Explosive Blast Loading Research Articles

Nonlinear dynamic analysis of aircraft CFRP sandwich wings under explosive blast loading: Introducing SVM-DNN algorithm to predict dynamical information

The aircraft wings are a crucial component, particularly during mechanical shock excitation. Thus, for the first time, an inventive adaptable model to simulate the nonlinear dynamics of the wings under explosive blast loading at the moment of the collision is described in this article. It is crucial to increase the structure's stability because of explosive blast loading. The mentioned structure is made of two composite face sheets and a carbon fiber-reinforced polymer (CFRP). Functionally graded (FG) graphene origami (GOri)-enabled auxetic metallic metamaterial (GOEAM) is introduced to improve the stability of this kind of applicable structure, especially in air maneuvers. The analysis is conducted utilizing Reddy's third-order shear deformation of Reddy theory (TSDRT), incorporating Hamilton's principle and Von Kármán nonlinear geometric assumptions. The governing and boundary equations are accurately computed at the domain and boundary edges of the doubly curved structure. The coupled mesh-free radial point interpolation method (MRPIM) and Newton-Raphson method are applied for numerically simulating the current doubly curved structure by employing Newmark's temporal integration method with a constant-average acceleration approach. The present findings are cross-checked against the machine learning method and open-source results from the literature. Based on physical data, machine learning integrates supervised machine learning to predict the nonlinear vibration of the system. In this case, nonlinear transient bending properties are found using hybrid machine learning methods and solutions. The findings demonstrate the significance of GOEAM for nonlinear vibrations of the composite system. The current study's conclusions could be used as a benchmark and useful recommendations for future structural design techniques with enhanced features.

Explosive blast loading effect on transient mechanical responses of aircraft panels with curvilinear fibers: 3D elasticity approach

In the present paper, for the first time, the dynamic loading effect on transient bending and stress distributions of aircraft nanocomposite sandwich panels including curvilinear fibers are presented and explained. Face sheets of the panel contain curvilinear fibers with an orientation angle varies linearly with respect to the horizontal coordinate. The core layer is made of polymer matrix reinforced by graphene platelets (GPLs) with uniform and random orientation distribution. 3-D elasticity theory is used to formulate the transient problem of the panel. The model of the panel is so general to include different time-dependent loads, especially explosive ones. A three-dimensional layerwise-differential quadrature method (LW-DQM) together with a non-uniform rational B-spline-based multi-step time integration scheme is employed to investigate the transient responses of the sandwich panel with variable stiffness composite laminated face sheets (VSCL-FS) and graphene platelets reinforced porous core (GPLR-PC) under dynamic loading. The convergence behavior of the method is examined numerically and to assure its accuracy, the results in the limit cases are compared with those available in the literature. Finally, through the parametric studies, the effects of core porosity distribution and amounts, GPLs weight fraction and boundary conditions on the transient responses of the sandwich panel with VSCL-FS and GPLR-PC subjected to explosive blast loading are investigated. The results show that the addition of GPLs to the core layer decreases the transverse displacement but increases the peak values of the stress components. Also, the core porosity increases the transverse displacement and the stress components. However, it has not significant effect on the period of oscillation of the field variables under explosive blast loading. On the other hand, the curvature of the fibers does not considerable effect on the plate response and on the period of oscillation of the field variables under explosive blast loading

Strength prediction and stochastic analysis of ultra-high performance concrete columns under the explosive blast load

The performance research based on numerical and experimental studies on ultra-high performance concrete (UHPC) generally considers it as an isotropic material, which is obviously different from what it really is in practical engineering. A database of UHPC compressive strength was investigated, having the same UHPC mix proportion as the field blast experiment, to show how the strength of UHPC varies in compression. It is found that Weibull distribution is the best fit of its probability model. A combination of Monte-Carlo and Finite Element method is used, adopting the available UHPC compressive strength, to reproduce the field blast test on UHPC columns. Both the non-spatial and spatial variability of material properties of the UHPC columns are under consideration to conduct the UHPC column strength prediction under blast loads. The residual loading capacity, damage index and failure mode of UHPC columns with different sizes damaged by different explosion severities are obtained by non-spatial simulation and spatial simulation respectively. It can be concluded that compared with the non-spatial model, the numerical simulation results of the spatial model are closer to the experimental situation. Therefore, inclusion of spatial variability is recommended for reliability-based blast-resistant design for UHPC column.

