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Assessing the seismic vulnerability of a historical building

Gaia Barbieri, Luigi Biolzi, Massimiliano Bocciarelli , Luigi Fregonese, Aronne Frigeri

Department of Architecture, Built Environment and Construction Engineering ABC, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy

a r t i c l e i n f o

Article history:

Received 17 October 2012

Revised 5 August 2013

Accepted 30 September 2013Available online 8 November 2013

Keywords:

Masonry

Seismic vulnerability

Finite element modeling

Restoration

a b s t r a c t

The work deals with the structural analysis of an historic masonry building,Palazzo del Capitanoin Man-

tua, subject to significant static instabilities due to an overturning of the longitudinal faades, probably

related to ground settlements.The exact geometry of the structure is acquired by means of the laser scanning technique and thanks to

previous investigations, the main mechanical properties of the materials are reasonably well defined.

Based on these information a three-dimensional finite element model of the entire structure is imple-

mented, taking into consideration all the geometrical (contact between not connected panels and large

displacement effects) and material (elasto plastic damage behavior of the masonry) nonlinearities, in

order to investigate the seismic behavior of the structure by means of nonlinear dynamic analysis.

The outcome of the analysis points out that the longitudinal faade, overlooking Piazza Sordello, is

poorly constrained both to the floors and to the transverse bracing elements, therefore not able to coun-

teract its deformation when a seismic event occurs.

Finally suggestions to reduce the seismic vulnerability of the building are critically assessed by the

implemented finite element model.

2013 Elsevier Ltd. All rights reserved.

1. Introduction

The conservation and the restoration of ancient buildingsbelonging to the culture heritage, preserving their main architec-

tural features, are becoming a very sensitive problem in Italy asin other Countries. In fact, many historically interesting structuresin most of the Italian cities are currently used with different func-tions, such as residential areas, offices, and museum centers; and

hence they require a sufficient level of safety against to both thevertical and horizontal loads. In particular, the seismic vulnerabil-ity of such structures is a point of extremely high concern sincethese buildings usually posses a very low seismic resistance.

Italy is one of the countries with the highest seismic risk in theMediterranean area. This is primarily due to the high frequency

and intensity with which earthquakes occur. These seismic phe-nomena are a consequence of the geographical position of the

country in the area where the African plate and the Eurasian oneconverge.

The seismic risk of a structure is a measure of the expectedfuture damage caused by the earthquake which is expected to

occur in the site of construction. It depends on three factors: haz-ard, the intensity of the expected seismic action; vulnerability, ameasure of the inadequacy of the structure to resist to seismicactions; and exposure, which is related to the architectural value

of the building and to the possible consequences of any structuraldamage in terms of loss of human lives.

In this paper we investigate the structural response ofPalazzodel Capitano in Mantua, in relation to both static and seismic

conditions. This building is located in the northern part of Italyin the Lombardia region, classified by the Italian code as an areaof low seismic hazard, but where on May 29th, 2012, a 5.2 Richterscale earthquake occurred. This building, whose construction dates

back to the thirteenth century, is part of the Palazzo Ducale com-plex and represents, for its position and for the majesty of its size,one of the most spectacular creations of the Italian architecturallandscape, see Fig. 1. The building has had significant static

problems related to the inclination of the longitudinal faades,probably due to ground settlements, for many centuries. The first

documents describing these problems date back to the early yearsof the eighteenth century. This deformation scenario appears to be

accentuated especially at the level of the second floor, where thegreat hall, calledSalone dellArmeria, takes up the whole storey. Be-tween the end of the eighteenth century and the early years of thetwentieth one provisions were taken to contain these out of plane

displacements, such as the inclusion in the Salone dellArmeria ofsome tie-rods and bracing walls.

The seismic behavior of old masonry structures is particularlydifficult to be investigated, see e.g.[1]. It depends on many factors

such as material properties, to be characterized by direct inspec-tion, see e.g.[2]; geometry of the structure, to be defined by propersurveys; stiffness of the floors (diaphragm effect) and connection

0141-0296/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engstruct.2013.09.045

Corresponding author. Tel.: +39 02 2399 4320; fax: +39 02 2399 4369.

E-mail address:[email protected](M. Bocciarelli).

