Rigid-Block Analysis in Large Displacements of Masonry Arches on Vertically Moving Supports

The paper deals with masonry arches on vertically moving supports due to soil settlements. An innovative numerical procedure to estimate the collapse mechanism and the limit settlement is proposed, exploiting rigid block analysis of masonry arches in large displacements. The numerical procedure was applied to a case study that models, in a simplified way, multi-span masonry bridges subject to a vertical settlement of a support in addition to gravitational and moving loads. Referring to literature data, a representative arch-pier system, extracted from a multi-span bridge, is analyzed. The numerical procedure matches the laws of combinatorial analysis with static and kinematic analysis to identify the position of the three hinges induced by the settlement. In detail, the procedure: (1) determines the initial three hinges that occur as a support starts moving; (2) checks the admissible equilibrium as the settlement increases; (3) identifies the possible new position of the hinges when a limit settlement is reached; (4) computes the collapse settlement in the new configuration and the collapse mechanism. For dead loads, results of the reference case study show that the load of the fill drives the hinge pattern, which is different from that of the arch which is subject only to its self-weight. A travelling point load further affects the hinge pattern when it reaches high values. The most dangerous position of the point load is one-third of the span.