Sustainability of the Dujiangyan Irrigation System for over 2000 Years–A Numerical Investigation of the Water and Sediment Dynamic Diversions

Abstract

The Dujiangyan Irrigation System (DIS), located in the western portion of the Chengdu Plain at the transitional junction between the Qinghai-Tibet Plateau and Sichuan Basin, has been in operation for about 2300 years. The system automatically uses natural topographical and hydrological features and provides automatic water diversion, sediment drainage and intake flow discharge control, thus preventing disastrous events in the region in a ‘natural’ way. Using a numerical modeling approach, this study aims to investigate the reasons behind this natural behavior of the system and provide a better understanding of the complex mechanisms which have caused the sustainability of the DIS for over two millennia. For this purpose, a two-phase flow model based on the Shallow Water Equations (SWEs) is developed to simulate the fluid and sediment motions in the DIS. A coupled explicit-implicit technique based on the Finite Element Method is applied for the fluid flow and a Sediment Mass (SM) model in the framework of the Lagrangian particle method is proposed to simulate the sediment motion under different flow discharge conditions. The results show how different components of the DIS make full use of the hydrodynamic and topographical characteristics of the river to effectively discharge sediment and excess flood to the downstream and create an environmentally sustainable irrigation system.

Full text

sustainability
Article
Sustainability of the Dujiangyan Irrigation System
for over 2000 Years–A Numerical Investigation of the
Water and Sediment Dynamic Diversions
Xiaogang Zheng 1,2 , Ehsan Kazemi 2, Eslam Gabreil 3, Xingnian Liu 1and Ridong Chen 1, *
1State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and
Hydropower, Sichuan University, Chengdu 610065, China; scuzhengxiaogang@163.com (X.Z.);
scucrs@163.com (X.L.)
2Department of Civil and Structural Engineering, University of Sheffield, Sheffield S1 3JD, UK;
e.kazemi@sheffield.ac.uk
3Department of Civil Engineering, University of Gharyan, Gharyan 52GG +FM, Libya;
eslamgabreil@yahoo.com
*Correspondence: chenridong1984@163.com
Received: 30 January 2020; Accepted: 10 March 2020; Published: 20 March 2020


Abstract:
The Dujiangyan Irrigation System (DIS), located in the western portion of the Chengdu
Plain at the transitional junction between the Qinghai-Tibet Plateau and Sichuan Basin, has been in
operation for about 2300 years. The system automatically uses natural topographical and hydrological
features and provides automatic water diversion, sediment drainage and intake flow discharge
control, thus preventing disastrous events in the region in a ‘natural’ way. Using a numerical modeling
approach, this study aims to investigate the reasons behind this natural behavior of the system and
provide a better understanding of the complex mechanisms which have caused the sustainability of
the DIS for over two millennia. For this purpose, a two-phase flow model based on the Shallow Water
Equations (SWEs) is developed to simulate the fluid and sediment motions in the DIS. A coupled
explicit-implicit technique based on the Finite Element Method is applied for the fluid flow and
a Sediment Mass (SM) model in the framework of the Lagrangian particle method is proposed to
simulate the sediment motion under different flow discharge conditions. The results show how
different components of the DIS make full use of the hydrodynamic and topographical characteristics
of the river to effectively discharge sediment and excess flood to the downstream and create an
environmentally sustainable irrigation system.
Keywords:
Dujiangyan; sediment mass model; hydraulic properties; sediment diversion;
sustainable development
1. Introduction
The ancient water conservancy projects, such as the control project of Nel-Hammurabi on the
Euphrates River built by the Babylon Kingdom, the manmade canals constructed by the ancient Roman
Empire [
1
], and the agricultural irrigation systems dating back to the 1st-6th centuries in Israel [
2
] have
long fallen into disuse. However, there are some old irrigation structures that are still in operation, such
as the irrigation in sediment-laden rivers developed in ancient Peru [
3
]. Moreover, the qanat system, a
subterranean aqueduct used to convey water for irrigation and domestic consumption, originated in
Iran as early as the 7th century BCE [
4
], was brought to Spain in the 8th century, and then to the New
World in the 16th century [5,6]. This system still irrigates farmlands in Iran at the present day.
The Dujiangyan Irrigation System (DIS) is one of the ancient irrigation systems which are still in
operation. This system began in the 3rd century BCE, is characterized by the non-dam intake project
Sustainability 2020,12, 2431; doi:10.3390/su12062431 www.mdpi.com/journal/sustainability

Sustainability 2020,12, 2431 2 of 15
and is still discharging its functions perfectly [
1
]. It was listed as a World Cultural Heritage Site in
2000 and a World Heritage Irrigation Structure in 2018. The main headworks of the DIS are located
in the transitional region, where the river flows from a gorge to an alluvial plain. The location has a
50 km distance and 273 m elevation difference from Chengdu City, China (Figure 1). This is on the
commanding point of the alluvial plain so as to prevent floodwater flowing directly to the Chengdu
Plain [
7
]. Natural topographical and hydrological features are used to exclude sediment and divert
water for irrigation without the use of dams. The system has produced benefits in flood prevention,
agricultural irrigation, and water consumption for many years [8].
Sustainability 2020, 12, x FOR PEER REVIEW 2 of 15
The Dujiangyan Irrigation System (DIS) is one of the ancient irrigation systems which are still in 43
operation. This system began in the 3rd century BCE, is characterized by the non-dam intake project 44
and is still discharging its functions perfectly [1]. It was listed as a World Cultural Heritage Site in 45
2000 and a World Heritage Irrigation Structure in 2018. The main headworks of the DIS are located 46
in the transitional region, where the river flows from a gorge to an alluvial plain. The location has a 47
50 km distance and 273 m elevation difference from Chengdu City, China (Figure 1). This is on the 48
commanding point of the alluvial plain so as to prevent floodwater flowing directly to the Chengdu 49
Plain [7]. Natural topographical and hydrological features are used to exclude sediment and divert 50
water for irrigation without the use of dams. The system has produced benefits in flood prevention, 51
agricultural irrigation, and water consumption for many years [8]. 52
Recently, a dam was constructed upstream of the DIS (about 4 km from the Fish Mouth). The 53
reservoir of the dam can be seen in Figure 1. The dam construction was completed in 2006, and since 54
then, it has provided a more stable water supply to the Dujiangyan areas during the dry season, and 55
also reduced the peak flow discharge of the river during the flood season. Since this dam is a 56
relatively new structure and the focus of the present study is on the historical performance of the DIS 57
based on its natural and topographical characteristics during the past 2000 years, the effect of the dam 58
is not taken into consideration in this study. 59
60
Figure 1. Sketch map of the study area. The inset map (top right) shows the location of the Dujiangyan 61
Irrigation System (DIS) in China. The Puyang, Baitiao, Zouma, and Jiang’an Rivers all flow from the 62
Baopingkou (the bottle-neck channel of the DIS). 63
The headworks of the DIS are composed of three primary components: (1) The Fish Mouth (the 64
front end looks like a fish mouth), a diversion embankment dividing the Minjiang River into the Inner 65
River, primarily for irrigation, and the Outer River, mainly for flood and sediment discharge; (2) 66
Feishayan, a low spillway dam removing sediment and excess water from the Inner River into the 67
Outer River; and (3) Baopingkou (bottle-neck channel), a water intake automatically controlling 68
intake discharge from the Inner River (Figure 2). 69
Figure 1.
Sketch map of the study area. The inset map (top right) shows the location of the Dujiangyan
Irrigation System (DIS) in China. The Puyang, Baitiao, Zouma, and Jiang’an Rivers all flow from the
Baopingkou (the bottle-neck channel of the DIS).
Recently, a dam was constructed upstream of the DIS (about 4 km from the Fish Mouth). The
reservoir of the dam can be seen in Figure 1. The dam construction was completed in 2006, and since
then, it has provided a more stable water supply to the Dujiangyan areas during the dry season, and
also reduced the peak flow discharge of the river during the flood season. Since this dam is a relatively
new structure and the focus of the present study is on the historical performance of the DIS based on
its natural and topographical characteristics during the past 2000 years, the effect of the dam is not
taken into consideration in this study.
The headworks of the DIS are composed of three primary components: (1) The Fish Mouth (the
front end looks like a fish mouth), a diversion embankment dividing the Minjiang River into the
Inner River, primarily for irrigation, and the Outer River, mainly for flood and sediment discharge; (2)
Feishayan, a low spillway dam removing sediment and excess water from the Inner River into the
Outer River; and (3) Baopingkou (bottle-neck channel), a water intake automatically controlling intake
discharge from the Inner River (Figure 2).
The need to understand how the DIS has preserved its functionality for more than 2000 years and
the need for protecting it have urged researchers and engineers to investigate the hydrodynamics of the
system, such as flow motion, sediment transport, and riverbed evolution. They have been conducting
research in the last few decades on the mechanisms of water and sediment diversion under different
discharge conditions in order to improve the methods of protecting the system. Since the first physical
model experiment of the DIS conducted in 1941 [
9
], scholars have studied the characteristics of the
water and sediment transport by using the prototype survey [
10
,
11
], physical hydraulics model [
12
],
and numerical model [
13
–
15
]. As for the dynamic water diversion process, based on the ancients’
experience, more than 60% of the Minjiang River typically goes into the Inner River for the use of the
Chengdu Plain during the low discharge period, while in the flood period, this ratio can reduce to
less than 40% [
16
]. The analysis of the prototype data carried out by Sun et al. suggested that after
the construction of the check gate across the Outer River in 1974, the water distribution into the Inner

