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Effects of macro-pores on water flow in coastal subsurface drainagesystems
Pei Xin , Xiayang Yu , Chunhui Lu , Ling Li
PII: S0309-1708(15)00266-3DOI: 10.1016/j.advwatres.2015.11.007Reference: ADWR 2503
To appear in: Advances in Water Resources
Received date: 24 June 2015Revised date: 4 November 2015Accepted date: 6 November 2015
Please cite this article as: Pei Xin , Xiayang Yu , Chunhui Lu , Ling Li , Effects of macro-poreson water flow in coastal subsurface drainage systems, Advances in Water Resources (2015), doi:10.1016/j.advwatres.2015.11.007
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Highlights 1
Macro-pores significantly reduce the leaching efficiency 2 3
The time and amount of water required for leaching increase remarkably under the 4 influence of macro-pores 5
6
Leaching efficiency is affected by the distribution of macro-pores 7
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Effects of macro-pores on water flow in coastal subsurface drainage 10
systems 11
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Pei Xin1,#
, Xiayang Yu1, Chunhui Lu
1,2, Ling Li
1,3 13
14
1 State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai 15
University, Nanjing, China 16
17
2 Monash Water for Liveability, Civil Engineering Department, Monash University, Victoria, 18
Australia 19
20
3 School of Civil Engineering, The University of Queensland, Queensland, Australia 21
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# Corresponding author: Pei Xin, State Key Laboratory of Hydrology-Water Resources and 24
Hydraulic Engineering, Hohai University, Nanjing, China. ([email protected]) 25
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Abstract 27
Leaching through subsurface drainage systems has been widely adopted to ameliorate saline 28
soils. The application of this method to remove salt from reclaimed lands in the coastal zone, 29
however, may be impacted by macro-pores such as crab burrows, which are commonly 30
distributed in the soils. We developed a three-dimensional model to investigate water flow in 31
subsurface drainage systems affected by macro-pores distributed deterministically and randomly 32
through Monte-Carlo simulations. The results showed that, for subsurface drainage systems 33
under the condition of continuous surface ponding, macro-pores increased the hydraulic head in 34
the deep soil, which in turn reduced the hydraulic gradient between the surface and deep soil. As 35
a consequence, water infiltration across the soil surface was inhibited. Since salt transport in the 36
soil is dominated by advection, the flow simulation results indicated that macro-pores decreased 37
the efficiency of salt leaching by one order of magnitude, in terms of both the elapsed time and 38
the amount of water required to remove salt over the designed soil leaching depth (0.6 m). The 39
reduction of the leaching efficiency was even greater in drainage systems with a layered soil 40
stratigraphy. Sensitivity analyses demonstrated that with an increased penetration depth or 41
density of macro-pores, the leaching efficiency decreased further. The revealed impact of macro-42
pores on water flow represents a significant shortcoming of the salt leaching technique when 43
applied to coastal saline soils. Future designs of soil amelioration schemes in the coastal zone 44
should consider and aim to minimize the bypassing effect caused by macro-pores. 45
46
Keywords 47
Macro-pores; Salt leaching; Preferential flow; Drainage; Soil heterogeneity 48
49
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50
Key Points 51
Macro-pores significantly reduce the leaching efficiency 52
The time and amount of water required for leaching increase remarkably under the influence of 53
macro-pores 54
Leaching efficiency is affected by the distribution of macro-pores 55
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1. Introduction 56
Soil salinization is a major problem in many arid and semi-arid regions worldwide [1]. 57
According to [2] published in 2003, the total area of salt-affected lands in the world was around 58
9.55 million km², approximately 10% of the total land area. The problem has worsened 59
dramatically due to global climate change and anthropogenic activities over the last decade [3, 4]. 60
Excess of salts in soils can alter significantly the physical and chemical soil properties, and 61
decrease the agricultural productivity [5]. To cope with this global issue, various physical, 62
chemical, biological and ecological methods have been developed for ameliorating saline soils 63
(see the review by Qadir et al. [1]). Among these methods, leaching is a traditional and still 64
globally adopted one. This method flushes excessive salts from upper to lower soil depths using 65
good quality water and removes the salts through drainage systems. Commonly, surface flushing 66
is accomplished by continuous ponding, intermittent ponding and sprinkling, while salt discharge 67
is performed by using pumping wells, subsurface drains and open ditches [1, 6]. As subsurface 68
drains are easy to set up, workable with no requirement for power and land saving, they are 69
prevailingly used in these drainage systems. 70
The salt leaching method has been studied extensively via analytical solutions [7-10], 71
laboratory experiments [11, 12], field investigations [13-15] and numerical simulations [16-19]. 72
It was found that in a drainage system with complete and continuous ponding, the surface water 73
infiltration rate decreases from the drain location to midway between drains (hereinafter, referred 74
to as “interior”). It takes much longer time to flush the interior area far away from the drains. To 75
remove salts over a particular crop rhizosphere depth across the whole area, the method with 76
continuous ponding would lead to significant waste of good quantity water. Therefore, various 77
