Shear strength assessment of a footwall slab using finite element modelling
Photogrammetry surveys were used to document a footwall slab failure that occurred at a surface coal mine located on the eastern slope of the Rocky Mountains. Photographs taken before and after the failure provided the pre- and post-failure geometry of the slope and the failed slab. Using photo-grammetry-derived digital terrain models, the measured surface area of the slabs involved in the failure was approximately 11,140 m2. The average thickness of the slab that failed was 5.4 m, giving a volume for the failed slabs of approximately 60,150 m3. At the time of the failure, the coal seams above the pit floor had been removed and the remaining slope had been supported with rock bolts.
2D finite element models were constructed using slope profiles. The purpose of this study was to use the models to assess the effect of stress relief unloading and stress redistribution due to mining. The models contained 69 elastic-perfectly plastic joint elements that represented the bedding surface upon which the slab slid. The in situ stresses, rock properties and the bedding surface shear strength and stiffness properties are discussed. Numerical analyses were conducted for models that had no rock bolts (unsupported) or contained rock bolts that were activated as the mining progressed (supported). The process of mining out a valley and exposing a highwall was modelled by a sequence of 11 excavation stages. The modelling results were used to investigate the effect of stress redistribution around the deepening pit and stress relief unloading on the distributions of shear stresses and displacements along of the bedding surface, as well as the slab stability at different mining stages. The joint elements were assigned a cohesion of 100 kPa and friction angle of 25º.
The measured displacements at a prism that was located on the slab were similar to those predicted by the model. As expected, elastic valley rebound occurred in the model, but shear stress and shear displacement reversals along the slip surface were also observed. The rebound caused by the unloading process and the stress redistribution due to pit excavation first resulted in upward slab sliding, followed by a reversal in the sense of the shear stresses acting along the bedding surface as the pit was deepened. The rebound of the slab due to the unloading process and the stress redistribution caused the shear stresses acting along the bedding surface to exceed the shear strength, and all joint elements yielded. However, because the slab was only partially exposed at this stage of mining, the slab could not experience large displacements. The slab was still constrained by the pit floor and yielded in a quasi-static manner. The yielding of the elastic-perfectly plastic joint elements when the slab was only partially exposed by mining highlights the importance of potential shear strength degradation of bedding surfaces caused by the stress redistribution and unloading and rebound processes. A limit equilibrium analysis for the final excavation geometry or a numerical analysis that does not model the full sequence of staged excavations will miss this potentially important aspect and may generate incorrect and non-conservative assessments of the slope stability.
The modelling results provide new insight into shear strength degradation that occurs when the pit floor approaches and then passes a specific point in the highwall. The cohesion was reduced in steps until the finite element model did not converge at the final excavation stage when the slab was fully undercut. The required cohesion to achieve a factor of safety of unity (non-convergence state in the finite element analysis) is about 25 kPa for a friction angle of 25º. This may suggest that the strength degradation processes reduced the cohesive strength by a factor of four, assuming the in situ cohesive strength before mining started was 100 kPa.