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The blast hazards are associated with extreme randomness. Thus, structures under blast should be properly designed for such highly uncertain phenomena. However, codal stipulations and existing literature do not consider important uncertainty-related design issues, such as record-to-record variation of blast load, high uncertainty levels associated with blast parameters, and robustness of structural behaviour under extreme blast events. In the present study, a computationally efficient robust optimisation (RO) approach is proposed for blast-excited structures by addressing these issues. In doing so, a new CDF-based constraint formulation is developed in the dual response surface-based metamodeling framework to avoid the use of direct Monte Carlo simulation (MCS) during RO iterations. Thereby, the proposed approach becomes computationally much efficient than the conventional direct MCS-based RO. Since the proposed approach resorts to matching the CDF of the actual response, instead of the conventional RO formulations based on the first two statistical moments only, the approach is more realistic. The present approach adopts the moving least-squares method instead of the usual least-squares method to retain accuracy in response approximation. The blast load time-history is generated by a stochastic field model with proper validation through real blast data. Three example problems have been investigated to establish the effectiveness of the proposed RO procedure. The RO results depict that the present method yields economic design solutions, which are also insensitive to high uncertainty levels associated with the extreme blast load. The COV of performance function is substantially low even when input parameter uncertainty is high.

The propagation of shock waves in confined environments is a complex phenomenon due to the potential for a multiplicity of reflections, diffraction and superposition of waves. The study of such wave propagation effects, which is different from the propagation of shock waves in free-field scenarios, is not entirely described in literature, especially when studying their influence on the response of structures. The analysis of such phenomena is of extreme relevance to the evaluation of protective structures to ensure the security of equipment and personnel. This paper studies the influence of shock wave related parameters on the mechanical response of simple structural elements. This is achieved through the analysis of the impulse train, multiple positive and negative pressure profiles and signal simplifications. This research uses the finite element code LS-DYNA to analyse the structural response sensitivity of a metallic plate to different parameters, when subjected to pressure data recorded from experimental tests. It is observed that the structural response is significantly influenced by the loading regime. Results indicate that the impulse has a significant effect on the deflection-time history of the structure in the impulsive regime and that the peak pressure and pulse duration affect the deflection response in the dynamic regime. It also shows that correctly defining the negative impulse train in the pressure-time history is one of the main factors leading to an accurate modelling of the mechanical response of the structure. It is also found that a complex and realistic pressure history profile can be reduced to a simplified pulse for structural analysis and design purposes.

The demand for the protection of important government and public buildings has increased in recent days to resist blast loads due to frequent terrorist activities occurring around the world. Sandwich panels are preferred structural elements that can be used to protect the parent structure by mitigating the blast pressure. Numerical analysis of sandwich panel consisting of steel plates of equal thicknesses separated by a saffil foam core is carried out to evaluate its response under blast load. Parametric analysis of sandwich panels with varying foam thicknesses and standoff distance is performed using LS-DYNA®. The steel face and back-sheets in sandwich panels are modelled using piecewise linear plasticity material model and saffil foam is modelled using crushable foam material model available in LS-DYNA®. Moreover, back sheet of sandwich panels is stiffened using six different stiffener configurations. Finally, behaviour of conventional sandwich foam panel is compared with the stiffened sandwich foam panels for the considered stiffener configurations. Response of these different configurations of sandwich panels is evaluated based on peak central point displacement at the back sheet of the panel and it is observed that provision of stiffeners considerably improves the blast mitigation capacity of the sandwich panel.

Blast doors are specially designed doors for military facilities and important civil buildings in potentially explosive environment. In the present investigation, Finite Element (FE) analysis is carried out to understand the dynamic response of blast door under a given blast loading using ABAQUS/Explicit®. Five different doors configurations with two different materials i.e. AISI 1045 steel and structural steel (ST37) are investigated. Further, effect of consideration of strain rate, on dynamic response of the doors, is investigated using rate dependent Johnson-Cook model. Blast load is applied using ConWep function to understand the dynamic response of blast door in terms of displacement at different locations along with their failure patterns. Based on this investigation, it is observed that central point displacement is significantly influenced by the geometry of door with all other parameters being same. Further, considerations of strain rate show no major effect on the peak displacement for both the materials considered in the present investigation.

After the numerical study of medium-to-large-scale Boiling Liquid Expanding Vapour Explosion’s (BLEVE) in open space ( Li and Hao, 2020 ), this second article focuses on the investigation of the interaction of blast wave with structures in obstructed environment. Currently, pressurized tanks are commonly used as the storage vessels in the oil and gas industry. Pressurized tanks contain high-energy liquid/vapour which, if accidentally released, originates a BLEVE. Although there are already a series of approaches available in literature to estimate blast waves generated from these pressurized tanks, most of these approaches are suitable to predict blast load in the open space only. In this paper, the authors intend to utilize their previously validated numerical approach to predict BLEVE’s peak pressure in different obstructed environments. By carrying out over 200 different simulations of BLEVE, the separation distance effect, obstacle geometry effect and BLEVE’s scale effect on blast wave generation and propagation are studied. A number of simulation-based correlations for pressure prediction are proposed. The Bologna BLEVE that occurred in 2018 is further modelled to investigate the accuracy of the proposed correlations in predicting the peak pressure in the event. The outcome of this study can be used to predict explosion loads for better assessment of their effects on structures.

