Under the condition of considering unexcavated coal seams as an elastic ground base

this paper deduces the equation of rock beam’s deflection line using the symbolic operation software—Maple 9.5. Then it deduces the equilibrium equation for the rock beam-coal pillar system when the system deforms in a quasi-static way

which is the equilibrium equation of fold catastrophe model. The discrimination of stability by using total potential energy function of fold catastrophe shows that

the system of rock beam and coal pillar is in an unstable equilibrium state in premonitory phase of rockburst

and critical condition of rockburst in coal pillar is Cook’s stiffness criterion. The criterion can be expressed dynamically that

the required energy input rate of the environment approaches to zero while the deformation of coal pillar increases. The releasing amount of earthquake energy is calculated; and it is clarified that the mechanism of rockburst in coal pillar is that the elastic energy released by rock beam exceeds the energy dissipated by the deformation of coal pillar with softening characteristics after peak value. The obtained findings is described by the geometric form in which the curves of energy input rate

rate of change of rock beam’s elastic energy and dissipated energy of coal pillar are given. Calculations show that

the stiffness coefficient of unexcavated coal bed has faint influence on the rock beam’s equivalent stiffness. The excavation of working surface and the increment of exhausted area lessen rock beam’s equivalent stiffness remarkably.