隧道地表沉降变形时间序列是具有分形特征的非线性体系,以狮子山隧道地表沉降监测为研究对象,基于分形理论,使用R/S分析法和V/S分析法计算了累计沉降和沉降速率时间序列的Hurst指数,并评价了地表沉降的稳定性,结合V统计量评价了这2种分析方法的有效性和地表变形的非循环周期;最后,使用分形插值函数与回归函数对地表沉降值进行了预测评价。结果表明,R/S分析法和V/S分析法对分析地表沉降时间序列具有较好的有效性,R/S分析法受短期记忆影响大,计算结果偏于安全,而 V/S分析法评价地表变形稳定性更加保守,3个监测点将长期处于稳定状态,且其时间序列的非循环周期约为20 d。使用分形插值得到的预测值与实测值间误差较小,且能正确反映变形演化趋势,较传统的回归分析优越,可以为地表沉降预测提供一种参考。

The time series of tunnel surface deformation is a nonlinear system with fractal characteristics. According to the surface subsidence monitoring of lion rock tunnel, we calculated the Hurst index of time series of accumulated subsidence and subsidence rate by using the R/S and V/S analysis based on fractal theory. Moreover, we evaluated the stability of surface subsidence, and analyzed the effectiveness of R/S and V/S analysis methods and the non-cyclic period of surface deformation in association with V statistic. We also predicted the surface subsidence values by fractal interpolation function and regression function. Results show that both R/S and V/S analysis methods has good validity for the analysis of time series of surface subsidence. R/S analysis method is prone to be influenced by short-term memory, which makes the result safe; whereas V/S analysis method is more conservative. Three monitoring points will be in stable state for a long time, and the time series of non-cyclic period is about 20 days. Compared with measured value, the error of the predicted value obtained by fractal interpolation is small. The method in this paper could reflect the deformation evolution trend correctly, and is superior to traditional regression analysis.