A hybrid predictive model of unstable rock blocks around a tunnel based on estimated volumetric fracture intensity and circular variance from borehole data sets

Abstract Several failure modes may occur around underground excavations, one of the most common being block failure. The size distribution and occurrence probabilities of unstable blocks depend on discontinuity parameters such as size, shape, intensity, and orientation. The knowledge about the size and the number of blocks provides critical information to optimize site characterization and design procedures, or at least to accomplish this more efficiently. In this work we introduce a new attribute, Circular Variance, to measure the degree of dispersion of the fracture poles in angular domain based on borehole data. In our study the final objective is to present a predictive model of the mean rate of the formation of unstable rock blocks and their uncertainty. To fulfill this goal, we introduce a hybrid approach based on the combination of probabilistic discrete fracture network modeling, rock block failure instability analysis and supervised vector machine concepts. The present research studies the impact of P32, circular variance, and mean radius of the fractures on the mean generation rate of unstable blocks in a tunnel at El Teniente mine, Chile. A two and three factors supervised Poisson regression models are compared against each other for the prediction of the mean generation rate of unstable blocks. The results showed a good agreement between the real number of unstable blocks and the estimated ones with supervised Poisson regression models.