Rock slope stability comparison between deterministic and probabilistic block theory analyses for an open pit mine

摘要

The ultimate slopes of an open pit mine are generally excavated to the steepest possible anglernbecause the economic consequences of the excavation angle are significant. For large scale open pits, changesrnin slope angle by approximately 2–3 degrees may correspond to hundreds of millions of dollars in projectrnvalue. However, steeper slope angles result in an increased probability of slope failure. Therefore, it is criticalrnto calculate the maximum safe slope angles (MSSA) and also to estimate probabilities of slope failure withrnrespect to different cut slope dip angles. The block theory is a very useful technique to investigate possiblernfailure modes of rock blocks and to determine MSSA for rock slopes. The block theory considers block formationrnby discontinuity planes along with a cut slope, without assuming presence of lateral release planes asrnin kinematic analysis. Therefore, the results obtained from the block theory analysis can be considered to berncloser to the reality than that coming from kinematic analysis. However, block theory is usually used to performrndeterministic analysis using single fixed values (typically mean values) to represent orientation of discontinuityrnsets and strength parameters. The open pit mine slope stability is one of the mining subjects dominatedrnby variability and uncertainty because the slopes are composed of natural heterogeneous materialsrncontaining many discontinuities. In discontinuous hard rock masses, the variability and uncertainty of rockrnslope stability analyses mainly arise from discontinuity geometry and strength. Therefore, it is important tornincorporate the said variability and uncertainty in performing block theory analysis. This requires developingrnnew formulations to perform probabilistic block theory analysis and comparing the results obtained betweenrndeterministic and probabilistic block theory analyses.rnThe objective of the study was to develop a new formulation to conduct a probabilistic block theory analysisrnand to apply that technique to perform a case study for a part of an open pit mine and to compare the resultsrnobtained between deterministic and probabilistic block theory analyses.rnThe slope had two major rock formations: (a) DRC rocks and (b) DP rocks. Needed geological and geotechnicalrndata for the analyses were obtained from field and laboratory investigations. Discontinuity orientationrndata were obtained through both manual and remote fracture mapping. The cut slope dip direction anglern(CSDD) varied between 140° and 245° at every 15° for the selected part of the open pit mine to investigaternstability. The instability cumulative probabilities are calculated for cut slope dip angles between 10° and 90°rnat every 10°. The variability of the discontinuity orientation and shear strength is incorporated in the probabilisticrnblock theory analysis. Discontinuity orientation is treated as a bivariate random variable including therncorrelation that exists between the dip angle and dip direction.rnThe deterministic analysis provided the following results: (a) the MSSA range between 62° and 74° forrnDRC rocks, and between 56° and 88° for DP rocks for the CSDD values in the range 140-245°; (b) whenrnthe CSDD is between 185° and 200°, the MSSA reached the minimum value of 62° for DRC rocks; when thernCSDD is 230°, the MSSA reached the minimum value of 56°for DP rocks; (c) hence, 185°-200° and 230°rnseem to provide the worst CSDD for possible instability of slopes in the DRC formation and DP formation,rnrespectively; (d) within the CSDD range of 140° to 245° the slope seem to be stable for both DRC and DPrnformations for cut slope dip angles less than 56°.rnResults of deterministic and probabilistic block theory analyses show very good agreement on the failurernmodes and the worst and best case CSDD values for both DRC and DP rocks. For DRC rocks, for each CSDDrnangle, the MSSA obtained through the deterministic analysis was found to be about 12° to 24° higher than thernMSSA obtained under the probabilistic analysis corresponding to zero instability cumulative probability. ForrnDP rocks, for each CSDD angle, the MSSA obtained through the deterministic analysis was found to be aboutrn10° to 28° higher than the MSSA obtained under the probabilistic analysis corresponding to zero instabilityrncumulative probability. These differences resulted from the variability of the discontinuity orientations. Thernresults confirmed that the design value selected for MSSA for a particular region in the open pit mine basedrnon the deterministic block theory analysis can be on the unsafe side. In summary, the results showed clearlyrnthe superiority of probabilistic block theory analysis over the deterministic block theory analysis in obtainingrnadditional important information with respect to design of rock slopes.