Mitigation of the blast load effects on a building structure using newly composite structural configurations

Ahmed K.Th .M.S.Zhrn .Zhengguo Go

a School of Transportation Science and Engineering.Beihang University (Beijing University of Aeronautics and Astronautics).Beijing,100191.PR China

b Department of Civil Engineering.Military Technical College.Egypt

Keywords: Concrete structures Blast waves Numerical simulation TNT

ABSTRACT In this study.a nonlinear three-dimensional hydrocode numerical simulation was carried out using AUTODYN-3D to investigate the effect of blasting of a high explosive material (TNT) against several configurations of the composite structure.Several numerical models were carried out to study the effect of varying the thickness of the walls and the effect of adding an air layer or aluminum foam layer inside two layers of concrete in mitigating the effect of blast waves on the structure walls.The results showed that increasing the thickness of walls has a good effect on mitigating the effect of blast waves.When a layer of air was added.the effect of blast waves was exaggerated,while when a layer of aluminum foam was added the blast wave effects were mitigated with a reasonable percentage.

1.Introduction

In the past few years.the probability of accidental explosions such as incident blasts and gas explosions have increased as well as the threat of terrorism.Public buildings and important structures should have a lot more resistance to impact and blast loads so as to protect the personnel inside from being injured [1-6].

When an explosive charge explodes outside a building,pressure waves in a spherical form resulting from this explosion applies tremendous loads on the existing buildings.These buildings are greatly affected by the incident and reflected waves resulting from the explosion [7,8].The effect of these waves on the existing buildings depends on a lot of factors including the orientation of the building with respect to the explosion.the structural configurations of the building.the properties.intensity of the explosive itself.the properties of the construction materials.and the connections type between structural components (beams/columns)[9-12].

State-of-the-art studies of building construction materials(concrete and steel) under dynamic loads or blast loads reveal several methods/techniques to study the response and effect of these components under blast loading.Such as.HL.Ren et al.[13]proposed an explicit phase field model for dynamic brittle fracture using a Verlet-velocity scheme.The explicit method has been validated by various numerical examples.The same result by the implicit dynamic scheme phase field model can be achieved by the investigated scheme.C.Diyaroglu et al.[14]presented the applicability of peridynamics to accurately predict nonlinear transient deformation and damage behavior of composites under shock or blast types of loadings due to explosions.This study presented that the ability of the peridynamics to predict residual durability and strength for improving structural designs of composites under such loading conditions.A.Shishegaran et al.[15]presented a new and significant technique to improve the flexural capacity of simply supported reinforced concrete beams.The proposed technique uses a new reinforcement bar system having bent-up bars,covered with rubber tubes.In the current study.an equation is formulated to calculate the bending capacity of a new reinforcement bar system beam.

Numerous theoretical.numerical and experimental researches have been conducted for studying the modelling structures under impulsive loads.For instance.A.Plotzitza et al.[16]carried out a numerical simulation of concrete under explosive loading using a mesh-based and a mesh free discretization technique.The proposed techniques are verified by experimental data.The results of the different numerical simulations have a good agreement with experimental data.T.Rabczuk et al.[17]introduced a technique fortreating fluid-structure interaction of fracturing structures under impulsive loads.Both the fluid and the structure are treated by mesh free methods.This technique is aimed at problems with lowpressure and high-velocity fluids.T.Rabczuk et al.[18]described a new method for modelling discrete cracks in mesh free particle methods in three dimensions.The cracks can be arbitrarily oriented.but their growth is represented discretely by activation of crack surfaces at individual particles.so no representation of the crack’s topology is needed.A.Huerta et al.[19]presented Meshless methods which have used as spatial discretization in order to solve partial differential equations.Most Meshless methods are higherorder continuous which is advantageous for the efficient solution of higher-order partial differential equations.

