For the examined building, ‘Palazzo Bosco Lucarelli’, an old noble palace located in Benevento (Italy), research in the archives of City Hall and in public libraries allowed collecting information about the different construction phases of the building thanks to historical reports, maps, urban plans and, for the XX century, photos.

The original nucleus of the current building probably goes back to the XI century; successively, some documents of XIII and XIV century confirm the presence of a construction with an adjacent church in the same site of the current palace. This building was severely damaged during the strong earthquake of 1702, after that it was rebuilt and amplified assuming the present ‘palace’ structure with an internal closed court. Some maps of Benevento of XVIII century (Figure 1a) show a central hallway, the entrance on the current back prospect of the palace (South-West prospect), and the adjacent church. In the years 1768–1774 the building was retrofitted and part of the church was incorporated in the construction, such as indicated in some maps of the beginning of XIX century and in the urban plan of the town dating back to 1880 (Figure 1b). At the end of XIX century, another floor was added and in 1926, when the church was completely demolished, the west wing of the building was doubled and the current geometrical configuration was assumed (Figure 1c, Figure 2a). Nowadays the court is not central anymore, but is located asymmetrically with respect to the west wing that is double the size compared to the east one (see the plan of the ground floor in Figure 2b).

The last interventions were carried out at the end of the 90s when the building became the headquarters of the Engineering Faculty of the University of Sannio. No substantial modifications were carried out in the structural or external architectural layout, only a functional redistribution of the rooms was realized.

Nowadays the structure has a rectangular holed floor plan (Figure 2b), consisting of an underground floor, which is not completely accessible, a ground floor, two upper levels, and an attic under the pitched roof. The largest dimensions in the plan are 20 m and 16 m, the total height is 18.2 m.

The thickness of the walls varies in the range of 0.3 m–1.0 m with the greatest values attained at the ground floor (Figure 2b). A complete geometrical and structural stwo main façades (northeast and northwest prospects, Figure 2c,d) and two orthogonal sections (Figure 2e,f) are reported to illustrate the geometry of the building.

The original floors in most cases have been substituted by double standard 'T' shaped steel profiles with a height of 200 mm (standard type IPE 200) and spaced at a distance of 0.85 m interspersed with bricks and covered by a concrete deck 100 mm thick. Only the ceilings of the staircase and of some rooms in the entrance hall on the ground floor are still made of the original masonry vaults. The floors can be considered as rigid diaphragms and some local tests evidenced a good connection with the vertical masonry walls (reinforced concrete joists are present along the upper perimeter), so that out-of-plane mechanisms can be neglected. The connections were probably improved when the old original floors were substituted by the current steel-concrete ones. Moreover, some steel chains are present below the first floor between the outside walls and the internal walls of the closed court; these chains were positioned at the beginning of the XX century when the last significant structural and geometrical changes of the building were performed (doubling of the west wing and construction of a new level) in order to improve the global behavior of the masonry walls between the ground and the first floor. Nowadays no sign of out-of-plane mechanism can be observed in the structure.

The roof is made of a steel truss that is supported on a perimetric reinforced concrete joist. A profiled steel sheeting, externally covered with brick tiles, closes the structure.

The in situ surveys allowed detecting a masonry structure made of different materials and textures at the three levels, due to the several construction phases of the building.

At the underground and ground levels, the walls are made of irregular blocks of limestone and conglomerates (Figure 3a) with some inclusions of tuff (Figure 3b) or bricks, probably used in the past to close existing openings. At the underground level, blocks are greater and more irregular suggesting that the underlying foundations were realized as further enlargement of the masonry walls. The first two levels probably date back the construction age of the original nucleus in the IX century, since the masonry texture is typical of coeval palaces present in Benevento and dating to the same period.

At the higher levels, the walls are made of clay bricks (Figure 3c) and were probably built at the end of XIX century, as confirmed by similar masonry textures evidenced in other coeval fabrics and by the information collected about the history of the building.

At each level the walls are covered by a reinforced cement plaster (with a thickness of 50 mm and with a grid of steel bars with a diameter of 4 mm and spaced at a distance of 150 mm in two orthogonal directions, see Figure 3b,c) which can be dated back to the XX century.

Few coring examples of masonry were extracted from the walls and endoscope tests were carried out in the corresponding drilling holes; the images evidence that the walls are made of blocks along the entire thickness, without spacing between the external panels.

