SEISMIC VULNERABILITY ASSESSMENT OF “SION CATHEDRAL” (SWITZERLAND): AN INTEGRATED APPROACH TO DETECT AND EVALUATE LOCAL COLLAPSE MECHANISMS IN HERITAGE BUILDINGS

Abstract

Seismic assessment of existing heritage buildings remains a challenging task. There is a high level of complexity and uncertainty compared with the assessment of standard buildings. Heritage masonry churches are usually prone to partial collapses during earthquake due to local loss of stability, and exhibit particular seismic vulnerabilities. An important step in the seismic analysis of heritage masonry buildings is the detection of local mechanisms. The Italian Building Code provides a simplified approach (LV1-churches) to assess the vulnerability of heritage churches evaluating and comparing 28 potential mechanisms. A general index of vulnerability and hierarchy between mechanisms is thereby provided. Verification of safety against local mechanisms can also be carried out using the kinematic approach. This procedure is based on evaluating the horizontal action needed to activate out-of-plane collapse mechanisms. Based on a full-scale study (Sion Cathedral), this paper evaluates the reliability of the “LV1-church” approach and of the kinematic approach through a comparison with the results obtained with a complex 3D model using the Applied Element Method.

Full text

SEISMIC VULNERABILITY ASSESSMENT OF “SION CATHEDRAL”
(SWITZERLAND): AN INTEGRATED APPROACH TO DETECT AND
EVALUATE LOCAL COLLAPSE MECHANISMS IN HERITAGE
BUILDINGS
L. Diana*, Y. Reuland* and P. Lestuzzi*
* École Polytechnique Fédérale de Lausanne (EPFL), Applied Computing and Mechanics Laboratory
(IMAC), EPFL ENAC IIC IMAC, Station 18, CH-1015 Lausanne, Switzerland
e-mails: lorenzo.diana@epfl.ch, yves.reuland@epfl.ch, pierino.lestuzzi@epfl.ch
Originally published in Prohitech ’17 proceedings (2017): 3rd International Conference on
Protection of Historical Constructions - 12 - 15 july 2017 . Lisbon | Portugal
Keywords: Seismic vulnerability assessment; Masonry structures; Local mechanisms;
Architectural heritage, Non-linear time-history analysis.
Abstract. Seismic assessment of existing heritage buildings remains a challenging task. There
is a high level of complexity and uncertainty compared with the assessment of standard
buildings. Heritage masonry churches are usually prone to partial collapses during earthquake
due to local loss of stability, and exhibit particular seismic vulnerabilities. An important step in
the seismic analysis of heritage masonry buildings is the detection of local mechanisms. The
Italian Building Code provides a simplified approach (LV1-churches) to assess the vulnerability
of heritage churches evaluating and comparing 28 potential mechanisms. A general index of
vulnerability and hierarchy between mechanisms is thereby provided. Verification of safety
against local mechanisms can also be carried out using the kinematic approach. This
procedure is based on evaluating the horizontal action needed to activate out-of-plane collapse
mechanisms. Based on a full-scale study (Sion Cathedral), this paper evaluates the reliability
of the “LV1-church” approach and of the kinematic approach through a comparison with the
results obtained with a complex 3D model using the Applied Element Method.
1 INTRODUCTION
Seismic vulnerability assessment of existing masonry buildings is a complex task.
Several difficulties need to be overcome, mainly related to heritage structures. Primary
uncertainties regard structural characteristics, materials properties, design drawings
and a general lack of knowledge of construction techniques. To overcome such
problems in seismic vulnerability assessment of existing historical masonry buildings,
chronological investigations, in situ surveys and experimental tests would be needed.
Unfortunately, some of these refined investigations cannot always be carried out due
to heritage preservation requirements. Approaches based on simplified mechanical,
statistical or qualitative models can be a useful tool for preliminary seismic assessment.
From the large amount of heritage masonry buildings, churches stand out as
particularly vulnerable for their architectural, typological and construction features [1].
Continuous additions of structural components, plan extensions, chronological
overlapping of construction techniques, the presence of thrusting elements and big
windows, weaken the structural response to seismic loads.