Probabilistic assessment and expression of load factor design model for explosive blast loading

Explosive blast loads are subject to variability and uncertainty, but most current studies of building blast resistance are deterministic. To quantitatively assess the safety and reliability of a structure under explosion, the variability of the blast load needs to be quantified. A probabilistic analysis method of blast loads based on the finite element model and Monte Carlo simulation was proposed, and the applicability of this method was verified. The blast load probability model was developed for the scaled distances range from 1 m/kg1/3 to 40 m/kg1/3. The effect of the mass safety factor of 20 % on the probability of exceeding the design blast load was assessed. At last, based on the established probabilistic model for the blast loads, the expression for calculating the load factor of any reliability level at any location was presented.

Spatial variability of explosive blast loading and its effect on damage risks to reinforced concrete buildings

Explosive blast loading is subject to inherent variabilities due to complex interactions between chemical reactions, air particles, fireball and shockwave. Explosive field trials have quantified this variability, and described herein is the probabilistic characterisation of spatial variability of airblast for pressure and impulse. In other words, pressure–time measurements from adjacent (close) gauges are not identical, but correlated based on the distance between adjacent gauges. The degree of correlation is moderate if distance between adjacent gauges is small (i.e., angle between gauges is small where each gauge has the same radial standoff from the charge), and reduces to a weak correlation for gauges spaced much further apart. The effect of spatial variability of airblast on damage and collapse risks is investigated for a 10 storey reinforced concrete building subject to a vehicle borne improvised explosive device (VBIED) attack, and the accidental detonation of explosive ordnance (EO). The structural reliability analysis considered load redistribution for failed columns, dead and live loading variabilities, and blast loading and resistance model errors. It was found that allowing for the spatial variability of airblast decreased progressive collapse probabilities by up to 65% when compared to the case of fully correlated airblast. Designing against progressive collapse using either a threat dependent design or the Alternate Path method reduced damage risks by over 90%, and in many cases by over 99%.

Simplified calculation of airblast variability and reliability-based design load factors for spherical air burst and hemispherical surface burst explosions

There can be significant uncertainty and variability with explosive blast loading. Standards and codes of practice are underpinned by reliability-based principles, and there is little reason not to apply these to explosive blast loading. This paper develops a simplified approach where regression equations may be used to predict the probabilistic model of airblast variability and associated reliability-based design load factors (or RBDFs) for all combinations of range, explosive mass and model errors. These models are applicable to (i) hemispherical surface bursts, and (ii) spherical free-air bursts. The benefit of this simplified approach is that the equations can be easily programed into a spreadsheet, computer code or other numerical methods. There is no need for any Monte-Carlo or other probabilistic calculations. Examples then illustrate how model error, range and explosive mass uncertainty and variability affect the variability of pressure and impulse, which in turn affect the damage assessment of residential construction.

Synergistic response of steel columns to explosive thermal and long duration blast loading

This paper investigates the response of steel columns to combined pre-cursor thermal and long duration blast loads. Blast waves are the primary damage mechanism from explosive events. However, explosive events also emit thermal loads. Depending upon the explosive size and standoff distance, the effective thermal load can reach a structure prior to the arrival of the blast. An effective thermal load can damage steel structures such that total damage from the combined thermal and blast load is different to, or greater than the blast load alone. There is limited research to date investigating the synergistic response of steel structures to explosive thermal and blast loading. This paper specifically focuses on the numerical and computational methods appropriate to predict the response of steel columns subject to focused thermal and long duration blast loads (positive pressure phase exceeding 100 ms). Results from a substantive study are presented, showing a synergistic response within a sensitivity envelope of load cases. Computational methods are verified with a novel series of explosive fireball trials and a series of combined thermal, compression and long duration blast trials.

