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Experimental studies on the effects of pipeflow on throughflow partitioning
Journal of
Hydrology Journal of Hydrology 165 (1995) 207-219
ELSEVIER [11
Experimental studies on the effects of pipeflow on throughflow partitioning R.C. Sidle a'*, H. Kitahara b, T. Terajima c, Y. Nakai c aUSDA Forest Service, Intermountain Research Station, 860 N. 1200 E., Logan, UT 84321, USA bForestry & Forest Products Research Institute, P.O. Box 16, Tsukuba Norin, Ibaraki 305, Japan CHokkaido Research Center, FFPRL Hitsujigaoka 1, Toyohira-ku, Sapporo 062, Japan
Revision 15 March 1994; revision accepted 22 June 1994
Abstract
Recent research has revealed that natural soil pipes provide important pathways for subsurface movement of water and solutes, as well as contributing to landslide initiation. A benchscale experiment (in a sloping box 1 m in length) was conducted with a uniform sand to evaluate the effect of pipeflow on the overall hydrologic regime. A single drainage pipe (13 mm inside diameter (ID)) composed of five 20 cm segments, each with a different roughness coefficient (Manning's n), was placed 5 cm above the base of the 12.8 ° sloping box. Roughness elements were arranged in four different spatial combinations during hydraulic experiments. Piezometric levels were highest and pipeflow was lowest when the high-roughness (n = 0.325) portion of the pipe was located at the downslope end of the box. Measured values of pipeflow for different hydraulic gradients in each experiment were related to piezometric head above the pipe raised to the 0.32-0.42 power. Pipeflow was proportional to matrix flow in the soil above the pipe raised to the power of 0.4-0.6. These findings may be useful in estimating pipeflow in uniform soils and in validating two-domain models involving preferential flow in soils.
1. Introduction Pipeflow in soils is recognized as an important component of the natural hydrologic cycle (Atkinson, 1978; Tsukamoto and Ohta, 1988; Kitahara et al., 1988, 1994). Extensive systems of soil pipes have been described in various areas (Jones, 1971; Pond, 1971; Atkinson, 1978; Kitahara et al., 1988). Soil pipes may result from a variety of factors, including subsurface hydraulic erosion (Zaslavsky and Kasiff, 1965; Berry, 1970; Terajima and Sakura, 1993), large decayed root channels * Corresponding author. 0022-1694/95/$09.50 © 1995 - Elsevier Science B.V. All rights reserved SSDI 0022-1694(94)02563-Q
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(Aubertin, 1971; Kitahara, 1989; Tsuboyama et al., 1994), animal burrows (Niijima, 1976; Hole, 1981), desiccation and tension cracks (Gilman and Newson, 1980; Sidle et al., 1985), and dissolution channels (Parker, 1963). Forest soils are known to have high numbers of soil macropores and pipes because of their deep organic horizons, extensive rooting systems, and biotic activity (Aubertin, 1971; Sidle, 1980; Kitahara et al., 1988). Several investigators have measured significant contributions of pipeflow to the overall throughflow in upland drainage basins (Gilman, 1971; Tsukamoto and Ohta, 1988; Kitahara and Nakai, 1991; Kitahara et al., 1994). Additionally, pipe systems can greatly influence the movement of dissolved chemicals in hillslope soils (Beven and Germann, 1982; Luxmoore et al., 1990) and have been associated with the buildup of pore water pressure related to landslide initiation (Blong and Dunkerley, 1976; Tsukamoto et al., 1982). Although there has been extensive research on the hydraulics of artificial drains used in agriculture, very little research has been conducted on the hydraulic properties of soil pipes that typically occur in natural slopes. In earlier studies directly related to this research, Kitahara (I 989) determined hydraulic properties of soil pipes within an undisturbed block of forest soil. Pipes occupied 10% of the total soil volume and had high Manning's roughness coefficients. The coefficient of roughness is inversely proportional to pipeflow velocity and is affected by tortuosity, soil characteristics, pipe formation element, and sedimentation within the pipe. Temporal and spatial variabilities of hydraulic attributes of individual pipes have been noted in several studies (Tsukamoto and Ohta, 1988; Kitahara, 1989; Tsuboyama et al., 1994). Kitahara et al. (1988, 1989) also conducted field investigations during the snowmelt season to measure flow velocities in individual pipes using salt tracers. Results from these studies show that pipeftow can be described by the Darcy-Weisbach equation. The objectives of this present investigation were to assess the effects of variable pipe roughness on throughflow partitioning (i.e. between the soil matrix and pipe) and on the distribution of piezometric head at different positions along an experimental slope. Additionally, the relationship between pipeflow and piezometric head was studied.
2. Methodology Artificial soil pipes were constructed to simulate functional characteristics of natural soil pipes. Seepage into the pipe was not restricted by boundary conditions around the pipe. Roughness coefficients of artificial pipes were similar to those measured by Kitahara (1989) in hydraulic experiments on soil blocks excavated from a forested hillslope in Hokkaido, Japan. Five artificial pipes, 0.2 m in length, 13 mm ID, and 18 mm OD, were constructed from PVC tubing (Fig. 1).Drain holes (4 mm diameter) were evenly spaced around the pipes at a density of 0.34 holes cm -2. A non-water-soluble adhesive was carefully applied to the inside perimeter of each pipe. Glass beads (average diameter 2 mm) were then poured into the pipes in different amounts to adjust the coefficient of roughness (n) of individual pipes. The end product was a pipe with the inner
R.C. Sidle et al. / Journal o f Hydrology 165 (1995) 207-219 Water
Drain-.~ ~ ' ~
I : ~.~
209
supply
~~~",,,,,.,,~-~
~ ~ ' - ' ~ L ,
r... ~ " Totaldischarge . f l o w ) M at 1 ~n o m (Pipe e t flow e xr+i rM ta~
Polyester felt k = 0.001 m/s
/
Drainholed = 4 mm
GlassI:~ead / d = 2 mm Fig. 1. Schematic of the bench-scale experiment with an enlarged view of the artificial pipe.
perimeter coated to a greater or lesser degree with glass beads (but not completely filled with glass beads) as illustrated in Fig. 1. To prevent the drain holes of the pipe from clogging with sand and to insure even seepage distribution into the pipe, each pipe was wrapped three times with polyester felt material (Fig. 1). The permeability of the felt is 0.001 m s-t, a slightly larger value than the measured k of the sand used in the experiments. The diameter of the wrapped pipe became about 20 cm. The roughness (n value) of each pipe was determined by hydraulic experiments using various hydraulic head differentials. Pipes were wrapped with vinyl tape (not felt) during these calibrations since there was no interaction with any soil material. Discharge from each of the five pipes was calibrated for seven hydraulic gradients ranging from 0.2 (20%) to 2 (200%). Calibration curves for the five pipes are shown in Fig. 2. Roughness coefficients (n, s m-°'333s) are derived from Manning's equation n = RO'667IO'Sv-I
(1)
where R is the hydraulic radius of the pipe (m), I is the hydraulic gradient (inclination of the pipe, m m-l), and v is pipeflow velocity (m s-1) calculated as pipe discharge
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R.C. Sidle et al. / Journal of Hydrology 165 (1995) 207-219
Pipe n~m be r 00--
o ~
~
_o
/3 / A
4
50--
'
I
o
'
1
I
2
Hydraulic Gradient (rlee/run) Fig. 2. Calibration curves for determining Manning's n coefficients for the five pipe sections.
