The protection of structures against explosive loadings T. Łodygowski and P.W. Sielicki Poznan University of Technology, pl. M.Skłodowskiej-Curie 5, 60-965 Poznań, Poland

The paper describes the behaviour of structures subjected to explosive loading. Modeling techniques in focus of retrofit design for increase the blast resistance of masonry walls are discussed. The structure vulnerability level under explosive is obtained in distance, charge weight and brick topology function. Forproperties of bricks the elastic constitutive relation is used and for the mortar the Cumulative Fracture Criterion (CFC) is accepted. The CFC criterion is adopted to describe the degradation of the mortar phase under fast dynamic processes and to present the wall destruction. The experimental analysis is performed in the environment of the finite element code Abaqus. The instructive conclusions are in focus of the presentation. Keywords: explosive, protection, reinforcement, masonry 1. Introduction to the explosive threats

Current design style is improved by some government agencies [x] dealing with amissing part of the structure (i.e. column, wall) scenario. This approach makes really sense for buildings subjected to the blast in particular. The headquarters likeembassies, banks, hotels etc. are very concerned about the possibility of this kind ofloading. The fundamental threat is terrorism and it may involve a combination ofthermal, impact and blast loads. Nowadays, retrofitting existing buildings to increase their explosive resistance is great challenge for the engineers. The accuracy of anexample of the blast retrofit [5] is presented in Fig.1.

a) b) Figure 1. Composite retrofit of the reinforced concrete column [5] a) Without any blast resistance system b) With use of carbon fibre

In summary with respect to reinforcement buildings to prevent collapse mucheffective research is still needed. The numerical modeling is the crucial point to reliable attains the objective. There is important because it can limit the costs of experiments and can lead to better understanding of the complex processes. The finiteelements method (FEM) may be helpful to estimate of the pressure distribution,caused by blast or impact loadings, which depends on time and position in surrounded space. The finite element code Abaqus/Explicit is used to serve as computationalenvironment to overcome the modeling difficulties. 2. Assessment of building explosive vulnerability The simple way to assess of the building explosive vulnerability provide to the analysis of nearest neighbourhood of the structure. The first step before taking any protective investigation is to consider the threat to which part of structure might besubjected. This is often the hardest aspect of general process. The response of the building personnel, the acceptable level of injuries are strongly connected with thestructure response. To accomplish effectively the blast influence on the structure the list of twelve checkpoints (Tab.1) is suggested to verify. Table 1. Blast-resistant pre-design questions by Baker et al. [4]

No questions 1 2 3 4 5 6 7 8 9

10 11 12

Where is the structure to be sited? What layout is required? What is the structure function? Design for static loads Assess threat Calculate blast loads Assess any fragment characteristics Calculate any fragment impact loads Assess level of any crater eject loading Assess whether ground-shock may be significant Carry out preliminary sizing Analyse response as simply as possible

The upper points seems be good only for a new designed buildings. To upgrade an existing structure the approach is so transparent and it requires some modification. Firstly, it is necessary to categorize the structure under consideration to enable to raterapidly the ability of the structures to resist the various dynamic loadings associatedwith particular threats. Categories could include different types of engineering structures like: underground arches or tunnels, masonry buildings, reinforced concreteor steel frames. Secondly, it will be necessary to assess the level of damage likelyfrom a particular threat. If they are available, this could be done by the use of damagecurves in the form of pressure-impulse diagrams. It will then be necessary to provide

