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

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 1 and Ridong Chen 1,* 1 State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University, Chengdu 610065, China; [email protected] (X.Z.); [email protected] (X.L.) 2 Department of Civil and Structural Engineering, University of Sheffield, Sheffield S1 3JD, UK; e.kazemi@sheffield.ac.uk 3 Department of Civil Engineering, University of Gharyan, Gharyan 52GG + FM, Libya; [email protected] * Correspondence: [email protected]

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, x FOR PEER REVIEW 2 of 15

43 The Dujiangyan Irrigation System (DIS) is one of the ancient irrigation systems which are still in 44 operation. This system began in the 3rd century BCE, is characterized by the non-dam intake project 45 and is still discharging its functions perfectly [1]. It was listed as a World Cultural Heritage Site in 46 2000 and a World Heritage Irrigation Structure in 2018. The main headworks of the DIS are located 47 in the transitional region, where the river flows from a gorge to an alluvial plain. The location has a 48 50 km distance and 273 m elevation difference from Chengdu City, China (Figure 1). This is on the Sustainability 2020, 12, 2431 2 of 15 49 commanding point of the alluvial plain so as to prevent floodwater flowing directly to the Chengdu 50 Plain [7]. Natural topographical and hydrological features are used to exclude sediment and divert 51 andwater is still for dischargingirrigation without its functions the use of perfectly dams. The [1]. sy Itstem was has listed produced as a World benefits Cultural in flood Heritage prevention, Site in 52 2000agricultural and a World irrigation, Heritage and Irrigationwater consumption Structure for in many 2018. years The main [8]. headworks of the DIS are located 53 in the transitionalRecently, a dam region, was where constructed the river upstream flows fromof the a DIS gorge (about to an 4 alluvialkm from plain. the Fish The Mouth). location The has a 54 50reservoir km distance of the and dam 273 can m be elevation seen in Figure difference 1. The from dam Chengduconstruction City, was China completed (Figure in 12006,). This and is since on the 55 then, it has provided a more stable water supply to the Dujiangyan areas during the dry season, and commanding point of the alluvial plain so as to prevent floodwater flowing directly to the Chengdu 56 also reduced the peak flow discharge of the river during the flood season. Since this dam is a Plain [7]. Natural topographical and hydrological features are used to exclude sediment and divert 57 relatively new structure and the focus of the present study is on the historical performance of the DIS water for irrigation without the use of dams. The system has produced benefits in flood prevention, 58 based on its natural and topographical characteristics during the past 2000 years, the effect of the dam agricultural irrigation, and water consumption for many years [8]. 59 is not taken into consideration in this study.

60 61 FigureFigure 1. 1.Sketch Sketch map map ofof thethe study area. The The inset inset map map (top (top right) right) shows shows the the location location of the of the Dujiangyan Dujiangyan 62 IrrigationIrrigation System System (DIS) (DIS)in in China.China. The Puyang, Baitia Baitiao,o, Zouma, Zouma, and and Jiang’an Jiang’an Ri Riversvers all allflow ﬂow from from the the 63 BaopingkouBaopingkou (the (the bottle-neck bottle-neck channelchannel of the DIS).

64 Recently,The headworks a dam wasof the constructed DIS are composed upstream of thre of thee primary DIS (about components: 4 km from (1) The the Fish Fish Mouth Mouth). (the The 65 reservoirfront end of looks the dam like a can fish be mouth), seen in a Figurediversion1. The emba damnkment construction dividing the was Minjiang completed River in into 2006, the and Inner since 66 then,River, it hasprimarily provided for airrigation, more stable and water the Outer supply River, to the mainly Dujiangyan for flood areas and during sediment the discharge; dry season, (2) and 67 alsoFeishayan, reduced a the low peak spillway flow dischargedam removing of the sediment river during and the excess flood water season. from Since the Inner this dam River is ainto relatively the 68 newOuter structure River; andand the(3) focusBaopingkou of the present(bottle-neck study channel), is on the a historical water intake performance automatically of the controlling DIS based on 69 itsintake natural discharge and topographical from the Inner characteristics River (Figure during2). 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 (Figure2). 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

