Advances in Civil Engineering

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Advancements in Analysis and Design of Protective Structures against Extreme Loadings

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Review Article | Open Access

Volume 2018 |Article ID 3780482 | https://doi.org/10.1155/2018/3780482

H. Draganić, D. Varevac, S. Lukić, "An Overview of Methods for Blast Load Testing and Devices for Pressure Measurement", Advances in Civil Engineering, vol. 2018, Article ID 3780482, 20 pages, 2018. https://doi.org/10.1155/2018/3780482

An Overview of Methods for Blast Load Testing and Devices for Pressure Measurement

Academic Editor: Xihong Zhang
Received13 Jun 2018
Revised18 Sep 2018
Accepted13 Nov 2018
Published27 Dec 2018

Abstract

A brief review of experimental methods for testing blast effects on structures is presented. Methods are classified in four groups: field tests, shock tubes, pendulum systems, and new techniques (blast simulator). Description of each method is given together with overall specification of possible instruments used in each test. In today’s modern era of computers which are becoming powerful tool implemented in all aspects of life and also scientific research, comparison of experimental and numerical techniques is also given. Comparison of data obtained from different experimental methods show that careful planning and execution leads to reliable results in terms of pressure, impulse, stress, and damage quantification.

1. Introduction

The blast resistance of different types of civilian and military structures against accidental explosions and terrorist attacks is an important security issue. Attacks towards vulnerable structures can cause a large number of casualties especially if total collapse occurs. Reducing vulnerability of existing and future buildings and transportation terminals is a topic of major concern for researchers in both civil and material engineering. The fields in which research is being focused are primarily blast loading predictions, material behaviour when subjected to high-rate loading, structural response to impulsive loading, and protective and retrofitting measures [1]. Structural damages caused by blast loading are the combination of both immediate effects and consecutive hazards, among which is progressive collapse. This catastrophic failure mode occurs when the initial failure of one or several key load-carrying members causes a more widespread failure of the surrounding members what leads to complete collapse of the whole structure [2]. Consequently, it is of great importance to investigate and improve the response of structures to blast loading. Compared to other construction materials, concrete is generally known to have a relatively high extreme blast resistance capacity. However, to improve resistance against extreme blast loads, some existing concrete structures require additional retrofitting [3]. To enhance the blast performance of concrete, two main procedures have been widely used. The first consists of adding steel, carbon, or polypropylene fibres as an internal reinforcement to get a fibre-reinforced concrete, and second method for reduction of damage is by protecting structure with external elements such as aluminium foam or steel sheets [4]. One of the most useful information when assessing the consequences of a blast event on a building would be the accurate evaluation of dynamic response and residual load-carrying capacity of the primary supporting members. There has been a growing trend in the engineering community to find integrated solutions for the design of infrastructures across various hazards, namely, multihazard engineering. Multihazard engineering is the search for a single design concept which can adequately fulfil the demands of multiple hazards [5]. Since protection is never an absolute concept and there is a level of high cost associated with a given damage level of protection, proper assessment tools must be employed to determine within reasonable degree of accuracy the level of vulnerability of existing and new structures. Furthermore, in blast design, one can also determine an acceptable level of damage that a structure can tolerate [6]. Blast testing in general seems to best mimic the real situation of blast action on an object. It definitely can replicate with high fidelity complex configurations and conditions that appear in a real situation and are extremely difficult if not impossible to simulate in a theoretical or a computational model. Testing naturally accounts for the real material behaviour no matter how complex they are, and for the real conditions, no matter how nonideal they look like, whether these are support conditions or connections with other elements, or poor workmanship. Testing may better simulate the behaviour of secondary systems, utilities, and buildings occupants’ response to the severe vibratory response of the building to blast. However, testing has its obvious limitations such as cost, environment hazard, safety risk, length of time to achieve results, limited number of repetitions, and almost inability to perform parameters studies [7].

The paper is divided into two main parts. The first part describes the most common types of experiments simulating blast loading. With the description of each type of the experiment, tables with names of the researchers and basic information (e.g., type of structural element and its dimensions, material, generated pressure, and impulse) are given. The second part describes numerical methods of blast-loading simulations.

2. Experimental Techniques

Experimental techniques can be classified as field tests, shock tubes, blast pendulum systems, blast simulator, blast chambers, and material property tests. Each technique has its own setup and specific characteristics but all have same final goal, and that is to try to simulate blast loading as realistically as possible.

2.1. Field Tests

Practical experience related to structural response of ordinary civilian buildings subjected to different military or terror attacks was accumulated in recent years, as a consequence of different terror actions and military conflicts. The accumulated data from actual incidents and experience gained from different studies, including blast tests, can be implemented in improvement of calculation and design tools, as well as design requirements and guidelines related to design of new buildings and for retrofitting (strengthening) of existing buildings [7].

The field blast tests involve tedious preparation of test specimens, prediction of blast load, and usage of high-end instrumentation such as high-speed cameras, pressure sensors, and validation of experiments. Due to the limitations of cost and possible blast charge weight to be used for the research, the charge weight usually has to be limited to a specific maximum value [8]. Blast resistance tests are normally performed on small-scale specimens of less than 2 m in each dimension. This is because full-scale tests are expensive, complex to handle, and difficult to monitor in terms of physical parameters that characterize the blast event and the specimen response [9]. The charges used are also scaled, and their dimensions became smaller than charges that can be potentially used in the eventual attack [4].

Experimental investigation using filed test can be conducted using one of the two potential test types. These are full-scale or small-scale blast test. There are advantages and disadvantages of both types of test. Small-scale tests are usually much cheaper and can be performed more easily than full-scale tests. If blast wave propagation is considered in many cases, this may lead to reliable results due to the existence of similarity laws. To satisfy the scaling laws, the scaled tests are conducted with reduced amounts of explosives, and this is an advantage that yields smaller safety distances and enables testing at more accessible testing areas. However, considerations may entirely change when structural response involving inelastic deformations and damage are considered. This is especially pronounced in cases of reinforced or masonry buildings which have complicated nonlinear characteristics and extremely complex cracking and failure and size-dependent constructional details. Under such conditions, full-scale tests often become the preferred alternative. Full-scale tests are not easy decision because they involve considerable higher costs, larger amounts of explosives, heavier elements, installation, and overall support. One possible field test setup can be seen in Figure 3 of Schenker et al. [9] that shows typical field test setup for full-scale test, military range with large open space for free blast pressure clearing, and an array of test specimens placed on a different standoff distance with regard to explosive charge. Small-scaled field test could provide valuable information on many different parameters important for blast design (windows tests, panel tests, steel elements, reinforced concrete (RC) elements, joint elements, and protective cladding) but they cannot offer information about interaction of those elements in global response of the structure. Testing of the entire building may identify the role of its different elements in the near-collapse case when these elements may form alternative paths for load transfer and reduce the likelihood of progressive collapse of the building under consideration. These phenomena can be tested only in full-scale tests [7].