The solution to many engineering problems is obtained through the combination of analytical, computational and experimental methods. In many cases, cost or size constraints limit testing of full-scale articles. Similitude allows observations made in the laboratory to be used to extrapolate the behavior to full-scale system by establishing relationships between the results obtained in a scaled experiment and those anticipated for the full-scale prototype. This paper describes the application of the Buckingham Pi theorem to develop a set of non-dimensional parameters that are appropriate for describing the problem of a distributed load applied to the rostrum of the paddlefish. This problem is of interest because previous research has demonstrated that the rostrum is a very efficient structural system. The ultimate goal is to estimate the response of a complex, bio-inspired structure based on the rostrum to blast load. The derived similitude laws are verified through a series of numerical experiments having a maximum error of 3.39%.

This paper introduces a novel hierarchical core structure to sandwich panel for bearing the blast loading, in which each vertex of a regular hexagonal cell was replaced with a smaller hexagonal unit. The finite element (FE) models of such hierarchical honeycomb sandwich panels were established and validated with the experiments under different impulse loads. The hierarchical honeycomb cores were compared with the regular honeycomb counterpart in terms of the peak deflection on the back facesheet, compression and specific energy absorption (SEA) of the core. The results showed that the maximum deflection at the back facesheet of the hierarchical honeycomb sandwich panels were smaller than the regular honeycomb counterpart for a higher level of blast load (specifically, the dimensionless impulse higher than 0.06). It was found that the structural hierarchical parameter γ (i.e. the ratio of the newly-introduced smaller hexagonal edge length (L1) to the regular hexagon edge length (L0)), had limited influence on the maximum deflection of back facesheet of the sandwich panel, but had a significant effect on the SEA of the cores.

A new fence type blast wall consisting of steel poles was recently proposed based on the idea that the blast wave-obstacle interaction could generate wave reflection, diffraction and out-of-phase interference to reduce the wave energy. The effectiveness of this kind of new blast wall in mitigating blast loading was investigated through 2D numerical simulations and field blasting tests. In this study, 3D numerical simulations are carried out as an extension of the previous studies for a more comprehensive understanding of the effectiveness of fence blast wall. The simulations are performed by using an explicit dynamic finite element analysis software AUTODYN 3D with validated material models. Responses of a reinforced concrete (RC) wall under blast load are also calculated for comparison. Influences of different parameters of the fence wall, including the cross-sectional shape of the steel poles, spacing between poles, number of fence layers and spacing between layers, on its effectiveness in mitigating the blast loadings are investigated. The peak overpressure, impulse and overpressure-time histories behind the fence and RC blast wall are compared with those in free field for evaluation. It is found that the fence blast wall, if properly arranged, could perform equally or even better than the RC wall in mitigating overpressure and impulse of blast wave. Moreover, fence blast wall is less likely to generate the secondary debris hazards associated with the RC and other solid walls when close-in explosion occurs. Therefore, it is an excellent alternative blast barrier in protecting critical structures in urban areas.

This paper presents an experimental investigation carried out to understand the behavior of reinforced concrete sandwiched panels (RCSPs) under blast load. An RCSP is composed of an EPS (Expanded Polystyrene) foam core, which is surrounded by spray-on reinforced concrete skins (like ferrocement overlay) on both sides. For this purpose blast load test on four free-standing RCSPs in 17 blast case scenarios were conducted and the physical behavior was analyzed through high quality visuals and fragility curves were developed. The fragility curve interprets the relationship between damage intensity with charge size and scaled of distance. On the basis of results it is concluded that RCSP panel has greater capability of absorbing and dissipating energy generated by blast, and stable against fragmentation as compared to other conventional building systems used in Pakistan. Based on the assessment RCSPs walls/panels are strongly recommended for protective barrier installed in the vicinity of critical infrastructure against blast loading.

In this study, a novel green construction material, high performance alkali-activated geopolymer concrete is introduced. Both numerically and experimentally investigations were conducted on a new type of structural slabs made of steel wire mesh reinforced geopolymer concrete against close-in ground surface explosion. Steel rebar reinforced conventional concrete slabs are also studied to compare the results. The experimental investigation was conducted to study the slab damage mechanism. It is found that the steel wire mesh reinforced geopolymer concrete slab showed less damage and fragmentation under 50 kg Trinitrotoluene (TNT) blast load within 3 m, 5 m and 7 m distances as compared to the C30 concrete slab. Numerical analysis was then conducted to further investigate the slab dynamic responses. Combining the steel wire mesh reinforcement with geopolymer concrete can help increase the blast resistance capacity leading to promising and environmental friendly structural protective design.

Blast effects are severe especially in case of close underbelly blast events. The hull of the structure must resist the blast load with limited deformation and on the other hand it should have sufficient rigidity also to have optimised structural design. Numerical analysis revealed the peak deformation areas on the hull structure which were further stiffened by adding the stiffeners to control the peak deformation. In the analysis, the stress-time, pressure-time and deformation-time graphs were also obtained for the blast events for with and without adding stiffeners. The optimised plate thickness with limited deformation by means of stiffeners was obtained.

The paper presents a study aimed at understanding the characteristics of an internal explosion within a chamber with limited venting. The study includes numerical simulations and analytical derivations. An in-house 3D code employing an improved weighted essentially non-oscillatory (WENO) conservative finite difference scheme was used to carry out the simulations. It is indicated that the proposed improved WENO scheme can resolve the shock waves with higher accuracy and resolution. Further, a simplified analytical model to predict the quasi-static overpressure was developed based on the conservation law of total energy and dimensional analysis theory. It is demonstrated that the proposed simplified approach for prediction of the quasi-static overpressure agrees well with simulation results for a wide range of explosive weights and venting hole sizes. The studies in this paper provide an efficient method to predict the blast load inside a partially confined chamber for the analysis of the consequences of explosion.

