Seismic Safety of the “Corpus Domini” Bell Tower

Seismic Safety of the “Corpus Domini” Bell Tower

Mariateresa GUADAGNUOLO1, Mariano NUZZO2

, Giuseppe FAELLA1

(1) Department of Architecture and Industrial Design “L. Vanvitelli”, Second University of Naples,

S.Lorenzo ad Septimum Abbey, Aversa (CE), Italy. [email protected]; [email protected] (2)

Ph.D., Caserta, Italy, [email protected]

Abstract Masonry towers constitute a huge amount of the Italian built heritage. Therefore, their safety assessment against earthquakes has a significant social importance. They are unique architectural typologies, usually conceived in ancient time exclusively to withstand vertical loads. On the other hand, the recent national and international codes require the actual ultimate behavior of these structures under strong horizontal excitations to be deeply studied, encouraging the use of sophisticated non-linear methods. Recent Italian earthquakes (Umbria and Marche 1997, Puglia and Molise 2002, Abruzzo 2009, Emilia 2012) provided wide observational information about the recurrent behavior, the damage patterns and the intrinsic vulnerability of bell towers. The mechanisms of damage and collapse of this type of structures are varied and depend on both the geometry (slenderness) and the structural characteristics (quality of masonry walls and constraints). The development of mechanical models able of analyzing the failure mechanisms for all types of bell towers is not always viable, so it is suggested to carry out specific checks too, even though approximated as specified in the Italian Guideline "Cultural heritage seismic risk assessment and reduction with reference to the Italian national building code NTC/2008". This paper presents the results of seismic analysis carried out on a seventeen-century masonry tower in Italy, the “Corpus Domini” bell tower in Maddaloni (Italy). The results of linear and nonlinear analysis are compared and discussed, in order to provide general guidance on the main structural problems of this specific type of bell tower (recurrent in several earthquake zones of Italy). Keywords: Seismic Safety, Bell Tower, Masonry, Code provisions.

1. Introduction Most of historical structures has deteriorated over time by natural and environmental effects, such as earthquakes, because of inadequate preservation, which is considered a fundamental issue in the cultural life of modern society. Therefore, if the actual behavior of structures is known, protective measures can be supplied. In bell towers, the systematic observation of damage caused by recent earthquakes highlighted the high seismic vulnerability of belfries, located in their upper part. This is due to the presence of top mass and wide openings that imply slender pillars. The vulnerability consequently rises from their modest vertical-load bearing (related only to dead weight) that does not ensure stabilizing effect with respect to overturning. Quite frequently, bell towers are in contact with other lower structures. Customary cases are towers built as part of or next to churches, towers incorporated in various ways within the urban setting and towers built into city walls. In these structures, the presence of horizontal constraints at different heights can deeply modify the seismic behavior: limiting the slenderness, introducing localized stiffening elements and producing stress-concentrations, thus the vulnerability is greatly increased. In the literature, there are several research studies dealing with the seismic assessment and the vulnerability analysis of masonry towers, with regard to different aspects: mechanical and numerical analysis by computational [1,2] or simplified

approaches [1,3], experimental testing methods and structural identification [4,5], modal identification through experimental data of full-scale environmental vibration testing [6,7], seismic assessment by nonlinear static analysis. In the Italian National “Guidelines for evaluation and mitigation of seismic risk to cultural heritage” [8], different simplified mechanical models are identified for the most diffuse types of historic structures: buildings, palaces and other structures with bearing walls and horizontal diaphragms [9], churches and other structures with large halls, without intermediate diaphragms [10], towers, bell towers, and other tall and slender structures. The adoption of these models, though affected by uncertainties, permits to supply a homogeneous evaluation on territorial scale and, thus, a preliminary design of future strengthening interventions. The analysis based on simplified mechanical models (LV1) allows the evaluation of collapse acceleration by means of a method based on a limited number of geometric and mechanical parameters or utilizing qualitative tools (analysis of the construction characteristics, critical and stratigraphic surveys). Seismic behavior of towers depends on certain specific factors: structure slenderness, degree of connection between walls, presence of adjacent structures in the lower portions (which may create horizontal constraints), presence of slender architectural elements at the top of the structure (steeples, towering gables, battlements, etc.) or in any case belfries. For towers, the Italian National Guidelines [8] propose a simplified model based on failure hypothesis due to combined axial force and bending moment. The model considers towers as cantilevers which, if loaded by lateral forces in addition to their dead loads, may be subject to crises in a generic section due to crushing in the compressed zone, after the reduction of the effective un-cracked area due to non-tensile-strength. In this paper, the “Corpus Domini” bell tower is studied applying the LV1 level proposed in [8]. The results of linear and nonlinear analysis are compared and discussed.

