海底碎屑流冲击海底管道的模型与某一特定原型的相似性分析

钱学生 徐景平

钱学生, 徐景平. 2021. 海底碎屑流冲击海底管道的模型与某一特定原型的相似性分析[J].工程地质学报, 29(6): 1831-1840. doi: 10.13544/j.cnki.jeg.2021-0196
引用本文: 钱学生, 徐景平. 2021. 海底碎屑流冲击海底管道的模型与某一特定原型的相似性分析[J].工程地质学报, 29(6): 1831-1840. doi: 10.13544/j.cnki.jeg.2021-0196
Qian Xuesheng, Xu Jingping. 2021. Model-prototype similarity analyses for submarine debris-flow impact on undersea pipeline[J].Journal of Engineering Geology, 29(6): 1831-1840. doi: 10.13544/j.cnki.jeg.2021-0196
Citation: Qian Xuesheng, Xu Jingping. 2021. Model-prototype similarity analyses for submarine debris-flow impact on undersea pipeline[J].Journal of Engineering Geology, 29(6): 1831-1840. doi: 10.13544/j.cnki.jeg.2021-0196

海底碎屑流冲击海底管道的模型与某一特定原型的相似性分析

doi: 10.13544/j.cnki.jeg.2021-0196
基金项目: 

国家自然科学基金 42106198

国家自然科学基金 41720104001

南方海洋科学与工程广东省实验室(广州)人才团队引进重大专项 GML2019ZD0210

详细信息
    通讯作者:

    钱学生(1989-),男,博士,研究助理教授,从事海洋工程地质与海洋地质灾害方面的研究. E-mail: qianxs@sustech.edu.cn

  • 中图分类号: P67

MODEL-PROTOTYPE SIMILARITY ANALYSES FOR SUBMARINE DEBRIS-FLOW IMPACT ON UNDERSEA PIPELINE

  • 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。
  • 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
    下载: 导出CSV

    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
    [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}}}}}$
    下载: 导出CSV

    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
    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
    下载: 导出CSV

    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
    下载: 导出CSV

    表  5  土工离心机实验中模型与原型之间各物理参数的比尺关系(孙柏涛,2014)

    Table  5.   Scale ratios between centrifuge model and prototype for various parameters(Sun, 2014)

    物理参数 量纲 比尺(原型:模型)
    长度 [L] N
    面积 [L2] N2
    体积 [L3] N3
    速度 [LT-1] 1
    加速度 [LT-2] N-1
    质量 [M] N3
    密度 [ML-3] 1
    [MLT-2] N2
    压强和应力 [ML-1T-2] 1
    应变 [-] 1
    弯矩 [ML2T-2] N3
    下载: 导出CSV
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  • 收稿日期:  2021-04-07
  • 修回日期:  2021-09-03
  • 刊出日期:  2021-12-25

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