The largest portion of conducted field tests is related to the research of behaviour of concrete slabs [4, 9, 1114]. Researchers are focused on detecting new ways for slab strengthening by using different types of materials as concrete aggregate [15], adding steel [1621], carbon [22], and polypropylene [4, 23] fibres or using higher resistance concrete classes [24]. Experiments on columns are also conducted in the attempt to determine whether or not seismically designed bridge or building columns are capable of sustaining significant blast load before collapsing or is it necessary to conduct retrofitting [5, 2531]. Tests are summarized in Table 1.


AuthorYearElement typeMaterialScale/dimensions (m)Charge typeCharge weight (kg)Standoff distance (m)

Đuranović [11]2002SlabsRC1 : 4 and 1 : 10PE40.0780.1–0.5
Rodriguez-Nikl [25]2006ColumnsRC and RC + ACJ1 : 1AFNO5584.36
Ohtsu et al. [23]2007SlabsRC, PPFRC, PVAFRC, and PEFRC0.6 × 0.6SEP10Contact
Wei et al. [12]2007SlabsRC1.22 × 1.22TNT1.16 and 1.71Contact
Fujikura et al. [26]2008ColumnsRC and CFST1 : 4N/AN/AN/A
Fujikura and Bruneau [27]2008ColumnsRC and RC+SJ1 : 4N/AN/AN/A
Schenker et al. [9]2008SlabsRC and FRC1 : 1TNT100020
Davis et al. [28]2009ColumnsRC1 : 2AFNON/AN/A
Wu et al. [16]2009SlabsNC, UHPFC, RUHPFC, and EBFRP2 × 1Comp B1–200.75–3
Williamson et al. [29]2010ColumnsRC1 : 2AFNON/AN/A
Fujikura and Bruneau [5]2010ColumnsRC and RC+SJ1 : 4N/AN/AN/A
Yusof et al. [8]2010PanelsRC and SFRC0.6 × 0.6N/A10.6
Fujikura and Bruneau [30]2011ColumnsRC and CFST1 : 4N/AN/AN/A
Wang et al. [13]2012SlabsRC1 : 1, 1 : 1.25 and 1 : 1.67TNT0.19–0.940.3, 0.4 and 0.5
Foglar and Kovar [17]2013SlabsRC and FRC6 × 1.5TNT2515–30
Tabatabaei et al. [22]2013PanelsRC and LCFRC1.83 × 1.83AFNO38.51.065, 1.37 and 1.675
Yankelevsky et al. [7]2013BuildingsRC1 : 1N/AN/AN/A
Zhao and Chen [14]2013SlabsRC1 × 1TNT0.2, 0.31 and 0.460.4
Castedo et al. [4]2015SlabsRC, RC+SS, SFRC, and PPFRC1 : 1PG2, RDX2 and 151 and 0.5
Foglar et al. [18]2015PanelsRC and FRC6 × 1.5TNT250.45
Li et al. [24]2015SlabsNSC and UHPC2 × 1N/A1 kgContact
Mao et al. [19]2015SlabsUHPFRC0.6 × 0.6PE40.2 10.5
Mazurkiewicz et al. [31]2015ColumnsHKS-3001 : 1HE40.5
Alengaram et al. [15]2016SlabsNC, OPSC, OPSFRC2 × 1TNT1, 5 and 101.5
Codina et al. [32]2016ColumnsRC1 : 1Gelamon VF6512.30.6 and 1
Xu et al. [33]2016ColumnsUHPFRC and HSRC1 : 1Emulsion exp.1.4–481.5
Wu and Li [20]2017SlabsRC and RC+ALFC2 × 0.8TNT6, 8 and 121.5

RC: reinforced concrete, NC: normal concrete, OPSC: oil palm shell concrete, OPSFRC: oil palm shell fibre-reinforced concrete, SS: steel sheet, SFRC: steel fibre-reinforced concrete, PPFRC: polypropylene fibre-reinforced concrete, FRC: fibre-reinforced concrete, CFST: concrete-filled steel tube, RC + SJ: reinforced concrete with steel jacket, NSC: normal strength concrete, UHPC: ultrahigh-performance concrete, HKS-300-steel I-shaped cross section, PVAFRC: polyvinyl alcoholic fibre-reinforced concrete, PEFRC: polyethylene fibre-reinforced concrete, PPFRC: polypropylene fibre-reinforced concrete, RC+ACJ: reinforced concrete with advanced composite jackets, LCFRC: long carbon fibre-reinforced concrete, UHPFC: ultrahigh-performance fibre concrete, RUHPFC: reinforced ultrahigh-performance fibre concrete, EBFRP: externally bonded fibre-reinforced polymer plates, RC+ALFC: reinforced concrete with aluminium foam claddings, UHPFRC: ultrahigh-performance fibre-reinforced concrete, and HSRC: high-strength-reinforced concrete.

Field tests are usually conducted on military test sites (Figures 1 and 2) and very rarely in laboratory setting, i.e., blast chambers, except in cases of small-scale tests where small amounts of explosives are used (milligrams or grams). Main reason for this is the full size of blast pressures that would be exerted on room walls if the experiment would be conducted inside relatively small laboratory. Usually there is no adequate venting of the laboratory that would enable safe clearing of blast waves without severely damaging room and injuring its occupants. Test sites are large open spaces usually located outside main urban centres (remote locations) appropriated for various activities of military training, among which is also training with explosive charges. Specialized personnel, trained for explosive handling and detonation, usually conduct experiments. Danger of personnel injury reduces to minimum because operators and researchers are securely located in protective structures, concrete bunkers, during the detonation of explosive charge. Depending on the needs of researchers, various instruments can be planned for data acquisition. Detailed descriptions of various instruments used can be found in Section 2.5. Depending on the tested element, supporting structure is usually constructed in order to provide desired boundary condition. If columns are tested, besides massive foundations that simulate fixed bearings, additional steel [5, 29] structure is constructed for simulating column top/head boundary condition. This additional structure is also used for mounting extra mass on the top of the column to simulate mass of the bridge superstructure, if bridge columns or mass of the upper building storeys are tested or if columns from public or residential buildings are tested. Possible setting for column testing is also to lay columns flat with the ground [32] or to bury the column [33]. Columns are buried in such a way that one of the faces is exposed to the blast pressure. This reduces the influence of clearing, additional pressure wave refraction, and reflection. In this setting, adequate standoff distance is provided with hanging or placing desired charge on the top of the styrofoam sheets. In buried settings, hydraulic jacks are usually used for providing additional level of axial force in the column [33]. Similar setup for charge placement is used in field-testing of slabs. Slabs are field tested utilizing steel reaction table [16] or trench [18], which can be dug in the earth and slab is then laid on top of it. Either of these setups is designed to provide clear space beneath the test specimen in order to enable free deformation. Steel reaction table beams can be designed to provide different boundary conditions on one, two, three, or all four edges/sides of the slab.

