M. S. BABEL, R. LOOF & A. DAS GUPTA. School of Civil Engineering, Asian Institute of Technology, PO Box 2754,. Bangkok 10501, Thailand. Abstract The ...
HydrologicalSciences -Journal- des Sciences Hydrologiques,W,I,
February 1995
1
Fingered preferential flow in unsaturated homogeneous coarse sands M. S. BABEL, R. LOOF & A. DAS GUPTA School of Civil Engineering, Asian Institute of Technology, PO Box 2754, Bangkok 10501, Thailand Abstract The occurrence of fingered preferential flow depends on both flow and porous media characteristics. The boundary condition of unsaturated infiltration has been investigated to assess whether it produces unstable wetting in homogeneous coarse sands. Laboratory tracer experiments were conducted in two coarse sand materials; for each sand material two initial conditions of air dry and field capacity were considered. Results indicate that the commonly occurring process of nonponding rainfall can provoke fingered preferential flow in homogeneous sandy soils. This phenomenon is very predominant in dry as compared to wet initial conditions. Models of water flow and solute transport in uniform coarse soils should incorporate the effects of such fingered flow phenomenon. Les écoulements préférentiels dans des sables grossiers, non-saturés et homogènes Résumé L'apparition de chemins préférentiels d'écoulement dépend des caractéristiques de l'écoulement et de celles du milieux poreux. Les conditions aux limites de l'infiltration insaturée ont été étudiées afin de déterminer si elles sont susceptibles d'induire une instabilité de l'humidification dans des sables grossiers homogènes. Des expériences de traçage au laboratoire ont été menées sur deux sortes de sables grossiers; pour chacun d'entre eux deux conditions initiales ont été considérées: la siccité et la capacité au champ. Les résultats obtenus montrent que dans les conditions courantes de précipitations n'excédant pas la capacité d'infiltration du milieu, des chemins d'écoulement préférentiels digités peuvent être observés. Ce phénomène est beaucoup plus fréquent pour un état initial sec que pour un état initial humide. Les modèles d'écoulement de l'eau et de transport de soluté dans des sols grossiers uniformes devraient prendre en compte les effets de ce cheminement préférentiel digité. INTRODUCTION Understanding flow and transport mechanisms in the unsaturated (vadose) zone has received increased attention in recent years as a result of environmental concern over potential soil and groundwater pollution caused by human activities on the land surface. Preferential flow, the accelerated movement of water through isolated regions in the vadose zone, has been recognized as a phenomenon responsible Open for discussion until 1 August 1995
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M. S, Babel et al.
for the faster transport of the solute in the vadose zone (Beven & Germann, 1982; Starr et al, 1978, 1986; Richard & Steenhuis, 1988; Hallberg, 1989; Rice et al., 1991; Ghodrati & Jury, 1992). Preferential flow may take place either through macropores, like decayed root channels, cracks, worm holes and other structural inhomogeneities, or by instability of the wetting front in porous media (Bouwer, 1991). Preferential flow caused by wetting front instability leading to fingered flow is termed here as "fingered preferential flow". Of many flow and porous media characteristics (Raats, 1973; Philip, 1975) favouring fingered preferential flow, the two layered configuration, where an upper fine layer restricts the flow through a lower coarse layer, and the process of redistribution have been well studied in the laboratory and found to occur in the field (Hill & Parlange, 1972; Starr et al, 1978, 1986; Diment & Watson, 1985; Tamai et al, 1987; Glass et al, 1988, 1989a, 1989b; Baker & Hillel, 1990). Predictions regarding instability of the wetting front under the boundary condition of unsaturated infiltration are contradictory. Based on the Green and Ampt infiltration model, Raats (1973) predicted that non-ponding infiltration should be unstable in all cases, while Philip (1975) predicted that fingered flow will not occur in a homogeneous soil under uniform non-ponding rainfall condition. This clearly indicates a need for experimental investigations to analyse the flow regime under the boundary condition of unsaturated infiltration. This paper presents the results of an experimental study to investigate the fingering phenomenon conducted in a large column of homogeneous coarse sand under continuous non-ponding infiltration. The effect of antecedent wetness on fingered flow is analysed and discussed. The implications of such fingered preferential flow on soil and aquifer contamination, the availability of water for plant growth, and solute transport modelling are also discussed.