Compressive tests were carried out on some single blocks extracted from the masonry. The compressive test on a calcareous stone sample (cube with a side length of 50 mm) extracted at the ground floor level provided a strength of 11.6 MPa, while tests on cubes made of bricks (side length of 60 mm) extracted from the walls at the first and second levels provided strengths of 3.7 MPa and 2.7 MPa (mean values of two tests), respectively. Penetrometer tests on the mortar of the joints gave a compressive strength of about 0.65 MPa for the ground floor and 0.40 MPa for the superior levels; these values allow to classify the mortar as being of a poor typology [27,28].

However, because these data refer to single stones and, thus, are not sufficient for a complete mechanical characterization of the whole masonry assembling, the main mechanical properties (compressive strength, f_m, shear strength without vertical loads, τ_o,m, and tensile strength, f_tm) were assessed based on the indications given by some recent national guidelines [28] (Table 11.D1, Appendix 11.D) because they provide lower values compared with the ones indicated in the applicative document [29] joined to the current Italian code [27]. The mechanical properties are provided as function of the masonry typology identified in situ by the surveys of materials (Table 1). In particular, the masonry of the ground and underground floors has been identified in the category “Cut stone masonry with good bonding”, while for the higher levels of the building, the masonry has been identified as being made of “clay bricks with lime mortar”. Considering an intermediate level of knowledge [27,28,30], achieved thanks to the in situ surveys, the central value of the interval reported in [28] was adopted for the compressive and shear strength. Then, an amplifying factor of 1.5 due to the beneficial effect of the reinforced plaster [27,29] and a reduction factor of 1.2 (confidence factor for taking into account the knowledge level) were considered to calculate the final values reported in Table 1.

For the estimation of the unit weight, the samples extracted from masonry provided values of 26 kN/m³, 17 kN/m³ and 19 kN/m³ for the calcareous stone, the bricks and the mortar, respectively; moreover, for the reinforced plaster a unit weight of about 24 kN/m³ can be assumed. Based on these values and on the observed brick texture, for the masonry of the first and second floors the unit weight has been estimated to be about 17.5 kN/m³, which is similar to the value of 18 kN/m³ suggested in both the Italian guidelines [28] and code [29]. If the layer of reinforced plaster is considered too, the unit weight increases up to about 20 kN/m³.

Similarly, for the irregular masonry of the ground and underground floors, the unit weight was estimated to be 22 kN/m³, which is comparable with the value of 21 kN/m³ suggested in both the Italian guidelines [28] code [29]. If the layer of reinforced plaster is considered too, the unit weight increases up to about 24 kN/m³.

On the contrary, it was not possible to develop an experimental evaluation of the Young’s modulus, E, of the masonry. Literature studies [31] show that the Young’s modulus of masonry assembling is affected by a large variability even within the same type of stone (values of CoV also greater than 40%). Some attempts have been made to furnish empirical correlations between the Young’s modulus and the compressive strength, but these correlations are a function of the stone type [32,33]. Both national guidelines and code [28,29] were considered for the assessment of Young’s modulus. The same range of values (1500–1980 MPa) is given for the “Cut stone masonry with good bonding” of the ground floor. Conversely, for the “clay bricks with lime mortar”, [28] and [29] suggest the ranges of 1800–2400 MPa and 1200–1800 MPa, respectively. The lower range suggested by [29] was considered for the “clay bricks with lime mortar”. Moreover, both codes specify that in case of historical masonry, the suggested values refer to masonry with poor characteristics, thick mortar joints, lack of regular horizontal layers and tidy texture, lack of transversal connecting elements between the internal and external panels of the same wall. Thus, the provided values should be reduced or increased, depending on the current conditions of the masonry. In particular, for the examined masonry types, the presence of the reinforced plaster hence also allows the use of an amplifying factor of 1.5 for the elastic modulus, as is done for the strength. In Table 1 the ranges of E for both types of masonry are reported together with the corresponding central values, assuming an intermediate level of knowledge (2610 MPa and 2250 MPa for the masonry of the ground and the upper floors, respectively). Note that these values represent the starting points for the numerical linear dynamic analyses, aimed at back-calculating the values of E by comparison between experimental and predicted values of frequencies. The above-mentioned values refer to un-cracked condition for the masonry and, thus, should be reduced considering the effective building loading history.