Several investigations have been performed experimentally,and numerically to study the effect of adding stiffeners on the structural components connections.For instance.A.Shishegaran et al.[20]introduced box-plate beam-to-column connections.They underwent hysteretic loading and it was found from their momentrotation curves that the bending capacity and ductility of the box-plate connection were more than ordinary rigid connection,and those of the latter were more than those of the normal typical one.A.Shishegaran et al.[21]proposed box-plate.box-plate with UNP.box-plate with L-plate and ordinary beam-to-column connections.The result of moment-rotation curves revealed that the bending capacity and ductility of the box-plate with UNP connection was higher than any other rigid connections.Also,it was found that stress concentration in box-plate with UNP connections disappear over the top and bottom flange plates.G.Reza et al.[22]proposed a new method of reinforcement in order to increase the bending capacity which depends on a sealed rubber tube of diameter twice that of the reinforcement bar covers the slanted part to separate it from the beam’s concrete.Therefore,it is obvious that a compressive force found by the solution of the first superposition equation is applied at the middle 1/3 of the lower part and causes up to 25%increase in the beam bending capacity.

In recent years,there are some new computational technologies that have been developed.such as mesh free SPH and Peridynamics.Fan.H.and S.Li [23]presented a computational study on Peridynamics modelling and simulation of soil fragmentation under buried explosive loads.A key technical ingredient of the simulation is the coupling between soil and explosive modelling methods.which is accomplished by coupling the state-based Peridynamics (soil) model with a modified smooth particle hydrodynamics (SPH) model (explosive).the developed computational model has been validated with measured experimental data and it is shown certain predictive capacity.X.Lai et al.[24]proposed nonlinear Peridynamics models of drained and saturated geomaterials.and applied them to simulations of dynamic fragmentation and ejecta formation due to impulse loads.Comparisons of analytical and numerical results indicate that the Peridynamics model has the ability to both matches traditional continuum compression examples.as well as simulate complex geo-material fragmentation processes resulting from impulse loads.

Y.Ferezghi[25]carried out dynamic behavior of non-symmetric functionally graded (FG) cylindrical structure under shock loading using dynamic equations in the polar coordinates by Meshless local Petrov-Galerkin(MLPG)method.This method has the capability to the dynamic analysis of non-symmetric FG cylindrical structure.The current method presents high capability.efficiency and accuracy to dynamic analysis of non-symmetric FG cylindrical structure with nonlinear grading patterns,which give a base for more flexible design.E.Hedayati and M.Vahedi[26]proposed a modified model based on radius of ceramic cone for ceramic/aluminum targets in order to investigate and evaluate accuracy of the presented analytic model.They concluded that.with increasing initial velocity and ceramic thickness and decreasing support layer thickness.the radius of ceramic cone decreases; this ends up increasing residual velocity of the projectile and penetration time and extending the area across which the pressure is distributed.

The response of the structure to these loads depends on the properties of the structure and its components.The response of any structure depends on a variety of factors which include mechanical characteristics of the material (especially its strength.way of failure.stress-strain diagram.behavior beyond the elasticity limit,etc.).and distribution of masses and structure rigidity with corresponding frequency tuning of the structure.characteristics of surfaces loaded by the impact blast wave.structure geometry compared to explosion wave characteristics.any previous failures of the structure,including changes in the structure material properties in the course of time for existing structures.etc [27-29].

The explosion results on the structures are catastrophic as it can collapse the whole building or part of it causing injuries and losses of lives to the personnel inside or surrounding the building[30-32].Therefore.important structures and public buildings’design have to be enhanced to provide an adequate resistance to blast loads and to assure the minimum safety for the occupants inside.

In this paper.the effect of blast waves on complete structures and how to enhance the response of these structures to blast waves is discussed.

2.Numerical simulations

Numerical simulation is the means of studying the effect of blast waves in this chapter.

2.1.Numerical tool: hydrocode

The numerical tool used for simulation is AUTODYN-3D which is a special code used to assess the effect of blast and impact loads[33].

2.2.Model validation

This paper presents a 3D hydro-code simulation using AUTODYN-3D [33]on the effect of explosion on a barrier wall target.The experimental data published by Radek Hajek [34]for two tests carried out using a 500 g explosive is used for validation.