MATERIALS AND METHODS One-dimensional laboratory tracer experiments were conducted in homogeneous coarse sands for investigating the partial volume/unstable flow phenomenon under the boundary condition of unsaturated infiltration, and for the estimation of transport parameters, namely the average pore water velocity and the dispersion coefficient. The general methodology of column tracer studies was followed. The procedure consisted of applying a tracer pulse during steady state flow to a vertical, unsaturated soil column, and subsequently measuring and analysing the tracer concentration in effluent collected from the column. The chloride (Cl~) ion in the form of calcium chloride (CaCl2) was used as a conservative tracer because of its low anion exchange capacity and the ease at which this ion can be analysed in terms of electrical conductivity (Bowman, 1984).
Fingered preferential flow in unsaturated homogeneous coarse sands
3
Experimental set-up The experimental set-up consisted of a large cylinder of 0.6 m internal diameter and 2.5 m height, made of 3 mm thick mild steel sheet. The lower 0.25 m portion of the column was partitioned into six equal areas of 460 cm2 each; these areas were hydraulically separated from each other. Each partition was independently monitored for discharge and tracer concentration by providing vent tubes for sampling at the bottom of the column. This was done to observe the non-uniform flow field developed due to instability of the wetting front. A schematic of the experimental set-up is shown in Fig. 1. The numbered partitions and sampling points at the bottom of the column are also depicted in this figure. Details of other necessary arrangements have been presented by Babel (1993).
M.S. Cylii
Over Hand Tank
Acrylic Over Row
Dimensions are in mm
-Sampling Point
Fig. 1 Schematic of experimental set-up for preferential flow/tracer experiments showing the partitions at the bottom of the column.
4
M. S. Babel et al,
Sand preparation and column packing The two sand materials (Sand A and Sand B) used for the experiments were prepared by sieving the raw sand for the desired sand fractions. Sand A was finer than 2,0 mm but coarser than 0.79 mm. Sand B passed through a 1.4 mm opening sieve but was retained on a 0.6 mm opening sieve. According to the USDA soil classification, Sand A was classified as Very Coarse Sand (VCS) and Sand B as Coarse Sand (CS) (Klute, 1986). The sand materials were thoroughly washed to remove dirt and dust and then were dried under sun and kept in the laboratory to achieve air dry condition before packing the columns. The column was packed in layers of 10 cm by pouring the known quantity of sand in such a way as to keep the height of the fall the same during the filling process. After the filling of each layer, the sand was tapped to achieve a uniform bulk density along the column. Average bulk densities of 1540 kg m~3 and 1560 kg m"3 were achieved for the very coarse sand and coarse sand columns, respectively. Water distribution system In order to apply water and tracer uniformly over the soil surface at a constant low flux, use was made of hypodermic syringe needles (Wierenga & van Genuchten, 1989). Based on the results of preliminary experiments, it was decided to use needles of 0.4 mm diameter opening and 37.5 mm length. A total of 416 needles were used at intervals of 2.5 cm. The needles were glued to the bottom of an acrylic container of 60 cm diameter and 15 