The Effect of Transversal Connection in the in-Plane Response of Double-Leaf Brick Masonry Walls

. The evaluation of structural safety derives from the knowledge of material properties. In case of existent masonry building, the definition of reliable mechanical parameters could be a very difficult task to be achieved. For this reason, an estimation of these values is useful, for example it is the first phase of the knowledge process, for simplified mechanical model or when NTD test is the only possibility. The transversal connection in masonry panels is a technological detail that affects the static and seismic behavior and could significantly increase the strength of the element. In this paper the effect of transversal connection in double-leaf brickwork masonry panels is evaluated by diagonal compression tests. To achieve this goal, a new set-up was designed to load each leaf independently. The results have shown an increment of about 20% in strength if transversal connection is present. If the leaves have very different mechanical parameters, the tests highlight an unexpected behavior.


Introduction
The seismic assessment of existent masonry structures is still a challenge in the retrofit design process (Mendes et al. 2017). A bad evaluation of the structural behavior can lead to an unexpected structural response with the possibility of high damage level. Three different cases can usually occur: i) identification of the correct response but an underestimation of the safety level; ii) identification of the correct response but an overestimation of the safety level; iii) wrong identification of the structural behavior. In the first case, invasive and extensive retrofit interventions are required to improve the structural seismic capacity. A high number of strengthening solution can significantly change the intrinsic behavior, bringing sometimes to new failure modes as the local mechanisms. In the second case, very soft interventions are needed, and only local solution are applied. The result is a vulnerable structure with a potentially high seismic risk. If a wrong identification of structural response occurs, the retrofit interventions distance further the structural behavior. Strengthening are located in the worst areas of the structure.
The correct knowledge help to reduce the possibility of errors and increase the confidence of seismic assessment (Kržan et al. 2015).
In the Italian Building Code, the mechanical properties of masonry could be evaluated starting from a min-max range defined on masonry typology, increased by modifying coefficients able to take into account the variability of this type of construction material (i.e. mortar quality, joints thickness, effect of transversal connection, etc). Sometimes it is necessary to use mechanical parameters without in-situ tests or to have a comparison with the experimental ones. The aim of this paper is to provide a quantitative estimation of the in-plane strength benefit of transversal connection in masonry panels.
As is of common knowledge, the morphology plays an important role in static and seismic behavior of masonry structures and for this reason should it be considered properly. The most important parameters in knowledge process are related to the masonry quality, in particular mechanical characteristics and technological details. These two aspects influence each other, both in the presence of static actions alone and combined with seismic actions. In both of them, the masonry quality plays an important role, especially if the walls have a multi-leaf section (Binda et al. 2006;Casolo et al. 2013;Egermann and Newald-Burg 1994;de Felice 2011;Vintzileou and Miltiadou-Fezans 2008). The presence of transversal elements that links the leaves, also called in Italian "diatoni" (this term will be used in the paper thanks to its conciseness), allows a better response of the panel. For this reason, the identification of diatoni is an important task. Sonic test and tomography are usually the best non-destructive test (NDT) to evaluate the leaves connection (Miranda et al. 2013;Miranda et al. 2016;Silva et al. 2014).
In absence of this technological detail, with the aim to prevent local failure and to increase compression and shear strength, a lot of research is being done on injections and "artificial" diatoni (Corradi et al. 2017;Silva et al. 2014;Valluzzi et al. 2004;Vintzileou 2011;Vintzileou and Tassios 1995).
In this paper only brickwork masonry panels have been considered. The selection of this type of masonry was been led by two main aspects: less uncertainties due to materials and assembly and the damage occurred during 2012 Emilia-Romagna earthquake ( Figure 1). To achieve this goal an experimental campaign was carried out analyzing the response of 12 masonry panels. Considering Figure 2a, two extreme configurations could be identified for a double-leaf brickwork masonry wall, depending on the orderly presence of connections. From a static point of view, the lack of bonding between the leaves, can lead an instability phenomenon before the ultimate compression load of the masonry is reached (Figure 2b). In particular, the Eulerian instability load of the wall can be up to eight times lower if there is no connection between leaves and it can condition the in-plane behavior. Regarding seismic load, if a simple overturning mechanism is considered, the activation multiplier is double in the case of efficient diatoni since only one rotation point for the system exists ( Figure 2c).   parameters, is not so easy (Calderini et al. 2010). Indeed, if a Turnšek and Čačovič model is used (Turnšek and Čačovič 1971), the diagonal cracking occurs when the maximum principal stress matches the diagonal tensile strength of the masonry ft. If a Mann and Müller model is adopted (Mann and Müller 1982), the definition of cohesion and friction angle requires two tests that must be defined properly. In this work, a Turnšek and Čačovič model is assumed since the main aim is to quantify the influence of transversal connection. Moreover, if the quality of mortar and block are not so different, it is possible to assume that, in the safe side of the analysis, the mechanism could be well represented by Turnšek and Čačovič model.
With reference to a diagonal compression test, Frocht demonstrated that the stress state at the center of the panel is very different from a pure shear stress state, by using photo-elasticity and theoretical approaches (Frocht 1931). The good approximation of Frocht's solution was confirmed by numerical elastic finite element analyses (Brignola et al. 2008;Yokel and Fattal 1976), where the stresses center of the panel (being P d the maximum diagonal load and A the transversal area of the specimen).