Two experimental tests were used for validation,in the first test,the air domain is modeled with 812,500 elements and 847,926 nodes.and the pressure was measured at standoff distance 6 m from the TNT charge as a typical free field detonation as shown in Fig.1.The model used to simulate the concrete is the RHT model,the compressive strain rate used in concrete is 0.032 while the tensile strain rate used is 0.036.The damage and failure in themodel is defined as RHT damage model.The results of the numerical simulation compared to the experimental test is as shown in Fig.2 where the pressure recorded in the experimental test is 22 kPa while the pressure measured from the numerical model is 22.5 kPa (after excluding the atmospheric pressure which is measured in the numerical simulation in contrary to the experimental test)with a percentage of error of 2.2%.

Fig.1.The numerical model used for validation for the first test.

In the second test the flat concrete target is modeled with 45,000 element while for the air domain it is modeled with 542,488 elements and 566,631 nodes the pressure was measured at the same standoff distance as the first test (6 m) from the charge as shown in Fig.1 but with the presence of a concrete barrier at a distance 5 m from the detonation point.Fig.3 shows the numerical model simulation for the experimental test as described by Radek[34].

The height of the barrier is 1.2 m,its width is 3 m and thickness is 10 cm and compressive strength of concrete used is 156 MPa.The pressure is measured at height 1.2 m from the ground level.The results of the pressure at the gauge point in the numerical test is compared to the results measured in the experimental test as shown in Fig.4 where the pressure recorded in the experimental test is 9 kPa while the pressure measured from the numerical model is 9.2 kPa(after excluding the atmospheric pressure which is measured in the numerical simulation in contrary to the experimental test)with a percentage of error of 2.2%.

2.3.Proposed structural configuration

The proposed structural configuration is a rectangular concrete structure which is subjected to the explosion of 5 kg of TNT detonated at a distance 3 m from the structure as shown in Fig.5 to detect the effect of blast waves on a structure as a whole.The dimensions of the structure are as shown in Fig.6 where the length of the structure is 5.0 m,width 4.0 m and height 3.0 m.The properties of the used materials are shown in Tables 1-3.

2.4.Finite element model

Fig.2.The pressure measured from the experimental test and the numerical Simulation of free field explosion.

Fig.3.The numerical model used for validation for the second test.

Fig.4.The pressure measured from the experimental test and the numerical simulation of explosion in the presence of a concrete barrier.

Four models were investigated in this study to compare between different configurations of structures and thicknesses of walls.The first model WS1 is a classic rectangular structure with walls of 20 cm thickness,the second model WS2 is the same as the first one but with 40 cm thickness of walls,the third model WS3 is distinguished with the presence of double walls with air filling inside the double wall.the fourth model WS4 is the same as the third model but the air inside the double wall is replaced with aluminum foam filling as shown in Fig.7 (the roof is eliminated from the figure to show the details of the walls).The walls of the structure are plain concrete except for one wall which is reinforced.Only one reinforced concrete wall is used to show the effect of reinforcement on the behavior of the wall without greatly increasing the computational cost of the model(the model needed about 240 h of running time on an I7 processor).

The mesh used in all models is unstructured rectangular grid as shown in Fig.8.where the space containing the whole model consists of 3,023,163 element,the concrete walls consist of 50,234 elements.the concrete roof consists of 7506 element while the aluminum foam part consists of 1400 element.The compressive strength of the normal strength concrete used in all concrete structures is 35 MPa.

First.the two models WS1 and WS2 were compared to assess the effect of increasing the thickness of walls from 20 cm to 40 cm then the models WS2.WS3 and WS4 are compared to assess the effect of splitting a single wall with 40 cm thickness to a double wallwith 20 cm thickness each and another model with aluminum filling instead of air filling.

Fig.5.Structural configuration of the proposed structure.

Fig.6.Dimensions of concrete structure.

Table 1 Physical properties for the aluminum foam material.

Remap technique is used in the numerical simulation [35].To allow the pressure of the blast to dissipate outside the air medium without reflecting and affecting the concrete target flow-out boundary conditions are applied on the exterior layer of the air medium except for the lower surface which reflects the pressure to imitate the effect of the ground.

Lagrange solver is used to describe the concrete target.TNT explosive is modeled using Jones-Wilkins-Lee equation of state.The equation of state used to model air is ideal gas equation of state.

2.4.1.Effect of wall thickness

The two models WS1 and WS2 were compared to assess the effect of increasing the thickness of walls from 20 cm to 40 cm.All the walls and the roof are modeled with ordinary concrete while wall No.4 is a reinforced concrete wall to assess the effect of reinforcement on the mitigation of blast waves while the other walls are simulated with ordinary concrete to reduce the computational time to a reasonable time.

