1 Introduction

International economic problems and power imbalances cause an increase in terrorist activities. These activities usually target people directly or civil engineering structures such as strategically important buildings and bridges. On the other hand, gas stations close to settlements and factories containing explosive substances may also lead to destructive explosions. Although various static and dynamic loads (dead, live, snow, wind, earthquake, etc.) are widely used in the design stage of civil engineering structures, explosion-based loads and effects are generally neglected (Altunlu 2008). The explosions caused by terrorism and/or accidental lead to serious damage and/or collapse in structures, economic losses, and most importantly endanger public safety. Therefore, the design of structures resistant to blasting loads has become one of the most important civil engineering issues in recent years (Toy and Sevim 2017).

In the past years, blasting effects on structural behavior and performance have been investigated from many perspectives using experimental, numerical, and empirical methods. The first studies on blasting behavior began in the early part of the twentieth century, and these studies have accelerated since the mid-center of the twentieth century. Hopkinson and Cranz (1915) conducted the first important study to investigate the explosion effects. In addition, various empirical formulas have been proposed in the literature to calculate the several blasting parameters such as peak pressure, impulse, and durations. The empirical formulas represent the relationship between the blasting peak pressure and the scaled distances of detonations that are calculated using the distance of the explosion center and charge weight. Brode (1955) performed numerical solutions of spherical blast waves and identified blasting parameters such as positive and negative phase impulses and durations for various radial distances. Henrych and Major (1979) presented the empirical formulas using several experimental data to the calculation of explosion parameters. Kingery and Bulmash (1984) proposed a polynomial formulation to estimate blasting peak pressure and impulse. Kinney and Graham (1985), Mills (1987), and Sadovskiy (2004) proposed useful empirical formulas to the determination of parameters of the explosion such as peak pressure and durations based on scaled distance. As well as empirical formulas, advances in computer technology have enabled the use of hydrocodes such as AUTODYN AND LS-DYNA that provide realistic modeling of the explosion behavior.

In the literature, the effects of blasting on the structural behavior were handled for various engineering structures such as buildings and bridges. Therein, many aspects of the subject have been examined using numerical, empirical, and experimental methods. The structures were exposed to blasting materials and blast-induced ground motions in these studies. Luccioni et al. (2004) investigated the blast-induced structural failure of RC building and presented a comparison of the real damages of an existing building subjected to explosion and the damages obtained from numerical analysis. Jayasooriya et al. (2011) examined the impact of near-field explosions on the load-bearing system of RC buildings in order to be used in designing strategies to mitigate the total and progressive collapse of the structures. Tang and Hao (2010), Son and Lee (2011), and Hashemi et al. (2017) numerically simulated the effects of explosions on the behavior of cable-stayed bridge and its structural elements. Kelliher and Sutton-Swaby (2012) stochastically modeled the blast load damage levels of RC building. Yalciner (2014) revealed the role of corrosion on the blasting response of RC buildings. Coffield and Adeli (2015) investigated the resistance of irregular steel structures with different bearing system types against blasting loads. Andreou et al. (2016) proposed a modeling approach to the evaluation of the effect of explosions on bridges. Hacıefendioğlu (2017) performed stochastic analysis of a highway bridge exposed to blast-induced ground motion. Sevim and Toy (2019) conducted numerical analyses of an existing building exposed to the explosion for different charge weights. In the literature, some researches were conducted on the blasting behavior of various engineering structures such as historical buildings, walls, and art structures, as well as buildings and bridges (Wu et al. 2005; Wei and Stewart 2010; Yusof et al. 2014; Hacıefendioğlu and Koç 2016). Besides, various studies were carried out to reduce the blasting effects and damages (Wu et al. 2004; Tan and Patoary 2009; Hao and Tang 2010; Aoude et al. 2015; Zhang and Philips 2016; Codina et al. 2017).