2. The “Corpus Domini” bell tower The “Corpus Domini” Basilica in Maddaloni is situated in the oldest part of the city called Olivet, near the ancient S. Aniello Church, on the slopes of the Maddaloni Hill. The building is very articulated and seems oversized as compared to the surrounding urban context. The Basilica was built in the eighteenth century on pre-existing late sixteenth [11]. The bell tower was designed by Orazio Salerno in 1781, on the right side of the main entrance of the church, about one meter from the front side. There is little historical information on the designer, but it is known that he worked in the years when Luigi Vanvitelli was directing the building of the Royal Palace in Caserta and the Carolingian aqueduct in the Maddaloni Valley. Also a wooden model of the tower, along with the graphics and the technical report, was commissioned to Orazio Salerno. The construction began on May 13, 1781 and was completed in 1790. Because of the damage caused by lightning on February 12, 2010, a restoration design was drafted by the architect Mariano Nuzzo; and the interventions ended on 2012. Although the tower shows good structural conditions, its safety against potential future earthquakes is of primary importance. The bell tower is about 49.12 m high, and has nine portions with both square and circular cross-section. Table 1 shows the dimensions of each portion, and the material by which it is made.

N. Height [m] Material Section [m] fmc [MPa] Weight [kN/m3]

side or diameter

1 00.00 – 00.75 limestone 8.02

4.5 22

2 00.75 – 10.25 brick 8.02* 2.4 18

3 10.25 – 11.05 limestone 8.40 4.5 22

4 11.05 – 20.65 tuff 7.66* 1.4 16

5 20.65 – 21.48 limestone 8.40 4.5 22

6 21.48 – 30.55 tuff 7.66* 1.4 16

7 30.55 – 31.38 limestone 8.02 4.5 22

8 31.38 – 39.86 tuff 6.44** 1.4 16

9 39.86 – 49.12 tuff 6.44** 1.4 16

* unless the openings

** variable

Table 1: Geometry and material of the "Corpus Domini" bell tower.

Figure 1: Plans and section of the “Corpus Domini” bell tower. 3. Simplified mechanical modeling and analysis The assessment of safety, as well as the necessity and the suitability of eventual retrofits, has to be determined from the comparison of the structure capacity, evaluated as the result of qualitative and quantitative knowledge and analysis of the building, and the seismic action demand [9]. This assessment can be performed by simplified methods, that are different from the specific ones used in the strengthening design. Safety index IS greater than 1 indicate structures able to withstand the required seismic forces, provided by the seismic code; on the contrary if IS is lesser than unity, the

safety is lower than that prescribed. Similarly to the index IS, it can be defined an acceleration factor fa, defined as:

a

af

SLV,g

SLVa = (1)

where ag,SLV is the design ground acceleration, corresponding to the assigned return period of the earthquake, related to subsoil A. The acceleration aSLV is the ground acceleration leading to the achievement of the structure ultimate limit state (SLV), computed as a function of the fundamental period of vibration T1 of the structure, as defined in the Eqn (5.26) of the “Guidelines for evaluation and mitigation of seismic risk to cultural heritage” [8,12]. The simplified model proposed in the Guidelines [8] is based on the assumption that towers are structures with cantilever-behavior. The analyzed bell tower was divided into n sectors with uniform geometric characteristics and the checks were performed in correspondence of each section change. The ordinate of the elastic response spectrum Se,SLV,i(T1), required by Eqn (5.26), corresponding to the ultimate limit state SLV in the i-th section of the bell tower (taking into account the confidence factor FC) is calculated by:

( )

C

n

ik

kk

n

ik

i2kk

n

1k

kki,u

1i,SLV,e

FzWzzWW85.0

zWMgq

TS

⋅

⋅⋅−⋅⋅⋅

⋅⋅⋅⋅

=

∑∑

∑

==

= (2)

where:

• q is the behavior factor;

• g is acceleration of gravity;

• zi is the height of section i with respect to the foundation;

• Wi is the weight of the ith sector;

• Mu,i is calculated as described below. Where the tower has got squared rectangular cross-section, under the hypothesis that normal forces are not larger than (0.85·fd·a·s), the resistant moment at the base of the sector may be computed by:

⋅⋅

⋅σ−⋅

⋅σ=

di

ii0i

ii0i,u

fa85.0

Ab

2

AM

(3)

where: • ai is the cross-section side orthogonal to the direction of the seismic action, depurated of any

eventual openings; • bi is the cross-section side parallel to the direction of the seismic action; • Ai is the total area of the section under analysis;

• σ0i is the average normal stress of the section; • fd is the design compression strength of the masonry, opportunely reduced in relation to the

knowledge level achieved. Where the tower has got circular cross-section, the resistant moment at the base of the same sector may be calculated as:

Gdseti,u yf85.0AM ⋅⋅⋅= (4)

where: • Aset is the area of the sector of the circular crown; • yG is the distance of the point of application of the resultant from the center of the circle. For each cross-section, the peak ground acceleration (demand) that causes the resistant moment (capacity) is estimated. The minimum value of the peak ground accelerations, among those obtained for the analyzed sections, represents the acceleration corresponding to the ultimate limit state for the bell tower. 3.1 Seismic safety of the “Corpus Domini” Bell Tower According to the above briefly described procedure LV1 outlined in [8], by considering the geometric features of the “Corpus Domini” Bell Tower, the acceleration factors (fa) of nine portions were computed. These portions are the most representative in terms of geometries and openings; their plans are reported in Figure 1. Seismic safety was evaluated according to the only one direction because all the examined portions are symmetrical. The safety verification was performed at different heights because it was not possible to identify a priori the most critical section, due to the tapers in wall thickness and the opening impairments. The acceleration factors fa are computed through Eqn (1), according to a seismic safety level corresponding to buildings of limited relevance and to a class

of normally crowded use (Class III), and assuming a ground motion acceleration ag,SLV of 0.202 g and a B soil class. The fundamental period of vibration was computed as T1=C·H

3/4, where H is the tower

height and C is equal to 0.05. In addition, in computing Eqn (5.26) of Guidelines and in Eqn (2), the S coefficient was assumed equal to 1.197, the F0 factor equal to 2.519, and the behavior factor q is equal to 3.6. The indexes are computed assuming a confidence factor of 1.35 (corresponding to a complete survey of the geometries and a limited one for constructive elements and mechanical properties of materials). The analyses led to Fa values lower than one for the tuff portion number 4 and 6, with values ranging between 0.4 and 0.6, and for the brick portion number 2, where is equal to 0.7.

4. FEM modeling and analyses The safety index of the tower was also evaluated using a finite element modeling. The analyses were performed using the "strumas" model of the computer program MidasGen®, specifically developed for the study of masonry structures. This a "micro-macro" modeling based on the hypothesis of homogeneous equivalent material [13], where, starting from the definition of a representative elementary volume and different constitutive models for the three constituents (brick, bed and head mortar joints), the properties of the equivalent masonry material are computed through a homogenization procedure. The technique of homogenization is the one proposed by Pande [14] and is based on the equality of the deformation energy. The properties of the equivalent masonry material depend, therefore, on the size of blocks, the thickness of horizontal and vertical mortar joints, on the Young's and Poisson moduli of blocks and mortar, on the tensile strength of blocks and mortar. The model assumes a indefinitely elastic behavior in compression. The analytical procedure is linear in each step, but if the principal tensile stress exceeds the strength of a constituent, its contribution to the new stiffness matrix of the homogenized material is reduced or canceled. The reduction depends on a parameter of stiffness abatement, assumed to be equal to 10e

-4, which corresponds to a nearly elasto-

plastic behavior [16]. The FEM model of the "Corpus Domini" tower is composed of 47976 brick elements (Fig. 2). Eight node solid elements of size about 0.3 x 0.3 x 0:25 m, with isotropic behavior were used for modeling the masonry structure. The material parameters, including the compressive strength, were selected according to the Italian National Building Code [15], and the selected values are listed in Table 2.

