Fracturing of an Euler–Bernoulli beam in coal mine pillar extraction

•Roof fracture in secondary coal mining.•Tensile fracture of an Euler–Bernoulli beam subjected to a compressive axial force.•Transition from a continuous elastic beam to a voussoir beam.•Maximum curvature and bending moment of a clamped Euler–Bernoulli beam.

The paper models the first stage of the process of pillar extraction in a coal mine. The problem of understanding how a coal mine roof collapses after secondary cutting of the supporting pillars to create small supporting snooks is considered. The fracture of the roof is considered when a set of snooks have failed and the roof must support itself between two pillars. Models that account for the relative importance of the overburden weight on the roof and the compressive stresses in the roof are examined using a simple strut and beam theory.