The infill walls are generally considered as a non-structural element and widely preferred for various purposes in civil engineering structures (Furtado et al. 2020). However, when the infill walls are exposed to loads, they interact with the load-bearing systems of structures. This interaction can lead to different failure modes in infill walls (Furtado et al. 2015). In addition, the load-bearing system and infill wall interaction remarkably contribute to the structural performance of structures. Therefore, the contributions and effects of infill walls on the structural behavior, especially considering earthquake loads, are an attractive research area. In the literature, many aspects of the responses and behaviors of the infill walls have been examined using numerical and experimental methods, in recent years (Al Hanoun et al. 2018; Furtado et al. 2018; Onat et al. 2018; De Risi et al. 2019; Di Domenico et al. 2019; Onat, 2019; Cavaleri et al. 2020; Ricci et al. 2020). On the other hand, the contributions and effects of infill walls in the design phase of the structures subjected to the explosion are generally neglected. However, the damages and/or failures of the walls subjected to explosive materials may lead to high-speed debris or structural collapse and may cause significant life and economic losses (Li et al. 2017). For this reason, the roles of infill walls on the blasting behavior should be considered in the design and construction of structures that may be exposed to bursting loads. The many aspects of the blasting responses of the walls have been examined using different methods. The experimental studies that can accurately represent the detonation behavior of the walls are among the frequently preferred methods for the walls. In these experimental studies, blasting responses of the walls built with different masonry units were handled for brick (Zapata and Weggel 2008), for clay brick (Shi et al. 2016; Li et al. 2017), for London brick (Keys and Clubley 2017). In addition to the blasting behaviors of the walls built with different masonry units, the strengthening materials were investigated to increase the blasting resistance of the walls. Davidson et al. (2004) and Chen et al. (2020) conducted experimental studies on the sprayed-on polymers to increase the blast resistance of the walls and panels. Besides, the fiber reinforced polymers such as carbon fiber reinforced polymer (CFRP) and glass fiber reinforced polymer (GFRP) were used by researchers to improve the detonation resistance of the walls and panels (Alsayed et al. 2016; Chen et al. 2020).

In this study, the effects of concrete strength and openings in the infill walls on blasting responses of RC buildings are investigated using numerical and empirical methods. In situ experimental tests are firstly carried out to verify the FE model criteria and assumptions. For this purpose, a test specimen was constructed using brick elements. The hollow ratio of the brick elements was determined in accordance with the requirements of the Turkish Earthquake Code (TEC 2018). The upper surface of the test specimen was constructed completely open to the atmosphere in order to compensate complex effects of blasting. The blasting experiments were executed using 40 g, 150 g, and 290 g capsule sensitive TNT explosives on the inner base center of the specimen. Then, two RC buildings are selected as application. FE models of the RC buildings are constituted in ANSYS Workbench (2016). The blasting analyses are carried out by using ANSYS AUTODYN (2016). The blasting pressures, displacements, absorbed and released total energies, and damage ratios are selected as comparison parameters. Moreover, the blasting peak pressure values are calculated by using empirical formulas purposed by Brode (1955) and graphs given in “Structures to Resist the Effects of Accidental Explosions” (UFC 3-340-02 2008). Figure 1 shows the flowchart of the study. The results show that the blasting responses of load-bearing systems and infill walls are changed significantly due to concrete strength and opening in infill walls.

Fig. 1
figure 1

The flowchart of the study

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2 Blast Theory

The detonation of high-intensity explosives leads to blast waves. The blast waves produce a shock wave effect that spreads from the explosion center to the atmosphere with hemispherical form. After the shock wave releases from the center of the explosion, it reaches the maximum pressure (\(P_{so}\)) and speed value in a short time like a millisecond. As the shock wave moves away from the explosion center, the surface area expands and the pressure value gradually decreases. This process continues until a balance is achieved with the air surrounding the shock wave. This process is defined as the positive phase duration (\(t_{o}\)). During the propagation of the shock wave, the pressure value in the region behind of the shock wave falls below the ambient pressure and creates negative pressure (\(P_{so}^{ - }\)). This process, which creates a vacuum effect, is defined as the negative phase duration (\(t_{o}^{ - }\)). The time-history graph of blast wave pressure is given in Fig. 2.

Fig. 2
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Evaluation of blast wave pressure (Ngo et al. 2007)

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In front of the shock wave, the air in the environment compresses according to the movement direction of the wave and moves together with the shock wave like a set. Thus, it creates a much larger positive pressure compared to the ambient pressure. This positive pressure in front of the shock wave is considerably higher than the negative pressure behind it. The negative phase duration is longer but less effective than the positive phase duration. It can be seen from the literature that the positive peak pressure that occur during the positive phase duration causes most of the damages in the structures and the negative pressure is neglected.

