The Fractal Characteristics of Ground Subsidence Caused by Subway Excavation

Abstract

The issue of uneven ground settlement caused by the excavation of subway tunnels represents a significant challenge in the design and construction of subway projects. This paper examined the fractal characteristics of surface settlement caused by subway excavation, employing wavelet transform and fractal theory. Firstly, the noise reduction effects of different wavelet functions, decomposition levels, threshold functions, and threshold selection rules were evaluated using the SNR and RMSE. Subsequently, 291 data points were derived from 18 interpolation points through fractal interpolation, representing a utilization of only 18% of the original data, to enhance the original monitoring data information by a factor of 2.94. The average relative error between the fractal interpolation results and the monitoring data was approximately 13%, which was indicative of a high degree of accuracy. Finally, the fractal dimension of the monitoring curves under different monitoring frequencies was calculated using the box-counting method. The denoising effect of the dbN wavelet function was found to be superior to that of the symN wavelet function in the denoising process of subway construction surface deformation monitoring data. Furthermore, the hard threshold method was observed to be more effective than the soft threshold method. As the monitoring frequency decreased, the fractal dimension of the deformation curves showed an overall decreasing trend. This indicated that high-frequency monitoring could capture more details and complexity of the surface settlement, while low-frequency monitoring led to a gradual flattening of the curves and a decrease in details.

Keywords

• ground subsidence
• wavelet de-noising
• fractal interpolation
• fractal dimension
• deformation monitoring