservations that no significant crack geometry changes took place during
infiltration of short-term precipitation events. Precipitation during hot summerdays occurred by means of relatively short-time rainfall events followed by
rapid drying of the surface soil layers due to high evaporation rates, and by
subsequent shrinkage of soil peds at and near the soil surface. The perimeters of
the soil cracks at the soil surface were not very distinct, which made it difficult
to accurately monitor and mathematically describe their changes.

V. Nov6k, J. Simirnek, M. Th. van Genuchten

It would be possible to accurately calculate changes in the soil crack
dimensions associated with soil water content, if an unambiguous relationship,
P,(w), between the crack porosity and the soil water content existed. Such an
approach is an approximation as well because it can be expected that thisrelationship (i. e., P,(w)) is hysteretic in that it will depend on the history of thesoil water content regime.
Conceptual modelA schematic of the conceptual FRACTURE model is shown in Fig. 1. The
precipitation or irrigation rate, qo(t), at the soil surface will be equal to theinfiltration rate, q(t), as long as the soil surface is unsaturated. The model
assumes that all precipitation water falls directly on the soil surface.
Precipitation into cracks is assumed to fall also on the soil surface. After the soil
surface becomes saturated, excessive water is first used to form a surface layerat ponding time to.It is assumed that the surface run-off or flow into the cracks
can start only after surface layer of critical thickness ft" has formed. Water thenkeeps flowing into the cracks as long as the potential flux is higher than theinfiltration flux. When the potential flux becomes smaller than the infiltration
rate, water flow into the cracks stops and water in the soil surface layer is used
for infiltration until the surface water eventually disappears. According to thismodel, the infiltration process can be divided into several stages (N o v d k etal. 2000):

l. Unsaturated infiltration when the soil surface is still unsaturated: q(t)= qs(t),t<tP;
2. The formation (or disappearance) of a surface water layer after the soil
surface becomes saturated: q(t) < qy(t) lor q(t)> qo(t)7;

3. Flow into cracks when the surface is saturated and the surface layer has
reached some certain critical height h": q(t) < qof);
4. Runoff when cracks are either full or not considered: q(t) < qo!);
5. Horizontal infiltration from the cracks into the soil matrix.
The influence of soil subsidence on crack development was not considered.
Horizontal infiltration of water from the cracks into the soil matrix was assumed
to occur only through crack surfaces that are in direct contact with water
standing in the cracks. Hence, the model does not consider infiltration of film
water flowing along cracks walls.

Infiltration into a swelling, cracked clay soil

" -rV->,trrrn,ttttrttra/tatt
aaa/alf/',',,,,.
tattatt
taaaaaarfg
iit+

I n,,,

Fig. 1. Schematic of the FRACTURE submodel. The potential infiltration rate (the applied
ruifu". flux), q6(r), is divided between the soil surface infiltration ftte q(t) and flow into thecracks 4y(l); ,S/z) is the horizontal infiltration rate from the cracks into the soil matrix'
Obr. 1. 3ch6ma submodelu FRACTURE. Rychlost potenci6lnej infiltr6cie (aplikovan! tok vodyna povrch p6dy) So(t) sa deli na infiltriiciu cez povrch pOdy q(l) a na tok vody do podnych puklin;
Sfz) je intenzita horizont6lnej infiltrdcie z puklfn do pOdnej matrice.

We further assume (case A) that soil cracks during a precipitation event do
not change their dimensions. This assumption is based on field observations ofcracks on the soil surface. Even during a heavy rain, soils generally swell soslowly that crack shrinking is not observable during the first few hours of therainfall event. This situation was described in our previous publication(N o v i{ k et al. 2000).
This situation is different for cracks deeper in the soil that are generally
invisible to observation. The lower parts of these cracks are filled with waterthat is slowly infiltrating into the soil matrix. The soil hence can swell in
response to this infiltration, and thus considerably change the dimensions andV. Novrik, J. Simrinek, M. Th. van Genuchten

physical parameters of the cracks. Therefore, the second goal of this paper is toevaluate the influence of changing crack dimensions during infiltration on theinfiltrating process itself.