2
The analysis of existing masonry churches affected by previous seismic events has
shown local collapse is expected instead of a global failure [2]. Poor brick corner
teething, inadequate connections between structural components, absence of rigid
floors and roof undermine the distribution of seismic forces between vertical resisting
elements for a global response. Single components behave as rigid isolated elements
undergoing out-of-plane failure [3]. Detection of local collapse mechanisms is a
challenge of particular importance for seismic analysis of heritage masonry buildings.
It involves many considerations and usually requires expert knowledge from previous
post-earthquake assessments.
This paper includes a study on the seismic vulnerability assessment of a stone
masonry heritage building, the “Sion Cathedral”. The building is located in Sion, in the
Canton of Valais. The Canton of Valais contains the highest seismic-hazard region in
Switzerland with a peak ground acceleration of 1.6 m/s2. For the city of Sion a specific
microzonation study is available [4]. The “Sion Cathedral” belongs to the microzone
MA3. The paper compares three different methodologies, characterized by an
increasing in-depth analysis. The goal is a cross-validation of the three approaches in
order to obtain a possible procedure for assessing heritage masonry churches. This
paper continues the study on heritage masonry buildings in the city of Sion, started
with the seismic assessment of the “Ancient Hôpital” [5, 6, 7].
A preliminary method taken from the Italian Building Code [8] is firstly performed. It
provides an approach, based on a simplified mechanical model, to assess the
vulnerability of heritage churches. The method using a standardized form (LV1-
churches) evaluates and compares 28 potential local mechanisms. The objective is to
determine the hierarchy between local collapse mechanisms and to provide a general
index of vulnerability, iv. Such an index is useful for comparisons on a regional scale
with other heritage churches. In addition, the most dangerous local collapse
mechanisms highlighted by the LV1-form have been studied using a detailed kinematic
approach [9, 10]. Verification of safety against local mechanisms can be carried out by
the kinematic approach if the walls are supposed to behave as rigid body and no local
disaggregation of masonry is admitted. The procedure is based on the definition of
appropriate collapse mechanisms and on the evaluation of the horizontal action that is
needed for their activation. Finally, a refined 3D model using the Applied Element
Method (AEM) has been developed for the entire cathedral. The AEM has the implicit
capacity to predict a large range of typical masonry failure mechanisms. A continuous
structural element of discrete materials is simulated as virtual elements connected
through springs [11]. Therefore, earthquake simulations using AEM incorporate large
displacements that lead to progressive formation and opening of separation joints. The
model has been developed to validate the previously obtained results.
2 INFORMATION ABOUT THE SION CATHEDRAL
The “Sion Cathedral” (or the “Cathedral of Our Lady of Sion”) is the seat of the
Diocese of Sion. The current gothic cathedral has been built at the end of the 15th
century on the foundations of a previous Romanesque church. The building is located
within the city of Sion, representing an isolated structure, without any connection with
surrounding buildings.
Early sources report an original Carolingian church of the 8th century destroyed by
fire in 1010. A second cathedral, in Romanesque style, has been built during the 11th
century. The massive bell tower has been built between the 12th and the 13th century

