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MODEL-PROTOTYPE SIMILARITY ANALYSES FOR SUBMARINE DEBRIS-FLOW IMPACT ON UNDERSEA PIPELINE
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摘要: 小尺度的水槽实验和数值模型被广泛应用于真实尺度条件下海底碎屑流对海底管道冲击力的研究，但模型与某一特定原型之间的相似性一直未能得到保证，从而严重影响模型结果的适用性。为此，本文采用幂律本构关系(Power-law)描述海底碎屑流的流变特性，并基于雷诺相似准则，推导出海底碎屑流冲击海底管道时模型与原型之间各物理参数的比尺关系。根据该比尺关系，本文对现有水槽实验中模型与某一特定原型之间的相似性进行了分析，发现该水槽实验与预期的原型工况并不相似，继而推算出与该水槽实验相似的原型工况，并设计出与预期的原型工况相似的模型工况。此外，本文还对基于幂律本构关系和雷诺相似准则推导得到的比尺关系的适用性进行了讨论，认为该比尺关系适用于常重力环境下(1g)海底碎屑流冲击海底管道的小尺度水槽实验和数值模型，但不适用于超重力环境下(Ng)的土工离心机实验，也不适用于海底碎屑流的低剪切应变率工况。本文的研究结果将为保证常重力环境下(1g)海底碎屑流冲击海底管道时模型与某一特定原型之间的相似性提供理论依据。Abstract: Small-scale flume tests and numerical simulations have been widely applied to investigate submarine debris-flow impact on an undersea pipeline. However, the model-prototype similarity has not yet been guaranteed, which prevents trustable application of model results to prototype scenarios. To this end, the Power-law constitutive relation is used to describe the rheological property of submarine debris flow. The scale ratios between model and prototype for various parameters are derived based on Reynolds criterion. The flume tests published in literatures are used to demonstrate the application of derived scale ratios to model-prototype similarity analyses. The parameters of a model can be converted to those of a prototype with reference to derived scale ratios, and vice versa. In addition, the applicability of derived scale ratios is discussed. It is found that, the derived scale ratios are not applicable to Ng geotechnical centrifuge model tests, but to 1g small-scale flume tests and numerical simulations with relatively high shear strain rate of a submarine debris flow. This study will provide theoretical foundation for reaching model-prototype similarity when studying submarine debris-flow impact on an undersea pipeline in a 1g environment.
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Key words:
- Submarine debris flow /
- Undersea pipeline /
- Model /
- Prototype /
- Scale ratio
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图 1 海底碎屑流对海底管道冲击影响示意图
Figure 1. Schematic of submarine debris-flow impact on undersea pipelines
图 2 基于赫巴本构关系和幂律本构关系的海底碎屑流流变曲线(改自Zakeri et al., 2008)
Figure 2. Flow curves of submarine debris flow characterized by Herschel-Bulkley and Power-law relations (modified from Zakeri et al., 2008)
表 1 小尺度的水槽实验和数值模拟研究工作列举
Table 1. Partial list of small-scale flume tests and numerical simulations
文献来源 技术手段 本构关系 雷诺数范围 悬跨高度 冲击角度/(°) Zakeri et al.(2008) 水槽实验 赫巴; 幂律 2~140 0.08 D; 1.0 D 90 Zakeri et al.(2009) 数值模拟 幂律 1.7~240 0.08 D; 1.0 D 90 Zakeri(2009) 数值模拟 幂律 2~320 2.5 D 0; 30; 45; 60; 90 Haza et al.(2013) 水槽实验 赫巴 7.95~92.64 2.0 D 90 Liu et al.(2015) 数值模拟 幂律 1~350 2.5 D 0; 7; 15; 30; 45; 60; 75; 90 李宏伟等(2015) 数值模拟 赫巴 1.7~317.1 0.08 D; 0.2 D; 0.4 D; 0.6 D; 1.0 D; 1.5 D; 2.5 D; 4.0 D; 4.5 D; 5.5 D; 6.5 D 90 王忠涛等(2016) 数值模拟 赫巴 1.06~234.8 0.08 D 0; 15; 30; 45; 60; 75; 90 Fan et al.(2018) 数值模拟 赫巴 10~10 184 1.0 D 90 Nian et al.(2018) 数值模拟 赫巴 0.24~410.12 1.0 D 90 Guo et al.(2019) 数值模拟 赫巴 0.24~410.12 0.08 D; 0.5 D; 1.0 D; 1.5 D; 2.0 D; 2.5 D; 3.0 D 90 Sahdi et al.(2019) 数值模拟 幂律 0.5~40 32.0 D 90 Qian et al.(2020) 数值模拟 赫巴 0.3~847.8 9.5 D 90 
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表 2 模型与原型之间各物理参数的比尺关系
Table 2. Scale ratios between model and prototype for various parameters
物理参数 量纲 比尺(原型︰模型) 长度 [L] λ 面积 [L2] λ2 体积 [L3] λ3 角度 [-] 1 时间 [T] $ {\lambda ^{\frac{2}{{2 - {n_2}}}}}$ 速度 [LT-1] ${\lambda ^{ - \frac{{{n_2}}}{{2 - {n_2}}}}} $ 加速度 [LT-2] ${\lambda ^{ - \frac{{2 + {n_2}}}{{2 - {n_2}}}}} $ 角速度 [T-1] ${\lambda ^{ - \frac{2}{{2 - {n_2}}}}} $ 角加速度 [T-2] ${\lambda ^{ - \frac{4}{{2 - {n_2}}}}} $ 剪切应变率 [T-1] $ {\lambda ^{ - \frac{2}{{2 - {n_2}}}}}$ 流量 [L3T-1] $ {\lambda ^{\frac{{4 - 3{n_2}}}{{2 - {n_2}}}}}$ 质量 [M] λ3 力 [MLT-2] ${\lambda ^{\frac{{4 - 4{n_2}}}{{2 - {n_2}}}}} $ 压强和应力 [ML-1T-2] $ {\lambda ^{\frac{{ - 2{n_2}}}{{2 - {n_2}}}}}$ 能量和功 [ML2T-2] $ {\lambda ^{\frac{{6 - 5{n_2}}}{{2 - {n_2}}}}}$ 功率 [ML2T-3] $ {\lambda ^{\frac{{4 - 5{n_2}}}{{2 - {n_2}}}}}$
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表 3 基于Zakeri et al.(2008)水槽实验的海底碎屑流类型及流变特性
Table 3. Type and rheology of submarine debris flow from Zakeri et al.(2008)flume tests
海底碎屑流 质量百分比/% 幂律本构关系 赫巴本构关系 高岭土 细砂 水 1# 10 55 35 τ=10.3γ0.14 τ=7.3+3γ0.35 2# 15 50 35 τ=25γ0.125 τ=20.5+5.5γ0.35 3# 20 45 35 τ=50γ0.12 τ=43+10γ0.35 4# 25 40 35 τ=91.5γ0.11 τ=85+12γ0.4 5# 30 35 35 τ=118γ0.125 τ=110+15γ0.45 6# 35 30 35 τ=165γ0.13 τ=161+25γ0.4
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表 4 基于Zakeri et al.(2008)水槽实验的模型与某一特定原型相似性分析结果
Table 4. Results of model-prototype similarity analyses for Zakeri et al.(2008)flume tests
直径/m 长度比尺 海底碎屑流 流动性指数 速度比尺 速度/m·s-1 原型 模型 模型 原型 原型 模型 0.1 0.0286 3.5 1# 0.14 0.910 0.5 0.455 10 10.988 1.4 1.274 2# 0.125 0.920 0.5 0.460 10.870 1.4 1.288 3# 0.12 0.923 0.5 0.462 10.832 1.4 1.292 4# 0.11 0.930 0.5 0.465 10.756 1.4 1.302 5# 0.125 0.920 0.5 0.460 10.870 1.4 1.288 6# 0.13 0.917 0.5 0.458 10.909 1.4 1.283 1 0.0286 35 1# 0.14 0.765 0.5 0.383 10 13.067 1.4 1.071 2# 0.125 0.789 0.5 0.395 12.674 1.4 1.105 3# 0.12 0.797 0.5 0.399 12.547 1.4 1.116 4# 0.11 0.813 0.5 0.407 12.298 1.4 1.138 5# 0.125 0.789 0.5 0.395 12.674 1.4 1.105 6# 0.13 0.781 0.5 0.391 12.803 1.4 1.093
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Bao C G, Rao X B. 1998. Principle of the geotechnical centrifuge model test[J]. Journal of Yangtze River Scientific Research Institute, 15 (2): 1-3. http://en.cnki.com.cn/Article_en/CJFDTOTAL-CJKB802.000.htm Bruschi R, Bughi S, Spinazzè M, et al. 2006. Impact of debris flows and turbidity currents on seafloor structures[J]. Norwegian Journal of Geology, 86 : 317-337. http://foreninger.uio.no/ngf/ngt/pdfs/NJG_86_317-337.pdf Dong Y K, Wang D, Randolph M F. 2017. Investigation of impact forces on pipeline by submarine landslide using material point method[J]. Ocean Engineering, 146 : 21-28. doi: 10.1016/j.oceaneng.2017.09.008 Dutta S, Hawlader B. 2015. Numerical modeling of drag force on submarine suspended pipelines using Finite Element and Finite Volume Methods[C]//International Ocean and Polar Engineering Conference. Hawaii: [s. n.]