divided by cross-sectional pipe area. Calculated n values for the five pipes are: 1, 0.158; 2, 0.049; 3, 0.042; 4, 0.044; 5, 0.325. These values are similar to n values measured in naturally occurring soil pipes (0.036-1.36) at a forest site in Hokkaido (Kitahara, 1989). In each of the pipeflow tests, five 0.2 m sections of pipe, each with a different n value, were arranged in various spatial combinations for a total pipe length of 1 m. The arrangement of roughness elements used in the four experiments (Table 1) was selected to determine the effect of the location of high-roughness elements (pipes 1 and 5) on the distribution of piezometric head and pipe discharge. High-roughness sections of pipe simulate restricted flow areas within natural pipes. Such components of pipes are believed to be significant in terms of water and solute distribution in field soils and headwater drainages (Sidle, 1984; Stephens, 1994). The upslope end of the composite experimental pipe was sealed. Table 1 Spatial arrangement of various pipe roughness (Manning's n values) elements in the four pipeflow experiments Run #
1 2 3 4
Distance from bottom of slope (m) 0-0.2
0.2-0.4
0.4-0.6
0.6-0.8
0.8-1.0
5:0.325 4:0.044 4:0.044 1:0.158
4:0.044 3:0.042 5:0.325 4:0.044
3:0.042 2:0.049 3:0.042 5:0.325
2:0.049 5:0.325 2:0.049 3:0.042
1:0.158 1:0.158 1:0.158 2:0.049
Values in Table 1 are pipe number followed by Manning's coefficient.
R.C. Sidle et al. / Journal of Hydrology 165 (1995) 207-219
211
One composite pipe was placed 0.05 m above the bottom and in the middle of a 0.6 m wide box (Fig. 1). The pipe was oriented perpendicular to the slope contours, parallel to the side walls of the box. The box was filled with sand to a depth of 0.40 m. Sand was collected from a beach at Ishikari seashore in Hokkaido and had a permeability of 0.000314 m s -1 as determined by a constant head test in a 0.0004 m 3 core. Before each experiment, sand was saturated to the surface by adjusting water levels at the top and bottom of the box (Fig. 1). Water was then allowed to drain for 24 h. During experiments, water was supplied to the upper end of the box and pipeflow (Qp) and total discharge (Qt) (pipeflow + matrix flow) were measured separately at the lower end (Fig. 1)~. Thus, matrix flow (Qd) is calculated as the difference of Qt - Qp. Gradient of the experimental box was fixed at 12.8 ° . Polyester felt was secured to the upper and lower faces of the soil block with wire mesh to insure even distribution of water entry and to prevent erosion from the block faces. Six manometers were installed at the following positions relative to the downslope end of the box: 0, 0.1, 0.2, 0.4, 0.6, and 0.8 m (Fig. 1). Inlets of manometers were placed at the bottom and adjacent to the side of the box, about 0.29 m from the pipe. A preliminary experiment showed that pressure head differences were negligible between the side and center of the box for a wide range of hydraulic conditions (Fig. 3). The absence of a convex drawdown profile in pressure head can be attributed to the high permeability of the sand and the scale of the experiment. No standing water was supplied to the downslope end of the box; thus, we could measure pipeflow and total throughflow at the lower end (Fig. 1). Before conducting pipeflow experiments, we investigated the relationship between piezometric head and matrix flow for the same sandy soil with no pipe. These results showed that matrix flow (Qd) obeyed Darcy's law, thus, mean hydraulic conductivity (k) could be calculated as k = Qd/(Idwho COS0)
(2)
0.4
~
~
I
I
i
J
i
0.i
0+2
0.3
o.3
++ j . - o.2
~'N
0.1
0 0
0.4
Pressure head at the center of the box (m) Fig. 3. Comparison of pressure heads measured at the side of the experimental box with those measured at the center of the box.
212
R.C. Sidle et al. / Journal of Hydrology 165 (1995) 207-219
where I d is the hydraulic gradient as measured between manometers located at 0 and 80 cm, w is the width of the box (0.6 m), h0 is the piezometric head (m) normal to the pipe as measured in the manometer at 0 cm, and O is the gradient of the box (12.8°). The value o f k for the sand as calculated by this experiment was 0.000887 m s -1. This approximation, which assumes a uniform saturated depth within the box, is about 2.8 times the value obtained from the disturbed core test. The difference may be related to packing of the sand.
3. Results and discussion 3.1. Piezometric response
Steady-state piezometric levels along the length of the box were measured for six to eight hydraulic conditions determined by the fixed water level (//up) at the upper end of the box (Figs. 1 and 4). Piezometric profiles for the case without a soil pipe (run 0) are shown in Fig, 4(a). Heads decreased linearly in the downslope direction for all applied hydraulic gradients. Piezometric levels in the mid- to upslope section of the box were always higher than corresponding levels during any of the experiments that included a soil pipe (i.e. runs 1-4). Piezometric profiles for the experiments with a soil pipe were highly influenced by the relative position of the highest roughness section (i.e. n = 0.325 from pipe 5) in the composite pipe. Actual values of piezometric head at 0, 0.1, 0.2, 0.4, 0.6, and 0.8 m from the bottom of the experimental box for a variety of inlet head conditions are given in Table 2 for runs 1-4. The highest overall piezometric heads were observed when the no. 5 section was located at the lowest slope position (run 1, Fig. 4b). The most efficient drainage (i.e. lowest piezometric levels) occurred when this highroughness section of pipe (no. 5) was positioned in the uppermost portion of the box near the water supply (run 2, Fig. 4c). Piezometric heads measured at the midslope piezometer (0.4 m from the bottom of the box) were at least twice as high during run 1 compared with run 2 (Table 2). Piezometric profiles were similar for run 3 (Fig. 4d) and run 4 (Fig. 4e) for all applied hydraulic gradients, except in the lower portion of the box. During run 3, there was a small increase in piezometric head in the lower half of the box owing to the position of the high-roughness section of pipe (0.2-0.4 m upslope) compared with the position in run 4 (40-60 cm upslope). Although the pipes effectively decreased piezometric head during these experiments, the relative positions of the lower roughness sections of pipe (nos. 1-4) had no apparent influence on piezometric head (Fig. 4; Table 2). These experimental data suggest that the distribution of high-roughness elements within naturally occurring soil pipes can greatly affect piezometric profiles along hiUslopes. 3.2. Pipeflow
Steady-state pipeflow rates for the four experiments are plotted over a range of piezometric heads (Fig. 5). For similar hydraulic gradients, Qp was approximately 5.5
R:C. Sidle et al. / Journal of Hydrology 165 (1995) 207-219
213
12.8 °
(b)R u ~
(c)R u ~
n-value for each pipe section
(d)Run3
I . , , , , ~ 0.0 °''
(e)Run4
~ ~ 0 . ~
j~ ~
O.Oa,~ u.--
Fig. 4. Piezometric profiles for various hydraulic experimental conditions: (a) without a soil pipe; (b)run 1, with a soil pipe; (c) run 2, with a soil pipe; (d) run 3, with a soil pipe; and (e) run 4, with a soil pipe.
times higher during run 2 compared with run 1. Smaller pipe discharge during run 1 is attributed to the location of the high-roughness section of the pipe at the bottom of the box. Pipeflows during runs 3 and 4 were smaller than those in run 2 owing to the lower slope position of the high-roughness section of the pipe in runs 3 and 4. The slightly higher values of Qp in run 3 versus run 4 may be attributed to the location of
214
R.C. Sidle et al. / Journal o f Hydrology 165 (1995) 207-219
Table 2 Piezometric head (H) measured at six distances from the bottom of the slope for a variety of inlet head (/-/up) conditions Run #
1
/-/up
Distance from bottom of slope (m) 0m
0.1m
0.2m
0.4m
0.6m
0.8m
0.355 0.308 0.256 0.217 0.135 0.088 0.050
-
0.195 0.180 0.165 0.155 0.127 0.110 0.095
0.213 0.195 0.174 0.161 0.125 0.103 0.086
0.226 0.199 0.168 0.150 0.104 0.076 0.054
0.233 0.199 0.162 0.137 0.082 0.048 0.025
0.254 0.212 0.168 0.137 0.072 0.032 0.007
0.334 0.281 0.230 0.188 0.140 0.095 0.339 0.287 0.229 0.188 0.144 0.089
0.091 0.080 0.074 0.064 0.039 0.051 0.108 0.097 0.091 0.079 0.071 -
0.096 0.083 0.075 0.065 0.039 0.051 0.127 0.115 0.102 0.087 0.076 0.060
0.107 0.090 0.077 0.063 0.053 0.041 0.149 0.131 0.111 0.090 0.075 0.054
0.117 0.093 0.077 0.055 0.032 0.013 0.171 0.141 0.111 0.084 0.060 0.023
0.161 0.126 0.097 0.068 0.040 0.007 0.185 0.150 0.111 0.077 0.045 0.004
0.209 0.166 0.129 0.094 0.058 0.018 0.214 0.174 0.129 0.089 0.050 0.002
0.338 0.280 0.230 0.187 0.140 0.097
0.105 0.095 0.086 0.079 0.070 0.061
0.117 0.103 0.094 0.084 0.072 0.061
0.133 0.113 0.100 0.087 0.070 0.057
0.161 0.131 0.107 0.085 0.061 0.037
0.195 0.155 0.120 0.089 0.055 0.023
0.220 0.171 0.128 0.091 0.051 0.013
the second highest roughness element (n = 0.158 f r o m pipe 1) at the d o w n g r a d i e n t e n d o f the box d u r i n g r u n 4. F o r o u r experimental conditions, Qp c a n be q u a n t i t a t i v e l y related to H as follows Qp = a ( H - 0.03) 8
(3)
where a a n d /3 are coefficients d e t e r m i n e d by linear regression analysis o f the logarithmic f o r m o f Eq. (3) a n d H is the average o f piezometric heads m e a s u r e d at h0, h20, h40, h60, a n d hs0. C o r r e l a t i o n coefficients for the four r u n s based o n the logt r a n s f o r m e d version o f Eq. (3) were high, 0.973-0.999. The value o f 0.03 in Eq. (3) represents the distance between the b o t t o m o f the pipe a n d the floor o f the box (0.03 m). Theoretically, n o pipeflow should occur if piezometric head is less t h a n 0.03 m, thus the value 0,03 is s u b t r a c t e d f r o m H i n Eq.(3). F r o m Fig. 5, it c a n be seen that two d a t a points showed small b u t m e a s u r a b l e pipeflow when H was less t h a n 0.03 m. This m a y be a t t r i b u t e d to a slight lag time between m a n o m e t e r response a n d m a n u a l pipeflow m e a s u r e m e n t s or to the effects o f storage a n d delayed d r a i n a g e in the
R.C. Sidle et al. / Journal of Hydrology 165 (1995) 207-219
Run 1:Op=1.686x10 "s. ( H - 0 . 0 3 ) Run 2:Op=S.016x10 " s - ( H - 0 . 0 3 ) Run 3:Op=7.880x10 -s. ( H - 0 . 0 3 ) Run 4:Op=6.272x10 -s- ( H - 0 . 0 3 )
215
o.42ss ( r = 0 . 9 9 3 3 ) o.z2o2 ( r = 0 . 9 7 3 2 ) o.zg~ ( r = 0 . 9 9 9 4 ) o.3sss ( r = 0 . 9 8 0 3 )
50 I
I II--
O
4O
°
!
O"'" .....
tt) .,-"
E
~. A "
.~
-.--13 Run ......O ......R u n 2 --6-.Run 3 - - - O .... Run 4
O
o 30 v-v
x
o
3"
..-
..6
,°'
."
............
20
_..o_
/
J. .
/- /
.O" ...............................................
/Z o / /"I~
o
13..
10
0
0.1 Piezometric
0.2 Head,
0.3
H (m)
Fig. 5. Relationships between measured pipeflow and piezometric head.
pipe. The coefficient /3, which represents the slope of the log-linear regression, was very similar for all runs and ranged from 0.320 to 0.424. Higher /3 values correspond to lower pipeflow discharges, i.e. when a high-roughness element was located near the downgradient end of the box. The constant a is related to hydraulic conductivity, roughness coefficient, hydraulic gradient, and pipe and box dimensions. Even though flow into a soil pipe is a complex three-dimensional hydraulic problem, the simple empirical relationship presented in Eq. (3) appears to give reasonable estimates of pipeflow for uniform soil conditions given the scale and flow geometry of the box. Larger scale experiments have also confirmed a direct relationship between Qp and H over a small range of hydraulic heads (Ohkura et al., 1992). Recently, such a simple relationship between pipeflow and H has been proposed for incorporation into a theoretically based, dual-porosity model for simulating preferential flow in a structured soil (Gerke and Van Genuchten, 1993).
