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STRUCTURES AND THE 1755 LISBON EARTHQUAKE

CASE STUDY - THE LISBON CATHEDRAL (SÉ DE LISBOA)

Zélia Beatriz Machado Fernandes, Instituto Superior Técnico, 2010

ABSTRACT

The aim of this thesis was to evaluate the structural safety of the Lisbon Cathedral, Sé de Lisboa, in

the event of an earthquake.

A 3D model was developed with the commercial program SAP 2000® (2005), based on the

geometrical characteristics of the various parts of the building. The dimensions which could not be

measured in situ were obtained from drawings of the cathedral (available at IHRU - Instituto da

Habitação e da Reabilitação Urbana).

Simplifying assumptions were introduced in the model. Due to the absence of reliable information on

the building foundations, these were simulated as restrained embedded supports. The model was

calibrated with the values of the natural frequencies of vibration of the structure taken from in situ

measurements. By means of static analysis, the model demonstrated that the building satisfies the

loads imposed by the Code (RSA, 1983).

An earthquake was simulated by response spectrum analysis defined by Portuguese safety code RSA

(Regulamento de Segurança e Acções). The value of 1.0 (Lisbon Area A) was taken for the seismicity

of the region. Soil type III and damping coefficient of 5% were considered.

Some discrepancy was found between the linear analysis model and the damage effects attributed to

the 1755 earthquake.

It was concluded that a linear dynamic analysis is not sufficient to evaluate the safety of the building in

case of earthquake, since, for instance it does not take into account the nonlinear behaviour of

materials. However, this model provides valid information on the monument parts where the cracking

probability will be greater in case of occurrence of an earthquake with the characteristics defined by

RSA.

Key-words: Sé de Lisboa, 1755 Lisbon Earthquake, Dynamic Analysis, Seismic Behaviour

1. INTRODUCTION

The Lisbon Cathedral was classified as National Monument in 1907 (Sucena, 2004). The monument

was built in late Romanesque style (as can be seen in the narthex, naves and transept) but saw later

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addictions of Gothic style. The construction started in 1148, and it suffered several modifications until

the 20th century. Some of these were of decorative nature reflecting the taste of each period, while

others were reconstructions after the damages caused by repeated earthquakes, and especially the

one in 1755. Several rooms were also added, as the Vestry and the Chapel dedicated to St.

Bartholomew (Bartolomeu Joanes) at late 13th century and the Sacristy at early 18

th century (Castilho,

1936).

Although most of the documents about the monument were lost on the fire following the Lisbon

earthquake of 1755, there are many descriptions on what happened to the building, such as the fall

down of the south tower of the main front and the upper two levels of an original bell tower standing

above the main dome. The Lisbon earthquake of 1755 is a well documented event.

The main goal of this work is the analysis of the seismic vulnerability of the Lisbon Cathedral, Sé de

Lisboa, as it stands today.

2. METHODS

A simplified linear material behaviour analysis was carried out using SAP 2000® (2005). Based on

plans (Figure 1), photographic material and site inspection, a three-dimensional model was created.

Figure 1 – Main front photo and a ground floor plan of Lisbon Cathedral as it is today (from

IHRU).

The information obtained from the historical and arquitectural research was taken into account in the

construction of the model.

In this model were defined 20 types of frame sections for the insertion of arches and columns and 25

kinds of areas to implement the sections of walls, vaults, ceilings and stairs. In total were used 1934

frames, 7270 areas (shells) and 6330 points.

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Nevertheless the monument has at least to types of limestone masonry construction, there was no

available information on the properties and mechanical characteristics for the various types of

limestone present in the structure and so the parameters for the material were uniformed.

The material properties considered for the structural components, such as density and modulus of

elasticity, are presented in Table 1, according to Reis et al., 2006 and Oliveira, 2003.

Table 1 – Materials’ properties

Material ρ [KN/ m3] E [GPa] ν

Limestone Masonry 24 4.5 0.2

Bricks Masonry 15 2.5 0.2

Wood (oak) 5 11 0.3

All internal and external walls were of limestone masonry. Ceilings are of wood (Sacristy, Chancel and

St. Vincent Chapel) and brick masonry vaults (lateral aisles). The remaining parts are limestone

masonry (Dionísio, 2002).

Although the soil upon which the cathedral was built is mainly constituted of sands and clays (Pereira

de Sousa, 1923), there is not enough data on the characteristics of the building foundations.

Therefore, for simplicity, these were simulated as restrained embedded supports.

The earthquake action used in the analysis was the response spectrum defined by the Portuguese

safety code (RSA, Regulamento de Segurança e Acções). The value of 1.0 (Lisbon, Area A) was

taken for the seismicity of the region. Soil type III and damping coefficient of 5% were considered.

Both seismic action Types I and II were analysed. They were applied simultaneously to the x and y

directions.

The CQC (complete quadratic combination) algorithm was used for the combination of the modal

participation while the SRSS (square-root of sum-of-squares) combination was used for the directional

combination. The vertical seismic action was not considered.

