A Simulation Model for Predicting Infiltration into Cracked Clay Soil1

W. B. HOOGMOED AND J. BoUMA2

ABSTRACTInfiltration into dry cracked clay soil was simulated by com-

bining two existing physical simulation models for verticaland horizontal infiltration, using boundary conditions for hori-zontal infiltration that were defined by morphological data.Vertical flow into the cracks occurred when the applicationrate exceeded the calculated vertical infiltration rate of pedsbetween cracks. Calculated horizontal infiltration from thecracks into adjacent dry peds was limited because it had tooccur from a few small vertical bands along which the watermoved. The contact area (S) of all bands had been determinedin situ in 0.5-m2 plots per 10-cm depth interval using mor-phological staining techniques. S was a function of the appliedflow regime. "Short-circuiting," which was defined as preferen-tial movement of free water along large pores through un-saturated soil, was predicted well by the model. Short-circuitingincreased when the initial moisture content of the soil washigher.

Additional Index Words: unsaturated flow, hydraulic con-ductivity, diffusivity, preferential movement of solutes.

Hoogmoed, W. B., and J. Bouma. 1980. A simulation model forpredicting infiltration into cracked clay soil. Soil Sci. Soc. Am.J. 44:458^161.

DRY CLAY SOILS consist of relatively large naturalaggregates (peds) which are separated from ad-

joining peds by vertical cracks. Vertical infiltrationof water occurs at the soil surface into the upper sur-faces of the peds. Vertical flow of water into the cracks(or into any other, relatively large vertically continu-ous voids) occurs only when the application rate ex-ceeds the vertical infiltration rate of the peds (directflow of rain into the cracks is insignificant). As waterflows downward along the walls of the cracks, theadjacent peds usually remain dry in clay soils becausehorizontal flow from the walls of the cracks into thepeds is limited. Such phenomena are of critical im-portance for predicting vertical transport processes inthe field. They are difficult to predict with existingphysical flow theory, but they have been widely ob-served (Blake et al., 1973; Kissel et al., 1973; Thomasand Phillips, 1979).

Bouma and Dekker (1978) introduced the term"short-circuiting" which describes preferential move-ment of "free" water (water having atmosphere pres-sure) along large pores in unsaturated soil. They useda morphological field technique for determining pat-terns and depths of penetration and a physical labora-tory technique to obtain a water balance (Bouma etal., 1978). They demonstrated that depth and patternsof vertical penetration of water along cracks in dry,heavy clay soils were a function of rain intensity andduration. Vertical penetration of water occurred along

1 Contribution from the Soil Tillage Laboratory, Diedenweg20, Agric. Univ., Wageningen; and the Netherlands Soil SurveyInstitute, Box 98, Wageningen, The Netherlands. Presented atthe meetings of the Eur. Geophysical Soc., Vienna. Sept. 1979.Received 31 May 1979. Approved 15 Jan. 1980.

2 Soil Scientists at the Soil Tillage Laboratory and the Dep.of Soil Physics of the Soil Survey Institute, respectively.

only a few 5- to 7-mm wide bands, made visible byblue stains on vertical ped faces. They sprayed adilute methylene blue solution on 37 rectangular plotsof 100 by 50 cm using different intensities and quan-tities. The large size of the plots was needed to ob-tain an adequate quantity of bands in all treatments.

After spraying, the plots were gradually excavatedto a depth of 1 m and the total width of all bands onvertical ped faces was counted and added togetherper 10-cm depth interval. This total width times the10-cm length was called the contact area S (cm2). Hori-zontal absorption of water into the peds has to occurthrough this contact area (within 50,000 cm3 of soilfor each 10-cm depth increment). The contact areaS was observed to increase as time progressed at anygiven rain intensity (Fig. 2). This observation, derivedfrom Bouma and Dekker (1978), implies that con-tinuation of steady rain results in formation of newbands because existing bands cannot conduct the in-creasing volume of water running into the cracks. Theincrease is due to a decrease of the vertical infiltra-tion rate at the soil surface. A population of bandswith different ages is found therefore. Initially, thehorizontal absorption rate from new bands is rela-tively high, because absorption occurs into dry soilwithin the peds. The absorption rate decreases as timeprogresses.

