Reinforced concrete mapping using full-waveform inversion of GPR data Sajad Jazayeri a,⇑ , Sarah Kruse a , Istiaque Hasan b , Nur Yazdani c a School of Geosciences, University of South Florida, Tampa, FL 33620, USA b Pennoni Associates Inc., Philadelphia, PA 19103, USA c Department of Civil Engineering, University of Texas at Arlington, TX 76019, USA article info Article history: Received 27 March 2019 Received in revised form 16 September 2019 Accepted 27 September 2019 Keywords: Ground penetrating radar Rebar Reinforced concrete Utilities Full-waveform inversion Deconvolution Sparsity abstract Mapping the location and dimension of reinforcing bars in concrete can be critical for assessing the struc- ture and state of reinforced concrete. Concrete structures, such as bridge pilings or cell phone tower foun- dations, are integral to modern life. Ground penetrating radar (GPR) is commonly used for mapping rebar grids, but traditional GPR data processing techniques fail to provide reliable information on the diameter of bars. Full-waveform inversion (FWI) of surface-coupled common-offset GPR B-scans (profiles) over reinforced concrete improves estimates of rebar diameters over more conventional ray-based methods. The method applies a sparse blind deconvolution (SBD) technique to obtain the optimized source wavelet and a sparse representation of the subsurface reflectivity series. A ray-based analysis is then performed on the estimated reflectivity model to define the initial geometry model to start the FWI. Applying this method to a synthetic data set and two real data cases with 1 and 2.6 GHz center frequency antennas results in errors in the rebar diameter estimates of less than 11% for rebars with concrete cover of 7.5 cm or less. These results compare favorably with those obtained from other methods that require cross-polarized antennas or ancillary equipment. The synthetic model demonstrates that the combina- tion of SBD and FWI also improves ray-based estimates of the concrete permittivity and conductivity. Ó 2019 Elsevier Ltd. All rights reserved. 1. Introduction Ground penetrating radar (GPR) is a non-invasive, exploratory tool widely applied to mapping reinforcing bars embedded in con- crete (e.g. [1–5]). As a GPR system is towed over concrete, high fre- quency electromagnetic (EM) pulses are emitted by a transmitting antenna. These pulses reflect off reinforcing bars, and are recorded at a receiving antenna. Data with high spatial density can be acquired at driving speeds, with obvious benefits for road and bridge deck monitoring [1]. GPR returns depend on the material properties of the concrete and reinforcing bars, specifically the dielectric constant (i.e. rela- tive permittivity, defined as the ratio of the electrical permittivity of the media to that of free space) and electrical conductivity. Because reinforcing bars are so distinctly different than surround- ing concrete, they strongly reflect the EM energy and generate characteristic hyperbolic returns on GPR profiles, or B-scans (e.g. Fig. 1). The shape and position of a hyperbola on a GPR profile is controlled by the depth and properties of the rebar, as well as the overlying concrete properties. 1.1. Rebar position The problem of locating the top of a bar (both laterally and in depth below concrete surface) from the arrival times of the peaks in the hyperbolic GPR return is relatively straightforward and is widely applied. A theoretical best fit curve to the hyperbola arrival times is used to estimate the velocity of the wave in the overlying concrete and thereby estimate the depth of the rebar (e.g. [3]). This calculation, referred to as ray-based analysis because it uses the travel times of selected ray paths, is typically satisfactory for stud- ies ‘‘mapping” the locations of rebars. However, the position esti- mates can be biased by human errors while fitting the hyperbolas and by noise (e.g. [6,7]), and more accuracy may be desirable for more quantitative assessments or studies monitoring changes. 1.2. Rebar diameter In contrast to the depth, the diameter of a bar is quite difficult to estimate when the diameter is small compared to the radar wave- length. With wavelengths greater than bar diameter, the arrival times of the peak returns in the hyperbola are simply relatively insensitive to the diameter. Such is commonly the case in concrete https://doi.org/10.1016/j.conbuildmat.2019.117102 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: sjazayeri@mail.usf.edu (S. Jazayeri). Construction and Building Materials 229 (2019) 117102 Contents lists available at ScienceDirect Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat