J. Cent. South Univ. (2016) 23: 461-469

DOI: 10.1007/s11771-016-3091-3

Mitigation of blast loadings on structures by an anti-blast plastic water wall

ZHANG Li(张力), CHEN Li(陈力), FANG Qin(方秦), ZHANG Ya-dong(张亚栋)

State Key Laboratory of Disaster Prevention & Mitigation of Explosion & Impact

(PLA University of Science and Technology), Nanjing 210007, China

 Central South University Press and Springer-Verlag Berlin Heidelberg 2016

Abstract: Seven in-situ tests were carried out in far field to study the blast mitigation effect of a kind of water filled plastic wall. Test results show that the mitigation effect of water filled plastic wall is remarkable. The maximum reduction of peak reflected overpressure reaches up to 94.53%, as well as 36.3% of the minimum peak reflected overpressure reduction in the scaled distance ranging from 1.71 m/kg^1/3 to 3.42 m/kg^1/3. Parametric studies were also carried out. The effects of the scaled gauge height, water/charge scaled distance (the distance between the explosive charge and the water wall), water wall scaled height and water/structure scaled distance (the distance between the water wall and the structure) were systematically investigated and compared with the usual rigid anti-blast wall. It is concluded that these parameters affect the mitigation effects of plastic water wall on blast loadings significantly, which is basically consistent to the trend of usual rigid anti-blast wall. Some formulae are also derived based on the numerical and test results, providing a simple but reliable prediction model to evaluate the peak overpressure of mitigated blast loadings on the structures.

Key words: water wall; blast mitigating effect; protective technique; prediction model

1 Introduction

Safety issues caused by accidental blast hazards have been paid high attention [1–6]. Advanced protective techniques are demanded to reduce casualties and economic loss in civilian or military applications under the increasing accidental explosions and terrorist attacks. Anti-blast barricades traditionally made by soil, sand or concrete have been commonly employed to mitigate accidental explosions. Meanwhile, the water barricade has drawn more and more attention owing to low construction cost, light weight and being easy to install.

Water barricades can be constructed in two commonly used ways, i.e. water splash and water barrier. They are called “passive” approaches because most of the explosion energy would either be reflected or dispersed by the water barricades [7]. The water wall is a construction form of water barriers. Heretofore, the passive approach has been successfully employed in protecting civilian facilities (e.g. embassies and high-rise buildings) and military facilities (e.g. ammunition storage and disposal sites).

Water was originally used in coal mines to suppress dust explosions [8]. From then on, more and more work had been done to study the blast mitigation effects by using water. Some tests were carried out in the David Taylor Research Center by requests from the Naval Civil Engineering Laboratory (NCEL). A 4.67 lb (2.17 kg) TNT explosive was first detonated in a closed chamber without water, and then surrounded by water. Both the average gas pressure and impulse inside the chamber were reduced by as much as 89% [9]. The U.S. Army Corps of Engineers (USACE) tested an ammunitions demolition container for unexploded ordnance disposal. Water bags as a form of barriers were placed around the explosive to mitigate the effects of this contained explosion. In the case of explosive charge equivalent to  4 lb (1.81 kg) TNT, the gas pressure was reduced from about 350 (2.41) to 100 psi (0.69 MPa), i.e. around 70% reduction [10]. A series of small-scaled explosive experiments were conducted to study the potential for water filled containers to mitigate blast loadings on armored vehicles [11]. The use of a water filled container was effective at mitigating the deformation. Moreover, it was found that the primary mitigation mechanism of the water was momentum extraction as there was insufficient time for water breakup and evaporation to occur prior to target loading.