alternative methods, such as drip irrigation (an irrigation method that allows water to drip slowly 78
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to the roots of plants through narrow tubes) and progressive ponding, have been proposed to 79
improve the efficiency of salt leaching. Based on analytical solutions, Youngs and Leeds-80
Harrison [10] provided a framework for analyzing the progressive ponding condition. This 81
method divides the whole soil area into different strips separated by bunds. Ponding starts from 82
the midway area between drains and progresses towards the drains until the whole area is 83
flooded. This method was tested against laboratory experiments and found to be significantly 84
more effective than the complete ponding method [11, 20]. Progressive ponding enhances the 85
local hydraulic head gradient in the interior. The leaching efficiency can be thus improved by up 86
to 4 times with respect to the amount of water needed to drain the soil to the required soil depth 87
[16, 17]. While salt transport in the soil is affected by both advection and diffusion/dispersion 88
processes, all these studies suggested that increasing the hydraulic head gradient between the 89
drain and interior is the key to improving the efficiency of salt leaching. 90
While these studies provide a theoretical basis for performing salt leaching analysis, it 91
remains a challenge to apply the leaching method in the field. The area of salt-affected soils in 92
China is around 0.35 million km², a quarter of which are coastal saline soils. This figure is still 93
increasing due to intensive land reclamation being carried out in the coastal zone [3]. How to 94
effectively utilize these coastal saline soils is now critically important to relieving the population 95
pressure and ensuring food safety in eastern China [21]. Adjacent to the coastal sea, these soils 96
are typically of high salinity and have to be ameliorated to satisfy the needs of agricultural use. 97
Salt leaching is prevailingly adopted in China and a significant amount of good quality water is 98
consumed every year for this purpose despite severe water shortage in China [22]. This study 99
was firstly motivated to test the efficiency of the leaching approach widely adopted in China’s 100
coastal areas. We conducted a couple of field surveys in these areas, including the Chongming 101
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Dongtan wetland (Shanghai) and the reclaimed land from the Jiangsu coastal wetlands. The 102
former is a natural marsh wetland linked to the sea and the latter is isolated from the sea in terms 103
of surface water connection. For the latter shortly after the reclamation, no agricultural activities 104
are presently carried out as sufficient soil amelioration is still needed to meet the condition for 105
crop growth. In these two coastal areas, we observed the following two typical types of soil 106
heterogeneity: 107
(1) Macro-pores produced by invertebrates, such as crab burrows, are commonly found in 108
coastal saline soils (Fig. 1a). Using polyester resin casting (Fig. 1b), Xin et al. [23] found that the 109
depth of these burrows can reach 70 cm (Fig. 1c). The density of burrows with diameters ranging 110
from 1 to 4 cm can be up to 8/m2. Macro-pores, as preferential flow paths, can significantly 111
affect the flow in various groundwater systems [24, 25]. Akay et al. [12] conducted a laboratory 112
study to examine the effect of a single vertical burrow on flow in a soil column overlying a drain. 113
The finding revealed that the open macro-pore collected the surface water significantly and 114
enhanced water infiltration. 115
(2) Coastal sediments possess a layered soil stratigraphy. Commonly, low-permeability silt 116
loams are found to overlie sandy deposits. The high-permeability sandy deposits, combined with 117
macro-pores, can create preferential flow paths affecting the pore-water flow in coastal 118
groundwater systems. In particular, the lower higher-permeability layer is likely to favor 119
drainage as long as the horizontal hydraulic gradient exists [17, 26, 27]. In a drainage system, 120
this kind of soil configuration is likely to lead to a more uniform flow field and increase water 121
infiltration in the midway area between drains [17]. 122
It should be noted that these two typical types of soil heterogeneity are not only just 123
commonly encountered in the coastal zone of China but also in other coastal areas around the 124
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world. Macro-pores created by plant roots, soil cracks, and soil fauna are found in most of soils 125
and have attracted increasing attention over the recent decades [24, 25, 28-31]. Coastal sediments 126
are often lay down by layers and lead to distinct soil strata [28, 32-34]. Therefore, amelioration 127
strategies for coastal saline soils need to carefully take these effects into account. There are 128
speculations about the effect of macro-pores on various groundwater systems. However, the 129
macro-pore effects have not yet been adequately understood [25, 35, 36]. To the best of the 130
authors’ knowledge, no quantitative analysis on the effect of macro-pores on pore-water flow in 131
coastal subsurface drainage systems has been conducted to date. 132
In this study, we developed a three-dimensional (3-D) model to investigate water flow in 133
coastal subsurface drainage systems affected by macro-pores. Firstly, we examined the effect of 134
regularly distributed macro-pores on uniform and layered drainage systems. Velocity flow fields, 135
and time and water needed for leaching were examined in detail. Secondly, we conducted 136
Monte-Carlo simulations to better represent the field conditions and examine the uncertainty 137
caused by randomly distributed macro-pores. 138
