On the condition that the kinetic energy of coal shell in premonitory phase of its outburst is ignored; the equilibrium equation of spherical symmetric force of pore medium is established, which is under the coupling action of ground stages, gas pressure and effluent seepage. The character of spherical symmetry makes the strain Lode parameter at elastic and plastic stages is the same, and meet the condition of the physical relation of single curve. Popularized the uniaxial constitutive model, it can be educed that the relational expression between stress intensity sigma(i) and strain intensity epsilon(i) of coal shell. It is discovered that, the educed expression of radial displacement u in elastic and plastic zones of coal shell, can be broken down into the displacement u(d) corresponding to deviatoric strain and the displacement u(m) corresponding to average strain. The energy analysis, which is carried through by using geometry equation, force equilibrium equation, physical equation and the relation of stress intensity and average stress synthetically, shows that the external force work change can be broken down into the external force work delta W-d, delta W-v and delta W-s corresponding to deviatoric stress, mean stress and seepage stress; they are respectively corresponding to changes of strain energy of deviatoric stress, volumetric strain energy and pore volume energy; i. e. delta U-v, delta U-d and delta U-s The findings of two work-energy increment equilibrium relationship can be educed. It builds up the foundation for engaging catastrophe theory analysis of disintegration and outburst of a single coal shell in the outburst process.
