Simple model of shock-wave attenuation in snow

• Published in: Journal of Glaciology
• Main Author: Johnson, Jerome B.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press (CUP) 1991
• Subjects: Earth-Surface Processes; Journal of Glaciology
• Online Access: http://dx.doi.org/10.1017/s0022143000005724; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000005724

Abstract A simple momentum model, assuming that snow compacts along a prescribed pressure–density curve, is used to calculate the pressure attenuation of shock waves in snow. Four shock-loading situations are examined: instantaneously applied pressure impulses for one-dimensional, cylindrical and spherical shock-wave geometries, and a one-dimensional pressure impulse of finite duration. Calculations show that for an instantaneously applied impulse the pressure attenuation for one-dimensional, cylindrical and spherical shock waves is determined by the pressure density (P– ρ ) compaction curve of snow. The maximum attenuation for a one-dimensional shock wave is proportional to ( X f – X 0 ) −1.5 for the multi-stage (P– ρ ) curve and ( X f – X 0 ) −2 when compaction occurs in a single step (single-stage compaction), where ( X f – X 0 ) is the shock-wave propagation distance. Cylindrical waves have a maximum attenutation that varies from ( R– R 0 ) −2 for single-stage compaction and ( R – R 0 ) −1.5 for multi-stage compaction, when ( R – R 0 ) ≪ R 0 , where R is the propagation radius and R 0 is the interior radius over which a pressure impulse is applied, to R −4 when ( R – R 0 ) ≫ R 0 Spherical waves have a maximum attenuation that varies from ( R – R 0 ) −2 for single-stage compaction and ( R – R 0 ) −1.5 for multi-stage compaction to R −6 when 〈 R – R 0 〉 ≫ R 0 . The shock-wave pressure in snow for a finite-duration pressure impulse is determined by the pressure impulse versus time profile during the time interval of the impulse. After the pressure impulse ends, shock-wave pressure attenuation is the same as for an instantaneously applied pressure impulse containing the same total momentum. Pressure attenuation near a shock-wave source, where the duration of the shock wave is relatively short, is greater than for a shock wave farther from a source where the shock wave has a relatively long duration. Shock-wave attenuation in snow can be delayed or reduced by increasing the duration of a finite-duration pressure ...