Three-Dimensional Limit-Equilibrium Comparison and Anchorage Design of a Multi-Plane Potentially Unstable Rock Block on a Hydropower Station Slope

Accurate stability assessment of potentially unstable rock blocks is essential for the safe construction and operation of hydropower infrastructure. This study applies a comparative limit-equilibrium workflow to a single, well-characterized sliding-type rock block (156.7 m3) bounded by three discontinuities (J1 250°/35°, J2 305°/75°, J3 215°/80°) on a hydropower station slope; discontinuity attitudes were measured with a geological compass and a terrestrial three-dimensional laser scanner, and the slope surface was reconstructed by UAV photogrammetry. A common, fully documented parameter set is used by a conventional two-dimensional method, a block-dividing limit-equilibrium method, and a three-dimensional residual-thrust method with moment equilibrium. With the site-suggested shear strengths and the lower-bound cohesion as the representative value, the block-dividing method gives factors of safety of 1.169, 1.063 and 0.903 under natural, heavy-rainfall and seismic conditions at optimal azimuths of 265.8°, 266.3° and 269.1°; the corresponding two-dimensional values are 1.037, 0.904 and 0.729, and the residual-thrust values are 1.497, 1.324 and 1.049. The block-dividing factors are 12.7–23.9% above the two-dimensional profile, whereas the residual-thrust result lies a further 16–28% higher (44–47% above the two-dimensional profile); this over-estimate is traced to the steep (75°, 80°) lateral release planes and to a mesh- and lambda-sensitive column solution, and is therefore non-conservative. A cohesion sensitivity analysis with fixed friction angle shows that the factor varies by 51–57% across the suggested cohesion interval. Under code-specified targets of 1.30/1.20/1.05, horizontal anchorage requires 366/427/566 kN versus 1150/1470/1413 kN for a perpendicular-to-slope layout, so a horizontal scheme of about 0.6 MN is adopted. Finite-element validation and field piezometric/displacement monitoring data, unavailable for this block, are identified as required future work.