The coal in front of the mining face presents strain softening deformation characteristics. An analytical model is proposed to simulate the abutment pressure distribution over the coal in front of the mining face under elastic and inelastic conditions. A new theoretical formula is derived from calculating the abutment pressure distribution and its width in elastic and inelastic regions of the coal under the limit equilibrium condition. The influences of UCS, residual strength, mining height, softening modulus, and deformation angle on the abutment pressure distribution are discussed. The study results show that (1) the stress gradient in the plastic area is larger than that in the crushed zone; (2) the width of the plastic region is independent of the peak abutment pressure, but it is dependent on UCS, residual strength, mining height, softening modulus, and deformation angle; (3) the width of the crushed zone in the inelastic area is closely related to the peak abutment pressure, coal-floor interface cohesion, and friction coefficient; (4) the width of the elastic zone is dependent on the mining height, coefficient of horizontal pressure, coal-floor interface friction coefficient, and peak abutment pressure, where the coefficient of horizontal pressure has the highest impact, in that the width of the elastic zone undergoes logarithmic decrease with the increase in the coefficient of horizontal pressure. A case study was carried out at longwall panel 07 of No. 5 coal seam in Dongjiahe Coal Mine to verify the analytical model. The abutment pressure distribution and the widths of the elastic and inelastic zones under the limit equilibrium condition are calculated based on the relevant parameters. The theoretical results are compared with the field monitoring data and show a very good fit. It is proved that the proposed analytical model has high accuracy, and the feasibility of the model is verified. The study results can provide guidance for similar engineering applications.

采煤工作面前的煤具有应变软化变形特征。提出了一个解析模型，模拟了弹性和非弹性条件下采煤工作面前煤的基台压力分布。通过计算极限平衡条件下煤的弹性区域和非弹性区域中的基台压力分布及其宽度，得出了一个新的理论公式。讨论了UCS，残余强度，采矿高度，软化模量和变形角度对基台压力分布的影响。研究结果表明：（1）塑性区的应力梯度大于破碎区的应力梯度。（2）塑性区域的宽度与最大支座压力无关，但取决于UCS，残余强度，采矿高度，软化模量和变形角；（3）非弹性区的破碎带宽度与峰值台压，煤层界面内聚力和摩擦系数密切相关；（4）弹性带的宽度取决于开采高度，水平压力系数，煤层界面摩擦系数和峰值邻接压力，其中水平压力系数影响最大，因为随着水平压力系数的增加，弹性区经历对数减小。以董家河煤矿5号煤层长壁07板为例进行了实例验证。根据相关参数计算极限平衡条件下的基台压力分布以及弹性和非弹性区域的宽度。将理论结果与现场监测数据进行比较，并显示出很好的拟合度。实践证明，所提出的解析模型具有较高的准确性，并验证了该模型的可行性。研究结果可为类似工程应用提供指导。