Engineering Structures 57 (2013) 523535

Contents lists available at ScienceDirect

Engineering Structures

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between orthogonal walls and structural and nonstructural ele-ments. In particular the key point is the material behavior model-

ing. In fact experience shows that masonry mechanical behavior isdominated by the nonlinear phase, characterized by cracks open-ing, dissipative and brittle behavior with a softening branch. Themodeling of these materials still represents a challenge in the

scientific community. Many efforts were made in the last years

to improve the modeling techniques for masonry structures, seee.g.[36]. Elasto-plastic analysis may be used to simulate masonrynonlinear behavior, however they fail to simulate crack formation

and the brittle behavior when the material enters the softeningregime. Limit analysis methods have been frequently applied in or-der to investigate the collapse mechanism of masonry structuressubjected to given load distributions, see e.g. [710]; however,

these approaches fail to consider the actual dynamic nature ofthe load condition under seismic excitation, which represents themajor concern for this type of buildings. Smeared crack approaches

or damage models may be used to simulate the local loss ofstrength masonry material suffers when it enters the nonlinearbehavior, see e.g. [1113]. However, the numerical analysis itselfis still a very difficult task especially when dealing with large

and complex structures. As an alternative to modeling masonryas a homogenized continuum, discrete element approaches maybe applied to model the structure as an assembly of blocks withsuitable interface laws, see e.g. [14,15].

In the present paper the importance of considering the exactnonlinear and three dimensional behavior of the masonry struc-ture is shown, in order to put in evidence all the structural defi-ciencies of the palace when an earthquake occurs. To this

purpose the exact geometry of the structure is reconstructed bymeans of a laser scanning technique, while information regardingthe mechanical properties on masonry material are derived by pre-vious investigations and literature search. Based on these informa-

tion a three dimensional finite element model, endowed with anelastic plastic damage constitutive law, is adopted to determinethe seismic vulnerability of the building by means of nonlinear dy-

namic analyses.After a careful diagnosis and evaluation of the safety of the

structure in its current state, suggestions for retrofitting the build-ing, without altering its original conception and historical value,and reduce its seismic vulnerability are critically assessed by the

above implemented finite element model.

2. History of the building

Some parts of the historical background ofPalazzo del Capitano

are still unknown, especially those referring to the ancient period,until the eighteenth century and the Austrian domination.

The Palace construction can be placed at the same living time of

the first Lords of Mantua, possibly between the last years of thethirteenth century and the first decade of the fourteenth century.It was originally used as the residence of the Lords until the secondhalf of the fifteenth century, when St. Giorgios Castle was built.

During thebonacolsianoperiod the building was lower with onesingle floor, narrower without the front arcade, and shorter be-cause the northern part originally coincided with an alley (locatedwhere the entrance to the palace currently is) that separated it

from the adjacent Magna Domus.Subsequently, probably around 1328, the Gonzaga family came

into possession of the original nucleus, expanded it with the crea-tion of the new front ofPiazza Sordelloand with the extension be-

yond the alley that separated the Magna Domusand finally raisedan upper floor, consisting of the great hall called Salone dellArmeria.

The new faade ofPalazzo del Capitano, overlookingPiazza Sor-dello, was built following the model of the adjacentMagna Domus.

It was proposed indeed a partition of the front: at the ground floora marble arcade, at the first floor a series of single lancet windows

and at the second floor double lancet ones with round arches, builtalways along the lines of those of the adjacent building.

The rear front ofPiazza Pallone conformed differently from thefront one. The ground floor had no arcade and on the whole faade

it is difficult to reconstruct the original openings, owing to the lim-

ited evidence and the numerous reconstructions.As far as the configuration of the faades is concerned, it is re-ported that in the second decade of the fifteenth century, Gian

Francesco Gonzaga closed the double lancet windows with roundarches on the second floor and opened others with pointed arches.

With regard to the original configuration of the interior spacesof the building, it is believed that the environment preserving more

traces of the past is the original gallery on the first floor, Corridoiodel Passerino. It was originally subdivided into various rooms bymeans of wooden partitions, then removed between 1902 and

1906, to reduce the load on the underlying arcade. The SalonedellArmeriawas conceived as a great open space initially used asa representation room and then as a weapon depot. It held its ori-ginal features until interventions were made in the twentieth

century.The beginning of the eighteenth century sanctioned the end of

almost four hundred years of Gonzaga domain. Between 1708and 1866 there was a period of transition characterized by foreign

domination starting from the Austrian Government then passing tothe French one. Throughout the course of the eighteenth centuryvarious restoration works were made to the roof and to the timberbeams in the Salone dellArmeria, as shown in various official sur-

veys and reports from the Austrian Government. In particular,the first documents stating the presence of inclination of the longi-tudinal faades and of some tie-rods in the great hall date back tothe first half of the eighteenth century.