The combined loading of blast and fragments on reinforced concrete (RC) elements has been studied in field tests of RC T-walls that were subjected to detonated cylindrical cased charges. Characterization of the combined loading has been experimentally studied and analyzed. This analysis includes the pressure time-history of a control bare charge and of the cased charges, the relation between them, and the distribution of the fragment masses and velocities over a vertical barrier that was impacted by them. The structural damage of the RC walls due to the fragmentation impact was also measured. The results indicate that while the detonation of a bare charge, without a casing, yielded negligible structural damage, major damage was caused due to the impact of the fragments. The importance of the findings that are reported in the paper relates to design of protective structures that are prone to be subjected to extreme loads caused by cased charges. Commonly, except for very small standoff distances, the fragments will reach the structure before the blast wave, which means that the damage that is created by the fragments should be considered for the global analysis of the element response to the blast load. Furthermore, the results reported here show that the smaller the standoff distance, the more significant the damage influence is on the response of the structure.

The purpose of the present study is to put forward an innovative method to improve dynamic response behaviors of protective concrete arches subjected to blast load. To achieve this goal eight arches were made, of which six were strengthened with carbon fiber reinforced polymers (CFRPs) on the intrados. Field explosion experiments were designed and carried out to reveal the strengthening effects of different CFRP strengthening schemes. The dynamic structural responses of the tested arches were recorded through linear variable differential transformers (LVDTs) and pressure sensors. The results of the experiments, such as the distribution of concrete cracks and the debonding length of the CFRP strips, indicate that CFRPs are effective in reducing concrete cracking and spalling of the protective arches, and that the fully-bonding method is significantly more effective than the partially-bonding method. Meanwhile, when the scaled standoff distance decreases, the strengthened arches experience failures ranging from ductile cracking to dynamic spalling. Simplified analysis models are proposed to estimate the equivalent static load and to reveal the protective mechanism of the CFRP strengthening. The research confirms that by using the CFRP bonding technique, an efficiently protective concrete arch structure with excellent anti-explosion performance could be constructed.

This study proposes a method for evaluating the displacement response of RC beams using the equivalent single-degree-of-freedom (SDOF) model considering a close-in blast load distribution. First, to examine the spatial distributions of the peak overpressure and impulse in a close-in explosion, explosion tests were conducted with C-4 explosives at scaled distances of 3.0–0.15 m/kg1/3. Approximation formulae for the spatial distributions of peak overpressure and impulse were proposed as functions of explosive mass, stand-off distance, and target member length. The peak overpressure and impulse estimated by the approximation formulae reproduced the test data adequately. Secondly, close-in explosion tests on RC beams using 110, 160, and 250 g C-4 explosives at a scaled distance of 0.20 m/kg1/3 were conducted to examine the failure states of the RC beams. The modified SDOF model considering blast load distribution owing to close-in explosion was proposed. The proposed SDOF model effectively evaluated the displacement response of the RC beam subjected to the close-in explosive load, while the experimental results were marginally overestimated.

In recent decades, vapor cloud explosions (VCEs) have occurred frequently and resulted in numerous personnel injuries and large property losses. As a main concern in the petrochemical industry, it is of great importance to assess the consequence of VCEs. Currently, the TNT equivalency method (TNT EM), the TNO multi-energy method (TNO MEM), and the Baker-Strehlow-Tang (BST) method are widely used to estimate the blast load from VCEs. The TNO MEM and BST method determine the blast load from blast curves based on the class number and the flame speed, respectively. To quantitatively evaluate the flame speed for the BST method, the experimental data is adopted to validate the confinement specific correlation (CSC) for the determination of the class number in the TNO MEM. As a bridge, a quantitative evaluation correlation (QEC) between CSC correlation and the flame speed is established and the blast wave shapes corresponding to different flame speeds are proposed. CFD software FLACS was used to verify the quantitative correlation with the numerical models of three geometrical scales. It is found that the calculated flame speeds by the QEC are in good agreement with the simulated ones. A petrochemical plant is selected as a realistic scenario to analyze the TNT EM, TNO MEM, BST method and FLACS simulations in terms of the positive-phase side-on overpressure and impulse at different distances. Compared with the flame speed table, the predicted overpressure from BST curves determined by the proposed QEC is closer to that from FLACS and more conservative. Furthermore, the predicted results of different methods are compared with each other. It is found that the estimated positive-phase side-on overpressure and impulse by the TNO MEM are the largest, and the estimated impulse by the TNT EM is the smallest. Moreover, the estimated overpressure and impulse are larger in the higher reactivity gas.

Blast mitigation of civil and transportation infrastructure is in focus due to the ever-present volatile geopolitical situation. Structures are not designed to withstand blast load, and in areas of an imminent attack, their sensitive elements require blast retrofit. The retrofit technique selected follows three criteria: speed and ease of application and relatively low price. Commercially available glass fibers, in the form of textiles and mats, were applied on RC slabs using epoxy resin. The test program consisted of two phases. The first phase consisted of laboratory four-point static bending tests of RC slabs to determine the feasibility and efficiency of devised retrofit. The second phase consisted of field blast tests of RC slabs to study blast behavior and determine the applicability of devised retrofits. Applied retrofit has been proved useful in reducing flying debris and maximum deflection in the tested range of explosion.

Being able to efficiently mitigate the effects of blast loads on structures, sacrificial cladding solutions are increasingly used to protect structural elements from the effects of accidental explosions and/or terrorist attacks. The present study analyses the loss of effectiveness of a deterministically designed sacrificial cladding when variability in the material properties and uncertainties in the mechanical model are considered. The results of an experimental campaign are used to validate the numerical models that allow the deterministic design of a sacrificial cladding which successfully improves the blast resistant capabilities of a given structural element. Nonetheless, it is shown that, taking into account the probabilistic variability of key parameters is of vital importance when designing sacrificial cladding solutions, since, when not properly designed for the structural element it intends to protect, adding a sacrificial cladding might negatively impact its blast resistant capabilities. Additionally, it is concluded that the deterministic approach might be against safety. In the reported case study, when comparing the admissible charge weight yielding from the deterministic and probabilistic approaches, one verifies that the former allows a higher charge weight.