139
2. Conceptual and numerical model 140
The model domain, with a simplified 3-D cuboid geometry, is representative of the 141
drainage systems commonly adopted in China’s coastal areas. The model is assumed to be 142
laterally bounded by two hydraulic divides in the middle between the simulated subsurface drain 143
and adjacent parallel drains (one on each side). The model domain is thus centred by the 144
simulated drain and extends in the along-drain (y [L]) direction by a width of 1 m (Fig. 1d). AB 145
shows the soil surface and CD is an impermeable base. The thickness of the aquifer is set to 5 m 146
and the distance between two parallel subsurface drains is set to 20 m. The drain with a diameter 147
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of 8 cm is set up at the 1 m soil depth. The soil stratigraphy is set up to represent the field 148
condition investigated by Xin et al. [23]. The domain is divided vertically into two zones (Fig. 1d, 149
the upper silt loam zone and lower sandy loam zone) separated by a horizontal interface at the 150
depth of 0.6 m from the soil surface. 151
To focus on the effect of macro-pores on the water flow in the first instance, the study 152
considered steady-state flow in the subsurface drainage system with complete and continuous 153
ponding. Therefore, only steady-state and water saturated (no air trapped) pore-water flow 154
occurred in the soil. The hydraulic head is be governed by the Laplace equation as follows, 155
2 2 2
2 2 20
x y z
(1a) 156
The pore-water velocity could be calculated based on Darcy’s law, i.e., 157
Kv
(1b) 158
where x is the horizontal coordinate with the origin set at the soil surface and right above the 159
drain [L]; is the total hydraulic head, and P z [L]; P is the pressure head [L]; z is the 160
elevation above a datum [L] (set at the soil surface in this study); v is the pore-water velocity 161
vector [L/T]; K is the soil hydraulic conductivity [L/T]; is the soil porosity [-]. 162
It is worth noting that salt leaching at a field site is subjected to both advection and 163
diffusion/dispersion. The density effect due to the salinity variations could also affect the water 164
flow and thus salt transport. The consideration of the salt diffusion/dispersion and density effect 165
may lead to transient flow simulations, which are expected to be computationally expensive. As 166
suggested by Molz [37] and Zheng et al. [38], solute advection commonly dominants over 167
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diffusion/dispersion in natural groundwater systems. To confirm this, we simulated salt transport 168
directly and carried out a particle tracking analysis. The results demonstrated that solute 169
diffusion/dispersion led to a mixing zone developed between the freshwater and saline water. 170
Overall, the salt transport was predominantly controlled by water flow (see details in 171
Supplementary material). Therefore, we neglected the solute diffusion/dispersion for simplicity 172
and aimed to link the transport of salts simply to water flow as done in most of previous studies 173
[16, 17]. 174
SUTRA [39] was adopted to solve the governing equation. In SUTRA, the governing 175
equation is discretized based on a 3-D rectangular finite-element mesh and the governing 176
equation for the pore-water flow is solved by the finite element method. SUTRA has been well 177
validated against analytical solutions and laboratory experiments and now widely adopted to 178
simulate flow and solute transport in various groundwater systems (e.g., [40, 41]). It is worth 179
noting that we have validated the model against Mirjat et al.’s [11] experiment, which considered 180
a completely ponded subsurface drainage system of a size of 1.0 m (length) × 0.15 m (height). 181
We did particle tracing to determine the average velocities of leaching streamlines and compared 182
them with the experimental results (Fig. 2d in [11]). Overall, the simulated average velocities of 183
leaching streamlines were close to those observed and the relative errors were within 20%. The 184
results suggested that SUTRA is a robust model for simulating water flow in the drainage system 185
subjected to subsurface drainage and continuous surface ponding (further results not shown here 186
for brevity). 187
Because of flow symmetry along the lateral (x) direction, only the right side of the drainage 188
system was simulated in this study in order to save the computational cost. For all simulations, 189
the elements with a size of 0.04 m × 0.04 m × 0.04 m (respectively in x, y and z directions) were 190
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used for the soil above the 2 m depth. For the lower soil, elements with a size of 0.04 m × 0.04 m 191
× 0.1 m were used. As such, the model domain was divided into 500, 000 elements. The results 192
based on the present model setting were found to agree well with those from models with a 193
further refined mesh, demonstrating that the simulation results were independent of the mesh size. 194
Four base numerical experiments were conducted to examine the effects of macro-pores on 195
salt leaching under different soil conditions: 196
Case U-NM, uniform soil without macro-pores. In this case, the soil hydraulic conductivity 197
( K ) was set to 1.18 × 10-6
m/s; 198
Case U-M, uniform soil with macro-pores, which is similar to Case U-NM except for the 199
macro-pores distribution; 200
Case L-NM, layered soil without macro-pores. The hydraulic conductivities of upper 201
(above the 0.6 m soil depth) and lower soils were set to 1.18 × 10-6
m/s and 6.25 × 10-6
m/s, 202
respectively. 203
Case L-M, layered soil with macro-pores, which is similar to Case L-NM except for the 204
macro-pores distribution. The parameter values used in Cases L-NM and L-M were set to reflect 205
