Subsurface explosions result in the propagation of stress waves through the soil, known as ground shock. This can damage buried and surface structures in events such as the detonation of unexploded ordnance from previous conflicts or deliberate attack. However, understanding of the mechanisms and magnitude of loading imparted to buried structures is limited by a lack of high-quality experimental data. Past testing utilised discrete measurement devices within the soil; results have often been characterised as incident, free-field values, when in fact they are influenced by the materials, size and shape of the measurement device. This paper describes an innovative approach to experimental determination of ground shock loading on a buried structure.Uniquely, digital image correlation from high-speed video at 100k frames per second has been utilised to determine ground shock loading at reduced scale on a deformable plate. Testing was conducted using a steel pipe with a deformable aluminium base plate, filled with varying depths of uniform sand at a consistent bulk density and moisture content. A constant scaled burial depth of 0.434m/kgTNTe1/3 was maintained using spherical PE10 charges with a varying stand-off distance. Two charge sizes were used, with nine tests conducted in total.Displacement histories from over 2500 locations across the plate were extracted from each test, greatly increasing the resolution of data capture possible. The experimental data has been used to validate numerical modelling approaches, using an existing soil material model. The numerical results show good agreement with the experimental data.

Soil-filled wire and geotextile gabions stand as vital bulwarks in military bases, harnessing soil’s innate capacity to absorb shock and safeguard both personnel and critical assets from blast and fragmentation effects. Yet, the dynamic response of cohesive soils under extreme loads remains largely unexplored, leaving engineers grappling with a significant void in knowledge as they strive to fortify structures against emerging threats. This paper considers the high-strain-rate behaviour of kaolin clay using the split Hopkinson pressure bar in both confined and unconfined configurations, with a range of moisture contents representing dry, partially-saturated and saturated conditions. Analysis of the results indicates distinct phase behaviours in transmitted and radial stress based on strain rate, moisture content and confinement. Leveraging cutting-edge machine learning models such as the Proper Orthogonal Decomposition (POD) and sparse Proper Generalised Decomposition (sPGD), data-driven parametric models were developed based on the experimental data. These models enable the prediction of cohesive soil behaviour at specified strain rate and moisture content, enabling engineers to rapidly predict soil behaviour in response to new threats and ground conditions.

For the first time, the high-strain-rate behaviour of water is investigated experimentally and validated to LS-DYNA numerical simulations, using Smooth Particle Hydrodynamics (SPH). This paper presents the application of a modified split-Hopkinson pressure bar (SHPB) fitted with a partial lateral confinement apparatus on a water specimen. The lateral confinement is provided by a water reservoir surrounding the specimen. A pressure transducer is installed in the reservoir wall to measure lateral stresses, and a dispersion correction algorithm, SHPB_Processing.py, is utilised to obtain accurate measurements of axial and radial stresses and strains. Experimental results underscore the capability of the modified apparatus to assess triaxial behaviour of water under high-strain rates. Comparisons with numerical modelling reveal that cohesion between water particles is non-existent, highlighting an intrinsic limitation in numerical modelling. These results highlight the capability to perform characterisation of fluids under high-strain rates. While limitations in numerical modelling still exist, numerical modelling and experimental testing using the modified apparatus can be applied to characterise fluid behaviour in the future.

This paper details the development of a rapid inverse approach to determine the yield and location of an explosion through trilateration of empirical laws for blast wave arrival time. A rigorous sensitivity analysis of measurement uncertainty is first performed. From this, a probabilistic framework is proposed that utilizes Monte Carlo sampling of datasets to mitigate the effects of the variability and uncertainties typically present in blast events. Subsequently, the trilateration method is successfully applied to two existing datasets. Analysing well-controlled small-scale laboratory experiments, charge mass is predicted within 6.3% of the true yield, and position within 3.65 charge radii of the true centre. Social media footage of the 2020 Beirut explosion is then used to assess performance against data collected under in-field conditions. The predicted yield of 0.52 kt[Formula: see text] shows good agreement with the literature, and charge position is predicted to within the radius of the crater. Trilateration is shown to be able to rapidly and reliably determine explosive yield and centre, despite large levels of sensor noise. The sub-second computation time of this approach offers the possibility to better model and predict the damage and injury patterns immediately after an explosion, facilitating more effective disaster response planning.This article is part of the theme issue 'Frontiers of applied inverse problems in science and engineering'.