Many researchers have found that the water-to- charge ratio (the ratio of the mass of the water to that of the explosive charge) and air gap between the charge and water were the common parameters that affected the mitigating efficiency by water barrier. In a series of small-scaled tests [12] conducted in a simplified tunnel with a chamber connected to a duct, the water-to-charge ratio ranged from 0.67 to 3.3 and a pressure reduction of 70% was reported in the test. It was also found that there was an upper limit for effective amount of suppression in this configuration, and using more water provided limited influence. Naval Facilities Engineering Service Center (NFESC) tests [13] demonstrated that water was effective in reducing the internal gas pressures with the water-to-charge ratio from 2:1 to 4:1, especially for low charge densities. The water-to-charge ratio of 2:1 was proposed to be the most effective. Air-gap was studied in tests conducted by TNO-PML in 1995 [14], a significant reduction 50% of quasi-static pressure (QSP) was observed, and the air-gap was revealed to be effective in the reduction of QSP. Numerical studies on mitigating efficiency of water with air-gap were also conducted using MSC-DYTRAN code and similar conclusions were drawn [15].

In most of the researches, no matter directly contacted or indirectly contacted, explosives were surrounded by the water to mitigate the blast loading. Actually, in real engineering scenario, the location and time of accidental explosion is difficult or sometimes impossible to predict in advance. Thus, the commonly used solution is to erect a water barrier that is called water wall physically separated from the explosive charge [16]. However, very limited study on the water wall has been found in literature. In this work, an engineering-plastic container filled with water as a kind of water wall, which possesses the advantage of efficient construction and low cost, is proposed. Seven in-situ blast experiments were carried out to examine the mitigation effects on target structures which were obstructed from the detonation by this water wall. A validated finite element model was also developed using commercial software LS-DYNA to calculate the mitigation effects of usual rigid protective wall. The effects of scaled gauge height, water/charge scaled distance, water wall scaled height and water/structure scaled distance on the peak reflected overpressure reduction were discussed and analyzed, by comparing the experimental results to those with usual rigid protective wall. An applicable prediction model of mitigated blast loading on structures by the plastic water wall was also built based on the numerical and test results.

2 Test program

Seven in-situ tests were conducted in far field to evaluate the mitigation effects of this kind of water wall quantitatively. The configuration of the test program and the detailed dimensions are shown in Fig. 1.

Fig. 1 Configuration of experiment

As shown in Fig. 1, the specially designed engineering-plastic containers filled with water to form the water wall were located between a steel chest structure and the TNT explosive charge. The containers stood on the flat ground without any constraint. The engineering-plastic container was made by polystyrene with the dimension of 0.5 m (long)×0.16 m (wide)× 0.405 m (high), and the thickness of engineering plastic was 5 mm. The cubic steel chest that was on behalf of the protected structure was 1.5 m (long)×0.75 m (wide)× 0.8 m (high) with 6 mm thick steel plate. A cubic-shape explosive equivalent to 0.2 kg TNT charge was placed 0.1 m above the ground. To study the mitigation effects and affecting factors in-depth and systematically, the engineering-plastic water wall with varied height  was located between the explosive and steel chest with varied water/charge distance. The distance between the explosive and the steel chest changed from 1 m to 2 m to alter the water/charge distance.

The pressure transducers were mounted on the steel chest to measure the mitigated overpressure by water wall. As the experimental model was symmetrical, nine pressure transducers, CA-YD_116A, were mounted on the right side of the steel-chest to record the overpressure in the experiments. Position and serial number of the pressure gauges were marked in Fig. 2. Dynamic signal test and analysis system DH5927 were used to deal with digital data captured by the pressure gauges.

The charge/structure scaled distance D, the water/ charge scaled distance L₁, the water wall scaled height H_W, the water/structure scaled distance L₂ and the scaled gauge height H_G is defined by Eqs. (1)–(5), respectively. Seven test scenarios are listed in Table 1.

                                  (1)

                                  (2)

                                (3)

                                  (4)

                                 (5)

where M is the mass of the explosive charge. The other parameters are shown in Fig. 1.

Fig. 2 Location of pressure gauges on chest

Table 1 Scheme of experiments

The in-situ tests were conducted in windless days, which could minimize the influence caused by environment. As observed in the tests, the water filled plastic wall that was constructed with three jointed engineering-plastic containers was overblown by the blast loading after each detonation, the water was splashed by the blast wave, and some water droplets hit on the steel chest. The test scenarios before and after detonation are shown in Figs. 3–6.

