A Geometry-Driven Structural Method for Supporting Archaeological Modelling in Partially Preserved Historic Constructions

The archaeological reconstruction of historic monuments from fragmentary remains requires transforming limited evidence into verifiable hypotheses. This study proposes a methodological framework in which structural analysis plays an active interpretative role, rather than serving merely as verification, provided that input data are independently constrained and modelling assumptions align with the available level of knowledge. The framework is designed to be replicable and transferable to archaeological contexts characterised by incomplete preservation. It combines non-invasive survey techniques— high-resolution digital documentation and ground-penetrating radar (GPR)—to establish reliable geometric and physical constraints. Thrust-based limit analysis, following the Heyman Safe Theorem, is then applied to evaluate reconstruction hypotheses through static equilibrium under self-weight. The methodology is tested on the cavea of the Circus of Maxentius in Rome, a Roman concrete construction in which significant portions of the vaulted substructure are collapsed or buried. Three typological cross-sections are virtually reconstructed using construction-archaeology reasoning, measured geometry, and geophysical evidence. Their stability is assessed through thrust-line admissibility and geometric safety factors. Only one section approaches limit equilibrium when analysed independently, while the others prove inadmissible, suggesting that rear backfills, transverse supporting walls near the imperial corridor, and vaulted structures were essential to the original structural system. Overall, the study demonstrates how integrating non-invasive data and limit analysis reduces interpretative uncertainty in reconstructing partially preserved Roman architecture.