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Journal of Changjiang River Scientific Research Institute >

2025 , Vol. 42 >Issue 11: 9 - 15

DOI: https://doi.org/10.11988/ckyyb.20240360

River-Lake Protection and Regulation

Physical Model Study of Natural Meander Cutoff in the Lower Jingjiang River

  • LIU Ya , 1 ,
  • YAO Shi-ming 1 ,
  • GUO Xiao-hu 1 ,
  • XIE Si-quan 2
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  • 1 Key Laboratory of River and Lake Management and Flood Control in the Middle and Lower Reaches of the Yangtze River of MWR, Changjiang River Scientific Research Institute, Wuhan 430010, China
  • 2 China Energy Engineering Group Hunan Electric Power Design Institute Co., Ltd., Changsha 410000, China

Received date: 2024-04-07

  Revised date: 2024-07-08

  Online published: 2024-12-27

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Abstract

[Objective] Continuous sharp bends in river channels are prone to significant river regime adjustments and abrupt changes under the impact of unsaturated sediment-laden flow, which have far-reaching implications for flood control, navigation, and water resource utilization. This study investigates the hydraulic characteristics of the river section with sharp bends in the lower Jingjiang River and the scour and siltation characteristics of the upstream and downstream bends after the natural cutoff through large-scale physical model experiments, aiming to deepen the understanding of the natural cutoff development process and provide references for the long-term regulation and planning of the river-lake confluence section in the middle reaches of the Yangtze River. [Methods] Taking the reach from Xiongjiazhou to Chenglingji in the middle reaches of the Yangtze River as the research object, a physical model was established with a horizontal scale of 1∶400 and a vertical scale of 1∶100. The model had a total straight-line length of about 70 m, a maximum width of about 40 m, and included two continuous sharp bends and upstream and downstream transition sections. Based on the hydrological data measured at Luoshan Station from 2003 to 2020, the model test water and sediment conditions were set up with different flow conditions of flood, medium, and drought. First, the hydraulic characteristics of the bend section under different flow levels were studied through fixed-bed model tests to identify the most likely flow conditions and locations for natural cutoff. Subsequently, movable-bed scour tests were conducted, applying flow conditions favorable for cutoff to study the cutoff development process. Considering that the flow in the Jingjiang section would be in a severely undersaturated state for a long time after the Three Gorges Reservoir is impounded, the inlet water and sediment conditions in this model test were simplified to clear water. [Results] The model test results showed that after the flow overtopped the bank, the main flow belt in the upstream Qigongling bend section gradually shifted from the main channel to the convex bank side. Three velocity concentration zones were formed at the neck, middle, and leading edge of the flow, with the peak velocity decreasing stepwise from the neck to the main channel. During the natural cutoff process of the Qigongling bend, the most likely location for the breach was between 1 300 m and 1 500 m away from the rear embankment. After 3 days of scouring by the overbank flow, gullies began to form, which developed into a fully connected breach over a period of about 30 days. After cutoff, the bend apex section tends to become narrower and deeper, while the transition section tends to become wider and shallower. [Conclusion] The results provide forward-looking guidance for the governance of the middle reaches of the Yangtze River system.

Key words： meandering river; bend cutoff; physical model; unsaturated sediment transport; Lower Jingjiang River

Cite this article

LIU Ya , YAO Shi-ming , GUO Xiao-hu , XIE Si-quan . Physical Model Study of Natural Meander Cutoff in the Lower Jingjiang River[J]. Journal of Changjiang River Scientific Research Institute, 2025 , 42(11) : 9 -15 . DOI: 10.11988/ckyyb.20240360

开放科学(资源服务)标识码(OSID):