71 FigureFigure 2. 2.General General layout layout of of the the DIS. DIS.

72 ManyThe need irrigation to understand projects in historyhow the were DIS abandoned has preserved due toits sedimentation. functionality for The more long-term than 2000 vitality years of 73 theand DIS the project need for is linked protecting to the it facthave that urged sediment research is automaticallyers and engineers excluded to investigate by natural the characteristics hydrodynamics of 74 theof system.the system, Sediment such depositionas flow motion, is primarily sediment formed tran bysport, the moving and riverbed bed load evolution. from May They to October have [been11]. 75 Basedconducting on the research distorted in movable the last model, few decades the amount on the of bedmechanisms load entering of water the Innerand sediment River through diversion the 76 Fishunder Mouth different is only discharge about 29% conditions of the total in order load in to the improve Minjiang the Rivermethods [17]; of and protecting that is 26% the basedsystem. on Since the 77 resultsthe first of thephysical prototype model observations experiment [ 18of]. the The DIS Feishayan conducted begins in to1941 discharge [9], scholars sediment have to studied the Outer the 78 Rivercharacteristics when the of flow the rate water of theand Inner sediment River transport is over 500 by musing3/s [12 the]. Theprototype larger survey the flood [10,11], discharge physical is, 79 thehydraulics higher is model the discharge [12], and diversion numerical ratio model at the [13–15]. Feishayan As for and the the dynamic more e ffiwatercient diversion is the system process, in 80 dischargingbased on the sediment ancients’ from experience, the Inner more River. than Under 60% the of the function Minjiang of the River Feishayan, typically over goes 90% into of the the Inner bed 81 loadRiver carried for the into use the of Inner the Chengdu River can Plain be discharged during the to low the downstreamdischarge period, area of while the Outer in the River flood [ 19period,]. In 82 addition,this ratio the can V-Shaped reduce to Dike less Spillway,than 40% an[16]. auxiliary The anal projectysis of of the the prototype DIS, also divertsdata carried sediment out by and Sun excess et al. 83 watersuggested during that periods after ofthe flood construction [20]. Finally, of the less chec thank 8%gate of across the total the sedimentOuter River of the in Minjiang1974, the Riverwater 84 candistribution reach the Baopingkou,into the Inner ensuring River was that close the irrigationto 75% in landsspring receive time and clear only water 37.5% [17 ].in Itthe is notableflood season that 85 there[10]. haveLater, also as beena complement small amounts to the of laboratory sediment depositionexperiments in theconducted Inner River in Si sectionchuan whichUniversity have [12], been a 86 dredgedtwo-dimensional annually (probably(2D) nume sincerical themodel irrigation has been system used wasto study first constructed).the performance of the system under 87 differentAt present, inflow the conditions prototype [13]. observations and model experiments can only explain the basics of the 88 sedimentMany discharge irrigation process projects in thein hist DIS.ory On were the abandoned other hand, due the to one-dimensional sedimentation. (1D)The long-term [14] and 2D vitality [15] 89 numericalof the DIS models project used is forlinked simulating to the riverbedfact that evolutionsediment in is the automatically DIS have di ffiexcludedculty in describingby natural 90 thecharacteristics ‘dynamic’ sediment of the system. diversion, Sediment which deposition has a key roleis primarily in the understanding formed by the of moving the dynamics bed load of from the 91 sedimentMay to October discharge [11]. processes Based on in thethe system.distorted For movabl 1D models,e model, this the is dueamount to the of one bed dimensionality load entering ofthe 92 theInner model River being through able tothe describe Fish Mouth the bed is only load about movement 29% of process the total only load in in one the channel Minjiang while River ignoring [17]; and it 93 inthat the is other 26% DISbased channels. on the results For 2D of models, the prototype when considering observations only [18]. the The continuity Feishayan of thebegins bed to load, discharge there 94 issediment often a large to the time Outer scale River difference when betweenthe flow flowrate of and the sediment Inner River motion, is over which 500 m results3/s [12]. in non-accurateThe larger the 95 estimationflood discharge of riverbed is, the morphology. higher is the In discharge addition, dive the grid-basedrsion ratio models,at the Feishaya due to then and Eulerian the more description efficient 96 ofisthe the sedimentsystem in medium,discharging are sediment unable to from provide the Inne detailsr River. of the Under motion the of function sediment of the particles Feishayan, between over 97 di90%fferent of the channels. bed load carried into the Inner River can be discharged to the downstream area of the 98 OuterIn River this study, [19]. In to addition, tackle these the V-Shaped difficulties, Dike the Spillway, fluid flow an in auxiliary the DIS project is simulated of the DIS, by solving also diverts the 99 Shallowsediment Water and excess Equations water (SWEs), during which periods can of efloodffectively [20]. dealFinally, with less the than large 8% scale of the of total the studysediment area, of 100 coupledthe Minjiang with aRiver newly can proposed reach the Sediment Baopingkou, Mass ensuri (SM)ng model that the for theirrigation bed load lands transport. receive clear The fluidwater 101 model[17]. It is is based notable on that the coupledthere have explicit-implicit also been smal solutionl amounts algorithms of sediment of the deposition SWEs and in the SMInner model River 102 issection developed which from have the Lagrangianbeen dredge particled annually modeling (probably concept, since considering the irrigation the orderly system movement was first (in 103 constructed). 104 At present, the prototype observations and model experiments can only explain the basics of the 105 sediment discharge process in the DIS. On the other hand, the one-dimensional (1D) [14] and 2D [15] 106 numerical models used for simulating riverbed evolution in the DIS have difficulty in describing the 107 ‘dynamic’ sediment diversion, which has a key role in the understanding of the dynamics of the 108 sediment discharge processes in the system. For 1D models, this is due to the one dimensionality of