In 1866 Mantua entered the Reign of Italy, which in 1946 be-came the Italian Republic. This was more specifically between1898 and 1937 the period of greatest activity around Palazzo

Ducale. While works of recovery of the Renaissance appearanceof the front faade of thePalazzo del Capitanobegan and were com-pleted, the fears for the stability of the structure of the palace werebecoming stronger and stronger. In 1906, to reduce the inclinationof both longitudinal walls (the one over Piazza Sordello leaning

toward the interior of the hall and the one overPiazza Pallonelean-ing toward the outside) the decision of building in the Salone

dellArmeria a bracing system consisting of tie-rods and threemasonry partitions walls was reached. In particular two walls

overlapping with the transverse walls of the rooms below were

Fig. 1. Picture ofPalazzo del Capitano in its current state taken fromPiazza Sordello.

524 G. Barbieri et al. / Engineering Structures 57 (2013) 523535


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built and the third one, abutment shaped, not relying on the pres-ence of a bearing wall below, limited to the portion above the Cor-

ridoio del Passerino.

3. Description of the building in its current configuration

3.1. Geometrical survey

Palazzo del Capitano has a rectangular plan (6768.5 m 16.5 m), with three floors above ground and is characterized by

a saddle roof (construction is 22 m high at the eaves line and24.5 m high at the ridge line). Thickness of the bearing walls variesbetween 100 cm and 80 cm at the ground and at the first floor andbetween 80 cm and 70 cm at the second floor, see Figs. 25. All

floors maintained the original structure of the fourteenth centuryexcept in some points where restoration actions were performed.In particular the structure of the first floor is made up with both

timber beams (with single, double or triple warping) and masonryvaults (barrel or cloister); while the second floor consists of timberbeams only. The roof structure is made up of wooden Palladiantrusses and timber beams, supported by the longitudinal walls.

In 1993 the geometrical survey of the entirePalazzo del Capitanowas performed [private communication from Magistrato delle Ac-que- Mantua]. It reproduced, with 1:100 scale of details, plans ofall floors, the two fronts and a cross section that includes the rep-

resentation of the inclination, seeFig. 2. Plans of the floors and sec-tion were obtained by direct measurements while the survey of thefaades were performed by photogrammetric techniques.

The technological progress achieved in the meantime allowed

us to perform new measurements with much more advancedinstruments such as 3D laser scanning which enables the auto-matic detection of the object of study through the acquisition ofa large number of scattered points in three-dimensional space,

see for instance[1619].

Between 2005 and 2007 some measurement campaigns werecarried out with laser scanner Leica HDS3000 (range up to

300 m, scan rate up to 4000 points/s and modeled surface preci-sion/noise of 2.0 mm) and Leica HDS6000 (range up to 79 m, scanrate up to 500,000 points/s, modeled surface precision/noise at25 m between 2.03.0 mm and at 50 m between 4.07.0 mm and40,000 points/360 detected in ultra high scan resolution),

mainly to investigate the magnitude of the inclination of the longi-tudinal walls very thoroughly. Substantially, the surveys concernedthe external front of Piazza Sordello, part of the front of PiazzaPallone, the passage between the two squares, part of the front ar-

cade, the interior space of the Salone dellArmeria with the roofstructure, the upper part of the underlying rooms of the first floorand the timber beams of the floor above these. Finally, between2011 and 2012, the movements of the main faade were monitored

Fig. 2. Cross section of the building visualizing the current permanent out of plane displacements.

Fig. 3. Ground floor plan.

G. Barbieri et al./ Engineering Structures 57 (2013) 523535 525
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by laser scanner Leica HDS7000 (range up to 187 m, scan rate up to

1,016,727 points/s, range noise at 25 m between 0.51.0 mm andat 50 m between 0.82.7 mm and until 100,000 points/360 de-tected in extremely high scan resolution). Currently, the geomet-rical survey of the building is the result of the integration of laser

data with measurements obtained with traditional methods (directmeasurement and photogrammetric techniques), but the futuredigital acquisition of the parts of the palace not yet detected withlaser technique will allow a complete and accurate geometrical

survey of the entire building.

The survey with the laser scanner over the entire surface underinvestigation allows to determine very precisely and continuouslythe state of permanent out of plane displacement of the longitudi-nal faades, on both external and internal surfaces of the walls. To

have an immediate idea of the degree of lack of stability, the laserdata are extrapolated to represent some significant cross-sections,seeFig. 5. Data show that the inclination begins in correspondenceof the upper part of the first floor and increases more or less line-

arly as a function of the height. Such permanent displacements,probably due to uneven ground settlement and nonuniform distri-bution of soil properties, are further caused by the fact that at thelevel of theSalone dellArmeriathe two longitudinal faades extend

along their entire length of the building without any constraint,(tie-rods and bracing walls were indeed inserted after the detec-

tion of such permanent displacements settlements). The majordeformations are found in the central part. From the analysis of