This paper reports on the response of cladding sandwich panels with tubular cores to uniform blast load. The core of the cladding sandwich panels consisted of empty or foam-filled thin-walled circular tubes (38 mm in diameter) made from either aluminium 6063-T6 or mild steel riveted laterally between the skin plates at varying spacing arrangements. The tubular cores were arranged to provide four different types of panels. The front plate skin of the panel, exposed to the blast load, was made from DOMEX 700 Steel while the back plate skin was made from mild steel. Three types of polymeric cellular foams, namely self-raising polyurethane, expanded polystyrene and cross-linked polyethylene, were used to fill the circular tubes. The “uniform” blast load was achieved by detonating varying charge masses of explosive (ranging from 6 g to 50 g) with a prescribed load diameter of 40 mm at a stand-off distance of 200 mm down a square tube. Energy was dissipated mostly through the plastic deformation of the tubular cores. The foam added extra energy absorbing capacity. The results showed an increase in average deflection with an increase in charge mass/impulse for the different types of panels. The cladding panels with the least interaction between the tubular cores were observed to have the highest energy absorption capabilities for a given charge mass.

The world has recently witnessed tremendous increase in terrorist activities. This led to the requirement of blast resistant design of structures. The progressive collapse of structures, being the most severe consequence of blast generated waves, has been the subject of several studies. Although structural engineers are developing methodologies for the mitigation of progressive collapse, there is a lack of adequate tools that can be employed for simulating and predicting the progressive collapse response of structures with acceptable confidence. An attempt has been made in this paper to develop a practical and acceptable procedure for the progressive collapse analysis of reinforced concrete (RC) framed structures. The adequacy of the procedure has been demonstrated by studying the progressive collapse behavior of a typical RC framed high-rise building in Riyadh when exposed to blast generated waves.

Two type novel aluminum foam filled energy absorption connectors were proposed to be inserted between the blast resistant facade and building to absorb blast energy and reduce blast load transferred to the building. In this paper, the nonlinear finite element (FE) method was adopted to study the energy absorption performances of the two type connectors. The FE models of the connectors under quasi-static compression loading were first established and the accuracies of the FE models were verified by comparing the force–displacement curves obtained from tests and FE analyses. Then, the FE models were used to investigate the effects of filled aluminum foam, plate thickness and geometry as well as aluminum foam width on the energy absorption performances of the two type connectors. It was found that the two type connectors showed comparable energy absorption performances and the specific energy absorption could be significantly improved by filling the connector with aluminum foam.

Due to the influence of strain-rate effect of rate dependent materials, the relations of responses between scale-down model and prototype plates under blast loads cannot assure the satisfaction of the scaling laws, which is known as non-scalability of structure under impact loads. In this paper, by employing the dimensional analytical method, the strain-rate effect involved in blast loaded plates with different scaled values was firstly analyzed, then a corrected equation was established by taking a correction factor of impulse per unit area into consideration. Besides, a set of empirical formulae used to calculate the impulse per unit area is given, in which the relations between the mass of TNT, the stand-off distance and the impulse per unit area is determined. Furthermore, this paper adopted the method presented by Oshiro and Alves [14] to establish the corrected similarity relation between incomplete scale-down models and prototype. On the basis of this, a rapid solution to predict the value of exponent n is proposed, guaranteeing this method could be used more smoothly in practical engineering.

For RC columns exposed to blast loads, fibre reinforced polymer (FRP) is employed to examine its effectiveness in strengthening the concrete structure against blast load. It should be noted that no systematic studies could be found in the literature to derive pressure and impulse (P-I) diagram for FRP retrofitted RC columns. Therefore, the objective of this research is to develop finite element model to provide data for use in the development of P-I diagram that can be used to mitigate blast hazards and predict damage in RC columns retrofitted with FRP. In this study, various strengthening scheme performed against blast loads numerically by running computer simulations using the commercial software LS-DYNA. Validation of the models is performed based on the blast field test to investigate the accuracy of model simulations to present the behaviour of the models. The research compared the structural behaviour of an un-strengthened RC column with various column strengthened with different FRP wrap thickness, strength and arrangement. The results of the simulations showed that strengthening with FRP is an effective way to increase the blast resistance capacity of columns. This information would allow the designer to identify the critical location for placing blast barriers for protection purpose.

Different from strengthening key structural members against potential blast load to make it thicker and stronger, an alternative approach of blast mitigation is to apply sacrificial claddings with lightweight core to the exterior of existing buildings and structures. Selected materials and structures of soft resistance and low density undergo large deformation with almost constant stress and absorb large amounts of energy, making them promising for structure protection. After a blast attack, replacing the sacrificed and damaged core with a new one immediately resumes the blast mitigation capacity, making the protection resilient. Applying such sacrificial claddings has multiple merits, including efficiency in protection, sustainability, and flexibility. However, there are still some problems to be addressed before such claddings can be successfully applied in engineering practice. In this study, a criterion based on energy approach is established, to determine the effectiveness of blast mitigation with lightweight claddings. The analytical model incorporates interaction among the blast load, the cladding system, and the protected structure member which is simplified as an SDOF system. The underlying mechanism of blast mitigation with lightweight claddings is analyzed in terms of energy. Key governing factors that determine the protection effectiveness are identified and their influence is discussed.