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 + (hu) = 0 (1) ∂t ∇·

2 D(hu) 2 gµ u u = AHh u gh η | | (2) Dt ∇ − ∇ − h1/3 where: η = water surface; t = time; h = flow depth; u = the velocity vector with the longitudinal and transversal components of u and v, respectively; AH = 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 t and 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 vr 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. " # 1 h µ √g vr = u F1(λ) F2(λ) (3) κ2 R − κh1/6 where: κ = von Karman constant (~0.4); R = radius of curvature; λ = normalized vertical co-ordinate 2 R λ 2 R λ 2 F ( ) = ln λ d + F ( ) = ln λ d (which is set to 0.3 here); 1 λ 2 0 1 λ λ 1 ; and 2 λ 0 1 λ λ 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 N is 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 t and t+∆T, respectively; and ua = the increase in the velocity of the sediment particle during ∆T. The magnitude of ua, i.e., ua, 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 Figure3a) 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]:

r ( 1 ) γs γ h 6 uc = 1.14 − gD( ) (6) γ D Sustainability 2020, 12, x FOR PEER REVIEW 6 of 15 and uw = mean flow velocity at the center of the SM, calculated as the arithmetic average of flow γ – γ D 192 invelocity which atψ = the s nodes and located J = insidethe bed the slope. influence The areadisplacement of the disk. of In the addition, SM inβ each= correction sub-step coe is ffithencient γhJ 3 (which is set to 0.1 in the present simulations), γs = specific weigh of sediment grains (= 26.5 kN/m 193 evaluated as Δx = uSM × ΔT. Figure 3 shows the resultant velocity of a sediment particle and the motion here), γ = specific weigh of flow (= 10 kN/m3 for water), and D = diameter of sediment grains. 194 of an SM according to its velocity.

Figure 3. Bed load velocity and mass motion: (a) sediment particle resultant velocity; and (b) sediment 195 Figuremass 3. motion Bed load over velocity the ﬂuid and domain mass motion: (which ( isa) discretized sediment particle by triangular resultant elements). velocity; and (b) sediment 196 mass motion over the fluid domain (which is discretized by triangular elements).

197 After the position of the SM disks is updated, the calculated properties of the sediment domain 198 are transported to the fluid domain. For this, the velocity and thickness of each disk is converted to 199 the flow domain nodes that are located inside the influence domain of the disk using a weighting 200 function (Spline here), and then the converted values at each node are summed up. This yields the 201 average thickness hs and velocity us of the sediment layer at the position of the nodes. Then, the bed 202 load transport rate qb is estimated using Equation (8), and the change of the riverbed elevation from 203 t to t + ΔT is computed by using Equation (9):

𝐪 =ℎ ×𝐮 (8)

𝜕𝑧 (1−𝜉) +∇⋅𝐪 =0 (9) 𝜕𝑡

204 where ξ = porosity; and zb = thickness of the movable bed layer. 205 Then, the fluid model equations are solved in the next sub-step, and this process is repeated until 206 the number of sub-steps reaches N. Then, for the next time step, i.e., at t + dt, SMs are regenerated 207 instead of turning the node information back to them. This will reduce the error related to the 208 diffusion effect without increasing extra calculation.

