关键词: 地表沉降, 变形时间序列, 分形理论, Hurst指数, 分形插值

Abstract: 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.

Key words: ground surface subsidence, deformation time series, fractal theory, Hurst index, fractal interpolation