基于量纲分析的巷道围岩松动圈预测模型

Prediction model for extent of excavation damaged zone around roadway based on dimensional analysis

为更合理地确定巷道围岩松动圈厚度,引入量纲分析理论,提出新的巷道围岩松动圈预测方法。选取岩石单轴抗压强度Rc、围岩节理系数F、围岩重度g、巷道埋深H、最大水平主应力σ_(Hmax)、巷道跨度B等物理量,应用量纲分析法构建巷道围岩松动圈厚度L与上述物理量间的无量纲关系式,其中L/H表征松动圈厚度L与巷道埋深H成正比,F表征巷道围岩的结构特征,γH/Rc、σ_(Hmax)/Rc表征巷道围岩的力学特征,B/H表征巷道的几何特征。结合实测数据,推导了各无量纲量间的定量函数表达式,残差平方和为0.003 1,相关系数为0.937 9。选取3个矿山巷道围岩松动圈测试实例对所建立的松动圈预测模型进行验证,结果表明该方法计算结果与实测结果较吻合,平均相对误差为7.38%,能满足工程需要。

In order to determine the extent of excavation damaged zone around roadway more reasonably, a new prediction method is proposed based on the dimensional analysis theory. Some physical quantities such as rock uniaxial compressive strength Rc, joint coefficient of rock F, unit weight of rock γ, depth of roadway H, maximum horizontal principal stress σHmaxand span of roadway B are selected; the dimensionless relations among the thickness of excavation damaged zone L and above mentioned physical quantities are established by means of dimensional analysis. Among them, L/H represented that the thickness of excavation damaged zone is proportional to depth of roadway; F represented structural characteristic of surrounding rock; both γH/Rc and σHmax/Rc represented mechanical characteristics of surrounding rock; B/H represented geometric characteristic of roadway. The quantitative function formula among these dimensionless relations is derived by combining with some field test data, the residual sum of square is 0.003 1, and the correlation coefficient is 0.937 9. Finally, the prediction model of the excavation damaged zone is validated with some testing examples from 3 mines. The results show that the calculation results satisfyingly agree with the measured data at the average relative error of 7.38%, which can be of interest from a practical viewpoint. © 2016, Science Press. All right reserved.