Various critical equipments are used in nuclear, defence and aerospace industries. These equipments which are used in these industries need to be strong and light in weight. Steel, aluminium and magnesium are widely used as structural material in these equipments. With increase in global terrorism it is important that these equipments are safe under blast. Hence, it is imperative to study the behaviour of these plates when subjected to blast loading. Explicit finite element technique using Abaqus@ is used to study the effect of blast load on these plates. Elastic plastic model is used for the materials and Conwep model is used to model the blast load. Numerical simulations are carried out for monolithic plates and layered plates of different materials of equivalent weight. Various combinations of plates for equivalent weight are also studied. The paper discusses the performance of these monolithic and layered plates under blast load.

Even though blast events in inhabited areas are characterized by a low probability of occurrence, they can present a high risk for buildings and their occupants. The means to reduce the vulnerability and prevent the progressive collapse of buildings includes large stand-offs, enhanced local strength of structural elements, and increased redistribution capacity after a local damage. Blasts are extremely complex events, especially when the charge is detonated at a small distance from the building. In such cases, the application of analytical methods may give inaccurate results. The paper presents the results of a combined experimental/numerical program, which focused on the response of steel frames to close-in detonations. Two identical specimens were tested inside a specialized bunker for different charge sizes and stand-off distances. Very similar behaviors and failure modes were observed for the two specimens. The numerical model, calibrated against test data, was able to accurately predict the deformations and failure mode of the specimens. The results of the parametric numerical study indicated that the local failure mechanism and resistance to progressive collapse of steel building frames depend very much on the blast load parameters but also on the level of gravity loads in columns.

Nonlinear response of laminated composite plates and cylindrical panels subjected to a parabolically distributed blast load is studied here using a shear deformable finite element method. The nonlinear finite element equations of motion are solved in the time domain by an energy and momentum conserving time integration technique. The state-of-stress inside the laminated panels is calculated at each time-step to predict the occurrence of damage using Tsai-Wu quadratic failure criterion. The effects of span-to-thickness ratio, radius-to-span ratio and peak pressure on the nonlinear dynamic response of laminated composite plates and curved panels are investigated.

Ongoing terrorist attacks on many structures around the world have increased the importance of analysis of structures under blast loading. Despite the progress made in this area, there is a need to better understand the structural performance of framed concrete structures under severe loading before, inevitably, adopting any mitigation measures. Most of the structures that are damaged by bombs or impact loading are not initially designed to resist blast loads. The severe vulnerability of these structures has led to ongoing development of new provisions and guidelines of effective techniques to mitigate risks associated with explosions. In this research, detailed finite element analyses were performed using ABAQUS to assess the structural performance of reinforced concrete frames under blast loading. A model of two dimensional, 4-story reinforced concrete frame was selected for the study. The response of the structural model under the simulated blast loads is presented, along with two alternative designs as a precursor to provide mitigation guidelines in the future. Results showed that changing the design of the external columns improved the response, especially using the concrete filled steel tube section.

Based on the governing equations of a fully clamped plate, a new dimensionless number for the dynamic response of box-shaped structures subjected to internal blast loading was suggested in this paper. The dimensionless number considered the influence of blast load, the strength of material and the structural dimensions. The parameters in the proposed dimensionless number can be easily obtained in practice. The dimensionless number has clear physical meaning and leads to good correlation between the response of box-shaped structures and the blast energy. It was also found that the structural response is inversely proportional to the material strength and the volume of the structure. The dimensionless number was applied to analyze the experimental data of box-shaped structures under internal explosion. The validity and efficiency of the dimensionless number were discussed, and an empirical expression was obtained which can be applied to the prediction of dynamic response of similar box-shaped structure under different internal explosive loads.

A novel multilayer facade system, which consisted of a water steel tank integrated with a layer of energy absorbing aluminum foam panel and a stiffened steel panel, was developed to resist blast loading. The blast resistance and response behavior of the proposed facade system were investigated using nonlinear finite element method. The accuracy of the numerical model was verified by comparing the predicted results with the test results. The analyses showed that the energy absorbing aluminum foam layer was capable of reducing the blast load acting on the facade panel and building. The blast resistance of the multilayer facade system could be further enhanced by increasing the aluminum foam layer thickness. An analytical model considering Dynamic Increase Factor (DIF) and coupled deflection mode shapes was developed to predict the displacement response of the facade system subjected to blast loading. The accuracy of the analytical model was validated by comparing the predicted results with the numerical results. It was found that the analytical model with varying DIF could provide better prediction of the displacement response of the multilayer water facade system as compared to the method using a constant DIF.

In recent years, the vulnerability and protection of subsurface structures under blast loads became a fundamental issue in terms of security (loss of lives and structural damage). A tunnel can be considered as an underground shelter and is a crucial structure owing to its conservative nature against explosions. This study is performed to obtain a further understanding of surface explosion influence on segmental tunnels. In this paper, a tunnel lining and its segmentation with planar and curved joints under dynamic loads were investigated. In this regard, a 2D finite-deference simulation of the Tehran metro segmental lining was conducted. Subsequently, an explosion wave stress of 500 kg of TNT explosive was considered as the reference loading case. The results indicated that the segmental lining with curved joints is efficient and succeeds in neutralizing the surface explosion. The maximum bending moments and axial forces in the curved segmental lining are lower than in the planar segmental and continuous lining. In terms of vertical and horizontal displacements of the tunnel lining, the segmental structure with curved joints induces the minimum deformation amount. The continuous lining and planar segmental lining show instability under the reference blast load. Finally, it can be concluded that the segmental lining with curved joints is highly efficient and stable in case of a surface explosion.

