Investigation on applicability of classical stiffness theory in pillar burst

Abstract Classical stiffness theory provides an important basis for interpreting pillar burst, but its applicability under nonelastic roof and floor conditions and different coal pillar sizes remains unclear. In particular, satisfying the classical stiffness condition does not explicitly indicate whether sufficient releasable energy exists to drive pillar burst. To address this issue, the applicability of classical stiffness theory was evaluated from the perspective of residual energy by considering roof and floor deformation behavior and coal pillar size. The results show that classical stiffness theory is mainly applicable to wide coal pillars when the roof and floor remain elastic. Its applicability becomes limited when plastic deformation develops in the roof or floor and is generally lost for narrow coal pillars dominated by continuous plastic deformation and energy dissipation. Numerical simulations further show that roof and floor plastic deformation shifts elastic strain energy concentration from the coal pillar toward the surrounding strata, thereby reducing the releasable elastic energy within the pillar. Verification based on the minimum energy principle confirms that satisfying the classical stiffness condition alone does not necessarily lead to pillar burst. On this basis, a triggering stiffness criterion considering post peak stress evolution and roof and floor plasticity was proposed. Compared with the classical stiffness threshold, the proposed criterion identifies potential pillar burst risk at an earlier stage. A critical displacement velocity ratio was further established to provide a measurable expression of the triggering stiffness state. These findings clarify the applicability boundary of classical stiffness theory and provide a theoretical basis for earlier identification of pillar burst risk.