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.

探地雷达（GPR）是检测盾构隧道衬砌后面的灌浆层的有效工具，但是从GPR数据估算厚度始终是困难的。我们在此提出一种概率反演方法，以根据GPR波形数据推断灌浆层的厚度及其相对介电常数和电导率值。该方法使用滑动窗和具有贝叶斯推断的马尔可夫链蒙特卡洛（MCMC）模拟来探索模型参数的后验分布。一个综合实例的反演结果表明，该方法成功地估计了灌浆层的厚度。我们还研究了建模误差对反演结果的影响，并使用修正的似然函数消除了建模误差。纠正了建模错误后，