cm height. The resulting arrangement of needles gave a spatially uniform application of water and tracer over the sand surface as indicated by a catch can test in which the coefficient of variation in the application rate was found to be 3.5% among eight collection bottles placed over the experimental area (Babel, 1993). Initial and boundary conditions In all, four experiments were conducted. Two sandy materials were used, and for each sand two initial conditions, i.e. air dry ("Dry") and field capacity ("Wet"). The field capacity conditions were obtained by saturating the column from the bottom and allowing the column to drain under gravity to achieve hydrostatic equilibrium. A flux-type boundary condition at the top and a free drainage condition at the bottom of the column prevailed during the experiments. Table 1 summarizes the initial and boundary conditions of the tracer experiments. Method of analysis Transport of non-reactive solute during steady state water flow in a onedimensional homogeneous system may be described by (van Genuchten & Alves, 1982):
Fingered preferential flow in unsaturated homogeneous coarse sands dc
= D
d2c _ ydc 'dz1
~di
5
(1)
3z
where c is the volume averaged concentration of the solute in the liquid phase [M L" 3 ], z is distance [L], t is time [T], D is the dispersion coefficient reflecting the combined effects of diffusion and hydrodynamic dispersion on transport [L 2 T 1 ] , and Vis the average pore water velocity [L T 1 ] . Table 1 Initial and boundary conditions for tracer experiments Experiment no. Applied flux (cm IV1) 1 2 3 4
0.60 0.85 0.60 0.58
Initial water content (cm3 cm"3) 0.0008 0.0530 0.0006 0.0560
Upper boundary condition Type
Function
Third Third Third Third
Continuous Pulse Pulse Pulse
Tracer application duration (h) 14.25 7.00 12.00 12.00
Equation (1) must be supplemented with auxiliary equations describing the initial and boundary conditions of the system under study to complete the mathematical description of the transport problem. The initial condition is assumed to be of the simple form: c(z,0)
(2)
c
i
where c, is a constant. The upper boundary condition of the flux type takes the following form: c-.
D
dc_
(3)
0
= cn
Tz
where c 0 is the constant concentration of the inlet solution. The lower boundary condition is taken with the consideration that the column is part of an effectively semi-infinite system: dc_ (oo,r) = 0 ~dz
(4)
The analytical solution of equation (1) subject to equations (2), (3) and (4) in terms of flux-type concentrations appropriate for effluent curves is given by (van Genuchten & Parker, 1984): c{z,t) = q + Cc-o^.) B{z,i)
(5)
where
' z-Vt
B(z,f) = — erfc 2{Dt)m 2
'
1 'Vz + —exp D
erfc
" z + Vt ~ 2(Dt)m
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M. S. Babel et al.
For a pulse-type input boundary conditions of the form: 0 < t < L
dc~ ~V dz
Z = 0
(6)
= • t > tn
Z = 0
solution is: Ci +
0 < t < tn
{cQ-c^B{z,t)
(7)
c{z,t) = ' c. + (c0 - c-)5(z, t) - c0B(z, t -10)
t > tn
where B{z,t) is as defined above. The nonlinear least squares curve-fitting technique CXTFIT (Parker & van Genuchten, 1984), which employs the maximum neighbourhood method of Marquardt to minimize the sum of squares of the residuals between observed and calculated concentrations, was used in this study to fit either equations (5) or (7) to the observed effluent concentration distributions depending on the type of input boundary used in the tracer experiments (Table 1).
