Two-dimensional characterization of railway subgrade using full-waveform inversion of elastic waves

Characterizing the subsurface structure of the railway subgrade is essential for addressing irregularities and settlements effectively. This study introduces a two-dimensional nonlinear inversion method to reconstruct the material properties of ballasted railway subgrades using velocity response measurements obtained from the railway surface. Elastic waves are generated using a light-falling weight deflectometer (LFWD), a portable ground-impact device, and the responses are captured by geophones for full-waveform inversion (FWI). The FWI process employs perfectly matched layers (PML) to truncate the semi-infinite subgrade domain, minimizing artificial boundary reflections during wave simulation. The inversion is formulated as a partial differential equation-constrained optimization problem, where the elastic moduli within the PML-truncated domain are iteratively refined by minimizing a Lagrangian functional. The Lagrangian integrates a least-squares objective and regularization terms, combined with the weak enforcement of PML-augmented elastic wave equations via Lagrange multipliers. A total variation regularization scheme is used to alleviate the ill-posedness of the inverse problem. The resulting Karush–Kuhn–Tucker (KKT) optimality conditions are solved to update the Lamé parameters in the reduced space of control variables. The methodology is demonstrated with detailed data acquisition setups and layouts involving the LFWD and geophones. The reconstructed profiles of Lamé parameters and shear wave velocities are shown to align closely with results from conventional lightweight deflectometer tests and spectral analysis of surface wave implementations, underscoring the method's feasibility and accuracy.