the required protection against the threat. To protect against blast overpressures the use of blast walls or any kind of obstacles has already been mentioned. Reinforced concrete could be deployed but considerationcould be given to the use of precast concrete planks or concrete blockwork built between rolled steel joints used as columns. It may also be possible to make use ofsuitably supported blockwork. Sacrificial roofs have been commonly used as integral parts of new structures. Here the use of scaffolding for temporary protective purposes of addition of trussed timber rafters for permanent protection could be the real option.Another option to provide extra stand-off could be encase a vulnerable part of the structure in precast cladding. The counter ballistic impact and other forms of impulsive loads, key structural elements can be protected by the use of steel skins tied to the parent structure with theintermediate energy absorbers. For example, a sand infill will absorb the jet form ashaped-charge attack. The use of stiffening elements can increase resistance where the strength of element joints: beam-column can be increased by the use of steel plates bolted or adhesively bonded to the structure (Fig.2b). Against ballistic penetration the use of arresting nets and screens is effective. Interlocking or mortar-bonded concrete block walls and rapidly assembled precastconcrete panel walls could be considered. It is well known that plain concrete can produce fragments on the front face and a kind of spall which is blown off the rear face, thereby creating secondary missiles. The use of steel or polypropylene fiberreinforced concrete is advocated which is effective both in improving tensile strengthand in energy absorption. The more conventional protections such as the steel-concrete sandwich construction are also applicable in the upgrade of existingstructures (Fig.2b).

a) b) Figure 2. Reinforcement method [5]

a) SidePlateTM retrofit connection b) Concrete filled hollow section of column In design and building a new protective structure consideration must be given to constraints on time and cost of construction as well as any constructional and technicalrestrictions. The comparison of protection costs with the cost of any losses is very useful. It is obvious that the cost of protection rises with the level of requirements. As

protection level is increasing so the cost associated with total protection increase too,but probability of any losses decrease as well. If the building will be 100% protectedthere are no losses. The optimum level, regarding the cost of protection is presented inthe following graph, Fig.3.

Figure 3. Cost of protection in comparison with protection level [1]

The sum of two curves (the total cost) corresponds to the minimum of total cost of protection with relatively good protection. 3. Blast analysis using FE There is prepared an example of virtual building (Fig.4) for which the different threatsare considered. The first goal is to define the real safing zones and real hazard of the building. The building represents a shopping centre which is covered with glass elevation and masonry walls. The high of the centre equals to 15m. There exist some preliminary features of the outline design. There are three different threats taken intoconsideration as an example. The first one is the explosions of the fuel train. The railsare located 100 m far from the side of elevation in a southern direction. The second threat is the explosion of vehicle bomb in the nearest car-park area, where vehiclebomb means: vehicle modified to conceal and deliver large quantities of explosive tothe target. The terrorists using bombing vehicle can inflict a large number of casualties and cause a lot of damage. The last one is the explosion of the gas tank which is located 120 meters from the west-south corner of the building.

Figure 4. Layout of virtual building and an exampled surrounding area

For every building always there are the natural and artificial explosive barriers, which can decrease the blast effects. The most popular of these obstacles are soil banks, trees, bollards and others. The bollards are designed to prevent any breakthrough ofthe perimeter protective area by any vehicle etc. The vehicle obstacles are located at the building entrance only. The broken line on the front of building, see Fig.4,represents the concrete bollards which constrain the car access to the building successfully. In that reason, in analyzed example the possibility of vehicle explosion inside the building is ignored. The exampled bollard schemes are presented in Fig.5.

a) b) Figure 5. a) The popular blast resistant barriers [6] b) Jersey-Barrier scheme

To obtain the most dangerous event the all three presented above cases have to be considered. In Table 3, the minimum scaled distance as a function of real distance and charge mass is determined basing on the commonly used simplified formula [7]:

,33 ⎥

⎥⎦

⎤

⎢⎢⎣

⎡=

kgm

wSZ (1)

where S is the distance from the charge in the meters and w means the charge mass expressed in kilograms of TNT. It estimates in the fastest way the most dangerous threat as well as the highest strength of explosion. At the first stage, the conversion of the actual charge mass into the equivalent TNT has to be done. The shortest way is to multiply the mass of the charge by a specific energy ratio. The conversion factors forthe most popular materials are collected in Table 2. Table 2. Conversion factors base on the specific energy [11]

Explosive Specific energy TNT Equivalent multiplier TNT Exampled Petrol Exampled Gas Liquid Nitro-glycerine Semtex C4