There is no universal test setup for field blast tests, especially if different types of construction elements are considered. Test setup depends on the specific requirements of the researcher, scale, type, and shape of the specimen and information which is needed from the experiment (if instrumentation is needed or not). Careful planning is essential to maximize test efficiency and minimize costs and safety concerns.

2.2. Shock Tubes

Shock tubes have been proven to be a most versatile and resilient tool for the investigation of shock-wave-related problems under a laboratory condition covering a wide variety of fields both in fundamental science and in applied technology. Tubes are used for analysis of the physical and chemical processes generating one-dimensional, nondissipative flows [3436]. They can be divided into large, medium, small, and microscale based on length and inner diameter of the tube [37]. Generally, the shock tube consists of two major sections, a driver section and an expansion section. Blast pressures are generated when a rupture diaphragm, placed between the two sections, fails due to pressure in the driver section. A shock wave then travels down the expansion section and loads the test specimen at the end of the expansion section. In some cases, the driver could be baffled to reduce the effects of reloading by smaller reflections that exist in the shock tube. Due to the construction and the functional principle of the shock tube, the structural element located at the end of the tube can be loaded with a precisely defined pressure-time history. It is adjustable by the initial pressure and the length of the high-pressure section of the shock tube. The resulting planar blast wave is exerted on the test specimen evenly and normal to the element surface [3841]. For larger test specimens the shock tube can be fitted with an additional expansion section making it possible to test larger structural systems [42]. If nonplanar specimens such as columns or beams are tested, a load transfer device, which consists of steel metal sheets connected to a series of steel beams, could be used. This additional apparatus is used to transfer shock-wave pressure as a uniformly distributed load along the compression face of the specimen. Table 2 gives a list of conducted shock tube experiments on construction elements.


AuthorYearElement typeMaterial typeScale/dimensions (mm)Shock wave (kPa)Impulse (kPa  ms)Load transfer

Toutlemonde et al. [43]1993SlabsRCφ 9001700N/APW
Schleyer et al. [42]2007PanelsSTS1 : 438–2212013–4358PW
Magnusson et al. [44]2010BeamsNSC and HSC1 : 11200–32006300–11130PW
Ellis et al. [10]2014PanelsUHPC1626, 864 and 51N/A810–2050PW
Stolz et al. [38]2014SlabsDUCON2410 × 114035–250N/APW
Zhang et al. [45]2014PlatesSteel 1008 and 101850.8 × 203.3375N/APW
Aoude et al. [46]2015ColumnsUHPFRC (CRC)1 : 112.6–108.6109–964LTD
Thiagarajan et al. [40]2015SlabsHSC-VR, HSC-NR, NSC-VR and NSC-NR1 : 3350–3906790–7710PW
Haris et al. [41]2017PanelsPolyurea, STF, foam, and STF-infused foam120 × 110186N/APW
Lee et al. [47]2018BeamsSFRC125 × 250 × 243822.78–67.81196.02–680.4LTD
Lacroix and Doudak [48]2018Beams24F-ES Spruce Pine glulam + FRP137 × 222 × 223541.2–76.2419.1–1110LTD
Poulin et al. [49]2018PanelsCLT SPF105 (175) × 445 x 25005.8–58.659.4–690.7LTD

UHPFRC: ultrahigh-performance fibre-reinforced concrete, CRC: compact reinforced concrete. UHPC: ultrahigh-performance concrete, STF: shear thickening fluid, NSC: normal strength concrete. HSC: high-strength concrete, STS: stainless steel, DUCON: ductile concrete, VR: high-strength low alloy vanadium reinforcement, NR: normal reinforcement, SFRC: steel fibre-reinforced concrete, FRP: fibre-reinforced polymer, CLT SPF: cross-laminated timber with Spruce pine fir, PW: pressure wave, and LTD: load transfer device.

The test gas flow between the shock wave and the interface has a very short duration, and it can be disturbed by the various wave systems that propagate in the tube because of its limited dimensions. The most significant effects concern the perturbations related to the presence of the wall boundary layer and noninstantaneous rupture (opening) of the diaphragm (and combined effects). However, if these effects are taken into account, it is possible to optimise parameters of interest independently of the disturbing phenomena [34].

There are several possibilities for improving the performance of shock tubes. Some of them are area reduction close to the diaphragm, use of double-diaphragm tube, combustion tube, and/or free piston tube. If area close to the diaphragm is reduced, there is a quasistationary expansion of driver gas in the area transition zone, which increases the efficiency of the thrust and consequently Mach number. Additional third section added to the double-diaphragm tube that is used as a test section. Expanded gas from the second chamber is used as a driver gas for the test gas in the third chamber what, again, consequently increases the Mach number and reduces the test time. Combustion tube is used to produce the increase in the sound of speed by temperature increase. The problem here is to obtain uniform combustion without detonation, and this is usually realized by arranging significant number of spark plugs in spiral along the high-pressure chamber. Increase in the Mach number is partly compensated by strong deceleration of the shock wave due to sharp pressure fall after the combustion. Free piston tube is used for fast compression of a light gas used as a driver. This compression carried out by a piston launched at high speed in a tube is serving as a compression chamber after which compressed hot gas ruptures the diaphragm. This is the most efficient process to create a shock wave of high intensity [34].

The BakerRisk test site in San Antonio [42] has a 0.75 m2 (8 ft2) target area in its normal configuration and can be configured to deliver a variety of blast pressure and impulse combinations with maximum possible peak pressure of 3 bar (45 psi) with a maximum impulse greater than 660 bar·ms (1000 psi ms). Shock tubes of similar construction and capability are blast load simulator (BLS) which are situated at the U.S. Army Corp of Engineers (USACE) Engineer Research and Development Centre (ERDC) in Vicksburg, Massachusetts, USA [10], at the University of Ottawa Blast Research Laboratory, Canada [46, 50], at the testing ground of Swedish Defence Research Agency (FOI) in Marsta, Sweden [44], and at the Ernst-Mach-Institute in Freiburg, Germany [39]. Listed tubes are slightly different by their internal cross section near the test area and pressure levels exerted on test specimens but their work mode is very similar. A wide range of measurements are possible during shock tube testing; dynamic measurements, dynamic load measurements, strain measurements, high-speed camera video, normal video, and still photography capabilities are available depending on shock tube setup and researcher requirements. A high-speed camera is used for recording the dynamic response of tested specimens. Usually the high-speed camera is mounted outside the shock tube and is oriented to record the motion of the specimen. If positioned perpendicular to the shock tube, it can record deflections and velocities which are determined from sequential images taken during testing [10, 38, 43, 46, 48, 49, 51]. Propagation of the damage pattern can also be analysed if the camera is placed in such a way to have a clear view of the specimen surface of interest. The schematic layout of the shock tube is presented in Figure 3, and the photography of the field-installed BakerRisk shock tube can be seen in Figure 8 of Schleyer et al. [42].