data provided by the laser survey we can see that at roof levelthe walls overlooking Piazza Sordello and Piazza Pallone present

an out of plane displacement ranging from 0.36 m to 0.38 m (from4.4% to 4.6% of the last storey height) and from 0.32 m to 0.40 m(from 3.9% to 4.9% of the last storey height), respectively. Finallyit has been measured an inclination of the floor structure at the le-

vel of the Salone dellArmeria of about 0.8% from Piazza Sordello

(upper level) to Piazza Pallone (lower level).According to a visual inspection, no significant structural cracksare present in the longitudinal faades, but only a surface crack

pattern quite common for masonry structures dating back to thethirteenth century and which is believed not to play a significantrole in the seismic behavior of the structure. Besides works ofrecovery of the front faade of the Palazzo del Capitano began and

were completed between 1898 and 1937.The surfaces of the 3D model obtained by the digital laser-scan-

ner survey are processed by other graphics utilities and then im-

ported into a suitable pre-processor. In this way we were able toobtain a solid model particularly accurate in reproducing the maingeometrical features of the building. The exact determination ofsuch existing permanent deformations in the geometry is indeed

of primary importance in assessing the current stability of thebuilding and especially its seismic vulnerability.

3.2. Material properties

According to experimental measurements carried out at variouspoints of the masonry structure in previous experimental cam-paigns [private communication fromMagistrato delle Acque Man-

tua] by means of single and double flat jacks, the average elasticmodulus of the ancient masonry and of the one added at thebeginning of the twentieth century are 1640 MPa and 2795 MPa,respectively, while the value of the cracking stress is always

around 2.052.10 MPa.The compressive strength of the material is defined on the basis

of what suggested by the Italian Code[20]in Annex C8A.2. Assum-ing a knowledge level of 2, an average value of the compressive

strength equal to 3.2 MPa is assumed, based on table C8A.2.1, forsolid brick and lime mortar. Applying then a confidence factor CFequal to 1.20, and the additional correction factors, according tothe table C8A.2.2 in[21], of 0.7 for the presence of an inner core

with poor mechanical properties and 1.5 for a mortar of good qual-ity, we obtain a final design compressive strength equal tofmcd

3:20:71:51:2

2:8 MPa. The tensile strength of the masonry isgenerally negligible; it can be estimated as 1/30 of the compressive

resistance and therefore equal to fmtd 2:830 0:09 MPa.

The material properties of the Veronese stone forming the col-umns of the front arcade are defined according to the technicalsheets available on the website of the Italian Civil Protection,

which are based on experimental tests performed according toEN standards. Since detailed information on the marble formingthe front arcade were not available, the minimum values proposedwere adopted. The elastic modulus is equal to 30,000 MPa while

compressive and tensile strengths are assumed equal to 60 MPaand 5.7 MPa, respectively. Applying then the confidence factor CFwe obtain the following design values: fmcd

601:2

50:0 MPa andfmtd

5:71:2

4:75 MPa. However these values are not very significantsince these stress limits are never achieved either in the static norin the seismic analysis.

4. Finite element modelling and structural analysys

The 3D cad geometrical model (i.e. .sat format) of the existing

deformed configuration, including also the permanent out of planedisplacements, is imported into the finite element program Abaqus

Fig. 4. Section BB.

Fig. 5. Sections CC and DD.



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[22], seeFig. 6. As a compromise between the conflicting require-ments of reasonable computing time and accuracy of the solutiona finite element discretization, based on four nodes tetrahedral ele-

ments, with the following features was adopted: (i) the front and

back faades, where the main failure mechanisms are located, werediscretized with elements having an average size of 0.4 m on thesurface and 0.2 m in the perpendicular direction, in order to haveat least four elements through the thickness to catch the flexural

behavior of the masonry wall under seismic action, see Fig. 6and(ii) the rest of the structure, which works primarily under mem-brane actions, was discretized with an average size of 0.70 m.The total number of elements is equal to 465,490 for a total num-

ber of 327,027 degrees of freedom. Since not negligible out of planedisplacement may occur during a seismic event large displacementeffects are considered. Perfect connection is assumed between per-pendicular walls.

At the Salone dellArmeria level the bracing walls built in thetwentieth century are not connected to the longitudinal faades,

therefore a monolateral contact is assumed between them. Thesteel tie-rods, present both at the first and second floor, are

modeled as linear springs having a negligible stiffness in compres-sion and a stiffness in tension equal to k=EA/L,E,Abeing modulusof elasticity and sectional area, respectively and L the length, see

Table 1for details.