Mathematical model
The FRACTURE mathernatical submodel is part of the HYDRUS-ET code
(S i m ri n e k et al., 1997). The classical one-dimensional Richards' equation isassumed to describe water flow in the soil matrix. Matrix and preferential flows

are mutually linked using an extension of the Richards' equation as follows(Feddes eta1.,1988):

y. t)l s. (z) + s, (z),1dt= 3["dzL&, z)( dz I

(t)

)J

where h is the water pressure head LLl, e - the volumetric water content[L'L-'], r * time [T], z - the vertical coordinate [L] (positive upward), K - theunsaturated hydraulic conductivity function [L T-'], ,S,(z) - a sink term (e.g.,root water extraction) [f31-r T-11 that quantifies the volume of water extracted
from soil by roots, and .Sy(z) is a source term accounting for the horizontal
infiltration of water from the water-filled parts of the cracks into the soil. The
latter term Slz) is calculated using the Green-Ampt approach:(h^-ft" )I\J/

L,

Sr =l Kok)-?

"

W,,

Q)

I

where Kri is the saturated hydraulic conductivity of the cracks-matrix interface[L T-t], hs-the positive pressure head.at the point of infiltration [L], /27- thepressure head (negative) at the leading edge of the moisture front at a distance /r"from the infiltration surface [L], and A. is the specific surface of the cracks

lL'L-tl.
Values of K7, and A, can be measured, while the wetting front distance lcan
be calculated using the Green-Ampt approach as follows:

f h-ht'=l2Knffi''(3)

Infiltration into a swelling, cracked clay soil

where 0; and 0" are the initial and saturated volumetric water contents,
respectively, / is the time interval since the start of infiltration.
T h o m a et al. (1992) experimentally showed that due to coatings at thecrack-matrix interface the hydraulic conductivity of this interface can differ
significantly fromthe matrix conductivity. V an G e n u c h t e n and
S u d i c k y (1999) reviewed other evidence indicating that the hydraulicconductivity of the crack-matrix interface can be smaller by several orders ofmagnitude than the conductivity of the matrix interior. Main reasons for this are
the changed physical and chemical properties of the interface resulting fromrepeated opening and closing of fractures, including coatings of this interface byrelicts of roots, other organic matter, and clay particles. Field observations haveshown that soil cracks are forming along the same internal soil surfaces, which
represent areas of minimum mechanical strength.
The Richards' Equat. (l) was solved numerically subject to the initial andboundary conditions described below.

Initial condition
The initial condition at the beginning of the precipitation event (rs) is givenby the soil water pressure head profile:

It,=f(z)forz>0andt=to,@)where hr is the initial pressure head and to the initial time.

Upper boundary conditions
The actual upper boundary condition during the infiltration event depends
on the state of the soil surface. Three different upper boundary conditions at thesoil surface are used to characterize different stages of the infiltration process.
1. A flux boundary condition for the unsaturated soil surface:- 4++11=q,(r)\ozfor h<0,/5\)

where qe is the potential infiltration rate, i. e., the difference between
precipitition and evaporation [L3 L-2 T-t].

V. Novrik, J. Simrinek, M. Th. van Genuchten

2. A "surface reservoir" boundary condition (M I s, 1982) is used when the soil
surface is saturated and a sub-critical surface layer (h < hr) of water on the soil
surface is being formed:-*{**,]= q,(il-#\dz

for O<h<h,,(6))

where & is the saturated hydraulic conductivity of the soil matrix, and ft" is thecritical head, i. e., the thickness of the water layer on top of the soil surface
when surface runoff is initiated, or when the water start flowing into cracks [L].
3. When the surface water layer reaches the critical thickness h, and water flows

into cracks (if they exist) or the surface runoff of intensity {J starts, thefollowing boundary condition is used:--,(**t)=qoe)-qrQ)

for h,1 h,(7)where q,,is the flow rate into the cracks [L3 L-2 T-t].

Boundary condition (6) permits water to build up on the soil surface. The
left side represents the actual infiltration rate into the soil profile through thesoil surface. The first term on the right side, {6, repreSents the potential
infiltration rate, i. e., the difference between precipitation and evaporation, andthe second term is the change in thickness of the water layer on the soil surface.
The volume of water in the cracks Vris calculated as follows:,, =(ln, 1t) dt -!,a r,@ o,),(8)where q6 is the water flux rate from the cracks into the soil matrix.