Airblast variability and fatality risks from a VBIED in a complex urban environment

Explosive blasts and prediction of fatality risks in urban environments is a complicated task due to the variability in blast wave reflection and propagation. The terrorist threats considered in this paper are vehicle-borne improvised explosive devices (VBIED) containing 225 kg or 450 kg of TNT or ammonium nitrate fuel oil (ANFO) detonated in an open street. This paper uses Viper::Blast CFD software to estimate the variability of explosive blast loads using Monte-Carlo sampling. To probabilistically model the blast wave, the paper takes into consideration the variability of explosive charge mass, detonation location, height of detonation, net equivalent quantity, atmospheric pressure and temperature, and model errors. The fatality risk assessment combines lung-rupture, whole-body displacement and skull fracture dependant on the pressure and impulse. It was found that the mean fatality risk for a 450 kg home-made ANFO explosive device detonated at a road T-intersection is 16% for people exposed in the street. If bollards were placed 10 m from the main street then fatality risk for people in the main street is reduced by over 90%. It was found that a deterministic analysis yielded fatality risks 10–60% higher than a probabilistic analysis, leading to an overly conservative assessment of safety risks.

Simplified reliability-based load design factors for explosive blast loading, weapons effects, and its application to collateral damage estimation

The paper describes a simplified approach to quantifying a reliability-based design load factor (RBDF) for the variability of explosive blast loading. The user can select range and explosive mass variability and model errors to derive RBDFs for pressure and impulse. These algorithms may be easily programmed into a spreadsheet, computer code, or other numerical method. There is a need by military planners to increase the predictive accuracy of collateral damage estimation (CDE) to ensure maximum damage to the target while minimizing harm to nearby civilians. This present paper uses the CDE damage criterion adopted by the USA and NATO to assess damage and safety risks and recommend safe collateral damage distances. Hence, the present paper utilizes RBDFs to simulate collateral damage risks to a hypothetical reinforced concrete residential building from a 2000 lb bomb using the 99th percentile of blast loads, engineering models, and Monte Carlo simulation analysis that considers variabilities of load and resistance. It was found that CDE is sensitive to airblast model errors and variability of structural resistance. It is recommended that these considerations be incorporated into CDE methodology since existing CDE methodology may be non-conservative, resulting in higher risks of collateral damage.

Risk-based assessment of blast-resistant design of ultra-high performance concrete columns

In conventional structural protective design against blast loads conservative structural designs are anticipated. However, unknown factors that include threat uncertainty, blast load variation, construction methods, material quality, etc., could impact the accuracy of assessment and design, sometimes even leading to an overestimation of structural capacity to explosive blast effects or an underestimation of actual blast pressures. In the present study, structural safety and reliability analyses of Ultra-high Performance Concrete (UHPC) columns under varying blast scenarios are performed. The variation in column dimensions, steel reinforcement, UHPC material strength, explosive range and mass, and numerical and blast load model errors are considered. The peak reflected pressure and impulse from the selected blast scenarios are derived based on variation in the explosive mass and standoff distance. Failure probabilities of columns made of this emerging high performance concrete material are then estimated. It was found that for a UHPC column designed for blast the probability of major damage given an explosive blast load varies from 1 × 10−2 to 1 × 10−5 for explosive ordnance and terrorism blast scenarios. This provides a reasonable margin of safety against major structural damage. It was also found that the risk reducing benefit of blast-resistant UHPC columns can be considerable.

Finite element modelling of the explosive blast response of carbon fibre-polymer laminates

A finite element (FE) modelling methodology is presented to analyse the dynamic response of carbon fibre reinforced polymer laminates when loaded by the shock wave generated by an airborne explosive blast. An FE model is developed to calculate the out-of-plane deformation of laminates over the entire duration of an explosive blast loading event. The FE model can also predict the initiation and propagation of delamination cracking and ply rupture in laminates. The response of the composite target plates to explosive blast loading was modelled in the FE program Abaqus using an explicit solver. The explosive air blast load was modelled using the ConWep algorithm. The accuracy of the FE model is assessed using experimental data obtained from small-scale far-field and near-field explosive blast tests performed on carbon-polyester and carbon-vinyl ester laminates. The FE model can predict the dynamic deformation of the laminates to within an accuracy of ~10%. The model can also accurately determine delamination cracks and broken plies.