Three different materials can be recognized: Mat. (1) ancientmasonry dating back to the original construction of the building;Mat. (2) masonry of the bracing walls added in the twentieth cen-tury in theSalone dellArmeria; and Mat. (3) Veronesestone used to

build the columns of the arcade in the front faade.It is worth observing that in the finite element analysis the ef-

fects of the adjacent building in Piazza Pallone are not consideredsince a careful examination shows that the respective faades are

Fig. 6. Geometrical model and finite element discretization of the building in its current state. Different colors refer to the different materials and the black lines represent the

steel tie-rods.

Table 1

Stiffness properties of steel tie-rods in tension.

Tie rods E(MPa) A(mm2) L(m) k(kN/m)

1st Floor 206,000 1000 6.10 33,770

2st Floor 206,000 1000 16.07 12,795

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not well connected to act as a reciprocal continuous restraint andtherefore the structural analysis is performed considering Palazzodel Capitanoas an isolated building.

There are different methodologies to account for seismic ac-

tion: static and dynamic both with a linear or nonlinear approach.It is shown that in order to capture all possible failure mecha-nisms the effect of the earthquake has to be considered by a non-linear dynamic analysis, namely, by applying at the base of the

building an acceleration history whose shape and intensity willbe determined hereinafter. Such kind of analysis is very time con-suming. However, it is much more accurate and reliable thanother approaches for its capability to evidence both in plane

and out of plane, both local and global failure mechanisms, see[23].

4.1. Constitutive law for masonry

For all the materials involved in the analysis a macroscopic non-linear model is adopted. The main features of the model are the fol-

lowing ones: (1) linear and isotropic behavior in the elastic regimeand (2) elastic plastic damageable behavior in the nonlinear range,taking into account the difference of compressive and tensilestrengths and the softening brittle behavior once the strength of

the material is reached.The plasticity-based damage model adopted assumes that the

main two failure mechanisms are tensile cracking and compres-sive crushing. Under uniaxial tension the stressstrain response

is linear elastic up to the value of the failure stress, fmtd, corre-sponding to the onset of micro-cracking in the material. Beyondthe failure stress the formation of micro-cracks is representedmacroscopically with a softening stressstrain relationship, which

induces strain localization, seeFig. 7. Under uniaxial compressionstressstrain relationship is linear until the value of the ultimatestress in compression, fmcd, is reached then the response is

assumed to be plastic followed by a strain softening regime, see

Fig. 7.It is assumed that when the material is unloaded from any point

on the softening branch, the response is characterized by a reducedelastic stiffness (damage): namelyE= (1 d)E0,E0being the initial

undamaged modulus of elasticity.The degradation d of the elastic stiffness is governed by two

damage variables, d cand dt, which are assumed to be function ofthe plastic strains. These variables may assume values from zero

(undamaged material) to one, which represents total loss ofstiffness.

Under cyclic loading conditions the degradation mechanisms

are quite complex, involving the opening and closing of previouslyformed cracks. Experimentally it is observed that there is somerecovery of the elastic stiffness as the stress changes sign. The stiff-ness recovery effect, also known as unilateral effect, is usually

more pronounced as the stress state changes from tension to com-pression, causing tensile cracks to close, which results in the recov-ery of the compressive stiffness.

In uniaxial stress conditions the loss of elastic stiffness is com-

puted according to:

1 d 1 stdc1 scdt 1

wherestand scare functions of the stress state and are introduced

to model stiffness recovery effects due to stress reversal. They are

defined according to:

st 1 wtHr 0 6 wt6 1

sc 1 wc1 Hr 0 6 wc6 1

2

Fig. 7. Stress strain behavior in the nonlinear regime: tensile behavior (above) and

compressive behavior (below).

Table 2

Material properties adopted in the analysis.

E0(MPa) m fmtd (MPa) etu fmcd (MPa) ec1 ecu wt wc c(kN/m3)

Mat. 1 1640 0.10 0.09 0.0015 2.80 0.005 0.015 0.0 1.0 1800

Mat. 2 2795 0.10 0.09 0.0015 2.80 0.005 0.015 0.0 1.0 1800

Mat. 3 30,000 0.15 4.75 0.0015 50.0 0.005 0.015 0.0 1.0 2900

Table 3

Load combinations adopted in the analysis.

Load combinations P A SY SX

LC1 1.0 1.0 0.0 0.0

LC2 1.0 0.3 1.0 1.0

Fig. 8. Picture of a floor whose structure is made by a double system of timber

beams.



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adopted with the multiplicative coefficient of the characteristic va-

lue of each single load.

