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Based on the radiated energy of 133 rock bursts monitored by a microseismic technique at the Jinping II hydropower station, in Sichuan province, China, we analyzed the advantages and disadvantages of qualitative classification methods for the rock burst intensity. Then, we investigated the characteristics, magnitude, and laws of the radiated energy, as well as the relationship between the rock burst radiated energy and intensity. Then, we selected the energy as an evaluation index for the rock burst intensity classification, and proposed a new rock burst intensity quantitative classification method, which utilized the hierarchical clustering analysis technique with the complete-linkage method. Next, we created a new set of criteria for the quantitative classification of the rock burst intensity based on radiated energy and surrounding rock damage severity. The new criteria classified the rock burst intensity into five levels: extremely intense, intense, moderate, weak, and none, and the common logarithms of the radiated energy of each level were >7 lg( E/J), >4 lg( E/J) and <7 lg( E/J), >2 lg( E/J) and <4 lg( E/J), >1 lg( E/J) and <2 lg( E/J), and <1 lg( E/J), respectively. Finally, we investigated the factors influencing the classification, and verified its feasibility and applicability via several practical rock burst examples. [ABSTRACT FROM AUTHOR]