R.C. Sidle et al. / Journal of Hydrology 165 (1995) 207-219
216
3.3. Relationship between pipeflow and matrix flow
The relationships between steady-state rates of Qp a n d Qd for all four experiments with a soil pipe are shown in Fig. 6. Average pipeflow discharges over the range of hydraulic gradients were 21.2, 83.1, 72.0, and 68.3% of total outflow (matrix flow + pipeflow) for runs 1, 2, 3, and 4, respectively. Curves plotted in Fig. 6 show very similar responses to the relationships between Qp and H (Fig. 5). In Fig. 6, all curves were forced through the x-intercept at Qd = 3.5 ml s -1 (0.0000035 m 3 s-I), the calculated value of matrix flow below the pipe; i.e. the product of w (0.6 m), depth below the pipe (0.03 m), k (8.87 x 10 -4 m 3 s-I), and Ia (sin 12.5°). This value for flow under the pipe can then be subtracted from Qd in the general exponential equation that describes the relationship between Qp and Qd Op = a(ad - 0.0000035) 8
(4)
where a and /3 are coefficients determined using the same log-linear regression methods as for Eq. (3). Exponential equations based on Eq. (4) for the four pipeflow experiments are Run 1 Qp = 0.0007044(Q d - 0.0000035) 0.437 r = 0.999
(5a)
Run 2
(5b)
Qp = 0.07504(Q d - 0.0000035) 0.605 r = 0.981
Run 2
"Run3
40
~.Run 4
E j= O
IL O
20
D. G. Run
0
I
I
3.5
20
'
I
40
Mat r i x Flow (ml/s) Fig. 6. Relationships between pipeflow and matrix flow in the four experiments.
R.C. Sidle et al. / Journal of Hydrology 165 (1995) 207-219
217
Run 3
Qp = 0.003728(Qd - 0.0000035) 0'411 r = 0.970
(5c)
Run 4
Qp = 0.01376(Qd - 0.0000035) 0.538 r = 0.993
(5d)
Correlation coefficients for the linearized form of these equations are very high (0.970-0.999). The exponential coefficients (~) ranged from about 0.4 to 0.6. These values were very similar to the exponential coefficients obtained in the relationships between Qp and H, especially for runs 1 and 3.
4. Summary and conclusions A series of experiments with a single artificial pipe in a sandy soil provided hydrologic information that may be useful for the study of streamflow generation, solute transport, landslide initiation, and surface erosion mechanisms in soils containing preferential flow pathways. Spatially varying properties of soil pipes (i.e. Manning's n coefficients) had a significant effect on piezometric response and relative discharge from pipes and the soil matrix. When the high-roughness portion (high n coefficient) of the pipe was located in the lower end of the sloping experimental box, piezometric levels were highest and pipeflow was lowest relative to matrix flow. This analogy can be extended to a hillslope where clogging, sedimentation, or a restriction may occur in a natural soil pipe. Thus, the position of the restriction (high n coefficient) in a given pipe can affect pore water pressure distribution within a slope segment. Such regions of pore water pressure buildup associated with discontinuous or restricted macropore networks have been suggested as contributing factors to landslide initiation (Tsukamoto et al., 1982; Pierson, 1983; Sidle, 1984). It is also evident from this research that subsurface flow regime and timing of solute transport can be greatly influenced by hydrologic properties of soil pipes. A simple exponential relationship between average piezometric head and pipeflow was observed for a wide range of hydraulic conditions given the scale and geometry of the experiment. This relationship may prove useful for estimating or modeling pipeflow in uniform soils.
Acknowledgments We express our gratitude to Dr. Tomoki Sakamoto, Takeshi Saito, and Yoshio Tsuboyama of the Forestry and Forest Products Research Institute (FFPRI) for their helpful discussions related to this research. A portion of this study was conducted while the senior author was funded by a fellowship (190056) from the Science and Technology Agency (STA) of Japan in 1991. Later research was sponsored in 1992 and 1994 when R.C.S. received Foreign Specialist Awards from STA. The authors wish to thank Drs. Makoto Tani, Hirotaka Ochiai, and Toshiaki Sammori of FFPRI in Tsukuba, Japan, for promoting this cooperative research.
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References Atkinson, T.C., 1978. Techniques for measuring subsurface flow on hillslopes. In: M.J. Kirkby (Editor), Hillslope Hydrology. John Wiley & Sons, Chichester, UK, pp. 73-120. Aubertin, G.M., 1971. Nature and extent ofmacropores in forest soils. USDA For. Serv. Res. Pap. NE-192, Radnor, PA. Berry, L., 1970. Some erosional features due to piping and subsurface wash with special reference to Sudan. Geogr. Annu., 52A(2): 113-119. Beven, K. and Germann, P., 1982. Macropores and water flow in soils. Water Resour. Res., 18(5): 13111325. Blong, R.J. and Dunkerley, D.L., 1976. Landslides in the Razorback area, New South Wales,Australia. Geogr. Annu., 58A: 139-147. Gerke, H.H. and van Genuchten, M.T., 1993. A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media. Water Resour. Res., 29: 305319. Gilman, K., 1971. A semi-quantitative study of the flow of natural pipes in the Nant Gerig sub-catchment. In: Subsurface Hydrology, Rep. 36, Institute of Hydrology, Wallingford, UK. Gilman, K. and Newson, M., 1980. Soil pipes and pipeflow - - a hydrologic study in upland Wales. Res. Monogr. 1, British Geomorphological Research Group, Geobooks, Norwich, UK. Hole, F.D., 1981. Effects of animals on soils. Geoderma, 25: 75-112. Jones, J.A.A., 1971. Soil piping and stream channel initiation. Water Resour. Res., 7: 602-610. Kitahara, H., 1989. Characteristics of pipe flow in a subsurface soil layer on a gentle slope (II) Hydraulic properties of pipes: J. Jpn. For. Soc., 71(8): 317-322 (in Japanese). Kitahara, H. and Nakai, Y., 1991. Response of pipeflow to rainfalls. Trans. of the 102nd Annual Meeting of the Japanese Forestry Soc., Nagoya, pp. 603-604 (in Japanese). Kitahara, H., Shimizu, A. and Mashima, Y., 1988. Characteristics of pipe flow in a subsurface soil layer of a gentle hillside. J. Jpn. For. Soc., 70(7): 318-323 (in Japanese). Kitahara, H., Shimizu, A. and Mashima, Y., 1989. Measurement and hydraulic properties of subsurface flow above bedrock. Trans. of the 100th Meeting of the Japanese Forestry Soc., Tokyo, pp. 645-646 (in Japanese). Kitahara, H., Terajima, T. and Nakai, Y., 1994. Ratio of pipe flow to througlfflow discharge. J. Jpn. For. Soc., 76: 10-17. Luxmoore, R.J., Jardine, P.M., Wilson, G.V., Jones, J.R. and Zelazny, L.W., 1990. Physical and chemical controls of preferred path flow through a forested hillslope. Geoderma, 46: 139-154. Niijima, K., 1976. Influence of construction of a road on soil animals in a case of sub-alpine coniferous forest on Mt. Fuji. Rev. Ecol. Biol. Sol, 13(1): 47-54. Ohkura, Y., Sammori, T., Ochiai, H., Sidle, R.C., Moriwaki, H., Tohei, M. and Amada, K, 1992. Experimental studies on effect of non-homogeneous soil on landslide initiation (I). In: Proc. of 1992 Annual Meeting of Erosion Control Eng. Soc. of Japan, Tokyo. Japan Soc. Erosion Control Eng., Tokyo, pp. 10-13 (in Japanese). Parker, G.G., 1963. Piping, a geomorphic agent in landform development of the drylands. Int. Assoc. Hydrol. Sci., Publ. 65, IAHS, Wallingford, pp. 103-113. Pierson, T.C., 1983. Soil pipes and slope stability. Q. J. Eng. Geol., 16:1-11. Pond, S.F., 1971. Qualitative investigation into the nature and distribution of flow processes in Nant Gerig. In: Subsurface Hydrology. Rep. 28, Institute of Hydrology, Wallingford, UK. Sidle, R.C., 1980. Slope stability on forest land. Pacific NW Ext. Publ. PNW209, Oregon State University, Corvallis. Sidle, R.C., 1984. Shallow groundwater fluctuations in unstable hillslopes of coastal Alaska. Z. Gletscherkd. Glazialgeol., 20: 79-95. Sidle, R.C., Pearce, A.J. and O'Loughlin, C.L., 1985. Hillslope stability and land use. Water Resources Monogr. 11, Am. Geophys. Union, Washington, DC. Stephens, D.B., 1994. A perspective on diffuse natural recharge mechanisms in areas of low precipitation. Soil Sci. Soc. Am. J., 58: 40-48.
