A CUSP CATASTROPHE MODEL TO INTERPRET LOSS OF STABLE EQUILIBRIUM IN ROCK QUASI-STATIC MOVEMENT

In order to study the stability in motion of a rock mass acted on by horizontal force(N) and vertical forces(P), a catastrophe theoretical model of a simplified rock mass system is proposed to interpret quantitatively the conditions of the stress which may cause the loss of stable equilibrium in motion.An expression of the total potential energy function for the rock mass model is derived. It has been proved that the above-mentioned system can be described by the CUSP catastrophe model. At. the same time, a bifurcation set B which makes the system to lose its stable equilibrium in the N-P control space is delimited.The primary results obtained are as follows: demarcation of the stability and unsta-bility regions in motion of the rock mass in the N-P control space, analysis of the process of sudden state variation due to the gradually changing forces and the influence of the paths of the point (N,P) in the control space on the stability in motion of the rock mass; and order of magnitude of the stress variation necessary for the sudden change of potential energy is discussed. On the basis of these preliminary results some earthquake phenomena are reviewed.