A geometry based mathematical model is established for the calculation of reliability index by use of the fuzzy random reliability theory for slope stability analysis.

Through analyzing rock failure due to rock burst in-situ, applying the rock burst strength theory and the stability theory, and using physical modelling experiment, the mathematical model is built.

Grey system theory has been firstly applied to the zoning evaluation on regional stability of the Pearl River Delta, and a mathematical model of grey system has been established in this paper.