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Terajima, T. and Sakura, Y., 1993. Effect of subsurface flow on a topographic change at a valley head of granitic mountains. Trans., Jpn. Geomorphol. Union, 14(4): 365-384 (in Japanese). Tsuboyama, Y., Sidle, R.C., Noguchi, S. and Hosoda, I., 1994. Flow and solute transport through the soil matrix and macropores of a hillslope segment. Water Resour. Res., 30(4): 879-890. Tsukamoto, Y. and Ohta, T., 1988. Runoff processes on a steep forested slope. J. Hydrol., 102: 165-178. Tsukamoto, Y., Ohta, T. and Noguchi, H., 1982. Hydrological and geomorphological studies of debris slides on forested hillslopes in Japan. Int. Assoc. Hydrol. Sci., Publ. 137, IAHS, Wallingford, pp. 89-98. Zaslavsky, D. and Kasiff, G., 1965. Theoretical formulation of piping mechanism in cohesive soils. Geotechnique, 15(3): 305-316.
Hydrology Journal of Hydrology 165 (1995) 207-219
ELSEVIER [11
Experimental studies on the effects of pipeflow on throughflow partitioning R.C. Sidle a'*, H. Kitahara b, T. Terajima c, Y. Nakai c aUSDA Forest Service, Intermountain Research Station, 860 N. 1200 E., Logan, UT 84321, USA bForestry & Forest Products Research Institute, P.O. Box 16, Tsukuba Norin, Ibaraki 305, Japan CHokkaido Research Center, FFPRL Hitsujigaoka 1, Toyohira-ku, Sapporo 062, Japan
Revision 15 March 1994; revision accepted 22 June 1994
Abstract
Recent research has revealed that natural soil pipes provide important pathways for subsurface movement of water and solutes, as well as contributing to landslide initiation. A benchscale experiment (in a sloping box 1 m in length) was conducted with a uniform sand to evaluate the effect of pipeflow on the overall hydrologic regime. A single drainage pipe (13 mm inside diameter (ID)) composed of five 20 cm segments, each with a different roughness coefficient (Manning's n), was placed 5 cm above the base of the 12.8 ° sloping box. Roughness elements were arranged in four different spatial combinations during hydraulic experiments. Piezometric levels were highest and pipeflow was lowest when the high-roughness (n = 0.325) portion of the pipe was located at the downslope end of the box. Measured values of pipeflow for different hydraulic gradients in each experiment were related to piezometric head above the pipe raised to the 0.32-0.42 power. Pipeflow was proportional to matrix flow in the soil above the pipe raised to the power of 0.4-0.6. These findings may be useful in estimating pipeflow in uniform soils and in validating two-domain models involving preferential flow in soils.
1. Introduction Pipeflow in soils is recognized as an important component of the natural hydrologic cycle (Atkinson, 1978; Tsukamoto and Ohta, 1988; Kitahara et al., 1988, 1994). Extensive systems of soil pipes have been described in various areas (Jones, 1971; Pond, 1971; Atkinson, 1978; Kitahara et al., 1988). Soil pipes may result from a variety of factors, including subsurface hydraulic erosion (Zaslavsky and Kasiff, 1965; Berry, 1970; Terajima and Sakura, 1993), large decayed root channels * Corresponding author. 0022-1694/95/$09.50 © 1995 - Elsevier Science B.V. All rights reserved SSDI 0022-1694(94)02563-Q
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(Aubertin, 1971; Kitahara, 1989; Tsuboyama et al., 1994), animal burrows (Niijima, 1976; Hole, 1981), desiccation and tension cracks (Gilman and Newson, 1980; Sidle et al., 1985), and dissolution channels (Parker, 1963). Forest soils are known to have high numbers of soil macropores and pipes because of their deep organic horizons, extensive rooting systems, and biotic activity (Aubertin, 1971; Sidle, 1980; Kitahara et al., 1988). Several investigators have measured significant contributions of pipeflow to the overall throughflow in upland drainage basins (Gilman, 1971; Tsukamoto and Ohta, 1988; Kitahara and Nakai, 1991; Kitahara et al., 1994). Additionally, pipe systems can greatly influence the movement of dissolved chemicals in hillslope soils (Beven and Germann, 1982; Luxmoore et al., 1990) and have been associated with the buildup of pore water pressure related to landslide initiation (Blong and Dunkerley, 1976; Tsukamoto et al., 1982). Although there has been extensive research on the hydraulics of artificial drains used in agriculture, very little research has been conducted on the hydraulic properties of soil pipes that typically occur in natural slopes. In earlier studies directly related to this research, Kitahara (I 989) determined hydraulic properties of soil pipes within an undisturbed block of forest soil. Pipes occupied 10% of the total soil volume and had high Manning's roughness coefficients. The coefficient of roughness is inversely proportional to pipeflow velocity and is affected by tortuosity, soil characteristics, pipe formation element, and sedimentation within the pipe. Temporal and spatial variabilities of hydraulic attributes of individual pipes have been noted in several studies (Tsukamoto and Ohta, 1988; Kitahara, 1989; Tsuboyama et al., 1994). Kitahara et al. (1988, 1989) also conducted field investigations during the snowmelt season to measure flow velocities in individual pipes using salt tracers. Results from these studies show that pipeftow can be described by the Darcy-Weisbach equation. The objectives of this present investigation were to assess the effects of variable pipe roughness on throughflow partitioning (i.e. between the soil matrix and pipe) and on the distribution of piezometric head at different positions along an experimental slope. Additionally, the relationship between pipeflow and piezometric head was studied.