. Elverhøi A, Issler D, De Blasio F V, et al. 2005. Emerging insights into the dynamics of submarine debris flows[J]. Natural Hazards and Earth System Sciences, 5 : 633-648. doi: 10.5194/nhess-5-633-2005 Fan N, Nian T K, Jiao H B, et al. 2018. Interaction between submarine landslides and suspended pipelines with a streamlined contour[J]. Marine Georesources & Geotechnology, 36 (6): 652-662. http://www.onacademic.com/detail/journal_1000040072576610_d60e.html Guo X S, Nian T K, Zheng D F, et al. 2018. A methodology for designing test models of the impact of submarine debris flows on pipelines based on Reynolds criterion[J]. Ocean Engineering, 166 : 226-231. doi: 10.1016/j.oceaneng.2018.08.027 Guo X S, Zheng D F, Nian T K, et al. 2019. Effect of different span heights on the pipeline impact forces induced by deep-sea landslides[J]. Applied Ocean Research, 87 : 38-46. doi: 10.1016/j.apor.2019.03.009 Haza Z F, Harahap I S H, Dakssa L M. 2013. Experimental studies of the flow-front and drag forces exerted by subaqueous mudflow on inclined base[J]. Natural Hazards, 68 : 587-611. doi: 10.1007/s11069-013-0643-9 Jia Y G, Zhu C Q, Liu L P, et al. 2016. Marine geohazards: review and future perspective[J]. Acta Geologica Sinica-English Edition, 90 (4): 1455-1470. doi: 10.1111/1755-6724.12779 Li C Y, Zhang W, Wu F D, et al. 2018. Run-out process simulation of submarine landslide using material point method[J]. Journal of Engineering Geology, 26 (S): 114-119. Li H W, Wang L Z, Guo Z, et al. 2015. Drag force of submarine landslides mudflow impacting on a suspended pipeline[J]. The Ocean Engineering, 33 (6): 10-19. http://en.cnki.com.cn/Article_en/CJFDTotal-HYGC201506002.htm Li J G, Wang Z T, Xu B, et al. 2015. Research and development of geotechnical drum centrifuge and its application to submarine landslides[J]. Journal of Yangtze River Scientific Research Institute, 32 (1): 106-111. http://en.cnki.com.cn/Article_en/CJFDTOTAL-CJKB201501024.htm Li J G, Xiu Z X, Shen H, et al. 2012. A review of the studies on submarine mass movement[J]. Coastal Engineering, 31 (4): 67-78. http://www.cqvip.com/QK/95947X/201204/662458365.html Liu J, Gao W, Li P, et al. 2018. Research process in submarine landslide and its enlightenment to study the seabed stability in the South China Sea[J]. Journal of Engineering Geology, 26 (S): 120-127. Liu J, Tian J L, Yi P. 2015. Impact forces of submarine landslides on offshore pipelines[J]. Ocean Engineering, 95 : 116-127. doi: 10.1016/j.oceaneng.2014.12.003 Malgesini G, Terrile E, Zuccarino L, et al. 2018. Evaluation of debris flow impact on submarine pipelines: a methodology[C]//Offshore Technology Conference. Houston: [s. n.]. Nian T K, Guo X S, Fan N, et al. 2018. Impact forces of submarine landslides on suspended pipelines considering the low-temperature environment[J]. Applied Ocean Research, 81 : 116-125. doi: 10.1016/j.apor.2018.09.016 Qian X S, Xu J P, Bai Y, et al. 2020. Formation and estimation of peak impact force on suspended pipelines due to submarine debris flow[J]. Ocean Engineering, 195: 106695. doi: 10.1016/j.oceaneng.2019.106695 Randolph M F, Gaudin C, Gourvenec S M, et al. 2011. Recent advances in offshore geotechnics for deep water oil and gas developments[J]. Ocean Engineering, 38 (7): 818-834. doi: 10.1016/j.oceaneng.2010.10.021 Sahdi F, Gaudin C, Tom J G, et al. 2019. Mechanisms of soil flow during submarine slide-pipe impact[J]. Ocean Engineering, 186: 106079. doi: 10.1016/j.oceaneng.2019.05.061 Sahdi F, Gaudin C, White D J, et al. 2014. Centrifuge modelling of active slide-pipeline