# Safety Assessment of Masonry Arch Bridges Considering the Fracturing Benefit
## 1 Introduction  
The essential structural shape of masonry bridges has been strikingly constant throughout the civilized world, from Roman times through the medieval European period up to nowadays [1]. As long as the Roman Empire lasted, bridge building was closely connected to the personality of the head of the Roman army, known as the [PERSON] Maximus, or chief bridge builder [2]. It is interesting to note that, with time, this title passed from the Roman emperors to the head of the Roman Catholic church, who is supposed to be the chief builder of bridges connecting Earth and heaven.  
Later, during 19 th and 20 th centuries, the Ecole Nationale des Ponts et Chaussees in Paris formalized the structural principles at the base of the masonry arch bridge shape [3, 4]. These structural principles are based on the fundamental concept of line of thrust (Figure 1).  
The line of thrust, or line of pressure, can be defined as the set of lines of action of the successive resultant forces acting on a structure, or rather, that act as internal constraint reactions, proceeding from one end to the other of the structure itself [5]. If we imagine constructing an arch that presents exactly the form of the pressure line, thus the bending moment vanishes at each point of the arch. Between one section and another, only a compressive force would then be transmitted, as the internal reaction is always tangential to the axis of the curved beam. This is the situation that tends to occur when non-tensile resistant materials are used, as for masonry bridges.  
Within elasticity theory, the distribution of stresses at the interfaces between masonry arch segments is proved to be function of the line of thrust. Classically, as masonry is supposed to be non-tensile resistant, the resulting pressure line has to lie within the central kern of the arch cross-section in order to prevent tension [6].  
On the other hand, by means of the plastic analysis [7] the notions mentioned above are further simplified by the understanding that the arch limit condition can be represented by a thrust line superimposed on the whole arch structure, and that the plastic condition is described by that thrust line being everywhere inscribed within the arch [8]. In spite of its plain basic assumptions, it must be remarked that plastic or limit analysis can hardly be used to describe the response and predict damage for moderate or service load levels in masonry arch bridges (Figure 1), not leading to their limit condition [9].  
Considering the aforesaid structural theories, a conceptual need arises, considering the damaging process, i.e., cracks initiation and growth between elastic and collapse mechanisms formation, in order to provide a better prediction of the actual behavior of masonry arch bridges [10,11].  
In the present work, the evolutionary analysis of the fracturing process is highlighted as an effective tool to assess the structural bearing capacity of masonry arch bridges. By means of damage assessment, this evolutionary analysis shows how the arch thrust line is affected by crack formation, and how the maximum admissible load evaluated by means of linear elastic fracture mechanics (LEFM) is greater than the load predicted by elasticity theory. Such an increment in terms of bearing capacity of the arch bridge can be defined \"fracturing benefit\", and it is analogous to the \"plastic benefit\" of the limit analysis. The fracturing process, taking into account crack initiation and propagation in the masonry arch bulk, occurs before the set-in of the conditions established by means of the plastic limit analysis. The study of the elastic-fracture-plastic transitions (Figure 1) returns an accurate and effective whole service life assessment of masonry arch bridges, and more in general for a great number of historical masonry structures still having strategic or heritage importance in the infrastructure systems.  
Figure 1: Elastic-fracture-plastic transitions in masonry arches: softening and fracturing process.