Back Analysis of Rock Mass Displacements Around a Deep Shaft Using Two- and Three-Dimensional Continuum Modeling

An instrumented section of a 10-m-diameter circular shaft located at a depth of 1.2 km in an average quality rock mass was back analyzed to establish the rock mass behavior. Extensometers were installed radially at four locations and provided the primary data for the back analyses. Three- and two-dimensional continuum models were analyzed using the numerical codes FLAC3Dand Phase2 to assess the rock mass behavior. An initial set of mechanical parameters obtained from empirical relationships were found to give a reasonable match to the measured response of extensometers 2 and 4, when using a Mohr-Coulomb strain softening model. A different set of parameters were needed for FLAC3D when trying to match the significantly higher displacements recorded by only one of the extensometer. It was noted that regardless of the material model and corresponding parameters, the three-dimensional models were not able to give reasonable match to the results of all extensometers. It was shown that for the given problem, there is a theoretical limit for ratio of displacements predicted for different extensometers using a continuum isotropic material model. The two-dimensional models in Phase2, however, gave an apparently better overall match to all the extensometers. Comparison of the results of three-dimensional models with the assumed longitudinal displacement profile for the two-dimensional model indicated that the three-dimensional effects were not adequately captured in the two-dimensional model.