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

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

1.
陆军工程大学爆炸冲击防灾减灾国家重点实验室，江苏南京 210007
2.
南京理工大学机械工程学院, 江苏南京 210094

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
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- 被引次数: 0
出版历程
- 收稿日期: 2023-12-24
- 修回日期: 2023-03-19
- 网络出版日期: 2024-03-26

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

1.
State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact, Army Engineering University of PLA, Nanjing 210007, Jiangsu, China
2.
School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China

摘要

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/kg^1/3）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。
- 水土交界面 /
- 冲击波传播 /
- 理论计算
Abstract: There is a lack of reliable calculation theory for the transmission and reflection pressures of shock waves at the water-soil interface. Using the mass conservation equation, momentum conservation equation, and the equations of state of water and soil, the Hugoniot relationship and p-u curve of the propagation of shock waves in water and soil medium are derived, and then the transmission and reflection pressures of the shock wave at the water-soil interface can be analyzed theoretically. Two-dimensional numerical models of the free field in water and water-soil layered medium field are established, in which the water and soil parameters are consistent with those in the three-phase medium saturated soil model used in the theoretical derivation. The calculation results show that the theoretical and numerical solutions of the water-soil interface transmission and reflection pressures are highly consistent. When using 80 g TNT explosives and exploding at 0.1–0.9 m from the water-soil interface (proportional burst distance of 0.232–2.089 m/kg^1/3), the error of the theoretical and numerical solutions for transmission and reflection pressures is less than 7%, and the coefficient of the reflection pressure is in the range of 1.6–1.8 according to the analytical solution of the reflection pressure and the ratio of the incident pressure in the water. When exploding at 0.5 m from the water-soil interface and the gas content of the saturated soil varies in the range of 0–10%, the transmission and reflection pressures are 63.8–70.0 MPa, and the reflection pressure coefficients are in the range of 1.55–1.70 at this time. The calculation method for the shock wave transmission and reflection pressure at the water-soil interface has a clear physical meaning and high precision and can provide a theoretical basis for the soil damage assessment of engineering structures in submerged soil caused by underwater explosions.
- water-soil interface /
- shock wave propagation /
- theoretical calculation

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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

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图 2 土和水的u-p曲线

Figure 2. u-p curves for soil and water

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图 3 水土交界面反射压

Figure 3. Reflected pressure at the water-soil interface

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图 4 应力-体积应变曲线^[22]

Figure 4. Stress-volume strain curve^[22]

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图 5 饱和土的应力-体积应变曲线

Figure 5. Stress-volume strain curve of saturated soil

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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

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图 7 网格敏感性分析

Figure 7. Grid sensitivity analysis

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图 8 水中自由场应力时间曲线

Figure 8. Free-field stress time curves in water

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图 9 水土交界面的反射压

Figure 9. Reflected pressure at the water-soil interface

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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

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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

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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

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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

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表 3 炸药参数

Table 3. Parameters of the explosive

ρ/（kg·m^–3）	p_cj/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

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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	p_c/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

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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/%
0.1	394.44	354.01	–10.25
0.2	124.74	132.66	6.3
0.3	78.73	78.90	0.2
0.4	56.88	54.44	–4.3
0.5	44.20	41.24	–6.7
0.6	35.97	32.98	–8.3
0.7	30.22	27.27	–9.8
0.8	25.99	23.05	–11.3
0.9	22.75	19.88	–12.6

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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

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