采动覆岩经历了卸荷膨胀与再压实的动态过程，将覆岩卸荷膨胀总量随卸荷高度及承受载荷不断累积而发生动态变化的现象称为采动覆岩卸荷膨胀累积效应。采动覆岩卸荷膨胀累积效应是岩层移动过程中的自然现象，对岩层移动规律具有重要影响。基于修正后的采动覆岩卸荷膨胀累积效应力学模型，以山西赵庄煤矿1311工作面内部岩层移动实测结果为基础，针对采高、采深和岩性对采动覆岩卸荷膨胀累积效应的影响开展了理论研究。结果表明：采动覆岩卸荷膨胀总量主要由垮落带和裂隙带的塑性膨胀与主关键层下部弯曲下沉带的弹性膨胀所组成，其中垮落带的塑性膨胀占比最大，弯曲下沉带的弹性膨胀占比最小。采动覆岩卸荷膨胀总量随覆岩卸荷高度的逐步增大呈现先增大到峰值后再逐步减小的过程，当覆岩主关键层破断后，弯曲下沉带的弹性膨胀量降为0，此时覆岩卸荷膨胀总量达到最小值，为覆岩残余膨胀量。采高对覆岩卸荷膨胀累积效应的影响主要体现在不同采高条件下垮落带与裂隙带高度不同。覆岩卸荷膨胀总量随采高的增大而增加，当采高由2.5 m增大至10.5 m时，卸荷膨胀总量峰值和残余碎胀量均增大3倍以上。与采高相比，采深变化一般不会改变垮落带与裂隙带高度，采深对覆岩卸荷膨胀总量峰值影响较小。采深对覆岩卸荷膨胀累积效应的影响主要体现在不同采深条件下覆岩残余膨胀量的不同，覆岩残余膨胀量随采深增大而减小，当采深由496.6 m增加至896.5 m时，覆岩残余膨胀量减少了32.5%。岩性对覆岩卸荷膨胀累积效应的影响主要体现在不同岩性碎胀煤岩被压实的难易程度不同，覆岩卸荷膨胀总量随岩性的变硬而增加。当初始切线模量和弹性模量由降低50%到增大50%时，覆岩卸荷膨胀总量峰值增加4.3%，但覆岩残余膨胀量增加110%。覆岩残余膨胀量决定了地表下沉系数大小，因此，覆岩卸荷膨胀累积效应可影响地表下沉系数变化规律。采高对地表下沉系数的影响并非单调线性的，下沉系数随采高增大是微量减小还是微量增大取决于关键层位置对裂隙带高度的影响情况。在充分采动条件下，由于塑性膨胀区残余膨胀量随采深增大而减小，下沉系数随采深增大而增大。当岩性由软变硬时，塑性膨胀区越不易被压缩，地表下沉系数相应减小。

The overburden strata undergo a dynamic process of stress relief-induced expansion and re-compaction. The phenomenon that the total amount of overburden unloading expansion changes dynamically with the continuous accumulation of unloading height and bearing load is defined as the cumulative effect of overburden strata expansion induced by stress relief. This cumulative effect caused by mining is a natural phenomenon in the process of strata movement and has an important impact on the movement law of strata. Based on the revised mechanical model of the cumulative effect, and the measured results of internal strata movement at the 1311 working face of Zhaozhuang Coal Mine, China, the impact of mining height, mining depth and lithology on the cumulative effect was studied theoretically. The results show that the total amount of overburden unloading expansion is mainly composed of the plastic expansion of the caving zones and the fracture zones and the elastic expansion of the continuous bending zones at the lower part of the primary key stratum. The plastic expansion of the caving zones accounts for the largest proportion, and the elastic expansion of the continuous bending zones accounts for the smallest proportion. With the gradual increase of the unloading height of the overburden strata, the total amount of overburden unloading expansion will first increase and then gradually decrease. When the primary key stratum of the overburden strata breaks, the elastic expansion of the continuous bending zones drops to 0, at this time the total amount of overburden unloading expansion reaches the minimum value. The influence of mining height on the cumulative effect is mainly reflected in the different heights of caving zones and fracture zones under different mining height conditions, which affects the total amount of overburden unloading expansion. The total amount of overburden unloading expansion increases with the increase of the mining height. When the mining height increases from 2.5 m to 10.5 m, the peak value of the total amount of overburden unloading expansion and the residual crushing expansion both increase by more than 3 times. Compared with the mining height, the mining depth variation generally does not change the height of the caving zones and the fracture zones, and the mining depth has less influence on the peak value of the total amount of overburden unloading expansion. The influence of mining depth on the cumulative effect is mainly reflected in the difference in the residual expansion of the overburden under different mining depth conditions. The residual expansion of the overburden decreases with the increase of mining depth. When the mining depth increases from 496.6 m to 896.5 m, the residual expansion of the overburden is reduced by 32.5%. The influence of lithology on the cumulative effect is mainly reflected in the different degree of compaction of the expansion coal and rock with different lithology. The total amount of overburden unloading expansion increases with the hardening of lithology. When the initial tangent modulus and elastic modulus vary from 50% decrease to 50% increase, the total peak amount of overburden unloading expansion increases by 4.3%, but the residual expansion of the overburden increases by 110%. The residual expansion of the overburden determines the surface subsidence factor. Therefore, the cumulative effect can affect the variation law of the surface subsidence factor. The influence of mining height on the surface subsidence factor is not monotonous linear. Whether the subsidence factor decreases or increases slightly with the increase of mining height depends on the influence of the position of the key stratum on the height of the fracture zones. Under the condition of critical mining, since the residual expansion of the plastic expansion zones decreases with the increase of mining depth, the subsidence factor increases with the increase of mining depth, and the increase rate keeps decreasing. When the lithology gradually changes from soft rock to hard rock, the plastic expansion zones is less likely to be compressed, and the surface subsidence factor decreases accordingly.

1 模型的修正与验证

   1.1 力学模型的修正

   1.2 计算方案

   1.3 计算结果验证

2 采高对卸荷膨胀累积效应的影响

   2.1 采高对垮落带膨胀量的影响

   2.2 采高对裂隙带膨胀量的影响

   2.3 采高对弯曲下沉带膨胀量的影响

   2.4 采高对卸荷膨胀累积总量的影响

3 采深对卸荷膨胀累积效应的影响

   3.1 采深对垮落带和裂隙带膨胀量的影响

   3.2 采深对弯曲下沉带膨胀量的影响

   3.3 采深对卸荷膨胀累积总量的影响

4 岩性对卸荷膨胀累积效应的影响

   4.1 岩性对垮落带和裂隙带膨胀量的影响

   4.2 岩性对弯曲下沉带膨胀量的影响

   4.3 岩性对卸荷膨胀累积总量的影响

5 覆岩卸荷膨胀累积效应对地表下沉系数的影响规律

6 结论