BOOTSTRAPPING METHODS FOR CONSTRUCTING CONFIDENCE INTERVALS FOR THE ESTIMATION OF MODEL PARAMETERS OF THE ZONAL DISINTEGRATION OF ROCKS AROUND UNDERGROUND EXCAVATIONS

Abstract

Abstract. Objectives The study of geomechanical phenomena and processes in rock massifs, manifested during the extraction of minerals, results in the need for research methods for solving the problem of zonal disintegration of rocks around deep underground excavations. In conditions of extremely small sample sizes, due to external circumstances, and the absence of a large number of deposits, the question of the quality of obtained results is very relevant. Methods As a solution to the problem, it is proposed to refine the results obtained by using numerical resampling methods, which include randomisation, bootstrap and Monte Carlo methods. Due to the specifics of the methods, special attention is paid to the number of bootstrapping implementations, which are inversely proportional to the size of the bootstrap sample. Results A solution to the problem of zonal disintegration of rocks around deep underground excavations is derived in which refined estimates of the significance of the analytic dependency of the defect function periodicity parameter on the position of the fracture zones are obtained using bootstrapping methods. The determination coefficient is chosen as the primary indicator in the work, allowing the most suitable form of the studied analytic dependency to be determined. The deviation of the determination coefficient in the nonlinear model reliably does not exceed 0.5% for any bootstrap sample size, while in the case of the linear model the deviation is less than 1% only for n≥122. Conclusion The interval estimates of the determination coefficients obtained by bootstrapping methods have a significant advantage in comparison with traditional approaches. Their quality is directly dependant on the number of bootstrap implementations and the volume of the bootstrapped sample. The latter is especially important in the context of considering extremely small data samples, since it becomes possible to reduce the dimension of confidence intervals to a given level at the initial significance level of the result.

Keywords

• бутстреп методы
• алгоритм
• зональное разрушение массива
• интервальные оценки параметров