Horizontal capacity of single-span masonry bridges with intrados FRCM strengthening
Introduction
The conservation and restoration of historic masonry constructions is a current need that has given rise to numerous scientific studies, with the objective of developing compatible, reversible strengthening techniques that do not alter the original static and inertial conditions of the strengthened structure. In line with this objective, in recent years FRP [1], [2], [3] has been replaced by FRCM, as the latter is more compatible with existing materials and has a higher degree of reversibility. Following numerous scientific studies, the use of FRCM for the strengthening of masonry structures has developed considerably, as in addition to being more compatible and more reversible than FRP, it also guarantees excellent structural performance. In fact, FRCM not only offers greater strength, but generally also increases the ductility of the strengthened structure. This system has also been studied and proposed for the strengthening of masonry bridges [4], however only a few studies have been carried out on FRCM as a seismic strengthening system for these types of bridges [5], [6], [7]. The aim of this study is to examine the behaviour of masonry bridges strengthened with FRCM when subject to seismic forces, considering finite non-associative friction [8], [9], [10]. Furthermore, the numerous experiments [11], [12], [13], [14] performed on FRCM-strengthened arches have only partly taken into account the actual geometric ratios [15] of the bridge arches and the effect of the filling weight on the effectiveness of strengthening. Both aspects are illustrated and discussed in this work.
Masonry bridges located in seismic areas require increased resistance to the horizontal forces generated during an earthquake. In such circumstances, the design solution that has the least impact on traffic is strengthening applied to the intrados of the arch [11], [16], [17]. However, this solution does not guarantee better performance than applying the strengthening to the extrados of the arch [18], [19], [20], [21], [22]. Indeed, when the strengthening is applied to the intrados of the arch, normal tensile stress arises between the interface of the composite material and the masonry substrate [23], [24]. Such stress causes a decline in adhesion/bond between the two materials, and consequently connectors may need to be inserted [4]. However, this solution does not require any work that would affect the regular transit of vehicles across the bridge, and as a result is the most frequently-used solution.
Within this context, this article examines the behaviour of masonry arches (based on the geometric and mechanical characteristics of arches used for the construction of bridges) that are strengthened using FRCM systems and subject to horizontal inertial forces. To do this, lower bound limit analysis was used, taking into account the main failure modes of FRCM-strengthened arches. In particular, as can be seen from the results obtained from experimental tests, there are four main types of failures on arches strengthened using composite materials on a cementitious matrix (Fig. 1):
- a)
Masonry crushing;
- b)
Composite rupture;
- c)
Shear-sliding;
- d)
Composite detachment/debonding.
Nonetheless, experimental evidence [25] has shown that FRCM-strengthened arch failure generally occurs due to a combination of two or more main failure types.
The numerical treatment shown below considers finite compressive strength of the masonry, non-associative friction and a maximum tensile strength of the composite that coincides with the debonding strength of the strengthening [4], [26]. The numerical procedure for the implementation of non-associative friction for FRCM-strengthened arches is an extension of the procedure proposed by Gilbert et al. [9].
With these additional hypotheses, compared to the well-known Heyman assumptions [27], [28], [29], [30], limit analysis [31], [32] can represent, with sufficient accuracy, the ultimate conditions of a masonry bridge strengthened with FRCM.
As will be shown below, friction plays a fundamental role in defining the ultimate load of a masonry arch bridge strengthened with FRCM. Indeed, for strengthened arches, the Heyman hypothesis of infinite sliding resistance cannot be assumed, because as the thrust line may be external to the arch [33], high shear forces arise between the joints that may exceed the sliding resistance of the masonry. Another important aspect concerning masonry arch bridges strengthened with FRCM is the effect of the backfill on the effectiveness of strengthening. The backfill in fact generates high axial forces in the arch that in turn reduce the effectiveness of strengthening compared to arches without filling. Finally, it is important to underline that the geometric dimensions of masonry arches on bridges are larger than and sometimes different to most of the arches strengthened with FRCM examined experimentally. This is the reason why the effect of strengthening with a layer of FRCM may be lower for bridge arches than the results obtained in experimental tests.
Section snippets
FRCM bond on the curved masonry substrate
The debonding strength (Pdeb) of FRCM applied to the masonry substrate is certainly the most important issue that must be considered in the FRCM strengthening design. In particular, it has been experimentally observed that the debonding failure occurs in the cement-based matrix-fibres interface [34]. Moreover, the maximum debonding strength (Pdeb), which corresponds to the debonding normal stress (σdb) and normal strain (εdb) of the fibres (Fig. 2), could be carried out from experimental tests,
Theoretical background
With reference to the single-span masonry bridge shown in Fig. 5, it can be seen that the arch is covered by backing and backfill in order to build the roadway. The backing and backfill have an effect on the behaviour of the structure [44], [45], as they transfer considerable weight to the arch and increase the arch’s load carrying capacity. In this article, the backing and the backfill were considered as the same material called “infill” or “infill material”. Moreover, the FRCM strengthening
Parametric analysis
In this section are reported the results of parametric analysis on a bridge with a span length of 10 m, and considering two values of f/L (0.4 and 0.25), five values of S/L (0.004, 0.06, 0.08, 0.10, 0.12) and two values of f/L (0.4 and 0.25) and four values of friction coefficient (µ) (0.3, 0.4, 0.5, 0.6). All geometrical (Fig. 3) and mechanical parameters used in the parametric analysis are reported in Table 1.
In particular, Fig. 3 considers backfill with a thickness at mid-span of the arch of
Conclusions
This article extensively analyses the structural problems of FRCM strengthening applied to masonry arches in order to increase the earthquake resistance of masonry arch bridges. The article highlights the main aspects of the subject examined through the use of lower bound limit analysis as a method for the structural analysis of masonry arches strengthened with FRCM applied to the arch intrados. Specifically, a numerical procedure is illustrated that takes into account the Coulomb friction on
CRediT authorship contribution statement
Paolo Zampieri: Conceptualization, Methodology, Software.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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