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Figure 10. Response of the model during the last test with intensity 0.35 g, scaling factor 1, phase 3.

Figure 11. The FE model of the Mosque and Minaret implemented for non-linear pushover analysis.

and no interface elements were considered. The parts of the Mosque model reinforced with bars were modelled with elastic solid elements through the whole thickness of the shear walls with Young's modulus equal to that of FRP material.

3.2 Material modeling

The material properties used for the two finite element models are reported in Table 3. In particular, the elastic parameters are referred to the values that have been calibrated on the basis of first random vibration tests performed on the original undamaged structure.

The strength properties were determined on the basis of both compression and shear experimental tests carried out on masonry wall samples.

As far as structural masonry, the elastic-perfectly plastic Drucker-Prager material model was considered.

In the case of Mosque, cohesion c and angle of internal friction y were calibrated in order to obtain values of 0.05 MPa and 1.0 MPa for tensile (ft) and compressive strengths (fc). For Minaret, the considered values for ft and fc were 0.1 and 1.0 MPa. In order to assign an associative flow rule for plastic strains, the assumed dilatancy angle S was equal to 0. With regard to composites, an elastic material model was considered. In particular, the adopted Young's modulus for sheets is equal to 240 GPa and the considered equivalent thickness is 1.0 mm, according to the nominal mechanical properties provided by the manufacturer.

3.3 Load modeling and boundary conditions

With regard to the load modelling approach implemented in pushover analyses for the evaluation of seismic capacity, a uniform and a linear acceleration distribution along the horizontal direction was applied to the FE models of Mosque and Minaret, respectively. As far as the boundary conditions are concerned, full restraints were assumed at the base of the structure in the performed analyses.

3.4 Results of the non-linear pushover numerical analyses

The assessment of the ultimate seismic strength of both the original and reinforced large scale model was

Figure 12. Distribution of first principal plastic strains on the original large scale model of the Minaret at collapse load.

Masonry Structures

Figure 13. Distribution of first principal plastic strains on the reinfroced large scale model of the Minaret at collapse load.

Figure 12. Distribution of first principal plastic strains on the original large scale model of the Minaret at collapse load.

Figure 13. Distribution of first principal plastic strains on the reinfroced large scale model of the Minaret at collapse load.

carried out by means of nonlinear pushover analyses performed on the implemented FE model.

On the basis of obtained numerical results, the evolution of damage distribution till collapse load on the investigated prototype has to be ascribed to the attainment of tensile or shear strength, while the com-pressive resistance is never exceeded. The collapse loads corresponding to the original and reinforced prototype were determined by checking the attainment of the maximum plastic strain calculated for masonry on the basis of the FE models calibrated against shear tests.

With regard to the Minaret, the results of numerical analysis show that the reinforcement increases the ultimate strength in terms of peak acceleration at the top from the value of 0.3 g corresponding to the original model to 1.2 g and the collapse mechanism shifts to the upper part without strengthening (Figs 12, 13).

As far as the Mosque is concerned and according to the implemented numerical model, the original prototype collapses with a mixed pier/spandrel mechanism of the vertical bearing structures, that is typical of weakly coupled perforated walls (Fig 14). On the basis of the numerical results, the evolution of collapse mechanism can be divided in different phases. According to the numerical model, the first diagonal tension cracks occur in the shear walls, namely in the spandrels between the first and second row of openings from the basement. In this phase, the damage also develops at the base of the walls perpendicular to the direction of ground motion, owing to bending stresses induced by

Figure 14. Distribution of first principal plastic strains on the original large scale model of the Mosque at collapse load.

out plane horizontal loads. In the second step, the damage extends to the upper spandrels, between the second and third row of opening in the shear walls parallel to the direction of seismic loads. In particular, it develops up to the dome, among the openings in the supporting polygonal drum and the ones in the shear walls. Finally, the seismic strength of the structure is attained when the central wall at the base of the Mosque and the lateral piers collapse for shear and bending mechanisms, respectively. The study of collapse mechanism, obtained from numerical analysis on both original and

012345678 Relative Displ. [mm]

Figure 16. Comparison between experimental and numerical response for the original and strengthened Minaret model.

Figure 15. Distribution of first principal plastic strains on the reinforced large scale model of the Mosque at collapse load.

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Figure 16. Comparison between experimental and numerical response for the original and strengthened Minaret model.

reinforced Mosque, allowed the effectiveness of FRP reinforcement to be analyzed. The wraps around the dome and the top of shear walls fully prevent the propagation of cracks from the bottom part to the drum, as shown in Figure 15.

The role played by FRP bars in the shear walls is to stiffen and strengthen the spandrels forming a sort of reinforced masonry beams at different levels able to distribute the seismic action among the piers.

According to the numerical model of the reinforced Mosque, in this case the collapse mechanism turns from a mixed into a weak piers/strong spandrel type.

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