基于简支梁模型的岩体超低摩擦效应理论分析

 考虑深部煤层开采情况，基于塑性动力学理论建立岩体超低摩擦效应简支梁模型，通过理论推导得到动载荷作用下顶板在弹性阶段和弹塑性阶段，岩层与顶板间接触界面法向应力解析表达式，分析动荷载P(t)作用下接触面法向应力与初始接触面法向应力的比值(q/p)与顶板位置参数 及时间t的关系曲线，据此得到岩体接触界面摩擦力变化规律，从塑性动力学角度解释岩体超低摩擦效应。研究结果表明：动载荷作用下，顶板在弹性和弹塑性状态，岩层与顶板间接触界面法向应力均有所降低，且降低幅度十分显著，即其接触界面摩擦力急剧下降，具有“摩擦消失”效应，这充分说明岩体超低摩擦效应的存在；比较弹性变形阶段与弹塑性变形阶段接触界面法向应力变化，前者降低幅度更大，说明顶板在弹性阶段岩层与顶板间接触界面更易发生超低摩擦效应。

THEORETICAL ANALYSIS OF EFFECT OF ANOMALOUSLY LOW FRICTION ON ROCK MASS BASED ON SIMPLY SUPPORTED BEAM MODEL

Based on theory of plasticity kinetics，simply supported beam model of effect of anomalously low friction on rock mass was established considering deep coal mining. Through theoretical deduce，analytical formulas of normal stress of contact interfaces between rock and roof in elastic stage and elastic-plasticity stage under dynamic load were both presented. The relationship curves between q/p， and t were analyzed. The variation rules of friction on contact interfaces in rock mass were obtained. The effect of anomalously low friction on rock mass was explained on the basis of plasticity kinetics. The results indicate that normal stress of contact interfaces between rock and roof in elastic stage and elastic-plasticity stage reduced sharply under dynamic load. And the reduction amplitudes were relatively large. It is shown that friction on the contact interfaces reduced，which presented obvious effect of friction disappearance. Therefore，the existence of effect of anomalously low friction on rock mass was proved. Comparing normal stress of contact interface on elastic stage with that on elastic-plasticity stage，reduction amplitude of the former was larger，which illustrated that effect of anomalously low friction on contact interface between rock and roof was easy to occur when the beam was in elastic stage.