Descripitve techniques and empirical experimentswill not result in needed procedures which inde-pendently predict the phenomena, as discussed, indifferent soils. A general simulation model will there-fore be presented here which predicts infiltration andredistribution of water in cracked clay soils. The com-plete model incorporates two well established onedimensional simulation models (van Keulen and vanBeek, 1971; van der Ploeg and Beneke, 1974). Thesemodels predict vertical and horizontal infiltration intoprismatic peds, using characteristic hydraulic conduc-tivity and diffusivity data. The model uses time de-pendent S values, derived from Bouma and Dekker(1978), as boundary conditions for horizontal flow.

MATERIALS AND METHODSSoil Procedures

The heavy clay soils that were studied were located in theriverine area of the Rhine in the Netherlands and were classi-fied as Typic Fluvaquents (very fine clayey, illitic, mesic) (SoilSurvey Staff, 1975). Staining techniques for determining infiltra-tion patterns and counting procedures for determining S, whichare both relevant for this study, were described in detail byBouma and Dekker (1978). Physical determination in thelaboratory of the magnitude of "short-circuiting", was discussedby Bouma et al. (1978). In summary, they used undisturbedcores with a height and diameter of 20 cm and applied rainat two intensities. The increase of weight and drainage rateswere measured as a function of time. First, duplicate corescontaining dry surface soil (pressure potential = —15 bar) wereused. These were later slowly wetted during a period of severalweeks to a moisture content corresponding with 0.1 bar. Rainintensities of 20 and 77 cm/day were well below the saturatedhydraulic conductivity (K,tt) of the dry and moist cores. (60and 8 m/day, respectively). AT,., was determined by shallowponding of water on top of the cores and by measuring the

458

HOOGMOED & BOUMA: SIMULATION MODEL FOR PREDICTING INFILTRATION INTO CRACKED CLAY SOIL 459

0.50 0.40 0.30 -10° -101 -102 -103 -104

8 (cm3 cm"3) i/j ' (mb)

Fig. 1 — Diffusivity (D— 6) and hydraulic conductivity (K— $ f )data, measured for soil within the peds. Dots represent re-sults from triplicate measurements.

flux. In pedal clay soils, K drops very sharply when the soilbecomes unsaturated. This is due to emptying of some rela-tively large continuous pores which influence /C,nt. Often, Knear saturation (e.g. <!/, = —5 mbars) is several orders of magni-tude lower than K,,,. Rain intensities used were representativeof spray irrigation rates as used by farmers in the area. Theshort duration of all experiments did not allow significant soilswelling or soil structure disturbances. Cracks remained opento the soil surface and they were vertically continuous. Datareported by Bouma et al. (1978) will be used to verify simula-tion results here. Diffusivity (D) as a function of the moisturecontent (9) and hydraulic conductivity (K) as a function of thepressure potential (^p) (Fig. 1) were determined for this study bythe hot-air method (Arya et al., 1975) using triplicate samplesinside prisms (Bouma and Dekker, 1978). The correspondingmeasured S values are shown in Fig. 2. The model discussedhere differs from a very recent model by Edwards et al. (1979)which describes infiltration into and filling of a single channel,followed by runoff at the surface. In contrast to our model,their application rate is higher than KKt, the single channel isnot vertically continuous and model results are not comparedwith measurements.

Simulation ModelThe computed simulation model covers three aspects: (i)

vertical infiltration into the upper surface of the peds; (ii)downward flow into the cracks, and (iii) horizontal absorptionfrom the cracks into the peds.

Vertical InfiltrationVertical infiltration of water into the upper surface of the

peds was simulated with a one-dimensional model in whichthe soil was 20 cm thick. The soil was divided from bottom totop into nine layers of 2 cm, one of 1.5 cm and one of 0.5 cm.Flow between the layers is calculated with the Darcy equationusing measured K— $, (Fig. 1) and S— $r relations. Models ofthis type are widely used (e.g. van Keulen and van Beek, 1971;Hillel, 1977). Physical boundary conditions are as follows:

z=0 -K dH/dz = R0 < H < w

H = wz=20 -K dH/dz = constant

0 < T < T(P)T(P) =£ T ^ TIC)

T > T(C)

where z = depth (cm) below the top of the soil, r(P)=time(days) when ponding starts, T(C)=time when ponding depth

200-

|1008

i = 77cm drl

i = 20 cm d

0.02 0.04 0.06 0.08 0.10

Time (days)

Fig. 2—Vertical contact area (S) for two steady applicationrates of water in a 10 cm thick segment of surface soil in aplot of 0.5 m2. (TIME = 0 at the time of the first drainagefrom the column). Reported values were measured in anearlier study (Bouma and Dekker, 1978).

reaches a preset threshold value of w cm, fl=rainfall intensity(cm day1), and H=hydraulic head (cm). For a certain rainintensity, the time to initial ponding and the rate of pondingof water on the surface can be determined. Depth of pondingat any given time is determined by the difference between rainintensity and infiltration rate.