2. Methodology Artificial soil pipes were constructed to simulate functional characteristics of natural soil pipes. Seepage into the pipe was not restricted by boundary conditions around the pipe. Roughness coefficients of artificial pipes were similar to those measured by Kitahara (1989) in hydraulic experiments on soil blocks excavated from a forested hillslope in Hokkaido, Japan. Five artificial pipes, 0.2 m in length, 13 mm ID, and 18 mm OD, were constructed from PVC tubing (Fig. 1).Drain holes (4 mm diameter) were evenly spaced around the pipes at a density of 0.34 holes cm -2. A non-water-soluble adhesive was carefully applied to the inside perimeter of each pipe. Glass beads (average diameter 2 mm) were then poured into the pipes in different amounts to adjust the coefficient of roughness (n) of individual pipes. The end product was a pipe with the inner
R.C. Sidle et al. / Journal o f Hydrology 165 (1995) 207-219 Water
Drain-.~ ~ ' ~
I : ~.~
209
supply
~~~",,,,,.,,~-~
~ ~ ' - ' ~ L ,
r... ~ " Totaldischarge . f l o w ) M at 1 ~n o m (Pipe e t flow e xr+i rM ta~
Polyester felt k = 0.001 m/s
/
Drainholed = 4 mm
GlassI:~ead / d = 2 mm Fig. 1. Schematic of the bench-scale experiment with an enlarged view of the artificial pipe.
perimeter coated to a greater or lesser degree with glass beads (but not completely filled with glass beads) as illustrated in Fig. 1. To prevent the drain holes of the pipe from clogging with sand and to insure even seepage distribution into the pipe, each pipe was wrapped three times with polyester felt material (Fig. 1). The permeability of the felt is 0.001 m s-t, a slightly larger value than the measured k of the sand used in the experiments. The diameter of the wrapped pipe became about 20 cm. The roughness (n value) of each pipe was determined by hydraulic experiments using various hydraulic head differentials. Pipes were wrapped with vinyl tape (not felt) during these calibrations since there was no interaction with any soil material. Discharge from each of the five pipes was calibrated for seven hydraulic gradients ranging from 0.2 (20%) to 2 (200%). Calibration curves for the five pipes are shown in Fig. 2. Roughness coefficients (n, s m-°'333s) are derived from Manning's equation n = RO'667IO'Sv-I
(1)
where R is the hydraulic radius of the pipe (m), I is the hydraulic gradient (inclination of the pipe, m m-l), and v is pipeflow velocity (m s-1) calculated as pipe discharge
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Pipe n~m be r 00--
o ~
~
_o
/3 / A
4
50--
'
I
o
'
1
I
2
Hydraulic Gradient (rlee/run) Fig. 2. Calibration curves for determining Manning's n coefficients for the five pipe sections.
divided by cross-sectional pipe area. Calculated n values for the five pipes are: 1, 0.158; 2, 0.049; 3, 0.042; 4, 0.044; 5, 0.325. These values are similar to n values measured in naturally occurring soil pipes (0.036-1.36) at a forest site in Hokkaido (Kitahara, 1989). In each of the pipeflow tests, five 0.2 m sections of pipe, each with a different n value, were arranged in various spatial combinations for a total pipe length of 1 m. The arrangement of roughness elements used in the four experiments (Table 1) was selected to determine the effect of the location of high-roughness elements (pipes 1 and 5) on the distribution of piezometric head and pipe discharge. High-roughness sections of pipe simulate restricted flow areas within natural pipes. Such components of pipes are believed to be significant in terms of water and solute distribution in field soils and headwater drainages (Sidle, 1984; Stephens, 1994). The upslope end of the composite experimental pipe was sealed. Table 1 Spatial arrangement of various pipe roughness (Manning's n values) elements in the four pipeflow experiments Run #
1 2 3 4
Distance from bottom of slope (m) 0-0.2
0.2-0.4
0.4-0.6
0.6-0.8
0.8-1.0
5:0.325 4:0.044 4:0.044 1:0.158
4:0.044 3:0.042 5:0.325 4:0.044
3:0.042 2:0.049 3:0.042 5:0.325
2:0.049 5:0.325 2:0.049 3:0.042
1:0.158 1:0.158 1:0.158 2:0.049
Values in Table 1 are pipe number followed by Manning's coefficient.
R.C. Sidle et al. / Journal of Hydrology 165 (1995) 207-219
211
One composite pipe was placed 0.05 m above the bottom and in the middle of a 0.6 m wide box (Fig. 1). The pipe was oriented perpendicular to the slope contours, parallel to the side walls of the box. The box was filled with sand to a depth of 0.40 m. Sand was collected from a beach at Ishikari seashore in Hokkaido and had a permeability of 0.000314 m s -1 as determined by a constant head test in a 0.0004 m 3 core. Before each experiment, sand was saturated to the surface by adjusting water levels at the top and bottom of the box (Fig. 1). Water was then allowed to drain for 24 h. During experiments, water was supplied to the upper end of the box and pipeflow (Qp) and total discharge (Qt) (pipeflow + matrix flow) were measured separately at the lower end (Fig. 1)~. Thus, matrix flow (Qd) is calculated as the difference of Qt - Qp. Gradient of the experimental box was fixed at 12.8 ° . Polyester felt was secured to the upper and lower faces of the soil block with wire mesh to insure even distribution of water entry and to prevent erosion from the block faces. Six manometers were installed at the following positions relative to the downslope end of the box: 0, 0.1, 0.2, 0.4, 0.6, and 0.8 m (Fig. 1). Inlets of manometers were placed at the bottom and adjacent to the side of the box, about 0.29 m from the pipe. A preliminary experiment showed that pressure head differences were negligible between the side and center of the box for a wide range of hydraulic conditions (Fig. 3). The absence of a convex drawdown profile in pressure head can be attributed to the high permeability of the sand and the scale of the experiment. No standing water was supplied to the downslope end of the box; thus, we could measure pipeflow and total throughflow at the lower end (Fig. 1). Before conducting pipeflow experiments, we investigated the relationship between piezometric head and matrix flow for the same sandy soil with no pipe. These results showed that matrix flow (Qd) obeyed Darcy's law, thus, mean hydraulic conductivity (k) could be calculated as k = Qd/(Idwho COS0)
(2)
0.4
~
~
I
I
i
J
i
0.i
0+2
0.3
o.3
++ j . - o.2
~'N
0.1
0 0
0.4
Pressure head at the center of the box (m) Fig. 3. Comparison of pressure heads measured at the side of the experimental box with those measured at the center of the box.