2.3. Blast Pendulum Systems

Blast measurements for experimental testing of smaller structural parts could be conducted using pendulum systems situated in blast chambers. Typically, a four-cable ballistic pendulum system is employed to measure the impulse imparted onto the front face of the specific specimen. The recorded pendulum swing gives a direct indication of the height reached by the pendulum and hence the maximum potential energy of the system after the dissipation of the energy in plastic work. The value of this maximum potential energy can be used to calculate the maximum velocity of the whole pendulum system as it swings back through its initial zero position. The linear momentum (mass times velocity) associated with the whole pendulum mass at this point must be equal to the initial impulse applied to the beam, as long as mass has been constant, and no other forces have been applied. In this way, the pendulum swing gives an accurate measure of the applied impulse [5255]. The balance weight is adjusted before each test to ensure that the centre of the mass of the whole pendulum system is close to the centre point between the two pairs of the cables. TNT charge is used to produce impulsive loading on the front face of the specimen which pushes the pendulum to translate. Based on the oscillation amplitude recorded by oscilloscope, the impulse exerted onto the pendulum can be calculated. Besides oscilloscope, laser displacement transducers could be used for translation measurements. The front of the pendulum consists of the steel frame onto which the specimen is clamped [5658]. Typical experimental setup for blast experimentation using ballistic pendulum system can be seen in Figure 1 in [56]. Figure 4 depicts the schematic view of the pendulum system. Charge weights in the pendulum blast test range from 3 to 50 g if experiments are conducted inside the blast chamber, but there are versions of pendulum systems which are adapted for larger weight sizes [59], up to 2500 g, and are installed in open spaces (Figure 5). Specimens vary in shape and size depending on research requirements. The most common shape of specimens for blast pendulum tests is rectangular with dimensions from 76 mm up to 400 mm (700 mm if exterior blast pendulum system is considered), but even circular or even small-scale beams can be tested. Table 3 gives summary of blast pendulum tests.


AuthorYearElement typeMaterial typeDimensions (mm)Charge typeCharge weight (g)Standoff distance (mm)Impulse (ns)

Humphreys [52]1965BeamsSteelN/ADuPont EL-506-DN/AN/AN/A
Jones et al. [53]1970PlatedMild steel and aluminium76 × 129DuPontN/AN/AN/A
Jones et al. [54]1971Beams and platesMild steel and aluminium128 (× 128)DuPontN/AN/AN/A
Hanssen et al. [59]2002PanelsAluminium foam684 × 700PE41000–2500500364.7–1305.3
Langdon et al. [60]2009PanelsGLARE200 × 200PE44–141311–32
Shen et al. [57]2010PanelsAl-5005 H34 sheets and ALPORAS foam400 × 400TNT20–60250 and 35015.8–41.2
Fallah et al. [61]2014PlatesDyneema300 × 300PE412–505017.7–114.4
Guan et al. [62]2014PanelsDivinycell HΦ 90PE43–7905.89–11.08
Henchie et al. [63]2014PlatesDomex-700 MC steelΦ 106PE45–4015010.4–63.98
Jing et al. [64]2014Sandwich shellAluminium sheets and foam250 × 250TNT10–401008.73–44.38
Li et al. [65]2014Sandwich panelsAluminium AL-1200H18250 × 250TNT10–30100–24011.8–26.7
Langdon et al. [56]2015PlatesMild steel, Armox 370T, AL-5083H116, and GFPP300 × 300, 400 × 400PE47–5025 and 3813–116.8
Ghoor [66]2018PanelsFRPMS and LCP400 × 400PE410–2510017.32–35.6
McDonald [58]2018PlatesRHA, IRHA, HHA, and ARS400 × 400PE430–755061.2–127.9

Dyneema: ultrahigh molecular weight polyethylene fibre composite, Divinycell H: crosslined PVC foam, GLARE: fibre metal laminate, GFPP: glass fibre-reinforced polypropylene, RHA: rolled homogeneous armour, IRHA: improved rolled homogeneous armour, HHA: high hardness armour, ARS: abrasive resistant steel, FRP+MS: fibre-reinforced polymer moulded sandwich (Airex C70:75 core), and LCP: laminated composite panels.

Pendulum systems are used for small-scale blast experiments in laboratory setup. They are used for investigation of local effects of blast loads and have a wide spectrum of experimental possibilities. Pendulum tests were conducted on metal [56, 63, 65], glass [51], and composite panels [57, 6062, 64]. Panels were tested for structural response on blast load in order to determine possibilities of their use for structural strengthening.

2.4. Blast Simulator

Field experiments, although generally effective, are often expensive, dangerous, and in many cases do not provide clear visual evidence and quantitative data of structural response throughout the blast event. In order to provide blast-like loadings on structures in a controlled laboratory setting, the blast simulator was designed and constructed (University of California, San Diego, USA, 2006.). The blast simulator is a ultrafast, hydraulically driven, computer-controlled impulse generator. It is designed to produce an impulse by impacting the specimen with a mass in a controlled manner. In this way, the simulator can produce quantitative and qualitative, high resolution data and what is most important is it ensures repeatability of experiments eliminating blast wave and fireball interference with measuring instruments. The simulator generates impulses using ultrafast, computer-controlled hydraulic actuators with a combined hydraulic/high-pressure nitrogen energy source called blast generators (Figure 6). The actuators are used in conjunction with appropriate loading media, which attached to the variable masses assist in the appropriate loading conditions for various blast loads. Detailed description of the blast simulator inner workings can be found in [6769]. Blast simulator construction and actuator configuration can be seen in Figure 1 in [69].

Tests are conducted using one of the two methods selected based on the test requirements. The procedure for determining force-time history and impulses is dependent on the type of experiment. The first method involves an unattached mass, and the second involves an attached mass. For the unattached configuration, a thin plate is attached to the piston rod, and it pushes the impact mass towards the specimen. At a specified time, the rod is retracted, letting the impact mass travel forwards and impact the specimen. The second, more common, test type is the attached test. In this type of test, the hydraulics is connected to the impact mass throughout the collision. At a specified time, the hydraulics begins to pull back on the impact mass near the end of the collision. This pulling back prevents a double-hit and tailors the impact so that the loading is blast-like in duration and shape [67]. The simulator can be applied to a wide range of interesting problems which include the development of novel hardening strategies [71] and the simulation of complex loading environments [72, 73]. The blast simulator is not limited to producing just external blast loads, but can generate a multitude of high-rate loading effects, such as shock loads of components and confined explosions. Comparing the data from blast simulator tests to computer simulations as well as a field tests using explosive charges, the experimental blast simulator impulse was verified. It was confirmed that short duration impulsive loading can be achieved from structures with planar geometry [6769]. Table 4 gives a list of test performed using the blast simulator.