0 引言

天然河流以弯曲河型为主。在天然状况下,弯曲河道通常表现出“凹冲凸淤”的演变特性。随着河道弯曲度的不断增加,遭遇漫滩洪水时,往往导致裁弯取直的发生。裁弯取直是弯曲河流周期性演变过程中的一种突变行为[1]。根据河湾平面形态和裁弯发生位置,自然裁弯可分为颈口裁弯和斜槽裁弯[2-4]。该类演变通过对河道长度、比降及弯曲程度的调整改变上游来水来沙的条件,以此建立新的平衡状态[5]。全球范围内,许多河流历经了大规模的人工裁弯取直[6-9],在人工裁弯的时机、引河的规划、裁弯后新河的调整、牛轭湖的形态演变等方面取得了丰富的成果。良好的裁弯可以稳定河势、缩短河长、降低上游洪水位、畅通流态[10-11];但也可能加剧新河上游的淤积[12],带来水资源及湿地资源的损失[13],同时河道坡降加大也会增加水流流速,对岸坡及堤防稳定带来不利影响。
三峡水库蓄水以来,长江中下游河床自上而下普遍发生冲刷[14-15],不同河段的断面形态[16]、过流能力均发生了明显调整[17]。下荆江弯道段普遍出现撇弯取直的现象,个别急弯段裁弯趋势日益明显[18]。下荆江弯道曲率的变化对荆江河势稳定起着决定性作用,也是影响荆江-洞庭湖相互关系的重要因素,对长江中下游及洞庭湖区防洪形势、水资源配置影响深远。由于天然河道自然裁弯通常发展迅速且不可预见,裁弯发生的过程很难进行观测捕捉,因此室内模型试验是研究裁弯的有效手段。本文通过大尺度物理模型试验,研究下荆江急弯河段水力特性及自然裁弯后上下游弯道的冲淤特性,以期深化对自然裁弯发展过程的认识,并对长江中游江湖汇流段的远期治理规划提供参考。

1 研究区域概况

下荆江上起石首、下至城陵矶,全长约176 km。下荆江属典型的蜿蜒型河道,历史上河道变迁频繁。新中国成立以来,下荆江先后发生了2次自然裁弯(1949年碾子湾裁弯、1972年沙滩子裁弯)及2次人工裁弯(1967年中洲子裁弯、1969年上车湾裁弯),裁弯位置见图1。裁弯后河道曲折率大大减小,水流动能增加、河床冲刷加剧,上下游河势发生显著调整。
图1 下荆江河势示意图

Fig.1 Lower Jingjiang River regime

三峡水库蓄水后,来水来沙条件发生明显改变,下荆江河段发生持续性冲刷。2002年10月—2021年4月,下荆江河段平滩河槽累计冲刷5.28 亿m3,年均冲淤量为0.28 亿m3。在强冲刷条件下局部河段发生显著的滩槽格局调整,如熊家洲至城陵矶河段的七弓岭及观音洲两弯道出现了明显的切滩撇弯[19]。随着上下游河道主流线的偏移,八姓洲两侧岸线逐渐崩退,截至目前狭颈处宽约700 m,而狭颈区土质为二元结构,上层为黏性土,下层为细砂,且黏性土层较薄,若遭遇特殊不利水文年,八姓洲漫滩保持滩面一定水深,在较大水面比降作用下,有可能导致狭颈区的集中冲刷,从而发生自然裁弯。

2 概化模型设计

2.1 模型平面形态

以下荆江熊家洲至城陵矶河段平面形态为参考,按平面比尺1∶400、垂直比尺1∶100进行缩放,并对河道的主槽及滩地的特征进行适当概化处理,模型布置如图2所示。模型直线距离全长71 m,最大宽度42 m。包含2个连续急弯河道及上下游过渡段。模型前池设置加压泵,通过回水渠及沉沙池实现水沙循环利用。模型用沙选择密度γs=1.38 t/m3、干密度γ0=0.65 t/m3的亲水性树脂基复合模型沙[20-21]。考虑到模拟区域河床组成的二元特性,本次试验通过在模型沙中添加适量固沙胶黏剂,增大模型沙的水下休止角[22],可实现河工模型中动岸变形的精确模拟。为精确测量沿程水力特性,沿河槽布置10个流速测量断面(CS1—CS10)和7个水位测量点(S1—S7)。模型进口流量控制采用电磁流量计、水位测量采用自动式水位测针,地形及流速测量分别采用光电式地形仪和超声多普勒流速仪。
图2 概化模型总体布置

Fig.2 Layout of generalized physical model

熊家洲至城陵矶河段位于下荆江尾闾段,在洞庭湖顶托影响下水位流量关系非常复杂。荆江河段与洞庭湖流域径流特性差异较大,荆江-洞庭湖水文组合条件众多。本研究主要着眼于自然裁弯发生的历程及裁弯后上下游弯道的冲淤特性,本次模型试验通过下边界螺山站水位流量关系反映洞庭湖入流的影响,对于研究目标的实现是可行的。

2.2 模型试验边界条件

本次模型试验以螺山站2003—2020年实测水文数据为基础,分别设置洪、中、枯不同水流条件(见表1),先通过定床模型试验研究不同流量级下弯道段的水力特性,寻求最有可能发生自然裁弯的水流条件及裁弯区域。然后开展动床冲刷试验,施放有利于裁弯的水流条件,研究裁弯发展过程。考虑到三峡水库蓄水后荆江河段水流将长时期处于严重次饱和状态,本次模型试验中进口水沙条件概化为清水。
表1 概化模型试验工况