the field condition in [23]. The soil porosity ( ) was 0.45 for all the soils. These parameter 206
values are representative of soils commonly encountered in coastal areas [42]. 207
The macro-pores were distributed at the central section of the drainage system (i.e., y = 0 m). 208
To set up macro-pores in the 3-D rectangular finite-element mesh that is used in SUTRA, each 209
pore was assumed to be a cube with the size of 4 cm × 4 cm × 60 cm in the base cases (Table 1). 210
This size reflects the upper range of the crab burrow measured in the field [23]. Macro-pores 211
were included in the model as highly conductive zones with saturated hydraulic conductivity (K) 212
of 1 m/s and porosity ( ) of 1. Numerical tests showed that as long as the hydraulic conductivity 213
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of the macro-pores is set high enough (e.g., K ≥ 1 m/s), its value does not affect the simulation 214
results (results not shown for simplicity). Similar techniques were previously used in simulating 215
surface water [43, 44] and macro-pores [12, 23]. 216
In all the simulations, the soil surface was specified with a constant pressure head of 0.05 m. 217
Nodes related to the drain were taken as seepage face nodes with the atmospheric pressure (P = 218
0). Other boundaries were set as a no-flow boundary as done in [16, 17]. The initial condition 219
was determined according to the hydrostatic pressure distribution with the pressure at soil 220
surface set to 0.05 m. As we focused on the steady-state flow, the initial condition did not affect 221
the results. 222
223
3. Results and discussions 224
3.1. Effects of macro-pores on pore-water flow 225
Firstly, the macro-pores with the depth of 0.6 m were evenly distributed at the central 226
section of the drainage system of the 3-D cuboid geometry. The macro-pore density (number of 227
macro-pores per square meter area) was set to 1 /m2. As expected, the simulated pore-water flow 228
was generally 3-D, especially in the areas near the macro-pores. Here we focused on the flow on 229
the vertical cross section perpendicular to the drains as it was two-dimensional due to symmetry 230
along the drain direction. 231
Simulation results show that for the uniform soil without macro-pores, the pore-water 232
velocity decreased by orders of magnitude from the drain to interior (Fig. 2a, Case U-NM). It can 233
be seen from the streamlines, the water infiltrating from the sediment surface took up a deeper 234
and longer travel path from the interior to the drain. These results were consistent with previous 235
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studies [7, 10, 12, 17], showing that considerable time is needed to flush the interior area far 236
away from the drains. 237
With macro-pores distributed (Fig. 2b, Case U-M), the velocity magnitude in the macro-238
pores increased remarkably, as they formed preferential flow paths for quick drainage. 239
Comparing Cases U-NM and U-M, it is hard to see an obvious change in pore-water velocity 240
besides areas near the macro-pores. However, the flow velocity in the shallow soil of the interior 241
decreased considerably. The presence of macro-pores reduced local surface water infiltration, 242
especially in the interior (quantitative analysis of this effect is given in the following section). 243
Once the lower high-permeability soil was included (Fig. 2c, Case L-NM), the overall pore-244
water velocity increased by one order of magnitude, in comparison with that in the first (Fig. 2a, 245
Case U-NM). This is consistent with the finding of Siyal et al. [17] that the lower high-246
permeability soil layer favors leaching. Similarly, with macro-pores distributed, pore-water 247
velocity in the shallow soil decreased, especially in the interior area (Fig. 2d, Case L-M). 248
To explore the cause of the pore-water velocity reduction, we examined the variations of 249
hydraulic head, which provides the essential drive for the pore-water flow. As shown in Fig. 3, 250
the hydraulic head increased from the drain to the interior, generating the hydraulic gradient 251
pointing to the drain for water drainage. Consistent with the model setup, hydraulic head at the 252
soil surface remained at 0.05 m. From the top to lower soil, the hydraulic head decreased as the 253
vertical downward flow toward the drain took place. 254
In Fig. 3, we plotted the contour of the 0.045 m hydraulic head, 90% of that at the soil 255
surface. It was clear that for Case U-NM, the distance from the 0.045 m contour to the soil 256
surface increased from the drain to interior (Fig. 3a). This was consistent with the velocity 257
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variations shown in Fig. 2a. Macro-pores considerably lowered the 0.045 m contour, particularly 258
in the soil interior (Fig. 3b). As mentioned earlier, the hydraulic head at the soil surface was 259
constant with the continuous ponding set up in the model. As the distance between the 0.045 m 260
contour and the soil surface increased but the head difference remained the same, the pore-water 261
velocity in the shallow aquifer for Case U-M decreased remarkably, compared with Case U-NM. 262
We also examined the contour of hydraulic head = -0.05 m. Affected by macro-pores, this 263
contour also moved deeper and closer to the drain (Fig. 3b compared with Fig. 3a), consistent 264
with the weakened velocity field in Case U-M (Fig. 2b in comparison with Fig. 2a). Such a 265
modification in the hydraulic head gradient is expected to reduce the leaching efficiency [16, 17]. 266
Consistent with the finding of Siyal et al. [17], the layered soil configuration favored vertical 267
water infiltration across the soil surface. The contour of the 0.045 m hydraulic head in Case L-268
NM was much close to the soil surface. This reflected increased velocities (Fig. 2c compared 269