Material E [MPa] G [MPa] fmt [MPa]

brick 1200 840 0.15

limestone 2400 1560 0.30

tuff 900 630 0.10 Table 2: Mechanical properties of the bell tower materials.

Figure 2: F.E.M. model of the “Corpus Domini” bell tower

4.1 Modal characterization In order to assess the seismic response of the bell tower, initially a multi-modal simplified analysis was performed, even though the ability of such an analysis to represent the actual behavior of masonry buildings is limited, due to the largely nonlinear behavior under dynamic seismic action. Moreover, the knowledge of eigen-values, eigen-modes and activated masses is needed for determining the shape of the horizontal load forces to utilize within the subsequent pushover procedure. The first three period of vibration are listed in Table 3.

Mode Frequency [Hz] Period [s]

1 4.196 1.278

2 5.009 1.254

3 15.424 0.407 Table 3: First three frequencies and periods of the “Corpus Domini” bell tower.

4.2 Pushover analysis The nonlinear static analysis was carried out applying loads in two stages: first the vertical loads and then the horizontal ones. Several distributions of lateral loads were applied. The corresponding capacity curves were subsequently converted to capacity curves of single-degree-of-freedom systems. Following the procedure described in [15], it was possible computing the safety indices in terms of capacity/demand ratio, to be also compared with those determined through the LV1 simplified analysis. The tower capacity was identified with the achievement of the maximum stresses in compression, thus making a conservative assumption. The control point was placed at the mass center of the ninth sector. This occurred for the Z-horizontal direction of loading; the corresponding maximum displacement is equal to 69 mm, showing a noteworthy large deformation capacity. Fig. 3 shows the vertical stresses in the entire bell tower at the above maximum displacement: the figure highlights that the maximum strengths are achieved in the lower tuff sector. Usually, the tall and slender shape of towers makes them more vulnerable at the base settlements, limiting the maximum allowable displacements under earthquake. In addition, the boundary condition of cantilever type makes them unsuitable for redistributing stresses and dissipating energy. The characteristic limited ductility of the masonry accentuates this brittle structural behavior [17], which is often accompanied by a concentration of stresses at the basement and can be amplified by the brittleness of deteriorated masonry. In the "Corpus Domini" bell tower, the noteworthy difference in terms of material properties between the intermediate diaphragms in limestone, the lower sector in bricks and the main portions in tuff, besides the achievement of the maximum stresses in the tuff portion, allowed larger deformation capacity of the whole tower. Fig. 4 shows the stress distribution in the tuff portions only, which are the most representative. The cracked zone is concentrated at the base of the pillars. Following the

Figure 3: Vertical stresses in MPa.

procedure provided in NTC/2008 [12], the displacement demand in the Z-horizontal direction is equal to 180 mm, and then the minimum safety index is equal 0.38. Therefore the safety assessment of the bell tower under horizontal loads is not verified also for the pushover procedure.

5. Conclusions and safety assessment remarks Masonry towers constitute a huge amount of the Italian built heritage. Therefore, their safety assessment against earthquakes has a significant social importance. They are unique architectural typologies, usually conceived in ancient times exclusively to withstand vertical loads. Many of these buildings are then characterized by structural schemes not suitable to withstand seismic events. This paper presents the results of the seismic analysis carried out on a seventeen-century masonry tower in Italy, the “Corpus Domini” bell tower in Maddaloni (Italy). The results of the LV1 simplified procedure and nonlinear static analysis are compared and discussed, in order to provide general guidance on the main structural problems of this specific type of bell tower (recurrent in several earthquake zones of Italy). The results obtained through FEM analysis essentially confirm those of the LV1 analysis. Moreover, the safety indexes obtained by the simplified analysis are larger than unity, except for the tuff portions. The response obtained by the FEM model confirmed the exceeding the allowable stress levels in the tuff masonry portions. It has to be considered, however, that in both models the brick coating of the tuff masonry was not considered, and then the possible increase in strength was not taken into account. Finally, the seismic safety evaluation of masonry towers should be performed both by global seismic analysis, controlling the entire structural system capacity, and by local failure mechanisms analysis, controlling all the possible out-of-plane mechanisms.

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