212
R.C. Sidle et al. / Journal of Hydrology 165 (1995) 207-219
where I d is the hydraulic gradient as measured between manometers located at 0 and 80 cm, w is the width of the box (0.6 m), h0 is the piezometric head (m) normal to the pipe as measured in the manometer at 0 cm, and O is the gradient of the box (12.8°). The value o f k for the sand as calculated by this experiment was 0.000887 m s -1. This approximation, which assumes a uniform saturated depth within the box, is about 2.8 times the value obtained from the disturbed core test. The difference may be related to packing of the sand.
3. Results and discussion 3.1. Piezometric response
Steady-state piezometric levels along the length of the box were measured for six to eight hydraulic conditions determined by the fixed water level (//up) at the upper end of the box (Figs. 1 and 4). Piezometric profiles for the case without a soil pipe (run 0) are shown in Fig, 4(a). Heads decreased linearly in the downslope direction for all applied hydraulic gradients. Piezometric levels in the mid- to upslope section of the box were always higher than corresponding levels during any of the experiments that included a soil pipe (i.e. runs 1-4). Piezometric profiles for the experiments with a soil pipe were highly influenced by the relative position of the highest roughness section (i.e. n = 0.325 from pipe 5) in the composite pipe. Actual values of piezometric head at 0, 0.1, 0.2, 0.4, 0.6, and 0.8 m from the bottom of the experimental box for a variety of inlet head conditions are given in Table 2 for runs 1-4. The highest overall piezometric heads were observed when the no. 5 section was located at the lowest slope position (run 1, Fig. 4b). The most efficient drainage (i.e. lowest piezometric levels) occurred when this highroughness section of pipe (no. 5) was positioned in the uppermost portion of the box near the water supply (run 2, Fig. 4c). Piezometric heads measured at the midslope piezometer (0.4 m from the bottom of the box) were at least twice as high during run 1 compared with run 2 (Table 2). Piezometric profiles were similar for run 3 (Fig. 4d) and run 4 (Fig. 4e) for all applied hydraulic gradients, except in the lower portion of the box. During run 3, there was a small increase in piezometric head in the lower half of the box owing to the position of the high-roughness section of pipe (0.2-0.4 m upslope) compared with the position in run 4 (40-60 cm upslope). Although the pipes effectively decreased piezometric head during these experiments, the relative positions of the lower roughness sections of pipe (nos. 1-4) had no apparent influence on piezometric head (Fig. 4; Table 2). These experimental data suggest that the distribution of high-roughness elements within naturally occurring soil pipes can greatly affect piezometric profiles along hiUslopes. 3.2. Pipeflow
Steady-state pipeflow rates for the four experiments are plotted over a range of piezometric heads (Fig. 5). For similar hydraulic gradients, Qp was approximately 5.5
R:C. Sidle et al. / Journal of Hydrology 165 (1995) 207-219
213
12.8 °
(b)R u ~
(c)R u ~
n-value for each pipe section
(d)Run3
I . , , , , ~ 0.0 °''
(e)Run4
~ ~ 0 . ~
j~ ~
O.Oa,~ u.--
Fig. 4. Piezometric profiles for various hydraulic experimental conditions: (a) without a soil pipe; (b)run 1, with a soil pipe; (c) run 2, with a soil pipe; (d) run 3, with a soil pipe; and (e) run 4, with a soil pipe.
times higher during run 2 compared with run 1. Smaller pipe discharge during run 1 is attributed to the location of the high-roughness section of the pipe at the bottom of the box. Pipeflows during runs 3 and 4 were smaller than those in run 2 owing to the lower slope position of the high-roughness section of the pipe in runs 3 and 4. The slightly higher values of Qp in run 3 versus run 4 may be attributed to the location of
214
R.C. Sidle et al. / Journal o f Hydrology 165 (1995) 207-219
Table 2 Piezometric head (H) measured at six distances from the bottom of the slope for a variety of inlet head (/-/up) conditions Run #
1
/-/up
Distance from bottom of slope (m) 0m
0.1m
0.2m
0.4m
0.6m
0.8m
0.355 0.308 0.256 0.217 0.135 0.088 0.050
-
0.195 0.180 0.165 0.155 0.127 0.110 0.095
0.213 0.195 0.174 0.161 0.125 0.103 0.086
0.226 0.199 0.168 0.150 0.104 0.076 0.054
0.233 0.199 0.162 0.137 0.082 0.048 0.025
0.254 0.212 0.168 0.137 0.072 0.032 0.007
0.334 0.281 0.230 0.188 0.140 0.095 0.339 0.287 0.229 0.188 0.144 0.089
0.091 0.080 0.074 0.064 0.039 0.051 0.108 0.097 0.091 0.079 0.071 -
0.096 0.083 0.075 0.065 0.039 0.051 0.127 0.115 0.102 0.087 0.076 0.060
0.107 0.090 0.077 0.063 0.053 0.041 0.149 0.131 0.111 0.090 0.075 0.054
0.117 0.093 0.077 0.055 0.032 0.013 0.171 0.141 0.111 0.084 0.060 0.023
0.161 0.126 0.097 0.068 0.040 0.007 0.185 0.150 0.111 0.077 0.045 0.004
0.209 0.166 0.129 0.094 0.058 0.018 0.214 0.174 0.129 0.089 0.050 0.002
0.338 0.280 0.230 0.187 0.140 0.097
0.105 0.095 0.086 0.079 0.070 0.061
0.117 0.103 0.094 0.084 0.072 0.061
0.133 0.113 0.100 0.087 0.070 0.057
0.161 0.131 0.107 0.085 0.061 0.037
0.195 0.155 0.120 0.089 0.055 0.023
0.220 0.171 0.128 0.091 0.051 0.013
the second highest roughness element (n = 0.158 f r o m pipe 1) at the d o w n g r a d i e n t e n d o f the box d u r i n g r u n 4. F o r o u r experimental conditions, Qp c a n be q u a n t i t a t i v e l y related to H as follows Qp = a ( H - 0.03) 8
(3)
where a a n d /3 are coefficients d e t e r m i n e d by linear regression analysis o f the logarithmic f o r m o f Eq. (3) a n d H is the average o f piezometric heads m e a s u r e d at h0, h20, h40, h60, a n d hs0. C o r r e l a t i o n coefficients for the four r u n s based o n the logt r a n s f o r m e d version o f Eq. (3) were high, 0.973-0.999. The value o f 0.03 in Eq. (3) represents the distance between the b o t t o m o f the pipe a n d the floor o f the box (0.03 m). Theoretically, n o pipeflow should occur if piezometric head is less t h a n 0.03 m, thus the value 0,03 is s u b t r a c t e d f r o m H i n Eq.(3). F r o m Fig. 5, it c a n be seen that two d a t a points showed small b u t m e a s u r a b l e pipeflow when H was less t h a n 0.03 m. This m a y be a t t r i b u t e d to a slight lag time between m a n o m e t e r response a n d m a n u a l pipeflow m e a s u r e m e n t s or to the effects o f storage a n d delayed d r a i n a g e in the
R.C. Sidle et al. / Journal of Hydrology 165 (1995) 207-219
Run 1:Op=1.686x10 "s. ( H - 0 . 0 3 ) Run 2:Op=S.016x10 " s - ( H - 0 . 0 3 ) Run 3:Op=7.880x10 -s. ( H - 0 . 0 3 ) Run 4:Op=6.272x10 -s- ( H - 0 . 0 3 )
215
o.42ss ( r = 0 . 9 9 3 3 ) o.z2o2 ( r = 0 . 9 7 3 2 ) o.zg~ ( r = 0 . 9 9 9 4 ) o.3sss ( r = 0 . 9 8 0 3 )
50 I
I II--
O
4O
°
!