Soil-filled wire and geotextile gabions are essential components of defensive infrastructure in military bases, leveraging the attenuating properties of soils to safeguard personnel and critical assets against blast and fragmentation effects. However, understanding the behaviour of cohesive soils under extreme loading conditions remains largely unexplored, presenting a crucial knowledge gap for design engineers tasked with developing robust soil constitutive models to address evolving threats. This study investigates the response of cohesive soils, focusing primarily on kaolin clay due to its homogeneity, widespread availability and consistent properties. Through high strain rate experimental testing of kaolin clay specimens, using the split-Hopkinson pressure bar (SHPB) apparatus, both unconfined and confined conditions are explored across varying moisture contents, spanning the spectrum from unsaturated to fully saturated states. The analysis of the experimental results uncovers the strain rate dependence of cohesive soils and identifies distinct phase behaviour for transmitted and radial stresses influenced by factors such as strain rate, moisture content and confinement. Utilising LS-DYNA, and the finite element method (FEM), the SHPB tests are modelled for comparison against experimental findings. While LS-DYNA, supplemented by Smooth Particle Hydrodynamics (SPH) node modelling, provides valuable insights, significant disparities between modelled and practical results underscore the challenges inherent with the accuracy in simulating the behaviour of cohesive soils. Nonetheless, this comprehensive exploration of cohesive soil’s high strain rate behaviour yields critical insights for engineers, enabling them to adapt defensive strategies to diverse threats and loading scenarios effectively.

Stress wave dispersion can result in the loss or distortion of critical high-frequency data during high-strain-rate material tests or blast loading experiments. The purpose of this work is to demonstrate the benefits of correcting stress wave dispersion in split-Hopkinson pressure bar experiments under various testing situations. To do this, an innovative computational algorithm, SHPB_Processing.py, is created. Following the operational run through of SHPB_Processing.py’s capabilities, it is used to process test data acquired from split-Hopkinson pressure bar tests on aluminium, sand and kaolin clay samples, under various testing conditions. When comparing dispersion corrected and simple time shifting data obtained from SHPB experiments, accounting for dispersion removes spurious oscillations and improves the inferred measurement at the front of the specimen. The precision of the stress and strain results gathered from its application emphasises its importance through the striking contrast between its application and omission. This has a significant impact on the validity, accuracy and quality of the results. As a result, in the future, this tool can be utilised for any strain rate testing situation with cylindrical bars that necessitates dispersion correction, confinement, or stress equilibrium analysis.

Obstacles arranged into a pre-fractal shape (Sierpinski carpet) were tested for their blast attenuation abilities using 250 g PE4 at three different scaled distances (Z = 1.87, 2.24, 2.99 m/kg(1/3)). Three pre-fractal iterations were tested, as well as free-field tests for comparative purposes. Reductions in peak overpressure up to 26% and peak specific impulse up to 19% were observed, attributed to a mechanism known as 'trapping'. This mechanism is characterised by a reduction in the ability of a blast wave to advect downstream, with corresponding increases in pressure observed within the bounds of the pre-fractal obstacle. Attenuation magnitudes and areas of reduced pressure and impulse were found to be drastically different with each pre-fractal iteration, with a transition from shadowing to wave trapping as the obstacles more closely resembled true fractals. A linear dependence on a newly-defined obstruction factor (OF) was found for arrival time, overpressure and impulse at the sensor locations, suggesting that the attenuation of a pre-fractal obstacle is inherently determinable. The results indicate that the mechanism of blast mitigation of pre-fractal obstacles is fundamentally different from singular or arrays of regular obstacles, and could be exploited further to develop novel protective structures with enhanced blast attenuation.