3 Test results and discussion

All the peak reflected overpressures captured by the pressure transducers in the seven tests are listed in  Table 2. Some overpressure data have exceeded the acceptable range, e.g. pressure gauge 7 in 3rd and 5th detonations, which are represented by “—” in Table 2.

Fig. 3 Position of explosive charge

Fig. 4 Scenarios before explosion

Fig. 5 Destruction of water walls (2nd detonation)

Fig. 6 Destruction of water wall (4th detonation)

As shown in Table 2, there are obvious mitigation effects on the peak reflected overpressure by comparing the 1st detonation (i.e. without water wall) with the 2nd to 5th detonations (i.e. with water wall). It is noted that the charge/structure scaled distance D of these three detonations equals 3.42 m/kg^1/3. The mitigation of the peak reflected overpressure captured by the pressure transducer 9 reaches up to 82.019% in the 2nd detonation. The minimum mitigation effect also reaches 36.284% on the pressure transducer 3 in the 3rd detonation.

The water wall scaled height in the 3rd detonation is 0.462 m/kg^1/3, which is 32.5% less than that of the 4th detonation (i.e. 0.654 m/kg^1/3). The peak reflected overpressure captured by Gauge 3, 6 and 9 in the 3rd detonation is 2.25, 2.37 and 2.23 times as much as that in the 4th detonation, respectively. It can be concluded that the higher the water wall is, the more mitigation effect of reflected overpressure on the steel chest will be achieved.

The water/charge scaled distance (L₁) in the 4th and 5th detonation is 3.5 and 6 times as much as that in the 2nd detonation, respectively. It is found that the peak overpressure captured by Gauge 3 in the 4th and 5th detonations is 1.75 and 2.08 times as much as that in the 2nd detonation, respectively. It is concluded that the closer the distance between the explosive and water wall is, the more the energy reflected by water wall will be.

Table 2 Peak reflected overpressure captured in experiments

The water/structure scaled distance (L₂) affects the overpressure mitigation significantly. The water/ structure distance in the 4th detonation is 1.949 m/kg^1/3, which is 78.2% more than that of the 6th detonation (i.e. L₂=1.094 m/kg^1/3). The peak reflected overpressure captured by Gauge 1, 2 and 3 in the 6th detonation is 1.906, 1.806 and 1.441 times as much as that in the 4th detonation, respectively. It could be found that the longer the distance between the water wall and the steel chest is, the more the mitigation of peak reflected overpressure will be.

To deeply and systematically understand the influences caused by construction parameters of the water filled plastic wall. The gauge scaled height (H_G), water/charge scaled distance (L₁), water wall scaled height (H_W) and water/structure scaled distance (L₂) are discussed in the following compared to that with commonly used rigid wall.

4 Parametrical study and comparison with rigid wall

In this section, the mitigation effect of presented plastic water wall is systematically studied by a numerical approach. A corresponding water wall FE model and a rigid anti-blast wall model are developed in LS-DYNA, respectively.

4.1 Material model

In the developed FE model, air, water and explosive (TNT) are modelled by Euler algorithm, while the steel chest structure is assumed to be rigid, and fixed at the position according to the tests.

Air is described by an ideal gas equation of state. The pressure is related to the energy by [17]

                              (6)

where g is the adiabatic coefficient of air, ρ is air density and e is the specific internal energy. In the present simulation, g, ρ and e are assumed as 1.4, 1.225 kg/m³ and 2.068×10⁵ kJ/kg, respectively.

Explosive is described by using the JWL equation of state, which models the pressure generated by chemical energy in an explosion. It is defined as [18]

                         (7)

where p is the hydrostatic pressure, V is the specific volume; e is the specific internal energy; C₁, C₂, r₁, r₂ and ω are material constants, and assumed as 3.7377× 10⁵ MPa, 3.7471×10³ MPa, 4.15, 0.9 and 0.35, respectively.

