Calculation of Reflected Pressure from Shock Wave Interaction with Typical Materials

doi:10.12382/bgxb.2025.0221

Abstract

Abstract:

Explosive shock waves interacting with typical materials at different angles of incidence can lead to severe reflected overpressure, posing significant threats to structures and personnel. However, the accuracy of existing reflected pressure prediction models remains limited. This study develops a theoretical model based on mass and momentum conservation equations, combined with the equations of state for air, granite, and 45# steel. A series of explosion experiments at different charge heights were conducted to measure both free-field and reflected pressures. Theoretical results were compared with experimental data, showing strong agreement. The proposed model effectively predicts reflected overpressure across a range of incidence angles and material types, offering valuable support for shock wave damage assessment and protection design.

Key words: typical materials, reflected overpressure, angle of incidence, reflection coefficient

LI Yuqi, NING Jianguo, XU Xiangzhao. Calculation of Reflected Pressure from Shock Wave Interaction with Typical Materials[J]. Acta Armamentarii, 2025, 46(10): 250221-.

Figures/Tables 23

Fig.1 Reflection and transmission of blast shock waves at the air-solid interface

Fig.2 Flowchart of reflected pressure calculation

Fig.3 Physical quantities before and after the blast shock wave

Table 1 Parameters of the equation of state for air

参数	数值	参数	数值
ρ/(kg·m^-3)	1.29	γ	1.4
c/(m·s^-1)	340	P₀/MPa	0.1

Table 2 Parameters of the equation of state for marble

参数	数值
ρ/(kg·m^-3)	2670
c/(ms^-1)	3030
S	1.66

Table 3 Parameters of the equation of state for 45# steel

参数	数值
ρ/(kg·m^-3)	7580
c/(m·s^-1)	4200
S	2.02

Fig.4 u-p curves of 45# steel, air, and their reflected waves

Fig.5 Experimental layout diagram with a charge height of 0.5m

Fig.6 Schematic diagram of ground sensors and their arrangement

Fig.7 Test site layout for blast experiment

Fig.8 Aerial photograph of the experimental site at a blast height of 0.5m

Fig.9 Free-field overpressure data from four trials

Table 4 Free-field overpressure data

传感器距离炸心距离/m	超压值/MPa	压力值/MPa
1.0	0.242	0.342
1.4	0.120	0.220
1.8	0.084	0.184
2.0	0.066	0.166

Fig.10 Reflected overpressure data from three trials

Table 5 Reflected overpressure data

传感器编号	炸高/ m	传感器距离炸心水平距离/m	地面介质	超压值/ MPa	压力值/ MPa
1	0.5	0.87	花岗岩	0.370	0.470
2		1.31		0.191	0.291
1		0.71	花岗岩	0.517	0.617
3	0.7	0.71	45^#钢板	0.545	0.645
4		1.21		0.350	0.450
2	0.9	1.07	花岗岩	0.256	0.356
4		1.07	45^#钢板	0.340	0.440

Fig.11 Free-field overpressure data at 2.0m

Fig.12 Vertical particle velocity ug,y of reflected airflow at the surface of granite

Fig.13 Vertical particle velocity us,y of reflected airflow at the surface of 45# steel

Table 6 Comparison of theoretical calculations and experimental results

传感器编号	地面介质	距离/ m	炸高/ m	反射压力值/MPa	计算结果/ MPa	误差/ %
1	花岗岩	0.87	0.5	0.470	0.420	10.0
2	花岗岩	1.31		0.291	0.243	16.4
1	花岗岩	0.71		0.617	0.595	3.6
3	45^#钢板	0.71	0.7	0.645	0.614	4.8
4	45^#钢板	1.21		0.450	0.366	18.6
2	花岗岩	1.07	0.9	0.356	0.314	11.7
4	45^#钢板	1.07		0.440	0.361	17.9

Fig.14 Relationship between incidence angle and pressure at a blast height of 0.7m

Fig.15 Relationship between incident angle and reflection coefficient under explosion condition with burst height of 0.7m

Fig.16 Relationship between incident angle and reflection coefficient under different detonation heights with 200g explosive

Fig.17 Relationship between incident angle and reflection coefficient at a detonation height of 0.7m for different explosive quantities

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