209 4. Model Applications in the DIS 210 In this section, the numerical model is applied to simulate the sediment processes in the DIS. 211 The flood control discharge and the 1000-year flood of the area are 800 m3/s and 10,120 m3/s, 212 respectively. Besides, if the Inner River discharge exceeds 1000 m3/s, a large amount of sediment can 213 be discharged into the Outer River via the Feishayan [12]. Considering these factors, three flow rates, 214 i.e., 800 m3/s (low discharge), 1800 m3/s (medium discharge), and 10,120 m3/s (high discharge), are 215 selected to simulate different sediment diversion conditions. At the initial time of each simulation, a 216 number of SM disks are placed at the inlet boundary with their velocity being determined according 217 to the desired flow discharge. The total simulation time is 7 days, and the grid and time step sizes are 218 set to 3 m and 10 s, respectively. Sections 4.1 and 4.2 present the results of the fluid flow and sediment 219 motion, respectively.

220 4.1. Simulation of Fluid Flow 221 Figures 4, 5, and 6 show the results of velocity of the numerical model for flow rates of 800, 1800 222 and 10,120 m3/s, respectively. The water diversion ratio, i.e., the ratio of the flow discharge in the 223 Inner River to that of the Minjiang River, is automatically regulated at the Fish Mouth due to the

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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 Figure3a). Then, the velocity of the SM is calculated as u = ut+ P, where the Einstein bed load theory is used to SM ∆T × estimate the incipient probability P:

1 Z 7 ψ 2 1 − t2 P = 1 e− dt (7) − √π 1 ψ 2 − 7 −

= (γs – γ) D in which ψ γhJ and J = the bed slope. The displacement of the SM in each sub-step is then evaluated as ∆x = u ∆T. Figure3 shows the resultant velocity of a sediment particle and the SM × 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 hs 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 t to t + ∆T is computed by using Equation (9): q = hs us (8) b × ∂z (1 ξ) b + q = 0 (9) − ∂t ∇ · b 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 m3/s and 10,120 m3/s, respectively. Besides, if the Inner River discharge exceeds 1000 m3/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 m3/s (low discharge), 1800 m3/s (medium discharge), and 10,120 m3/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 Figures4–6 show the results of velocity of the numerical model for flow rates of 800, 1800 and 10,120 m3/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 (Figure2). In the dry season, the central shoal is unsubmerged. As a result, according to the historical record (Figure7), 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. Figure7 presents the water diversion ratio of the Inner River obtained from Sustainability 2020, 12, x FOR PEER REVIEW 7 of 15 Sustainability 2020, 12, x FOR PEER REVIEW 7 of 15 224 central shoal located upstream of it (Figure 2). In the dry season, the central shoal is unsubmerged. 224 central shoal located upstream of it (Figure 2). In the dry season, the central shoal is unsubmerged. 225 As a result, according to the historical record (Figure 7), more than 60% of the total discharge runs 225 As a result, according to the historical record (Figure 7), more than 60% of the total discharge runs 226 into the Inner River, which is beneficial for the water intake of the irrigation area. In the wet season, 226 into the Inner River, which is beneficial for the water intake of the irrigation area. In the wet season, 227 the shoal is fully submerged, and the current tends straight into the Outer River, so the water 227 the shoal is fully submerged, and the current tends straight into the Outer River, so the water 228 diversion ratio is reverse. Due to these, the DIS, naturally, has functions of water intake and flood 228 Sustainabilitydiversion2020 ratio, 12 ,is 2431 reverse. Due to these, the DIS, naturally, has functions of water intake and flood7 of 15 229 drainage during the dry and wet seasons, respectively. Figure 7 presents the water diversion ratio of 229 drainage during the dry and wet seasons, respectively. Figure 7 presents the water diversion ratio of 230 the Inner River obtained from the present simulations for different flow discharges in the Minjiang 230 the Inner River obtained from the present simulations for different flow discharges in the Minjiang 231 River in comparison with the historical records in the site, where good agreement is observed. It 231 theRiver present in comparison simulations with for ditheff erenthistorical flow records discharges in the in site, the Minjiangwhere good River agreement in comparison is observed. with It the 232 clearly shows that the diversion ratio of the Inner River decreases when the Minjiang River flow 232 historicalclearly shows records that in thethe site,diversion where ratio good of agreementthe Inner River is observed. decreases It clearlywhen the shows Minjiang that theRiver diversion flow 233 discharge goes up. 233 ratiodischarge of the Inner goes up. River decreases when the Minjiang River flow discharge goes up.