Precast concrete structures have been widely applied in civil engineering recently due to the better quality, non-pollution, and fast construction. In this study, the finite element model and theoretical analytical model are proposed to study the blast performance of precast concrete slabs under blast load. Firstly, the accuracy of the finite element model is validated by an experiment. Then, the effects of the explosive charge, the thickness of the slab, and the compressive strength of concrete on the dynamic behaviors of fabricated concrete slabs are parametrically investigated. At last, a theoretical analytical model of the precast concrete slab is proposed to predict the maximum deflection under blast load. It is indicated that the failure modes of the slabs are changed from bending failure to shear failure as the explosive charge increases. The thickness, explosive charge, and the compressive strength of concrete have significant influences on the anti-blast performance of the fabricated concrete slab. The theoretical analytical model can reasonably predict the maximum displacement of the precast concrete slab under blast load.

This paper presents the results of a study examining the influence of steel fibers on the static and blast performance of beams built with high-strength concrete (HSC) and high-strength steel reinforcement. As part of the study, a series of fiber-reinforced HSC beams designed with Grade 690 MPa ASTM A1035 reinforcement are tested under static and blast load conditions using a shock-tube. The performance of the beams is compared to that of a control set of specimens built with plain HSC and high-strength bars. In addition to the effects of the steel fibers, the effects of reinforcement type (Grade 690 MPa vs. 400 MPa) and high-strength steel ratio (ρ = 1–2.2%) are also investigated. Under static loads the provision of fibers is found to significantly enhance the ductility of the high-strength reinforced concrete beams. Under dynamic conditions, the use of fiber-reinforced HSC leads to important enhancements in blast behavior, including better control of displacements, increased blast capacity and improved damage resistance. As part of the numerical study the blast response of the beams is predicted using 2D finite element (FE) modelling.

Increasing terrorist attacks towards ordinary or strategic buildings and soft targets represent one of the major impetus to improve existing methods of design for blast-resistant structures. When a building undergoes an extreme dynamic event such as blast or impact, local damage of its key structural components (i.e., the columns) may lead to severe failure and even collapse of the entire building. Consequently, the availability of simplified, time efficient and reliable methods of analysis can be relevant for design. In this paper, H-section steel columns subjected to blast loads are numerically investigated, so as to derive practical formulations for damage evaluation assessment. The strategy is based on parametric Finite Element (FE) models (with up to 5600 configurations), validated towards experiments and, used as an extensive data bank, for further elaboration via Gene Expression Programming. Analytical formulations are in fact proposed for calculating some relevant parameters of design, such as (a) the initial and (b) the residual axial capacity of the examined columns. The collected results show that the proposed formulations can offer a good level of accuracy and high calculation efficiency for blast loaded H-section steel columns. In addition, an expression is proposed to relate the damage index (based residual axial capacity) to the conventional displacement/rotational index. Sensitivity analyses and some calculation examples are finally presented, to further investigate the potential of the approach for design purposes.

Dome structures are often employed for industrial buildings and may be potential targets of terrorist attacks or accidental explosion. Military design manuals that are commonly used for structural design practice are based on the assumption that the blast wave reflects on an infinite or finite flat surface. These semi-empirical formulae ignore the blast wave propagation behaviour on a finite and variable-curvature reflector. The purpose of this research work is to estimate the blast load on dome structures during an external explosion. To achieve this objective, two laboratory-scale spherical dome structures were tested experimentally with 11 different blast cases. Following the experimental analysis, numerical parametric analysis based on ANSYS/AUTODYN was carried out to study the propagation and reflection on dome roofs. In addition, the performance of the Mach effect, reflection effect, diffraction effect, clearing effect and decay coefficient of the blast wave on the dome roof were investigated for different structural and explosion parameters. Based on this, a series of empirical equations are proposed to describe the temporal and spatial blast load distribution on a dome roof mounted on a supporting structure. This new load model described in the paper has been validated as it is able to predict the results of the experimental measurement on dome structures within experimental error.

A commercial finite element package, LS-DYNA, was employed to simulate the response of a single-layer reticulated dome to an interior blast. The dome, which was initially stressed by static preloading, encountered an interesting phenomenon namely counter-intuitive collapse, which was found during the blast analysis. The Johnson–Cook constitutive model for mild steel was used to identify different failure modes of the dome for more than 2430 samples. A seemingly counter-intuitive collapse was identified due to dynamic instability. This unusual collapse was explained using total potential curves, and the critical blast load was defined. The effect of different static preloads, which is the other determination factor of counter-intuitive collapse, was investigated. A relationship between collapse and static/dynamic loads was also obtained. The results indicate that single-layer reticulated domes, with large initial stresses, may collapse at lower dynamic loads than expected.

An innovative cement-based soft-hard-soft (SHS) multi-layer composite has been developed for protective infrastructures. Such composite consists of three layers including asphalt concrete (AC), high strength concrete (HSC), and engineered cementitious composites (ECC). A three dimensional benchmark numerical model for this SHS composite as pavement under blast load was established using LSDYNA and validated by field blast test. Parametric studies were carried out to investigate the influence of a few key parameters including thickness and strength of HSC and ECC layers, interface properties, soil conditions on the blast resistance of the composite. The outcomes of this study also enabled the establishment of a damage pattern chart for protective pavement design and rapid repair after blast load. Efficient methods to further improve the blast resistance of the SHS multi-layer pavement system were also recommended.

This paper provides a systematic study of the performance of ultra high performance fibre reinforced concrete (UHPFRC) slabs under close-in explosions. In the study, the UHPFRC slabs were manufactured with varying amounts and types of steel fibres. In field tests, various PE4 charge sizes were employed to generate blast load until a sudden increase in maximum deflection was observed. Peak 1/4 span deflections and development of slab cracks were recorded. With the results, the effect of steel fibres on performance of UHPFRC slabs can be better clarified. Static tests were also used to study the effect of fibres on the behaviour of UHPFRC specimens, results indicate that fibre distribution and orientation can clearly affect UHPFRC slab behaviour. Finally, finite element modelling was employed to simulate the performance of UHPFRC slabs under blast loading and these modelling results were compared to test data. Based on the comparison results, potential further enhancement of numerical models is discussed.

