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Article

Multiple Fractal Analysis and Prediction of the Settlement of the Upper Existing Highway Pavement Induced by Shallow-Buried Tunnel Construction

1
School of Resources and Safety Engineering, Central South University, Changsha 410083, China
2
Road & Bridge International Co., Ltd., Beijing 101100, China
*
Author to whom correspondence should be addressed.
Fractal Fract. 2026, 10(7), 430; https://doi.org/10.3390/fractalfract10070430 (registering DOI)
Submission received: 18 April 2026 / Revised: 18 June 2026 / Accepted: 22 June 2026 / Published: 25 June 2026

Abstract

In recent years, it has become inevitable to dig underneath existing highways when excavating tunnels. The soil settlement induced by ground excavation may adversely affect existing highways. In this study, a settlement monitoring system is used to obtain the settlement sequence of multiple measurement points on the pavement. Multifractal detrended fluctuation analysis (MF-DFA) is used to focus on analyzing the multiple fractal features of the pavement settlement rate. The results show that the settlement rates of the highway caused by the tunnel excavation and construction process all show multiple fractal characteristics. The fluctuations in the measurement points above and near the entrance of the tunnel are more complex and intense. Based on the moving-average method (MA), convolutional neural network (CNN), and Extreme Learning Machine (ELM), MA-CNN and MA-ELM prediction models are constructed to predict the settlement value sequences of the fluctuating points. The results indicate that the MA-ELM prediction model demonstrates superior predictive performance (with R2 values of 0.956, 0.950, and 0.979 on the test set). Further, with the help of the Dung Beetle Optimizer (DBO), a meta-heuristic algorithm for parameter optimization, the hybrid model DBO-MA-ELM greatly improves the prediction performance (R2 of 0.975, 0.997, 0.998 for the testing set).
Keywords: existing highways; shallow buried tunnel; Multifractal Detrended Fluctuation Analysis (MF-DFA); Extreme Learning Machine (ELM); Dung Beetle Optimizer (DBO) existing highways; shallow buried tunnel; Multifractal Detrended Fluctuation Analysis (MF-DFA); Extreme Learning Machine (ELM); Dung Beetle Optimizer (DBO)

Share and Cite

MDPI and ACS Style

Liu, D.; Yuan, D.; Zhang, Y.; Zhu, Z. Multiple Fractal Analysis and Prediction of the Settlement of the Upper Existing Highway Pavement Induced by Shallow-Buried Tunnel Construction. Fractal Fract. 2026, 10, 430. https://doi.org/10.3390/fractalfract10070430

AMA Style

Liu D, Yuan D, Zhang Y, Zhu Z. Multiple Fractal Analysis and Prediction of the Settlement of the Upper Existing Highway Pavement Induced by Shallow-Buried Tunnel Construction. Fractal and Fractional. 2026; 10(7):430. https://doi.org/10.3390/fractalfract10070430

Chicago/Turabian Style

Liu, Dunwen, Dan Yuan, Yong Zhang, and Zhengwei Zhu. 2026. "Multiple Fractal Analysis and Prediction of the Settlement of the Upper Existing Highway Pavement Induced by Shallow-Buried Tunnel Construction" Fractal and Fractional 10, no. 7: 430. https://doi.org/10.3390/fractalfract10070430

APA Style

Liu, D., Yuan, D., Zhang, Y., & Zhu, Z. (2026). Multiple Fractal Analysis and Prediction of the Settlement of the Upper Existing Highway Pavement Induced by Shallow-Buried Tunnel Construction. Fractal and Fractional, 10(7), 430. https://doi.org/10.3390/fractalfract10070430

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