Observed airblast variability and model error from repeatable explosive field trials

Explosive field trials have been conducted to measure the peak incident pressure, impulse and time of positive phase duration following the detonation of 15 different masses of the Plastic Explosive No #4. A novel aspect of these field trials was the repeatability of tests. Eight pressure gauges collected data during each blast, and at each scaled distance. In all, 4 blasts were conducted for each scaled distance (i.e. up to 32 measurements recorded for each scaled distance) – 60 blasts were fired in total. Consequently, this repeatability of testing allowed the mean and variance of blast pressure–time histories to be quantified, with a view to better characterise the variability of a blast itself and model error variability. This article describes the explosive field trials, and the statistical analysis of blast load variability and model error for peak incident pressure, impulse and time of positive phase duration. It was found that the mean model error is close to unity with a coefficient of variation of up to 0.15 for pressure and 0.21 for impulse. The lognormal probability distribution best fits the model error data. The probabilistic models derived from these tests can be used for a variety of structural engineering applications, such as calculating reliability-based design load or partial safety factors for explosive blast loading, and estimating the probability of damage and casualties for infrastructure subject to explosive blast loading. This is illustrated for a terrorist explosive scenario involving a spherical free-air burst, where the damage modes of interest are breaching and spalling of a concrete slab. It was found that the variability of charge mass, range and model error have a significant effect on reliability-based design.

A New Analytical Prediction for Energy Responses of Hemi-Cylindrical Shells to Explosive Blast Load

This study presents a new analytical model on the dissipation process of the initial total energy of the hemi-cylindrical shell subjected to the explosive blast load. The analytical formulation has been established using the energy method. The analytical predictions have been validated and found to be in excellent agreement with numerical simulations calculated by explicit finite element method (via LS-DYNA). The variational parameters considered are the shell thickness, elastic modulus, densities of the shell, and the positions of the detonation. Considering varieties of the parameters, the analytical and numerical results demonstrate that the pattern of vibrating deformations can be classified into two types according to the detonation positions. If the detonation position was at the midpoint of the width, there was no main frequency, whilst if the detonation position was at the edge of the width, the shell vibrated with a main frequency. It was also found from both analytical and numerical models that the total initial energy is inversely proportional to the thickness of the shell ( T ), namely, the exact formula can be written as β = ρ a c / ρ s T . Surprisingly, this study is the first to highlight that the total energy decreases with time by the exponential function, and the exponential ratio ( β ) is inversely proportional to the thickness of the shell as well.

Reliability-based load factors for airblast and structural reliability of reinforced concrete columns for protective structures

Reliability-based design allows the decision-maker to select the level of reliability for a specific explosive blast loading scenario. Important to this is an understanding of airblast and resistance uncertainty. Reliability-based load factors are calculated and are dependent on the variability of model error, explosive mass and range. Reliability-based design load factors (RBDFs) are estimated for explosive ordnance, terrorism, weaponeering and other scenarios. The effect of RBDFs on structural reliabilities for reinforced concrete (RC) columns is then calculated where resistance and loading are random variables, and compared to target values. It was found, for realistic combinations of range and explosive mass variabilities, that RC columns designed to existing standards have a significant margin of safety with a probability of failure of 1 × 10−3 to 1 × 10−5. However, if there is large airblast variability, then the application of RBDFs is necessary to ensure that safety levels are acceptable according to international standards.

Blast response of Hollow glass (H-glass) fibre reinforced epoxy matrix composites

The studies on response of materials against explosive blast loads have enormously increased in the recent years due to the increased blast incidents across the globe. Few studies have been reported on the blast performance of glass fibre reinforced composites. However, no studies were reported on the response of the Hollow glass (H- glass) fibre reinforced polymer composites against explosive blast loads. The present paper focuses on the experimental investigation of the response of the H- glass/epoxy composite laminates against air blast loading. The explosive loading on 5mm thick composite laminates at both 300mm and 400mm stand-off distances (SoD) was generated by detonating 142 gms of plastic explosive. The incident and reflected pressures at both the SoDs were recorded using piezo-electric pressure sensors. H-glass composites exhibited mode-I failure (large in-elastic deformation) at both SoDs, whereas E-glass composites showed mode –I failure at 300mm SoD only. The change in failure modes of composites with change in SoD was also discussed. The blast performance of the H-glass composite was compared with the performance of the solid glass fibre (E-glass) composites.

