The Brilliant Shape of Equilibrium: Structural Analysis for the Conservation of the Arch of Ctesiphon

The Taq-i Kisra, or Arch of Ctesiphon, erected in the 6th century AD in central Mesopotamia, is the largest self-supporting masonry vault of the ancient world and a unique achievement in construction history. This thesis investigates the geometry, the construction principles that enabled its erection without centering, and the mechanisms that today govern its equilibrium. Photogrammetric analyses and mechanical assessments are combined to understand the monument’s “shape of equilibrium” and to provide tools for its conservation. The first part examines the construction technique and failure patterns. The analysis identifies a longitudinal, progressive, and self-supporting logic based on brick courses laid with a monotonic angular variation Δθᵢ, typical of Nubian Vaults. Only retrospectively does the multi-catenary frontal profile prove compatible with the longitudinal brick layout that ensured the structure’s buildability. Photogrammetric modeling enabled the extraction of longitudinal sections on which the inclination angles θᵢ were measured. These data allowed verification of the hypothesis of monotonic course variation, the estimation of the vault’s original length, and comparison with Choisy’s 18th century reconstruction. Mechanical checks were developed to evaluate local stability through an energetic–geometric approach, representing equilibrium configurations as functions of longitudinal and transverse angles. Finally, a parametric model integrating the stability equation was created, making it possible to visualize the construction stage and identify stable and unstable configurations, as well as critical conditions relevant both during construction and today. The thesis shows that the current shape of the Arch results from a refined geometric and constructional balance, now threatened by long-term settlements and deformations. Understanding this equilibrium provides essential technical foundations for the conservation of this masterpiece of Late Antiquity.