Hyperbola Occurrence in GPR Radargrams of Cracked Road Pavements: A Numerical Comparison of Top-Down and Bottom-Up Cracking

Ground-penetrating radar is widely used in non-destructive pavement evaluation, but the occurrence of multiple hyperbolic signatures in radargrams of cracked pavements remains insufficiently characterized, particularly for top-down and bottom-up cracking. This study investigates the occurrence of detectable hyperbolas in numerical GPR radargrams by comparing two crack models under a controlled two-dimensional numerical design. Model A represents top-down cracking, and Model B represents bottom-up cracking. For each model, four parametric studies were performed by varying crack width, crack depth, asphalt-layer thickness, and granular-layer thickness, yielding 32 simulations in total. All cases were modeled in gprMax2D at 2300 MHz and processed in MATLAB through radargram pre-processing, central A-scan candidate detection, lateral tracking of hyperbolic events, and final classification based on stable retained trajectories. Model A was predominantly characterized by 3H responses, whereas Model B was predominantly characterized by 2H responses, with no 3H case observed. In Model A, crack-width increase was associated with the strongest occurrence change, whereas in Model B, greater asphalt-layer thickness was associated with a reduction from 2H to 1H. The first apex TWT provided a complementary discriminator between the two models. These findings provide controlled numerical reference trends that may support the interpretation of hyperbola occurrence in GPR-based pavement crack assessment.