Sustainability 2020,12, 2431 3 of 15
River was close to 75% in spring time and only 37.5% in the flood season [
10
]. Later, as a complement
to the laboratory experiments conducted in Sichuan University [
12
], a two-dimensional (2D) numerical
model has been used to study the performance of the system under different inflow conditions [13].
Sustainability 2020, 12, x FOR PEER REVIEW 3 of 15
70
Figure 2. General layout of the DIS. 71
The need to understand how the DIS has preserved its functionality for more than 2000 years 72
and the need for protecting it have urged researchers and engineers to investigate the hydrodynamics 73
of the system, such as flow motion, sediment transport, and riverbed evolution. They have been 74
conducting research in the last few decades on the mechanisms of water and sediment diversion 75
under different discharge conditions in order to improve the methods of protecting the system. Since 76
the first physical model experiment of the DIS conducted in 1941 [9], scholars have studied the 77
characteristics of the water and sediment transport by using the prototype survey [10,11], physical 78
hydraulics model [12], and numerical model [13–15]. As for the dynamic water diversion process, 79
based on the ancients’ experience, more than 60% of the Minjiang River typically goes into the Inner 80
River for the use of the Chengdu Plain during the low discharge period, while in the flood period, 81
this ratio can reduce to less than 40% [16]. The analysis of the prototype data carried out by Sun et al. 82
suggested that after the construction of the check gate across the Outer River in 1974, the water 83
distribution into the Inner River was close to 75% in spring time and only 37.5% in the flood season 84
[10]. Later, as a complement to the laboratory experiments conducted in Sichuan University [12], a 85
two-dimensional (2D) numerical model has been used to study the performance of the system under 86
different inflow conditions [13]. 87
Many irrigation projects in history were abandoned due to sedimentation. The long-term vitality 88
of the DIS project is linked to the fact that sediment is automatically excluded by natural 89
characteristics of the system. Sediment deposition is primarily formed by the moving bed load from 90
May to October [11]. Based on the distorted movable model, the amount of bed load entering the 91
Inner River through the Fish Mouth is only about 29% of the total load in the Minjiang River [17]; and 92
that is 26% based on the results of the prototype observations [18]. The Feishayan begins to discharge 93
sediment to the Outer River when the flow rate of the Inner River is over 500 m3/s [12]. The larger the 94
flood discharge is, the higher is the discharge diversion ratio at the Feishayan and the more efficient 95
is the system in discharging sediment from the Inner River. Under the function of the Feishayan, over 96
90% of the bed load carried into the Inner River can be discharged to the downstream area of the 97
Outer River [19]. In addition, the V-Shaped Dike Spillway, an auxiliary project of the DIS, also diverts 98
sediment and excess water during periods of flood [20]. Finally, less than 8% of the total sediment of 99
the Minjiang River can reach the Baopingkou, ensuring that the irrigation lands receive clear water 100
[17]. It is notable that there have also been small amounts of sediment deposition in the Inner River 101
section which have been dredged annually (probably since the irrigation system was first 102
constructed). 103
At present, the prototype observations and model experiments can only explain the basics of the 104
sediment discharge process in the DIS. On the other hand, the one-dimensional (1D) [14] and 2D [15] 105
numerical models used for simulating riverbed evolution in the DIS have difficulty in describing the 106
‘dynamic’ sediment diversion, which has a key role in the understanding of the dynamics of the 107
sediment discharge processes in the system. For 1D models, this is due to the one dimensionality of 108
Figure 2. General layout of the DIS.
Many irrigation projects in history were abandoned due to sedimentation. The long-term vitality of
the DIS project is linked to the fact that sediment is automatically excluded by natural characteristics of
the system. Sediment deposition is primarily formed by the moving bed load from May to October [
11
].
Based on the distorted movable model, the amount of bed load entering the Inner River through the
Fish Mouth is only about 29% of the total load in the Minjiang River [
17
]; and that is 26% based on the
results of the prototype observations [
18
]. The Feishayan begins to discharge sediment to the Outer
River when the flow rate of the Inner River is over 500 m
3
/s [
12
]. The larger the flood discharge is,
the higher is the discharge diversion ratio at the Feishayan and the more efficient is the system in
discharging sediment from the Inner River. Under the function of the Feishayan, over 90% of the bed
load carried into the Inner River can be discharged to the downstream area of the Outer River [
19
]. In
addition, the V-Shaped Dike Spillway, an auxiliary project of the DIS, also diverts sediment and excess
water during periods of flood [
20
]. Finally, less than 8% of the total sediment of the Minjiang River
can reach the Baopingkou, ensuring that the irrigation lands receive clear water [
17
]. It is notable that
there have also been small amounts of sediment deposition in the Inner River section which have been
dredged annually (probably since the irrigation system was first constructed).
At present, the prototype observations and model experiments can only explain the basics of the
sediment discharge process in the DIS. On the other hand, the one-dimensional (1D) [
14
] and 2D [
15
]
numerical models used for simulating riverbed evolution in the DIS have difficulty in describing
the ‘dynamic’ sediment diversion, which has a key role in the understanding of the dynamics of the
sediment discharge processes in the system. For 1D models, this is due to the one dimensionality of
the model being able to describe the bed load movement process only in one channel while ignoring it
in the other DIS channels. For 2D models, when considering only the continuity of the bed load, there
is often a large time scale difference between flow and sediment motion, which results in non-accurate
estimation of riverbed morphology. In addition, the grid-based models, due to the Eulerian description
of the sediment medium, are unable to provide details of the motion of sediment particles between
different channels.
In this study, to tackle these difficulties, the fluid flow in the DIS is simulated by solving the
Shallow Water Equations (SWEs), which can effectively deal with the large scale of the study area,
coupled with a newly proposed Sediment Mass (SM) model for the bed load transport. The fluid
model is based on the coupled explicit-implicit solution algorithms of the SWEs and the SM model
is developed from the Lagrangian particle modeling concept, considering the orderly movement (in

