Controlled Roof Collapse during Secondary Mining in Coal Mines
The problem considered is an investigation of the possible collapse of the roof between the pillar next to be mined in secondary coal mining and the first line of pillar remnants called snooks. The roof rock between the pillar, which is the working face, and the snook is modelled as an Euler-Bernoul...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2012/806078 |
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| _version_ | 1832549500859711488 |
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| author | Ashleigh Hutchinson |
| author_facet | Ashleigh Hutchinson |
| author_sort | Ashleigh Hutchinson |
| collection | DOAJ |
| description | The problem considered is an investigation of the possible collapse of the roof between the pillar next to be mined in secondary coal mining and the first line of pillar remnants called snooks. The roof rock between the pillar, which is the working face, and the snook is modelled as an Euler-Bernoulli beam acted on at each end by a horizontal force and by its weight per unit length. The beam is clamped at the pillar and simply supported (hinged) at the snook. The dimensionless differential equation for the beam and the boundary conditions depend on one dimensionless number 𝐵. We consider the range of values of 𝐵 before the displacement and curvature first become singular at 𝐵=𝐵1. The model predicts that for all practical purposes, the beam will break at the clamped end at the pillar. The failure of the beam for values of 𝐵 greater than 𝐵1 is investigated computationally. |
| format | Article |
| id | doaj-art-438a9bb88e07480fa89c6e232d4b5a79 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-438a9bb88e07480fa89c6e232d4b5a792025-02-03T06:11:04ZengWileyInternational Journal of Differential Equations1687-96431687-96512012-01-01201210.1155/2012/806078806078Controlled Roof Collapse during Secondary Mining in Coal MinesAshleigh Hutchinson0School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South AfricaThe problem considered is an investigation of the possible collapse of the roof between the pillar next to be mined in secondary coal mining and the first line of pillar remnants called snooks. The roof rock between the pillar, which is the working face, and the snook is modelled as an Euler-Bernoulli beam acted on at each end by a horizontal force and by its weight per unit length. The beam is clamped at the pillar and simply supported (hinged) at the snook. The dimensionless differential equation for the beam and the boundary conditions depend on one dimensionless number 𝐵. We consider the range of values of 𝐵 before the displacement and curvature first become singular at 𝐵=𝐵1. The model predicts that for all practical purposes, the beam will break at the clamped end at the pillar. The failure of the beam for values of 𝐵 greater than 𝐵1 is investigated computationally.http://dx.doi.org/10.1155/2012/806078 |
| spellingShingle | Ashleigh Hutchinson Controlled Roof Collapse during Secondary Mining in Coal Mines International Journal of Differential Equations |
| title | Controlled Roof Collapse during Secondary Mining in Coal Mines |
| title_full | Controlled Roof Collapse during Secondary Mining in Coal Mines |
| title_fullStr | Controlled Roof Collapse during Secondary Mining in Coal Mines |
| title_full_unstemmed | Controlled Roof Collapse during Secondary Mining in Coal Mines |
| title_short | Controlled Roof Collapse during Secondary Mining in Coal Mines |
| title_sort | controlled roof collapse during secondary mining in coal mines |
| url | http://dx.doi.org/10.1155/2012/806078 |
| work_keys_str_mv | AT ashleighhutchinson controlledroofcollapseduringsecondaryminingincoalmines |