3
with the addition of the last stage and the masonry spire in 1403. After a sequence of
fire and rubbery, the church, still in function, needed important restauration measures.
Between the end of the 15th and the beginning of the 16th century the current gothic
church has been constructed. In 1947-1948 two bays have been added to the apse.
Last restauration works took place in 1986. Under the first part of the apse, an
interesting crypt, dating back to the Romanesque period, is present [12].
The “Sion Cathedral” is a stone masonry building, with overall plan maximal
dimensions of 64 m x 37 m (see Figure 1a). External views of the south and west
building facades are shown in Figure 2a and 2b. A cross-section of the bell tower is
reported in Figure 1b.
The church is cruciform in plan with the interior covered by cross vaults. The nave,
which has 3 bays, is 25 m long and 8 m wide to pillars and rises to 15 m in keystone
of cross vaults. The massive cruciform pillars (2.85 m2 in base section) separate the
main nave from the two aisles. The two aisles are 4.40 m wide and rise to 9.30 m. The
transept, 28 m wide, is composed of 3 cross vaulted bays, high as the nave vaults. In
axis with the nave, the apse is 18.50 m long, raised at least 1 m above the level of the
rest of the church. Three chapels surround the transept, two in the north side and one
in the south side. The Saint-Barbe chapel, in the south east corner, is the oldest one
(dated 1474). In the west side, the entrance is surmounted by a tall and massive bell
tower having a height of approximately 35 / 40 m to the top of the spire. An important
entrance is present in the south facade. The general thickness of the walls is about
1.00 m. Impossibility of inspection undermines the evaluation of the total external
height.
The structure of the “Sion Cathedral” is composed of masonry walls defining the
internal space of the church mainly covered with cross vaults. A timber and slate tile
roof covers the vault system. The uncertainties about the top are due to the
impossibility to visit the extrados of cross vaulted structure and to obtain clear cross
section drawings. Assessing the quality of masonry typology by hole drilling has been
impossible.
The external and internal outer layer of walls is covered by plaster, except in the
corners where type, arrangement, state and characteristics of stones can be seen. The
stones used are regularly shaped, but with different dimensions. The masonry walls
show a good corner brick teething. The horizontal thrust of the roof, of arches and
vaults is supported by the presence of massive buttresses all around the walls of the
church. The presence of such buttresses is a good protection against seismic actions.
In the transept, the presence of several metal rods contributes to the box behaviour of
walls and to the protection against seismic actions and local overturning. The general
state of conservation of the structure is good. Little and non-dangerous cracks are
identified in the south facade, in the nave vaults and in the upper wall of the colonnade.

4
a) b)
Figure 1: Plan (a) and cross section of the bell tower (b) of Sion Cathedral
Figure 2: West facade (a) and south facade (b) of Sion Cathedral
3 SIMPLIFIED APPROACH
3.1 Analysis of a simplified index of vulnerability
The Italian Building Code, through the application of a simplified survey-form based
on mechanical models, provides a qualitative method to assess the general
vulnerability of masonry churches [8]. The goal of the church survey-form (LV1-
churches) is the assessment of the global index of vulnerability, iv. Such an index is
useful for comparisons on a regional scale with other heritage churches. The form
evaluates and compares 28 potential local mechanisms. The assessment consists of
two complementary shares: vulnerability indicators and specific seismic
reinforcements. Vulnerability indicators include poor masonry, presence of thrusting
elements such as vaults and arches, as well as big windows that are considered as
weaknesses for the portion analysed. On the other hand, seismic reinforcements
comprehend buttresses, tie rods, brick teething and devices reducing the vulnerability

5
of the mechanism. In Table 1 a specific evaluation form for the mechanism of the
overturning of facade is shown.
The global index of vulnerability is given by the following expression:
 
28
128
1
11
62
k ki kp
k
v
k
k
vv
i








(1)
where:
iv is the global index of vulnerability;
k are the twenty-eight possible collapse mechanisms;
ρk is the importance weight of the mechanism (between 0.5 and 1.0; equal to 0 if
the mechanism is absent) ;
vki is the generic score evaluated for the examined mechanism in term of
vulnerability;
vkp is the generic score evaluated for the examined mechanism in term of protection
devices.
The evaluation of the vki and vkp score is obtained from the survey-form and a
standardization process. By the global index of vulnerability, iv, it is possible to define
the seismic limit acceleration,
*()g SLU
a
, that the structure is supposed to resist to:
5.1 3.44
*()
0.025 1.8 iv
g SLU
a

(2).
The application of the LV1-church form is shown in Table 2 with each mechanism
evaluated in term of vki, vkp, ρk and ivk. The ivk index is the local index of vulnerability
and is defined as the difference between vki and vkp. The global index of vulnerability,
iv, obtained is 0.55 (see Table 3), leading to seismic limit acceleration
*()g SLU
a
equal to
1.606 m/s2. The comparison with the seismic demand leads to a value of the safety
coefficient αeff equal to 1.24. For the microzone of Sion MA3 where the church is
situated [4], the seismic demand, with an importance factor γ1 = 1.2 and assuming a
strength reduction factor q = 2, is equal to [13]:
12
() 1.84 1.2 1.296
2
gd
g SLU
a
a m s
q