To characterize the foundation soil, a few in situ tests carried out near the building were interpreted. In particular, the following tests were considered: (i) a borehole carried out by the local administration very close to the building (SG-003, Figure 4a); (ii) one standard penetration test (SPT) and (iii) one down-hole test (DH). The borehole SG-003 is very deep and reaches a maximum depth of 70 m below ground level (Figure 4b). After the first six to seven meters of man-made ground and historical ruins, the subsoil is made of almost nine meters of fine-grained materials (silt and clay) followed by an alternation of coarser soils, i.e., conglomerate and sandstone up to 60 meters below ground level. The succession ends with grey-azure clay (Pliocenic Age), which is typical of the Benevento area [34] and represents the bedrock formation from the viewpoint of seismic wave propagation. With the velocity of the S-waves in the first 30 meters of the subsoil, V_S30, was estimated around 700 m/s. This value allows classifying the site where Palazzo Bosco is located into the category B [27,30].

A continuous monitoring system made of nine couples of mono-axial accelerometers was placed on the three floors of the building and a three-axial accelerometer was located on the ground floor. Each couple of sensors is able to measure separately along the X and Y direction. The position of the instruments is reported in Figure 5. The sensors were aligned as accurately as possible along three vertical lines: one corresponding approximately to the center of the building and the other two to the external edges (see Figure 5). On the first floor, the sensors were placed at about 100 mm from the first floor intrados, on the second floor at about 100 mm from the second floor extrados, and on the third floor at about 100 mm from the third floor extrados.

Different sets of accelerometric recordings are available caused by ambient noise and impulsive sources (i.e., the fall of 1 m³ concrete block on a truck placed close to the building, the rapid braking of the truck along the Y direction of the building, some knocks of an instrumented hammer).

In particular, the fall of the concrete block originated vibrations in the building with well-defined peaks that were used to have a first rough estimation of the building’s dynamic response. The frequency domain representation of such recordings (acquired with a sampling frequency of 500 Hz) was carried out by performing the Fast Fourier Transform (FFT) during a signal-window of eight seconds, centered on the peak value. The energy content of the recorded signals was low at frequencies higher than 50 Hz; for this reason, a low-pass FIR (Finite Impulse Response) filter was adopted in correspondence of 50 Hz. A standard baseline correction was also carried out on the original accelerometric data.

The values of the first two frequencies of the building (in X and Y direction) identified by each couple of sensors are listed in Table 2 together with the mean value, the standard deviation and the Coefficient of Variation (CoV) of the measured data for each direction.

The frequencies are low scattered among the measures of the nine sensors in both X and Y direction with very small CoVs (3.1% and 1.7% for the X and Y direction, respectively). The frequency identified for the X direction is slightly greater (4.69 Hz vs. 4.24 Hz, +10%) than the one associated with the Y direction.

Based on the geometrical survey of the building, a three-dimensional Finite Element Model was implemented with the software DIANA TNO (release 9.4 [35]). The model is made of three-dimensional ‘brick’ elements, about square shaped in the X-Y plane. The side dimension in the X-Y plane is about 0.3 m which corresponds to half, the third or the whole thickness of each masonry wall, with the masonry thickness variable being in the range of 0.3–1.0 m. The third dimension along the Z-axis is at maximum equal to 1.0 m and allows having a maximum shape ratio between the sides of about three.

The 3D model is made of about 20’000 elements (Figure 6); the three floors were modeled by means of a stiff constraint in each plane and the vertical loads acting on the floors were applied directly on the corresponding masonry walls. The building was modeled both with (Model B, Figure 6b) and without (Model A, Figure 6a) the underground floor according to the type of analysis, as will be explained in the following.

As gravity loads the self-weight of masonry walls was computed using the unit weight reported in Table 1; the dead load of the floors was estimated as G_k = 5.40 kN/m², while for the accidental loads, at the ground level, the first and the second floor, the values Q_k = 3.00 kN/m² for eventually crowded ambient [27] were considered and at the level under the roof the lower value of Q_k = 0.50 kN/m² [27] was assumed. The weight of the steel roof was estimated to be 1.75 kN/m², while the weight of the masonry stairs was neglected. The loads of the balconies were applied directly on the external walls (G_k = 3.60 kN/m², Q_k = 4.00 kN/m²).

