石膏矿矿柱-护顶层支撑体系的流变力学模型分析

Rheological mechanical model of pillar-protective roof supporting system in gypsum mines

采用房柱法开采石膏矿体,将石膏矿柱简化为满足西原模型的黏弹塑性体流变模型,采空区上部留设的护顶层简化为弹性矩形薄板,建立了石膏矿矿柱-护顶层支撑体系的流变力学体模型。在此模型的基础上推导了矿柱支撑下采空区护顶层受流变作用的挠度微分方程,并根据其在不同阶段的边界条件采用伽辽金方法对该微分方程进行了求解。研究结果表明:当作用在矿柱上的应力σ大于极限摩阻力σ_s时,石膏矿柱的塑性流变大变形将随时间逐渐增大,极易导致石膏矿柱-护顶层支撑体系破裂直至坍塌;所建立的考虑矿柱流变特性的石膏矿采空区矿柱-护顶层支撑体系力学模型,可以对支撑体系的稳定时间进行预测。

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 σ on the pillar is greater than the limit friction resistance σ_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.