Table 1 Generalized physical model test conditions

进口流量/
(L·s-1)		 下边界水位/
cm		 进口流量/
(L·s-1)		 下边界水位/
cm
18.7 16.43 83.8 26.79
24.1 17.84 100.0 28.38
37.5 20.62 125.0 29.81
56.5 23.57 137.5 30.53
67.3 24.94 153.8 31.47

3 急弯段水力特性

不同流量下研究河段纵比降变化如图3所示。
图3 不同流量下水流漫滩前后纵比降对比

Fig.3 Comparison of longitudinal gradients at different flow discharges before and after bankful discharge

水流漫滩前比降沿程呈总体减小的趋势,漫滩后急弯段比降随流量的增大而减小,最大比降出现在水流刚漫滩时(流量为100 L/s)。
在弯道进口段(如图4(a)所示),河道主流随流量增加明显偏向凸岸,水流漫滩后主槽流速大幅降低,断面流速分布均匀化;在弯道顶点段(如图4(b)、图4(c)所示),主流带位于断面深槽处,水流漫滩前主槽流速随着流量的增加而增加,漫滩后主槽流速逐渐降低、滩面流速加大,且上游急弯段主槽流速明显大于下游急弯段,最大达0.42 m/s。出口段(CS8)深槽居中(如图4(d)所示),主流带亦逐渐偏移至河道中间。水流漫滩后,主槽流速逐渐降低,主流带转移至滩地上。
图4 典型断面不同流量下流速分布

Fig.4 Velocity distribution at different flow discharges of typical cross-sections

在弯道狭颈段,水流漫滩后主槽流速逐渐降低、滩地流速增加,主流带逐渐从凹岸河槽偏移到凸岸滩地。水流漫滩后狭颈流速分布如图5所示。水流在颈口处、中部与滩头分别产生流速集中区(图5中A、B、C三个区域),峰值流速以颈口向主河槽呈阶梯状下降,最大流速分别约为0.41、0.29、0.2 m/s。根据流速分布与比降变化,总结得出研究河段最可能发生自然裁弯的部位为A区域。换算成原型为距离后方堤防1 300~1 500 m之间的区域。
图5 水流漫滩后狭颈流速分布示意图

Fig.5 Schematic of velocity distribution in narrow neck after overbank flow

4 自然裁弯模型试验

裁弯试验首先采用漫滩以上流量125 L/s进行造床,30 min(换算为原型约3 d)后上游弯道凸岸颈口处产生自下而上的窜沟;发展成溃口后将流量调整为114.3 L/s继续造床,历时5.5 h溃口基本贯通,河道主流开始偏移;此时调整流量至87.8 L/s,水流不再漫滩、但仍可经溃口下泄至下游,历时23 h停水,最终得到裁弯新河如图6所示。
图6 研究河段裁弯后实况

Fig.6 Actual conditions after natural bend cutoff

4.1 河势总体变化特征

裁弯过程中研究河段河势变化见图7。模型试验5.5 h(换算为原型约30 d)后凸岸狭颈处溃口贯通初步形成新河槽,大部分水流经溃口下泄,直接顶冲对岸河床,形成新的冲刷坑。泥沙在溃口进口以下的原河道大幅落淤形成横跨河槽的浅梗。23 h(换算为原型约140 d)后,溃口全线贯通,宽度与上游河槽一致,新河道基本形成。随着出口处冲刷坑的不断发展下延,尾部切割下游弯道凸岸边滩并沿程贯穿形成新的深槽,使得下游弯顶段形成“两滩两槽”的格局。
图7 裁弯发生后弯道河势变化

Fig.7 Changes in river regime after bend cutoff

1972年7月15—19日下荆江沙滩子曾发生自然裁弯。在此期间,长江干流流量>20 000 m3/s,滩面水深约2.4 m。城陵矶站流量仅在4 500~7 300 m3/s之间,洞庭湖对长江干流顶托作用大为减弱、滩面流速较大,此时河道发生裁弯。本次试验中裁弯发生的水流条件及狭颈处产生溃口的历时和沙滩子自然裁弯相当,裁弯模式为典型的“颈口裁弯”。

