Abstract
Numerical modelling techniques enable forcing function at the point of contact in a hail impact to be predicted, but many models available in commercial software have not been verified by experiments. A recently developed deterministic model is only able to simulate the impact action of an idealised spherical hailstone. Results recorded from the impact testing of non-spherical simulated hail ice specimens show wide scatters and are different to spherical specimens. A stochastic model has been developed in this study to incorporate the variability of the modelling parameters representing the behaviour of non-spherical ice specimens and to generate time histories of contact force for given impact scenarios. A probabilistic model which was developed previously to provide predictions of the distribution of the size of hailstones in a severe category hailstorm has also been further developed to provide predictions of the maximum contact force values in probabilistic terms. For any given pre-defined forcing function denting into the surface of a steel plate can be estimated by finite element analysis or experimentally on a test machine. The new knowledge base introduced in this paper can be used by manufacturers and designers to re-assess existing products and in making improvements to future installations taking into account cost–benefit considerations.
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Appendices
Appendix 1: Time step integration algorithm for solving nonlinear viscoelastic 2DOF mass–spring–damper system model
Summary of time step integration algorithm for contact phase
Summary of time step integration algorithm for separation phase
Appendix 2
The values of peak contact force generated by spherical SHI and non-spherical SHI specimens at that particular impact velocity were first measured using the custom-made measuring device. The mean value of the peak contact force for spherical SHI specimens (shown in Table 3) was then calculated based on averaging the test results across ten number of spherical SHI specimens. For non-spherical SHI specimens, the average value of the peak contact force was obtained based on averaging the test results of at least 30 number of non-spherical SHI specimens impacting onto the target at that specific velocity.
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Perera, S., Lam, N., Pathirana, M. et al. Probabilistic modelling of forces of hail. Nat Hazards 91, 133–153 (2018). https://doi.org/10.1007/s11069-017-3117-7
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DOI: https://doi.org/10.1007/s11069-017-3117-7