4.520e6 J/kg 4.395e6 J/kg 4.410e6 J/kg 6.700e6 J/kg 5.660e6 J/kg 4.870e6 J/kg

1.000 0.970 0.975 1.481 1.250 1.078

Table 3. The Blast threats in order

Event name Distance from the building

TNT Equivalent Scaled distance Threats

in order 10 tanks (496t) of fuel Vehicle bomb Gas tank 785m3 (533t)

100m 20m 120m

482 000 kg 1600 kg 520 000 kg

1.275 m/kg1/3

1.799 m/kg1/3

1.492 m/kg1/3

1 3 2

The scaled distance results as a popular approximation of real hazard indicates the fuel train as the most dangerous threat. Nevertheless, there are exist the natural barriers which predispose the vehicle bomb as the primary hazard. The first reason is the railway line is situated 5m below the clearing of the land, and the second one is the district around the gas tank which is covered with 5m high concrete wall and densely wooded area. The both barriers strongly decrease the blast wave effects on the building. The vehicle threat is accepted to further analysis. 3.1. Numerical study This chapter contains the numerical computations dealing with blast propagation in the surrounding air space and its distribution on the walls of the centre. There are prepared 3-D numerical examples: three global investigations to prove that the vehiclebomb is the most dangerous threat and the fourth one analysis in which the selected structure element, the masonry wall, is subjected to explosion of vehicle bomb. The graphic scheme of the analyzed task is presented in Fig.6. The origin points of thecharges are located in different distances from the front surface of the building

according to the results presented in Table 3.

Figure 6. Plan of the area

The space area under consideration is of dimensions about 500m by 500m. The building is placed in the center. The right part of Fig. 6 represents the cross-sections along the action line of the charges. The pressure changes close by the walls aremeasured, to assess the blast wave action on the side elevation of the building. The virtual 3-D space is built in the environment of Abaqus CAE. The space area contains building and the terrain topology. The ground and shape of the structure are accepted as rigid. The air is meshed by cubic finite elements and subjected to analysis of acoustic pressure distribution using an ideal gas equation:

( ),ZA TTRpp −=+ ρ (2)

where pA is the ambient pressure, ρ is initial density of air, R is gas constant, TZ and Tare the temperatures. TZ corresponds to -273.15°C. Moreover, to describe correctly the pressure wave propagation in the air, which is produced by detonation, it is necessaryto simulate the behavior of the charge. In all three examples the charge mass ofseparate threats are converted to TNT equivalent mass. For the numerical solution ofthe detonation process, the pressure p was is accepted according to the Jones-Wilkins-Lee [11] equation of state for an explosive material:

( ) ,exp1exp1, 00

20

202

01

010 mm ER

RBR

RAEp

ρωρ

ρρ

ρωρ

ρρ

ρωρρ +⎟⎟

⎠

⎞⎜⎜⎝

⎛−⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛−⋅⎟⎟

⎠

⎞⎜⎜⎝

⎛−= (3)

where A, B, R1, R2, ,ω are material constants, Em0 is the internal energy per unit mass, ρ0 is the initial density of explosive material and ρ is the current density of

detonation product. The values of material constants accepted for the numerical analyses are presented in Table 4. Table 4. Used constants

Air Explosive R 287 [J/(kg K)] A 3.73e11 [Pa] ρ 1.293 [kg/m3] Β 3.74e9 [Pa] pA 101325 [Pa] R1 4.15 [-] Em0 0.193e6 [J/kg] R2 0.9 [-] TZ 0 [K] Em0 5e6 [J/kg] T0 288.4 [K] Ω 0.35 [-] cv 1003.5 [J/(kg K)] νd 6930 [m/s] ρ0 1630 [kg/m3]

