Annotation of total potential energy function for dynamic failure of rock

It had been expatiated quantitatively that the rock system had different values of the total potential energy at different positions on the quasi-static deformation path.The relationship between the energy,?Π,released by rock system dynamic failure and that at the failure starting point j and the failure halting point s was Π s= Π j + ?Π,and it was essential that ?Π <0.It had also been discovered that the differential of the potential function of fold catastrophe model was the total differential.Based on the characteristic that the integration value of the total differential was not related to the path of integration,the phenomenon that the rock sample failed in stepped form as a result of energy output to environment by oil drainage of the cylinder on a servo experimental machine had been expatiated,and the rock sample failed in brittle form while it was loaded on an ordinary experimental machine.It was indicated that the energy output to environment by oil drainage of the cylinder was equal to the energy released by the system in dynamic form while the rock sample failued in brittle form.By using Green formula,it was obtained that the released elastic energy while the equilibrium position of system leaping along straight line on fold catastrophe equilibrium path could be expressed by negative value of the area D enclosed by the straight line and quasi-static equilibrium path.Furthermore,it was also obtained that the total potential energy of the rock system in limit state always changed towards decreasing direction no matter whether it was in quasi-static or dynamic course of deformation.