with Fig. 2a). Similarly, macro-pores formed bypasses for the surface water, and developed high 270
hydraulic head in the deep soil (Fig. 3d). Under such a condition, the water infiltration across the 271
soil surface would be considerably inhibited in the areas near the macro-pores (further discussed 272
later). 273
The above results suggest that for both the uniform and layered soil configurations, macro-274
pores raised the hydraulic head in the area near the drain and hence reduced the hydraulic 275
gradient between the interior and the drain. This weakened the drainage flow significantly and 276
would reduce the leaching efficiency. 277
3.2. Effects of macro-pores on water infiltration 278
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To quantify further the effect of macro-pores, we examined per unit area influx ( inF ) across 279
the sediment surface. This influx significantly controls the amount of water and time required for 280
leaching [10, 16, 17]. As suggested by Youngs and Leeds-Harrison [10], the time (T ) needed to 281
remove the salts to a preset soil depth ( D ) could be approximately described as follows, 282
inF
TD
, (2) 283
It should be noted that the effect of horizontal flow is neglected in Eq. 2. This is a reasonable 284
simplification in this study as the water flow near the soil surface was predominantly vertical 285
(e.g., Fig. 2). As inF is variable across the soil surface, the amount of water (V ) needed for 286
leaching can be estimated as, 287
ininmax mean
FV F
D
, (3) 288
It can be seen from Fig. 4 that, for the four base cases, the per unit area influx ( inF ) across 289
the sediment surface decreased by orders of magnitude from the drain to the interior soil. With 290
the macro-pores distributed, the influx near the macro-pores decreased significantly for both the 291
uniform (Fig. 4c in comparison with Fig. 4a) and layered (Fig. 4d in comparison with Fig. 4b) 292
soils. As the reduction was on orders of magnitude, we calculated the percentage of the area with 293
the influx at different magnitudes (Fig. 5). For Case U-NM, the area percentages for the ranges 294
from 10-3
to 10-2
m-3
/m-2
/d (Zone B), 10-2
to 10-1
m-3
/m-2
/d (Zone C) and 10-1
to 100 m
-3/m
-2/d 295
(Zone D) were, respectively, 67%, 31% and 2% (Table 1). With the macro-pores distributed in 296
the uniform soil (Case U-M), the areas of Zone B and Zone C decreased by around 10%. 297
Furthermore, a low influx range from 10-4
to 10-3
m-3
/m-2
/d (Zone A) appeared in 21% of the soil 298
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area (0% in Case U-NM). This low-influx zone mainly occurred near the macro-pores. Based on 299
Eqs. 2 and 3, we calculated the time and water volume needed to remove the salts to the 0.6 m 300
soil depth (note that only solute advection was considered). To achieve a uniform salt removal, it 301
took surprisingly 4,635 days ( max T ) in Case U-M, about 12 times longer than that in Case U-302
UM (337 days). Clearly, this extremely prolonged period was due to an increased fraction of area 303
near the macro-pores with near-zero hydraulic gradients. The water used was increased by 304
around 18 times (Fig. 6 and Table 1). These figures of time and water consumption highlighted 305
the significant effects of macro-pores on leaching. 306
Layered soil configuration remarkably improved the leaching efficiency. Comparison 307
between Case L-NM and Case U-NM indicated saving by 92% and 72%, respectively, for the 308
required time and water. As mentioned earlier, layered soil configuration is common in coastal 309
areas. This would significantly favor leaching. However, macro-pores also caused an increase of 310
water consumption by more than one order of magnitude (Fig. 6 and Table 1) in this case, 311
reducing the leaching efficiency significantly. We further calculated the pore volume flushed per 312
unit time (the total influx across the soil surface divided by the total pore volume of the 313
subsurface drainage system). This metric represents how fast the pore space gets flushed. It can 314
be seen from Fig. 3c that the pore volumes flushed per unit time for the two cases with layered 315
soil configuration (Cases L-M and L-NM) were around 4 times greater than those with uniform 316
soil (Cases U-M and U-NM). This demonstrated further that the layered soil configuration would 317
significantly favor leaching. 318
4. Sensitivity analyses and discussions 319
4.1. Sensitivity of depth of macro-pores 320
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Three additional simulations were conducted to examine the effect of macro-pore depth. The 321
results, together with that from Case L-M, are shown in Figs. 7 to 10. The overall flow in the 322
central section decreased as the macro-pore depth increased from 0.2 to 1.4 m (Fig. 7). This 323
reduction was mainly caused by high hydraulic heads developed in the deeper soil. It can be seen 324
from both the 0.045 m and -0.05m contours in Fig. 8, the effect of macro-pores was more 325
profound in the interior area. From the left to right side, the two contours started from being 326
close to the soil surface and became lower when moving far away from the drain. Interestingly, 327
fluctuations appeared on the curve near the drain (e.g., x = 0 to 5 m in Fig. 8c). The local 328
“funnels” caused by macro-pores increased in depth as the macro-pore depth increased (Figs. 8a-329
8d). However, in the soil interior, the curve became smooth, demonstrating the intensified effect 330
of macro-pores (e.g., x = 7 to 10 m in Fig. 8c). This uniform reduction in hydraulic gradient was 331
expected to lead to an expansion of the low infiltration zone. 332
Consistent with the four base cases discussed earlier, the per unit area influx across the 333
sediment surface varied by orders of magnitude (Fig. 9). As the macro-pore depth increased, the 334