Lower boundary conditions

A variety of boundary conditions, the same as those used in the HYDRUSET model (S i m fi n e k et al. 1997), can be prescribed at the lower boundary.
The conditions include constant or variable pressure heads or fluxes, seepage
faces, and deep or free drainage conditions.

10Infiltration into a swelline. cracked clav soil

Input data
The FRACTURE submodel is part of the HYDRUS-ET model. In addition
to parameters needed by HYDRUS-ET, the FRACTURE submodel needs two
extra input parameters characterizing the soil cracks:
The crack porosity P, as a function of the soil water content expressed inmass units: P,--flw). This relationship, also known as the soil shrinkage
characteristic curve ( M i t c h e I l, 1992),is a soil characteristic and can be

estimated in the laboratory using undisturbed soil samples. In thisprocedure, a soil sample is allowed to dry slowly and its changes in heightand diameter are measured together with the soil water content w. It is
assumed that deformation of the soil sample will be equal to the soil crack
porosity, P.. From this data the relationship P"(w) can be established(N o v 6k 1999). The crack porosity profile, P,(z), can be estimated using
the soil water content profile w(z), which is output from the HYDRUS-ET
model, and the shrinkage curve P,(w).

The specific length of cracks /, is the "length" of cracks in a unit soil
surface area. This parameter is assumed to be constant in the region where
cracks are expect:d to exist, i. e., constant along the soil profile with cracks.
Value of /" can tre easily estimated in the field by direct measurement or byimage analysis of the site under consideration.

Application of the new FRACTURE submodel (version B)

The HYDRUS-ET model with versions A and B of the FRACTURE
submodel was applied to the experimental site at Trnava (Western Slovakia).
Properties of the silty loam soil at the site are given elsewhere (N o v 6 k and
Maj e r d 6 k 1992, N o v 6 k et al.2000). The saturated hydraulicconductivity was 5 cm/day and the saturated water content 0.407 . Experimental
P,(w) data were approximated using a linear function (N o v 6 k 1999) as
follows:

Pr=- ay w * Prg,(9)where ayrs & slope of the P.(w) function and P,6 is the maximum crack porosity
corresponding to a zero soil water content (dry soil).
Experiments conducted by T h o m a et al. (1992) and others showed thatthe saturated hydraulic conductivity of the cracks-matrix interface Kr' can be

11V. Nov6k. J. Siminek. M. Th. van Genuchten

much smaller than the matrix conductivity K". This decrease in K" can be
expressed as follows:
Kn = tt K",(10)

where rp is a reduction factor accounting for hydraulic resistance across thecrack-soil matrix interface. As mentioned earlier, this decrease in the hydraulicconductivity at the interface is probably due to coatings resulting from changed
physical and chemical properties.
The following crack characteristics were used in our numerical experiment:
Zr= 40 crrr, ay = 0. 178, P,o = 0.O429, 11, = 0.1, where 2, is the depth of soil
cracks. The precipitation rate q0 was assumed to be 25 cm/day during a periodof 2 hours. Flow into cracks was assumed to start when the thickness of thesurface water layer reached 0. I cm.
Results and discussion

In our previous paper (N o v 6 k et al. 2000) we showed the importance ofsoil cracks in determining infiltration rates during a precipitation and/or
irrigation event. As is demonstrated in Fig. 2, infiltration from cracks into a soil
with stable crack dimensions increased the total infiltration rate significantly
during the infiltration event. Having stable cracks may not be very realistic. In
reality, the soil water content during infiltration will change and the soil will
swell correspondingly, thus decreasing the crack dimensions. The question iswhat we can expect when using the FRACTURE submodel with crack
dimensions changing due to soil swelling during infiltration (version B)
contrary to the submodel with constant crack dimensions (version A).
t

The soil water content should increase in both cases (in comparison to a soil

without cracks) due to infiltration through the soil surface, as well as
infiltration through the crack surfaces. Because of soil swelling, cracks
should be narrower when using version B of the FRACTURE submodel
since their dimensions are constantly reevaluated based upon the actual
water content. This as compared with version A, which assumes that thecracks remained constant during the infiltration process.
2. The water level (pressure height) in the soil cracks should be higher for theversion B submodel in comparison to version A since the volume of cracks
diminishes as time progresses, and hence less water is needed to fill thecracks up to some given level. Water storage in the cracks during infiltration
in a soil whose cracks change dimensions was found to be lower intz

Infiltration into a swelling, cracked clay soil

comparison to the soil with stable cracks. This is shown to be the case in Fig.

