## International Journal of Differential Equations

### Controlled Roof Collapse during Secondary Mining in Coal Mines

Ashleigh Hutchinson

#### Abstract

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 $B={B}_{1}$. 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 ${B}_{1}$ is investigated computationally.

#### Article information

Source
Int. J. Differ. Equ., Volume 2012, Special Issue (2012), Article ID 806078, 21 pages.

Dates
Accepted: 10 April 2012
First available in Project Euclid: 25 January 2017

https://projecteuclid.org/euclid.ijde/1485313350

Digital Object Identifier
doi:10.1155/2012/806078

Mathematical Reviews number (MathSciNet)
MR2959771

Zentralblatt MATH identifier
1248.34028

#### Citation

Hutchinson, Ashleigh. Controlled Roof Collapse during Secondary Mining in Coal Mines. Int. J. Differ. Equ. 2012, Special Issue (2012), Article ID 806078, 21 pages. doi:10.1155/2012/806078. https://projecteuclid.org/euclid.ijde/1485313350

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