In general, the analysis of blasts is a very complex problem. For this reason there isassumed the splitting into two steps. In the first one the pressure that reaches the structure and in consequence predisposes the most dangerous pressure loading schemeis considered. This loading is transferred to the second step which contains only structural element i.e. a masonry wall which is subjected to blast wave action. The masonry wall will be retrofitted by steel reinforcement in the last analysis to improve the resistance of the structure. The last example is the masonry wall which is used to cover the front entrance to thebuilding. The wall is build periodically of regular bricks (0.25m by 0.12m by 0.06m) and mortar with bad and head joints of 0.01m thick. The structure under considerationis of dimensions 2m by 2m. The wall thickness as for single brick is 0.12m. Themasonry wall combines two separate phases as bricks and mortar and is divided into two material sections. The constitutive model for bricks is elastic without any damagecriteria while for mortar there is employed CFC (Cumulative Fracture Criterion):

( ) ( )

( ) ,00 0

0eqF

eqF

t T

eqF

eqF

c tifdtttc

σσσ

σα

>⎟⎟⎠

⎞⎜⎜⎝

⎛= ∫ (4)

which was specified and discussed in other works [8,9]. In the numerical examples themortar elements are deleted only if the CFC is accomplished. The three edges of thewall are fixed while the top one remains free. This one is loaded by compressive pressure and simulates the loading which comes from the ceiling. Finally, there is assumed the ideal spherical blast of medium vehicle bomb (1600kg of TNT charge) infront of the main entrance of the building. The ground reflection is taken into consideration. The job uses the replaced loading surfaces, see Fig.7, where α parameter is directly connected with a scaled distance. The numerical model is symmetric and it consists of 0.24e6 linear 8-node finite elements. This approach allows for neglecting a contact problem on the mortar-brick bond.

Fig.7 Analytical loading topology function

This approach considerably accelerates the time of computation without any substantial influences on the results. The alpha corresponds to the distance between the obstacle and the charge. The evolution of pressure surfaces depending on α ispresented in Fig.7. The α parameter is changing in the range from 0.001 to 10; the lower value corresponds to the explosion directly on the obstacle; α grows withincreasing the distance from the charge. The further study of the α influence is not thegoal of this presentation, but the following formula is used:

.)(

),,( 22 ααα

++=

yxyxp (5)

The values, surface obtained from Eq.5, are multiplied by the pressure received of the most dangerous threat which is presented in Fig.9. The loading surface is thensubjected to the masonry wall, what is presented in the last example. 3.2. Results and remarks There are performed numerical analyses for all considered threats. The graphs, Fig.8, represent the pressure maps, obtained only for the 1st threat in agreement with Tab.2. The maps show the pressure in different time instants after detonation: a) t=0.019s, b) t=0.063s, c) t=0.090s. The introduced numerical analyses are performed for 3D space to obtain results close to reality. The part of our research [12] shows that 2D solution is only a simplification of real outcome and may be used only as the first approximation of the pressure data estimation.

a) b) c) Figure 8. Pressure map for three 1st threat

The upper maps represent the pressure changes in the air after explosion of ten tanks of fuel. The down-left corner of the graphs is the charge center and the pressure waveis propagating to the right side which is in the distance of 100 m. The bottom edge represents the rigid ground and the right edge the building surface. The values of over-pressure are compared with the commonly used [2,3,13] empirical solutions. The results of the comparison for all the threats are collected in Fig.9.

Figure 9. Comparison of pressure evolution for considered threats The numerical solutions are performed with consideration of terrain topology also (1a: sand bank and 2a: rigid concrete wall). The continuous lines show the air pressurechanges, obtained in an empirical way, in distance dealing with Table 3. where the history of over-pressure in time function for spherical space is often presented byexponential functions such as the most important Friedlander equation [1,13]:

.)(exp1)(00

⎟⎟⎠

⎞⎜⎜⎝

⎛ ⋅−⎟⎟

⎠

⎞⎜⎜⎝

⎛−⋅=

ttpb

ttptp C

CFR (6)