Self weight of the masonry walls and vaults is applied as gravityload, function of the corresponding specific weight. Floors at thefirst and second level are made by a system of timber beams sup-ported by the bearing walls to which they transfer the vertical

loads, see e.g.Fig. 8. Their in plane stiffness is not considered suf-ficient to assume the hypothesis of rigid diaphragm and thereforefloors are not inserted into the finite element model and their con-tribution consist only of vertical loads applied directly to the bear-

ing walls. The same simplification is assumed for the timber roof.Fig. 9andTable 4visualize and report, for each floor, the timber

beams distribution and the corresponding self weight and live loadif any (for the roof live load corresponds to the snow action).

Vertical degree of freedom of the nodes at the base of the build-ing is restrained both for the static and dynamic analysis.

According to [20], the seismic analysis is performed at theUltimate Limit State of Life Safety (SLV) and is motivated by the

Table 6

Values of the base shear coefficient for the present and the strengthened configuration, with reference to the Ultimate limit state (SLV) and the Damage limit state (SLD), being: q

the behavior factor estimated according to[21],T1the first natural period, Wthe total weight of the structure, sthe base shear coefficient and Fthe total base shear force (F=sW).

q T1 (s) W(V) s F(N)

Present configuration SLV 2.7 0.57 7.73 107 0.130 1.00 107

SLD 1.0 0.57 7.73 107 0.133 1.03 107

Strengthened configuration SLV 2.7 0.57 7.60 107 0.130 0.99 107

SLD 1.0 0.57 7.60 107 0.133 1.01 107

Fig. 11.Vertical stress state (expressed in (N/m2)) in the longitudinal (a) and transversal (b) faades induced by the static load combination LCI; and position of the performed

flat jack tests. The red numbers indicate tests on internal walls, the black ones indicate tests on external walls.

Table 7

Comparison in terms of vertical stress component between the measurements of

single flat jacks and the corresponding numerical predictions.

Flat jack Experimental (MPa) Numerical (MPa) Error (%)

1 0.18 0.19 2.8

2 0.21 0.23 9.5

3 0.26 0.20 23.1

4 0.25 0.13 8.0

5 0.18 0.18 2.8

6 1.14 1.08 5.3

7 0.17 0.20 17.7

8 0.17 0.15 14.7

9 0.21 0.21 0.0

10 0.23 0.17 28.3

11 0.23 0.16 30.4

12 0.14 0.18 25.0

13 0.40 0.26 35.0

14 0.51 0.50 2.0

15 0.45 0.45 0.0

16 0.41 0.42 1.2



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desire to safeguard the preservation of the building and the safetyof the occupants in the event of rare and intense earthquakes. In

particular, in order to not overcome this limit state it is requiredthat as a result of an earthquake the construction may suffer cracksand collapses in non-structural components and significant dam-age to structural components which is associated with a significant

loss of stiffness against horizontal actions; however the construc-tion has to retain its structural integrity and a residual load bearingcapacity for vertical actions and a margin of safety against collapsedue to horizontal seismic actions.

Nonlinear dynamic analyses are carried out using an artificialaccelerogram compatible with the elastic response spectrum ofthe Italian Seismic Code, see [20]. The intensity of the seismic

action depends on the site of construction (latitude and longitude),the return period TRof the design earthquake, the reference life of

the building VR and the type of soil foundation expressed byparameter S. Assuming the parameters contained in Table 5, thecorresponding acceleration history applied at the basis of thebuilding, having a total duration of 25 s, is visualized inFig. 10.

This means that the structural safety of the building is verifiedagainst an earthquake with return period of 427 years and 10%probability of exceedance in 45 years.

Values of the base shear coefficient for the actual and the

strengthened configuration, with reference to the Ultimate limitstate (SLV) and the Damage limit state (SLD), are reported inTable 6.

Fig. 12. Deformed configuration and compressive damage distribution due to the artificial earthquake accelerogram applied. Frames are returned at the instants 0.0 s, 1.0 s,

2.0 s, 3.0 s, 4.0 s, 5.0 s, 6.0 s and 7.0 s. Scaling factor = 1x.

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4.3. Static analysis

Fig. 11 visualizes the vertical stress component relatively to

load combination LC1. The structure is almost everywhere com-pressed and only in a few points the analysis detects the presenceof tensile stresses, which however are small enough not to lead tothe partition of the section. Differently from other Italian masonry

historical buildings, the static stress state due to the vertical loadsonly is large and close in some points to the material resistance, as-sumed equal to 2.80 MPa. The highest compressive stress in the

masonry walls is registered on the front of Piazza Sordello, near

the springers of the arches, due to the strong reduction of the resis-

tant section. The absolute highest value of the compressive stressstate is reached in the stone columns (11.5 MPa), however, this va-lue is not of any concern considering the large compressivestrength of this material.