3. Notice, that the amount of water stored in the cracks also decreased

significantly.
3. Higher instantaneous and cumulative infiltration rates were calculated aswell for soils with changing crack dimensions (version B) in comparison to
the submodel with stable cracks (version A) (see Fig. 4 and Fig. 5); thisbecause larger crack surfaces are exposed to infiltration in the former case.

However, the effects are not as significant as those pertaining to water
storage in the cracks.

-25

a
o -20
o
(tt
E -ts

- Applied Surface Flux
- Surface Infiltralion (Sur{ace Layer)- Surface Infiltration (Run Off/Cracks)- Fracture Iniiltration- Run Oll/Flux to Cracks

c

.9
(E

:-10
-5

0,2

Tim e [d]Fig. 2. Infiltration rate versus time calculated using the FRACTURE submodel (version A) withsoil cracks not changing their dimensions during infiitration: 1 - potential infiltration rate
(irrigation rate),2 - infiltration into the soil without cracks, with water accumulating on the soil
surface. 3 - infiltration into the soil through the soil surface without cracks, but with surface
runoff, 4 - infiltration rate from cracks into the soil, and 5 - flow into the cracks.
Obr. 2. Rfchlost' infiltr6cie v z6visiosti na dase, vypoditan6 pomocou submodelu FRACTURE(verzia Aj s pddnymi puklinami, ktor6 nemenia svoje rozmery podas infiltr6cie: I - rychlost
potenci6lnej infiltrdcie (r,j'chlost' zdvlahy),2 - infilffecia do pddy bez puklfn, voda sa akumuluje
na povrchu-pddy, 3 - infiltr6cia do p6dy cez jej povrch, bez puklin, ale s povrchov;fm odtokom, 4infiltr6cia z puklfn do pOdy a 5 - prftok vody do p6dnych puklin'

-

1a
IJ

V. Nov6k, J. Simfinek, M. Th. van Genuchten

0.00

0.30

Level(case A)
Level(case B)

t 0.00

E

I

0,

0.25

-water-----.-Waler Storage (Case A)- - - Water Storage (Case B)--waterE

0.20-20.00

0.1 5

o
J
€,

0.1 0

-30.00

o
ol
o
o

6

o

t!
-40.00-50.00

I

o

0.1

0.2

Time [d]

0.3

0.05

o

0.00

=

-0.05
0.4

Fig. 3. Water level and water storage in cracks during infiltration for soil cracks with constant(case A) and changing (case B) dimensions during the infiltration event.
Obr. 3. Hladina vody v p6dnych puklin6ch a ich obsah vody, ak sri rozmery pOdnych puklfn st6le(pripad A) a ak pukliny menia svoje rozmery podas infiltrdcie (pripad B).
25.00

Cracks (Case A)-Constanl Cracks (Case B)-V31i3fls

E' 20.00
Eoc 15.00.o.g= 10.00
E
o
3

5.00

()
(E

lr

0.0 0

-5.00
0

0.1

0.2

0.3

0.4

Time [Days]
Fig. 4. Infiltration rate versus time for soil cracks being constant (case A) and changing during
infiltration (case B).
Obr. 4. Intenzita infiltriicie v zA,vislosti na dase pre p6dne pukliny so st6lymi rozmermi (pripad A)
a pre pukliny meniace svoje rozmery podas infiltr6cie (pripad B).

14

Inhltration into a swelling, cracked clay soil

1.60
1.40

E 1.20C)e.9 1.00
(t
c
6'

0,80
0,60

=
o
G
E 0.40
c,

.=
6

=
E
o=

0.20

Cracks (Case A)-Constanl
0.0 0Cracks (Case B)-Variable

.0.20
0.1

0.2

0.3

0.4

Time [days]
Fig. 5. Cumulative infiltration versus time for soil cracks being constant (case A) and changing
during infiltration (case B).
Obr. 5. Kumulativna infiltr6cia v z6vislosti na dase pre p6dne pukliny so sti{lymi rozmermi(prfpad A) a pre pukliny meniace svoje rozmery podas infiltr6cie (pripad B).