RESULTS AND DISCUSSION Flow field structure Table 2 provides the observed arrival times of the stable/unstable wetting front in different partitions at the bottom of the very coarse and coarse sand columns. The average and the standard deviation of the arrival time calculated for each experiment are also presented in Table 2. The average wetting front took only 1.85 h for the dry experiment, as compared to 9.50 h for the wet experiment, to reach the bottom of the very coarse sand column. Similarly, the average time required for the front to travel 2 m in the initially dry coarse sand was 6.7 h, as compared to 13.9 h when the coarse sand was initially at field capacity. These observations are in contrast with the general understanding of Table 2 Arrival time of unstable/stable wetting front at the bottom of the very coarse and coarse sand columns Sand
vcs VCS CS CS
Initial conditions
Applied Arrival time in partition since the start of experiment (h) flux 1 5 6 Av.$ (cmh- ) 1 2 3 4
dry wet dry wet
0.60 0.85 0.60 0.58
2.58 1.75 9.00 23.00* 11.50* 8.00 15.00 19.00*
1.58 9.50 4.17 13.25
5.75* 7.33 9.00 13.75
1.78 11.00 8.00 14.50
1.58 10.67 4.17 13.17
1.85 9.50 6.67 13.93
SDJ 0.42 1.46 2.32 0.80
VCS = very coarse sand; CS = coarse sand; Av. = average; SD = standard deviation; dry denotes air dry; and wet means at field capacity. $ calculated excluding * data,
Fingered preferential flow in unsaturated homogeneous coarse sands
7
flow in unsaturated porous media that wetting fronts will move faster in wet as compared to dry conditions. The amounts of water collected from each partition during the dry and wet experiments conducted in the very coarse sand are depicted in Figs 2 and 3 respectively. Similar observations were also obtained for the coarse sand. The Figures show that steady state flow conditions prevailed during and after the application of tracer so that the analytical solutions can be used to estimate the transport parameters. Discharge (cm/h)
1.0 o.a
Partition 1
- + - Partition 2
-*-
Partition 3
Partition 5
- $ - Partition 6
-A-
Total
Partition 4
0.6
0.4
0.2
-£-fr--e-e-e-&-£--e_e—$_ 0.0*
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
Time (h) Fig. 2 Observed discharge from different partitions at the bottom of the initially dry column of very coarse sand (experiment no. 1).
Discharge (cm/h) 1.2
1.0
Partition 1
Partition 2
-*-
Partition 3
Partition 5
Partition 6
-A-
Total
-B-
Partition 4
0.8
0.6 0.4
0.2 0.0 L 80 40 Time (h) Fig. 3 Observed discharge from different partitions at the bottom of the initially wet column of very coarse sand (experiment no. 2).
10
30
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M. S. Babel et al.
Table 3 presents the steady state distribution of flow in six partitions at the bottom of the columns. The data indicate extreme variability, about one order of magnitude, among the discharge measurements in the six partitions. This variability is an indication of the presence of unstable wetting fronts (fingers) in the column. In experiment no. 1, partitions 3 and 6 combined accounted for 63% of all the water discharged. Similar patterns were also observed in other experiments. In experiment no. 2, two partitions with the maximum discharge transported approximately 58% of all the water. In the third experiment, 67% of the water was collected from partitions 3 and 6, whereas these two partitions yielded 63% of total the water collected in experiment no. 4. In all experiments (except no. 2) the central partition (Fig. 1) contributed the most to flow. Table 3 Distribution of flow as sampled from the bottom of the column in six partitions during steady state flow Sand
Initial conditions
% of total flow observed in partition
vcs vcs s s
dry wet dry wet
10.3 22.7 7.4 7.5
1
2
3
4
14.7 2.2 4.4 3.2
43.3 18.2 43.7 31.8
7.2 34.7 14.7 19.1
5 5.0 5.7 6.6 6.9
6 19.7 16.5 23.2 31.5
VCS = very coarse sand; CS = coarse sand; dry denotes air dry; and wet means at field capacity.
