深部巷道破坏灾变机理及应力梯度控制模型

Catastrophic failure mechanism of deep roadways and stress gradient control models

  • 摘要: 巷道围岩变形和控制影响因素较多,应力梯度和支护预紧力是其中2个关键因素。为探究应力梯度与支护预紧力间的内在联系,求解最优的支护预紧力,基于统一强度理论,考虑中间主应力效应,针对两向不等压条件下的圆形巷道弹塑性问题,构建了应力梯度求解模型,分析了不同参数对巷道围岩支护效果的影响,结合应力梯度理论和应力梯度补偿准则,推导出围岩应力梯度补偿系数,为预应力精准确定提供了理论依据。模型推导中以围岩应力重分布、塑性区扩展及弹塑性交界面连续条件为基础,引入中间主应力系数、侧压系数和支护预紧力等关键参量,获得了巷道围岩应力、塑性区范围及应力梯度的解析表达,并进一步建立了预紧力与应力梯度补偿系数之间的定量关系。利用已有算例验证了应力梯度求解方式的适用性,该模型表明中间主应力系数选择不当,会导致巷道灾变风险的增加或者支护成本的上升,而锚杆预应力的施加,可减弱中间主应力系数选择不当造成的影响,并且随着预应力的增加,巷道围岩塑性区内应力梯度增大,弹性区内应力梯度不断减小,围岩劣化程度减弱。通过对不同锚杆预紧力条件下应力梯度的分布规律及支护效果的量化分析,证明预紧力与巷道锚固效果为正相关关系,塑性区范围在预紧力影响下不断缩小,围岩稳定性随着应力梯度增加而不断提高,据此得出锚杆预紧力与应力梯度对应的补偿关系并提出最优补偿比。工程应用结果表明,采用应力梯度补偿方法确定预紧力后,现场监测巷道累计变形量由传统支护条件下的约450 mm降低至约250 mm,变形量降低约40%,巷道围岩变形趋于稳定,验证了该方法用于锚杆支护参数确定的适用性。

     

    Abstract: Numerous factors influence the deformation and control of roadway surrounding rock, with stress gradient and pre-tension being two key factors. To investigate the intrinsic relationship between stress gradient and pre-tension and determine the optimal pre-tension, a stress gradient solution model was developed based on the unified strength theory, incorporating the effects of intermediate principal stress. This model addresses the elastic-plastic behavior of a circular roadway under bidirectional unequal pressure conditions, analyzes the impact of various parameters on roadway surrounding rock support, and, by combining stress gradient theory with the stress gradient compensation criterion, derives the surrounding rock stress gradient compensation coefficient, thereby providing a theoretical foundation for the precise determination of pre-tension. In the model derivation, the redistribution of surrounding-rock stress, plastic zone expansion, and continuity conditions at the elastoplastic interface are considered. Key parameters, including the intermediate principal stress coefficient, lateral pressure coefficient, and support pretension, are introduced to derive analytical expressions for the surrounding-rock stress, plastic zone extent, and stress gradient, and to establish a quantitative relationship between pretension and the stress gradient compensation coefficient. The applicability of the stress gradient solution method was assessed through comparisons with existing case studies. The model shows that improper selection of the intermediate principal stress coefficient may increase the risk of roadway failure or lead to higher support costs. However, the application of anchor rod pre-tension mitigates the adverse effects caused by an inappropriate b value. Furthermore, as pre-tension increases, the stress gradient within the surrounding rock’s plastic zone increases, while the gradient in the elastic zone decreases, thereby reducing the degradation of the surrounding rock. Quantifying the distribution of the stress gradient and support effectiveness under varying pre-tension conditions reveals that pre-tension is positively correlated with roadway support effectiveness. The range of the plastic zone continuously decreases as pre-tension increases, and the stability of the surrounding rock improves as the stress gradient rises. Based on these findings, a compensation relationship between pre-tension and stress gradient has been established, and the optimal compensation ratio has been proposed. Engineering application results show that, when the pretension is determined using the stress-gradient compensation method, the field-measured cumulative roadway deformation is reduced from approximately 450 mm under conventional support conditions to approximately 250 mm. The deformation is reduced by approximately 40%, and the surrounding-rock deformation tends to stabilize, indicating that the method is applicable to the determination of rock-bolt support parameters.

     

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