In this equation pc is the peak of overpressure and t0 positive phase duration, b is so called wavefront parameter and it depends on pc, t means time. These parameters are crucial to obtain real pressure time relation. The dash lines represent the numerical results performed with rigid ground. The last type of lines: the doted ones shows the numerical results which take into account the true terrain topology. The extra outcomes: maximum over-pressures, arrival time, positive time duration and a positive impulse of pressure are collected in Table 5. Table 5. Results comparison

Finite elements analysis Empirical results

use of rigid ground and terrain topology

Threat 1 Threat 2 Threat 3 Threat 1 Threat 2 Threat 3 Threat 1 Threat 2

Wave arrival time [s] 0.139 0.191 0.035 0.120 0.149 0.023 0.175 0.233

Over-pressure duration [s] 0.109 0.119 0.019 0.025 0.018 0.012 0.045 0.037

Positive impulse [Pa·s] 27857 23194 2947 7193 4042 4132 9041 10129

Maximum over-pressure [Pa] 509263 388508 317025 573148 461926 688642 405438 541677

The pressure values obtained in empirical way are compared with FE analysis. The results of maximum over-pressures predisposes the vehicle bomb threat to next analysis as the most dangerous. Finally, the failure scheme of the masonry wall under vehicle bomb is analyzed. The 1-side brick wall has been totally destroyed in the analysis, in that reason the retrofitting of the structure is undertaken. There are fixed the steel profiles on the rear side of the wall to reinforce the structure, see Fig.10. There are proposed some different reinforced schemes.

a) b) Figure 10. Reinforced profiles: a) un-reinforced scheme b) reinforced scheme

The reinforcement is fixed by rigid anchors which connect the profiles with separatebricks. The failure analysis is performed with yield stress equals to 250 MPa. The selected schemes of the structure failure, before and after retrofitting process, are presented in Fig.11. The time moment is fixed the same for both the maps.

a) b) Figure 11. Wall under explosion: a) un-reinforced scheme b) reinforced scheme

The above picture shows destroyed elements of mortar for 0.1 s after detonation (0.06 s under blast wave) and the global failure of the brick wall. In the second graph, Fig.11b, the masonry remains really stable. The employing of steel profiles as the reinforcement causes in substantial increasing of blast resistant of the wall and may be used as a good solution to protect the brick structure under explosion of conventionalcharges.

4. Conclusions Overall, the three analyses of threats successfully demonstrate the possibility of using FE-modeling. The results from the retrofit analyses are presented in Fig.11. There is explained and proved that FE-modeling technique can be useful when considering the analyses of explosion processes and the structural response. The calculations prove that proposed retrofit concept can provide a valuable study on how to add theprotection in traditional structure design. The retrofitting of brick wall structure with the steel profiles as the reinforcement improves significantly the blast resistant. The reduction of the computational time can be successfully reached by introducing the empirical solutions of pressure values and FE-modeling technique. In the future study [13], the results of the initial compression stress of the wall (pre-stressing) may involve the influence of the mortar damage with the reinforcement at the same time. Acknowledgement The support of the Ministry of Science and Higher Education under the grant N519419435 is kindly acknowledged.

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13. Łodygowski T. and Sielicki P.W., Failure of the masonry structure under blast loading, Dynamic fracture and damage of brittle and ductile materials and its industrial applications, Poznań 2008. Zabezpieczenie konstrukcji narażonych na działanie wybuchu W pracy omówiono zachowanie się konstrukcji pod wpływem wybuchu. Oceniając potencjalnezagrożenia powstałe w wyniku eksplozji materiału wybuchowego, analizowano podatność na uszkodzenie wirtualnego budynku. Modelowano różne warianty wzmocnienia ściany murowanejpoddanej działaniu fali uderzeniowej. Uwzględniono dwie fazy materiału o różnych właściwościach dlacegły i zaprawy. Sprężysty model materiału zaproponowano dla cegieł natomiast, zachowanie się wraz zezniszczeniem zaprawy opisano przy pomocy kumulatywnego kryterium (CFC). Zastosowano metodę elementów skończonych, obliczenia wykonano w środowisku Abaqus/Explicit.