The explosions can be classified from various perspectives such as explosive substances and the blasting waveforms (Ullah et al. 2017). In general, these can occur in four main types: physical, chemical, electrical, and nuclear detonations. The environment in which the explosion occurs affects the explosion waves and the explosions can also be classified in this respect: free air blast, airburst, surface burst, fully vented, partially confined, and fully confined (UFC 3-340-02). The explosion responses of the buildings determine by using numerical, experimental, and empirical methods. Although experimental methods provide the realistic results, they are generally not preferred due to the dangers, difficulties, and formal procedures. In addition, it is impossible to conduct experiments in structures for all types of explosives. Therefore, empirical formulas used to estimate the parameters of large-scale explosions for various distances and charge weights can be preferred. Many empirical formulas for detonation parameters have been presented in the literature. In most of these, detonation parameters such as peak pressure and positive phase duration are identified with the scaled distance. The scaled distance (Z) calculates by using Eq. (1). In Eq. (1), R is an explosion distance between structure and explosion center (m) and W is the mass of explosive substances expressed in TNT explosive (kg).

$$Z = \frac{R}{{\sqrt[3]{W}}}$$
(1)

In this study, the maximum pressures were obtained with the empirical formula proposed by Brode (1955) and the graph given in UFC 3-340-02. These pressures were compared with the FE analyses results. The formulas purposed by Brode in 1955 for calculation of peak pressure based on the scaled distance are presented with Eq. (2).

$$\begin{gathered} P_{so} = \frac{6.7}{{Z^{3} }} + 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,for\,P_{so} > 10bar \hfill \\ P_{so} = \frac{0.975}{Z} + \frac{1.455}{{Z^{2} }} + \frac{5.85}{{Z^{3} }} - 0.019\,\,\,for\,0.1bar < P_{so} < 10bar \hfill \\ \end{gathered}$$
(2)

In the design of the structures, the graphs are presented by UFC 3-340-02 to determine the shock wave parameters of several blasting types. The graph of the positive phase shock wave parameters for a spherical TNT explosion from free air bursts is given in Fig. 3. In this graph, parameters such as peak pressure, reflected pressure, impulse, and velocity can be obtained depending on the scaled distance. In Fig. 3, Lw, Pr, and U are the wavelength of positive pressure phase, peak positive normal reflected pressure, and shock velocity. Besides, ir, is, ta, and to are represented reflected impulse, incident impulse, time of arrival of the blast wave, and duration of blast pressure, respectively.

Fig. 3
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Positive phase shock wave parameters for a spherical TNT explosion from free air bursts (UFC 3-340-02 2008)

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3 Experimental Tests

To determine the blasting response of structures, the experimental tests are not frequently preferred due to measurement costs, construction difficulties, risks, and formal procedures. For this reason, comparative studies are generally conducted using numerical and empirical methods in the literature. In this section, the experimental tests were carried out to verify the FE model. For this purpose, a test specimen was constructed using brick elements and blasting tests were conducted considering various charge weights which lead to different damage levels of the walls. Throughout this section, detailed information about the test specimen such as material properties and geometric dimensions was firstly presented. Then, details of the blasting test protocols and explosive substance to be used in the tests were described.

3.1 Specimens’ Detailing

According to the TEC, 2018, the hollow ratio of the brick elements was chosen as 45%. The material properties of the selected brick elements are given in Table 1. The width, length, and thickness of each masonry wall are 122 cm, 113 cm, and 8.5 cm, respectively. The mortar thickness was selected as 10 mm. While creating the test specimen, it is aimed to compare the experimental results with the numerical results and to show the accuracy of the parameters considered in numerical analysis. For this reason, a special scale coefficient was not taken into consideration and the simplest model features were used. The upper surface of the constructed model is completely open to the atmosphere. The wall supports were embedded in the foundation to prevent translations and rotations. The blasting loads have complex effects on the structures. If the slab and different boundary conditions are considered during the experiments, a variety of details such as the behavior of slab to wall connection and soil–structure interaction should be taken into account in the numerical analyses. This situation can cause the blasting effects on the wall to be more complex. For this reason, the complexity of structural behavior was reduced with these conditions that were considered during the experiments. The dimensions and photographs of the test specimen are given in Fig. 4.

Table 1 Material properties of the selected brick elements
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Fig. 4
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The constructed test specimen for blasting tests (all dimensions in cm)

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3.2 Test Methodology

Blasting tests were carried out 28 days after the walls construction to gain sufficient strength of mortars. During the experiments, 40 g, 150 g, and 290 g capsule sensitive TNT explosives were preferred to evaluate progressive blast damage of the test specimen. These charge weights were taken into consideration to investigate the blasting responses and behaviors of the wall in undamaged, damaged, and collapsed situations. The explosive substances were placed on the inner base center of the specimen. The TNT explosives were covered with a layer of sand to prevent the explosive from spreading around due to high pressure. The tests were performed by monitoring the damages levels without measurement devices, thanks to the selected explosive substance weights. Figure 5 presents the experimental setup and selected TNT explosives.

