基于弹性地基梁理论的端面顶板稳定性分析

端面冒顶一直是影响工作面安全高效开采的一大技术难题。本文采用弹性地基梁理论建立了端面顶板挠度微分方程，并运用PHASE 2D有限元软件建立了端面顶板稳定性数值模型，获得了煤层埋深、支架刚度、煤体刚度等因素对充填开采工作面端面顶板稳定性的影响。研究结果表明：（1）采深越大或液压支架刚度越小，端面顶板下沉越明显；煤层地基系数或顶板弹性模量增大时，端面顶板下沉有所减小，但影响较为有限；从可行性考虑，提高液压支架刚度，可以有效控制工作面顶板变形，降低端面冒顶及煤壁片帮的风险。（2）煤层埋深从200 m增加至250 m、300 m时，工作面前方塑性区宽度及支承压力显著增大，直接顶最大下沉量分别为61 mm、78 mm、96 mm。（3）煤层弹性模量从2 500 MPa增大至3 500 MPa、4 500 MPa时，工作面前方支承压力峰值略微增大，工作面前方煤体塑性区宽度也略微增大；直接顶下沉量略微减小。（4）现场观测表明，充填开采条件下支架阻力较小，工作面区域矿压显现不明显，顶板下沉得到有效控制。

Stability Analysis of Tip-to-Face-Roof Based on Elastic Foundation Beam Theory

End face caving has always been a major technical problem affecting safe and efficient mining of working face. In this paper, the elastic foundation beam theory is used to establish the differential equation of the end face roof deflection, and the PHASE 2D finite element software is used to establish the numerical model of the end face roof stability, and the influence of coal seam depth, support stiffness, coal body stiffness and other factors on the stability of the backfill mining face end face roof. The results show that :(1) the larger the mining depth or the smaller the hydraulic support stiffness, the more obvious the end face roof subsidence; When the foundation coefficient or elastic modulus of coal seam roof increases, the subsidence of the end face roof decreases, but the influence is limited. Considering the feasibility, improving the stiffness of hydraulic support can effectively control the deformation of working face roof, and reduce the risk of end face roof falling and coal wall sheet wall. (2) When the buried depth of coal seam increases from 200 m to 250 m and 300 m, the plastic zone width and abutment pressure in front of the working face increase significantly , and the maximum subsidence of the direct roof is 61 mm, 78 mm and 96 mm, respectively. (3) When the elastic modulus of coal seam increases from 2 500 MPa to 3 500 MPa and 4 500 MPa, the peak value of abutment pressure in front of working face increases slightly, and so does the width of coal plastic zone in front of working face. The amount of direct roof subsidence decreases slightly. (4) The field observation shows that the support resistance is small under the backfill mining condition, the ore pressure in the working face area is not obvious, and the roof subsidence is effectively controlled.