In this study

a rheological mechanical model was developed for the pillar-protective roof system in gypsum mines. The gypsum pillar was considered as a visco-elastoplastic body in the rheological model satisfying the Nishihara model

and the pre-setting protective roof on the top of the goaf was simplified as an elastic rectangular sheet. On the basis of the established model

a deflection differential equation was derived for the stabilization time of protective roof under the support of the pillar. Besides

a solution of Galerkin method was applied to the equation in accordance with the boundary conditions of the protective roof at three stages. When the stress ? on the pillar is greater than the limit friction resistance ?s

the plastic rheological deformation of the pillar gradually increases with time

which eventually results in the failure of the pillar-protective roof system. Based on a case study

the proposed mechanical model can forecast the stable time of the roof rock in the pillar-protective roof system of mined-out area by considering the rheological behaviour of pillars.