冲击波在水土交界面透射和反射压力的计算

严富怀 岳松林 邱艳宇 王明洋 何勇

严富怀, 岳松林, 邱艳宇, 王明洋, 何勇. 冲击波在水土交界面透射和反射压力的计算[J]. 爆炸与冲击. doi: 10.11883/bzycj-2023-0440
引用本文: 严富怀, 岳松林, 邱艳宇, 王明洋, 何勇. 冲击波在水土交界面透射和反射压力的计算[J]. 爆炸与冲击. doi: 10.11883/bzycj-2023-0440
YAN Fuhuai, YUE Songlin, QIU Yanyu, WANG Mingyang, HE Yong. Calculation of shock wave transmission and reflection pressures at water-soil interface[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2023-0440
Citation: YAN Fuhuai, YUE Songlin, QIU Yanyu, WANG Mingyang, HE Yong. Calculation of shock wave transmission and reflection pressures at water-soil interface[J]. Explosion And Shock Waves. doi: 10.11883/bzycj-2023-0440

冲击波在水土交界面透射和反射压力的计算

doi: 10.11883/bzycj-2023-0440
基金项目: 爆炸冲击防灾减灾全国重点实验室基金(LGD-SKL-202201)
详细信息
    作者简介:

    严富怀(2000- ),男,博士研究生,13101890239@163.com

    通讯作者:

    岳松林(1987- ),男,副教授,硕士生导师,yuesonglin163@163.com

  • 中图分类号: O382.1

Calculation of shock wave transmission and reflection pressures at water-soil interface

  • 摘要: 冲击波在水土交界面的透射、反射压力计算尚缺乏可靠的计算理论,利用质量守恒方程、动量守恒方程以及水、土的状态方程,分别推导得到冲击波在水、土介质中传播的Hugoniot关系以及p-u曲线,进而从理论上解析得到冲击波在水土交界面处的透射和反射压力。分别建立了水中自由场、水-土分层介质场的二维数值计算模型,其中水、土参数与理论推导时采用的三相介质饱和土计算模型中的参数保持一致。计算结果表明,水土交界面透射、反射压力的理论解与数值解具有高度一致性。采用80 g TNT炸药,距离水土交界面0.1~0.9 m(比例爆距为0.232~2.089 m/kg1/3)爆炸时,得到的透射、反射压力的理论解与数值解误差均小于7%,根据解析解得出反射压力与水中入射压力之比,反射压力系数在1.6~1.8范围内;距离水土交界面0.5 m时,饱和土的含气量在0~10%范围内变化,得到的透射、反射压力的范围为63.8~70.0 MPa,此时其反射压力系数在1.55~1.70范围内。推导得出的冲击波在水土交界面透射、反射压力的计算方法,物理意义明确、计算精度高,可为开展水下爆炸对水底土中工程结构的毁伤评估提供理论基础。
  • 图  1  爆炸波在水土交界面的透射和反射

    Figure  1.  Transmission and reflection of blast wave at the water-soil interface

    图  2  土和水的u-p曲线

    Figure  2.  u-p curves for soil and water

    图  3  水土交界面反射压

    Figure  3.  Reflected pressure at the water-soil interface

    图  4  应力-体积应变曲线[22]

    Figure  4.  Stress-volume strain curve[22]

    图  5  饱和土的应力-体积应变曲线

    Figure  5.  Stress-volume strain curve of saturated soil

    图  6  纯水和水土交界面模型及测点布置

    Figure  6.  Pure water and water-soil interface models and measurement point layout

    图  7  网格敏感性分析

    Figure  7.  Grid sensitivity analysis

    图  8  水中自由场应力时间曲线

    Figure  8.  Free-field stress time curves in water

    图  9  水土交界面的反射压

    Figure  9.  Reflected pressure at the water-soil interface

    图  10  水土交界面压力时程曲线及压力云图

    Figure  10.  Soil-water interface pressure-time curves and pressure nephogram

    图  11  含气量对水土交界面透射、反射压力的影响

    Figure  11.  Effect of air content on transmission and reflection pressures at the water-soil interface

    表  1  式(12)中的参数

    Table  1.   Parameters in equation (12)

    C1/(m·s−1 C2/(m·s−1 C3/(m·s−1 ρ0/(kg·m−3 ρ1/(kg·m−3 ρ2/(kg·m−3 ρ3/(kg·m−3
    340 1 500 4 500 2 210 1.2 1 000 2 650
    α1 α2 α3 k1 k2 k3 S1
    0.001 0.3 0.699 1.4 3.0 3.0 1.92
    下载: 导出CSV

    表  2  水参数

    Table  2.   Water parameters

    ρ/(kg·m−3 C/(m·s−1 γ0 α S1 S2 S3 E
    1025 1520 0.28 0 1.92 0 0 0
    下载: 导出CSV

    表  3  炸药参数

    Table  3.   Parameters of the explosive

    ρ/(kg·m–3 pcj/GPa A/GPa B/GPa R1 R2 ω E/GPa
    1 583 19.4 307 3.898 4.485 0.79 0.3 6.968 4
    下载: 导出CSV

    表  4  饱和土参数

    Table  4.   Saturated soil parameters

    ρ/(kg·m−3) G/MPa K/MPa a0/MPa a1/MPa a2/MPa pc/MPa ε1 ε2
    2 210 2 693 9 659 3.339×10−7 0.2251 3.794 –6.9×10−3 0 –0.001 868
    ε3 ε4 ε5 ε6 ε7 ε8 ε9 ε10 p1/MPa
    –0.003 276 –0.004 649 –0.005 887 –0.008 206 –0.009 398 –0.010 043 –0.012 787 –0.014 439 0
    p2/MPa p3/MPa p4/MPa p5/MPa p6/MPa p7/MPa p8/MPa p9/MPa p10/MPa
    7.2 16.8 26.4 35.2 52 60.8 65.6 86.4 99.2
    下载: 导出CSV

    表  5  80 g TNT对应不同爆距下的水中自由场峰值压力及偏差

    Table  5.   Peak pressures and deviations of free-field in water at different burst distances for 80 g TNT

    爆距/m公式结果/MPa模拟结果/MPa偏差/%
    0.1394.44354.01–10.25
    0.2124.74132.666.3
    0.378.7378.900.2
    0.456.8854.44–4.3
    0.544.2041.24–6.7
    0.635.9732.98–8.3
    0.730.2227.27–9.8
    0.825.9923.05–11.3
    0.922.7519.88–12.6
    下载: 导出CSV

    表  6  不同爆距下的理论和模拟反射压、偏差、反射系数

    Table  6.   Theoretical and simulated reflection pressures, deviations, and reflection coefficients at different blast distances

    比例爆距/(m·kg–1/3 入射压/MPa 理论反射压/MPa 模拟反射压/MPa 偏差/% 反射系数
    0.232 354.01 632.8 589.9 –6.8 1.788
    0.464 132.66 228.8 229.5 0.3 1.730
    0.696 78.90 133.6 133.6 0 1.693
    0.928 54.44 91.60 91.21 –0.4 1.683
    1.160 41.24 68.80 68.82 0.2 1.668
    1.392 32.98 54.40 53.49 –1.7 1.649
    1.625 27.27 45.10 43.79 –3.0 1.654
    1.857 23.05 37.60 36.75 –2.3 1.631
    2.089 19.88 32.40 31.42 –3.1 1.630
    下载: 导出CSV
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  • 收稿日期:  2023-12-24
  • 修回日期:  2023-03-19
  • 网络出版日期:  2024-03-26

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