Table 7reports the comparison in terms of vertical stress com-ponent between the measurements of single flat jack tests, whosepositions are visualized inFig. 11, and the corresponding numericalpredictions. An average error of 12.9% and a maximum error as

high as 35% are registered. Taking into account the intrinsic errorin flat jack test measurements, we may conclude that the finiteelement model is able to represent the static stress state quite

accurately.

Fig. 13. Example of connections between timber beams and bearing walls (a) and

between beams of adjacent rooms (b).

Fig. 14. Scheme of the bracing system designed at the roof level.

Fig. 15. Picture of Salone dellArmeria in its current state (a) and render of the

bracing system designed at the roof level (b).



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4.4. Seismic analysis

Similarly to the results of the static analysis, in case of an earth-quake the front faade overlooking Piazza Sordello exhibits majorproblems of stability, reaching a collapse mechanism after a few

seconds from the beginning of the seismic action for excessivedamage and consequent exhaustion of the material strength. Dif-ferently, the rear faade does not show any damage as severe ifnot at the level of the second floor. The evolution of the damageof the structure starts, as usual, at the openings and near the

springers of the arches and in particular in correspondence of theleft archway passage from Piazza Sordello to Piazza Pallone. Afterentering in the nonlinear softening regime material exhausts itscompressive resistance in about 6 s, consequently the front faade

starts to collapse due to its own weight, see Fig. 12 (where thecompressive damage variable dcis visualized). The section of thefaade that collapses first is the one close to theMagna Domusbe-tween the north transverse wall and the first partition. Indeed, in

its actual state the front faade does not possess at the level oftheSalone dellArmeriaany effective connection either to the parti-tions walls of the twentieth century nor to any tie-rod system.

This lack of box behavior, with the consequent impossibility to

redistribute the seismic loads and the possible occurrence of localmechanisms of partial collapse, is typical of many masonry histor-ical structures which exhibited poor performance in many pastearthquakes, see[23].

5. Suggestions for restoration

Conservation and restoration should be taken into consider-ation after a careful diagnosis and evaluation of the safety of thestructure in its current state and of the techniques and materials

used in the construction of the monument. The extent and natureof the actions must then be balanced between the conflictingrequirements of achieving a new required safety level and regard-ing for the original conception and historical value, see[24]. How-

ever, it must be paid attention to the fact that in some cases a toostrict application of this approach may lead to erroneously accepthigher risks to avoid or limit works that are recommended froma structural point of view, see e.g. [25]. The philosophy followed

in the restoration process tends to prefer measures that complywith the concepts of reversibility, recognizability, minimum

impact and compatibility of the intervention with the existingstructure, considering the possibility that in the future a better

intervention can be carried out, as a result of more accurate studiesor the evolution of technologies.

The results emerged from the seismic analysis of the buildingshow that at present the main structural deficiencies are: (1) thelack of connection of the front faade to the rest of the structureand (2) the high stress level masonry in subjected to in the arches

of the front faade already in static conditions. Therefore, the res-

toration actions should affect the entire structure to restore a box-like behavior, able to transfer the horizontal actions to all bearingwalls and should consider the possibility of increasing the material

resistance in the most stressed regions. However to purse the lattereffect, it would be necessary to implement actions (such as infiltra-tion of epoxy resin) which are in contrast with the concept ofreversibility of the intervention and therefore only the former will

be investigated in the following.Hence, we suggest that floors have to be stiffened in their plane

in order to be considered as rigid diaphragms and the timber

beams have to be anchored to the bearing walls. In its current statethe connections to the vertical structural elements rely exclusivelyon friction between them. Such connection improvement can beachieved by means of metal bars fixed through end anchored

plates of various types to the bearing walls, seeFig. 13(a). Otherconnections should be also established between the beams of adja-cent rooms, as inFig. 13(b).

Generally, a rigid diaphragm behavior can be achieved by oper-

ating both at the intrados, e.g., with metal rods, steel elements andother reinforcement systems of the beams; or at the extrados byimplementing a second timber panel over the original one, insert-ing metal rods into the top light concrete layer or metal plates to be

fixed to the timber beams or adding a new reinforced concrete thinslab properly connected to the walls. Interventions at the extradospresent the advantage of being less invasive since they are hiddeninside the floor and does not alter the architectural identity of the

building.Differently from the first two floors, the rigid diagraph behavior

at the roof level cannot be easily achieved with noninvasive

actions.In view of a possible reuse of theSalone dellArmeriafor civic or

cultural events (such as exhibitions, museums, conference room)and in order to restore its original majestic configuration charac-terized by an open space, the three bracing walls positioned in

the twentieth century are removed and a composite steel truss,working as diaphragm element positioned in an horizontal planeunder the roof structure, is designed to counteract the deforma-tions of the longitudinal faades.