The mechanics of downstream blast wave attenuation caused by interaction with obstacles arranged into a pre-fractal shape based on the Sierpinski carpet was numerically investigated using a high-fidelity CFD solver. The blast mitigation was qualitatively and quantitatively assessed for four pre-fractal iterations at three different scaled distances (Z = 1.87, 2.24, 2.99 m/kg(1/3)). Mitigation was seen to occur in zones associated with the location of destructive wave interference patterns in the downstream region. Crucially, these zones were found to widen spatially with increasing pre-fractal iteration, and strong shock-shock interactions that result in load amplification, commonly encountered in downstream regions of a solitary block-like obstacle, were not observed for the more fractal-like obstacles. The mechanisms of attenuation are explored in terms of wave impedance. It is found that pre-fractals reduce wave transmission in the downstream, increase reflection of the blast wave, and enhance trapping within the confines of the pre-fractal obstacle, dramatically changing the directionality and hence the strength of the transmitted wave. Reductions in peak pressure of up to 60% and peak specific impulse of up to 40% were recorded for the highest iteration pre-fractal, that is, obstacles that most closely represent a true fractal, thereby highlighting the effectiveness of such shapes for protective structure design for improved blast mitigation.

A significant amount of scientific effort has been dedicated to measuring and understanding the effects of explosions, leading to the development of semi-empirical methods for rapid prediction of blast load parameters. The most well-known of these, termed the Kingery and Bulmash method, makes use of polylogarithmic curves derived from a compilation of medium to large scale experimental tests performed over many decades. However, there is still no general consensus on the accuracy and validity of this approach, despite some researchers reporting consistently high levels of agreement. Further, it is still not known whether blast loading can be considered deterministic, or whether it is intrinsically variable, the extent of this variability, and the range and scales over which these variations are observed. This article critically reviews historic and contemporary blast experiments, including newly generated arena tests with RDX and PETN-based explosives, with a view to demonstrating the accuracy with which blast load parameters can be predicted using semi-empirical approaches.

When explosives detonate in a confined space, repeated boundary reflections result in complex shock interactions and the formation of a uniform quasi-static pressure (QSP). For fuel-rich explosives, mixing of partially oxidized detonation products with an oxygen-rich atmosphere results in a further energy release through rapid secondary combustion or 'afterburn'. While empirical formulae and thermochemical modelling approaches have been developed to predict QSP, a lack of high-fidelity experimental data means questions remain around the deterministic quality of confined explosions, and the magnitude and mechanisms of afterburn reactions. This article presents experimental data for RDX- and PETN-based plastic explosives, demonstrating the high repeatability of the QSP generated in a sealed chamber using pressure transducers and high-speed infrared thermometry. Detonations in air, nitrogen and argon atmospheres are used to identify the contribution of afterburn to total QSP, to estimate the duration of afterburn reactions and to speculate on the flame temperature associated with this mechanism. Computational fluid dynamic modelling of the experiments was also able to accurately predict these effects. Understanding and quantifying explosions in complex environments are critical for the design of effective protective structures: the mechanisms described here provide a significant step towards the development of fast-running engineering models for internal blast events.

We suggest that pain processing has a modular architecture. We begin by motivating the (widely assumed but seldom defended) conjecture that pain processing comprises inferential mechanisms. We then note that pain exhibits a characteristic form of judgement independence. On the assumption that pain processing is inferential, we argue that its judgement independence is indicative of modular (encapsulated) mechanisms. Indeed, we go further, suggesting that it renders the modularity of pain mechanisms a default hypothesis to be embraced pending convincing counterevidence. Finally, we consider what a modular pain architecture might look like, and question alleged counterevidence to our proposal.

Buried charges pose a serious threat to both civilians and military personnel. It is well established that soil properties have a large influence on the magnitude and variability of loading from explosive blasts in buried conditions. In this study, work has been undertaken to improve techniques for processing pressure data from discrete measurement apparatus; this is performed through the testing of truncation methodologies and the area integration of impulses, accounting for the particle size distribution (PSD) of the soils used in testing. Two experimental techniques have been investigated to allow for a comparison between a global impulse capture method and an area-integration procedure from a Hopkinson Pressure Bar array. This paper explores an area-limiting approach, based on particle size distribution, as a possible approach to derive a better representation of the loading on the plate, thus demonstrating that the spatial distribution of loading over a target can be related to the PSD of the confining material.