Post-processing of diagonal compression results
The applied load and the diagonal displacements on each sides of the panels are usually recorded during the test (Figure 4). According to Turnšek and Čačovič, only one parameter is necessary to define the failure domain. The tensile stress reached at the center of the panel could be directly derived from The shear strength design parameter can be easily derived dividing the maximum tensile stress by 1.5 obtaining t norm = f t / 1.5 = 0.333P d A. The estimation of other mechanical parameters, as shear deformation γ or shear modulus G, require the definition of shear deformation vs shear stress curve. The tangential stress is evaluated starting from the "exact" solution as t = 1.05P A while the tangential deformation γ is obtained as the difference between the compressive strain and The curve could be retrieved for each loading cycle or for the envelope of the test. The procedure ( Figure   5) usually adopted by the author is to define a bilinear curve with the following criteria: the equivalence of underneath area for a fixed value of shear stress t and the maximum shear deformation is defined when a reduction of 0.1×t max is reached. With these assumptions the yielding deformation γ y could be obtained from Eq. 1, being E the area under the envelope curve.
The shear stress t is varied starting from τ max and decreasing it up to 0.9×t max , choosing the solution with the minimum standard deviation ( t = a ×t max ).
It is possible to evaluate directly from the recorded data, an instantaneous shear modulus as G = τ/γ = 1.05P/A/γ but a useful estimation of elastic shear modulus could be derived from the bilinear curve, evaluated for the envelope curve (but the same operation could be done for each cycle) obtaining a value representative of a cracked behavior, as stated in Eq. 2: (2) Figure 5. Graphical representation of post-processing of recorded data.
The analysis of shear (or axial) deformations usually shows a different behavior between the two sides of the panel (Brignola et al. 2008), an example is illustrated in Figure 4b. This response could be ascribed to a non-centered diagonal load with respect to the wall thickness, different stiffness of steel loading frame and different response of masonry leaves. The result is a rotation of element B ( Figure   3) with a different load transferred to each leaf. To avoid this behavior, a modified set-up was design to separately load the leaves and understand the role of diatoni in the in-plane response.

New set-up
With the traditional diagonal compression set-up, it is not possible to analyze the influence of transversal connection since the applied load is uniformly transferred to the panel. For this reason, a new set-up was developed to evaluate the different response of the leaves in double-leaf masonry panels.
The goal is to obtain a loading scheme that allows to subdivide, as needed, the force applied to each leaf. Element B of traditional scheme was split in two independent parts (Element H) and two steel cylinders were added upon them (Element G). The latter elements ensure to change the load transferred to each leaf modifying their position. In particular, the cylinders were always arranged in the middle of each leaf to proportionally transfer the overall load to the thickness of the leaves. In Figure 6 the new steel elements are identified and a tridimensional representation of the set-up is shown. Figure 6. New set-up: new elements added or modified and a 3D sketch of the whole steel frame.

