有限长迹线块体理论及其在围岩块体滑落概率分析中的应用

BLOCK THEORY OF LIMITED TRACE LENGTHS AND ITS APPLICATION TO PROBABILITY ANALYSIS OF BLOCK SLIDING OF SURROUNDING ROCK

关键块体理论假设结构面完全贯通所研究岩体,与实际结构面迹线有限长相矛盾,计算得到的关键块体数量偏多且安全系数偏小。根据块体理论赤平解析法求得关键块体棱长以及实际迹线长度,运用结构面迹长概率分布理论将关键块体概率重新定义为绝对关键块体概率、相对关键块体概率及非关键块体概率。以等长三棱锥为例,研究发现,当迹棱比大于100时,绝对关键块体概率接近1.0,可认为此时结构面迹线贯通岩体;当迹棱比等于1.5时,相对关键块体概率达到0.75;当迹棱比大于7.5时,非关键块体概率接近0。通过对布伦口—公格尔水电站地下洞室某关键块体进行稳定性分析,计算得到该块体安全系数为3.145,基于绝对关键块体概率的修正安全系数为4.591~5.233,增幅可达46.0%-66.4%。

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%.