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Abstract The key block theory assumes that the rock masses are crossed over completely by structural planes，which is in conflicting with the fact that the lengths of traces of structural planes are finite，leading to the overestimation of the number of key blocks and the underestimation of the safety factor in calculations. The edge lengths of key blocks and the actual lengths of traces were thus computed according to the stereo-analytical method of block theory. The key block probability was redefined as absolute key block probability，relative key block probability and non-key block probability according to the probability theory of traces of structural planes. Calculations on the example of an equilateral triangular pyramid showed that when the ratio of length of trace to edge was larger than 100，the absolute key block probability was nearly 1.0 and structural planes could be considered to cross through rock mass in this case. If the ratio of length of trace to edge was equal to 1.5，the relative key block probability reached 0.75 and if the ratio of length of trace to edge was greater than 7.5，the non-key block probability was close to 0. The safety factor of the underground cavern at Bulungl-Gongur hydropower station was 3.145 according to the stability analysis of key block theory and was 4.591–5.233 based on the absolute key block probability，increased 46.0%–66.4%.
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Received: 22 August 2013
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2014, Vol. 33 
