Fast Adaptive Limit Analysis of Masonry Arch Bridges in Presence of Differential Settlements of Bridge Piles

In this work, we present a fast and reliable NURBS-based kinematic approach for the evaluation of the settlements-response of masonry arch bridges. This method is based on a discretization of the arch through NURBS rigid blocks. Here, the use of NURBS (Non-Uniform Rational B-Spline) approximating functions allows composing mesh through very few elements maintaining the exact representation of the three-dimensional curved shape. The main non-linear properties of masonry (almost null tensile strength, high crushing resistance, and frictional behavior in shear) are assigned at interfaces, which represent possible hinges between the curved macro-blocks. Starting from a known displacement applied at the external boundaries, a simple linear programming problem can be written to determine the discontinuous displacement field. Then, a meta-heuristic mesh-adaptation procedure is applied to exclude mesh dependency effects. The initial mesh is adjusted by modifying the shape of macro-blocks until interfaces coincide with the correct position of cracks. The settlement-response is so obtained.