Simple model of shock-wave attenuation in snow
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 sp...
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Cambridge University Press (CUP)
1991
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Online Access: | http://dx.doi.org/10.1017/s0022143000005724 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000005724 |
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crcambridgeupr:10.1017/s0022143000005724 2023-06-11T04:13:30+02:00 Simple model of shock-wave attenuation in snow Johnson, Jerome B. 1991 http://dx.doi.org/10.1017/s0022143000005724 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000005724 en eng Cambridge University Press (CUP) Journal of Glaciology volume 37, issue 127, page 303-312 ISSN 0022-1430 1727-5652 Earth-Surface Processes journal-article 1991 crcambridgeupr https://doi.org/10.1017/s0022143000005724 2023-05-01T18:18:39Z 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 ... Article in Journal/Newspaper Journal of Glaciology Cambridge University Press (via Crossref) Journal of Glaciology 37 127 303 312 |
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Open Polar |
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Cambridge University Press (via Crossref) |
op_collection_id |
crcambridgeupr |
language |
English |
topic |
Earth-Surface Processes |
spellingShingle |
Earth-Surface Processes Johnson, Jerome B. Simple model of shock-wave attenuation in snow |
topic_facet |
Earth-Surface Processes |
description |
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 ... |
format |
Article in Journal/Newspaper |
author |
Johnson, Jerome B. |
author_facet |
Johnson, Jerome B. |
author_sort |
Johnson, Jerome B. |
title |
Simple model of shock-wave attenuation in snow |
title_short |
Simple model of shock-wave attenuation in snow |
title_full |
Simple model of shock-wave attenuation in snow |
title_fullStr |
Simple model of shock-wave attenuation in snow |
title_full_unstemmed |
Simple model of shock-wave attenuation in snow |
title_sort |
simple model of shock-wave attenuation in snow |
publisher |
Cambridge University Press (CUP) |
publishDate |
1991 |
url |
http://dx.doi.org/10.1017/s0022143000005724 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022143000005724 |
genre |
Journal of Glaciology |
genre_facet |
Journal of Glaciology |
op_source |
Journal of Glaciology volume 37, issue 127, page 303-312 ISSN 0022-1430 1727-5652 |
op_doi |
https://doi.org/10.1017/s0022143000005724 |
container_title |
Journal of Glaciology |
container_volume |
37 |
container_issue |
127 |
container_start_page |
303 |
op_container_end_page |
312 |
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1768390617696567296 |