Andrew Tyas

Explosive weapons may cause damage through both blast loading and fragmentation of their casings. Although air-detonated ordnance has been extensively studied, fragmentation hazards from underwater munitions remain underexplored, and therefore no standardised procedure exists to calculate safe standoff distances as a function of depth and charge mass in naval environments. This significantly hampers the safety planning process for underwater explosives ordnance disposal activities. Building on prior laboratory investigations of underwater fragmentation, this study extends the analysis toward full-scale applicability by estimating maximum fragmentation ranges and applying injury-criteria models to assess associated hazard limits. A series of well-controlled small-scale experiments compared cased explosive charges detonated in air and at varying submersion depths. Three casing configurations were tested to quantify the influence of depth and casing configuration type on fragment generation, in-flight behaviour, and size–velocity distributions. High-speed videography and in-situ witness panels were utilised to track fragmentation post-detonation and estimate velocities during flight and after impact. An in-house analysis code with optical and panel data was developed to compute fragment trajectories, maximum ranges, and soft-tissue penetration probabilities using established injury thresholds. Results indicate a pronounced reduction in fragment count, velocity and launch angle with increasing submersion depth, producing substantially shorter predicted penetration distances for all tested submerged charges. This paper outlines a practical methodology for scaling experimental observations toward larger charge masses and discusses implications for risk assessment and mitigation during underwater munitions clearance operations.

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 _{⁣ TNT} 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’.

Classical layout optimization is a well-established structural design tool, however it considers only truss structures composed solely of axially loaded bars, limiting its applicability to many structures. To address this limitation, this study introduces a novel approach that takes into account moment-resisting beams in the optimization framework. The interaction between moment, shear, and axial forces is simplified for inclusion in the optimization problem, solved effectively via a sequential conic programming scheme. Various numerical examples show that the proposed approach identifies structures with lower-volume than the classical layout optimization in problems involving multiple load cases or pre-existing members. Additionally, the method can also be used to solve problems that classical layout optimization cannot address, including constrained design spaces and point moment loads. The findings indicate that the proposed approach provides greater flexibility and efficiency in designing hybrid truss and beam structures, paving the way for versatile structural solutions.

As the detonation product cloud from a high explosive detonation expands, an arresting flow is generated at the interface between these products and the surrounding air. Eventually this flow forms an inward-travelling shock wave which coalesces at the origin and reflects outwards as a secondary shock. Whilst this feature is well known and often reported, there remains no established method for predicting the form and magnitude of the secondary shock. This paper details an empirical superposition method for modelling the secondary shock, based on the physical analogy of the secondary loading pulse resembling the blast load from a smaller explosive relative to the original. This so-called dummy charge mass is determined from 58 experimental tests using PE4, PE8, and PE10, utilising Monte Carlo sampling to account for experimental uncertainty, and is found to range between 3.2–4.9% of the original charge mass. A further 18 “unseen” datapoints are used to rigorously assess the performance of the new model, and it is found that reductions in mean absolute error of up to 40%, and typically 20%, are achieved compared to the standard model which neglects the secondary shock. Accuracy of the model is demonstrated across a comprehensive range of far-field scaled distances, giving a high degree of confidence in the new empirical method for modelling the secondary shock from high explosives.

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.

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.

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.

Rapid, accurate assessment of the yield of a large-scale urban explosion will assist in implementing emergency response plans, will facilitate better estimates of areas at risk of high damage and casualties, and will provide policy makers and the public with more accurate information about the event. On 4 August 2020, an explosion occurred in the Port of Beirut, Lebanon. Shortly afterwards, a number of videos were posted to social media showing the moment of detonation and propagation of the resulting blast wave. In this article, we present a method to rapidly calculate explosive yield based on analysis of 16 videos with a clear line-of-sight to the explosion. The time of arrival of the blast is estimated at 38 distinct positions, and the results are correlated with well-known empirical laws in order to estimate explosive yield. The best estimate and reasonable upper limit of the 2020 Beirut explosion determined from this method are 0.50 kt TNT and 1.12 kt TNT, respectively.