地下采矿工程中的巷道、开切眼、各种开采硐室空间、人工钻孔及天然洞穴等，在地下无限大的空间范围内，其围岩破坏及稳定性问题均可统一到孔洞周围岩体力学的研究中。结合煤矿井下的工程条件，采用理论计算与数值模拟对比分析的方法，研究了静水压力下的理论公式与非均匀应力场中的塑性区边界方程，详细分析了理论计算的力学模型、推导原理、推导过程、计算精度，进而对其适用性进行评价分析。研究结果表明：静水压力下的理论公式推导过程严密，精度较高，适用于静水压力及偏应力不高条件下围岩塑性区范围的计算，偏应力较高环境下不再适用；非均匀应力场中圆孔围岩塑性区边界方程推导过程做了简化，其结果为近似解，与数值模拟计算结果相比在精度上有一定误差，但是可以很好地反映非均匀应力场中孔洞围岩塑性区形态演化规律，对于研究地下高偏应力场中巷道围岩的破坏规律及致灾机理有重要的指导意义。通过对已有孔洞围岩塑性区边界计算理论的分析评价，明确了不同理论方法的优劣势以及适用条件，对于合理应用理论指导工程实践有重要的实用意义。

In underground mining engineering, there are roadways, openings, various mining chamber spaces, artificial boreholes and natural caves, etc.The failure and stability of their surrounding rock can be unified into the study of rock mass mechanics around the hole in the infinite underground space. Combined with the engineering conditions of underground coal mines, the theoretical formula under hydrostatic pressure condition and the boundary equation of plastic zone under non-uniform stress field were studied by using the method of comparative analysis between theoretical calculation and numerical simulation. The mechanical model, the derivation principle, the derivation process and the calculation accuracy of the theoretical calculation were analyzed in detail, and its applicability was evaluated and analyzed. The results show that the derivation process of theoretical formula under hydrostatic pressure is rigorous and the calculation accuracy is high. It is suitable for the calculation of plastic zone range of surrounding rock under hydrostatic pressure, approximate hydrostatic pressure and low deviator stress conditions, but not under high deviator stress conditions. The derivation process of the plastic zone boundary equation in non-uniform stress field was simplified, and it was an approximate solution. The approximate solution has some errors in accuracy compared with the numerical simulation results, but it can well reflect the plastic zone evolution law of the surrounding rock in the non-uniform stress field. It has important guiding significance for studying the failure law and disaster-causing mechanism of the surrounding rock in the underground high deviating stress field. Based on the analysis and evaluation of the existing theory for calculating the plastic zone boundary of surrounding rock, the advantages and disadvantages of different theoretical methods and applicable conditions are clarified, which is of great practical significance for the rational application of theory to guide engineering practice.

0 引言

1 静水压力条件下的芬纳公式及卡斯特奈公式

   1.1 推导原理和过程

   1.2 评价认识

2 非均匀应力场中圆孔周围弹性应力解

   2.1 推导原理和过程

   2.2 评价认识

3 非均匀应力场中圆孔围岩塑性区边界方程

   3.1 卡斯特奈近似解

   3.2 于学馥圆形隧道围岩塑性区边界的近似计算

   3.3 基于统一强度理论的圆形巷道围岩塑性区边界线方程式

   3.4 非均匀应力场中圆形巷道围岩塑性区边界八次方隐性方程

   3.5 评价认识

4 分析评价

   4.1 静水压力条件下理论计算的可靠性分析

   4.2 塑性区边界方程的可靠性分析

   4.3 两个理论公式的适用性分析

5 结论