Assuming a reduction factor for the accidental loads of ψ₂ = 0.6 under the quasi-permanent loading condition [27,36], the total weight is about 68700 kN for Model A and 88900 kN for Model B.

Linear dynamic analyses were developed through the 3D FE Model considering all the vibration modes characterized by a participating mass ratio greater than 5%. The aims of such an analysis and its comparison with the dynamic in situ tests are multiple, even if they are correlated with each other: (1) to identify the dynamic behavior of the building in terms of main vibration shapes and frequencies; (2) to confirm and/or assess the reliability of the unit weight and the Young's modulus of masonry previously estimated; (3) to have indications about the interaction with the foundation soil. These topics are strictly correlated because the values of the main frequencies depend both on the mechanical properties of masonry (unit weight and Young’s modulus) and on the soil-structure interaction effects. Assuming that the geometrical survey of the building is very detailed and conforms to reality and that the estimation of the unit weight of masonry is reliable (this means the global mass of the building is well-defined), the dynamic analysis will be used to assess only the Young’s modulus and estimate the effect of the soil-structure interaction, if present. This latter point has been investigated thanks to some information available about the mechanical properties of the foundation soil (see Section 3.3). In order to achieve these results, (1) the mean values of the first two frequencies estimated by the dynamic measurements in situ (see Table 2) were used as target for the numerical values of frequencies given by the dynamic analyses; (2) the Young’s modulus of masonry were varied in reliable ranges.

Firstly, the effect of the Young’s modulus was investigated and, in order to take into account the cracking phenomena as suggested by the codes, the central values of the ranges reported in Table 1 (Young’s modulus for the ground floor E_G = 2610 MPa, Young’s modulus for the 1^st and 2^nd floor and E_1–2 = 2250 MPa) were reduced. For reinforced concrete structures it is in general suggested to reduce the inertia of the element by 50%, taking into account the cracking phenomena [27]; this hypothesis can be simply introduced into the modeling by reducing the Young’s modulus of concrete. For masonry structures it is expected that the reduction of the inertia due to cracking phenomena is lower because of the high compressive stresses usually acting on the masonry walls. Thus, three reductions, lower than 50%, of the Young’s modulus were assumed in order to: (1) verify the variation with E of the theoretical values of frequencies given by the FE model, and (2) compare them with the experimental ones:

Case 1: - 30% (E_G = 1850 MPa and E_1–2 = 1550 MPa);

Case 2: - 45% (E_G = 1450 MPa and E_1–2 = 1250 MPa);

Case 3: - 15% (E_G = 2200 MPa and E_1–2 = 1850 MPa).

For these analyses in both Models A and B, the basement was considered completely restrained. Moreover, for the model with the underground level (Model B, Figure 7b), the pressure of the lateral soil was considered as acting on the underground walls by means of an earth pressure coefficient k_o at rest equal to 0.7 (no kinematism was hypothesized).

The numerical values of the first four frequencies are listed in Table 3 for the three cases examined, while the shapes of the first two vibration modes are reported in Figure 7 and Figure 8 for Models A and B of the only Case 1, since they are identical for Cases 2 and 3.

In both models, the first and the second modal shapes are completely translational in direction Y (Figure 7a and Figure 8a) and X (Figure 7b and Figure 8b), respectively, with a participating mass ratio of about 75% for each direction. In agreement with the experimental results, the first frequency (direction Y) is always about 10% lower than the second one (direction X); this evidences a tendency of the building to be more deformable in direction Y that is parallel to the shorter side (East-West direction, see Figure 2b).

In the model with the underground level (Model B), the first two frequencies are reduced by about 16% with respect to Model A, clearly indicating a greater deformability of the building when the underground floor is modeled too.

The third modal shape, having a share of participant mass equal to 10 % only, is local and regards a wall of the Northwest façade (Figure 2d) on the second floor. This wall is particularly deformable due to the presence of many openings in comparison with the other façades (the two parallel façades along the X direction are not perfectly symmetrical, see plan of the building in Figure 2b). The fourth mode is local too and characterized by mass participant ratios lower than 5%.