Variations in the collected outflow are attributed to the fingering phenomenon involving the formation of fingers, a meandering path followed by the fingers, and the possible merger of fingers as they move down the column. A three-dimensional experiment conducted by Glass et al. (1990) in a 29.7 cm diameter, 40 cm tall PVC tube containing 0.85-1.40 mm sand showed 59 distinct fingers at a depth of 10 cm, and the number of fingers reduced to 31 (a 48% reduction) at 40 cm depth due to merging. Similar results were also obtained by Selker et al. (1989) who observed 43, 37 and 28 fingers at depths of 10, 20 and 30 cm in a column experiment. This decrease in finger count resulted from merging of fingers as verified by inspection of frozen column sections. Solute breakthrough curves The observed effluent concentration distributions were analysed using the computer program CXTFIT (Parker & van Genuchten, 1984) to obtain estimates of the parameters in the transport equation (1). A similar approach of estimating transport parameters from field tracer experiments was adopted by Bowman & Rice (1986) and Porro et al. (1993). For experiment no. 1 conducted in air-dry very coarse sand, the breakthrough curves (defining relative effluent concentration with respect to time) as observed from the six partitions are displayed in Fig. 4. Observed and calcu-
Fingered preferential flow in unsaturated homogeneous coarse sands
9
lated average effluent curves for experiment no. 1 are shown in Fig. 5. The observed curve was obtained using flux-weighted average concentrations of individual partition concentrations. The experimental curve agreed closely with the fitted curve based on the convective-dispersion equation. The measured and fitted chloride concentration distribution curves for experiment no. 2 conducted in wet conditions in very coarse sand are shown in Fig. 6. Again, the match between observed and fitted data is quite good. Relative concentration
6 8 10 Elapsed time (h) Fig. 4 Observed breakthrough curves from different partitions at the bottom of the initially dry column of very coarse sand (experiment no. 1).
Relative concentration 1.0
^-——"•—'—r 0.8
*
. / ^
0.6
-
0.4
-
/ /
0.2
Observed Fitted (CD model)
\ 0
2
4
6
8
10
12
14
16
Elapsed time (h) Fig. 5 Observed and fitted chloride breakthrough curves for the effluent from the initially dry column of very coarse sand (experiment no. 1).
10
M. S. Babel et al. Relative concentration 1.0 Observed Fitted (CD model)
0.8
0.6
0.4
0.2
0.0
10
20
40
30
50
60
Time (h) Fig. 6 Observed and fitted chloride breakthrough curves for the effluent from the initially wet column of very coarse sand (experiment no. 2).
Table 4 presents the experimental observations and the values of fitted parameters obtained from the optimization routine for the very coarse sand. While the maximum variation in outflow discharge differed by about nine times (0.18 cm h"1 in partition no. 5 compared to 1.56 cm h"1 in partition no. 3), the data in Table 4 indicate that for the dry sand experiment the maximum variation in pore water velocity is less than two times (27.9 cm If1 in partition no. 4 as compared to 50.9 cm h"1 in partition no. 3). This result reflects the fact that the area contributing to flow in each partition was different. Relatively more flow channels entered partition 3 as compared to other partitions. Similar results were obtained for the wet sand experiment. Table 4 Optimized values of average pore water velocity (V) and dispersion coefficient (D) for dry and wet experiments conducted in very coarse sand Partition no.
Dry experiment
1
0.37
2
0.53
3
1.56
4
0.26
5
0.18
6
0.71
Observed outflow (cm lr1)
Combined 0.60
V (cm h"1) 32.49 (0.37) 38.62 (0.53) 50.87 (1.31) 27.87 (0.67) 32.99 (0.54) 49.03 (1.37) 41.82 (0.71)
Wet experiment D (cm2 lr 1 ) 1692.55 (59.40) 2183.11 (94.03) 3289.75 (272.32) 949.01 (86.38) 1665.34 (86.11) 3420.90 (290.52) 2962.42 (142.90)
r2
Observed outflow (cm lr1)
0.998
1.14
0.998
0.11
0.994
0.93
0.991
1.77
0.997
0.29
0.992
0.84
0.997
0.85
Standard error in parenthesis; r is the coefficient of determination.