Fig. 5
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The selected capsule sensitive TNT explosive and blasting test setup

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3.3 Experimental Blasting Test Results

In the blasting tests performed with 40g TNT explosive, micro-cracks which provide the immediate occupancy performance level were monitored. The damages on the wall were also developed with the increase in the charge weight from 40 to 150 g. During the blasting tests carried out with 290 g TNT explosives, it was seen that the walls collapsed by separating from supports. Moreover, it was observed that the brick fragments spread to the environment at high speed due to the high-pressure effect caused by blasting. This situation clearly shows that if the necessary security measures are not taken during the blasting tests, serious dangers may occur for the safety of life and property. Figure 6 shows the collapsed masonry walls after the blasting test performed with 290 g TNT explosive.

Fig. 6
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The collapsed masonry walls after blasting test performed with 290 g TNT explosive

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3.4 FE model of the Test Specimen

FE model of the test specimen walls was constituted using the explicit dynamic analysis section in ANSYS Workbench. The blasting analyses were performed in ANSYS AUTODYN. The Lagrange theory that includes calculations for the conservation of mass, energy, and momentum was used for solid elements. Air volume and TNT explosives were modeled according to Euler’s theory. The macro-modeling approach was selected for the FE model of the walls. Mesh sizes were chosen as 100 mm for solid elements and 15 mm for air and TNT explosives as a result of the mesh converge analyses. During the experimental tests, the wall supports were embedded in the RC foundation to prevent translations and rotations. Therefore, fixed boundary condition was assumed at the bottom surfaces of the masonry walls. The 3D FE model of the masonry walls and the location of the TNT explosive are given in Fig. 7.

Fig. 7
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The 3D FE model of the masonry walls and the location of blasting material

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The analysis duration and time increment were taken as 3 ms and 0.01 ms to observe the pressure changes, precisely. In blasting analysis, suitable material properties and models should be selected to measure the overloads occurring within milliseconds. To this aim, Riedel–Hiermaier–Thoma (RHT) model (Riedel et al. 1999) was selected for brick and concrete in this study. This model has been experimentally tested on test specimens subjected to impulsive loads and has been determined to adequately reflect concrete material behavior during the explosion. Moreover, the P-alpha (Hermann 1969) equation of state was used for brick material. The air volume containing the brick elements and TNT explosives was modeled as ideal gas equation of state. The air is a gaseous substance and stress in itself is not occur. The air volume, which is not affected by fracture and principal stress changes, serves as a material that transfers stresses caused by the explosion. For the air volume, the density, room temperature, specific temperature, and threshold energy were used as 1.25 × 10−3 g/m3, 288.20 K, 717.59 J/kg K, and 2.07 × 105 kJ/kg, respectively. In the numerical model of the wall, the TNT explosives were represented using the Jones–Wilkens–Lee (JWL) equation of state. This equation of state, which is described by using the various parameters such as hydrostatic pressure, density, and the specific internal energy corresponding to the unit weight of TNT, reflects the properties of rapid expansion and diffusion, accurately. For the TNT explosives, the density, threshold energy, velocity, energy, and pressure of the blasting were used as 1.63 g/m3, 3681 kJ/kg, 6930 m/s, 6 × 106 kJ/m3, and 2 × 104 MPa, respectively. Table 2 summarizes the material properties and equations considered in analyses.

Table 2 Material properties and equations of state considered in the blasting analyses
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As a result of blast analyses, damage contour diagrams and maximum pressure values were obtained. The maximum pressure values were measured as 341 kPa at 0.50 ms for 40 g TNT explosive and 867 kPa at 0.41 ms for 150 g TNT explosive. As a result of analysis with 290 g TNT explosives, maximum pressure was obtained as 1590.7 kPa at 0.37 ms. The pressure value of 1590.7 kPa is considerably greater than the allowable stress of brick elements. This situation shows that similar to experimental tests, the masonry walls are completely demolished with 290 g TNT explosive. Also, it was revealed that the FE model was correctly constituted. The damage contour diagrams obtained for each scenario are given in Fig. 8.