AuthorYearElement typeMaterial typeDimensions (m)Impact velocity (m/s)Pressure (MPa)Impulse (MPa  ms)

Gram et al. [74]2006ColumnsRC0.36 × 0.36 × 3.281.5–30N/A15.8
Oesterle [75]2009WallsCMU and CMU + CFRP (RC + frangible panels)0.268 × 0.146
0.350 × 0.122
4–8 (5–23)N/A0.7–1.9 (1.9–5.9)
Oesterle et al. [76]2009WallsCMU and CMU + CFRP2.68 × 1.464–81.551.1–2.0
Stewart [77]2010ColumnsA992 Gr. 50 steel0.25 × 0.25 × 3.32
0.37 × 0.37 × 3.32
4–451.1–131.3 (233.3)2.4–55.6 (53.1)
Huson et al. [73]2011Water bladderXR-5 polyester and U1940 nylon0.41 × 0.4110–250.5–10.62–16.2
Rodriguez-Nikl et al. [68]2011ColumnsRC and RC CFRPN/AN/A106.8–16.9
Huson [72]2012JointsCFRP and balsa0.60 × 1.22 × 1.2210–253.1–10.346.9–34.5
Li et al. [50]2012ColumnsRC LS and RC NS0.26 × 0.26 × 2.410–25N/A5.3–15.9
Stewart [78]2012ColumnsA992 Gr. 50 steel0.37 × 0. 37 × 3.32 (S and W)13–45
22–65
N/A15 ()–53.8 (39.4–107.4)
Freidenberg [69]2014WallSure-board3.7 × 1.31032004
Stewart et al. [67]2014ColumnsA992 Gr. 50 steel0.25 × 0.25 × 3.32
0.37 × 0.37 × 3.32
4–451.1–131.3 (233.3)2.4–55.6 (53.1)

Sure-Board: C-shaped studs of high-strength low alloy vanadium steel with cement-board and gypsum-board panel. UCSD: University of California, San Diego. CFRP: carbon fibre-reinforced polymer. RC LS: reinforced concrete limited seismic. RC NS: reinforced concrete nonseismic. S: strong axis. W: weak axis.

Data comparison shows very good overlap of measured and simulated values based on which it can be concluded that the blast simulator can provide realistic blast results. Measured and numerically simulated displacements from concrete wall subjected to blast load can be seen in Figure 10 in [67]. Oesterle in 2009 tested thirty specimens of different types of concrete walls at Blast Simulator Facility. These tests included reinforced concrete walls, unreinforced and reinforced concrete masonry unit walls, and same wall types retrofitted with carbon fibres and polyurea [75, 76]. Comparison of steel column displacements measured from the blast simulator and field tests can be seen in Figure 14 in [67]. Steel columns were tested to simulate vehicle-borne explosives of 454 kg (1000 lbs) to 680 kg (1500 kg) located at the curb side. Such blast scenarios generated a nonuniform load along the height of the column with a higher impulse at the base and a decreasing impulse along the height of the column. This required precise configuration of the valve commands and the initial position of the piston rod in order to ensure a synchronized impact. Comparison of results showed that the simulator is effective in producing loads which can capture the maximum displacement and overall response of the column when scaled distance is equal or above two. However, the blast simulator cannot generate blast load with sufficient accuracy due to temperature effects and other parameters because of the close proximity of the charge and subsequent fireball when the scaled distance is smaller than two [7779].

2.5. Blast Chambers

Blast chambers are structures used to fully or partially contain the effects of high explosions. They are produced for a number of different uses: for the research of different aspects of explosive loading and explosive characteristics, for development purposes of different types of materials or construction elements, as well as for destruction of munition. Based on the intended purpose, the chamber is designed accordingly. The chamber intended to withstand multiple detonations without sustaining any damage is designed considering liner-elastic response, while chambers intended for one-time extreme event is designed considering plastic response. Majority of blast chambers are intended for multiple use and can sustain 20% to 27% larger charge weights in comparison with the designed value [80]. At this charge weight level, first detectable plastic strains can be detected in the chamber. Usually chambers are designed to sustain detonation of up to 1 kg of explosive charge. Basic geometry of blast chambers is either spherical or cylindrical, but if spatial or operational requirements dictate, a rectangular geometry can also be designed to contain internal detonation. Charge is usually detonated in the centre of the spherical chamber, while charge can be placed optionally in the rectangular chamber. Characteristic of blast chamber is that the tested element as well as chamber walls is loaded with multiple pressure spikes as a result of pressure reflection from chamber walls resulting in nonuniform load at different locations inside the chamber. Chambers usually have places intended for instrumentation placement for recording pressures inside the chamber. These instruments are side-on and face-on pressure sensors, and if partially confined chambers are considered, high-speed cameras can be installed to monitor blast door opening and pressure wave expansion. Table 5 gives list of conducted research in blast chambers.


AuthorYearElement typeMaterial typeScale or dimensions (m)Charge typeCharge weight (g)Standoff distance (m)Pressure (kPa)Impulse (kPa  ms)

Whenhui et al. [81]1997Chamber wallSteel0.852 × Φ 0.425RDX9.1, 18.2 and 27.40.212N/AN/A
Wu et al. [82]2007SlabsRC and RC NSM CFRP1.3 × 1.0Pentolite and comp B60 and 20000.6N/AN/A
Wu et al. [83]2009SlabsRC and RC NSM CFRP1.3 × 1.0Comp B20000.6N/AN/A
Wu et al. [70]2013Chamber wallN/A1 : 1PE495–2001.3 and 1.5250–110050–225
Snyman et al. [84]2016Blast chamberMS and MS nylon1:5 (1.2 × Φ 1.0)Comp B24 and 400.54129 (476)312–597
Jiba et al. [85]2018Shock waveFine water mist1.2 × Φ 1.0PE4200.5N/AN/A

NSM CRFP: near-surface-mounted carbon fibre-reinforced polymer. MS: mild steel.

Research is conducted on small-scale specimens, usually slabs [82, 83], but there is several research about strain growth in chamber walls [70, 81, 84] and shock wave expansion and reflection inside the chamber [85] Examples of blast chambers used in experiments can be seen in Figures 7 and 8.