Sustainability 2020,12, 2431 4 of 15
the form of bed load transport belt) of large amounts of sediment. With the SM model, due to its
Lagrangian framework, we can understand how sediment particles move from one channel to another,
i.e., ‘dynamic’ sediment diversion. Examples of such particle modeling approaches in fluid flow
simulation and sediment transport process were developed by Pu et al. [
21
], Ran et al. [
22
], and Zheng
et al. [23].
The developed coupled model is used to simulate the sediment motion in the DIS under different
flow conditions; and the results are discussed to explain why the DIS has operated for 2300 years and
is still functioning well.
2. Fluid Flow Model
The 2D Shallow Water Equations (Equations (1) and (2)) are solved for the fluid flow:
∂η
∂t+∇·(hu)=0 (1)
D(hu)
Dt =AHh∇2u−gh∇η−gµ2|u|u
h1/3(2)
where:
η
=water surface; t=time; h=flow depth;
u
=the velocity vector with the longitudinal and
transversal components of uand v, respectively; A
H
=the horizontal eddy viscosity coefficient;
g
=
gravitational acceleration; and µ=the bed roughness coefficient.
The solution is based on the method used in Zheng et al. [
24
]. The water level and flow velocity
are calculated by the implicit Eulerian-Lagrangian method (ELM), i.e., the quantities at time t+dt are
updated using those at time t, implicitly, where dt is the time step size in the flow model; and then
the temporary ELM traced lines are corrected explicitly by using the Characteristics-based Splitting
method, i.e., the intermediate values between times tand t+dt are explicitly computed. This leads
to the enhancement of the computational efficiency of the model as the detailed flow information
lost in the implicit computation can be recovered by increasing the number of explicit intermediate
computational steps. In fact, the coupled method merges the merits of the high computational accuracy
from the explicit scheme with the high numerical efficiency and stability from the implicit scheme.
For the ELM computations, the computational domain is discretized by triangular mesh elements,
and the governing equations are solved by using the Finite Element Method. For the boundary
conditions, three types of boundaries are considered:
(1) an open boundary applied in the flow inlet and outlet;
(2) a land boundary satisfying slip and non-penetration conditions; and
(3) a moving boundary relating to the continuous changes of flow and sediment transport. More
details on the numerical discretization and boundary conditions can be found in Zheng et al. [
24
] and
Chen et al. [25].
The model has previously been used for a few applications including dam-break flow [
24
],
long-term river meandering process [24], and unsteady flow propagation [26].
Due to the bending section of the Minjiang River and the diversion of flow at the Fish Mouth, the
effect of secondary flow is not negligible in the present application, an effect which is often neglected
in 2D SWE models. To include the secondary flow effect in the present model, a transversal velocity
v
r
is computed at the nodes of the computational domain by using the Rozovskii formula (Equation
(3), [
27
]), and added to the transversal component of
u
(i.e., v) with the magnitude of velocity |
u
|being
unchanged. This applies a modification to the direction of the velocity vector, while its magnitude
remains unchanged.
vr=u1
κ2
h
R"F1(λ)−F2(λ)µ√g
κh1/6#(3)
where:
κ
=von Karman constant (~0.4); R=radius of curvature;
λ
=normalized vertical co-ordinate
(which is set to 0.3 here); F1(λ)=−2Rλ
0
ln2λ
1−λdλ+1;and F2(λ)=Rλ
0
ln2λ
1−λdλ2
−2.

Sustainability 2020,12, 2431 5 of 15
3. Sediment Transport Model
In the present study, bed load is considered as the dominant form of sediment transport, and a
particle-based SM model is proposed to model the convection motion of bed load in a disk-like form,
considering sediment as a discrete medium and bed load as a motion of a group of sediment grains. In
the following, a description of the SM model is presented.
Taking only the convective motion into account, in order to minimize the error caused by the
omission of the sediment diffusion, a time step size smaller than the one used in the flow model
is set for the calculation of sediment motion, i.e.,
∆
T=dt/N, where Nis the number of segments
determined based on the velocity gradient (set to 2~10 in this study). Disks, representing SMs, are
used to discretize the sediment domain. Each disk contains a number of sediment particles virtually,
with a circular bottom area defining the influence domain of the SM, and a height (thickness) equal to
the multiplication of the porosity of sediment medium by the mean diameter of the sediment grains
within the disk influence area. The disks can overlap each other and move over the fluid domain based
on their velocity, which is determined as follows.
Firstly, in each sub-step ∆T, the velocity of a virtual sediment particle is calculated as follows:
ut+∆T=ut+ua(4)
where:
ut
and
ut+∆T
=the sediment particle velocity vector at times tand t+
∆
T, respectively; and
ua
=the increase in the velocity of the sediment particle during
∆
T. The magnitude of
ua
, i.e., u
a
,
is calculated by Equation (5); and its direction is determined by considering a normal distribution
for the angle between it and the streamline (as depicted in Figure 3a) based on the assumption that
the direction of
ua
is random due to the randomness of sediment particle collisions during bed load
transport:
ua=(uw−uc)×β(5)
where uc=critical incipient velocity computed by the Sharmove formula [28]:
uc=1.14 rγs−γ
γgD(h
D)
(1
6)
(6)
and u
w
=mean flow velocity at the center of the SM, calculated as the arithmetic average of flow
velocity at the nodes located inside the influence area of the disk. In addition,
β
=correction coefficient
(which is set to 0.1 in the present simulations),
γs
=specific weigh of sediment grains (=26.5 kN/m
3
here), γ=specific weigh of flow (=10 kN/m3for water), and D=diameter of sediment grains.
Sustainability 2020, 12, x FOR PEER REVIEW 6 of 15
in which ψ
=

