To study the different global behaviour of the examined cases study buildings, parametric analyses were conducted by varying both the floor typology (deformable floor or rigid diaphragm, the latter to guarantee a building box-behaviour) and the masonry type (squared stones or stones arranged chaotically).
4.2. Masonry Properties
As a further intervention, variation of mechanical properties of masonry that can be associated to strengthening interventions was done simply by considering different masonry types. As discussed in
Section 2, the basic mechanical properties refer to the tuff masonry stones, whose mechanical properties derived from Italian code are in line with experimental values achieved from some literature sources [
25,
26]. To this purpose, according to what was discussed in
Section 4, two masonry types were considered. In particular, a masonry type made of squared blocks with better mechanical properties than those of tuff stones was considered. In addition, for comparison purposes, a chaotic masonry type with worst features than those of tuff masonry stones was also taken into account. All the mechanical features were assumed from the NCT18 standard [
18] adopting a limited knowledge level (LC1) with a confidence factor (FC) of 1.35.
The main characteristics of the squared masonry blocks, assumed congruently to the NTC18 [
18], are shown as follows:
- -
average compressive strength, fm = 5.8 MPa;
- -
average shear strength, fv0 = 0.18 MPa
- -
Young modulus, E = 2850 MPa
- -
shear elastic modulus, G = 950 MPa
- -
density, W = 22 kN/m3.
The second masonry type is the chaotic one, which is characterized by the following mechanical properties [
18]:
- -
average compressive strength, fm = 1 MPa
- -
Young modulus, E = 870 MPa
- -
Shear modulus, G = 290 MPa
- -
density, W = 19 kN/m3.
The results of pushover analyses are presented in
Figure 13 by comparing the performances of inspected buildings in terms of the strength, stiffness, ductility and safety index. In this figure, the horizontal blue line indicates the target attained by buildings made of the basic material (tuff stones) before the proposed interventions.
The results highlight how the use of good quality masonry provides an important increase in terms of resistance and stiffness rather than the structural ductility, which has increased by 22% both for the whole aggregate and the head SU in aggregate condition and only by 10% for the intermediate SU placed in aggregate. Moreover, as expected, the characteristics in terms of the stiffness, strength, and risk factor are reduced considering the poor mechanical characteristics of the masonry.
4.3. Fragility Analysis of the Typological Building Classes
In this section, the fragility curves were analysed for the case study buildings, taking into consideration the structural behaviour of their original state (seismic safety factor
ξ < 1) and the design one (seismic safety factor
ξ > 1). As is known, fragility curves represent the probability of exceeding a certain damage threshold varying the intensity measurement, IM, generally represented by the PGA or spectral displacements,
Sd. The evaluation of the fragility curves is carried out according to the methodology proposed in [
26]. In particular, four damage levels, namely D1 (slight), D2 (moderate), D3 (near collapse), and D4-D5 (collapse), were considered as proposed in [
27]. Such damage states were defined considering the yielding displacement (
dy) and ultimate displacement (
du) of the SDoF system.
Methodologically, fragility curves were defined according to Equation (1):
where Φ is the cumulative distribution function, PGA
DS is the median acceleration value associated with each damage threshold, and β is the standard deviation of the log-normal distribution. Specifically, concerning the median values of PGA
DS, these were evaluated according to provisions depicted in [
27,
28], which provide the values of
Table 3.
The above-mentioned median threshold values were obtained by converting the spectral displacements,
dy and
du associated with the SDoF system, into spectral accelerations,
Sa,e according to Equation (2)
where,
T is the vibration period associated with the structural system and
SDK is the spectral displacement range [
27].
Consequently, the dispersion,
β, generally depends on the uncertainties associated with the seismic demand. This parameter is function of the ductility,
μ, of the structural system, intended as the ratio between the ultimate displacement,
du, and the corresponding yielding displacement,
dy, which was evaluated according to the formulation proposed in Ref. [
28] (see
Table 4).
Based on these considerations, the typological fragility curves were plotted considering the most adverse structural analysis conditions, both for the existing whole aggregate and the other isolated and aggregated SUs, as reported in
Figure 14.
Furthermore, for an exhaustive correlation with the presented curves,
Table 5 shows the data relating to the median and standard deviation values associated with the damage thresholds considered.
Consequently, by systematically adopting the same derivation procedure presented previously,
Figure 15 shows the comparison between the monitored SUs (intermediate and head) placed in aggregate and the same units in isolated configuration.
As reported in
Figure 15a, the HSU provides expected damage higher than the intermediate one. For the sake of example, it was noted that for PGA = 0.2 g, the damage thresholds D1 (slight) and D2 (moderate) for both SUs are comparable. Conversely, for PGA > 0.2 g, there is a marked difference between the expected damage level.
More in detail, for PGA = 0.4 g, referring to the damage threshold D3 (near collapse), the probability of damage associated to the HSU is 98%. Instead, for the ISU this damage probability reduces to 80%, with a damage percentage decrease of about 18%. On the other hand, considering the damage threshold D5 (collapse) and the PGA = 0.4 g, the ISU shows a percentage reduction of 41% compared to the corresponding HSU.
The same structural performance condition was also found by comparing the same SUs in the isolated configuration (see
Figure 15b). In a general overview, by considering a PGA = 0.2 g, a D1 and D2 damage levels were found to be reached for the SUs monitored. However, considering an increase of the intensity measurement, for PGA equal to 0.4 g, it was possible to observe that for the ultimate limit state, D5, the HSU provides a probability of damage equal to 60%. Contrary, the ISU exhibits a percentage decrease of 42%, highlighting once again how it is less susceptible to damage than the HSU [
27].
Besides, the fragility curves were derived even for the retrofitted buildings by adopting rigid floors. The results are plotted in
Figure 16.
Similarly,
Table 6 suggests the values of the median and standard deviation for the derivation of the typological fragility functions associated with consolidated structural systems.
The results achieved show a clear increase of the structural performance levels provided by all the monitored configurations examined (whole aggregate and two SUs). Specifically, by examining the performance thresholds obtained through the proposed strengthening interventions with those presented previously (see
Figure 14), an improvement of the capacity response of the examined structural units was observed with a consequent reduction of the corresponding damage probabilities thresholds, DS
i.
In particular, we ascertained that the adoption of the rigid floor system offers an increment in terms of expected displacements favouring, as previously analysed in
Section 4.2, a progressive enhancement of the corresponding structural ductility
µs.