考虑时间效应的采空区顶板稳定性分析

Stability analysis of roof in goaf considering time effect

根据红岭铅锌矿采场顶板受力特征,基于Reissner厚板理论,建立了采场顶板的厚板力学模型;根据顶板不同边界条件,推导了固支和简支两种条件下顶板内部最大应力、弯矩和挠度方程;基于Kachanov蠕变损伤理论,构建了采场顶板蠕变损伤模型,并对采场顶板损伤失稳时间进行了深入分析。结果表明:固支条件下,顶板最大弯矩及应力出现在四边中点处,即四边中点处首先出现损伤,由蠕变损伤模型可知,长边中点损伤孕育时间为110.32d,短边中点损伤孕育时间为121.19d,之后损伤逐渐向外侧扩展;简支条件下,顶板最大弯矩及应力出现在顶板中心处,此时中点处损伤孕育时间为49.89d,应在此时间之内充填采空区保证顶板稳定性。工程实例分析表明,顶板损伤孕育时间与顶板厚度呈正比关系、与上覆岩层压力呈反比关系,即顶板越厚,损伤孕育时间越长,上覆岩层压力越大,损伤孕育时间越短。

According to the stress characteristics of the roof in the Hongling lead-zinc mine,based on the Reissner thick plate theory,the thick plate mechanical model of the stope roof was established. Based on different boundary conditions of the roof,the maximum inside of the roof under the conditions of solid support and simple support were derived. The stress,bending moment and deflection equations are based on the Kachanov creep damage theory. The creep damage model of the stope roof was constructed and the damage time of the roof damage was analyzed. The results showed that under the condition of solid support,the maximum bending moment and stress of the roof appeared at the midpoint of the four sides. Therefore,the initial damage occurred at the midpoint of the four sides. It can be known from the creep damage model that the long-side midpoint damage was 110.32 d,and for the short side, the midpoint injury incubation time was 121.19 d,and then the damage gradually expanded to the outside. Under the simple support condition,the maximum bending moment and stress of the roof appeared at the center of the roof,and the damage time at the midpoint was 49.89 d. Filling the goaf at this time ensures the stability of the roof. The engineering example analysis showed that the incubation time of the roof damage was proportional to the thickness of the roof and inversely proportional to the pressure of the overburden. The thicker the roof,the longer the damage incubation time. Therefore,the greater the pressure of the overburden and the shorter the damage incubation time.