When the effect of the Young’s modulus is reduced by about 20% (i.e., Case 2 vs. Case 1) both first and second frequencies reduce by 10%. Adopting Young’s moduli lower than those assumed in Case 2 is unrealistic, because very small numerical frequencies are obtained, and, thus, they are not reliable with the experimental evidence. Moreover, any interaction with the foundation soil has not been considered yet in these analyses, and it is known that the SSI can induce a further reduction of the main frequencies. Similarly, when the Young’s modulus increases by about 20% (i.e., Case 3 vs. Case 1), the theoretical frequencies increase by about 10%. In conclusion, as expected, a relevant sensitivity of the frequencies to the variation in Young’s modulus has been observed: It can be concluded that, for the examined building, a variation of 50% in E leads to a variation of about 25% in terms of frequencies.

In the last column of Table 3, the mean values of the first two frequencies experimentally indentified are listed too. As confirmed by the numerical FE analyses, higher frequencies have not been experimentally identified, probably due to the low rate of participating mass corresponding to these modes and the low intensity energy of the dynamic source. The experimental frequency of the first mode is the mean value of the values corresponding to the first peak of the FFT for each sensor measuring in the Y direction; the same applies analogously for the X direction.

Considering Model A (without the underground level), the results of Case 2 are closer to the experimental evidence (+2.8% and +3.8%). By contrast, considering Model B (with the underground level) that furnishes lower frequencies than Model A, the experimental results are best fitted by the Case 1 (–0.7% and +0.4%).

It is clear that a correct assessment of the Young’s modulus of masonry should not ignore the effect of the foundation soil deformability that, in these analyses, has been completely neglected in both Models A and B because the structure has been considered fixed at the basement.

In Section 3.2 it has been observed that for Model B, where the underground floor is modeled and lateral pressures of the subsoil are applied on the perimetric underground walls, the first two frequencies decrease by about 16% with respect to Model A (see Table 3), independently of the Young's modulus of masonry.

A first simple approach to consider also the deformability of the foundation soil consists in substituting the fixed constraint at the basement level with vertical elastic springs identified by a coefficient of sub-grade reaction, k [37]. This approach, even if it is widely adopted by designers to take into account soil deformability in the global modeling of the structures, is strongly influenced by the values assigned to the parameter k. Note that an uncorrected estimation of k could lead to an excessive and unrealistic deformability of the structure.

For the case at hand, several values of k have been assigned to the vertical springs placed under the basement walls, and it was found that for k = 0.10 N/mm³ the same results of the completely fixed-base schemes are obtained. This led to consider k = 0.10 N/mm³ as an upper limit of the variability range of this parameter. Moreover, varying k in the range of 0–0.10 N/mm³, it was found that the main frequencies reduce as k decreases with a quite linear trend: i.e., for k = 0.05 N/mm³, that corresponds to 50% of the upper limit, the frequencies reduce by about 25% compared to the fixed-base schemes. Notwithstanding the simplicity of this approach, the parametric study enhances, thus, that the effect of k is similar to that given by the variation of the masonry Young’s modulus discussed in Section 3.2. This aspect highlights how soil deformability could be important in modeling the structure response. However, different and more refined approaches for taking into account Soil-Structure Interaction exist and their use for the case at hand has been illustrated in [38].

By means of the 3D FE model of the building, the stress distribution under gravity loads was estimated in order to check the eventual presence of anomalous stress concentrations. The gravity loads were defined in Section 3.1 and were amplified by the coefficients γ_g = 1.3 and γ_q = 1.5 for permanent and accidental loads, respectively, in order to carry out verifications at the ultimate limit state [27,39].

In Figure 9 the distributions of the vertical stresses (σ_zz) in the entire building (Figure 9a) and at the ground floor (Figure 9b) are reported for Model A. The highest values of the compressive stresses are 0.85 MPa for the ground floor, 0.70 MPa for the first, and 0.45 MPa for the second one. These values, referring to the strength reported in Table 1 (2.20 MPa for the ground floor and 2.70 MPa for the superior ones), correspond to safety factors of 2.6, 3.9 and 6.0, respectively. However, these values are singular peaks relieved at corners or openings, while the stresses are on average about 0.55 MPa at the ground, 0.45 MPa at the first and 0.35 MPa at the second floor.

When the underground level is modeled too (Model B) and the pressure of the foundation soil is taken into account on the lateral underground walls by means of the coefficient k_o = 0.7, a contrasting action of the soil on the transversal dilatation of the underground walls is observed. The compressive stresses are a little higher than Model A and are on average equal to 0.90 MPa at the underground level, that is, however, significantly lower that the masonry strength.