2.6. Material Property Tests

Dynamic behaviour of materials is strain-rate dependent. If compared to statically determined properties, increase in strength strain capacity and fracture energy is observed. This increase is taken into account by using dynamic increase factor (DIF). There are several possible methods to determine dynamic properties of materials as the Charpy pendulum, drop-weight impact, plate impact, servo-hydraulic test machine, Split-Hopkinson pressure bar (SHPB), gas gun, and explosive field tests [87, 88]. Most commonly used test is SHPB (Figure 9) but all depends on the availability of certain method to researcher. In Charpy pendulum test, the specimen (usually thick beam) is impacted by swinging pendulum directly opposite the notch which is machined in the middle of the specimen supported in a horizontal plane. The test can be easily instrumented, and information about energy dissipation or strains can be recorded during impact test. Drop-weight test (plate impact) consists of a known weight dropping from a predetermined height to the test specimen supported in the horizontal plane. Impact speed can be determined using equations of motion or by optical sensors located in the vicinity of the test specimen. Advantage of this type of test is a wider range of test specimen geometries. High-strain-rate testing of various specimens can be conducted using servo-hydraulic testing machines. Specimens can be loaded with pulsating or alternating loads using periodic or random signals. There is a wide range of force capacity of these machines (5 kN to 2500 kN) with different grip types depending on intended use, flat for compression testing, or clamping for tensile testing. Usually machine has an integrated force and displacement sensor for recording information during testing. Hopkinson bar technique can be employed for determination of different material properties. There are several types of Hopkins bar tests, the punch-loaded Hopkinson bar, the compression bar, the tensile bar, and the Hopkinson bar shear test. Main principle for this test is to bind specimen into the inertia bar and the input bar which is then loaded through the weight bar accelerated using gas projectiles. The specimen should have an adequate interface with bars in order to avoid shear failure within grip and the specimen and to avoid stress concentration. Strain gauges on input and inertia bar record incident and reflected stress waves. Impact testing of materials can also be conducted using a high-pressure gas gun. Projectile is accelerated down the barrel by gas that is fled to a chamber. Gas is restrained by a plastic diaphragm, and when the predetermined pressure value is achieved, diaphragm is burst to produce acceleration of projectile. A gun barrel is usually instrumented and can capture force-displacement histories for further analysis.

2.7. Instrumentation

Measuring of blast loads on structures is a complex task. Instruments should be placed in such a way that they do not interfere with the load distribution on the surface of the observed element and to avoid their damage and/or destruction when subjected to blast wave. The properties of blast waves as they strike the structure are most commonly recorded in terms of pressure, and the design and use of pressure gauges suitable for recording the history of blast wave pressure is an important aspect of structural loading research [90]. The damage potential of a blast wave is associated with both the force it exerts on an object and the duration over which the force is applied. An assessment of this damage potential requires measurements of the peak static overpressure and the total impulse per unit area of the blast wave. During blast measurements there are several undesired environmental influences which can severely distort the signal output. Influences include high temperatures, ground shocks and their associated strain waves, intense light, fragment impact, ionized gases which coupled with submicrosecond pressure-time rise and extremely high-frequency response from the measuring transducers and signal conditioning make blast measurements an extremely challenging task [91, 92]. Broad spectrum of various instruments is used in blast measurements depending on required data for analysis. From conventional instruments linear variable differential transformer (LVDT), both mechanical and laser, are used for deformation measurements, different types of accelerometers used for measuring test specimen acceleration after blast wave impact (specimen velocity and deformation can be determined in postblast analysis) and strain gauges, typically for measuring strains on reinforcement in reinforced concrete specimens or on steel plates. These instruments are usually mounted on opposite side of test specimen in relation to blast wave incidence in order to provide protection against damage or destruction. Mentioned instruments are usual in static experimental setups while in dynamic they are required to have greater acquisition speeds in order to capture high strain rates produced by dynamic loading. Mentioned instruments are used for measuring secondary blast effects; deformations, accelerations and strains of tested specimens but not for primary detonation products; blast incident and reflected pressure, impulses and blast duration. First attempts to develop blast pressure transducers to measure static overpressure was made by U.S. and British laboratories in 1950s and 1960s in order to measure pressures originated from atmospheric nuclear testing [91]. Two types of pressure transducers were researched: pencil and lollipop probes. Lollipop probes were in time abandoned, and nowadays pressure transducers for measuring blast pressures at locations above ground level are mainly pencil probes. In addition to transducers for measuring free air blast pressures there are transducers for measuring reflected pressures, ground-surface transducers. Pencil probes and ground-surface transducers are very different in their design [91, 93].

2.7.1. Pencil Probe

Pencil probes are side-on transducers that record free field pressures at varying distances from blast source. Their design must minimize interference with the flow behind the shock front (Figure 10). Blast wave will become distorted at its higher frequencies when encountering the probe tip, but it will reconstitute itself by the time it arrives at the sensing face that is located transverse to the longitudinal axis of the probe. The probe is tapered over its first 5 cm of length and then widens into a cylindrical body with a flat sensing surface on one side [94, 95]. Probes tip should be pointed to an incident, planar blast wave in order to permit accurate measurement of it static overpressure preventing wave reflection and amplification. From the first appearance of the probe, there was little change in its design. Significant changes include replacement of probe material from ceramic to quartz and ICP® electronics (registered brand of PCB Piezoelectronics Corporation) were integrated enabling 5 V full-scale output for each of its various pressure ranges [91, 93]. Probe axis should be aligned incident to the incoming air blast wave in order to avoid errors of the measurement. Proper placement of pencil probe can be seen on Figure 3 in Walter [91]. Field test have shown that the maximum misalignment of probe axis should be within ±5° in order to conduct accurate measurements [96].

Both mechanical and electrical isolation should be provided. Transducer is mechanically adapted to an electrically conductive test stand or holder by a nonconductive material because it provides electrical isolation between the probes case and the path for any electrical grounding through the stand. Probes placed on hard surfaces are susceptible to blast ground shocks that could disturb the measurements but this problem is solved by placing the probe stand on low-density foam that would block this transmission path. Exposure to high temperatures can also result in an error in measurements; it can cause false negative pressure that is occurring due to a thermal expansion in the internal housing of the transducer. The expansion results in a slight release of the preload on the stacked quartz elements. This problem is resolved with a tight wrap of black electrical tape around the sensor [91, 97, 98].

Transducer placement is dependent on the test configuration and quantity of the explosive test items, on other items located in the test area, on the height of the test specimen and explosive at detonation, on preparation of the ground surface, etc. One possible field sensor setup can be seen in Walter [99] It is desired to have the sensors located in the Mach stem what enables the easiest data collection and interpretation. The sensor array should be planned to acquire large enough data set in order to conduct statistical analysis by varying distances and azimuths between sensor locations (Figure 11). Probe stands should not shadow or interfere with each other when placed in a row. Shadowing can be avoided by proper incrementing of sensor height and/or relative displacement between each. Fragmentation poles can be placed in front of a row of sensors along a radius to protect sensor from fragmentation impact and damage. After collecting, data (signal) needs to be transferred to the acquisition system that is usually situated several hundreds of meters from the blast site in some sort of protective structure (bunker). This is done usually by burying in the ground cables that could also be damaged or destroyed if not properly protected. During signal transmission distortions can occur which influence on data accuracy. In order to avoid signal distortions cables should be properly terminated preventing reflections at higher frequencies, i.e. proper attention should be directed to cable inductance and capacitance [93, 98].

