基于尖点突变理论的深部砂岩失稳诱灾预测研究

Research on prediction of instability-induced disasters in deep sandstone based on cusp catastrophe theory

  • 摘要: 砂岩巷道的长期稳定是确保深部煤炭资源安全高效开发的重要前提,其突发性失稳极易引发重大灾害事故。针对深部砂岩的失稳预警这一关键难题,建立一种有效的失稳前兆识别方法,实现对深部砂岩灾变前临界状态的精准预警。以尖点突变理论为基础,采用数值模拟软件RFPA2D (Realistic Failure Process Analysis)建立砂岩数值模型,开展了单轴及5、10、15、20 MPa围压下常规加载全过程数值模拟,同步获取声发射数据;基于应力-应变全过程曲线,分析了加载过程中弹性应变能的演化特征,构建了以弹性应变能为关键状态变量的尖点突变模型及时间序列势函数,以弹性应变能分叉集特征量化了深部砂岩的失稳预警信号。结果表明:在加载破坏过程中,弹性应变能分叉集函数值均出现2次明显的负值阶段,将第2次负值阶段的起始时刻定义为失稳预警时刻,同时将该时刻对应的轴向应力定义为预警应力;基于尖点突变模型的预警时刻在表征深部砂岩的失稳预警信号时具有充分提前量,预警时刻占最终失稳破坏时刻的比值普遍在80%以上,预警应力占峰值强度的比值亦稳定在80%以上;声发射活动的前兆特征在时序上与弹性应变能突变特征未表现出显著的一致性,其起始时间始终早于弹性应变能突变指标的预警时刻,客观反映了微观损伤的累积与活跃,而弹性应变能突变则标志着系统宏观稳定性的丧失,基于两者在信息源上的互补性,获取了自“失稳启动”早期预警点至“失稳临界”预警时刻的砂岩失稳诱灾“有效预警区间”;该研究通过系统数值模拟,揭示了围压对深部砂岩能量积聚-释放模式及预警时序特征的影响规律,从能量角度深化了对深部砂岩灾变演化机制的认识。

     

    Abstract: The long-term stability of sandstone roadways is essential for the safe and efficient exploitation of deep coal resources, as their sudden instability can readily cause major disasters. To address the critical challenge of instability warning for deep sandstone, an effective method for identifying precursors is established to achieve precise early warning of its pre-failure critical state. Based on the cusp catastrophe theory, a sandstone model was built using the numerical simulation software RFPA2D (Realistic Failure Process Analysis). Complete loading process numerical simulations under uniaxial and confining pressures of 5, 10, 15 and 20 MPa were conducted, with acoustic emission (AE) data acquired synchronously. The evolution characteristics of elastic strain energy during loading were analyzed from the complete stress-strain curves. A cusp catastrophe model with elastic strain energy as the key state variable and a time-series potential function were constructed. The bifurcation set characteristics of the elastic strain energy were then used to quantify early warning signals. The results show that the bifurcation set function value exhibits two distinct negative phases during loading. The starting moment of the second negative phase is defined as the instability warning moment, and the corresponding axial stress at this moment is defined as the warning stress. The warning moment derived from the cusp catastrophe model provides sufficient lead time, with its ratio to the final failure moment generally exceeding 80%, and the ratio of the warning stress to the peak strength also consistently above 80%. The temporal characteristics of AE precursors are not consistent with those of the elastic strain energy mutation; the onset of AE activity always precedes the warning moment indicated by the elastic strain energy mutation. This objectively reflects the accumulation and activity of micro-damage, whereas the elastic strain energy mutation signifies the loss of macroscopic system stability. Leveraging their complementary information sources, an “effective warning interval” for sandstone instability-induced disasters is obtained, ranging from the early warning point of “instability initiation” to the warning moment of “instability criticality”. Through systematic numerical simulation, this study reveals the influence of confining pressure on the energy accumulation-release pattern and the temporal characteristics of the warning signals in deep sandstone, thereby deepening the understanding of its disaster evolution mechanism from an energy perspective.

     

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