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Numerical Simulation of Blast Wave Propagating on the Soil Surface
Abstract:
A numerical simulation of TNT explosion on the soil surface is presented in this paper. It demonstrates how the blast wave propagates on the soil surface and interacts with the soil surface. Compared with the explosion in air, a comparative analysis on the distribution of the shock wave overpressure is implemented. The results show that the space on the soil surface close to the explosion source can be divided into a relatively high pressure region and a relatively low pressure region. Moreover, by defining the scaled height H, the interface of two regions comes about H = 0.35.
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3256-3260
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Online since:
August 2014
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© 2014 Trans Tech Publications Ltd. All Rights Reserved
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[6] 930 371. 2.
[3] 231.
[4] 15.
95.
30.
[7] 0×107 Air uses the material model MAT_NULL and described by the equation EOS_LNIEAR_P-OLYNOMIAL [] HUANG Zheng-ping. Explosion and Shock electrical measurement technology[M]. Beijing: National Defense Industry Press, 2006. ] (Eq. 2). The parameters settings refer to Table 2. (2) Table 2 Air material model parameters settings Density r0/( kg/m3) C0/( kg/m3) C1/MPa C2 C3 C4 C5 C6 E/MPa V0.
[1] 290.
[1] 290 -0. 1 0 0 0 0 0.
25.
[1] 0 Soil use the material model SOIL_AND_FOAM [] SHI Dang-yong, ZHANG Yu-chun, ZHANG Sheng-min. Explicit dynamic analysis based on ANSYS/LS-DYNA8. 1 [M]. Tsinghua University Press, 2005, 200-210. ]. Parameters settings refer to table 3. Table 3 Soil material model parameters settings r /( g/cm3) G /GPa B a0 /GPa a1 /GPa a2 /GPa.
[1] 8.
[1] 60×10-6.
[1] 382.
[3] 3×10-5.
[1] 31×10-9.
[1] 23×10-3.
05×10-2 9×10-4 P2/GPa.
[1] 1×10-3.
[1] 5×10-3.
[1] 9×10-3.
[2] 1×10-3.
[2] 2×10-3.
[2] 5×10-3.
[3] 0×10-3.
[3] 42×10-4 P3/GPa P4/GPa P5/GPa P6/GPa P7/GPa P8/GPa P9/GPa P10/GPa.
DOI: 10.3102/1569408
[4] 53×10-4.
[6] 76×10-4.
[1] 27×10-4.
[2] 08×10-4.
[2] 71×10-4.
[3] 92×10-4.
[5] 66×10-4.
[1] 23×10-4 Numerical simulation.
[1] Material verification The air explosion model is illustrated in Fig. 1. Fig. 1 TNT explosion in the air Considering the symmetry, only 1/4 model been created. TNT explosive equivalent is 25. 5kg, Set coordinate origin for the explosion point. Xy coordinates of the measuring point M is (200, 150). The interval between two points is 50cm. According explosion similarity law, air blast overpressure P is a function of the scaled distance Z = R/W1/3, where R for the distance (m) between the measuring point and the source of the explosion , W for the TNT equivalent (kg). The empirical formula [] J. Henryeh. Explosion dynamics and its use [M]．XIONG Jian-guo，Translation．Beijing: Science Press, 1987. ] proposed by Henryeh in 1979 is regarded as a reference by many researchers [] LU Hong-qin, LIU Wei-qing. Numerical simulation of the air blast[J]. Journal of WuhanUniversity of Technology. 2009, 31(19): 105-108. , [] MA Yun-ling, ZHAO Li-jun, NIE Jian-xin. Numerical simulation of shock resistance by special - shaped anti - explosion walls[J]. Blasting. 2010, 27(1): 26-30. ]. The empirical formula can be expressed as (3) Fig. 2 Comparison of simulation and the formula The results of overpressure are shown in Fig. 2. It is very close to the value calculated by Eq. 3. It indicates that the material models and parameters settings can meet the requirements of the simulation very well.
[2] Model and boundary setting Establish explosion model to simulate two cases that TNT explodes in infinite air space and on ground. Considering the symmetry of the model, only 1/2 model is created and displacement constraints is imposed on the symmetry plane. Twice numerical simulations are performed. In case1, part I and II are both air, and for case 2, part I is soil and part II is air. Air interfaces are set to be non-reflective and bottom of the soil is set to be completely reflective. TNT equivalent is 178kg. Ale algorithm is adopted in the simulation. Fig. 3 Numerical simulation model.
[3] Results of numerical simulation （1）Blast wave propagation process.
1ms 0. 5ms 1ms d 5ms a) Shock overpressure distribution at different times.