γs –
γ

D
γhJ and J = the bed slope. The displacement of the SM in each sub-step is then 192
evaluated as Δx = uSM × ΔT. Figure 3 shows the resultant velocity of a sediment particle and the motion 193
of an SM according to its velocity. 194
Figure 3. Bed load velocity and mass motion: (a) sediment particle resultant velocity; and (b) sediment 195
mass motion over the fluid domain (which is discretized by triangular elements). 196
After the position of the SM disks is updated, the calculated properties of the sediment domain 197
are transported to the fluid domain. For this, the velocity and thickness of each disk is converted to 198
the flow domain nodes that are located inside the influence domain of the disk using a weighting 199
function (Spline here), and then the converted values at each node are summed up. This yields the 200
average thickness hs and velocity us of the sediment layer at the position of the nodes. Then, the bed 201
load transport rate qb is estimated using Equation (8), and the change of the riverbed elevation from 202
t to t + ΔT is computed by using Equation (9): 203 𝐪=ℎ×𝐮 (8)
(1−𝜉)𝜕𝑧
𝜕𝑡 +∇⋅𝐪=0 (9)
where ξ = porosity; and zb = thickness of the movable bed layer. 204
Then, the fluid model equations are solved in the next sub-step, and this process is repeated until 205
the number of sub-steps reaches N. Then, for the next time step, i.e., at t + dt, SMs are regenerated 206
instead of turning the node information back to them. This will reduce the error related to the 207
diffusion effect without increasing extra calculation. 208
4. Model Applications in the DIS 209
In this section, the numerical model is applied to simulate the sediment processes in the DIS. 210
The flood control discharge and the 1000-year flood of the area are 800 m3/s and 10,120 m3/s, 211
respectively. Besides, if the Inner River discharge exceeds 1000 m3/s, a large amount of sediment can 212
be discharged into the Outer River via the Feishayan [12]. Considering these factors, three flow rates, 213
i.e., 800 m3/s (low discharge), 1800 m3/s (medium discharge), and 10,120 m3/s (high discharge), are 214
selected to simulate different sediment diversion conditions. At the initial time of each simulation, a 215
number of SM disks are placed at the inlet boundary with their velocity being determined according 216
to the desired flow discharge. The total simulation time is 7 days, and the grid and time step sizes are 217
set to 3 m and 10 s, respectively. Sections 4.1 and 4.2 present the results of the fluid flow and sediment 218
motion, respectively. 219
4.1. Simulation of Fluid Flow 220
Figures 4, 5, and 6 show the results of velocity of the numerical model for flow rates of 800, 1800 221
and 10,120 m3/s, respectively. The water diversion ratio, i.e., the ratio of the flow discharge in the 222
Inner River to that of the Minjiang River, is automatically regulated at the Fish Mouth due to the 223
Figure 3.
Bed load velocity and mass motion: (
a
) sediment particle resultant velocity; and (
b
) sediment
mass motion over the fluid domain (which is discretized by triangular elements).

Sustainability 2020,12, 2431 6 of 15
To determine the direction of the velocity vector
ua
a normal distribution is considered for the
angle between the streamline and the direction of the
ua
vector (as depicted in Figure 3a). Then, the
velocity of the SM is calculated as
uSM
=
ut+∆T×
P, where the Einstein bed load theory is used to
estimate the incipient probability P:
P=1−1
√πZ1
7ψ−2
−1
7ψ−2
e−t2dt (7)
in which
ψ=(γs–γ)D
γhJ
and J=the bed slope. The displacement of the SM in each sub-step is then
evaluated as
∆x
=
uSM ×∆
T. Figure 3shows the resultant velocity of a sediment particle and the
motion of an SM according to its velocity.
After the position of the SM disks is updated, the calculated properties of the sediment domain
are transported to the fluid domain. For this, the velocity and thickness of each disk is converted to the
flow domain nodes that are located inside the influence domain of the disk using a weighting function
(Spline here), and then the converted values at each node are summed up. This yields the average
thickness h
s
and velocity
us
of the sediment layer at the position of the nodes. Then, the bed load
transport rate
qb
is estimated using Equation (8), and the change of the riverbed elevation from tto t+
∆Tis computed by using Equation (9):
qb=hs×us(8)
(1−ξ)∂zb
∂t+∇·qb=0 (9)
where ξ=porosity; and zb=thickness of the movable bed layer.
Then, the fluid model equations are solved in the next sub-step, and this process is repeated until
the number of sub-steps reaches N. Then, for the next time step, i.e., at t+dt, SMs are regenerated
instead of turning the node information back to them. This will reduce the error related to the diffusion
effect without increasing extra calculation.
4. Model Applications in the DIS
In this section, the numerical model is applied to simulate the sediment processes in the DIS. The
flood control discharge and the 1000-year flood of the area are 800 m
3
/s and 10,120 m
3
/s, respectively.
Besides, if the Inner River discharge exceeds 1000 m
3
/s, a large amount of sediment can be discharged
into the Outer River via the Feishayan [
12
]. Considering these factors, three flow rates, i.e., 800 m
3
/s
(low discharge), 1800 m
3
/s (medium discharge), and 10,120 m
3
/s (high discharge), are selected to
simulate different sediment diversion conditions. At the initial time of each simulation, a number
of SM disks are placed at the inlet boundary with their velocity being determined according to the
desired flow discharge. The total simulation time is 7 days, and the grid and time step sizes are set
to 3 m and 10 s, respectively. Sections 4.1 and 4.2 present the results of the fluid flow and sediment
motion, respectively.
4.1. Simulation of Fluid Flow
Figures 4–6show the results of velocity of the numerical model for flow rates of 800, 1800 and
10,120 m
3
/s, respectively. The water diversion ratio, i.e., the ratio of the flow discharge in the Inner
River to that of the Minjiang River, is automatically regulated at the Fish Mouth due to the central
shoal located upstream of it (Figure 2). In the dry season, the central shoal is unsubmerged. As a result,
according to the historical record (Figure 7), more than 60% of the total discharge runs into the Inner
River, which is beneficial for the water intake of the irrigation area. In the wet season, the shoal is fully
submerged, and the current tends straight into the Outer River, so the water diversion ratio is reverse.
Due to these, the DIS, naturally, has functions of water intake and flood drainage during the dry and
wet seasons, respectively. Figure 7presents the water diversion ratio of the Inner River obtained from

Sustainability 2020,12, 2431 7 of 15
the present simulations for different flow discharges in the Minjiang River in comparison with the
historical records in the site, where good agreement is observed. It clearly shows that the diversion
ratio of the Inner River decreases when the Minjiang River flow discharge goes up.
Sustainability 2020, 12, x FOR PEER REVIEW 7 of 15
central shoal located upstream of it (Figure 2). In the dry season, the central shoal is unsubmerged. 224
As a result, according to the historical record (Figure 7), more than 60% of the total discharge runs 225
into the Inner River, which is beneficial for the water intake of the irrigation area. In the wet season, 226
the shoal is fully submerged, and the current tends straight into the Outer River, so the water 227
diversion ratio is reverse. Due to these, the DIS, naturally, has functions of water intake and flood 228
drainage during the dry and wet seasons, respectively. Figure 7 presents the water diversion ratio of 229
the Inner River obtained from the present simulations for different flow discharges in the Minjiang 230
River in comparison with the historical records in the site, where good agreement is observed. It 231
clearly shows that the diversion ratio of the Inner River decreases when the Minjiang River flow 232
discharge goes up. 233
234
Figure 4. Flow velocity field under a flow discharge of 800 m3/s. 235
236
Figure 5. Flow velocity field under a flow discharge of 1800 m3/s. 237
Figure 4. Flow velocity field under a flow discharge of 800 m3/s.
Sustainability 2020, 12, x FOR PEER REVIEW 7 of 15
central shoal located upstream of it (Figure 2). In the dry season, the central shoal is unsubmerged. 224
As a result, according to the historical record (Figure 7), more than 60% of the total discharge runs 225
into the Inner River, which is beneficial for the water intake of the irrigation area. In the wet season, 226
the shoal is fully submerged, and the current tends straight into the Outer River, so the water 227
diversion ratio is reverse. Due to these, the DIS, naturally, has functions of water intake and flood 228
drainage during the dry and wet seasons, respectively. Figure 7 presents the water diversion ratio of 229
the Inner River obtained from the present simulations for different flow discharges in the Minjiang 230
River in comparison with the historical records in the site, where good agreement is observed. It 231
clearly shows that the diversion ratio of the Inner River decreases when the Minjiang River flow 232
discharge goes up. 233
234
Figure 4. Flow velocity field under a flow discharge of 800 m3/s. 235
236
Figure 5. Flow velocity field under a flow discharge of 1800 m3/s. 237
Figure 5. Flow velocity field under a flow discharge of 1800 m3/s.
Sustainability 2020, 12, x FOR PEER REVIEW 8 of 15
238
Figure 6. Flow velocity field under a flow discharge of 10,120 m3/s. 239
240
Figure 7. Computed and measured water diversion ratio for different flow discharges. There is no 241
historical record for the high discharge condition (10,120 m3/s). The historical record is from field 242
measurements in the DIS [10]. 243
4.2. Simulation of Sediment Processes 244
In order to understand how under different flow regimes, the sediment transport is distributed 245
over the channels of the DIS, i.e., the Inner and Outer Rivers, the results of the bed load movement 246
simulated by the proposed model in Section 3 are presented. Figures 8, 9, and 10 show these results 247
under the low, medium, and high flow discharge conditions (800, 1800, and 10,120 m3/s, respectively). 248
As seen in Figure 4, when the discharge is low (800 m3/s), the flow velocity in the Inner River is 249
not significant (the average velocity in the middle of the channel is about 3 m/s). Therefore, only a 250
small amount of sediment moves through the Inner River (see Figure 8). 251
During the medium flow discharge condition (1800 m3/s), the sediment and surplus water are 252
discharged through the Feishayan (Figure 5; Figure 9). This can be explained by the mutual 253
functionality between the Feishayan and the Baopingkou. The Feishayan is a low spillway weir with 254
a width of 240 m, average weir crest elevation of 728.25 m, and distance of 710 m away from the Fish 255
Mouth; the Baopingkou, with a width of 20.4 m, bottom elevation of 716.3 m, and a distance of 120 m 256
away from the Feishayan, serves as a water intake throat to the downstream irrigation areas (Figure 257
Figure 6. Flow velocity field under a flow discharge of 10,120 m3/s.