Fig. 8
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Damage contour diagrams of test specimen for different blast scenarios

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4 Numerical Application

In this section, two RC building models were selected as an application to investigate the effects of concrete strength and openings in the infill walls on blasting responses. For these purposes, different opening ratios in the infill walls of the building models were taken into account, during the blasting analyses. Moreover, C25/30 (fck = 25 MPa), C30/37 (fck = 30 MPa), C35/45 (fck = 35 MPa), C40/50 (fck = 40 MPa), C45/55 (fck = 45 MPa), and C50/60 (fck = 50 MPa) concrete classes were used in the analyses to investigate the concrete strength effect on blasting behavior. The explosion material was selected as 100 kg TNT, and it was placed at the façade of the buildings. The TNT explosive was defined 0.5 m away from the buildings. Besides the numerical analyses, the maximum pressure values caused by the explosion are calculated using the empirical formula proposed by Brode (1955) and the graph given in UFC 3-340-02 2008.

The load-bearing frame of the RC buildings was formed with high ductile moment frames. The buildings were designed according to the requirements of the Turkish Standard 500 (TS500, 2000) and TEC 2018. The building models have two bays in the x-direction with 4.50 m and one bay in the z-direction with 6.20 m. The height of the structures is 3.00 m. The cross-sectional dimensions of the columns and beams are 60 × 30 cm and 50 × 30 cm, respectively. The slab thickness is selected as 12 cm. The reinforcing steel class is considered as S420 (fyk = 420 MPa). Longitudinal bars in all columns and all beams are calculated as 6ϕ20 and 6ϕ16, respectively. The confinement bars in all columns are ϕ8/100 mm for the confinement zone and ϕ8/195 mm for others. Moreover, the confinement bars in all beams are ϕ8/100 mm for the confinement zone and ϕ8/200 mm for others. The geometrical dimensions, plan views of the selected RC buildings, and cross sections of structural elements are shown in Fig. 9.

Fig. 9
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The 2D views of the RC buildings and the cross sections of the structural elements (all dimensions are in mm)

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FE models of the buildings were constituted using ANSYS Workbench and were transferred into ANSYS AUTODYN to perform explicit analyses. The Lagrange theory was used for solid elements. Air volume and TNT explosives were modeled according to Euler’s theory. To observe the homogeneous distribution of the explosion effects on the structure, an air volume was constituted, and the buildings were placed symmetrically in the center of air volume. Therefore, the dimensions of the air volume were calculated as 11 m × 4.5 m × 13.2 m in the x, y, and z directions, respectively. The mesh sizes were chosen as 100 mm for air and TNT explosives. The FE model of the buildings is given in Fig. 10.

Fig. 10
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The FE model of the building models

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In blasting analysis, suitable material properties and models should be selected to measure the overloads occurring within milliseconds. To this aim, the RHT model was selected for concrete material. Moreover, the P-alpha equation of state was used for concrete material. During the blasting analyses, the selected material parameters and mechanical properties for concrete material are given in Table 3. In addition, the Poisson ratio and weight per unit volume for all concrete classes are selected as 0.2 and 2.4 g/cm3, respectively. In Table 3, K, Ec, Gc, fck, and fctk are the bulk modulus, elasticity modulus, shear modulus, compressive strength, and tensile strength of concrete, respectively.

Table 3 The selected material parameters and mechanical properties of concrete material
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The reinforcing steel was considered as linear elastic, isotropic, and strain hardening. Johnson–Cook model (Johnson and Cook 1983) was used for the plastic response of reinforcing steel. The linear equation of state was used for steel material. The air volume containing the structures and explosives was modeled as the ideal gas equation of state. The JWL equation of state, which accurately reflects the properties of rapid expansion and diffusion, was selected for TNT explosives. The selected properties for reinforcing steel, brick, air volume, and TNT explosive are summarized in Table 4.

Table 4 The properties of reinforcing steel, brick, air volume, and TNT explosives
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In the blasting analyses performed with 100 kg TNT explosive, 29 gauge points for buildings were specified to monitor the displacements, pressures, damages, and total energies. In order to obtain the structural responses occurring at the different scaled distances and different facades of buildings, gauge points were placed in various specific points on all facades of the buildings including joints of the load-bearing system elements, structural elements-infill wall interaction regions, areas close to opening in infill walls. The structural responses of the models obtained from all gauge points were comparatively analyzed to accurately monitor the effects of concrete strength and openings in infill walls on blasting responses of the buildings. As a result of the comparisons, the critical gauge points where the maximum structural responses were obtained in both the load-bearing system and the infill walls were determined. The maximum responses were obtained from the gauge 27 for Model 1 and gauge 13 for Model 2. The gauges 27 and 13 are located on the façades of buildings and are closest to the explosion center. Similarly, the maximum responses in the infill walls are obtained from the façades of buildings, and these gauge points were determined as gauge 12 for Model 1 and gauge 26 for Model 2. In addition to the gauge points on the façade of the buildings, critical gauge points of both the load-bearing system and the infill walls (gauge 19, gauge 28 for Model 1 and gauge 6, gauge 29 for Model 2) were also determined on the back frontage to observe the effects of openings in infill walls on blasting responses. In the further sections of the study, the results obtained from the critical gauge points were investigated, comparatively. These all gauge points and determined critical gauge points are given in Fig. 11.