[2] 5ms 5ms 10ms b) Soil layer deformation process Fig. 4 Overpressure distribution and soil deformation Compared with the explosion in the air, the process of the blast propagation is of great difference when it explodes on the soil surface. Blast waves go into to the interior layer of soil and spread in the form of seismic waves which is much more faster than that in the air. Simultaneously, the soil begins to deform and eventually forms into a crater of which the radius is 1. 2 m and depth is 1. 9m. As shown in the Fig. 4, during this process, overpressure distribution in the air is uneven which close to the soil surface is of little lower than that in the upper areas. Due to the hinder of the soil, the near-surface air blast wave propagation velocity is slower than other regions in the air. (2) Comparative analysis of simulation results Fig. 5 Arrangement of the measuring points In the soil surface explosion model, A, B, C, D and E are five groups of measuring points parallel to the surface of the soil. The symbol h denotes the height equaling to 20cm, 50cm, 100cm, 200cm and 300cm, respectively. In the air explosion model, the measuring points are A1, B1, C1, D1 and E1. Distance between two adjacent points in each group is 112cm. In order to compare the results better, we define q to be P/P1, P for the overpressure in case 1 and P1 for case 2. The trend of q changes by using variable h, and the experiment results is shown in Fig. 6. Table 4 Blast wave overpressure in two simulation Z (m/kg1/3).
8 1.
[1] 2.
[1] 4.
[1] 6.
[1] 8 2.
[2] 2.
[2] 4 Distance (cm) 112 224 336 448 560 672 784 896 1008 1120 1232 1344 A.
[4] 94.
[2] 36.
[1] 55.
954.
687.
528.
418.
256.
173.
132.
107.
075 B.
[4] 609.
[3] 373.
[2] 395.
[1] 135.
594.
439.
323.
243.
168.
119.
087.
068 C.
[3] 42.
[2] 922.
[2] 013.
[1] 29.
816.
515.
338.
229.
175.
124.
084.
063 D.
[2] 51.
[1] 91.
[1] 34.
94.
725.
582.
47.
367.
248.
161.
114.
08 E.
[1] 795.
[1] 239.
925.
779.
568.
459.
37.
318.
267.
208.
166.
12 A1.
[4] 548.
[3] 236.
[1] 962.
[1] 35.
[1] 019.
806.
626.
486.
331.
223.
152.
079 B1.
[6] 401.
[3] 4.
[1] 92.
[1] 35.
[1] 019.
806.
637.
486.
331.
223.
152.
079 C1.
[4] 851.
[2] 606.
[1] 474.
[1] 03.
809.
642.
513.
411.
319.
24.
187.
122 D1.
[2] 618.
[1] 6.
[1] 03.
716.
499.
372.
287.
218.
164.
119.
083.
043 E1.
[1] 726.
[1] 1.
844.
621.
423.
276.
176.
109.
081.
064.
051.
027 Fig. 6 Trend of q changes with distance As shown in Fig. 6, there is a great difference between two cases. On the whole, the air space upper to the soil can be divided into two regions, relatively low pressure region where soil absorption dominates and hight pressure region where soil reflection effect dominates. In the space close to the surface, pressure decreases beccause of absorption and restriction from ground. Howere, in the upper space, pressure values go up because part of energy been refleted at the beginning of explosion. As h incereaing, q becomes larger. This phenomenon is particularly evident at the condition of distance more than 6 m. Define scaled hight H=h/W1/3, according to the article data, interface of the two regions mentioned above is about H = 0. 35. When H <0. 35, q <1, blast wave pressure is smaller than that in the air. When H> 0. 35, energy been reflected let to overpressure become relatively larger. In practical engineering applications, people always take blast wave propagation in air for reference and determine the safe range according to the results caculated from empirical formula. According to results of this paper, soil surface explosion differs a lot from that explosion in the infinite air space. Accordingly, people should pay more attention to the relatively high pressure region. Conclusion In this paper, the simulation of TNT explosin on the soil surface is implemented by LS-DYNA. Compared with the explosin in the infinite air space, some conclusions can be drawn as follow: 1) After TNT exploded on the soil surface, a large part of the energy is absorbed by the soil layer and propagates in the groun very fast in form of seismic waves. 2) Propagation of blast waves along surface is different from conventional reflection. There is no enhanced reflective wave formed in the space of close to the soil. Instead, blast waves weakened because of the absorption and hindered caused by soil. 3) Due to reflection and absorption, the space on the soil surface close to the explosion source can be divided into a relatively high pressure region and a relatively low pressure region. By defining scaled hight H, conclusion is made that the interface of two regions comes about H = 0. 35. Acknowledge This paper is supported by foundation of key laboratory of missle test and identification technology. References.