low infiltration zone extended to the soil interior. For the case with 0.2 m depth macro-pores, the 335
per unit area influx appeared to vary by two orders of magnitude (Fig. 9a), suggesting relatively 336
uniform water infiltration. The area percentages of Zone C (10-2
to 10-1
m-3
/m-2
/d) and Zone D 337
(10-1
to 100 m
-3/m
-2/d) were, respectively, 84% and 14% (Fig. 10 and Table 1). These 338
percentages of high infiltration area were close to those for Case L-UM without macro-pores. In 339
other words, the effect of 0.2 m depth macro-pores was minor. In contrast, deeper macro-pores 340
led to a large fraction of low infiltration zone. For the macro-pores with 1.4 m depth, the area 341
fraction for Zone A (10-4
to 10-3
m-3
/m-2
/d) and Zone B (10-3
to 10-2
m-3
/m-2
/d) reached, 342
respectively, 57% and 26%. Based on the water required to remove the salts to the 0.6 m soil 343
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depth, the leaching efficiency decreased by three orders of magnitude, in compassion with Case 344
L-UM without macro-pores. 345
4.2. Sensitivity of distribution of macro-pores 346
In the simulations above, we set up macro-pores deterministically with uniform depths. In 347
nature, macro-pores distribute randomly with varying depths. To reflect the natural condition, we 348
conducted Monte-Carlo simulations (i.e., repeated random sampling) [45] with the density of 349
macro-pores, respectively, set to 1/m2 and 0.6/m
2. In these two sets of simulations, the layered 350
soil configuration, the same as Case L-UM, was used as it is typical in coastal areas. The depth 351
of the macro-pores was allowed to change between 0.2 and 1.0 m, with the averaged depth of 0.6 352
m (same as that in Case L-M). It should be noted that the Monte-Carlo method requires a large 353
random sample size to get a converged statistical result. This is computationally expensive in the 354
present study based on a 3-D model. For each set of cases with different densities of macro-pores, 355
100 Monte-Carlo simulations were conducted. To save the computational cost, the model 356
geometry was reduced in the along-drain (y) direction by half (0.5 m for the width). 357
While macro-pores distributed randomly altered significantly the local per unit area influx 358
across the sediment surface, the overall water infiltration patterns remained largely similar (Fig. 359
11). High water infiltration zones appeared in the area near the drain, in contrast to the low 360
infiltration zones in the interior. With the macro-pore density fixed at 1 /m2, the area of Zone B 361
(10-3
to 10-2
m-3
/m-2
/d) and Zone C (10-2
to 10-1
m-3
/m-2
/d) took place in a large area of the soil 362
surface, regardless of the random variations (Fig. 12). 363
We calculated the mean and standard deviation of the distribution of the per unit area influx 364
across the soil surface. With the macro-pores distributed randomly, the mean area percentages of 365
Zone B and Zone C, were, respectively, 58% and 41%. As expected, these percentages were 366
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different from those in the deterministic simulation (i.e., 37% and 56% from Case L-M). With 367
regards to the uncertainty as represented by the standard deviation (around 15% for both Zone B 368
and Zone C), the results from deterministic and random simulations were consistent, reflecting 369
the significant effect of macro-pores (Fig. 13). With the macro-pore density fixed at 0.6/m2, the 370
mean area percentages of Zone B and Zone C, were, respectively, 46% and 54%. That is, Zone C 371
with a relatively high water infiltration rate increased by 13%, in comparison with that form the 372
Monte-Carlo simulations with the macro-pore density fixed at 1 /m2. 373
In summary, the sensitivity analyses demonstrated that the negative effect of macro-pores 374
was intensified with increased depth or density of macro-pores. In the simulations with macro-375
pores distributed deterministically or randomly, the leaching efficiency decreased by more than 376
one order of magnitude. 377
378
5. Concluding remarks 379
Based on a 3-D steady state flow model, we have examined water flow in continuously 380
ponded subsurface drainage systems affected by macro-pores. The model setup reflected the 381
characteristics of coastal soils. Under the assumption that salt advection dominates over 382
diffusion/dispersion, the results showed that macro-pores bypassed the surface water infiltration 383
and thus decreased the efficiency of salt leaching in both the uniform and layered soils. The 384
quantitative analysis demonstrated that with the macro-pores distributed, the water needed for 385
leaching increased by one order of magnitude. That is, macro-pores may lead to a significant 386
waste of good quality water. The negative effect of macro-pores would be more severe as the 387
depth and density of macro-pores increased. 388
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As pore-water flow plays an important role in the salt transport in subsurface drainage 389
systems, these findings have the following implications for salt leaching designs and associated 390
policy-making: 391
1) For all the simulation cases examined here, water infiltration across the soil surface 392
decreased by orders of magnitude from the drain to interior area. Flooding the whole area for 393
surface flushing would lead to the prolonged elapsed time and the increased amount of water 394
required for leaching in the interior area. This would cause significant waste of good quantity 395
water. 396
2) Surface flushing accomplished by ponding creates head-specified boundary conditions 397
across the soil surface. This allows macro-pores to bypass the surface water infiltration and leads 398
to water loss. 399
3) Layered soil configuration would decrease the elapsed time and the amount of water 400