2.4.2.Effect of filling material

Three models are compared to assess the effect of the presence of a filling material inside the walls of the concrete structure where the first model WS2 has no filling at all with wall thickness of 40 cm.the second model WS3 has a double wall each with 20 cm thickness and an air filling between the two walls with 20 cm thickness.The fourth model WS4 has also a double wall each with 20 cm thickness and an aluminum foam filling between the two walls with 20 cm thickness as shown in Figs.6 and 8.

2.5.Numerical results and discussion

This section presents and discusses the different effects of blast phenomena on different configurations of complete structures where four numerical models were established with different configurations and thicknesses of walls to investigate the effect of blast waves on deflection of walls.

Four gauges are fixed on the walls of the structures.The displacement vs.time history is investigated at each gauge to evaluate the peak displacement for the desired locations.Fig.9 shows the location of different gauges along the walls of the structure for model WS1 and WS2 to capture the maximum displacement that the wall experiences along the detonation process where the gauges are placed in the mid-point of each wall which is the point of maximum displacement.While for models WS3 and WS4 the gauges are placed in the mid-point of the inner wall to assess the effect of the material embedded between the two walls as shown in Fig.10.

The investigated parameters are the displacement and impulse which the wall experiences due to blast waves.The displacementtime and impulse-time histories for the models are shown below to compare between the effects of blast waves on different configurations of structures.

2.5.1.Thickness of walls

For Gauge 1 which is present in the midpoint of Wall 1.the maximum displacement measured in the Z-direction(which is the direction of the blast wave) is 411.66 mm for the model WS1 as shown in Fig.11 where the thickness of the wall is 20 cm while when the thickness of the walls was 40 cm in the model WS2 the maximum displacement of the wall in the Z-direction was 15 mm.

For Gauge 2 which is present in the midpoint of Wall 2.the maximum displacement measured in the X-direction(which is the direction of the blast wave) is 447.77 mm for the model WS1 as shown in Fig.11 where the thickness of the wall is 20 cm while when the thickness of the walls was 40 cm in the model WS2 the maximum displacement of the wall in the X-direction was 41.6 mm.It is observed that values of maximum displacement are too large asthis wall is the wall facing the detonation and the closest to the center of detonation.

Table 2 Physical properties for the concrete material.

Table 3 Physical properties for the steel material.

Fig.7.Configurations of WS1.WS2.WS3 and WS4.

Fig.8.Elements of the proposed model.

For Gauge 3 which is present in the midpoint of Wall 3.the displacement measured in the X-direction(which is the direction of the blast wave)is 307.48 mm for the model WS1 as shown in Fig.12 where the thickness of the wall is 20 cm while when the thickness of the walls was 40 cm in the model WS2 the displacement of the wall in the X-direction was 16.78 mm.

For Gauge 4 which is present in the midpoint of Wall 4.the displacement measured in the Z-direction(which is the direction of the blast wave)is 390.95 mm for the model WS1 as shown in Fig.12 where the thickness of the wall is 20 cm while when the thickness of the walls was 40 cm in the model WS2 the displacement of the wall in the Z-direction was 17.54 mm.By comparing the results of displacement for Wall 1(unreinforced)and Wall 4(reinforced),it is observed that the results are the same which shows that adding reinforcement has an insignificant effect on reducing the displacement but it should affect the damage and fragments ejected from the walls after the blast.These parameters are not discussed in this study as they need a very long processing time to get their values so this would double or triple the computational time which is already too long (～240 h) as the number of elements for the structure is huge (more than 3 million elements).

By comparing the curves above,it is observed that by increasing the thickness of walls from 20 cm to 40 cm the displacement decreases tremendously by an average percentage of 94.25%.this is due to the increase in the integrity and rigidity of the walls due to the increase in the thickness.

Fig.13 shows the values measured for impulse for Gauge 1 for models WS1 and WS2.This figure shows that the maximum impulse of WS1 is 8.017 × 104and the maximum impulse of WS2 is 4.03 × 104.so the model WS2 has lower impulse than WS1.

