Identifying Two-Parameter Pasternak Foundation Stiffness from Plate Vibration Frequencies: A Bayesian Framework with Cross-Platform Verification for Soft-Ground Highway Widening

Winkler models transmit no shear and cannot reproduce the differential settlement and lateral squeezing that drive soft-ground widening distress. The Pasternak model restores shear coupling, but its shear layer stiffness has remained unmeasurable without static loading. This study identified the compression coefficient k and shear layer stiffness G^ from lightweight plate vibration tests. A Hamiltonian eigenvalue formulation distinguished the parameters through their different geometric weights in the fundamental mode; a Chebyshev–Ritz solver established internal convergence, with independent verification by a SAP2000 v27 solid model against laboratory frequencies. Bayesian MCMC with a K30-informed prior and a resolution-consistent noise model returned k = 5.99 ± 0.58 MPa/m and G^ = 0.153 ± 0.008 MN/m, with prior sensitivity and leave-one-plate-out checks. Transferred to Abaqus 2026 and SAP2000 v27 without retuning, the model agreed with a published finite element benchmark—a consistency check, not a field validation—within 5% on the shear-driven responses, whereas a matched-stiffness Winkler model deviated by roughly 20%. Recalibrating the Winkler stiffness closed that gap only by shifting the stiffness estimate by approximately two posterior standard deviations from the identified value, and the trough extent remained unreproduced. The Sobol indices indicated that these responses were driven primarily by G^. A three-plate campaign can be completed within one working day without requiring lane closure; field instrumentation is under way.