Urban blasts have become a significant concern in recent years. Whilst free-field blasts are well understood, the introduction of an urban setting (or any complex geometry) gives rise to multiple blast wave interactions and unique flow complexities, significantly increasing the difficulty of loading predictions. This review identifies commonly agreed-upon concepts or behaviours that are utilised to describe urban shock wave propagation, such as channelling and shielding, in conjunction with exploring urban characterisation metrics that aim to predict the effects on global blast loading for an urban blast. Likewise, discrepancies and contradictions are highlighted to promote key areas that require further work and clarification. Multiple numerical modelling programmes are acknowledged to showcase their ability to act as a means of validation and a preliminary testing tool. The findings contained within this review aim to inform future research decisions and topics better.

Historically, most testing with shallow buried charges has focussed on soils which are predominantly quartz (silica)-based. Particle size, moisture content and density have previously been investigated to ascertain their importance, along with other geotechnical parameters, in governing the magnitude of an impulsive output. This has shown that, in order of importance, moisture content, density and particle size drive the total impulse imparted. The work in this paper presents the results of blast testing carried out with carbonate sands to investigate the difference that particle mineralogy (and hence, propensity for breakage) has on both the localised loading and the total impulse using an array of 17 Hopkinson pressure bars known as the Characterisation of Blast Loading (CoBL) apparatus. Carbonate sands are thought to have more friable particles due to their plate-like morphology, as opposed to the rounded morphology of quartz-based sands. Testing was conducted with low moisture content samples and compared with the well-established Leighton Buzzard uniform sand to isolate the effect of particle mineralogy/morphology on the loadings measured. The results show that, despite attaining a 23% lower bulk density, carbonate soils deliver almost identical total impulses (0.7–3.0% higher) when compared with quartz soils for nominally identical moisture contents.

The design of blast-resistant structures and protective systems requires a firm understanding of the loadings imparted to structures by blast waves. While empirical methods can reliably predict these loadings in the far field, there is currently a lack of understanding on the pressures experienced in the very near field, where physics-based numerical modelling and semi-empirical fast-running engineering model predictions can vary by an order of magnitude. In this paper, we present the design of an experimental facility capable of providing definitive spatially and temporally resolved reflected pressure data in the extreme near field (Z<0.5 m/kg1/3). The Mechanisms and Characterisation of Explosions (MaCE) facility is a specific near-field evolution of the existing Characterisation of Blast Loading (CoBL) facility, which uses an array of Hopkinson pressure bars embedded in a stiff target plate. Maraging steel pressure bars and specially designed strain gauges are used to increase the measurement capacity from 600 MPa to 1800 MPa, and 33 pressure bars in a radial grid are used to improve the spatial resolution from 25 mm to 12.5 mm over the 100 mm radius measurement area. In addition, the pressure bar diameter is reduced from 10 mm to 4 mm, which greatly reduces stress wave dispersion, increasing the effective bandwidth. This enables the observation of high-frequency features in the pressure measurements, which is vital for validating the near-field transient effects predicted by numerical modelling and developing effective blast mitigation methods.

Obstructing the passage of blast waves is an effective method of mitigating blast pressures downstream of the obstacle. To this end, the interaction between a blast wave and a simplified structural shape, such as a cylinder, has been widely investigated to understand the complex flow pattern that ensues around the obstacle. The patterns include the interference zones of the incident wave, the diffracted wave, and other secondary waves in the downstream region. Such zones are responsible for causing significant modifications to the blast wave parameters. This research aims to identify and study the factors that serve to mitigate the resulting blast loads downstream of a cylindrical obstacle – both on the ground, and on a rigid wall target that the obstacle is aiming to protect. Inputs from this numerical study are also used to develop a fast-running predictive method based on an artificial neural network (ANN) model. It was found that the size of the cylinder, the strength of the blast wave, the position of the cylindrical obstruction, and the target length, all have remarkable effects on the development of the complex flow-field downstream, and on the impulse mitigation on a reflective target. A number of key mitigation mechanisms are identified, namely shadowing and interference, and their origins and significance are discussed. An ANN model trained using scaled input parameters could successfully predict impulse values on such a reflective target. Using this model to predict the response of previously unseen configurations (for the ANN) gave excellent correlation, thereby demonstrating the high fidelity of this fast-running tool, and its ability to predict the effectiveness of various wave-cylinder interactions in mitigating blast loading.