234 234 235 Figure 4. Flow velocity field under a flow discharge of 800 m3/s.3 235 FigureFigure 4. 4.Flow Flow velocityvelocity ﬁeldfield under a flow ﬂow discharge discharge of of 800 800 m m3/s./ s.

236 236 Figure 5. Flow velocity ﬁeld under a ﬂow discharge of 1800 m3/s. 237 Sustainability 2020, 12, x FORFigure PEER 5. REVIEW Flow velocity field under a flow discharge of 1800 m3/s. 8 of 15 237 Figure 5. Flow velocity field under a flow discharge of 1800 m3/s.

238 3 239 FigureFigure 6. 6.Flow Flow velocity velocity ﬁeldfield underunder a ﬂowflow discharge of of 10,120 10,120 m m3/s./s.

240 241 Figure 7. Computed and measured water diversion ratio for different flow discharges. There is no 242 historical record for the high discharge condition (10,120 m3/s). The historical record is from field 243 measurements in the DIS [10].

244 4.2. Simulation of Sediment Processes 245 In order to understand how under different flow regimes, the sediment transport is distributed 246 over the channels of the DIS, i.e., the Inner and Outer Rivers, the results of the bed load movement 247 simulated by the proposed model in Section 3 are presented. Figures 8, 9, and 10 show these results 248 under the low, medium, and high flow discharge conditions (800, 1800, and 10,120 m3/s, respectively). 249 As seen in Figure 4, when the discharge is low (800 m3/s), the flow velocity in the Inner River is 250 not significant (the average velocity in the middle of the channel is about 3 m/s). Therefore, only a 251 small amount of sediment moves through the Inner River (see Figure 8). 252 During the medium flow discharge condition (1800 m3/s), the sediment and surplus water are 253 discharged through the Feishayan (Figure 5; Figure 9). This can be explained by the mutual 254 functionality between the Feishayan and the Baopingkou. The Feishayan is a low spillway weir with 255 a width of 240 m, average weir crest elevation of 728.25 m, and distance of 710 m away from the Fish 256 Mouth; the Baopingkou, with a width of 20.4 m, bottom elevation of 716.3 m, and a distance of 120 m 257 away from the Feishayan, serves as a water intake throat to the downstream irrigation areas (Figure

Sustainability 2020, 12, x FOR PEER REVIEW 8 of 15

238 Sustainability 2020, 12, 2431 8 of 15 239 Figure 6. Flow velocity field under a flow discharge of 10,120 m3/s.

240 241 FigureFigure 7. ComputedComputed and and measured measured water water di diversionversion ratio ratio for for different different fl flowow discharges. There There is is no 3 242 historicalhistorical record record for the high discharge condition (10,120 m3/s)./s). The The historical historical re recordcord is is from from field field 243 measurementsmeasurements in the DIS [10]. [10]. 4.2. Simulation of Sediment Processes 244 4.2. Simulation of Sediment Processes In order to understand how under different flow regimes, the sediment transport is distributed 245 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 246 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 Section3 are presented. Figures8–10 show these results under the 247 simulated by the proposed model in Section 3 are presented. Figures 8, 9, and 10 show these results low, medium, and high flow discharge conditions (800, 1800, and 10,120 m3/s, respectively). 248 under the low, medium, and high flow discharge conditions (800, 1800, and 10,120 m3/s, respectively). As seen in Figure4, when the discharge is low (800 m 3/s), the flow velocity in the Inner River is 249 As seen in Figure 4, when the discharge is low (800 m3/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 250 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 Figure8). 251 small amount of sediment moves through the Inner River (see Figure 8). During the medium flow discharge condition (1800 m3/s), the sediment and surplus water are 252 During the medium flow discharge condition (1800 m3/s), the sediment and surplus water are discharged through the Feishayan (Figure5; Figure9). This can be explained by the mutual functionality 253 discharged through the Feishayan (Figure 5; Figure 9). This can be explained by the mutual between the Feishayan and the Baopingkou. The Feishayan is a low spillway weir with a width of 240 254 functionality between the Feishayan and the Baopingkou. The Feishayan is a low spillway weir with m, average weir crest elevation of 728.25 m, and distance of 710 m away from the Fish Mouth; the 255 a width of 240 m, average weir crest elevation of 728.25 m, and distance of 710 m away from the Fish Baopingkou, with a width of 20.4 m, bottom elevation of 716.3 m, and a distance of 120 m away from 256 Mouth; the Baopingkou, with a width of 20.4 m, bottom elevation of 716.3 m, and a distance of 120 m the Feishayan, serves as a water intake throat to the downstream irrigation areas (Figure2). The width 257 away from the Feishayan, serves as a water intake throat to the downstream irrigation areas (Figure 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 (Figure5). 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, x FOR PEER REVIEW 9 of 15