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238
Figure 6. Flow velocity field under a flow discharge of 10,120 m3/s. 239
240
Figure 7. Computed and measured water diversion ratio for different flow discharges. There is no 241
historical record for the high discharge condition (10,120 m3/s). The historical record is from field 242
measurements in the DIS [10]. 243
4.2. Simulation of Sediment Processes 244
In order to understand how under different flow regimes, the sediment transport is distributed 245
over the channels of the DIS, i.e., the Inner and Outer Rivers, the results of the bed load movement 246
simulated by the proposed model in Section 3 are presented. Figures 8, 9, and 10 show these results 247
under the low, medium, and high flow discharge conditions (800, 1800, and 10,120 m3/s, respectively). 248
As seen in Figure 4, when the discharge is low (800 m3/s), the flow velocity in the Inner River is 249
not significant (the average velocity in the middle of the channel is about 3 m/s). Therefore, only a 250
small amount of sediment moves through the Inner River (see Figure 8). 251
During the medium flow discharge condition (1800 m3/s), the sediment and surplus water are 252
discharged through the Feishayan (Figure 5; Figure 9). This can be explained by the mutual 253
functionality between the Feishayan and the Baopingkou. The Feishayan is a low spillway weir with 254
a width of 240 m, average weir crest elevation of 728.25 m, and distance of 710 m away from the Fish 255
Mouth; the Baopingkou, with a width of 20.4 m, bottom elevation of 716.3 m, and a distance of 120 m 256
away from the Feishayan, serves as a water intake throat to the downstream irrigation areas (Figure 257
Figure 7.
Computed and measured water diversion ratio for different flow discharges. There is no
historical record for the high discharge condition (10,120 m
3
/s). The historical record is from field
measurements in the DIS [10].
4.2. Simulation of Sediment Processes
In order to understand how under different flow regimes, the sediment transport is distributed
over the channels of the DIS, i.e., the Inner and Outer Rivers, the results of the bed load movement
simulated by the proposed model in Section 3are presented. Figures 8–10 show these results under the
low, medium, and high flow discharge conditions (800, 1800, and 10,120 m3/s, respectively).
As seen in Figure 4, when the discharge is low (800 m
3
/s), the flow velocity in the Inner River is
not significant (the average velocity in the middle of the channel is about 3 m/s). Therefore, only a
small amount of sediment moves through the Inner River (see Figure 8).
During the medium flow discharge condition (1800 m
3
/s), the sediment and surplus water are
discharged through the Feishayan (Figure 5; Figure 9). This can be explained by the mutual functionality
between the Feishayan and the Baopingkou. The Feishayan is a low spillway weir with a width of 240
m, average weir crest elevation of 728.25 m, and distance of 710 m away from the Fish Mouth; the
Baopingkou, with a width of 20.4 m, bottom elevation of 716.3 m, and a distance of 120 m away from
the Feishayan, serves as a water intake throat to the downstream irrigation areas (Figure 2). The width
of the Baopingkou is only one-tenth of that of the Feishayan. Therefore, once the discharge in the Inner
River exceeds the intake capacity of the Baopingkou, most of the excess flood flows out into the Outer
River via the Feishayan (Figure 5). Another important function of the Feishayan is sediment diversion.
The Minjiang River carries large amounts of materials flowing into the Inner River and may cause the
siltation of the Baopingkou, changes in the elevation of the riverbed, and reduction of the irrigation
water intake. However, due to the diversion of sediment at the Feishayan, these impacts are effectively
mitigated. The reason behind that the Feishayan is able to discharge sediment to the Outer River is that
it is located on the convex bank of the slightly curved Inner River section. Under the function of the
centrifugal force, the surface flow with low sediment concentration flows to the Baopingkou located
on the concave bank, whereas the bottom water containing high concentration moves to the Feishayan
located on the convex bank (see Reference [
29
]). The larger the flood discharge is, the higher is the
water division ratio of the Feishayan and the more efficient is the sediment diversion of the Feishayan.

Sustainability 2020,12, 2431 9 of 15
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2). The width of the Baopingkou is only one-tenth of that of the Feishayan. Therefore, once the
discharge in the Inner River exceeds the intake capacity of the Baopingkou, most of the excess flood
flows out into the Outer River via the Feishayan (Figure 5). Another important function of the
Feishayan is sediment diversion. The Minjiang River carries large amounts of materials flowing into
the Inner River and may cause the siltation of the Baopingkou, changes in the elevation of the
riverbed, and reduction of the irrigation water intake. However, due to the diversion of sediment at
the Feishayan, these impacts are effectively mitigated. The reason behind that the Feishayan is able
to discharge sediment to the Outer River is that it is located on the convex bank of the slightly curved
Inner River section. Under the function of the centrifugal force, the surface flow with low sediment
concentration flows to the Baopingkou located on the concave bank, whereas the bottom water
containing high concentration moves to the Feishayan located on the convex bank (see Reference
[29]). The larger the flood discharge is, the higher is the water division ratio of the Feishayan and the
(a)
(b)
(c)
Figure 8.
Bed load movement process under the discharge of 800 m
3
/s on: (
a
) Day 1; (
b
) Day 4; and (
c
)
Day 7.

