Shield tunnel grouting layer estimation using sliding window probabilistic inversion of GPR data

The ground penetrating radar (GPR) is an effective tool to detect the grouting layer behind shield tunnel linings, yet to estimate the thickness from GPR data is always difficult. We herein present a probabilistic inversion method to infer the grouting layer thickness together with its relative permittivity and electric conductivity values from GPR waveform data. This method uses a sliding window and Markov chain Monte Carlo (MCMC) simulation with Bayesian inference to explore the posterior distribution of model parameters. The inversion results of a synthetic example demonstrate that the proposed method successfully estimates the grouting layer thickness. We also investigate the impact of the modeling error on the inversion results, and use a modified likelihood function to eliminate the modeling error. With the modeling error corrected, the posterior model parameters converge correctly to their true values, and the associated uncertainties are quantified.

Automated summary

A probabilistic inversion method is proposed to infer the grouting layer thickness, relative permittivity, and electric conductivity values from GPR waveform data. The method successfully estimates the grouting layer thickness in a synthetic example, and the impact of modeling error on the inversion results is investigated. Correcting the modeling error allows the posterior model parameters to converge correctly to their true values and quantify associated uncertainties.