Fig. 11
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The selected gauge points for RC building models

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5 Evaluation of Blasting Analyses Results

This study is focused on the evaluation and comparison of concrete strength and openings in the infill walls effects on blasting responses of RC buildings. To this aim, two building models that have different opening ratios in the infill walls were taken into account, during the blasting analysis. In Model 1, openings were designed on the infill walls of all frontages so that the pressure caused by the explosion can easily enter and exit the building. In Model 2, the infill walls of the back frontage were considered as without openings. The other characteristics of the buildings were designed to be the same in order to make an accurate comparison. The openings in the infill walls are given in Fig. 12. During the blasting analyses, concrete strength was also used as an analysis parameter. To evaluation of the blasting analysis results, the pressures, displacements, absorbed and released total energies, and damage ratios obtained from blasting analysis were selected as comparison parameters. Four critical gauge points located on the façade and back frontage of building models were selected to evaluate these effects more clearly.

Fig. 12
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The opening ratios in the infill walls of all frontages

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To monitor the concrete strength effects on blasting responses, the time-histories of pressures at the all frontage for Model 1 and Model 2 are presented in Figs. 13 and 14. The pressure contour diagrams in the time step when the peak pressure is obtained are given in Figs. 15 and 16. The decreases in peak pressures with the increasing concrete strength were calculated based on C25/30 and presented in Fig. 17. It is shown from Figs. 13, 14, 15 and 16 that the peak pressures are found at the gauge 27 for Model 1 and gauge 13 for Model 2. The gauges 27 and 13 are located on the façades of buildings and are closest to the explosion center. Similarly, the peak pressures in the infill walls are obtained from the façades of buildings (gauge 12 for Model 1 and gauge 26 for Model 2). With the increase in concrete strength from C25/30 to C50/60, the peak pressure values decreased from 83.85 MPa to 74.45 MPa for Model 1 and 88.81 MPa to 68.83 MPa for Model 2. It can be seen from Fig. 17 that the peak pressures decrease by 11.21% for Model 1 and 22.50% for Model 2 with the increasing concrete strength. Moreover, the peak pressures in the infill walls of Model 1 and Model 2 are found as 2.70 MPa and 1.82 MPa for all concrete classes, respectively. These situations point out that the concrete strength is considerably effective on peak blasting pressures that occurred at carrier systems of RC buildings, although it is not effective on peak blasting pressures of infill walls.

Fig. 13
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The time-histories of pressures obtained from critical gauges of Model 1

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Fig. 14
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The time-histories of pressures obtained from critical gauges of Model 2

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Fig. 15
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The pressure contour diagrams obtained from 100 kg TNT explosive for Model 1

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Fig. 16
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The pressure contour diagrams obtained from 100 kg TNT explosive for Model 2

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Fig. 17
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The decreases (%) in peak pressures of Model 1 and Model 2 due to the increased concrete strength according to the C25/30

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The peak pressure values were obtained with empirical formulas recommended by Brode (1955) and graphs given in UFC 3-340-02. The scaled distance (Z) was calculated as 0.171 because 100 kg of TNT explosive was considered 0.5 m away from the building models. Therefore, the peak pressures were determined as 135.70 MPa for empirical formulas and 82.00 MPa for UFC 3-340-02. Moreover, it was determined that the peak pressures obtained with UFC 3-340-02 are similar to the values determined by numerical methods. The peak pressures of selected building models obtained from 100 kg TNT explosive are given in Table 5.

Table 5 Peak pressure values obtained from 100 kg TNT explosive
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On the other hand, the time-histories of pressures at all frontage for Model 1 and Model 2 are comparatively presented in Fig. 18 to determine the effects of infill wall openings on the blasting responses of the RC buildings. To this aim, the pressure C25/30 is considered. Also, the changes in peak pressures of Model 2 due to the openings in infill walls are shown in Fig. 19 for all concrete classes. It can be seen from Figs. 18 and 19 that the openings reduce the peak pressures of the infill walls contrary to the load-bearing system. The peak pressure of Model 2 increases 5.58% for C25/30, 3.99% for C30/37, 3.27% for C35/45, and 4.48% for C40/50, although it decreases 2.14% for C45/55 and 8.16% for C50/60, according to Model 1. In the literature, the infill walls which are regarded as the non-structural element and are directly exposed to blasting loads are generally evaluated for two perspectives: (1) a defense element against debris caused by explosion and (2) losses due to high-speed debris caused by damages or failures of the walls. Therefore, the contributions and effects of the infill walls and its opening on the blasting responses of the structures are generally neglected. However, the analysis results revealed that the peak pressures of carrier systems and infill walls are changed significantly due to opening in infill walls. Therefore, the roles of infill walls on the blasting behavior should be considered in the design and construction of structures that may be exposed to bursting loads.