Sustainability 2020,12, 2431 10 of 15
Sustainability 2020, 12, x FOR PEER REVIEW 10 of 15
(c)
Figure 8. Bed load movement process under the discharge of 800 m3/s on: (a) Day 1; (b) Day 4; and (c) 271
Day 7. 272
There is a small amount of sediment which is not discharged through the Feishayan, but deposits 273
in the Fengqiwo Section. This is because the narrow Baopingkou is not located at the middle of the 274
width of the Inner River. The flood flows to the Lidui and then a backwater is formed in front of it. 275
The effect of the backwater propagates upstream with the increase of the Inner River discharge. Once 276
the backwater effect reaches the Feishayan, some amount of the sediment deposits at the Fengqiwo 277
Section due to a large reduction in the bottom flow velocity. The deposited sediment is removed in 278
the annual dredging project.Under a high discharge condition, the upstream central shoal is 279
submerged, thus the main flood current carrying most of the moving bed load diverts directly toward 280
the Outer River. At the same time, due to the fact that the Inner River is located on the concave bank 281
of the curved river section, the bed load is transported into the Outer River along the convex bank 282
under the function of the bend flow. In summary, the major amounts of the flood and the bed load 283
are diverted into the Outer River at the Fish Mouth ( Figure 6; Figure 10). 284
(a)
(b)
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(c)
Figure 9. Bed load movement process under the discharge of 1800 m3/s on: (a) Day 1; (b) Day 4; and 285
(c) Day 7. 286
The rest of the sediment and water which flow into the Inner River is diverted once again at the 287
Feishayan. After this diversion, if the flood discharge is still high, then the excess amount is 288
automatically discharged through the V-Shaped Dike Spillway. The V-Shaped Dike is an auxiliary 289
project located downstream of the Feishayan and is a low spillway dam with 60 m width and 729 m 290
average weir crest elevation which is slightly higher than that of the Feishayan. Under low and 291
medium flood conditions, the influence of the backwater is not substantial in front of the Baopingkou, 292
meaning that the water level of the Inner River only reaches the crest of the Feishayan and is below 293
that of the V-Shaped Dike (i.e., the V-Shaped Dike Spillway is effectively dry at low and medium 294
discharges). Thus, the flood entering the Inner River is mainly discharged via the Feishayan (see 295
Figures 4 and 5). However, during the high flood discharge period, the upstream backwater of the 296
Baopingkou is considerable and the water level is higher than the V-Shaped Dike, enabling part of 297
the flood to discharge into the Outer River via the V-Shaped Dike Spillway (Figure 6). The flood 298
diversion through the V-Shaped Dike Spillway causes a reduction in the upstream water level and 299
therefore is beneficial for the reasonable water intake of the Baopingkou. The larger the discharge in 300
the Inner River is, the more effective is the function of the V-Shaped Dike Spillway. 301
In summary, the results showed that most of the flood in the Inner River is discharged to the 302
Outer River via the Feishayan; and under the high flood discharge condition, a part of it can also be 303
discharged through the V-Shaped Dike Spillway to the Outer River. In addition, as shown in Figure 304
7, a larger flood discharge in the Minjiang River results in smaller water diversion ratios at the 305
Baopingkou, a function that protects the Chengdu Plain from disastrous floods. 306
Figure 9.
Bed load movement process under the discharge of 1800 m
3
/s on: (
a
) Day 1; (
b
) Day 4; and (
c
)
Day 7.

Sustainability 2020,12, 2431 11 of 15
Sustainability 2020, 12, x FOR PEER REVIEW 11 of 15
(c)
Figure 9. Bed load movement process under the discharge of 1800 m3/s on: (a) Day 1; (b) Day 4; and 285
(c) Day 7. 286
The rest of the sediment and water which flow into the Inner River is diverted once again at the 287
Feishayan. After this diversion, if the flood discharge is still high, then the excess amount is 288
automatically discharged through the V-Shaped Dike Spillway. The V-Shaped Dike is an auxiliary 289
project located downstream of the Feishayan and is a low spillway dam with 60 m width and 729 m 290
average weir crest elevation which is slightly higher than that of the Feishayan. Under low and 291
medium flood conditions, the influence of the backwater is not substantial in front of the Baopingkou, 292
meaning that the water level of the Inner River only reaches the crest of the Feishayan and is below 293
that of the V-Shaped Dike (i.e., the V-Shaped Dike Spillway is effectively dry at low and medium 294
discharges). Thus, the flood entering the Inner River is mainly discharged via the Feishayan (see 295
Figures 4 and 5). However, during the high flood discharge period, the upstream backwater of the 296
Baopingkou is considerable and the water level is higher than the V-Shaped Dike, enabling part of 297
the flood to discharge into the Outer River via the V-Shaped Dike Spillway (Figure 6). The flood 298
diversion through the V-Shaped Dike Spillway causes a reduction in the upstream water level and 299
therefore is beneficial for the reasonable water intake of the Baopingkou. The larger the discharge in 300
the Inner River is, the more effective is the function of the V-Shaped Dike Spillway. 301
In summary, the results showed that most of the flood in the Inner River is discharged to the 302
Outer River via the Feishayan; and under the high flood discharge condition, a part of it can also be 303
discharged through the V-Shaped Dike Spillway to the Outer River. In addition, as shown in Figure 304
7, a larger flood discharge in the Minjiang River results in smaller water diversion ratios at the 305
Baopingkou, a function that protects the Chengdu Plain from disastrous floods. 306
Sustainability 2020, 12, x FOR PEER REVIEW 12 of 15
(a)
(b)
(c)
Figure 10. Bed load movement process under the discharge of 10,120 m3/s on: (a) Day 1; (b) Day 4; 307
and (c) Day 7. 308
5. Discussion 309
Three key components of the DIS (i.e., the Fish Mouth, the Feishayan, and the Baopingkou) 310
combining with ancillary embankments and watercourses ensure there is efficient sediment diversion 311
and regular water supply for the Chengdu Plain. The reason behind that the DIS is still performing 312
designated functions today is that the sediment is automatically transported in an orderly manner 313
without causing adverse effects on the system. A summary of the operation of the DIS is the 6-314
character maxim “deeply clearing channel (specially meaning the channel at the Fengqiwo Section), 315
building low dike” [1]. 316
The purpose of a “deeply clearing channel” is to keep the sediment transport in an equilibrium 317
state during a year, namely, the equilibrium of erosion and deposition in the Inner River. This 318
requires the longitudinal profile of the riverbed to reach the balanced section. Therefore, annual 319
dredging is necessary. Also, the dredging level needs to reach the iron bar markers (the position of 320
the riverbed balanced section) buried in the Fengqiwo Section. If the dredging depth is shallower 321
than the iron bar markers, the sediment will further deposit, which is an adverse effect to the 322
sediment diversion and the water intake of irrigation areas. If the dredging depth exceeds the iron 323
bar markers (equivalent to the reduction of the erosional basis), then the erosion will strengthen and 324
cause the non-equilibrium of the sediment supply and transport. The DIS is a successful case where 325
the theory of riverbed balanced section can be applied to the water conservancy project [30]. 326
“Building low dike” means that the height of the Feishayan should be low, which is conducive 327
to discharge water and sediment in the flood period. It shows that floods have been a key factor in 328
Figure 10.
Bed load movement process under the discharge of 10,120 m
3
/s on: (
a
) Day 1; (
b
) Day 4; and
(c) Day 7.
There is a small amount of sediment which is not discharged through the Feishayan, but deposits
in the Fengqiwo Section. This is because the narrow Baopingkou is not located at the middle of the
width of the Inner River. The flood flows to the Lidui and then a backwater is formed in front of it. The
effect of the backwater propagates upstream with the increase of the Inner River discharge. Once the
backwater effect reaches the Feishayan, some amount of the sediment deposits at the Fengqiwo Section

