片岩隧道围岩稳定性与断面轮廓分形维数关系

Fractal Dimension Relationship Between Schist Tunnel Surrounding Rock Stability&Section Profile

在薄层状片岩隧道中,隧道超欠挖对于围岩稳定性有一定的影响。通过Python编程,采用盒维数法计算断面轮廓分形维数的方法,对某隧道10个超欠挖断面进行分形维数的计算。并通过数值模拟的方法,计算了薄层状片岩隧道在超欠挖状态下拱顶的应力集中系数和最大位移影响系数,作为评价围岩稳定性的指标。结合分形理论建立的断面轮廓分形维数与薄层状片岩隧道围岩稳定性关联模型,发现分形维数和围岩稳定性的最佳函数关系为线性关系,回归系数为0.87;而超欠挖百分比与二者并没有直接的线性关系。研究此种围岩条件下隧道超欠挖与围岩受力状况之间的规律关系,对指导薄层状片岩中隧道的开挖有现实意义。

In thin-bedded schist tunnels, tunnel over excavation has a certain influence on the stability of surrounding rock.In this paper, the fractal dimension of 10 overcut and undercut sections of a tunnel is calculated by using the box dimension method to calculate the fractal dimension of the section outline through Python programming.The stress concentration coefficient and maximum displacement influence coefficient of thin-layer schist tunnel under overcut and undercut condition are calculated by numerical simulation, which are used as indexes to evaluate the stability of surrounding rock.Based on the correlation model between the fractal dimension of section profile and the stability of the surrounding rock of thin-layered schist tunnel, it is found that the best functional relationship between the fractal dimension and the stability of the surrounding rock is linear, and the regression coefficient is 0.87.However, there is no direct linear relationship between the percentage of overcut and undercut.It is of practical significance to study the relationship between tunnel overcut and undercut and stress state of surrounding rock under such conditions.