This paper present the experimental analysis of square mild steel plates subjected to blast loads in three different degrees of confinement (free air burst, fully vented and fully confined). Varying spherical masses of explosive were detonated at a constant stand-off distance from three different thickness target plates in the three different degrees of confinement to investigate the effects of confinement as well as the effect of plate thickness on the final plate deformations. Plate deformations ranging from one to fourteen plate thickness were obtained. The experimental results show that the midpoint deflection ratio between two different thickness plates subjected to identical blasts is inversely proportional to the ratio of the plate thicknesses. Equations for predicting the final midpoint deflection of square mild steel plates subjected to blast loading in the three degrees of confinement are presented.

Relation between blast wave parameters resulted from a condensed high explosive (HE) charge detonation and a surrounding gas (air) pressure has been studied. Blast wave pressure and impulse differences at compression and rarefaction phases, which traditionally determine damage explosive effect, has been analyzed. An initial pressure effect on a post-explosion quasi-static component of the blast load has been investigated. The analysis is based on empirical relations between blast parameters and non-dimensional similarity criteria. The results can be directly applied to flying vehicle (aircraft or spacecraft) blast safety analysis.

A numerical study of hollow and concrete-filled square tubular steel columns subjected to near-field detonations has been undertaken and validated through the experimental results. The experiments used concrete-filled and hollow square tubular columns (100 × 5 mm SHS Grade C350) made out of cold-formed structural steel hollow sections (SHS) that were simply supported at both ends. High explosives TNT charges were placed above the top surface of the column at two different scaled standoff distances of 0.12 m/kg 1/3 and 0.15 m/kg 1/3 . Failure patterns and permanent mid-span deformations were recorded and compared with the numerical analysis results. Arbitrary Lagrangian–Eulerian (ALE) formulations coupled with fluid–structure interaction (FSI) algorithms that are available in the advanced finite element code LS-DYNA were used in the numerical study. A detailed description of the numerical technique adopted in the study is presented. The models were validated with the experimental results and were used to obtain the failure pattern, permanent plastic deformation, pressure and impulse time histories, stress distribution, and energy absorption of the different configurations of the columns. The performance of hollow and concrete-filled SHS tubes for blast load mitigation was assessed and discussed.

Landmine detonation continues to be a serious threat to Army military vehicles in theater. One strategy to mitigate its effects is to use engineering design techniques to reshape the underbody of the hull. Previous works have shown that reshaping the hull's underbody can change the vehicle's response to blast loading. In the presented work, a metamodel-based shape optimization methodology is proposed for optimizing shallow-buried blast-loaded underbody structures. The shallow-buried blast load is simulated using an empirical model. Additional studies are conducted on target positions with respect to the blast load and load positioning and the effects of optimization parameters on the optimal solution. It is shown that target vertical position affects impulse response comparison, and for center-buried loads, the v-shaped underbody target produces a lower impulse than that of other shaped targets. Optimal solutions obtained using an adaptive domain reduction strategy produce more accurate solutions than a single iteration strategy. Based on the proposed optimization method, a unique v-like underbody shape is presented as the optimal underbody solution.

This paper presents the results of an experimental and numerical investigation into the response of circular Domex-700 MC steel plates to repeated uniform blast loads. The Domex 700 steel tests plates of thickness either 2 or 3 mm are mounted onto a ballistic pendulum and subjected to uniform blast load up to five times for repeated loading. In general, the plates show large inelastic global deformation with thinning occurring at the clamped boundary and in some cases tearing. A trend of increasing permanent mid-point deflection is observed for an increase in charge mass and number of witnessed blast loads. The results also show a decrease in the incremental mid-point deflection and an increase in the Vickers hardness of the plate at the boundary and central region with increasing number of witnessed blast loads. Numerical simulations are carried out to gain further insight into the deformation of plates subjected to repeated blast loading using ABAQUS/Explicit v6.10.1 in conjunction with the inbuilt blast function code, ConWep. A scaling factor is adopted to model the amplified blast wave resulting from the detonation of cylindrical charges at one end of a cylindrical tube. Very good correlation is obtained with regards to midpoint deflection and deformation profiles. The plastic strain obtained numerically shows good qualitative correlation with the experimental Vickers hardness tests.

The recent terrorist attacks all around the world and the evidence of the threats found especially in the Kingdom of Saudi Arabia have prompted the concerned authorities to address the risks to the critical infrastructure of the Kingdom. Understanding of the progressive collapse mechanism is an essential step to protect buildings against blast attacks. Buildings are very vulnerable to progressive collapse if one or more columns are lost due to extreme loadings. It is also important to study the likelihood of progressive collapse of buildings in Riyadh to avoid catastrophic events. The paper presents progressive collapse analysis of a typical multi-storey steel framed building in Riyadh to establish its vulnerability when subjected to accidental or terrorist attack blast scenarios. A commercial finite element (FE) package (LS-DYNA) was used to simulate the building response under blast generated waves. The numerical modeling was validated using the results of a published example of tubular steel beam subjected to blast load. Based on the FE analysis results, recommendations are given to mitigate (or control) the progressive collapse potential of steel buildings.

