Dynamic response and spacing optimization of a tailings dam reinforced with grid-pattern waste rock inclusions under representative ground motions

This study investigates the dynamic reinforcement mechanism and spacing optimization of grid-pattern waste rock inclusions (WRIs) in an upstream tailings dam. Three-dimensional FLAC3D models were established for an unreinforced dam and dams reinforced with WRIs at transverse center-to-center spacings of 30, 40, and 50 m. Under the assumed continuous connection through shared gridpoints between waste rock and tailings, four representative ground motions were used for steady-state seepage, dynamic response under the resulting fixed pore-pressure field, and post-earthquake stability analyses. Highly permeable drainage paths and a stiff spatial framework jointly reduced pore-water pressure and restrained deformation. Relative to the unreinforced dam, maximum pore-water pressure decreased by 23.7%–38.0%, and the post-earthquake, statically re-equilibrated factor of safety increased by 36.8%–39.2%. The four-motion mean peak horizontal displacement decreased by 42.2%–54.6%, and mean permanent displacement decreased by 73.9%–81.6%. Meanwhile, local acceleration amplification increased by 18.9%–44.4%, demonstrating simultaneous restraint of global deformation and enhancement of local inertia. A comprehensive engineering efficiency index was developed from pore-pressure control, displacement reductions, stability improvement, local dynamic response, and waste rock volume. Within the compared spacing range, safety benefits increased as spacing decreased, although the marginal improvement declined. The 30 m scheme provided the greatest absolute safety benefit. Under equal benefit weights and a baseline acceleration penalty coefficient of β = 0.2, the 40 m scheme achieved the highest efficiency per unit waste rock volume and was the relatively preferred option among the three compared spacings for balancing safety enhancement and construction demand. These findings support the beneficial use of mine waste rock and the seismic design of reinforced tailings dams.