Blast–obstacle interaction is a complex, multi-faceted problem. Whilst engineering-level tools exist for predicting blast parameters (e.g. peak pressure, impulse and loading duration) in geometrically simple settings, a blast wave is fundamentally altered upon interaction with an object in its path, and hence, the loading parameters are themselves affected. This article presents a comprehensive review of key research in this area. The review is formed of five main parts, each describing: the direct loading of a blast wave on the surface of a finite-sized structure; the modified pressure of the blast wave in the wake region of three main obstacle types – blast walls, obstacles, wall/obstacle hybrids; and finally, a brief description of some methods for predicting loading parameters in such blast–obstacle interaction settings. Key findings relate to the mechanisms governing blast attenuation, for example, diffraction, reflection (diverting away from the target structure), expansion/volume increase, vortex creation/growth, as well as obstacle properties influencing these, such as porosity (blockage ratio), obstacle shape, number of obstacles/rows, arrangement and surface roughness.

In the UK, High Speed Rail 2, (London to the ‘North’) is surrounded by a number of questions regarding construction technologies which can minimise the impact of the route. The rail industry in the UK has vast experience based with ballasted track, but this is not necessarily the most appropriate choice for new high speed rail construction when crossing problematic soils. This paper aims to investigate the use of different track types (ballasted and ballastless) and the influence they will have on the underlying soil in areas predominated by non-engineered mudrock backfills, relics of the UK’s mining heritage. Mudrocks are a class of fine-grained siliciclastic sedimentary rocks. Structural performance of the railway track strongly depends on the level of stress that is transmitted to the ground and this must be reduced to an acceptable level to minimise deterioration in the mudrock if they are to be utilised effectively. The main objective for this paper is to investigate the impact of the initial stress conditions and dynamic stress on the permanent deformation of mudrock under different physical conditions. Triaxial testing is used to estimate the stiffness characteristics of the mudrock. The results show that the resilient modulus increases with a decrease in the stress amplitude. In addition, ballasted track shows a higher suitability for use in design in terms of the stiffness generated within the mudrock.

The understanding of blast loads is critical for the development of infrastructure that protects against explosions. However, the lack of high-quality experimental work on the characterisation of such loads prevents a better understanding of many scenarios. Blast loads are typically characterised by use of some form of pressure gauge, from which the temperature can be inferred from a pressure measurement. However, such an approach to temperature measurement is limited; it assumes ideal gas laws apply throughout, which may not be the case for high temperature and pressure scenarios. In contrast, infrared radiation thermometers (IRTs) perform a measurement of temperature based upon the emitted radiance from the target object. The IRTs can measure fast changes in transient temperature, making them seemingly ideal for the measurement of a fireball's temperature. In this work, we present the use of a high-speed IRT for the measurement of early-stage explosive development and fireball expansion within a confined blast, with the temperature of the explosive fireball measured from its emitted radiance. The temperature measured by the IRT was corroborated against the temperature inferred from a pressure gauge measurement; both instruments measured the same temperature from the quasi-static pressure (QSP) point onwards. Before the QSP point, it is deduced that the IRT measures the average temperature of the fireball over a wide field-of-view (FOV), as opposed to that inferred from the singular shocks detected by the pressure gauge. Therefore, use of an IRT, in tandem with a pressure gauge, provides a potential invaluable measurement technique for the characterisation the early stages of a fireball as it develops and expands.

The ability to accurately determine blast loading parameters will enable more fundamental studies on the sources of blast parameter variability and their influence on the magnitude and form of the loading itself. This will ultimately lead to a better fundamental understanding of blast wave behaviour, and will result in more efficient and effective protective systems and enhanced resilience of critical infrastructure. This article presents a study on time of arrival as a diagnostic for far-field high explosive blasts, and makes use of the results from a large number of historic tests and newly performed experiments where the propagating shock front was filmed using a high-speed video (HSV) camera. A new method for optical shock tracking of far-field blast tests is developed and validated, and full-field arrival time results are compared against those determined from the historic data recorded using traditional pressure gauges. Arrival time variability is shown to be considerably lower than peak pressure and peak specific impulse, and is shown to decrease exponentially with increasing scaled distance. Further, the method presented in this article using HSV cameras to determine arrival time yields further reductions in variability. Finally, it is demonstrated that the method can be used to accurately determine far-field TNT equivalence of high explosives.