  
(3).
By Table 2, it is possible to prove that the most dangerous mechanisms are
highlighted by high values of the local index of vulnerability ivk. These are: the
mechanism related to the apse roof elements (N. 21) and the mechanism of the belfry
(N. 28), both with ivk equal to 2.
Other important mechanisms are those with high values related to local vulnerability
aspects (vki = 3); this because of the uncertainties related to the evaluation of the real
capacity of same existing protection devices (especially metal rods). It is possible to
identify: overturning of the south facade (N. 1); apse overturning (N. 16); in-plane shear
mechanism in the apse (N. 17); mechanisms related to the bell tower (N. 27). All these
mechanisms have the index of local vulnerability aspects vki equal to 3.
In relation to simplified evidences of LV1-church survey form, it must be underlined
that the belfry, during the latest significant seismic event in this region in 1946, was the
only section of the cathedral that has been subjected to damage. This damage is still

6
visible by the presence in the upper mullioned windows of the bell tower of timber
support elements.
Table 1: Section of the LV1-churces form related to the mechanism of the overturning of the
facade.
01 - Overturning of the facade
Possibility of activation of collapse mechanism: YES [ ] NO[ ]
YES
NO
Seismic protection devices
Importance
[ ]
[ ]
Presence of metal chains
[ ] [ ] [ ]
[ ]
[ ]
Presence of counter-action elements
[ ] [ ] [ ]
[ ]
[ ]
Good brick corner teething
[ ] [ ] [ ]
[ ]
[ ]
………………………………….
[ ] [ ] [ ]
YES
NO
Vulnerability aspects
Importance
[ ]
[ ]
Presence of pushing elements (arches, vaults, hip beam)
[ ] [ ] [ ]
[ ]
[ ]
Presence of big windows
[ ] [ ] [ ]
[ ]
[ ]
………………………………….
[ ] [ ] [ ]
Table 2: Application of the LV1-church form to the Sion Cathedral
Mechanism number
Mechanism
ki
v
kp
v
k

vk
i
1
Overturning of south facade
3
3
1
0
2
Collapse of the top of the facade
-
-
0
-
3
In-plane mechanism of the facade
-
-
0
-
4
Narthex
-
-
0
-
5
Cross response of the church
2
2
1
0
6
In-plane shear mechanism of the side facade
2
2
1
0
7
Lengthwise response of the colonnade
2
1
1
+1
8
Nave vaults
1
0
1
+1
9
Aisles vaults
0
0
1
0
10
Overturning of the transept walls
2
3
1
-1
11
In-plane shear mechanism of the transept walls
2
2
1
0
12
Transept vaults
1
0
1
+1
13
Triumphal arches
0
1
1
-1
14
Dome - tambour
-
-
0
-
15
Lantern
-
-
0
-
16
Apse overturning
3
3
1
0
17
In-plane shear mechanism in apse
3
2
1
+1
18
Apse vaults
1
0
1
+1
19
Nave and aisles roof elements
1
2
1
-1
20
Transept roof elements
1
0
1
+1
21
Apse roof elements
2
0
1
+2
22
Overturning of chapels
1
1
1
0
23
In-plane shear mechanism in chapels
1
2
1
-1
24
Chapels vaults
0
0
1
0
25
Interaction with irregular elements
2
2
1
0
26
Projections
-
-
0
-
27
Bell tower
3
2
1
+1
28
Belfry
3
1
1
+2

7
Table 3: Value of global index of vulnerability, seismic limit acceleration, seismic demand and
safety factor
v
i
Seismic limit
*2
()g SLU
a m s


Seismic demand
2
()g SLU
a m s


 
eff


0.55
1.606
1.296
1.24
4 KINEMATIC ANALYSIS OF COLLAPSE MECHANISMS
4.1 Linear and non-linear approaches
Local collapse mechanisms can be evaluated by the limit equilibrium analysis
according to linear and non-linear kinematic approaches with conventional rigid body
mechanics [2, 9]. The procedure is based on the analysis of appropriate collapse
mechanisms and on the evaluation of the horizontal load multiplier (α0) that leads to
their activation [10]. Therefore, the application of such analyse needs initial detection
of mechanisms that may activate during a seismic event. These mechanisms can be
identified on the basis of the presence of pre-existing cracks or by considering the
damage experienced by similar structures under previous seismic actions. In addition,
the quality of masonry element connections, the masonry arrangement and
interlocking as well as the presence of elements such as ties or ring beams must be
taken into account when defining possible collapse mechanisms.
In particular, for the linear analysis, the spectral acceleration,
*
0
a
, activating the
mechanisms, is given by the following expression:
*0
0*
g
ae