The pressure of the water is calculated by the Gruneisen equation of state in LS-DYNA which can be written as [19]

 μ<0 (Tension)      (8)

 μ>0 (Compression)           (9)

where ρ₀ is the initial density of water; e is the specific internal energy per unit volume; μ=η–1 and η are the ratios of the densities after and before disturbance; g₀ is the Gruneisen gamma; a is the first order volume correction to g₀; S₁, S₂ are S₃ are the coefficients; C is the intercept of the cubic shock velocity–particle velocity curve. In this work, ρ₀, S₁, S₂, S₃, C and a are assumed as 1000 kg/m³, 1.920, –0.096, 0, 1.650 and 0, respectively.

The steel chest structure and rigid wall are set by material model 20 in LS-DYNA [19]. The mass density, elastic modulus and Poisson ratio are assumed as 7.8× 10³ kg/m³, 2.1×10² GPa and 0.3, respectively.

4.2 Analytical model

Figure 7 shows the developed analytical model corresponding to the field test programme. Only half of the model is built due to the symmetry. A numerical convergence study of the air blast is firstly performed in order to study the effect of model discretization. The problem is isolated to only include the gas dynamics by using successively small elements from 2 cm to 1 cm in the Euler domain. Prevented outflow is defined as u_i/t=0, where u_i/t is the velocity in the direction i normal to the boundary. As shown in Fig. 7, prevented outflow is applied at the symmetry plane as well as the lower Euler boundary, and the rest of outer lateral boundaries have free outflow.

Figure 8 shows the effect of element size on peak reflected overpressure when element size decreases from 2 cm to 1 cm. Because only the blast pressure for no barrier case is available in the literature (such as, in TM5-855-1 [20]), the case without barrier is considered in the model validation due to the limited available experimental data. It is found that the numerical results come to convergence and produce enough precision when element size goes to 1 cm. Further decreasing element size has insignificant influence on the numerical results, but might lead to the risk of computer memory overflow and substantially increase the computing time. Thus, the element size of 1 cm is employed for the Euler domain, resulting in a total of 990000 elements, in the subsequent analysis.

The calculated peak reflected overpressure of numerical simulation agrees basically well with that captured in the 1st experimental detonation and calculated by TM5-855-1, which is a validation of developed numerical model. The error attributes to two points: (1) the ground in the numerical model is set as reflected boundary, which would strengthen the blast wave reflection; (2) the coarse mesh size might lead to the existence of the rising time. ZHANG et al [21] presented that the decreasing of element size couldreduce the rising time, however, the numerical model in this work already has 990000 elements, and further deceasing element size could not be accepted by normal computers.

4.3 Numerical results and parametrical study

Figure 9 shows the typical scenario of blast wave propagation process calculated by the developed model. The wave reflection on the water wall, the diffraction of blast wave and the wave reflection on the structure are clearly shown.

Figure 10 shows the splashing process of the water wall at different intervals of time. It can be seen that, the water wall has been destroyed and the water is splashed in the air by the blast wave.

In order to evaluate the blast mitigation effect of water walls in the tests quantitatively, a non-dimensional index R_P is defined as the ratio of peak reflected overpressure with water walls to that without water wall. It can be given as

                              (10)

where P_{no_wall} is the maximum reflected overpressure in the case of no water walls and P_{with_wall} is the peak reflected overpressure in the existence of water wall.

The blast mitigation effect is not uniform along the height of the protected structure. Figure 11 shows the mitigation effects on the peak reflected overpressure considering different scaled gauge heights. Three scaled gauge heights (i.e. H_G=0.308 m/kg^1/3, 0.680 m/kg^1/3 and 1.060 m/kg^1/3) are considered in the analysis. Three water/charge distances (i.e. L₁=0.342, 1.197 and 2.051 m/kg^1/3) are also compared for the scaled gauge height. It is noted before further investigation that the average peak reflected overpressure is the average value captured by gauges at the scaled height, e.g. the average peak reflected overpressure on H_G=0.308 m/kg^1/3 is referred to the arithmetic average value of peak reflected over- pressure captured by Gauges 7, 8 and 9.