4.2 河床冲淤变化

在裁弯过程中,研究河段总体表现为先淤后冲的发展趋势,冲淤量见表2。在模型试验历时0~5.5 h之间,由于溃口分流,河道水流发生调整,研究河段整体表现为淤积抬升。其中枯水位以下的深槽部位淤积较为明显,淤积量占河床淤积总量的95%,且上游弯道淤积远大于下游弯道。平滩水位以上的岸坡略有冲刷,此阶段主要表现为老河段的消亡。在模型试验历时5.5~23 h之间,研究河段总体均表现为“滩槽皆冲”,冲刷主要集中在河道深槽,冲刷量占河床冲刷总量的72%,且下游弯道冲刷幅度远大于上游,此阶段主要表现为新河道的形成。此后河道调整总体趋于稳定,水流大部分经新河道下泄。
表2 裁弯阶段河道冲淤量

Table 2 Amount of scour and deposition during bend cutoff

模型试验
历时/h		 河槽水位 冲淤量/(万cm3)
上游急弯段 下游急弯段 总计
枯水位 127.72 47.81 175.53
0~5.5 平滩水位 120.18 64.57 184.75
洪水位 113.16 60.20 173.36
枯水位 -48.92 -134.97 -183.89
5.5~23 平滩水位 -47.46 -189.70 -237.17
洪水位 -54.04 -201.94 -255.99
枯水位 78.80 -87.16 -8.36
总计 平滩水位 72.72 -125.13 -52.42
洪水位 59.12 -141.74 -82.63

4.3 滩槽变化

由裁弯试验河段高低滩的冲刷发展过程可见,溃口是自下而上逐步冲刷下切产生的。狭颈高滩部分溃口的贯通主要发生在试验进行的前5.5 h,溃口整体呈喇叭形向出口处收缩(图8(a));进出口宽度分别为512 cm和173 cm。试验的前5.5 h低滩部分溃口尚未完全冲开,至试验进行23 h以后才全线贯通,进出口宽度分别为326 cm和172 cm(图8(b))。
图8 裁弯后河道滩槽变化

Fig.8 Changes in channel-shoal pattern after bend cutoff

在整个裁弯过程中,高滩除了溃口下泄水流顶冲处有所冲蚀外,其余部位基本无变化,河床冲淤变形主要发生在河道低滩及深槽部位。溃口形成后5.5 h,上游急弯段凹岸深槽内的低滩淤积并岸,平面位置有所下移。下游急弯段凸岸低滩大幅崩退,5.5 h末最大崩退117 cm,水下岸坡冲刷变陡。
深泓线的走向体现了总体河势格局。裁弯过程中,试验进行5.5 h后除了上游急弯段深泓线有所右移外,其余部位基本无变化。随着冲刷的发展,试验进行23 h后深泓线移至新河道,长度仅为原河道深泓线的1/3(图8(c))。

4.4 断面形态变化

裁弯后各特征断面变化如图9所示。溃口上游河道(CS1断面,图9(a))左侧岸线持续崩退,枯水河床在试验进行的前5.5 h略有淤积,此后大幅冲刷下切。上弯道弯顶(CS10断面,图9(b))原深槽由“W”型逐渐转化为偏“V”型,深槽向凹岸偏移,平滩水位以上河床基本无变化。凸岸溃口产生后5.5 h内迅速冲刷拓宽,此后以纵向冲深为主,平滩水位下新河宽度约110 cm。下弯顶(CS7断面,图9(c))由于直接承接溃口处水流冲击,凸岸近岸局部河床下切形成次河槽,最大冲深20 cm,原凹岸深槽略有淤积抬升,断面过流面积明显增加。河道出口(CS9断面,图9(d))在最初5.5 h内有所冲刷下切,23 h后逐渐回淤,深槽较初始河床略有抬升。
图9 裁弯后典型断面变化

Fig.9 Changes in typical cross-sections after bend cutoff

裁弯前后断面宽深比变化如图10所示。裁弯后弯顶段宽深比减小、过渡段宽深比增加,但河段总体趋势是宽深比有所增加,且平滩水位下断面宽深比变化幅度大于洪水位。平滩水位下弯顶段、过渡段宽深比最大变化值分别为-0.2、+0.73(负值表示减小,正值表示增加)。
图10 裁弯前后断面宽深比变化

