周期来压是矿山压力显现的典型特征，准确进行采场周期来压步距预测是有效降低采场事故发生的重要途径。针对基本顶自身缺陷与直接顶耦合作用对周期来压步距的影响，视采场顶板为自带裂缝的有限板模型，根据覆岩协调变形机理，基于断裂力学理论建立采场顶板断裂力学模型，推导直接顶−基本顶耦合作用下周期来压步距函数式，以陕北某矿区2个工作面为例，分析基本顶岩石断裂韧度、裂缝深度、直接顶厚度和弹性模量等参数对周期来压步距的作用规律。研究表明：基本顶断裂韧度与周期来压步距呈近似线性关系；裂缝深度比(裂缝深度/顶板厚度)对周期来压步距影响较大，裂缝深度比达到0.8后，基本顶失稳破坏；直接顶厚度小于3 m时对周期来压步距影响较小，超过3 m后对周期来压步距影响显著。研究结果对采场顶板周期来压步距预测及支架选型具有重要的理论意义和工程价值。

Periodic weighting is a typical characteristic of mine pressure. Accurate prediction of stope periodic weighting step is an important way to effectively reduce the occurrence of stope accidents. Aiming at the influence of the coupling between the basic roof defects and the direct roof on the periodic weighting step, the stope roof was regarded as a finite plate model with cracks. According to the coordinate deformation mechanism of the overburden rock, the fracture mechanics model of the stope roof was established based on the fracture mechanics theory. On this basis, the periodic weighting step function under the coupling between the direct roof and basic roof was derived. In addition, the influence of the parameters such as the fracture toughness of the basic roof rock, crack depth, direct roof thickness and elastic modulus on the periodic weighting step was analyzed based on 2 working faces of a mine area in northern Shaanxi. The research shows that: (1) The fracture toughness of the basic roof is in approximately linear relation with the periodic weighting step. (2) The crack depth ratio (crack depth/roof thickness) has a great influence on the periodic weighting step. In particular, the basic roof is unstable and destroyed when the crack depth ratio reaches 0.8. (3) The direct roof with the thickness less than 3 m has little effect on the periodic weighting step, but that with the thickness greater than 3 m has a significant effect on the periodic weighting step. Generally, the research results have important theoretical significance and engineering value for the prediction of periodic weighting step of stope roof and the selection of support.