Fig. 7 Numerical analytical model:

Fig. 8 Results comparison between numerical results and TM5-855-1

As shown in Fig. 11, the numerical results simulating water wall agree with the tests basically,which is also a validation of developed numerical model. The mitigation effect on upper gauges is better than that on lower ones when L₁ is small, i.e. L₁=0.342 m/kg^1/3. However, the mitigation effect on middle gauges becomes the most significant while the anti-blast wall is separated away from the explosive charge. This trend is similar to that of the rigid wall. It is found that the mitigating effect of the rigid wall is a little better than that of water wall on most of the pressure gauges. In some special cases, e.g. upper gauges at L₁=0.342 and 1.197 m/kg^1/3, the water wall performs better than rigid wall. This is because the plastic water container is overblown under the blast loading, and the splashed water droplet from plastic container mitigates the power of blast wave.

Figure 12 shows the mitigation effect on the peak overpressure considering different water/charge scaled distance (L₁). The influences caused by L₁ are divided into two different conditions: one is with fixed D (Fig. 12(a)), and the other is with fixed L₂ (Fig. 12(b)). Three water/charge scaled distances (i.e. L₁=0.342 m/kg^1/3, 1.197 m/kg^1/3 and 2.052 m/kg^1/3) are considered in the analysis.

Fig. 9 Blast wave propagation (L₁=1.197 m/kg^1/3, H_W=0.684 m/kg^1/3):

Fig. 10 Splashing of water wall (L₁=1.197 m/kg^1/3, H_W=0.684m/kg^1/3):

Fig. 11 Protective effect along different H_G

Fig. 12 Effect of L₁ on R_P:

It can be concluded from Fig. 12 that the smaller the L₁ is, the smaller the R_P will be. It is because more energy of the blast loading would be reflected when the water wall gets closer to the explosive charge. This trend is similar to that of the rigid wall. As shown in Fig. 12(a), R_P values of the rigid wall whose L₁ equals 0.352 m/kg^1/3, 1.197 m/kg^1/3 and 2.052 m/kg^1/3, are 0.625, 0.946 and 0.935 times, respectively, as much as that of the water wall. It is indicated that the mitigation effect of water wall is the most similar to that of the rigid wall when the water wall is located at a certain place between the explosive charge and the structure while the charge/ structure scaled distance D is fixed. As shown in     Fig. 12(b), R_P values of rigid wall whose L₁ equals 0.352m/kg^1/3, 1.197 m/kg^1/3 and 2.052 m/kg^1/3, are 0.465, 0.716 and 0.935 times, respectively, as much as that of the water wall. It is indicated that the mitigation effect of water wall is far more different from that of the rigid wall when the water wall is near the explosive charge and the structure while the water/structure scaled distance L₂ is fixed.

Figure 13 shows the mitigating effect on the peak reflected overpressure considering different water wall scaled heights. Two water wall scaled heights (i.e. H_W= 0.462 m/kg^1/3 and 0.684 m/kg^1/3) are considered in the analysis.

Fig. 13 Effect of H_W on R_P

As shown in Fig. 13, in the case of rigid wall, the factor R_P is 0.947 and 0.946 times as much as that of water wall when H_W=0.462 and 0.684 m/kg^1/3, respectively. It is concluded that the mitigating effect of the rigid wall is a little better than that of water wall. The higher the water wall is, the smaller the R_P will be, and this trend is similar to that of the rigid wall. This is because the blast diffraction occurs when the blast wave arrives on the water wall, and the influence of diffraction wave on the peak reflected overpressure will be weakened as the water wall scaled height gets larger.

The mitigation effect on the peak reflected overpressure considering different water/structure scaled distance L₂ is shown in Fig. 14. Two water/charge distances (i.e. L₂=0.342 m/kg^1/3 and 1.197 m/kg^1/3) are considered in the analysis.

As shown in Fig. 14, the closer the structure water wall is, the better the mitigating effect on peak reflected overpressure will be. It is because the influence causedby diffraction wave is more obvious when the distance between the water wall and the structure is farther.