Fig. 18
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The time-histories of pressures obtained from Model 1 and Model 2 for C25/30

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Fig. 19
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The differences (%) in peak pressures of Model 2 due to the openings in infill walls according to the Model 1

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The time-histories of displacements and contour diagrams of Model 1 and Model 2 are presented in Figs. 20, 21, 22 and 23, comparatively. Also, the maximum displacements and calculated differences for Model 1 and Model 2 with the increasing concrete strength (C25/30 referenced) are presented in Table 6 and Fig. 24. It can be seen from Figs. 20, 21, 22 and 23 that the gauges 27 and 13 for building models and gauges 12 and 27 for infill walls are critical in terms of displacements. These gauges are closest to the explosion center. The maximum displacements in Model 1 are calculated as 34.55 mm for C25/30, 32.82 mm for C30/37, 31.50 mm for C35/45, 28.72 mm for C40/50, 27.20 mm for C45/55, and 27.10 mm for C50/60. In similar to the Model 1, the maximum displacements in Model 2 decreased from 40.14 mm to 27.23 mm with the increasing concrete strength from C25/30 to C50/60.

Fig. 20
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The time-histories of displacements obtained from critical gauges of Model 1

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Fig. 21
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The time-histories of displacements obtained from critical gauges of Model 2

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Fig. 22
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The displacement contour diagrams obtained from 100 kg TNT explosive for Model 1

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Fig. 23
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The displacement contour diagrams obtained from 100 kg TNT explosive for Model 2

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Table 6 Maximum displacements obtained from 100 kg TNT explosive
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Fig. 24
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The decreases (%) in maximum displacements of Model 1 and Model 2 with the concrete strength increasing from C25/30 to C50/60

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It can be seen from Fig. 24 that maximum displacements decreased as 21.56% for Model 1 and 32.16% for Model 2 with the increasing of concrete strength. Moreover, the maximum displacements in the infill walls of Model 1 and Model 2 were found as 5.11 mm (gauge 12) and 4.75 mm (gauge 27) for all concrete classes, respectively. The results show that the concrete strength is considerably effective on maximum displacements of carrier systems, although it is not effective on maximum displacements of infill walls.

To determine the effects of infill wall openings on displacements, the time-histories of displacements at all frontage of Model 1 and Model 2 are presented in Fig. 25 for the C25/30 concrete class. Figure 26 presents the changes in maximum displacements of Model 2 compared to Model 1 due to the openings in infill walls for all concrete classes. According to Model 1, the maximum displacements in Model 2 increase 13.92% for C25/30, 11.98% for C30/37, 11.69% for C35/45, 10.80% for C40/50, 8.81% for C45/55, and 0.47% for C50/60. It can be seen from Figs. 25 and 26 that the maximum displacements in carrier systems and infill walls changed significantly due to opening in infill walls.

Fig. 25
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The time-histories of displacements obtained Model 1 and Model 2 for C25/30

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Fig. 26
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The differences (%) in maximum displacements of Model 2 due to the openings in infill walls according to Model 1

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The released-total energy from the explosion, absorbed-total energy by the materials, and air volume are given in Table 7. It can be seen from Table 7, 3.6 × 1014 μJ of energy was released from 100 kg TNT explosive and a significant part of the released-energy was absorbed by the air volume (2.63 × 1014 μJ). However, the total released-energy was not absorbed by the air and other elements. Therefore, many elements were damaged. The energy absorbed by other solid elements (concrete, brick, etc.) is too small and can be neglected. Therefore, the concrete strength and openings on the infill walls have not significant effect on absorbed-total energy.

Table 7 The released-total energy and absorbed-total energy after detonation
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The damage contour diagrams obtained from blasting analyses are given in Figs. 27 and 28 for Model 1 and Model 2, respectively. It can be seen from Figs. 27 and 28 that damage distributions are similar for all blasting scenarios because the peak pressures caused by 100 kg TNT explosive are greater than the strength of the selected concrete classes and infill walls.