Experimental campaign
The goal of this research is understanding the role of transversal connection in multi-leaf brick masonry panel. To achieve this result, 12 different double-leaf specimens were realized, 6 with diatoni and 6 without them. The courses organization and the position of transversal elements was defined to preserve the same texture for each panel as shown in Figure 8. If no diatoni are present, the two leaves have been built independently, with no connections. In all the cases, a gap of 1 cm was left to avoid inadvertent contact, filled step by step with gravel ( Figure 7). The role of leaf thickness was taken into account.
Different configurations were defined with equal leaf thickness 12+12 cm (one-head leaf) or 24+24 cm  In Table 1 specifications of the 12 panels are shown where the different configurations are able to investigate 3 different parameters: materials, leaf thickness and transversal connections. The specimens ID has an alternation between presence or not of diatoni, in order to have an identifier Pi for the panel without transversal connection and P i+i for the same panel configuration but with diatoni.
For each panel, compression tests were performed with the new set-up described in §2.3. The load was applied through a hydraulic jack with 300 kN of capacity (for panels P3-P4 a jack with maximum capacity of 1000 kN was used instead). The diagonal elongations were measured with traditional potentiometric transducers with 50 mm gauge length. The acquiring system recorded simultaneously the displacements of the 4 diagonal transducers and the pressure applied to the hydraulic jack. Some loading cycle was made to remove mechanical play, to train the masonry and to verify the load-unload quasi-elastic path. After that, at least 4-5 cycles incrementing the maximum load were done before the collapse of the specimen.  Figure 9, where the panels were organized by row with and without diatoni, to quickly identify, by column, the differences among the specimens. Panel with transversal connections and low thickness (24 cm) show a high peak velocity. On the contrary, on the Panels P4, with 48 cm thickness, the identification of diatoni exact position is quite unattainable. is due to the path of sonic waves that is not so dissimilar among diatoni and the other points. In the first case, the waves need to go through a brick-mortar-diatono-mortar-brick sequence while, in the second case, for example, brick-gravel-brick. The difference in waves traveling time is not so different to identify the correct position of diatoni. Subsequently, further investigation was carried out to understand the influence of diatoni near their boundaries. Several sonic measurements were performed on these elements and the results are contained in Figure 10. Velocity decreasing is uniform and a value higher than 2500 m/s could be also observed 15 cm far from the center. For this reason, a grid 20x20 cm is enough dense. If the thickness is very high, the presence of transversal elements could be not so clear.

Indirect identification of diatoni
Nevertheless, for field-stone masonry, the sonic velocity difference between lithotype and mortar is high enough to compensate the thickness of the panel and to make possible the detection of diatoni.

