The objective of the work is to detect anomalies in waterproof membranes in bridges using ground-penetrating radar (GPR). Defects are determined indirectly by detecting the presence of water (variation of complex permittivity) under the damaged layer. In a first step of the research, Ultra-Wide Band GPR technology is used with a Full-Waveform Inversion (FWI) approach as a punctual and calibration method before the use of deep learning methods for global inversions. This allows them to extract the dielectric and geometric parameters of the sandwich structure and to evaluate the moisture content of concrete. We have used the FWI approach, using gprMax software as a numerical forward model to the multi-layer configuration, to perform parametric study in variations such as: the approximate parameters are known with low accuracy (within large regions). There are some additional complexities we optionally add to the model: noise; some additional layers; a situation with the influence of the antenna factor on the sandwich structure. The modified and extended Nelder-Mead method Shuffled Complex Evolution (SCE), is a robust and model-independent global optimization approach used to optimize the model parameters. It permits us to avoid the inversion being trapped at local minima, so that the global minimum can always be found. Here, instead of the compression step of the Nelder-Mead algorithm, random points are found. After every few cycles, the worst points are replaced with random points in the amount of 33%. FWI was developed and performed for a 2D model using the method described above. The considered sandwich structure is one-dimensional. Thus, we have proved that the method is applicable for various structures (these are layers of different materials). The method allows to restore with good accuracy all the parameters of the structure according to the temporal signal (A-scan), including the dielectric permittivity of concrete. In consequence, we determine whether the concrete is wet or not.