required for leaching, in comparison with uniform soil configuration. Layered soil configuration 401
is commonly encountered in coastal areas and would favor salt leaching in subsurface drainage 402
systems without macro-pores. 403
In this study, we set up a simplified 3-D cuboid geometry. The effect of soil topography is 404
likely to alter the local groundwater flow pattern and hence leaching. We also set simplified 405
surface-connected vertical macro-pores in the model. In nature, the morphology and distribution 406
of macro-pores are of high variability, e.g., buried and unconnected macro-pores commonly exist 407
as well. Human activities such as coastal land reclamation and tillage may alter soil structures. 408
These are expected to complicate the drainage process. More significantly, steady-state 409
conditions were considered with salt diffusion/dispersion neglected in this study. This was 410
suggested to overestimate the leaching requirement in comparison with transient-state conditions 411
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[46]. How macro-pores affect the salt leaching under transient-state conditions remains to be 412
examined. Under transient conditions, rainfall and evapotranspiration would affect the 413
subsurface flow, in comparison with the present study based on continuous and complete 414
ponding. Entrapped air can also play a role in affecting water movement in the vadose zone 415
under transient conditions. Notwithstanding these questions that require future investigations, the 416
present study has shed light on the effects of macro-pores on the water flow in subsurface 417
drainage systems and serves as a good starting point for further investigations in this field, 418
including research on modification of the leaching method to avoid and minimize the macro-pore 419
effects. 420
421
Acknowledgements 422
This work was supported by the National Natural Science Foundation of China (51579077). 423
PX acknowledges the Fundamental Research Funds for the Central Universities (2014B05714 424
and 2014B17214). 425
426
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556
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Table 1. Simulated cases with model parameter values and key results. 557
Cases Soil
configuration
Macro-
pores
Density
(/m2)
Depth of
macro-
pores (m)
Percentage of water influx (m-3
/m-2
/d) across the
soil surface (%) max(T)
(d)
V
(m3/m
2) Zone A
10-4
to 10-3
Zone B
10-3
to 10-2
Zone C
10-2
to 10-1
Zone D
10-1
to 10-0
U-NM Uniform Without 0 0 0 67 31 2 337 2.5
U-M Uniform With 1 0.6 21 56 22 0 4635 36.2
L-NM Layered Without 0 0 0 0 83 17 27 0.7
L-M Layered With 1 0.6 0 37 56 6 556 17.9
L-M* Layered With 1 0.2 0 1 85 14 70 4.3
L-M* Layered With 1 1.0 21 55 21 2 1897 172.3
L-M* Layered With 1 1.4 57 26 14 1 7435 735.0
Random Layered With 1# 0.6# 1 58 41 0 NA NA
Random Layered With 0.6# 0.6# 0 46 54 0 NA NA
# indicates the mean value. * indicates cases of sensitivity analyses with different macro-pore depths. max(T) and V are, respectively, 558
the time and the amount of water needed to remove the salts to the 0.6 m soil depth. NA means not applicable. 559
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560
Fig. 1. a) Illustration of coastal soils with macro-pores (crab burrows) distributed (picture taken 561
in the Chongming Dongtan wetland, Shanghai, China). A crab is shown at the lower left corner. 562
b) Illustration of using polyester resin casting to measure the structure of burrows. c) 563
Morphology of a casted crab burrow. A ruler is placed for comparison. d) Three-dimensional 564
schematic diagram of a drainage system subjected to continuous and complete surface ponding. 565
The elevation datum is set at the soil surface. Soil configuration and macro-pores are also 566
illustrated. 567
568
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569
Fig. 2. Two-dimensional pore-water flow in the central section where macro-pores are 570
distributed (y = 0 m): a) Case U-NM, uniform soil without macro-pores; b) Case U-M, uniform 571
soil with macro-pores; c) Case L-NM, layered soil without macro-pores; and d) Case L-M, 572
layered soil with macro-pores. The black lines show the streamlines. The contours show the 573
velocity magnitude in log10 (m/d). The solid circles indicate the subsurface drains. 574
575
x (m)
z (m
)
a)
0 1 2 3 4 5 6 7 8 9 10
-4
-2
0log10 (m/d)
-4
-2
0
x (m)
z (m
)
b)
0 1 2 3 4 5 6 7 8 9 10
-4
-2
0log10 (m/d)
-4
-2
0
x (m)
z (m
)
c)
0 1 2 3 4 5 6 7 8 9 10
-4
-2
0log10 (m/d)
-4
-2
0
x (m)
z (m
)
d)
0 1 2 3 4 5 6 7 8 9 10
-4
-2
0log10 (m/d)
-4
-2
0
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31
576
Fig. 3. Contours of hydraulic head in the central section where macro-pores are distributed (y = 0 577
m): a) Case U-NM, uniform soil without macro-pores; b) Case U-M, uniform soil with macro-578
pores; c) Case L-NM, layered soil without macro-pores; and d) Case L-M, layered soil with 579
macro-pores. The solid circles indicate the subsurface drains. Black lines indicate the contour for 580
the hydraulic head of 0.045 m (i.e., 90% of that at soil surface). White lines indicate the contour 581
for the hydraulic head of -0.05 m. 582
583
x (m)
z (m
)
a)
0 1 2 3 4 5 6 7 8 9 10-2
-1
0Head (m)
-2
-1
0
x (m)
z (m
)
b)
0 1 2 3 4 5 6 7 8 9 10-2
-1
0Head (m)
-2
-1
0
x (m)
z (m
)
c)
0 1 2 3 4 5 6 7 8 9 10-2
-1
0Head (m)
-2
-1
0
x (m)
z (m
)
d)
0 1 2 3 4 5 6 7 8 9 10-2
-1
0Head (m)
-2
-1
0
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32
584
Fig. 4. Per unit area influx across the soil surface: a) Case U-NM, uniform soil without macro-585
pores; b) Case U-M, uniform soil with macro-pores; c) Case L-NM, layered soil without macro-586
pores; and d) Case L-M, layered soil with macro-pores. The contours show the water influx in 587
log10 (m3/m
2/d). 588
589
x (m)
y (m
)
a)
0 1 2 3 4 5 6 7 8 9 10-0.5
0
0.5log10 (m
3/m
2/d)
-4
-2
0