2.7.2. Ground-Surface Transducer

Ground-surface transducers are probes used for measuring reflected blast pressures based on the principle of a pressure bar. Example of ground-surface transducer can be seen on Figure 12. The bar is acoustically impedance-matched to the tourmaline, resulting in a 1.5 MHz resonant frequency for the transducer [93]. The sensing face of the transducer must be levelled with the surface of the element in which they are mounted [94]. If the transducer should protrude from the surface, the protrusion will introduce errors by partially reflecting the blast wave. In some cases, deviations from flush mounting are required in order to isolate transducer from unwanted effects as high temperature interference. Alternately, if the transducer is recessed in the surface, the resultant acoustic cavity can act as a resonator [92, 95, 96]. These sensors are also susceptible to errors in measurements by environment influences, like high temperatures, intense light, element accelerations, etc. Mentioned influences are omitted by applying appropriate material as a base, such as Teflon, Delrin or nylon in order to dampen unwanted accelerations, applying ceramic or rubber coating over the sensing face in order to prevent heat transfer, and applying opaque grease behind the screen on sensing face to block error signals due to intense light [91, 100]. Ground-surface transducers are not intended to record the entire pressure-time history but are limited to short record times. Longer record times require use of acceleration compensated pressure transducers but those are susceptible to thermal problems. The by-product of thermal induced housing expansion is negative signal residing after the blast event is clearly over. This is mitigated by use of ceramic or Room-Temperature-Vulcanizing silicone (RTV) coatings [100].

2.7.3. High-Speed Cameras

Useful instrument for monitoring specimen deformation in time is the high-speed camera. There are high-speed cameras with different capabilities in terms of sampling frequency, from 2000 Hz to 2000000 Hz (ultrahigh-speed camera) depending on the required usage [101]. Available recording time depends on sampling frequency, camera hard memory and photo resolution. Higher sampling frequency requires larger memory for recording same event duration with same photo resolution than for lower sampling frequencies, respectively. Cameras used in blast measurements are typically positioned in safe distance in order to avoid damage by blast shock and/or fragment impact. They have limited capabilities if used for field blast tests in sense that the specimen is usually obscured by explosion fireball. Because of that camera usually is not capable of recording specimen behaviour, deformation and damage propagation. Nevertheless, with smart placement of the camera (for example behind the slab-like specimen opposite the explosion) it might be possible to record useful data. Additionally, a special benefit of high-speed camera is possibility of calculating blast wave velocity from the recording that is then used to calibrate numerical simulations. In field tests, cameras can be used for recording blast fireball and wave expansion for further analysis. They are useful in other types of tests were camera has a clear view of the specimen, especially in shock tube tests where blast wave without any explosion by-products loads test specimen and blast simulator where specimen is loaded directly with hydraulic actuators.

3. Comparison to Numerical Simulations

To understand the behaviour of structures under blast loading, as stated before, full-scale blast tests would be the best course of action. However, these tests are limited due to security restrictions and a lack of the considerable resources required. Therefore, numerical modelling and simulation have recently been proven to be a valuable tool in simulating the behaviour of structures under blast loading [102106]. Simulations are conducted using hydrocode software that is specialized numerical program for fluid dynamics. Table 6 gives a short list of conducted numerical simulations of blast effects on structural elements. Nonlinear dynamic blast analysis using hydrocodes [107109] can be conducted using a 2D axis-symmetry simulation or a full 3D simulation. If 2D simulations are used, running times are reasonable and results are adequate but stiffer than the experimental results. In order to capture the true physics of the problem, 3D simulation can be applied because it resembles the actual situation. However, despite great advances in computation performance, there are still limitations when computing 3D simulations for blast analysis. Run times can be in order of days or weeks or even longer particularly when basic serial computing is used, but this can be somewhat reduced if parallel processing is applied. The numerical analysis of structures under irregular blast loading is also influenced by mesh geometries. This mesh size dependence is occurring due to gaps between the explosive energy and internal energy of structures and specific mechanical properties within the material model [3]. Numerical simulations can supply quantitative and accurate details of stress, strain, and deformation fields that are difficult to reproduce experimentally.


Test typeAuthorYearElement typeSoftwareFormulationFE typeSymmetryMesh size (mm)

Field testsOhtsu et al. [23]2007SlabBEMN/AN/AN/AN/A
Wei et al. [12]2007SlabABAQUSN/ASolid, shellYes (1 : 4)N/A
Schenker et al. [9]2008SlabLS-DYNAN/AShellN/AN/A
Wu et al. [86]2011ColumnLS-DYNAMM-ALESolid, beamNo50
Foglar and Kovar [17]2013SlabLS-DYNAN/ASolid, beamNo30 and 50
Tabatabaei et al. [22]2013SlabLS-DYNALagrangeSolid, beamNoN/A
Zhao and Chen [14]2013SlabLS-DYNAN/ASolid, beamYes (1 : 4)N/A
Castedo et al. [4]2015SlabLS-DYNALagrangeSolid, shell, beamYes (1 : 2)15, 5 and 50
Foglar et al. [18]2015SlabLS-DYNAN/ASolid, beamNoN/A
Li et al. [24]2015SlabLS-DYNASPHSolid, beamNo8 and 40
Mao et al. [19]2015SlabLS-DYNAN/AN/ANoN/A
Mazurkiewicz et al. [31]2015ColumnLS-DYNAEuler Lagrange MM-ALEShellNoN/A
Codina et al. [32]2016ColumnAUTODYNEuler LagrangeSolid, beamNo10

Shock tubesEllis et al. [10]2014SlabABAQUSN/ASolidNo12.7 and 16
Thiagarajan et al. [40]2015SlabLS-DYNAN/ASolid, beamNo25.4, 12.7 and 6.35

Blast pendulum systemsHeinchie et al. [63]2014PlateABAQUSMM-ALESolidNoN/A
Fallah et al. [61]2014PlateAUTODYN and ABAQUSN/ASolidNoN/A
Guan et al. [62]2014PlateABAQUSN/ASolid, shellNoN/A
Li et al. [65]2014PanelAUTODYNMM-ALEShellYes (1 : 4)0.05

Blast simulatorOesterle [75]2009WallLS-DYNALagrangeBrick, beam, shellNoN/A
Stewart [77]2010ColumnLS-DYNALagrangeShellNo12.7
Huson [72]2012Beam and plateLS-DYNAN/AContinuum elementsNoN/A
Li et al. [50]2012ColumnLS-DYNAN/AN/ANoN/A
Stewart [78]2012ColumnLS-DYNALagrangeShellNoN/A
Stewart [79]2014ColumnLS-DYNALagrangeShellNo12.7
Stewart et al. [67]2014ColumnLS-DYNALagrangeShellNoN/A

Blast chambersWu et al. [70]2013ChamberAUTODYNEulerN/ANo10
Snyman et al. [84]2016ChamberAUTODYNEuler LagrangeN/Aaxi10 and 4

Hydrocode software can utilize several different numerical techniques: Eulerian, Lagrangian, arbitrary Lagrange Euler (ALE), and smoothed particle hydrodynamics (SPH) to optimise the analysis of nonlinear dynamic problems.

