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基于分数阶微积分的煤系砂岩渗流-蠕变模型研究

Study on seepage-creep model of coal measure sandstonebased on fractional order calculus

  • 摘要: 由于地下渗流对围岩蠕变规律的研究对于深部采掘工程的长期稳定性及安全性具有重要意义,基于岩石蠕变理论、分数阶理论,以煤系砂岩渗流-蠕变耦合试验结果为基础,建立了整数阶与分数阶煤系砂岩渗流-蠕变模型,并通过最小二乘法确定了模型的相应参数,经对模型进行验证与对比发现:整数阶模型与分数阶模型都能够反映砂岩渗流-蠕变特性曲线的变化趋势,但分数阶模型理论曲线与试验更加吻合,模型精度更高,可以为富水区域巷道围岩稳定控制提供参考。

     

    Abstract: Due to the study on the surrounding rock creep law affected by underground seepage would have the important significances to the long term stability and safety of the mining and excavation engineering in the mine deep depth. Therefore, based on the rock creep theory, fractional order model and the coal measure sandstone seepage-creep coupling test results as the basis, the seepage-creep model of the integral order and fractional order coal measures sandstone was established. A least square method was applied to determine the relevant parameters of the model and the verification and comparison on the model showed that the integer order model and the fractional order model both could reflect the variation tendency of the sandstone seepage-creep characteristics curve, but the theoretical curve and the test of the fractional order model could be well fitted, the accuracy of the model would be higher and could provide references to the stability control of the surrounding rock along the mine roadway in the water rich area.

     

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