Conclusions

The effects of changing soil crack dimensions during infiltration were
quantified by comparison of infiltration characteristics as modeled by two
versions of the FRACTURE submodel. Version A assumed non-changing
cracks dimensions during the infiltration event, while version B assumed thatthe cracks dimensions can change during the infiltration event depending uponsoil water content changes. The results of our numerical experiments are as
follows:
1. The ratio of the maximum infiltration velocities into the soil with changing
crack dimensions during infiltration, v*,v, and with stable cracks, vretc, was7.23 for the illustrative example presented in this contribution'
2. The ratio of cumulative infiltrations (1'l1.) as estimated by both submodels(versions B and A) for a given precipitation event was 1.20'

15

V. Novdk, J. Simirnek, M. Th. van Gehuchten

3. By comparing both modeling approaches (stable cracks and cracks changing
their dimensions), it is shown that the crack "retention capacity" (i. e., theability of cracks to accumulate and infiltrate "in-flowed" water) is increasedin case of the cracks changing their dimensions. Although the soil is swellingand cracks are becoming narrower during infiltration (i. e., smaller crack
volumes), the larger exposed wetted crack surface area due to a higher waterlevel in the cracks increases the actual infiltration rates. The increased
pressure heights in the deforming cracks, in comparison to the stable cracks,
also increases the infiltration velocity.
4. The many complex processes affecting infiltration into a soil with cracks are
difficult to measure, especially when the cracks change their dimensions.
Modeling such an event greatly helps to understand the importance of thevarious processes involved, and ultimately in determining the effects ofcracks on infiltration.
Acknowledgements. This work has been carried out under the support from the
Slovak Grant Agency (VEGA), Project 2 - IO84 - 21.
List of symbols

af h hs hi 4 -slope of the P.(w) function [-],^
specific surface ofthe cracks lL'L-'|,pressure head [L],positive pressure head at the point of infiltration [L],initial pressure head [L],pressure head (negative) at the wetting front at a distance \away from the crack surfaceh, -critical head, i.e., thickness of the water layer on the soil surface when surface runoff isA" -K K1, K, L lf P" P6 q Qo qf qf, 11, -tl-l,
initiated, or when water starts to flow into soil cracks [L],
unsaturated hydraulic conductivity tL T-ll,
hydraulic conductivity of the crack-matrix interface tL T'1,
saturated hydraulic conductivity of the soil matrix [L T"],
specific length ofcracks per unit soil surface area[LL-'],distance of the wetting front from the infiltration surface [L],crack porosity [L'L-'],maximum crack porosity corresponding to a zero soil water content w 1L3 L-31,
actual infiltration rate [L3 L-2 T-'],
potential infiltration rate [L3 L-2 T-r],
flow into soil cracks, or surface runoff [L3L-2T-r],tl,water flux rate from the cracks into the soil matrix lL3 L'zT
reduction factor for the saturated hydraulic conductivity of the crack-soil matrix interfacet-- l.S. J1tl6-sink term quantifying the volume of water extracted from soil by roots (the root extractiont],term) [L3 L-tT
. .. I. - 1--lhorizontal infiltration rate of water from cracks into the soil matnxlL-L r L

time [T],Inhltration into a swelling, cracked clay soil
,0

initial time [T],tftime interval since the start of infiltration [T]'ponding time [T],volume of water in the cracks [tt !'-']runder a unit square area of soil surface,soil gravimetric water content [M'M"],
vertical coordinate IL], (positive upward),
volumetric water content [L'L-'], ^initial volumetric water content [-L'L-'],
residual soil water content [L'!-'1,
saturated soil water content [L'L"].

tp

vf
w
z

e
0i
0,
e,

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Hydrology, 100, 1988, 69-1 1 1.
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Received 14 August 2001

Scientific paper accepted 18 September 2001

INFILTRACIA DO NAPUEIAVAruCEJ PODY S PUKLINAMI

Viliam N o v 6k, Jifi S imrinek, Martinus Th. van Genuchte n
Pomocou dvoch verzif submodelu FRACTURE sme kvantihkovali vplyv zmien
rozmerov vfsu5nfch puklin v p6de podas infiltr6cie vody do p6dy. Verzia A
predpoklad6 nemeniace sa rozmery puklin podas infiltr6cie, verzia B umoZiluje vypodetrozmerov puklin - vyvolanfch zmenami vlhkosti podas infiltr6cie - a zahrnutie tfchto