V (cm IT1)
D (cm2 lr 1 )
r
10.23 (0.14) 3.52 (0.08) 9.22 (0.13) 11.46 (0.18) 6.61 (0.11) 9.12 (0.11) 9.87 (0.13)
180.69 (9.50) 36.55 (3.32) 119.19 (8.11) 142.84 (10.12) 106.11 (5.52) 105.75 (6.12) 154.26 (8.42)
0.967 0.900 0.953 0.957 0.959 0.969 0.967
Fingered preferential flow in unsaturated homogeneous coarse sands
11
It is interesting to note that in the case of the very coarse sand the average pore water velocity for the initially wet column was less than one quarter of the velocity of the initially dry column indicating that a higher initial water content (field capacity) reduces the transport velocity drastically (Table 4). The observed breakthrough curves from different partitions for the wet experiment in coarse sand are shown in Fig. 7. As for the other experiments, the average observed concentration distribution could be described well with the convection-dispersion equation, as shown in Fig. 8, except near the peak and the presence of some tailing. The maximum difference between the observed and calculated concentration was about 5%, a reasonable agreement. Relative concentration
0
20
40
Time (h) 60
80
100
Fig. 7 Observed breakthrough curves from different partitions at the bottom of the initially wet column of coarse sand (experiment no. 4). Relative concentration 1.0 Observed Fitted (CD model)
0.8
0.6
0.4
\
0.2
/ 0
20
/
V 40 Time (h) 60
80
100
Fig. 8 Observed and fitted chloride breakthrough curves for the effluent from the initially wet column of coarse sand (experiment no. 4).
M. S. Babel et al.
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The observed effluent concentration data from the six partitions for the initially dry and wet columns of coarse sand were utilized to predict the transport parameters as presented in Table 5. For the dry experiment, the convective-dispersion equation could represent the observed data reasonably well except for partition no. 1 where the coefficient of determination of regression, r2, was only 0.23. The fit for the average concentration distribution may be considered also good (r2 = 0.78). Here also, as in the very coarse sand, the variation in the pore water velocity among the different partitions was much less as compared to the variation of one order of magnitude in the observed outflow rates. Table 5 Optimized values of average pore water velocity (V) and dispersion coefficient (D) for dry and wet experiments conducted in coarse sand Partition n
°'
Dry experiment Observed outflow (cm h"1)
1
0.27
2
0.16
3
1.60
4
0.54
5
0.24
6
0.85
Combined 0.60
V (cm h~!) 11.71 (2.08) 12.64 (1.95) 19.17 (2.27) 16.05 (1.68) 15.91 (2.96) 17.30 (2.74) 16.74 (2.34)
Wet experiment D (cm2 h"1) 667.08 (257.77) 714.03 (243.51) 1341.58 (316.77) 880.77 (210.11) 1076.72 (396.51) 1384.49 (392.39) 1206.50 (321.55)
2
i
Observed outflow (cm h"')
0.232
0.26
0.598
0.11
0.859
1.10
0.829
0.66
0.513
0.24
0.746
1.09
0.775
0.58
V (cm h'1)
D (cm2 h"1)
4.01 (0.05) 2.80 (0.04) 6.04 (0.09) 5.77 (0.12) 4.09 (0.07) 7.04 (0.13) 5.83 (0.11)
48.14 (2.67) 22.13 (1.57) 35.20 (4.41) 55.43 (6.35) 33.54 (3.34) 63.32 (8.01) 64.22 (6.37)
i2
0.942 0.854 0.909 0.887 0.869 0.916 0.908
Standard error in parenthesis; i2 is the coefficient of determination.
Figure 9 compares the measured effluent curves for similar boundary conditions in the dry and wet experiments of the coarse sand. A pulse of 12 h duration reached its peak relative concentration of 0.75 in about 15 h in the dry experiment whereas the same pulse took 35 h to reach a peak of 0.5 for the wet experiment. The average pore water velocity reduced from 16.7 cm If1 to 5.8 cm h"1 (Table 5) from the dry to the wet experiment. This indicates that convective transport was more pronounced in the dry as compared to wet conditions. These results confirm the findings of the experiments carried out in the very coarse sand. Flow and transport parameters Table 6 summarizes the estimated or calculated water flow and tracer transport parameters for the experiments. The water content (6 = qlv) and longitudinal dispersivity (aL D/y) were calculated with known values of the applied flux and the optimized average pore water velocity and dispersion coefficient. The
Fingered preferential flow in unsaturated homogeneous coarse sands
13
Relative concentration 1.0
0.8
0.6
0.4
0.2
0.0 0
20
40 Time (h)
60
80
Fig. 9 Comparison of observed effluent curves from the initially dry and wet columns of coarse sand for similar input boundary condition.
