Models of three-dimensional arching stress and strength requirement for the backfill in open stoping with subsequent backfill mining

In two steps open stoping with subsequent backfill mining method for underground thick metal ore bodies,a reasonable balance between the stability and strength requirement of the exposed cemented backfill in primary stopes has significant effects on the safe and economic mining operations. In order to build a reasonable three-dimensional analytical model and method for estimating the strength requirement of cemented backfill in this mining method,and solve the problems that empirical analogy is usually applied to determine the required strength of backfill for the lack of scientific and reasonable calculation methods,the spatial contact properties of the backfills in adjacent stopes in the processes of excavating and filling have been analyzed based on the arching theory borrowed from soil mechanics. Stress distributions of the uncemented backfill in secondary stopes and the exposed cemented backfill in primary stopes have been investigated separately. Three-dimensional analytical models for the arching stress of these backfills have been developed from Marston two-dimensional arching stress model,to reveal the stress transfer laws and quantitative characterization methods of these contact boundaries among the uncemented backfill in secondary stopes,cemented backfill in primary stopes and surrounding rock. The analytical results of arching stress have been compared and veri- fied against the numerical arching stress through FLAC3D simulations. The proposed analytical models of arching stress are further applied to Mitchell model of strength requirements evaluation. The three-dimensional arching lateral pres- sure from the uncemented backfill acting on the exposed cemented backfill,and the contact friction between the ce- mented backfill and surrounding rock masses have been considered. The potential failure modes of exposed cemented backfill are quantitatively characterized by the different values of direction angles of sliding plane and the frictional force along the interfaces between the cemented backfill and surrounding rock masses. Four kinds of three-dimensional analytical models and methods for the safety factor and strength requirement of cemented backfill are proposed based on these failure modes. Numerical solution search and calculation of backfill strength requirements have been carried with FLAC3D under different stope sizes (length,width,height) and different backfill parameters (bulk density,inter- nal friction angle),to compare and verify the proposed four kinds of three-dimensional analytical solutions. The analyt- ical and numerical solutions for the strength requirements of cemented backfill have the best consistency when the di- rection angle of the sliding plane α = 45°+φc / 2 and the direction angle of the frictional force along the interfaces be- tween the cemented backfill and surrounding rock masses β = 45° - φc / 2. The optimal three-dimensional analytical model and method for the strength requirements of the cemented backfill in primary stopes have been obtained.