(4)
where:
g is the gravitational acceleration;
α0 is the load multiplier for the activation of the mechanism;
e* is the fraction of mass participating to the mechanisms.
The linear safety of the structure against the considered collapse mechanism is
satisfied if:
*
0 ( )g SLU
aa
(5)
where
()g SLU
a
is the seismic acceleration demand obtained from Eq. (3).
Then, through a nonlinear kinematic analysis, the capacity curve that describes the
evolution of the load multiplier α for displaced configuration of the element can be
determined as a function of the displacement dk of a control point. In terms of
equivalent single degree of freedom (s.d.o.f.) systems, it is possible to define the
spectral capacity curve (a* − d*). The ultimate displacement capacity of the element,
du*, is taken as the minimum between the 40% of the spectral displacement d0*
corresponding to the null value of a* and the displacement that causes local instability
(e.g. beams slip out of walls) [10, 13, 14]. The displacement demand, Δd = SDe(Ts), is
defined on the response spectrum, as the elastic displacement demand at a certain
secant period Ts. The Italian Building Code defines the secant period Ts as:

8
*
*
2s
ss
d
Ta


(6)
where
**
0.4
su
dd
and
0
*
**
0
*
1s
sd
d
aa

 



.
The non-linear safety against the considered collapse mechanism is satisfied if:
*
ud
d
(7).
4.2 Verification of the local mechanisms
The analysed local collapse mechanisms are: overturning of the south facade;
overturning of the apse; vertical bending of the apse; mechanisms of the central arch.
These collapse mechanisms have been chosen as the most dangerous identified by
the LV1-form. The central arch has been added as a term of comparison. In the case
of the central arch the analysis of the mechanism has been carried out with the support
of software Mc4 Loc (Mc4 Software ®). The apse roof elements (ivk = 2) have not been
taken into account due to lacking of information on the junction of the roof elements to
the wall. The same lack of information has been found concerning the belfry (ivk = 2)
and the bell tower (vki = 3).
First, the linear verification is carried out and the results are summarized in Table 4.
The data provided are: the horizontal load multiplier α0 for the activation of the collapse
mechanism; the participant mass M*, evaluated considering the virtual displacement of
the point of application of vertical loads as a modal shape; the fraction of mass e*
participating to the mechanisms; the seismic spectral acceleration a*0 activating the
mechanism associated to the equivalent s.d.o.f. system; the demand in terms of
acceleration ag(SLU); the safety factor αeff is calculated considering an importance factor
γ1 = 1.2.
The obtained linear safety factor for the vertical bending of the apse is higher than
one and the mechanism related to the central arch is slightly below one. The safety
factors of the overturning of the south facade and of the overturning of the apse are
widely under one, underlining the risk related to these mechanisms.
The verification was also carried out by a kinematic non-linear approach, taking into
account the ultimate displacement capacity of the macro-elements. The results are
summarized in Table 5. The data provided are: the spectral displacement d0*
corresponding to a null value of a*; the ultimate spectral displacement d u * associated
to the equivalent s.d.o.f. system and the corresponding ultimate acceleration a*u; the
secant displacement d*s and the secant acceleration a*s, necessary for the
determination of the secant period Ts; the displacement demand Δd(Ts).
In the case of non-linear verification, the safety factors are all above one. In general
the non-linear verification provides higher safety factors than the linear verification,
meaning a more reliable prediction compared to the results from numerical model (see
Section 5). Only vertical bending shows a non-linear safety factor lower than that
provided by linear analysis. In Figure 3 overturning of the south facade is shown.