Sustainability 2020,12, 2431 12 of 15
due to a large reduction in the bottom flow velocity. The deposited sediment is removed in the annual
dredging project.Under a high discharge condition, the upstream central shoal is submerged, thus the
main flood current carrying most of the moving bed load diverts directly toward the Outer River. At
the same time, due to the fact that the Inner River is located on the concave bank of the curved river
section, the bed load is transported into the Outer River along the convex bank under the function of
the bend flow. In summary, the major amounts of the flood and the bed load are diverted into the
Outer River at the Fish Mouth (Figure 6; Figure 10).
The rest of the sediment and water which flow into the Inner River is diverted once again at
the Feishayan. After this diversion, if the flood discharge is still high, then the excess amount is
automatically discharged through the V-Shaped Dike Spillway. The V-Shaped Dike is an auxiliary
project located downstream of the Feishayan and is a low spillway dam with 60 m width and 729
m average weir crest elevation which is slightly higher than that of the Feishayan. Under low and
medium flood conditions, the influence of the backwater is not substantial in front of the Baopingkou,
meaning that the water level of the Inner River only reaches the crest of the Feishayan and is below
that of the V-Shaped Dike (i.e., the V-Shaped Dike Spillway is effectively dry at low and medium
discharges). Thus, the flood entering the Inner River is mainly discharged via the Feishayan (see
Figures 4and 5). However, during the high flood discharge period, the upstream backwater of the
Baopingkou is considerable and the water level is higher than the V-Shaped Dike, enabling part of the
flood to discharge into the Outer River via the V-Shaped Dike Spillway (Figure 6). The flood diversion
through the V-Shaped Dike Spillway causes a reduction in the upstream water level and therefore is
beneficial for the reasonable water intake of the Baopingkou. The larger the discharge in the Inner
River is, the more effective is the function of the V-Shaped Dike Spillway.
In summary, the results showed that most of the flood in the Inner River is discharged to the
Outer River via the Feishayan; and under the high flood discharge condition, a part of it can also be
discharged through the V-Shaped Dike Spillway to the Outer River. In addition, as shown in Figure 7, a
larger flood discharge in the Minjiang River results in smaller water diversion ratios at the Baopingkou,
a function that protects the Chengdu Plain from disastrous floods.
5. Discussion
Three key components of the DIS (i.e., the Fish Mouth, the Feishayan, and the Baopingkou)
combining with ancillary embankments and watercourses ensure there is efficient sediment diversion
and regular water supply for the Chengdu Plain. The reason behind that the DIS is still performing
designated functions today is that the sediment is automatically transported in an orderly manner
without causing adverse effects on the system. A summary of the operation of the DIS is the 6-character
maxim “deeply clearing channel (specially meaning the channel at the Fengqiwo Section), building
low dike” [1].
The purpose of a “deeply clearing channel” is to keep the sediment transport in an equilibrium
state during a year, namely, the equilibrium of erosion and deposition in the Inner River. This requires
the longitudinal profile of the riverbed to reach the balanced section. Therefore, annual dredging is
necessary. Also, the dredging level needs to reach the iron bar markers (the position of the riverbed
balanced section) buried in the Fengqiwo Section. If the dredging depth is shallower than the iron bar
markers, the sediment will further deposit, which is an adverse effect to the sediment diversion and
the water intake of irrigation areas. If the dredging depth exceeds the iron bar markers (equivalent to
the reduction of the erosional basis), then the erosion will strengthen and cause the non-equilibrium of
the sediment supply and transport. The DIS is a successful case where the theory of riverbed balanced
section can be applied to the water conservancy project [30].
“Building low dike” means that the height of the Feishayan should be low, which is conducive
to discharge water and sediment in the flood period. It shows that floods have been a key factor in
designing the DIS. If a hydraulic system is designed without taking floods into consideration, it is
unlikely that it can remain in working condition. There are numerous examples of hydraulic works

Sustainability 2020,12, 2431 13 of 15
built in which usage for irrigation and the hydraulic profile for the flood period have been combined.
A few examples are the spate irrigation system in Africa [
31
–
34
] and the ancient irrigation system in
the Central Negev desert [35].
Principles of the DIS are still valuable references in modern diversion project design, including:
making full use of the natural bend flow to discharge water and sediment; annual well-organized
maintenance to dredge a specific river section; and coexistence of water intake and flood control. This
is a good example of comprehensively utilizing natural water resources and realizing harmonious
coordination between humans and the nature.
6. Conclusions
The DIS, both naturally and with the aid of man-made structures, has been functioning for
2300 years, excluding sediment, preventing flood, and diverting water for irrigation in the Chengdu
plain. To better understand the hydrodynamics and sediment transport processes in the system,
numerical modeling approaches were used in this study. A coupled explicit-implicit numerical scheme
was applied to simulate the fluid flow, coupled with an SM model for the sediment transport. The
simulations were carried out for three different flow regimes: low, medium, and high (based on the
1000-year flood event) discharges; and the water and sediment diversions at the Fish Mouth, Feishayan,
and V-shaped Dike Spillway were investigated in detail.
According to the model results, (1) under the low discharge condition, the system mainly diverts
the water flow at the Fish Mouth for irrigation; (2) under the medium discharge condition, the current
carries more bed load flowing into the Inner River, which is then discharged through the Feishayan
to the Outer River; and (3) under the high discharge condition, the main current flows straight into
the Outer River, thus the bed load is discharged directly through that channel. The model was able
to demonstrate these processes numerically and complement the findings of the previous studies.
The processes are mainly attributed to the central shoal located upstream of the Fish Mouth and the
bending channel, i.e., at low discharges, the shoal is unsubmerged, thus it diverts more water into the
Inner River; and when coming to the high discharge conditions, the shoal is submerged and the water
flows straight into the Outer River.
In summary, the water flow and sediment diversion project (Fish Mouth), the discharge projects
(Feishayan and V-shaped Dike Spillway) and the intake project (Baopingkou) make full use of the flow
dynamics and topographical characteristics (e.g., the bending channel and the elevation differences
between these components) to effectively discharge excess floodwater and provide a reliable water
supply to the irrigation areas. The results and discussions in this study clearly explain why the DIS
has operated for thousands of years, and provide useful references for the engineering design of such
systems. The proposed numerical models, however, still need rigorous and comprehensive validations
based on benchmark tests of flow and sediment transport, different channel geometries, and various
flow conditions. These are considered as future study areas.
Author Contributions:
X.Z. and R.C. performed the model simulations and analyses; X.Z., E.K., and E.G. prepared
the manuscript and carried out reviews and editing; X.L. took the leadership of the project and gave suggestions
during the whole work; R.C. developed and tested the numerical code used in the project. All authors have read
and agreed to the published version of the manuscript.
Funding:
This research was funded by the National Natural Science Foundation of China (No. 51609161), National
Key Research and Development Program of China (No. 2016YFC0402302) and Open Funding of the State Key
Laboratory of Hydraulics and Mountain River Engineering, Sichuan University (SKLH 1710; 1712; 1911).
Acknowledgments:
The authors would like to thank the anonymous reviewers for their helpful comments.
Xiaogang Zheng thanks the fund from the China Scholarship Council for supporting his visit to the University
of Sheffield.
Conflicts of Interest: The authors declare no conflict of interest.

