Three-dimensional adaptive limit analysis of masonry arch bridges interacting with the backfill

In this paper, the collapse behavior of masonry arch bridges interacting with the backfill is investigated through an adaptive procedure based on the kinematic theorem of limit analysis and a NURBS (Non-Uniform Rational B-Spline) representation of the geometry. The initial model is subdivided into few macro-blocks considered rigid and with dissipation occurring only along element interfaces, in turn represented by planar or curved NURBS surfaces. The properties of the materials are considered using homogenized failure domains and the initial mesh subdivision is then adjusted by means of a Genetic Algorithm. Particular attention is focused on the characterization of the arch-backfill interaction problem. The backfill is here represented first in terms of equivalent vertical and horizontal loads and then by following a direct modeling through NURBS curved macro-blocks. In particular, this latter approach allows to take into account the backfill contribution also in terms of internal dissipation. However, material parameters must be defined with particular attention: the use of a very rough discretization with the assumption of rigid blocks requires the utilization of equivalent ultimate resistance values for backfill-backfill interfaces to correctly estimate the internal dissipation at failure. Meaningful numerical examples dealing with different geometries and considering both load-carrying capacity and foundation settlement problems are reported. Finally, two geometrically complex examples are analysed through a recently presented modeling strategy via NURBS solids.