Flow into CracksFlow of water into the cracks from the surface starts at time

T(C) when the ponding depth reaches a preset threshold value(w). A value for w of 0.2 cm was used here, which was basedon visual observations made during the experiments of theearlier studies. The excess water (rainfall minus vertical infil-tration into the peds) flows into the cracks.

Horizontal AbsorptionWater flowing into the cracks is absorbed horizontally into

the peds. A one-dimensional computer model was used to sim-ulate the process of horizontal water adsorption by an initiallydry soil. In this model (van der Ploeg and Benecke, 1974), therelation between absorption rate and time (using a measuredD — 6 relation, as shown in Fig. 1) was calculated. The fol-lowing equation applied for absorption during each timestepin each compartment:

axasdt

subject to the following boundary conditions:

x = 0 39

39x > x, — =

T > T(c)

T > T(c)

where x = distance (cm) from surface of infiltration, 9 = mois-ture content; T(c) = time when flow into the cracks starts, andx, = horizontal penetration of the wetting front at time f.

460 SOIL SCI. SOC. AM. J., VOL. 44, 1980

cm2-

1 -

CUMRAIN

CUMDRN

-CUMINF

RAIN = 20cmcT8. = 0.38

.CUMABS

0 0.041T(J) = 0.046

0.08 0.12Time (days)

0.16 0.20

theFig. 3—Cumulative rain (CUMRAIN), infiltration intoupper surface of the peds (CUMINF), horizontal absorptionfrom the contact area into the peds (CUMABS), and drainagefrom a 20-cm core (CUMDRN) as calculated by the simula-tion model. Rain intensity was 20 cm /day and the initialmoisture content of the soil (61) was 0.38 cm* cnr3. T(J) rep-resents the tune of the first drainage from the column.

During a small time increment, the volume of water infiltrat-ing horizontally from the cracks into a single depth compart-ment is a function of (i) the vertical contact area for the par-ticular depth compartment (which is increasing with time asshown in Fig. 2), and (ii) the absorption rate (which decreaseswith time).

S increases with time because new bands develop which arein contact with dry soil. Thus, for each time increment, thisincrease of contact area is associated with the initial (high) ab-sorption rate for time T(C) when flow occurs into dry soil.Horizontal absorption is reduced when the wetting front fromabove, which is due to vertical infiltration, reaches the com-partment into which horizontal absorption has to occur. Drain-age from the soil starts at time T(J) when the flow rate intothe cracks exceeds the total horizontal absorption of all layers.Water exiting at z = 20 cm is considered drainage water.

Output of the simulation model includes (i) cumulative vol-ume of water infiltrated vertically into the surface peds(CUMINF), (ii) cumulative volume of water absorbed horizon-tally by all layers (CUMABS), and (iii) cumulative volume ofwater draining from the bottom layer of the model (CUMDRN).The sum of these three factors (plus the threshold pondingvalue) should equal the rain input. The program was writtenin CSMP III language, and has been run on the DEC 10 com-puter of the Agricultural University in Wageningen, the Neth-erlands. A program listing is available from the Soil TillageLaboratory, Wageningen.

RESULTSRain intensities of 20 cm/day or 77 cm/day were

applied to initially dry soil for a maximum of 5 hours(Fig. 3 and 4). The high intensity was also applied tothe initially moist soil (Fig. 5). The graphs show rain-fall (CUMRAIN), vertical infiltration on top of thepeds (CUMINF), horizontal absorption of water intothe peds from the contact area S (CUMABS), anddrainage from the 20-cm high soil core (CUMDRN).All values are cumulative (TIME = 0 at start of rain).

__.__——— CUMINF

• • • • CUMABS

0 \ 0.04T(J) = 0.0073

0.16 0.200.08 0.12Time (days)

Fig. 4—As in Fig. 3, but for a rain intensity of 77 cm/day.