Sustainability 2020,12, 2431 14 of 15
References
1.
World Heritage Committee. Mount Qingcheng and the Dujiangyan irrigation system. In World Heritage
Committee Nomination Documentation; The United Nations Educational, Scientific and Cultural Organization
(UNESCO): Paris, France, 2000.
2.
Hadas, G. Ancient agricultural irrigation systems in the oasis of Ein Gedi, Dead Sea, Israel. J. Arid Environ.
2012,86, 75–81. [CrossRef]
3.
Hesse, R.; Baade, J. Irrigation agriculture and the sedimentary record in the Palpa Valley, southern Peru.
Catena 2009,77, 119–129. [CrossRef]
4.
Neely, J.A. Sasanian and early Islamic water-control and irrigation systems on the Deh Luran Plain, Iran. In
Irrigation’s Impact on Society; Downing, T.E., Gibson, M., Eds.; University of Arizona Press: Tucson, AZ, USA,
1974; Chapter 3; pp. 21–42.
5.
Beekman, C.S.; Weigand, P.C.; Pint, J.J. Old World irrigation technology in a New World context: Qanats in
Spanish colonial western Mexico. Antiquity 1999,73, 440–446. [CrossRef]
6.
Butzer, K.W.; Mateu, J.F.; Butzer, E.K.; Kraus, P. Irrigation agrosystems in eastern Spain: Roman or Islamic
origins? Ann. Assoc. Am. Geogr. 1985,75, 479–509. [CrossRef]
7.
Li, K.K.; Xu, Z.F. Overview of Dujiangyan irrigation scheme of ancient China with current theory. Irrig.
Drain. 2006,55, 291–298. [CrossRef]
8.
Xu, Y.J. Dujiangyan: Could the ancient hydraulic engineering be a sustainable solution for Mississippi River
diversions? In Proceedings of the Ocean Sciences Meeting 2016, New Orleans, LA, USA, 21–26 February
2016; American Geophysical Union: Washington, DC, USA, 2016; EC41A-08.
9.
Tan, X.M. Record History on the Dujiangyan; China Water Power Press: Beijing, China, 2009; p. 273. (In Chinese)
10.
Sun, Y.F.; Peng, S.M.; Wang, X.K.; Zheng, J.; Xu, X.W. Study on water-diversion of Dujiangyan project. J.
Hydroelectr. Eng. 2006,25, 11–15. (In Chinese)
11.
Wang, X.K.; Sun, Y.F.; Tan, X.P.; Zheng, J. Study on scour and slit of Neijiang River at Dujiangyan. J.
Hydroelectr. Eng. 2006,25, 16–20. (In Chinese)
12.
Du, G.H. Sedimentation Research and Practice of Hydraulic Engineering; Waterpower Press: Beijing, China, 2008;
pp. 126–212. (In Chinese)
13.
Gan, F.Y.; Zhang, J.; Liu, X.N.; Guo, Z.X. Analysis on flow characteristics of Dujiangyan reach under various
inflow conditions. Water Resour. Hydropower Eng. 2013,44, 39–43. (In Chinese)
14.
Fang, D.; Cao, S.Y.; Liu, X.N.; Chen, J.Y. Computer model of the bed changes caused by pebble in Dujiangyan.
J. Sediment Res. 1988,1, 12–22. (In Chinese)
15.
Xie, G. Two-Dimensional Flow and Sediment Numerical Model for River of Mountain Area. Master’s Thesis,
Sichuan University, Chengdu, China, 2004. (In Chinese).
16.
Chinese Local Chronicles Compilation Committee in Sichuan Province (CLCCCSP). Dujiangyan History;
Sichuan Cishu Press: Chengdu, China, 1993. (In Chinese)
17.
Cao, S.Y.; Liu, X.N.; Huang, E. Dujiangyan irrigation system-a world cultural heritage corresponding to
concepts of modern hydraulic science. J. Hydro-Environ. Res. 2010,4, 3–13. [CrossRef]
18.
Zheng, J. Research on the Flow and Sediment Transport of Dujiangyan Project. Ph.D. Thesis, Tsinghua
University, Beijing, China, 2008. (In Chinese).
19.
Zhang, S.H.; Yi, Y.J.; Liu, Y.; Wang, X.K. Hydraulic principles of the 2268-year-old Dujiangyan project in
China. J. Hydraul. Eng. 2013,139, 538–546. [CrossRef]
20.
Tian, J.J.; Wang, B.; Chen, Y.L.; Yang, X.L. Discussion of “Hydraulic principles of the 2268-year-old Dujiangyan
project in China” by Shanghong Zhang, Yujun Yi, Yan Liu, and Xingkui Wang. J. Hydraul. Eng.
2014
,140,
07014005. [CrossRef]
21.
Pu, J.H.; Cheng, N.S.; Tan, S.K.; Shao, S.D. Source term treatment of SWEs using surface gradient upwind
method. J. Hydraul. Res. 2012,50, 145–153. [CrossRef]
22.
Ran, Q.H.; Tong, J.; Shao, S.D.; Fu, X.D.; X, Y.P. Incompressible SPH scour model for movable bed dam break
flows. Adv. Water Resour. 2015,82, 39–50. [CrossRef]
23.
Zheng, X.; Shao, S.D.; Khayyer, A.; Duan, W.Y.; Ma, Q.W.; Liao, K.P. Corrected first-order derivative ISPH in
water wave simulations. Coast. Eng. J. 2017,59, 1750010. [CrossRef]

Sustainability 2020,12, 2431 15 of 15
24.
Zheng, X.G.; Pu, J.H.; Chen, R.D.; Liu, X.N.; Shao, S.D. A novel explicit-implicit coupled solution method of
SWE for long-term river meandering process induced by dambreak. J. Appl. Fluid Mech.
2016
,9, 2647–2660.
[CrossRef]
25.
Chen, R.D.; Shao, S.D.; Liu, X.N. Water-sediment flow modeling for field case studies in Southwest China.
Nat. Hazards 2015,78, 1197–1224. [CrossRef]
26.
Ding, Y.F.; Liu, Y.; Liu, X.N.; Chen, R.D.; Shao, S.D. Applications of coupled explicit-implicit solution of
SWEs for unsteady flow in Yangtze River. Water 2017,9, 91. [CrossRef]
27.
Rozovskii, I.L. Flow of Water in Bends of Open Channels, 2nd ed.; Academy of Sciences of the Ukrainian SSR:
Jerusalem, Israel, 1957.
28.
Chien, N.; Wan, Z.H. Mechanics of Sediment Transport; American Society of Civil Engineers (ASCE) Press:
Reston, VA, USA, 1999; p. 323.
29.
Bhuiyan, F.; Hey, R.D.; Wormleaton, P.R. Bank-attached vanes for bank erosion control and restoration of
river meanders. J. Hydraul. Eng. 2007,136, 583–596. [CrossRef]
30.
Guo, Y.W. Analysis on effects of river geomorphology on water conservancy construction. J. Sediment Res.
1994,2, 56–58. (In Chinese)
31.
Tesfai, M.; Stroosnijder, L. The Eritrean spate irrigation system. Agric. Water Manag.
2001
,48, 51–60.
[CrossRef]
32.
Komakech, H.C.; Mul, M.L.; van der Zaag, P.; Rwehumbiza, F.B.R. Water allocation and management in an
emerging spate irrigation system in Makanya catchment, Tanzania. Agric. Water Manag.
2011
,98, 1719–1726.
[CrossRef]
33.
Embaye, T.G.; Beevers, L.; Mehari Haile, A. Dealing with sedimentation issues in spate irrigation systems.
Irrig. Drain. 2012,61, 220–230. [CrossRef]
34.
Gebrehiwot, K.A.; Haile, A.M.; De Fraiture, C.; Chukalla, A.D.; Embaye, T.G. Optimizing flood and sediment
management of spate irrigation in Aba’ala Plains. Water Resour. Manag. 2015,29, 833–847. [CrossRef]
35. Shanan, L. Runoff, erosion, and the sustainability of ancient irrigation systems in the Central Negev desert.
In The Hydrology-Geomorphology Interface: Rainfall, Floods, Sedimentation, Land Use; IAHS Press: Wallingford,
UK, 2000; pp. 75–106.
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