考虑流变的两向不等压深埋软岩巷道围岩塑性区近似解

Approximate solution of plastic zone in deep soft roadway surrounding rock under unequal stress field in two directions considering rheology

深埋软岩巷道围岩通常表现出较明显的流变特性,为确定两向不等压深埋软岩巷道围岩的塑性区,跳过围岩复杂的流变变形过程,直接以达到稳定后的巷道围岩为研究对象。稳定深埋软岩巷道围岩的峰值应力为一定围压下的长期强度,基于这一点并在考虑岩体峰后应变软化特性的情形下将围岩分为弹性区、塑性软化区和破裂区;然后,从轴对称应力场塑性区公式出发,结合围岩总荷载不变的规律推导了两向不等压深埋软岩巷道围岩水平(及竖向)轴上塑性区半径的解析解,并基于既有文献求解的塑性区形状相对准确地给出了两向不等压深埋软岩巷道围岩塑性区的近似范围;最后,将该理论应用于工程实例的分析计算,并就考虑流变特性与否的2种情况进行对比。结果表明:考虑岩体流变,塑性区分布相对合理;否则,塑性区以“滑动楔形”状分布于围岩较小范围内,围岩几乎仅产生弹性变形。可见,岩体流变特性对围岩塑性区分布具有重要的影响,不计岩体流变特性得到的围岩塑性区范围偏小。因此,理论研究及工程实际中,应兼顾到岩体的流变特性,以确保巷道围岩的长期稳定与安全。该近似解在不考虑岩体峰后应变软化时的结果与既有文献给出的相应解析结果完全吻合,且与有限元法计算的结果较为接近,是一种相对合理且准确的两向不等压深埋软岩巷道围岩塑性区的估算方法。

The surrounding rock of deep soft rock roadway usually shows an obvious rheological property.In order to determine the elastoplastic interface of surrounding rock in deep soft roadway under unequal stress in two directions,the stable roadway surrounding rock is directly taken as the research object by skipping the complex rheologic deformation process of surrounding rock.Based on the fact that the peak stress of stable surrounding rock in deep-buried soft rock roadway is the long-term strength under a certain confining pressure,surrounding rock is divided into elastic zone,plastic softening zone and ruptured zone by considering post-peak strain-softening of rock mass.On the basis of the formulas of plastic zone under axisymmetric stress field and the constant assumption of total loads,the plastic zone analytical radius on horizontal(and vertical)axis of deep soft rock roadway surrounding rock under non-uniform stress field is derived.Then combining with the plastic zone shape determined by the method of the existing literature,the plastic zone of surrounding rock under unequal compression in two directions is relatively accurately determined.Finally,based on the application of above theory to the analysis of an engineering example,the differences between considering rock mass’s rheology and without considering it are compared.The results show that plastic zone distributition is relatively reasonable if rock mass’s rheology is in consideration,otherwise the plastic zone will distribute in a very small range of surrounding rock in a form of sliding wedge,which means surrounding rock almost only produces elastic deformation under this circumstance.It can be seen that rheology has great impact on the plastic zone of roadway surrounding rock,and the plastic zone is relatively small if the rheologic property of rock mass is not considered.It is better to take rock mass’s rheology into account in theoretical research and engineering practice,so that the long-term stability and safety of roadway surrounding rock can be ensured.It is found that the result of the proposed algorithm in this paper is in perfect agreement with the corresponding analytical one presented in the existing literature if the post-peak strain-softening of rock mass is not considered,and is close to that of the finite element method.Therefore,the algorithm can be used as a relatively reasonable and accurate estimation method for quantifying the plastic zone of deep soft roadway surrounding rock under unequal stress in two directions.