O"'" .....
tt) .,-"
E
~. A "
.~
-.--13 Run ......O ......R u n 2 --6-.Run 3 - - - O .... Run 4
O
o 30 v-v
x
o
3"
..-
..6
,°'
."
............
20
_..o_
/
J. .
/- /
.O" ...............................................
/Z o / /"I~
o
13..
10
0
0.1 Piezometric
0.2 Head,
0.3
H (m)
Fig. 5. Relationships between measured pipeflow and piezometric head.
pipe. The coefficient /3, which represents the slope of the log-linear regression, was very similar for all runs and ranged from 0.320 to 0.424. Higher /3 values correspond to lower pipeflow discharges, i.e. when a high-roughness element was located near the downgradient end of the box. The constant a is related to hydraulic conductivity, roughness coefficient, hydraulic gradient, and pipe and box dimensions. Even though flow into a soil pipe is a complex three-dimensional hydraulic problem, the simple empirical relationship presented in Eq. (3) appears to give reasonable estimates of pipeflow for uniform soil conditions given the scale and flow geometry of the box. Larger scale experiments have also confirmed a direct relationship between Qp and H over a small range of hydraulic heads (Ohkura et al., 1992). Recently, such a simple relationship between pipeflow and H has been proposed for incorporation into a theoretically based, dual-porosity model for simulating preferential flow in a structured soil (Gerke and Van Genuchten, 1993).
R.C. Sidle et al. / Journal of Hydrology 165 (1995) 207-219
216
3.3. Relationship between pipeflow and matrix flow
The relationships between steady-state rates of Qp a n d Qd for all four experiments with a soil pipe are shown in Fig. 6. Average pipeflow discharges over the range of hydraulic gradients were 21.2, 83.1, 72.0, and 68.3% of total outflow (matrix flow + pipeflow) for runs 1, 2, 3, and 4, respectively. Curves plotted in Fig. 6 show very similar responses to the relationships between Qp and H (Fig. 5). In Fig. 6, all curves were forced through the x-intercept at Qd = 3.5 ml s -1 (0.0000035 m 3 s-I), the calculated value of matrix flow below the pipe; i.e. the product of w (0.6 m), depth below the pipe (0.03 m), k (8.87 x 10 -4 m 3 s-I), and Ia (sin 12.5°). This value for flow under the pipe can then be subtracted from Qd in the general exponential equation that describes the relationship between Qp and Qd Op = a(ad - 0.0000035) 8
(4)
where a and /3 are coefficients determined using the same log-linear regression methods as for Eq. (3). Exponential equations based on Eq. (4) for the four pipeflow experiments are Run 1 Qp = 0.0007044(Q d - 0.0000035) 0.437 r = 0.999
(5a)
Run 2
(5b)
Qp = 0.07504(Q d - 0.0000035) 0.605 r = 0.981
Run 2
"Run3
40
~.Run 4
E j= O
IL O
20
D. G. Run
0
I
I
3.5
20
'
I
40
Mat r i x Flow (ml/s) Fig. 6. Relationships between pipeflow and matrix flow in the four experiments.
R.C. Sidle et al. / Journal of Hydrology 165 (1995) 207-219
217
Run 3
Qp = 0.003728(Qd - 0.0000035) 0'411 r = 0.970
(5c)
Run 4
Qp = 0.01376(Qd - 0.0000035) 0.538 r = 0.993
(5d)
Correlation coefficients for the linearized form of these equations are very high (0.970-0.999). The exponential coefficients (~) ranged from about 0.4 to 0.6. These values were very similar to the exponential coefficients obtained in the relationships between Qp and H, especially for runs 1 and 3.
4. Summary and conclusions A series of experiments with a single artificial pipe in a sandy soil provided hydrologic information that may be useful for the study of streamflow generation, solute transport, landslide initiation, and surface erosion mechanisms in soils containing preferential flow pathways. Spatially varying properties of soil pipes (i.e. Manning's n coefficients) had a significant effect on piezometric response and relative discharge from pipes and the soil matrix. When the high-roughness portion (high n coefficient) of the pipe was located in the lower end of the sloping experimental box, piezometric levels were highest and pipeflow was lowest relative to matrix flow. This analogy can be extended to a hillslope where clogging, sedimentation, or a restriction may occur in a natural soil pipe. Thus, the position of the restriction (high n coefficient) in a given pipe can affect pore water pressure distribution within a slope segment. Such regions of pore water pressure buildup associated with discontinuous or restricted macropore networks have been suggested as contributing factors to landslide initiation (Tsukamoto et al., 1982; Pierson, 1983; Sidle, 1984). It is also evident from this research that subsurface flow regime and timing of solute transport can be greatly influenced by hydrologic properties of soil pipes. A simple exponential relationship between average piezometric head and pipeflow was observed for a wide range of hydraulic conditions given the scale and geometry of the experiment. This relationship may prove useful for estimating or modeling pipeflow in uniform soils.
Acknowledgments We express our gratitude to Dr. Tomoki Sakamoto, Takeshi Saito, and Yoshio Tsuboyama of the Forestry and Forest Products Research Institute (FFPRI) for their helpful discussions related to this research. A portion of this study was conducted while the senior author was funded by a fellowship (190056) from the Science and Technology Agency (STA) of Japan in 1991. Later research was sponsored in 1992 and 1994 when R.C.S. received Foreign Specialist Awards from STA. The authors wish to thank Drs. Makoto Tani, Hirotaka Ochiai, and Toshiaki Sammori of FFPRI in Tsukuba, Japan, for promoting this cooperative research.
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