Tests results
For each specimen in Table 1 diagonal compression test with the new set-up was carried out and the recorded data were analyzed with the procedure described in Section 2. In Table 2 the results of the tests are shown. At the end of the tests on the 12 panels, 3 more investigations were carried out on the single leaf survived after such tests. The capitol letter after the specimen ID is referred to the tested leaf.
In the table, the maximum reached load, the shear strength according to Turnšek and Čačovič model (τ norm = f t /1.5) and the cracked shear modulus G crack are summarized.
Thanks to these results, several information and conclusion could be carried out. Considering the strength of P3A specimen, it is representative of a two-leaf panel with an infinite transversal connection. The strength of P2 (without diatoni) panel is exactly the double of the P3A ones, highlighting that the system works in a parallel way and the maximum load reachable is twice the value of the single leaf. With transversal elements the strength increases by 20% (270 kN → 318 kN). Similar behavior can also be found in panels P1-P2 (99 kN → 116 kN). Pu of P3A is the maximum value that could be obtained by a 12+12 cm double-leaf panel if high number of diatoni is present (about 35%). If the leaves are different in materials (P7-P8), the presence of diatoni has caused a lower maximum load, roughly the 90% with respect to the absence of transversal connection. Analyzing leaf deformations ( Figure 11) it is possible understand this unexpected behavior. In absence of diatoni, the two leaves are loaded in the same way and the collapse involved the weakest leaf (P7 side A). This behavior is also justified by the single leaf remained intact after the tests which have an odd ID (P3A-P7B-P9B). In presence of transversal connections, the different stiffness leads first to the collapse of the strongest leaf. Since it is less deformable, it absorbs also a ratio of the other leaf transferred by diatoni, and subsequently the carrying load is moved to the other leaf in an impulsive way. Obviously, the weaker leaf is not able to support all the load, and for these reasons, the failure of the entire panel occurs (Figure 11). Unfortunately, P9 panel (P9-P10 panels are a reply of P7-P8) has shown a maximum load of only 34 kN with the collapse of the weaker leaf (side B) in the case of absence of diatoni. Since the single leaf P9A collapsed for 108 kN, probably the panel P9 could have reached a higher value with respect P10, confirming the result of the previous panels (P7-P8). These results seem lead to the following assumption: if the masonry panel is made with two or more leaf with nonhomogeneous properties, but couple together, the weak leaf is able to lead the entire panel to the collapse. The behavior must be ascribed to the different stiffness of masonry leaves. Indeed, this deduction could find a support also in P5-P6 tests. Even if the two leaves were been loaded in their barycentre, the stiffness of the 24 cm leaf is higher than the twice of 12 cm ones, due to the effect of an infinity transversal connection, as already stated in the case of P1-P2-P3A. The load-deformation behavior of these panels was exactly analogous to P5-P6 cases, as shown in Figure 11. It is correct to highlight that, despite the P11-P12 specimens were a reply of P1-P2 panels, the results did not confirm the previous ones. The effect of transversal connection could be found analyzing the damage pattern occurred after the tests ( Figure 12). The even specimens have always a specular damage path, while in the odd panels the absence of transversal connection allows a different behavior between the leaves. In most of the cases, the cracks affected the mortar joints with the classic pattern and without relation with the presence of diatoni. Sometimes a horizontal sliding mechanism occurred, probably due to a non-perfect-diagonal load but also to the effect of transversal element as stated in case P12. This failure mechanism, that involved from P9 to P12 panels, could be the reason for the unexpected results of this specimen. It is worth noting that, the disassembly of the panels after the test was made carefully for even specimens to check the status of the transversal elements. In all the analyzed cases, diatoni remained intact ( Figure   13) highlighting that only few elements can be sufficient to transfer the carrying load among the leaves.
On the other hand, a high number of transversal elements can modify the crack path and increase the shear strength of the panel.

Conclusions
In this paper the evaluation of transversal connection in double-leaf masonry panels was analyzed through experimental tests with an innovative set-up for the diagonal compression test. 12 specimens were built with different blocks and mortar materials and were tested applying the loading forces to each leaf independently. The results highlight that, less the homogeneous of leaves is, less the maximum load that could be reached is. Moreover, according to the Italian National Code, a masonry with transversal connection could exhibit a maximum shear strength of about 130% with respect to a doubleleaf masonry without diatoni. Moreover, the sonic tests made on the specimens, confirm the grid spacing of 20 cm. With this geometry, the presence of diatoni, could be defined very well. On the contrary, if a good transversal texture is it present, the single transversal element could not be so clearly identified. Nevertheless, the overall sonic velocity is high enough to ensure a "monolith" response. Figure 1 Damage due to separation of multi-leaf brickwork masonry wall after 2011 Emilia earthquake. Finale Emilia: a) Church of SS. Filippo e Giacomo; b) Modenesi's Tower.

Figure 2
Two leaves walls under static and seismic action: a) transversal sections; b) instability due to vertical loads if no transversal connection exists; c) seismic behavior: simple overturning mechanism.

Figure 3
Loading scheme example with steel frame elements required for standard diagonal compression test.

Figure 4
Example of recorded data: different behavior between sides A and B of the panel.

Figure 5
Graphical representation of post-processing of recorded data.

Figure 6
New set-up: new elements added or modi ed and a 3D sketch of the whole steel frame.

Figure 7
Some images of specimens and test setup: leaves construction in the case a) without diatoni (panel P5), and b) with diatoni (panel P8); c) transversal connection in non-uniform thickness leaves (panel P6) and d) just before the start of compression test on P8 element.  Sonic test.

Figure 10
Sonic identi cation of diatoni. Test points (in red) and distribution of velocity around transversal element of P12 specimen.

Figure 11
Test results for P7 and P8 specimens. For clarity, the continuous lines is referred to the weaker leaf while the dashed line to the stronger one.  Transversal elements after tests in P8 (left) and P6 (right) panels.