zmien do vfpodtu charakteristik procesu infiltr6cie. Vj'sledky numerickfch

experimentov sf tak6to:
1. Pomer maximiilnych rfchlostf infiltr6cie do p6dy s premenlivlimi rozmermi puklin
Vmax,y v porovnanf s rj'chlost'ami infiltr6cie do stabilnych puklin vmu,c pre pouZitf
ilustrat(vny pripad bol 1,23.
2. Pomer kumulatfvnych infiltrdcii (,,/1,), urdeny oboma modifik6ciami submodelov(verzie A a B) pre danf pripad bol 1,20.
3. Zporovnania vfsledkov modelovania s vyuZitim oboch verzii submodelov vyplfva,
Le tzv. retendn6 kapacita (schopnost' akumulovat' vpuklin6ch vodu, ktor6 do nichvtedie a infiltrovat' ju) sa zviid5uje, ak sa menia - zmen5ujri rozmery puklfn. P6da
podas infiltr6cie vody do nej napudiava, pukliny sa zuLuj6, av5ak zvy5uje sa
inhltradn6 plocha puklin a tlakov6 vj'Ska vody v nich, do sp6sobuje v porovnani sostabilnimi puklinami zvfSenie rfchlosti infiltriicie.
4. Mnoh6 zlo2it6 proaesy ovplyvilujrice infiltr6ciu do p6dy s puklinami sir faZkomeratel'n6, predovletkym v pripade menitetnych rozmerov puklin. Modelovanie

18

Infiltration into a swelling, cracked clay soil

takj'chto pripadov umoZiuje pochopit' vyznam prebiehajircich procesov, ale aj
urdenie vplyvu puklin na infiltr6ciu vody do p6dy.

hznam symbolov

ayAchhshihfhr-s/-sklon funkcie PIw) [-],^
merni povrch puklin [L2 L-3],
tlakov6 v9Ska [L],kladnA tlakov6 vj'Ska na infiltraEnom povrchu [L],poiiatodnri tlakov6 vf5ka IL],tlakov6 vfska (z6porn6) na iele om6dania, vo vzdialenosti I od povrchu pukliny [L],kritick:i vjSka, t. j. hrubka vrstvy vody na povrchu pddy na zadiatku povrchov{ho odtoku,
alebo na zadiatku pritoku vody do puklin vp6de [L],nenaslirten6 hydraulickri vodivost' p6dy [L T'],
hydraulick6 vodivost' rozhrania puklina - matrica p6dy [L T'],
nasliten6 hydraulick6 vodivost' pddnej matrice [L T'],
mern6 diZka puklin, pripadajirca na jednotku plochy povrchu pOdy [L L'],vzdialenosf dela om6dania od infiltradn6ho povrchu [L],puklinov6 p6rovitost' tL3 L-'1,
maxim6lna puklinov6 p6rovitost', zodpovedajica nulovej vlhkosti p6dy [L'L-'],skutodne rychlost' infiltr6cie [L'L:'T:'], ,potenci6lna rj,chlost' infiltracie [L'L* T-'],rj'chlost' rtoku vody do puklin, alebo povrchovy gdtok [L3 L'2 T-t],
rlchlost' vtoku vody z puklin do matrice p6dy 1L3 L-21"t1,
redukEnf faktor 1,re nasftenri hydraulickf vodivost' rozhrania puklina - p6dna matrica [-],
odberoqi dlen, cirarakterizujrici objem vody odobranf koreimi rastlin [L3 L-2 T-r],
horizontalna rychlost' infiltr6cie vody z puklin do matrice p6dy [L3 L-31*t1,

tg

das [T],
podiatoinf das [T],

K-

K6-

K"l" lfP"P6q4oqfqfs -

rk-

srtf-

vfw

z-

e-

eierer-dasovf interval od zadiatku infiltricie [T],das vjtopy [T],objem vody v puklin6ch, pripadajrici najednotku plochy povrchu p6dy [L'L-'],hmotnostn6 vlhkost' pddy [M'M-'],vertikdlna sriradnica IL], (pozit(vna smerom hore),objemovii vlhkost'pddy [L3 L"],
podiatodnd objemov6 vlhkost pddy [L' L-'],rezidu6lna objemov6 vlhkost' p6dy t^L'!'1,
naslten:l objemovii vlhkost' p6dy [L' L''].

I9