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 Sustainability 2020, 12, 2431 9 of 15 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 m3/s on: (a) Day 1; (b) Day 4; and (c) Day 7. Sustainability 2020, 12, x FOR PEER REVIEW 10 of 15

(c)

271 Figure 8. Bed load movement process under the discharge of 800 m3/s on: (a) Day 1; (b) Day 4; and (c) 272 Day 7.

273 There is a small amount of sediment which is not discharged through the Feishayan, but deposits 274 in the Fengqiwo Section. This is because the narrow Baopingkou is not located at the middle of the 275 width of the Inner River. The flood flows to the Lidui and then a backwater is formed in front of it. 276 The effect of the backwater propagates upstream with the increase of the Inner River discharge. Once 277 the backwater effect reaches the Feishayan, some amount of the sediment deposits at the Fengqiwo 278 Section due to a large reduction in the bottom flow velocity. The deposited sediment is removed in 279 the annual dredging project.Under a high discharge condition, the upstream central shoal is 280 submerged, thus the main flood current carrying most of the moving bed load diverts directly toward 281 the Outer River. At the same time, due to the fact that the Inner River is located on the concave bank 282 of the curved river section, the bed load is transported into the Outer River along the convex bank 283 Sustainabilityunder the 2020function, 12, 2431 of the bend flow. In summary, the major amounts of the flood and the bed10 load of 15 284 are diverted into the Outer River at the Fish Mouth ( Figure 6; Figure 10).

(a)

Sustainability 2020, 12, x FOR PEER REVIEW (b) 11 of 15

(c)

285 FigureFigure 9. 9. BedBed load load movement movement process process under the dischargedischarge ofof 18001800 m m3/3s/s on: on: ( a(a)) Day Day 1; 1; ( b(b) Day) Day 4; 4; and and (c ) 286 (cDay) Day 7. 7.

287 The rest of the sediment and water which flow into the Inner River is diverted once again at the 288 Feishayan. After this diversion, if the flood discharge is still high, then the excess amount is 289 automatically discharged through the V-Shaped Dike Spillway. The V-Shaped Dike is an auxiliary 290 project located downstream of the Feishayan and is a low spillway dam with 60 m width and 729 m 291 average weir crest elevation which is slightly higher than that of the Feishayan. Under low and 292 medium flood conditions, the influence of the backwater is not substantial in front of the Baopingkou, 293 meaning that the water level of the Inner River only reaches the crest of the Feishayan and is below 294 that of the V-Shaped Dike (i.e., the V-Shaped Dike Spillway is effectively dry at low and medium 295 discharges). Thus, the flood entering the Inner River is mainly discharged via the Feishayan (see 296 Figures 4 and 5). However, during the high flood discharge period, the upstream backwater of the 297 Baopingkou is considerable and the water level is higher than the V-Shaped Dike, enabling part of 298 the flood to discharge into the Outer River via the V-Shaped Dike Spillway (Figure 6). The flood 299 diversion through the V-Shaped Dike Spillway causes a reduction in the upstream water level and 300 therefore is beneficial for the reasonable water intake of the Baopingkou. The larger the discharge in 301 the Inner River is, the more effective is the function of the V-Shaped Dike Spillway. 302 In summary, the results showed that most of the flood in the Inner River is discharged to the 303 Outer River via the Feishayan; and under the high flood discharge condition, a part of it can also be 304 discharged through the V-Shaped Dike Spillway to the Outer River. In addition, as shown in Figure 305 7, a larger flood discharge in the Minjiang River results in smaller water diversion ratios at the 306 Baopingkou, a function that protects the Chengdu Plain from disastrous floods.