9
Table 4: Results of the linear analysis
Mechanism
Load
multiplier
α0
[-]
Participant
mass
M*
[kNs2/m]
Fraction of
part. mass
e*
[-]
Spectral
accel.
a0*
[m/s2]
Seismic
demand
ag(SLU)
[m/s2]
Safety
factor
αeff
[-]
Overturning south facade
0.095
561.33
0.98
0.948
1.296
0.73
Overturning of the apse
0.091
240.89
0.97
0.920
1.296
0.71
Vertical bending of the apse
0.362
245.05
0.98
3.618
1.296
2.79
Central Arch
0.149
330.37
0.85
1.276
1.296
0.98
Table 5: Results of the non-linear analysis
Mechanism
Spectral
displ.
d*0
[m]
Ultimat
e displ.
d*u
[m]
Secant
displ.
d*s
[m]
Ultimate
accel.
a*u
[m/s2]
Secant
accel.
a*s
[m/s2]
Secant
period
Ts
[s]
Displ.
deman
d
Δd(Ts)
[m]
Safety
factor
αeff
[-]
Overturning south facade
0.625
0.250
0.100
0.569
0.797
2.23
0.168
1.49
Overturning of the apse
0.806
0.300
0.080
0.692
0.829
1.95
0.166
1.21
Vertical bending of the
apse
0.561
0.200
0.080
2.329
3.102
1.01
0.118
1.69
Central Arch
0.975
0.390
0.156
0.766
1.072
2.50
0.168
2.32
Figure 3: Overturning of the south facade mechanism: example of the mechanism and
spectral capacity curve (a*-d*) with non-linear verification.
5 NUMERICAL MODEL OF THE CHURCH
A numerical model was built using the Applied Element Method (AEM) [15]. The
AEM has the implicit capacity to describe possible failure mechanisms that are typical
for masonry buildings. With AEM, the structure is modelled as an assembly of small
elements. The elements are connected by normal and shear springs, located at the
edges of the elements. Spring properties directly represent material features and are
used to determine strains, stresses and failure criteria. The model developed using
AEM thereby has the implicit capacity to predict a large range of typical masonry failure
0.000
1.000
2.000
3.000
4.000
5.000
6.000
7.000
0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700
a*[m/s2]
d*[m]
ADSR spectrum
Spectral capacity curve
Δd (Ts)
(d*s ;a*s)
ADRS spectrum
Spectral capacity curve
(d*u ;a*u)

10
mechanisms. Therefore, earthquake simulations using AEM incorporate large
displacements that lead to progressive formation and opening of separation joints. The
model is here used to validate the previously obtained results.
The material behaviour is shown is Figure 4. Masonry behaviour is supposed to be
similar to concrete, using Maekewa compression model [16]. The compression stress-
strain diagram is defined by the initial Young’s modulus, the fracture parameter and
the compressive plastic strain (see Figure 4a). For the springs subject to tension, the
stiffness equals the initial stiffness until reaching of cracking point. After cracking,
stiffness of spring subject to tension is set to be equal to zero. The material cracks
when the major principal stress reaches the tensile strength [17]. The relationship
between shear strains and stresses (see Figure 4b) is supposed to remain linear till
the cracking of the material. After that, the stresses drop down. The height of the drop
depends on the aggregate interlock and friction at the crack surface. When the
separation strain is reached, all the springs on the edge of the contact surface are cut.
Separation strain represents the strain at which adjacent elements result totally
separated. When elements are separated, if contact occurs again, they behave as rigid
bodies. The new contacts are ruled by the normal and shear contact stiffness factors,
the contact spring unloading stiffness factor and the friction coefficient [5, 6, 7].
Regarding the “Sion Cathedral”, specific in situ in-depth surveys and experimental
tests have not been performed. The material parameters have been chosen using
Table C8A.2.1 of the Italian “Circolare Esplicativa NTC 2008 n° 617 del 02/02/2009”
(pag. 403) for a masonry stone building with regular shaped stones with good
arrangement and mortar. The material properties are reported in Table 6.
Figure 4: Assumed material behaviour: (a) tension/compression, (b) shear (pictures taken
and adapted from [17]).
Table 6: Mechanical parameters for masonry
Unit
weight
[kN/m3]
Young’s
modulus
[N/mm2]
Shear
modulus
[N/mm2]
Tensile
strength
[N/mm2]
Compressi
ve
strength
[N/mm2]
Separation
strain
[-]
External
damping ratio
[-]
22
3840
1128
0.60
8
0.1
0
5.1 Seismic input
For the city of Sion, a specific microzonation study is available and provides the
design spectra according to a return period of 475 years [4]. The “Sion Cathedral” is
situated in the middle of the microzone MA3. The response spectrum of microzone
MA3 is plotted as a dashed line in Figure 5b. The earthquake record chosen from
a)
b)