Fig. 14 Effect of L₂ on R_P

5 Blast loading prediction model

The parameters, i.e., the water/charge scaled distance and the scaled height of water wall, can significantly influence the mitigating efficiency of the water wall. However, what we most concerned is the reflected overpressure on the structures, i.e., it is very important to predict the mitigated overpressure on the target structure by water wall in engineering application. Based on the calibrated numerical model above, a mitigated blast loading prediction model is proposed.

It is noted that the peak reflected overpressures recorded by gauges are different from each other on the surface of target structure. A representative portion of target structure is selected to evaluate the mitigating effect by using water wall. In this section, Gauge 6 at the central point of the target is selected. Figures 15 and 16 show the R_P as a function of the water/charge scaled distance and the scaled height of water wall, respectively. Their corresponding empirical formulae are fitted in Eq. (11) and Eq. (12), respectively.

Fig. 15 R_P with different water/charge scaled distances

Fig. 16 R_P with different scaled heights of water wall

                     (11)

            (12)

where denotes the variation of R_P as a function of L₁ and is the variation of R_P as a function of H_W.

It is noted that the scaled height of water wall equals 0.684 m/kg^1/3 when the effect of water/charge scaled distance is evaluated. If the R_P when the scaled height of water wall equals 0.684 m/kg^1/3 is set as base point, Eq. (12) can be corrected as

                      (13)

where K is the ratio of R_P with different H_W to that with H_W equal to 0.684 m/kg^1/3, and  represents the R_P when H_W equals 0.684 m/kg^1/3. Thus, the R_P with different L₁ and H_W can be solved as

                             (14)

Therefore, the peak reflected overpressure at the center of the structure can be solved by

                        (15)

Taking a typical reinforced concrete slab as the target structure, an application case of this prediction model is presented. The square slab with a dimension of 1.5 m×0.8 m is built 1 m away from the explosive charge with TNT equivalent to 60 g. The plastic water wall with height of 27 cm is constructed 47 cm away from the charge. The reflected overpressure–time history on the center of the structure and predicted peak reflected overpressure are shown in Fig. 17. It is found that the proposed theoretical model results agree well with the numerical results.

Fig. 17 Comparison of numerical and theoretical results

6 Conclusions

1) An engineering-plastic container filled with water as a kind of anti-blast water wall is proposed. The mitigation effect of this water wall is validated by a series of in-situ blast experiments. The mitigation ratio of the peak reflected overpressure reaches up to 94.53%.

2) A finite element model validated by TM5-855-1 is also developed using commercial software LS-DYNA to calculate the mitigation effect of the water wall and usual rigid protective wall. The effects of scaled gauge height, water/charge scaled distance, water wall scaled height and water/structure scaled distance on the overpressure reduction are discussed and analyzed.

3) It can be concluded that both the proposed water filled plastic wall and commonly used rigid wall can mitigate the blast loading efficiently. Basically, the mitigating effect of the rigid wall on peak reflected overpressure is a little better than that of the proposed water filled plastic wall, however, the water wall possesses the advantage of efficient construction and low cost. Moreover, the water/charge scaled distance, water wall scaled height and water/structure scaled distance affect the mitigation effect of proposed water wall significantly. The mitigating effect on the peak reflected overpressure will be much better if the water/charge scaled distance is smaller, the water wall scaled height is larger and the water/structure scaled distance is smaller.

4) The proposed blast loading prediction model derived from the numerical results provides a reliable estimation of the peak reflected overpressure on the center of the structure in the real engineering mitigated by water wall.

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(Edited by YANG Bing)

Foundation item: Projects(2015CB058003, 2012CB026204) supported by the National Basic Research Program of China; Projects(51238007, 51210012) supported by the National Natural Science Foundation of China

Received date: 2014-12-03; Accepted date: 2015-01-31

Corresponding author: CHEN Li, Associate Professor, PhD; Tel: +86–13913875519; E-mail: chenli1360@qq.com