Facility Siting has received considerable attention in recent years. There are a number of generally accepted simplified methods for the prediction of vapor cloud explosion (VCE) blast loads, one of which is the Multi-Energy Model (MEM) (TNO, 2005). This paper presents an approach to improve the consistency in TNO MEM blast load predictions by providing explicit implementation guidance. A rule set was developed to improve the consistency with which key model parameters are determined. These rules incorporate no new science, but can be applied in a repeatable manner and are intended to reduce analyst variability and results which are more consistent with other approaches, such as the Baker-Strehlow-Tang (BST) method.

This paper presents a mixed numerical approach to model the blast waves generated by the detonation of a spherical stoichiometric mixture of propane and oxygen, impacting a plate-liquid system. The problem is split into two parts. The first calculation part relies on the modeling of the blast load and its propagation. Over-pressure distribution, in this part, is presented and reveals a very good level of agreement with experimental results. The time and space scales of the blast load data must be compatible with the plate-liquid system. This compatibility is ensured by an appropriate spatio-temporal interpolation technique. This technique is presented and its effectiveness and accuracy are demonstrated. The second part consists in modeling the response of the coupled plate-liquid system under the numerical blast load model. Experiments at reduced scale are carried out in two configurations in order to assess the effectiveness of this mixed numerical approach. Convincing results are obtained and discussed.

In this paper, a new multi-layer pavement system subject to blast load was developed. This multi-layer pavement system consisted of Asphalt Concrete (AC) layer reinforced with Geogrid (GST), followed by High Strength Concrete (HSC) layer and then Engineered Cementitious Composites (ECC) layer, taking into account their relative advantages in terms of strength and relative ductility. A series of field blast test was conducted to evaluate the behavior of the new multi-layer pavement in the field condition. Two pavement slabs were cast and tested. One is a normal concrete pavement, as control, and the other is the new multi-layer pavement. It was found that the new multi-layer pavement performed better than conventional pavement system when subjected to blast load. At the same time, a 3D finite element numerical modeling is employed to evaluate the dynamic behavior of the normal concrete pavement and the new multi-layer pavement system subject to blast load. For this modeling, a 3D dynamic numerical model using LSDYNA with appropriate material models and suitable boundary conditions are developed. Actual measurements from the field blast test were used as a validation for the numerical model developed. It was shown that the results from numerical model and field blast test measurements compared very well in terms of damage pattern, crater diameter, acceleration and total pressure cell readings. It is also observed that the new multi-layer pavement system had better blast resistance than conventional pavement system. The developed 3D numerical model using LSDYNA seems to be able to model the real behavior of the pavement subjected to blast load.

This article presents the results of a numerical study on the response of cladding sandwich panels with tubular cores that can be used as blast mitigators. The core of the cladding sandwich panels consisted of empty thin-walled aluminum circular tubes (38 mm in diameter) riveted laterally between the skin plates in different configurations (varying number of tubes and spacing between the tube). The skin of cladding sandwich panels consisted of a “rigid” DOMEX700 steel front plate which was exposed to the blast load and a back plate made of mild steel. The uniform blast load was achieved by detonating varying charge masses of explosive (ranging from 6 g to 50 g) at a stand-off distance of 200 mm down a square mild steel tube. The numerical model, developed in ANSYS AutoDYN 15.0, was validated for average deflection of the front plate and crush mode of the tubular cores using the experimental results that were presented in a previous paper [1] . The results of the simulations provided insights into the transient response of the cladding panels. The effects of the spacing between the tubular cores which also influenced the interaction between the tubular cores were also investigated. The number of plastic hinges formed was increased whilst the rotation angle of plastic hinges decreased with increasing interaction between the tubular cores.

Experimental and numerical studies are conducted to investigate the blast behavior of small-scale reinforced concrete slab (RCS), which is proposed to overcome the disadvantage of the previous studies without verification. A three-dimensional finite element model is established with validated material parameters, blast load model and reasonable choice of boundary conditions. Three small-scale RCSs are designed and cast, two RCS are subject to the explosion at a scaled distance of 0.611 m/kg1/3 and another RCS is subjected to blast load at a scaled distance of 0.77 m/kg1/3 to calibrate and validate the finite element model. The experimental results of damage area and linear variable differential transformers (LVDTs) are analyzed and compared with finite element analysis prediction. The comparison indicates that the failure patterns of these slabs are categorized as three types, including the low damage, moderate damage and severe damage in both experimental tests and numerical simulations. In addition, the numerical results of RCSs are consistent with test results, except for the formation of cracks, which demonstrates that the blast-resistant capacities of RCSs can improve with the reinforcement ratio increasing and the explosive charges decreasing.

This paper concerns the irreversible deformation and failure of metal plates to brief, but intense, dynamic (impulsive) load encountered in an air-blast. Hitherto, nearly all of the dynamic structural plasticity models of ‘fully-clamped’ plate only calculates its inelastic (mode I) deformation but have largely ignored damage and failure – exemplified by the partial and/or complete detachment (modes II*, II and III) of a plate from its support through material rupture – that occurs when the blast load is sufficiently intense. An analytical model that captures all three modes of the plate deformation is developed in this paper where emphasis shall be on providing the simplest formulation that contains all the essence of a material and deformation effect needed to quantify the problem. The proposed model adopts an energy density failure criterion of Shen and Jones [19] to delineate the various inelastic failure modes; employs the constitutive framework of limit analysis for simplicity; accounts for the simultaneous influence of bending, membrane stretch and transverse shear through an interaction yield criterion; and, include the effects of strain rate on the material flow stress through the Cowper–Symonds relation. Accuracy of model predictions for square mild-steel plates are assessed through comparison with results from finite element analysis, and experimental data compiled from the literature for a range of impulsive load intensities – they will be shown to be in good general agreement. Design maps delineating the different deformation regimes for different combinations of blast impulse and length versus thickness ratio are constructed for plates of equal mass.