11
international databases for the non-linear dynamic analysis has been the Record ESD
198
1
, reported in Figure 5a, cut after 18 seconds. The earthquake is the same chosen
for similar studies in Sion [5, 6, 7 ], so to have a term of comparison of the building
behaviour. The response spectra in X (N-S) and Y (E-W) directions are plotted in
Figure 5b.
5.2 Non-linear analysis results
The non-linear dynamic analysis was performed considering the accelerations
reported in section 5.1. After such analysis, the bell tower is found to be the most
vulnerable part of the church, in particular the upper part, which presents high damage
and important out-of-plane failures. Most of the external walls of the church do not
suffer damage. Some cracks and elements loss of connectivity can be identified in the
last arch of the apse, in the upper part of the corner wall S-W and in the roof elements.
The resulting damage state of the church after the application of the seismic
registration can be seen at Figure 6. Some cracks and collapses appear also in the
vault-resisting system that is not shown in Figure 6. It must be stressed that for
computational reason the vault system has been modelled in a simplified. It is limited
to provide stiffness and to connect different walls and not to simulate the real behaviour
of vaults. Thus, these failures should not be considered unless a more refined and
detailed model is performed.
6 SUMMARY AND CONCLUSIONS
The seismic vulnerability assessment of the “Sion cathedral” has been performed
using increasingly complex methods. These different methodologies have been
applied in order to provide a possible procedure to follow in the seismic analysis of
such type of heritage masonry structures. The AEM model is used to cross-validate
the results previously provided by a simplified approach of the LV1-church form and
by a kinematic approach.
The model predictions validate the mechanism that has been identified to be the
most vulnerable by the LV1-form (the mechanism related to the belfry). After a dynamic
time-history simulation of an historic earthquake, the belfry (and in general the upper
part of the bell tower) sustains important damage and out-of-plane failure. The other
vulnerable elements stressed by the form were the apse roof elements that do not
suffer direct damage. It must be stressed that some cracks are shown anyway in the
last arch of the apse, meaning the weakness of this part of the church. The global index
of vulnerability (iv = 0.55) and the related safety factor (αeff = 1.24) provided by the form
has a general reliable evidence if related to the performance shown by the model.
The other mechanisms identified as possible vulnerable elements are studied in
depth by the kinematic approach, both linear and non-linear. The results provided by
the linear approach seem to be over-conservative. Three mechanisms (overturning of
the south facade, overturning of the apse and the mechanism of the central arch) have
safety factors that are below one, according to linear verification. In the non-linear
verification, all the safety factors exceed one. Therefore, the non-linear verification
seems to be more realistic and consistent with the damage configuration provided by
the AEM model that does not show important cracks for the aforementioned
mechanisms.
1
Record ESD 198 (European Strong Motion Database, Montenegro Earthquake, MS=7.1, PGA = 0.224g) [18]

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To improve the seismic assessment on the “Sion cathedral”, in the next future other
time-history dynamic analyses will be performed on the model with other seismic
registrations that fit with the response spectrum of the microzone MA3. Furthermore,
a detailed model concerning exclusively one or two bays of the nave and the aisles will
be carried out in order to validate the behaviour of the vault system.
Figure 5: Record ESD 198 (European Strong Motion Database, Montenegro Earthquake,
MS=7.1, PGA = 0.224g) [18]: recorded ground accelerations in X and Y directions (a) and
elastic response spectra for 5% damping together with response spectrum of microzone Sion
MA3 (b).
Figure 6: Damage distribution in the model after 18 seconds.
a)
b)

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