loading in soft clay[J]. Géotechnique, 64 (1): 16-27. doi: 10.1680/geot.12.P.191 Schofield A N. 1980. Cambridge geotechnical centrifuge operations[J]. Géotechnique, 30 (3): 227-268. doi: 10.1680/geot.1980.30.3.227 Sun B T. 2014. Centrifuge modeling test on submarine landslides[D]. Dalian: Dalian University of Technology. Wang J Q, Zhang G X, Chen D X. 2019. Geological hazards in Lingshui region of Qiongdongnan Basin: type, distribution, and origin[J]. Marine Geology & Quaternary Geology, 39 (4): 87-95. http://en.cnki.com.cn/Article_en/CJFDTotal-HYDZ201904009.htm Wang Z T, Wang H Y, Zhang Y. 2016. CFD numerical analysis of submarine landslides impact on laid-on-seafloor pipeline[J]. Haiyang Xuebao, 38 (9): 110-117. http://en.cnki.com.cn/Article_en/ http://search.cnki.net/down/default.aspx?filename=SEAC201609011&dbcode=CJFD&year=2016&dflag=pdfdown White D J, Randolph M F, Gaudin C, et al. 2016. The impact of submarine slides on pipelines: outcomes from the COFS-MERIWA JIP[C]//Offshore Technology Conference. Houston: [s. n.]. Wu S G, Qin Y S. 2009. The research of deepwater depositional system in the Northern South China Sea[J]. Acta Sedimentologica Sinica, 27 (5): 922-930. http://www.cnki.com.cn/Article/CJFDTotal-CJXB200905017.htm Xiu Z X, Liu L J, Xie Q H, et al. 2015. Runout prediction and dynamic characteristic analysis of a potential submarine landslide in Liwan 3-1 gas field[J]. Acta Oceanologica Sinica, 34 (7): 116-122. doi: 10.1007/s13131-015-0697-2 Zakeri A, Høeg K, Nadim F. 2008. Submarine debris flow impact on pipelines-part I: experimental investigation[J]. Coastal Engineering, 55 : 1209-1218. doi: 10.1016/j.coastaleng.2008.06.003 Zakeri A, Høeg K, Nadim F. 2009. Submarine debris flow impact on pipelines-part Ⅱ: numerical analysis[J]. Coastal Engineering, 56 : 1-10. doi: 10.1016/j.coastaleng.2008.06.005 Zakeri A. 2009. Submarine debris flow impact on suspended(free-span) pipelines: normal and longitudinal drag forces[J]. Ocean Engineering, 36 : 489-499. doi: 10.1016/j.oceaneng.2009.01.018 Zuo D Q. 1984. Theory and method of model experiment[M]. Beijing: Water Resources and Electric Power Press. 包承纲, 饶锡保. 1998. 土工离心模型的试验原理[J]. 长江科学院院报, 15 (2): 1-3. https://www.cnki.com.cn/Article/CJFDTOTAL-CJKB802.000.htm 李宏伟, 王立忠, 国振, 等. 2015. 海底泥流冲击悬跨管道拖曳力系数分析[J]. 海洋工程, 33 (6): 10-19. https://www.cnki.com.cn/Article/CJFDTOTAL-HYGC201506002.htm 李家钢, 王忠涛, 徐博, 等. 2015. 土工鼓式离心机研发及在海底滑坡研究中的应用[J]. 长江科学院院报, 32 (1): 106-111. doi: 10.3969/j.issn.1001-5485.2015.01.022 李家钢, 修宗祥, 申宏, 等. 2012. 海底滑坡块体运动研究综述[J]. 海岸工程, 31 (4): 67-78. doi: 10.3969/j.issn.1002-3682.2012.04.009 厉成阳, 张魏, 吴方东, 等. 2018. 海底滑坡运动全过程的物质点法模拟[J]. 工程地质学报, 26(增): 114-119. doi: 10.13544/j.cnki.jeg.2018117 刘杰, 高伟, 李萍, 等. 2018. 深海滑坡研究进展及我国南海海底稳定性研究的现状与思考[J]. 工程地质学报, 26(增): 120-127. doi: 10.13544/j.cnki.jeg.2018199 孙柏涛. 2014. 海底滑坡的离心模型试验研究[D]. 大连: 大连理工大学. 王俊勤, 张广旭, 陈端新, 等. 2019. 琼东南盆地陵水研究区海底地质灾害类型、分布和成因机制[J]. 海洋地质与第四纪地质, 39 (4): 87-95. 王忠涛, 王寒阳, 张宇. 2016. 海底滑坡对置于海床表面管线作用力的CFD模拟[J]. 海洋学报, 38 (9): 110-117. doi: 10.3969/j.issn.0253-4193.2016.09.011 吴时国, 秦蕴珊. 2009. 南海北部陆坡深水沉积体系研究[J]. 沉积学报, 27 (5): 922-930. https://www.cnki.com.cn/Article/CJFDTOTAL-CJXB200905017.htm 左东启. 1984. 模型试验的理论和方法[M]. 北京: 水利电力出版社. -
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