T(J) represents the moment of initial drainage fromthe column. As expected, vertical infiltration decreaseswith time, particularly in initially dry soil. Horizontalabsorption is low and increases only slightly over a0.2 day (5-hour) period. The increase is due to anincrease of S. The drainage rate from the soil can beexpressed as a percentage of the application rate, thusproviding a measure of short circuiting (Bouma etal., 1978). Measured and simulated percentages (thelatter calculated for the period 0.18 to 0.20 days) com-pare favorably (Table 1). Short circuiting is highest

0 \ 0.04 0.08 0.12 0.16 0.20T(J) = 0.0037 Time (days)Fig. 5—As in Fig. 3, but for 6, = 0.49 cm' cm-8.

HOOGMOED & BOUMA: SIMULATION MODEL FOR PREDICTING INFILTRATION INTO CRACKED CLAY SOIL 461

Table 1—A comparison of measured and simulated drainagerates of relatively dry columns of a heavy clay soil, which

were subjected to two application rates ofwater during 0.3 days (5 hours), t

Applicationrate

cm/day207777

Initial moisture contentand correspondingpressure potential

cm1 cm'3 (bar)0.38 (-15 bar)0.38 (-15 bar)0.49 (-0.1 bar)

Drainage rate("short-circuiting")

Measured Simulated% of application rate

88 7994 9098 97

t Drainage rates were determined for TIME 0.18 to 0.20 days (4 hours,20 min; 5 hours, respectively). Measured values cited are based on dupli-cate measurements (Bouma et al., 1978).

for the initially moist soil (Fig. 5, Table 1) wherevertical infiltration and horizontal absorption are rela-tively low. Measurements do not allow a separationbetween vertical infiltration and horizontal absorp-tion, as found by simulation (Fig. 3-5). Simulationis needed therefore to conclude that vertical infiltra-tion is more important than horizontal absorption inthese soils.

Short-circuiting implies movement of free wateralong the walls of unsaturated peds which are mutual-ly separated by air-filled voids. Drainage from thesoil starts at a time when the wetting front has verti-cally penetrated to a depth of only approximately 2cm. The remainder of the soil still has it's originalmoisture content.

DISCUSSIONThe model discussed has a quasi three-dimensional

character. It predicts vertical infiltration into thesurface peds in terms of rate, depth of penetration ofthe wetting front and moisture content of the wettedzone. The prediction of flow into the cracks is lessspecific because this occurs randomly along isolatedvertical bands on vertical ped faces into an area of5,000 cm2. Horizontal absorption from these bandsinto the peds results therefore in small, isolated poc-kets of water, which may be well available for plantroots, the more so since roots follow the cracks aswell. The simulation model for horizontal absorp-tion, as discussed, offers the possibility to estimate therelative volume of the pockets and the pressure po-tential of the water they contain. Physical measure-ment of water in these pockets with tensiometers ormoisture probes is, .of course, impossible. The heavyclay soil studied had low horizontal absorption rates.Different results would be expected for soils withcoarser textures where horizontal absorption may bequite significant.

The contact area S is an essential element of pre-dicting short circuiting. The standard soil profile de-scription, made in the context of soil survey, notes the

presence of large prisms, which would, conceptually,have a total vertical surface area of approximately20,000 cm2 in a 50 X 100 X 10cm soil block. Usingthis high S value, simulation predicted that waterentering the cracks was horizontally absorbed in thefirst 2-cm depth. Short circuiting is therefore not onlydue to low horizontal absorption rates, but also tothe low number of pathways for flow along verticalped faces. S can only be determined by characteriza-tion of the flow patterns using a dye. Standard de-scriptions of soil structure, are not sufficiently informa-tive. Attention was confined in this study to the dyepatterns as such; relations with different crackingpatterns or soil surface characteristics were not ex-plored. This study presents one application of thesimulation model which could be validated by mea-sured data. Testing and validation on different soilswill be needed for further development.

Short circuiting starts as soon as a threshold pond-ing depth has been reached on top of the peds. Thisponding depth, which is difficult to determine inde-pendantly due to the irregular microtopography ofthe soil surface, hardly affects vertical infiltrationrates and horizontal absorption as such. Higherlevels of the threshold ponding depth (which couldpossible be induced by superficial tillage) would in-crease cumulative vertical infiltration by postponingthe moment of initial flow into the cracks.