dispersivity, a characteristic property of a porous medium, has been calculated with the assumption that the dispersion coefficient is linearly related with the pore water velocity. The calculated water content value in experiment no. 2 (very coarse sand wet experiment) is about six times higher than that in experiment no. 1 (very coarse sand dry experiment). Similarly, the water content in experiment no. 3 (coarse sand dry experiment) is less than one-third of the water content in the wet experiment in the coarse sand (experiment no. 4). The general physical understanding of flow in unsaturated porous media is that for the same hydraulic gradient, the average pore water velocity, V, increases with the water content, 6. However, these results did not support this rule. It may be concluded that the flow had taken place through fingers having higher moisture content and causing higher transport velocities and early arrival at the bottom of the column. As seen from Table 6, the intrinsic dispersivity, aL, was a function of the initial conditions, being very high for the dry as compared to the wet experiments for the same medium. This may indicate that the assumed linear relationship between the pore water velocity and the dispersion coefficient may Table 6 Estimated or calculated flow and transport parameters for the tracer experiments Experiment no. Applied flux, q (cm h'1) 1 2 3 4
0.60 0.85 0.60 0.58
Pore water velocity, V (cm lr r ) 41.82 9.87 16.74 5.83
Dispersion coefficient, D (cm2 Ir1)
0 = qlv (cnr cm )
2962.42 154.26 1206.50 64.22
0.0143 0.0861 0.0358 0.0995
aL = D/V (cm) 70.84 15.63 72.07 11.02
14
M. S. Babel et al.
not be appropriate for unstable flow conditions. Also, for highly convective flow as observed in the dry experiments, the dispersivity cannot be so large (about 70 cm) over a travel distance of 200 cm, the length of the sand columns. The higher value of the dispersivity in the dry conditions is due to the fact that the estimated dispersion coefficient also represents lateral movement of solute between fingers and the surrounding soil matrix, as well as other mixing processes operating in the system. Hence, the estimated values of the pore water velocity and the dispersion coefficient presented in Table 6 are merely the fitted parameters obtained by forcing the convective-dispersive model to hold for the observed effluent concentration data. These parameters as such do not have much physical significance except for providing a qualitative understanding of the fingered flow phenomenon. The relationship between pore water velocity, V, and dispersion coefficient, D, was also investigated by fitting the calculated values of these parameters for different partitions in each experiment (Tables 4 and 5) to the following relation (Nielsen et al., 1986): D = aLVb
(8)
where aL and b are empirical constants. In the above equation, molecular diffusion has been ignored due to its negligible contribution to the dispersion coefficient in advection-dominated flow. A linear regression analysis was carried out on the estimated log-transformed pore water velocity and dispersion coefficient data. Table 7 gives the values for the parameters aL and b for the individual experiments, and for the data of experiments 1 and 2 and experiments 3 and 4 combined. The value of b was found to be larger than unity in all cases except for the wet experiment in the coarse sand (experiment no. 4) where it had a value very close to unity; ctL in that case becomes analogous to the dispersivity. The values of b for experiments 1, 1 and 2, and 3 and 4, were close to or exceeded 2.0, implying that the dispersion coefficient is a function of the square of the pore water velocity. When the combined data were used, equation (8) could describe the data better as reflected by the coefficient of determination from a regression (Table 7). While investigating the relationship between the average
Table 7 Relationship between the pore water velocity (V, cm h"1) and the dispersion coefficient (D, cm2 h"1) during experiments in very coarse and coarse sands according to equation (8) Experiment no. _ 2 1 and 2 combined 3 4 3 and 4 combined
Parameter aL in equation (8) _ _ 8.714 2.645 14.332 10.023 1.033
Parameter b in equation (8) _ _ 1.205 1.812 1.548 0.898 2.457
Coeff. of determination, i2 0.952 0.894 0.979 0.876 0.626 0.931
No. of data points, N 6 6 12 6 6 12