The system is formed by two plates of section 500 30 mmpositioned along the longitudinal walls, to which the system ofstruts and tie-rods is connected, seeFigs. 14 and 15. Struts consistof hollow tubular of 250 250 16 mm square section and are

suitable to react to both compressive and tensile forces. The 18

steel ties, suitably post-tensioned and having a circular sectionwith diameter = 30 mm, work for traction forces only and areplaced diagonally, to counteract also the parallel sliding betweenthe two opposite walls.

The suggested solution respects the principles mentioned in theintroduction: it is reversible, recognizable and does not affect inany way the elements of the roof, thus leaving open to the possibil-ity that in the future a better intervention can be carried out, as a

result of more accurate studies or the evolution of technologies.At the first and second floor the concept of rigid diaphragm has

been implemented into the model as kinematic constrains on thedegrees of freedom of the nodes, while the designed bracing

system at the roof level has been modeled by a system of trusselements, seeFig. 16.

Fig. 17 visualizes the performance of the restored masonrybuilding subjected to the same acceleration history previously

Fig. 16. Geometrical model of the building implementing the restoration actions.

The different colors refer to the different materials and the black lines represent the

old tie rods preserved and the new elements added as bracing system under the

roof.

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12/13

analysed. We observe that now the structure does not overcomethe ultimate limit state SLV.

As a proof that a box-like behavior has been now achieved, thedamage pattern involves the entire structure and is particularlyconcentrated in the front faade at the second floor level.

6. Conclusions

Usually, historic buildings are retrofitted as a result of damageinduced by past earthquake and only seldom such buildings are

systematically strengthened, in order to avoid possible futuredamage.

However costs to recover a building severely damaged by anearthquake are greater than those needed to strengthen it and

prevent future damage. Furthermore, sometimes it is not even pos-sible to recover the building since it collapsed, and this results in

an unrecoverable loss of the cultural heritage of a Country.Restoration means repeating the design of an existent structure

in order to meet, if possible, the requirements of the present stan-dards. Therefore, even in case of heritage buildings, which were not

designed according to technical standards but by consideringhandcraft rules, restoration implies to calculate the structuralresistance twice: first to point out structural deficiencies and thenafter the retrofitting operations to evaluate the new load bearing

capacity.To this purpose the use of advanced numerical tools to perform

nonlinear three dimensional dynamic analyses is shown to be

necessary in order to investigate all possible failure mechanisms,both local and global, of a masonry structure, when subjected to

Fig. 17. Deformed configuration and tensile damage distribution due to the artificial earthquake accelerogram applied. Frames are returned at the instants 0.0 s, 4.0 s, 8.0 s,

12 s, 16 s, 20 s, 24 s and 28 s. Scaling factor = 1x.



13/13

an earthquake. The complexity of this type of analysis requires tovalidate accurately the implemented model. We believe that the

model we adopted to study the seismic response ofPalazzo delCapitanois sufficiently accurate to estimate the actual seismic vul-nerability of the structure. We also believe that the estimation ofthe beneficial effects of the proposed restoration actions is even

more precise, since such estimation is based on the difference be-

tween the seismic vulnerability of the structure in the current stateand in the restored one, both of them analyzed with the same finiteelement model.

Our analysis points out that Palazzo del Capitano in Mantuaresults to be very vulnerable to seismic actions and therefore wesuggest some restoration actions to reach a certain level of struc-tural safety but at the same time to remain in line with the require-

ments of preservation of the historic and architectural value of thebuilding. In particular the following restoration actions should beimplemented to provide to the building a box-like behavior and

consequently reduce its seismic vulnerability: floors should bestiffened in their plane and anchored to the bearing walls and anew ad hocdesigned bracing system should be added under theroof. After these operations the bracing walls present in the SalonedellArmeria may be removed in view of a possible reuse of thisroom for civic or cultural events (such as exhibitions or conferenceroom, and museums).

Thanks to these actions it was shown that the building pos-

sesses a seismic resistance sufficient for an earthquake having re-turn period of 427 years. In order to further decrease its seismicvulnerability it would be necessary to increase the materialstrength in correspondence of the arches of the front faade, but

this operation is not here considered since in contrast with therequirement of reversibility of the intervention.

Acknowledgements

The authors express their thanks to Dr. LOccaso Stefano and toDr. Paolozzi Strozzi Giovanna Soprintendente BSAE di Mantova,

Brescia e Cremona for having contributed to this work by makingavailable all the information and data at their disposal.

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