Fig.13 shows the values measured for impulse for Gauge 2 for models WS1 and WS2.This figure shows that the maximum impulse of WS1 is 1.02 × 105and the maximum impulse of WS2 is 1.62 × 104.So the model WS2 has lower impulse than WS1.

Fig.14 shows the values measured for impulse for Gauge 3 for models WS1 and WS2.Thisfigure shows that the maximum impulse of WS1 is 7.9 × 104and the maximum impulse of WS2 is 3.96 × 104.So the model WS2 has lower impulse than WS1.

Fig.9.Locations of gauges for WS1 and WS2.

Fig.14 shows the values measured for impulse for Gauge 4 for models WS1 and WS2.This figure shows that the maximum impulse of WS1 is 7.39 × 104and the maximum impulse of WS2 is 4.11 × 104.So the model WS2 has lower impulse than WS1.

By reviewing the results of the impulse for Gauge 1.Gauge 2,Gauge 3.and Gauge 4 from Figs.13 and 14.We can observe that increasing the thickness of the walls decreases the impulse applied on the wall for the whole four walls either it is reinforced or unreinforced so the effect of the average blast forced applied on the walls decreases by increasing the thickness of the walls.where when the thickness is increased from 20 cm to 40 cm the impulse decreased by an average percentage of 57.24%.

Fig.10.Locations of gauges for WS3 and WS4.

2.5.2.Filling of walls

For Gauge 1 which is present in the midpoint of Wall 1.the maximum displacement measured in the Z-direction(which is the direction of the blast wave)is 15 mm for the model WS2 where the wall is one unit with a thickness of 40 cm while when the wall is splitted to 2 walls with 20 cm thickness each with an air filling inside in model WS3.the maximum displacement of the wall increased to 256.1 mm.while the displacement of the wall for the model WS4 was 3.79 mm as the filling was aluminum foam as shown in Fig.15.

For Gauge 2 which is present in the midpoint of Wall 2.the maximum displacement measured in the X-direction(which is the direction of the blast wave) is 41.6 mm for the model WS2 where the wall is one unit with a thickness of 40 cm while when the wall is splitted to 2 walls with 20 cm thickness each with an air filling inside in model WS3.the displacement of the wall increased to 205.18 mm while the maximum displacement of the wall for the model WS4 was 3.24 mm as the filling was aluminum foam as shown in Fig.15.

For Gauge 3 which is present in the midpoint of Wall 3.the maximum displacement measured in the X-direction(which is the direction of the blast wave) is 16.7 mm for the model WS2 where the wall is one unit with a thickness of 40 cm while when the wall is splitted to 2 walls with 20 cm thickness each with an air filling inside in model WS3.the displacement of the wall increased to 230.28 mm while the maximum displacement of the wall for the model WS4 was 3.73 mm as the filling was aluminum foam as shown in Fig.16.

For Gauge 4 which is present in the midpoint of Wall 4.the maximum displacement measured in the Z-direction(which is the direction of the blast wave)is 17.54 mm for the model WS2 where the wall is one unit with a thickness of 40 cm while when the wall is splitted to 2 walls with 20 cm thickness each with an air filling inside in model WS3.the displacement of the wall increased to 251.5 mm while the maximum displacement of the wall for the model WS4 was 8.49 mm as the filling was aluminum foam as shown in Fig.16.

We can observe from the results shown above for the four gauges that the values of displacement for all the gauges for WS2 increased tremendously in WS3,this is due the presence of the air fliling between the double wall which reflects the blast wave inside the two walls and magnifies the blast wave and increases the displacement measured in the inner wall greatly unlike the effect of the aluminum foam present in WS4 which absorbs the blast wave instead of magnifying it and reduces the values of displacement to the minimum value.

Fig.17 shows the values measured for impulse for Gauge 1 for models WS2.WS3 and WS4.This figure shows that the maximum impulse of WS2 is 4.03 × 104.the maximum impulse of WS3 is 2.64 × 104while the maximum impulse for WS4 is 2.31 × 104.So the model WS2 has the highest impulse followed by WS3 then WS4 which has the lowest impulse.