Sustainability 2020, 12, x FOR PEER REVIEW 11 of 15

(c)

285 Figure 9. Bed load movement process under the discharge of 1800 m3/s on: (a) Day 1; (b) Day 4; and 286 (c) Day 7.

287 The rest of the sediment and water which flow into the Inner River is diverted once again at the 288 Feishayan. After this diversion, if the flood discharge is still high, then the excess amount is 289 automatically discharged through the V-Shaped Dike Spillway. The V-Shaped Dike is an auxiliary 290 project located downstream of the Feishayan and is a low spillway dam with 60 m width and 729 m 291 average weir crest elevation which is slightly higher than that of the Feishayan. Under low and 292 medium flood conditions, the influence of the backwater is not substantial in front of the Baopingkou, 293 meaning that the water level of the Inner River only reaches the crest of the Feishayan and is below 294 that of the V-Shaped Dike (i.e., the V-Shaped Dike Spillway is effectively dry at low and medium 295 discharges). Thus, the flood entering the Inner River is mainly discharged via the Feishayan (see 296 Figures 4 and 5). However, during the high flood discharge period, the upstream backwater of the 297 Baopingkou is considerable and the water level is higher than the V-Shaped Dike, enabling part of 298 the flood to discharge into the Outer River via the V-Shaped Dike Spillway (Figure 6). The flood 299 diversion through the V-Shaped Dike Spillway causes a reduction in the upstream water level and 300 therefore is beneficial for the reasonable water intake of the Baopingkou. The larger the discharge in 301 the Inner River is, the more effective is the function of the V-Shaped Dike Spillway. 302 In summary, the results showed that most of the flood in the Inner River is discharged to the 303 Outer River via the Feishayan; and under the high flood discharge condition, a part of it can also be 304 discharged through the V-Shaped Dike Spillway to the Outer River. In addition, as shown in Figure 305 7, a larger flood discharge in the Minjiang River results in smaller water diversion ratios at the 306 SustainabilityBaopingkou,2020 a, 12function, 2431 that protects the Chengdu Plain from disastrous floods. 11 of 15

Sustainability 2020, 12, x FOR PEER REVIEW 12 of 15

(a)

(b)

(c)

307 FigureFigure 10. 10. BedBed load load movement movement process process under the dischargedischarge ofof 10,120 10,120 m m3/3s/s on: on: ( a()a Day) Day 1; 1; (b ()b Day) Day 4; and4; 308 and(c) ( Dayc) Day 7. 7.

309 5. DiscussionThere 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 310 Three key components of the DIS (i.e., the Fish Mouth, the Feishayan, and the Baopingkou) width of the Inner River. The flood flows to the Lidui and then a backwater is formed in front of it. The 311 combining with ancillary embankments and watercourses ensure there is efficient sediment diversion effect of the backwater propagates upstream with the increase of the Inner River discharge. Once the 312 and regular water supply for the Chengdu Plain. The reason behind that the DIS is still performing backwater effect reaches the Feishayan, some amount of the sediment deposits at the Fengqiwo Section 313 designated functions today is that the sediment is automatically transported in an orderly manner 314 without causing adverse effects on the system. A summary of the operation of the DIS is the 6- 315 character maxim “deeply clearing channel (specially meaning the channel at the Fengqiwo Section), 316 building low dike” [1]. 317 The purpose of a “deeply clearing channel” is to keep the sediment transport in an equilibrium 318 state during a year, namely, the equilibrium of erosion and deposition in the Inner River. This 319 requires the longitudinal profile of the riverbed to reach the balanced section. Therefore, annual 320 dredging is necessary. Also, the dredging level needs to reach the iron bar markers (the position of 321 the riverbed balanced section) buried in the Fengqiwo Section. If the dredging depth is shallower 322 than the iron bar markers, the sediment will further deposit, which is an adverse effect to the 323 sediment diversion and the water intake of irrigation areas. If the dredging depth exceeds the iron 324 bar markers (equivalent to the reduction of the erosional basis), then the erosion will strengthen and 325 cause the non-equilibrium of the sediment supply and transport. The DIS is a successful case where 326 the theory of riverbed balanced section can be applied to the water conservancy project [30]. 327 “Building low dike” means that the height of the Feishayan should be low, which is conducive 328 to discharge water and sediment in the flood period. It shows that floods have been a key factor in

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 (Figure6; 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 Figures4 and5). 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 (Figure6). 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 Figure7, 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

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