Fig. 27
figure 27

The damage contour diagrams obtained from 100 kg TNT explosive for Model 1

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Fig. 28
figure 28

The damage contour diagrams obtained from 100 kg TNT explosive for Model 2

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6 Conclusion

In this study, the effects of concrete strength and openings in infill walls on blasting responses of RC buildings are examined. For this purpose, in situ experimental tests were firstly conducted on a test specimen constructed with brick elements to verify the FE model. Moreover, two RC buildings were selected as an application and blasting analyses were performed by using numerical and empirical methods. The numerical models were constituted using ANSYS Workbench and were transferred into ANSYS AUTODYN to perform explicit analyses. In Model 1, openings were designed on the infill walls of all frontages so that the pressure caused by the explosion can easily enter and exit the building. In Model 2, the infill walls of the back frontage were considered as without openings. Moreover, C25/30 (fck = 25 MPa), C30/37 (fck = 30 MPa), C35/45 (fck = 35 MPa), C40/50 (fck = 40 MPa), C45/55 (fck = 45 MPa), and C50/60 (fck = 50 MPa) concrete classes were used in the analyses to investigate the concrete strength effect on blasting behavior. The pressures, displacements, damages, and total energies were considered as comparison parameters. By analyzing the results of the numerical and empirical studies, the following conclusions were obtained;

  1. 1.

    It was determined that the increase in concrete strength efficiently contributes to the blasting behavior of the load-bearing elements. As a result of the analyses, the peak pressure values in the load-bearing system decreased from 83.85 MPa to 74.45 MPa for Model 1 and 88.81 MPa to 68.83 MPa for Model 2 with the increasing concrete strength from C25/30 to C50/60. The peak pressures decrease by 11.21% for Model 1 and 22.50% for Model 2 with the increasing concrete strength.

  2. 2.

    The peak pressures in the infill walls of Model 1 and Model 2 were found as 2.70 MPa and 1.82 MPa for all concrete classes. This situation points out that the concrete strength is not effective on peak blasting pressures of infill walls.

  3. 3.

    The peak pressure values were obtained with empirical formulas. According to formulas recommended by Brode (1955) and graphs given in UFC 3-340-02, the peak pressures were calculated as 135.70 MPa and 82.00 MPa, respectively. Comparing the peak pressures obtained with numerical and analytical methods, it is apparent that the UFC 3-340-02 is similar to the FE results.

  4. 4.

    The maximum displacements decreased by 21.56% for Model 1 and 32.16% for Model 2 as the concrete strength increased from C25 / 30 to C50 / 60. The maximum and minimum displacements in Model 1 and Model 2 were obtained as 34.55 mm and 40.14 mm for C25/30, 27.10 mm and 27.23 mm for C50/60, respectively.

  5. 5.

    The maximum displacements in the infill walls of Model 1 and Model 2 were found as 5.11 mm and 4.75 mm for all concrete classes. Similar to the peak pressure, the concrete strength is not effective on displacements of infill walls.

  6. 6.

    It is seen that the openings in infill walls lead to a change of 8.16% in peak pressures and 13.92% in maximum displacements. It is apparent that the peak pressures and maximum displacements of carrier systems and infill walls are changed significantly due to opening in infill walls.

  7. 7.

    It has been determined that the critical gauge points at which maximum structural responses are obtained in both the load-bearing system and the infill walls are the closest points to the explosion center.

  8. 8.

    It is observed from numerical analyses that a significant part of the released-energy from the explosion was absorbed by the air volume and the energy absorbed by other solid elements can be neglected. Since the total released-energy was not absorbed by the elements, many structural and non-structural elements were damaged.

Although the explosions caused by terrorism and/or accidental lead to serious damage and/or collapse in structures, explosion effects are generally neglected in the design stage of civil engineering structures. However, all comparisons show that the concrete strength and openings in infill walls are significantly effective on the blasting responses of RC buildings. Therefore, explosion-resistant structures can be designed using at least these parameters. The study can be extended with the following issues;

  1. 1.

    For strategically important civil engineering structures such as buildings and bridges, studies can be conducted on city development plans and building layouts that can reduce blasting effects.

  2. 2.

    The parametric studies using multiple variables can be done to examine the effects of various parameters such as charge weights and load-bearing types that can be used in explosion-proof building design.

  3. 3.

    The blasting responses and blastwave effects on the structures can be investigated by using detailed numerical models including various interactions such as soil–structure, load-bearing system-wall, and walls-mortar. Thus, the effects of these interactions on blasting behavior can be investigated.