Fig.17 shows the values measured for impulse for Gauge 2 for models WS2.WS3 and WS4.This figure shows that the maximum impulse of WS2 is 1.62 × 104.the maximum impulse of WS3 is 2.44 × 104while the maximum impulse for WS4 is 1.97 × 104.So the model WS3 has the highest impulse followed by WS2 then WS4 which have the lowest impulse.

Fig.18 shows the values measured for impulse for Gauge 3 for models WS2.WS3 and WS4.This fgiure shows that the maximum impulse of WS2 is 3.96 × 104.the maximum impulse of WS3 is 2.42 × 104while the maximum impulse for WS4 is 1.81 × 104.So the model WS2 has the highest impulse followed by WS3 then WS4 which has the lowest impulse.

Fig.18 shows the values measured for impulse for Gauge 4 for models WS2.WS3 and WS4.This fgiure shows that the maximum impulse of WS2 is 4.11 × 104.the maximum impulse of WS3 is 2.39 × 104while the maximum impulse for WS4 is 2.04 × 104.So the model WS2 has the highest impulse followed by WS3 then WS4 which have the lowest impulse.

We can observe from the results shown above for the four gauges that the values of impulse for all the gauges decreases when we split the wall into two walls with the same thickness and an air filling inside in WS3 with an average percentage of 38.38% when compared to WS2 and the impulse decreases again in WS4 with the aluminum foam filling with an average percentage of 49.11%compared to WS2.The only exception for these conclusions is the results of Gauge 2 where the impulse increased in WS3 and WS4 compared to WS2 and this is probably Gauge 2 is the nearest one to the center of explosion and Wall 2 is perpendicular to the directionof the waves so splitting the wall increases the impulse.

Fig.11.Displacement for gauge 1 and gauge 2.

Fig.12.Displacement for gauge 3 and gauge 4.

Fig.13.Impulse for gauge 1 and gauge 2.

Fig.14.Impulse for gauge 3 and gauge 4.

Fig.15.Displacement for gauge 1 and gauge 2.

Fig.16.Displacement for gauge 3 and gauge 4.

Fig.17.Impulse for gauge 1 and gauge 2.

Fig.18.Impulse for gauge 3 and gauge 4.

3.Conclusion

In the current work.the effect of blast waves on complete structures and how to enhance the response of these structures to blast waves using different structural configuration is studied.A nonlinear three-dimensional hydro-code numerical simulation was carried out using AUTODYN-3D to investigate the effect of blasting of a high explosive material(TNT)against several configurations ofthe composite structure.Numerous numerical models were established to study the effect of varying the thickness of walls and the effect of adding an air layer or aluminum foam layer inside two layers of concrete in mitigating the effect of blast waves on the structure walls.The main findings of this study can be drawn as follows:

1.Generally.increasing the thickness of the concrete walls decreases the deflection and impulse of different walls with a reasonable percentage.

2.It is concluded that by increasing the thickness of walls from 20 cm to 40 cm the displacement decreases tremendously by an average percentage of 94.25%.this is due to the increase in the integrity and rigidity of the walls due to the increase in the thickness.

3.It is observed that increasing the thickness of the walls decreases the impulse applied on the wall for the whole four walls either it is reinforced or unreinforced so the effect of the average blast forced applied on the walls decreases by increasing the thickness of the walls.where when the thickness is increased from 20 cm to 40 cm the impulse decreased by an average percentage of 57.24%.

4.Reinforcing the walls has an insignificant effect on the deflection of the walls while it may have a good effect on damage and fragments.

5.Generally.Splitting the thickness of the wall to two walls with an air gap between the walls has a negative effect of the deflection and impulse as it increases it tremendously while putting aluminum foam as a filling decreases the deflection with a reasonable percentage.

6.In case of filling.the values of displacement increase tremendously.this is due the presence of the air filling between the double wall which reflects the blast wave inside the two walls and magnifies the blast wave and increases the displacement measured in the inner wall greatly unlike the effect of the aluminum foam present which absorbs the blast wave instead of magnifying it and reduces the values of displacement to the minimum value.

7.In case of filling.the values of impulse decrease when we split the wall into two walls with the same thickness and an air filling inside with an average percentage of 38.38% and the impulse decreases with the aluminum foam filling with an average percentage of 49.11%.