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.

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.

Article:Barr, A. orcid.org/0000-0002-8240-6412, Clarke, S.D., Petkovski, M. et al. (4 more authors) (2016) Effects of strain rate and moisture content on the behaviour of sand under one-dimensional compression. Experimental Mechanics, 56 (9). pp. 1625 -1639 . ISSN 1741 -2765 https://doi.org/10.1007/s11340-016-0200-z eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request.Experimental Mechanics manuscript No. Abstract The influence of strain rate and moisture content on the behaviour of a quartz sand was assessed using high-pressure quasi-static (10 −3 s −1 ) and high-strain-rate (10 3 s −1 ) experiments under uniaxial strain.Quasi-static compression to axial stresses of 800 MPa was carried out alongside split Hopkinson pressure bar (SHPB) experiments to 400 MPa, where in each case lateral deformation of the specimen was prevented using a steel test box or ring, and lateral stresses were recorded. A significant increase in constrained modulus was observed between strain rates of 10 −3 s −1 and 10 3 s −1 , however a consistently lower Poisson's ratio in the dynamic tests minimised changes in bulk modulus. The reduction in Poisson's ratio suggests that the stiffening of the sand in the SHPB tests is due to additional inertial confinement rather than an inherent strain-rate dependence. In the quasi-static tests the specimens behaved less stiffly with increasing moisture content, while in the dynamic tests the addition of water had little effect on the overall stiffness, causing the quasi-static and dynamic series to diverge with increasing moisture content.

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Experimental measurements of blast loading using Hopkinson pressure bars are affected by dispersion which can result in the loss or distortion of important high-frequency features. Blast waves typically excite multiple modes of propagation in the bar, and full correction of dispersive effects is not currently possible as the magnitude of stress propagating in each mode is not known. In this paper we develop an algorithm for multiple mode dispersion correction based on rigorous interrogation of the results from a series of finite element analyses. First, a finite element model is validated against first-mode and higher-mode theory. The dispersion of short raised-cosine windowed pulses is then used to isolate the contribution of each propagating mode, enabling a relationship between frequency and modal apportioning of stress to be obtained for the first four propagating modes. Finally, four-mode dispersion correction is successfully applied to an experimental signal using an algorithm based on the derived relationships for modal apportioning. The four-mode results show significant improvement in the capture of high-frequency features over existing first-mode corrections, and demonstrate the potential of this method for the full correction of dispersion in experimental measurements of blast loading.