Dynamic response of a structure to an explosive detonation can be best described using the Eulerian approach for the explosive detonation while structural response is generally best modelled using a Lagrangian method. Solid continua and structures are usually modelled using a Lagrange processor which operates on a structured (I-J-K) numerical mesh consisting of either quadrilateral (2D) or solid (3D) elements depending on the type of analysis, planar or spatial, respectively. Main characteristic of the Lagrange processor is that the numerical mesh moves and distorts with the motion of material, and there is no transport of material from cell to cell. Such a shape has an advantage that the motion tracking of material is very accurate, and the material interface and free surfaces are clearly defined. Severe material deformations result in high numerical mesh distortions which can lead to loss of calculation accuracy and efficiency or even calculation failure. Fluid, gases, and large distortions are usually modelled using the Euler processor. It includes first-order and second-order accuracy schemes. Material flows through the fixed numerical mesh. The equations of mass, momentum, and energy conservation are solved through a control volume method. The advantage of such a scheme is that large material flows and distortions can be easily treated. Because material interfaces and free surfaces are not easily distinguished in this method, sophisticated techniques must be utilized in order to track material interfaces. This leads to a numerical solver that allows both solutions in a single simulation with coupling between these solvers in the temporal and spatial domains [3]. Most commonly used processor is the arbitrary Lagrange–Euler (ALE) processor that combines the best features of both methods. It is a hybrid processor that enables free numerical mesh movement and distortion in accordance with user conditions. The calculation procedure is supplemented with an additional computational step that moves the grid and remaps the solution onto a new grid. Smoothed particle hydrodynamics (SPH) is a numerical meshless method that does not need definition of nodes and elements, instead, only a collection of points (particles) is necessary to represent a given body (element). A prescribed set of continuum equations is discretized by interpolating the properties at a discrete set of points distributed over the solution domain using a fully Lagrangian modelling scheme. Its main advantage is the Lagrangian nature associated with the lack of a fixed mesh.

These employ partial differential equations that govern the basic physics principles of conservation of mass, momentum, and energy (Table 7). The equations to be solved are time-dependant and nonlinear. Constitutive models that describe material behaviour and a set of initial and boundary conditions together with differential equations define the complete system for blast analysis [3]. Numerical programs usually used in blast modelling, which are proved to provide most reliable results, are LS-DYNA [111], AUTODYN [112], and ABAQUS [113].


EulerLagrange

Mass
Momentum
Energy

where represents the material density, is the velocity, t time, is the global Cartesian coordinate, is the stress tensor, is the deviatoric part of stress tensor, is the pressure (hydrostatic part of stress tensor), is the external body force by unit mass, is the deviatoric strain rate, and is the specific internal energy.

Due to material complex behaviour in blast analysis, a wide range of phenomena have to be modelled, for example, strain hardening, nonlinear pressure response, compaction, crushing, etc. Because of that, models are often broken into three components: equation of state, material strength model, and material failure model. An equation of state defines the hydrodynamic response of a material (important due to the air environment in which blast pressures are generated and through which are blast waves transferred to structures). Material strength models define nonlinear elastic-plastic response, and material failure models simulate the various ways in which materials fail. There is a wide range of predefined explicit material models available in each software material library. Each model can be modified in order to better correspond to specific situation that is analysed. Blast load is modelled using detonation of high explosives that is initiated at specific point inside the defined explosive material. High explosives are modelled using Jones–Wilkins–Lee equation of state derived from cylinder test data [106]. One of the possible problems in numerical simulations of blast loading and interaction with structures is mesh size. Optimal mesh size is very difficult to obtain, and parametric study is often required in order to obtain balance between result accuracy and calculation time [114]. Large mesh sizes can cause convergence issues and poor quality results, while small mesh size can cause prolonged calculation times, in scale of days or even weeks. This can be solved either by mesh size sensitivity analysis or by using parallel processing, or both.

Figure 9 in Wu et al. [86] represents comparison of experimentally tested and numerically simulated damage of RC column subjected to close-in detonation of charge equivalent to 25 kg of TNT. The computed crack profile of concrete as well as the large lateral deformations of longitudinal and transverse reinforcement is correctly reproduced if compared to the tested specimen.

Figure 9 in Castedo et al. [4] shows comparison of experimentally tested and numerically simulated damage of RC slab strengthened with steel plate on the upper side of the slab, directly under the explosive charge. A numerical model was developed in order to simulate the structural behaviour of full-scale RC slabs under blast loading. The numerical results were validated with experimental data in three field tests in which a standard RC slab was blasted under the same conditions. The extent of surface damage on each face was used to assess the performance of numerical modelling in comparison to tests. Conclusion was that the numerical models are able to predict the damage distributions successfully even when the test characteristics change. While these models are not perfect, they can be used to explore the feasibility of other slab reinforcement concepts prior to explosive testing and to model more complex structures affected by blast loads.

4. Conclusion

The most realistic representation of blast loading can be obtained only with full-scale field tests which best mimic real-life situations. Field tests are the most widespread method for blast experimentation but also the most dangerous; in addition, if full-scale field tests are conducted, then the costs of conducting this kind of tests are exponentially higher. Blast experimentation is usually conducted on scaled specimens what reduces the need for large explosive quantities and consequently lowers the overall danger of injury. Except field tests, researchers are trying to design tests that are able to produce blast-like action on experimental specimens with new procedures without using explosives. One of the examples is the BakerRisk blast simulator that uses dynamic actuators for inducing blast-like impulse loading. The simulator is capable of blast testing of all types of structural elements and large-scale complex specimens from which interaction of elements can be observed, which is important for force distribution and overall structure behaviour studies. Usually researchers are adopting the test method that is best suited for their resource capability.

Same instruments are used for blast measurements regardless of the experimental method used. In the course of years, instruments are developed and designed to be more robust, not only in their design in order to withstand high pressures and debris impact but also in their reliability to transmit recorded signals without any distortions.

Although blast phenomena can be difficult to model, because of the large number of variations in parameters which describe material models, finite element types and sizes, and boundary conditions and explosive loading, numerical models can be used to predict structural behaviour with fairly good accuracy in comparison to experimental tests. Use of advanced computer modelling (sophisticated material models, parallel processing, etc.) is essential to understand the behaviour of structures subjected to a blast load.

Further development of blast tests and measuring instruments can lead to better numerical representation of phenomena and consequently, maybe, to full substitution of field or any other kind of tests to numerical simulation. However, in order to achieve this, high reliability of accumulated test data and considerable speed-up of computer-processing capabilities have to be ensured.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

This paper was supported in part by the Croatian Science Foundation (HRZZ) under the project (UIP-2017-05-7041) “Blast Load Capacity of Highway Bridge Columns,” and support for this research is gratefully acknowledged.

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