Fingered preferentialflowin unsaturated homogeneous coarse sands pore water velocity and the dispersion coefficient under continuous flood and dosed irrigation in the field, where preferential flow has taken place, Jaynes et al. (1988) also found the value of b to be more than unity. CONCLUSIONS The experimental results showed strong evidence of fingering during flow through homogeneous coarse sands under continuous unsaturated infiltration, It is expected that unstable flow occurs in any sandy soils with non-ponding rainfall. These laboratory findings are supported by the field experiments of Hendrickx & Dekker (1991), where fingered flow was prominent in homogeneous soils under natural rainfall conditions. These results suggest that fingering may be much more common than generally recognized, perhaps even being the norm rather than exception for solute transport under natural conditions in sandy soils. The convective-dispersion equation could represent the observed effluent concentration distributions satisfactorily for both dry and wet initial conditions. The relationship between the estimated pore water velocity and dispersion coefficient was found to be nonlinear with the value of the exponent being close to two. The pore water velocity reduced drastically from dry to wet initial conditions. This indicates that a higher antecedent water content suppresses the fingering phenomenon. The experiments described above indicate that, during unstable flow, the entire cross-sectional area of the profile does not take part in the flow and transport processes, but that flow is limited to some fraction of soil matrix. The results of numerical studies carried out by Babel (1993) to simulate laboratory experiments with the assumption of complete matrix flow (no fingering) clearly demonstrated the occurrence of fingered flow for both the dry and wet initial conditions. These results are supported by the field experiment of Kung (1990), who found that water flowed through less than 50% of the whole soil matrix from 1.5 to 2.0 m, less than 10% from 3.0 to 3.5 m and less than 1% from 5.6 to 6.6 m in the profile. Given the findings of Glass et al. (1989c) regarding the persistence of fingers once they are formed, it may be that the soil needs to be in dry to a very low moisture content state at one point in time in order to give rise to fingers. The fingers could then persist for very long periods of time until the profile becomes completely dry or saturated. Fingered preferential flow provides a mechanism for partial wetting of the root zone soil. The resulting smaller and non-uniform availability of water for plant growth and surface evaporation will ultimately affect crop production. Fingering may also increase the amount of groundwater recharge by promoting a faster movement of water and a reduction in évapotranspiration losses. But, at the same time, fingering leads to greater groundwater loading due to reduced partitioning of chemicals in the soil matrix and a smaller contaminant residence
15
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M. S. Babel et al.
time in the unsaturated zone where the most rapid microbial degradation and detoxification of potentially harmful organic compounds take place. In fingered flow water moves through isolated and widely scattered regions and this makes solute monitoring and modelling in the vadose zone a difficult task. If the sampling point is away from fingers, then misleading interpretation such as rapid degradation, volatilization, or plant uptake, could be made to account for the missing chemical which had moved down to groundwater. It is therefore necessary to incorporate this unique phenomenon in flow and transport modelling to improve the predictive power of models for minimizing groundwater pollution, especially for arid and semiarid environments where the climatic settings and porous media characteristics favour the development of fingering. Acknowledgements The authors would like to thank the reviewers for their valuable comments, which improved the quality of the paper. The study reported herein is a part of the research work conducted by the first author for the degree of Doctor of Engineering at the Asian Institute of Technology (AIT), Bangkok, Thailand. The authors gratefully acknowledge the financial support provided by AIT for carrying out this study.
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