Modelling failure of natural rock columns

Natural rock columns often assume strange geometries that look unstable under the static loading of the rock mass itself and even more so under the resonance inducing, dynamic loads of seismic shaking. A two-dimensional finite element stress model was applied to the analysis of six selected rock columns formed in welded, horizontally jointed tuff in the Chiricahua Mountains, Arizona. The columns were selected for precarious appearing geometries, such as asymmetrical overhangs, narrow aspect, and severely incut “hourglass” profiles. In none of the cases did the stress modelling indicate proximity to either compressional or tensile failure. The modelling revealed that failure because of slip along inclined joints penetrating the rock was much more likely. Surprisingly, columns with pronounced “hourglass” morphologies were found to be more stable than cylindrical columns in rock with non-horizontal joints. The uniformity of column heights suggests that either rare, high velocity winds or prehistoric seismicity cropped the previous generation of columns. An estimate of the resonant frequencies of a typical column provides some idea of the dynamic response of the columns to seismic shaking. The question of seismic destruction is intriguing because the columns were apparently unaffected by a magnitude 7.2 earthquake 120 km away in 1887.