Parametric prediction of GPR diffraction hyperbolas from top-down pavement cracks using gprMax FDTD simulations

Ground penetrating radar is used in asphalt pavement condition assessment due to rapid acquisition and sensitivity to dielectric contrasts. For top down cracking, interpretation often relies on diffraction hyperbolas, while the relation between crack geometry and measurable hyperbola descriptors is frequently handled by visual inspection. This study defines a parametric physics based workflow that links detected hyperbolas to crack depth ratio and crack aperture using gprMax forward simulations and automatic hyperbola parameter extraction.

Two dimensional finite difference time domain simulations are performed in gprMax for a layered pavement composed of an asphalt layer over a granular base. Electromagnetic properties are prescribed by relative permittivity and effective conductivity, using relative permittivity 5.50 and conductivity one times ten to the minus four siemens per metre for asphalt, and relative permittivity 6.00 and conductivity one times ten to the minus four siemens per metre for the granular layer. The parametric space includes asphalt thickness between 0.05 and 0.30 m, crack aperture from 2 to 20 mm, crack depth ratio between 0.20 and 1.00 of the asphalt thickness, and antenna central frequencies of 1.6 GHz and 2.3 GHz. Representative configurations are selected from the full combination space.

Synthetic B scans are processed by time zero correction, dewow filtering, background subtraction using trace mean removal, and repeated moving average smoothing. Peak candidates are identified on a central trace defined by the maximum absolute amplitude at an early time sample. Each candidate is tracked laterally by a local maximum search within a symmetric vertical window around the previous pick, yielding a set of points that describe the diffraction trajectory. Each trajectory is parameterised by fitting a quadratic time squared versus offset squared model, with the apex position set by the estimated trajectory centre. The fit provides the apex time, the curvature parameter, and the asymptote slope derived from the curvature. The maximum absolute amplitude along each trajectory is extracted as an amplitude indicator with its space time coordinates. Upper and lower trajectories are assigned by ordering apex times.

The workflow outputs a frequency and thickness conditioned mapping between crack geometry and paired hyperbola descriptors for the upper and lower trajectories, including apex times, curvature based parameters, asymptote slopes, and amplitude indicators. The prediction model is expressed as a conversion from the detected upper and lower hyperbola descriptors, conditioned on frequency, asphalt thickness, and prescribed material properties, to the crack depth ratio and crack aperture. This formulation answers the guiding question by providing an explicit link between measured hyperbola parameters and quantitative crack characteristics under controlled acquisition and material conditions.