Fig.10 Changes in the ratio of width to depth before and after bend cutoff

5 结论

本文以下荆江熊家洲至城陵矶河段为研究对象,通过物理模型试验研究了不同流量级下急弯段的水力特性,模拟了自然裁弯,分析了裁弯过程中上下游河床冲淤变化特征。得到以下结论:
(1)定床模型试验表明,水流漫滩后上游七弓岭弯道段主流带逐渐从主河槽向凸岸滩地转移。水流在颈口处、中部与滩头产生3个流速集中区,峰值流速以颈口向主河槽呈阶梯状下降。
(2)模型试验历时30 min(换算为原型约3 d)漫滩水流冲刷,弯道凸岸狭颈出现自下而上的窜沟,历时5.5 h内(换算为原型约30 d)迅速冲刷拓宽形成贯通的溃口,模型试验历时23 h(换算为原型约140 d)新河基本形成,新河宽度与老河道主槽相当,深泓线全程缩短近2/3。在溃口贯通之前,河道整体处于淤积态势,上游弯道淤积幅度大于下游;溃口贯通之后,全河道开始冲刷发展,下游弯道冲刷幅度大于上游。
(3)在新河发展过程中,老河道淤积、深槽向凹岸偏移;下游弯道承接新河水流冲击,凸岸边滩冲刷形成深槽,断面发展成“W”型。弯顶段断面窄深化发展、过渡段断面则有宽浅化发展趋势。

References

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COLES D R, KLINGEMAN P C. Channel Avulsion Dynamics in Meandering Rivers[C]// Proceedings of World Environmental and Water Resources Congress 2014. Portland, Oregon: American Society of Civil Engineers. June 1-5, 2014: 1475-1485.

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李志威, 王兆印, 赵娜, 等. 弯曲河流斜槽裁弯模式与发育过程[J]. 水科学进展, 2013, 24(2): 161-168.

(LI Zhi-wei, WANG Zhao-yin, ZHAO Na, et al. Development Processes of Chute Cutoffs on Meandering Rivers[J]. Advances in Water Science, 2013, 24(2): 161-168. (in Chinese))

[3]
FARES Y R. Changes of Bed Topography in Meandering Rivers at a Neck Cutoff Intersection[J]. Journal of Environmental Hydrology, 2000, 8(13):1-18.

[4]
CONSTANTINE J A, MCLEAN S R, DUNNE T. A Mechanism of Chute Cutoff along Large Meandering Rivers with Uniform Floodplain Topography[J]. 2010, 122(5/6):855-869.

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李志威, 袁帅, 朱玲玲, 等. 荆江河段4次裁弯后干流河道调整研究[J]. 长江流域资源与环境, 2018, 27(4):882-890.

(LI Zhi-wei, YUAN Shuai, ZHU Ling-ling, et al. Channel Adjustments Induced by Four Meander Cutoffs in the Middle Yangtze River(Jinjiang Reach)[J]. Resources and Environment in the Yangtze Basin, 2018, 27(4): 882-890. (in Chinese))

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DOI

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KISS T, FIALA K, SIPOS G. Alterations of Channel Parameters in Response to River Regulation Works since 1840 on the Lower Tisza River (Hungary)[J]. Geomorphology, 2008, 98(1/2): 96-110.

DOI

[8]
SCHWENK J, FOUFOULA-GEORGIOU E. Meander Cutoffs Nonlocally Accelerate Upstream and Downstream Migration and Channel Widening[J]. Geophysical Research Letters, 2016, 43(24):437-445.

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长江水利水电科学研究院河流研究室. 下荆江裁弯经验总结[J]. 人民长江, 1978(1):11-33.

River Research Office of Yangtze River Water Resources and Hydropower Research Institute. Summary of Experience in Bends Cutoff in The Lower Jingjiang Reach[J]. Yangtze River, 1978(1):11-33. (in Chinese))

[10]
陈天伟. 宁夏苦水河沟湾段裁弯治理及效果分析[J]. 人民黄河, 2019, 41(3):65-68.

(CHEN Tian-wei. Analysis of the Cut-off Management of Gouwan Section of Kushui River in Ningxia and Its Effect[J]. Yellow River, 2019, 41(3): 65-68. (in Chinese))

[11]
王长松. 近代海河河道治理与天津港口空间转移的过程研究[D]. 北京: 北京大学, 2011.

(WANG Chang-song. Research on the Treatment of Haihe River and the Process of Tianjin Port Space Shifting in Modern Times[D]. Beijing: Peking University, 2011. (in Chinese))

[12]
熊绍隆, 徐慧, 潘存鸿. 五甲渡裁弯工程主要效益与负面的影响[J]. 东海海洋, 2003, 21(2): 59-64.

(XIONG Shao-long, XU Hui, PAN Cun-hong. Preliminary Argumentation of Principal Benefits and Negative Influence for the Wujiadu Cutoff Works[J]. Donghai Marine Science, 2003, 21(2): 59-64. (in Chinese))

[13]
焦飞宇. 裁弯取直对河流健康状况的影响研究[D]. 天津: 天津大学, 2012.

(JIAO Fei-yu. Research on the Impact of River Cut-off on the Health Status of Rivers[D]. Tianjin: Tianjin University, 2012. (in Chinese))

[14]
董炳江, 许全喜, 袁晶, 等. 近年来三峡水库坝下游河道强烈冲刷机理分析[J]. 泥沙研究, 2019, 44(5):42-47.

(DONMG Bing-jiang, XU Quan-xi, YUAN Jing, et al. Mechanism of Serious Scour Along the Downstream of Three Gorges Reservoir in Recent Years[J]. Journal of Sediment Research, 2019, 44(5):42-47. (in Chinese))

[15]
王华琳, 郑珊, 谈广鸣, 等. 三峡水库运行后宜昌-城陵矶河段冲刷重心下移与时空演变[J]. 水利学报, 2021, 52(12): 1470-1481.

(WANG Hua-lin, ZHENG Shan, TAN Guang-ming, et al. Spatio-temporal Channel Evolution and the Migration of Erosion Center in Yichang-Chenglingji Reach after the Operation of the Three Gorges Project[J]. Journal of Hydraulic Engineering, 2021, 52(12): 1470-1481. (in Chinese))

[16]
李明, 胡春宏, 方春明. 三峡水库坝下游河道断面形态调整模式与机理研究[J]. 水利学报, 2018, 49(12): 1439-1450.

(LI Ming, HU Chun-hong, FANG Chun-ming. Study on Pattern and Mechanism of River Section Topography Adjustment in the Downstream of the Three Gorges Project[J]. Journal of Hydraulic Engineering, 2018, 49(12): 1439-1450. (in Chinese))

[17]
林芬芬, 夏军强, 周美蓉, 等. 下荆江河槽形态及过流能力调整对上下游边界条件的响应[J]. 水利学报, 2019, 50(5): 641-649.

(LIN Fen-fen, XIA Jun-qiang, ZHOU Mei-rong, et al. Recent Response of Bankfull Channel Geometry and Flood-discharge Capacity in the Lower Jingjiang Reach to Upstream and Downstream Boundary Conditions[J]. Journal of Hydraulic Engineering, 2019, 50(5): 641-649. (in Chinese))

[18]
LI Z, YANG H, XIA J, et al. Channel Morphologic Processes of a Highly Sinuous Bend Approaching Neck Cutoff by Bank Erosion in the Middle Yangtze River[J]. International Journal of Sediment Research, 2021, 36(4): 457-467.

DOI

[19]
谢思泉, 刘亚, 卢金友. 三峡水库运用后连续急弯河道冲淤特性分析[J]. 长江科学院院报, 2021, 38(1): 8-13, 26.

DOI

(XIE Si-quan, LIU Ya, LU Jin-you. Scour and Deposition Characteristics of Continuous Sharp Bend River Channel after Operation of Three Gorges Reservoir[J]. Journal of Yangtze River Scientific Research Institute, 2021, 38(1): 8-13, 26. (in Chinese))

DOI

[20]
卢金友, 魏国远, 孙贵洲, 等. 泥沙实体模型试验用复合塑料模型沙及其制备方法:中国, CN101955612B[P].2012-07-25.

(LU Jin-you, WEI Guo-yuan, SUN Gui-zou, et al. Composite Plastic Model Sand for Sediment Physical Model Test and Its Preparation Method, CN101955612B[P].2012-07-25. (in Chinese))

[21]
芦露华. 亲水性树脂基复合模型沙性能研究与优化[D]. 武汉: 武汉理工大学, 2007.

(LU Lu-hua. Analyze and Optimization of Hydrophilic Resin Based Composite Sand[D]. Wuhan: Wuhan University of Technology, 2007. (in Chinese))

[22]
姚仕明, 汪在芹, 渠庚, 等. 一种河工模型试验中动岸模拟材料及其应用:中国, CN105801747B[P].2017-09-22.

(YAO Si-ming, WANG Zai-qin, QU Geng, et al. A Dynamic Bank Simulation Material and Its Application in River Model Experiments, CN105801747B[P]. 2017-09-22. (in Chinese))

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