Towards developing a test method for military pelvic protection

Prior to adoption of the pelvic protection system (PPS), one of the signature injuries suffered by H.M. Armed Forces who served in Afghanistan was caused by buried improvised explosive devices (IEDs) accelerating secondary fragmentation from the ground environment into the groin, perineum, genitals, buttocks and legs of personnel. In the current work, a test method was developed which considered the combined effects of explosive blast and fragment loading of targets of Tier 2 PPS. The work identified that it is possible to explosively propel fragments of the ground environment into the specimens of Tier 2 PPS and to analyse each specimen. In doing so, a scenario peculiar to the IED threat faced in Afghanistan was able to be replicated. Such work allows insights into injuries suffered and will assist in the development of future protective clothing systems that require dual blast and fragment protective properties.

Reliability analysis of circular reinforced concrete columns subject to sequential vehicular impact and blast loading

This study investigates the first-order second-moment structural reliability of circular reinforced concrete (RC) bridge columns subjected to vehicular impact, explosive blast, and sequential vehicular impact and explosive blast loading. The analysis is performed for five vehicle types of increasing size, mass, and explosive charge capacity. The structural reliability under vehicular impact is shown to be highly sensitive to column diameter, reinforcement ratio, and vehicle velocity. The structural reliability under explosive blast loading is shown to be highly sensitive to column diameter, reinforcement ratio, and blast standoff distance. In general, the structural reliability is lower under explosive blast loading. The structural reliability under sequential loading is evaluated by the newly proposed resistance reduction method and by fault tree analysis. A resistance reduction factor for the second event is defined as a function of the probability of failure under the first event. The resistance reduction method is shown to be more conservative than fault tree analysis and has the added benefit of allowing for the derivation of the density function for performance under sequential loading.

A review of Pochhammer–Chree dispersion in the Hopkinson bar

This paper presents a detailed review of the current state of the art in Hopkinson pressure bar (HPB) data analysis. In particular, the underlying theory of the HPB is discussed, and methods of correcting signals for Pochhammer–Chree dispersion and other associated effects are described. The theory of multiple mode propagation is presented, followed by a review of the current methods for correcting multiple mode dispersion, which are especially pertinent when using the HPB as a dynamic force transducer to measure rapidly changing loading events such as explosive blast loads.

Reliability-based load factor design model for explosive blast loading

The risk of damage to infrastructure and people is affected by airblast variability. Reliability-based design allows the decision-maker to select the level of reliability for a specific blast loading scenario. Reliability-based load factors are calculated where the nominal load is multiplied by the load factor to ensure that the actual load is equal to the reliability level. A design model for predicting reliability-based load factors is developed where model error, explosive mass and stand-off distance are random variables, and calculated reliability-based design load factors (RBDF) are independent of explosive mass, net equivalent quantity, angle of incidence, temperature or pressure. Hence, a design model describing reliability-based load factors are presented for reliability levels of 0.05 to 0.99, and for coefficients of variation of explosive mass and range each varying from 0.0 to 0.3. The paper then shows the significant effect that range and explosive mass variability have on RBDFs, and how this affects structural design and damage predictions for reinforced concrete columns and glazing.

Damage and Risk Assessment for Single-Layer Reticulated Domes Subject to Explosive Blast Loads

In order to provide a better understanding of the dynamic behavior of single-layer reticulated domes subjected to explosive blast loads, a number of analyses are carried out on structures with different standoff distances ([Formula: see text]), explosive weights ([Formula: see text]), rise–span ratios ([Formula: see text] and other parameters. An equation for a structural damage factor is proposed to evaluate structural damage quantitatively. The damage states for single-layer reticulated domes are defined based on their structural dynamic performance and corresponding damage factors. Structural reliabilities for different standoff distances are obtained using the Monte-Carlo Analysis. A typical protective measure is bollards which are used to help ensure a minimum standoff distance. To illustrate the cost-effectiveness of such a protective measure, structural damage states and various losses, including direct and indirect economic loss and maimed and fatality loss, are considered for assessing the risk reduction, costs and benefits. It was found that the bollards significantly reduce the likelihood of structural progressive collapse or severe damage, and the optimal standoff distance can be determined.