基于厚板与散体理论的充填体下倾斜矿体开采顶板安全厚度研究

Study on the safety thickness of roof in mining of inclined orebody under filling based on the theory of thick plate and loose body

摘要

【目的】金属矿山地下充填开采中不同中段之间顶板厚度的确定对于采场稳定性至关重要，尤其对于厚跨比较大、矿体倾斜条件下顶板安全厚度计算方法的研究还不充分。【方法】基于Reissner厚板理论(厚跨比>0.125~0.2),考虑厚板横向剪切变形，推导四边固支条件下的顶板挠度表达式。采用传统杨森散体压力理论，针对倾斜矿体开采后顶板上覆松散充填体的情况，推导出倾斜角度下的散体压力表达式。最终根据第一强度理论，建立了计算倾斜充填体下顶板临界安全厚度的力学模型。【结果】研究结果表明：摩擦角的变化对顶板安全厚度的影响较内擦角更为显著。顶板自身尺寸也会对安全厚度产生影响，当长宽比小于1.5时，安全厚度呈线性增长，增长较快；长宽比在1.5~3.0之间，安全厚度增加速率逐渐变缓，为急速增长到趋于稳定的过渡阶段；长宽比大于3.0之后，安全厚度将趋于稳定。当矿体倾角从水平逐渐变为垂直，顶底板岩石侧壁对充填体摩擦力减小，更多的荷载也逐渐转移到顶板，预留的安全厚度也会相应增加。【结论】通过工程实例验证，使用Reissner厚板与扩展后的杨森散体压力理论求解顶板安全厚度，能够提供较为合理的倾斜矿体开采充填后顶板临界安全厚度，获得的顶板安全厚度值兼具经济性与安全性，进一步丰富了金属矿山地下开采顶板安全厚度的确定方法，为类似矿山开采顶板安全管理提供一定的理论依据。

Abstract

[Objective] The determination of roof thickness between different sections in underground filling mining of metal mines is very important for stope stability, especially the research on the calculation method of roof safety thickness under the condition of large thickness span ratio and inclined ore bodies is not sufficient. [Methods] Based on the Reissner theory of thick plate(thickness to span ratio >0.125~0.2) and considering the transverse shear deformation of thick plate, the expression of roof deflection under the condition of four sides fixed support is derived. Based on the traditional Janssen's theory of granular pressure, the expression of granular pressure under the inclined Angle is derived for the situation of the roof covered with loose backfill after mining of inclined orebody. Finally, according to the first strength theory, a mechanical model is established to calculate the critical safety thickness of the roof under the inclined backfill. [Results] The result show that the influence of friction Angle on the safety thickness of the roof is more significant than that of the internal friction Angle. The safety thickness is also influenced by the roof size. When the aspect ratio is less than 1.5, the safety thickness increases linearly and rapidly. Between 1.5 and 3.0, the increase rate of safety thickness gradually slows down, and it is a transition stage from rapid growth to stability. When the aspect ratio is greater than 3.0, the safety thickness will become stable. When the dip Angle of the ore body gradually changes from horizontal to vertical, the friction force of the rock side wall on the backfill body decreases, more loads are gradually transferred to the roof, and the reserved safety thickness will increase accordingly. [Conclusion] Through engineering examples, the calculation of roof safety thickness by Reissner theory of thick plate and the extended Janssen's theory of granular pressure can provide a reasonable critical safety thickness of roof after mining and filling of inclined orebody, and the obtained value of roof safety thickness is both economical and safe, the method of determining the safety thickness of underground mining roof in metal mines is further enriched, and the theoretical basis for the safety management of mining roof in similar mines is provided.

关键词

Reissner厚板理论 / 倾斜矿体 / 散体压力 / 充填体 / 顶板厚度 / 变形 / 力学性能 / 影响因素

Key words

Reissner thick plate theory / inclined orebody / scattered body pressure / backfill / thickness of the roof / deformation / mechanical properties / influence factor

基金资助

湖北省自然科学基金项目(E0312502)

国家自然科学基金项目(42377177)