x (m)
y (m
)
b)
0 1 2 3 4 5 6 7 8 9 10-0.5
0
0.5log10 (m
3/m
2/d)
-4
-2
0
x (m)
y (m
)
c)
0 1 2 3 4 5 6 7 8 9 10-0.5
0
0.5log10 (m
3/m
2/d)
-4
-2
0
x (m)
y (m
)
d)
0 1 2 3 4 5 6 7 8 9 10-0.5
0
0.5log10 (m
3/m
2/d)
-4
-2
0
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33
590
Fig. 5. Comparison of the distribution of the per unit area influx across the soil surface (cases 591
indicated in the figure legend). 592
593
<0.0001 0.0001 to 0.001 0.001 to 0.01 0.01 to 0.1 0.1 to 1 > 10
10
20
30
40
50
60
70
80
90
100
Per unit area flux (m3/m
2/d)
Perc
en
tag
e (
%)
One layer, without pores
One layer, with pores
Two layers, without pores
Two layers, with pores
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34
594
Fig. 6. Time (a) and the amount of water (b) needed to remove salts to the 0.6 m soil depth. (c) 595
The pore volume flushed per unit time. Cases are indicated in the x-axis. 596
One layer, without pores One layer, with pores Two layers, without pores Two layers, with pores0
2000
4000
Tim
e n
ee
de
d (
d)
a)
One layer, without pores One layer, with pores Two layers, without pores Two layers, with pores0
20
40
Wa
ter
ne
ed
ed (
m3/m
2) b)
One layer, without pores One layer, with pores Two layers, without pores Two layers, with pores0
0.005
0.01
0.015
Po
re v
olu
me
flu
sh
ed
per
un
it t
ime
(m
3/m
3/d
) c)
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35
597
Fig. 7. Two-dimensional pore-water flow in the central section where macro-pores are 598
distributed (y = 0 m): a) layered soil with macro-pores of the 0.2 m depth; b) layered soil with 599
macro-pores of the 0.6 m depth (Case L-M); c) layered soil with macro-pores of the 1 m depth; 600
and d) layered soil with macro-pores of the 1.4 m depth. The black lines show the streamlines. 601
The contours show the velocity magnitude in log10 (m/d). The solid circles indicate the 602
subsurface drains. 603
604
x (m)
z (m
)
a)
0 1 2 3 4 5 6 7 8 9 10
-4
-2
0log10 (m/d)
-4
-2
0
x (m)
z (m
)
b)
0 1 2 3 4 5 6 7 8 9 10
-4
-2
0log10 (m/d)
-4
-2
0
x (m)
z (m
)
c)
0 1 2 3 4 5 6 7 8 9 10
-4
-2
0log10 (m/d)
-4
-2
0
x (m)
z (m
)
d)
0 1 2 3 4 5 6 7 8 9 10
-4
-2
0log10 (m/d)
-4
-2
0
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36
605
Fig. 8. Contours of the hydraulic head distribution in the central section where macro-pores are 606
distributed (y = 0 m): a) layered soil with macro-pores of the 0.2 m depth; b) layered soil with 607
macro-pores of the 0.6 m depth (Case L-M); c) layered soil with macro-pores of the 1 m depth; 608
and d) layered soil with macro-pores of the 1.4 m depth. The solid circles indicate the subsurface 609
drains. Black lines indicate the contour for the hydraulic head of 0.045 m (i.e., 90% of that at soil 610
surface). White lines indicate the contour for the hydraulic head of -0.05 m. 611
612
x (m)
z (m
)
a)
0 1 2 3 4 5 6 7 8 9 10-2
-1
0Head (m)
-2
-1
0
x (m)
z (m
)
b)
0 1 2 3 4 5 6 7 8 9 10-2
-1
0Head (m)
-2
-1
0
x (m)
z (m
)
c)
0 1 2 3 4 5 6 7 8 9 10-2
-1
0Head (m)
-2
-1
0
x (m)
z (m
)
d)
0 1 2 3 4 5 6 7 8 9 10-2
-1
0Head (m)
-2
-1
0
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613
Fig. 9. Per unit area influx across the soil surface: a) layered soil with macro-pores of the 0.2 m 614
depth; b) layered soil with macro-pores of the 0.6 m depth (Case L-M); c) layered soil with 615
macro-pores of the 1 m depth; and d) layered soil with macro-pores of the 1.4 m depth. The 616
contours show the flux in log10 (m3/m
2/d). 617
618
x (m)
y (m
)
a)
0 1 2 3 4 5 6 7 8 9 10-0.5
0
0.5log10 (m
3/m
2/d)
-4
-2
0
x (m)
y (m
)
b)
0 1 2 3 4 5 6 7 8 9 10-0.5
0
0.5log10 (m
3/m
2/d)
-4
-2
0
x (m)
y (m
)
c)
0 1 2 3 4 5 6 7 8 9 10-0.5
0
0.5log10 (m
3/m
2/d)
-4
-2
0
x (m)
y (m
)
d)
0 1 2 3 4 5 6 7 8 9 10-0.5
0
0.5log10 (m
3/m
2/d)
-4
-2
0
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619
Fig. 10. Comparison of the distribution of the per unit area influx across the soil surface with 620
different macro-pore depths (indicated in the figure legend). 621
622
<0.0001 0.0001 to 0.001 0.001 to 0.01 0.01 to 0.1 0.1 to 1 > 10
10
20
30
40
50
60
70
80
90
100
Per unit area flux (m3/m
2/d)
Perc
en
tag
e (
%)
20 cm
60 cm
100 cm
140 cm
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39
623
Fig. 11. Per unit area influx across the soil surface for the four cases with randomly distributed 624
macro-pores (macro-pore density: 1 /m2). 625
x (m)
y (m
)
a)
0 1 2 3 4 5 6 7 8 9 100
0.5log10 (m
3/m
2/d)
-4
-2
0
x (m)
y (m
)
b)
0 1 2 3 4 5 6 7 8 9 100
0.5log10 (m
3/m
2/d)
-4
-2
0
x (m)
y (m
)
c)
0 1 2 3 4 5 6 7 8 9 100
0.5log10 (m
3/m
2/d)
-4
-2
0
x (m)
y (m
)
d)
0 1 2 3 4 5 6 7 8 9 100
0.5log10 (m
3/m
2/d)
-4
-2
0
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40
626
Fig. 12. Distribution of the per unit area influx across the soil surface for 100 simulation cases 627
with randomly distributed macro-pores (macro-pore density: 1 /m2). 628
629
<0.0001 0.0001 to 0.001 0.001 to 0.01 0.01 to 0.1 0.1 to 1 > 10
10
20
30
40
50
60
70
80
90
100
Per unit area flux (m3/m
2/d)
Perc
en
tag
e (
%)
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41
630
Fig. 13. Mean (a) and standard deviation (b) of the distribution of the per unit area influx across 631
the soil surface. Results are for 100 simulation cases with randomly distributed macro-pores with 632
the density, respectively, at 1 /m2 and 0.6 /m
2. For comparison, the result from the deterministic 633
simulation (Case L-M) is also shown. 634
<0.0001 0.0001 to 0.001 0.001 to 0.01 0.01 to 0.1 0.1 to 1 > 10
20
40
60
80
100
Per unit area flux (m3/m
2/d)
Perc
en
tag
e (
%)
a)
Random, Density of macro-pores: 1/m2
Random, Density of macro-pores: 0.6/m2
Deterministic, Density of macro-pores: 1/m2
<0.0001 0.0001 to 0.001 0.001 to 0.01 0.01 to 0.1 0.1 to 1 > 10
20
40
60
80
100
Per unit area flux (m3/m
2/d)
Sta
nda
rd d
evia
tion
(%
)
b)
Random, Density of macro-pores: 1/m2
Random, Density of macro-pores: 0.6/m2