The standard values of ultimate stresses (Reis et al., 2006; Tassios, 2010) (Table 2), were used for

the safety verification of the building under self-weight (static analysis) or seismic conditions (dynamic

analysis).

Table 2 – Ultimate strength

Material σ Compression [MPa] σ Tension [MPa]

Limestone Masonry ~ -6 +0.2

Bricks Masonry -3 up to -8 +0.1

Wood (oak) -50 +90

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3. RESULTS AND DISCUSSION

To analyse the seismic model simulation it was helpful to compare it with what happed in the

earthquake of 1755. An historical investigation about what happened to the structure was performed

and Table 3 presents a summary of the main conclusions.

The lapidary signatures method was used to confront the information taken from pictures and

testimonials. This method allows to determine the age of each part of the monument.

These signatures are fine traits written on one side of each stone, made by the medieval stonemason

and that identifies him as part of a school or even as an individual. It is thus possible to place each

part of the building, almost exactly, in every generation of schools and therefore in different

construction periods.

Table 3 – Damages on the cathedral in the 1755 Lisbon earthquake

North

tower

South

tower

Facade

Portal

Bell

tower

Transept

and nave

Chancel, ambulatory

and apse chapels

Pictures - ± - + ± ±

Written testimonials (1) + (1) + ± (1)

Lapidary signatures

method (Van de

Winckel,1964)

± (2) ± (2) - ± (3) ± (4) - (5)

- did not fall

+ fall completely

± partially fall

(1) there are no references

(2) did not fall from the ground floor to the first floor

(3) what remains today of the tower didn’t fall

(4) did not fall from the ground floor to women’s gallery

(5) neither the ambulatory nor the gothic apse chapels had no problem; no reference to the chancel

The modal analysis results are given in Table 4. The first mode corresponds mainly to translation in x

direction; the second mode corresponds to translation in y direction. The third mode corresponds to

torsion.

Table 4 – Modal frequencies and modal mass participation ratios

Mode Freq. UX UY UZ RX RY RZ ∑UX ∑UY ∑UZ ∑RX ∑RY ∑RZ

Hz N-S (%) E-W (%) % % % % % % % % % %

1 2.59 0.32 0.00 0.00 0.00 0.21 0.02 0.32 0.00 0.00 0.00 0.21 0.02

2 3.59 0.00 0.40 0.00 0.12 0.00 0.05 0.33 0.40 0.00 0.12 0.21 0.07

3 3.85 0.17 0.01 0.00 0.00 0.04 0.25 0.49 0.41 0.00 0.13 0.25 0.32

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Measurements made at the site showed that, the first natural frequency on NS direction (x) occurs at

2.5 Hz, the second on EW (y) direction occurs at 3.5 Hz, and the third frequency (corresponding to

torsion) occurs at 4 Hz (Oliveira, 1997).

Figure 2– First mode, corresponds to translation in x direction (N-S), view from the top

Figure 3– Second mode, corresponds mainly to translation in y direction (E-W), view from the

south facade

Figure 4– Third mode, corresponds mainly to torsion, view from the top.

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STATIC ANALISYS

Since the measured values of natural frequencies were similar to the ones of the model, analysis of

structural safety was made for dead-loads and permanent and variable loads.

Modelation results of ultimate limit states, taking into account dead-loads and variable imposed loads,

are shown in 3D graphics with coloured areas representing the tensions and compressions to which

the structure is submitted.

The software used assigns positive values to tension (towards the blue colour) and negative values to

compression (towards the fuccia colour). For comparative effects, all graphics are presented with the

same scale of colours.

Figure 5 – South view of the maxim stress (σmax) under self-weight and variable imposed

loads.

Under self-weight structural safety is assured, since no main structural damages can be detected on

the simulation. The values of tension and compression are lower than the ultimate strength for each

material.

DYNAMIC ANALYSIS

After the determination of the most relevant vibration modes, a dynamic analysis of the structure

behaviour under a seismic simulation was made.

The panels in Figure 6 shows a cross-section of the main front where the areas of greater

compression can be observed.

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Figure 6 – Minim normal Stress (σ min) at the main front (left) and at a longitudinal section of

the Cathedral which comprises the internal wall of one of the towers (right), both under seismic

combination.

The panels in Figure 7 shows a cross-section of the main front where the areas of greater tension can

be observed on the frames. These are likely zones where the building may crack under seismic

activity. Nevertheless, historical record of 1755 Lisbon earthquake indicates that at least the ground

floor facade portal did not fall down.

The lower panel of Figure 7 shows a longitudinal cross-section of the Cathedral, which comprises the

internal wall of one of the towers. The areas showing greater tension are the bottom of the bell tower

and the connection areas of the front towers to central nave.

Figure 7 – Maxim normal Stress (σ max) at the main front (top) and at a longitudinal section of

the Cathedral, which comprises the internal wall of one of the towers (bottom), under seismic

combination. The inset in the upper panel shows the stress of the building’s under self-weight

and variable imposed loads combination.

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The model, as it is, does not give any indications as to why the South front tower felt down in 1755

while the North tower remained intact. The reason for this could be a different type of the foundations

soil.

There is a discrepancy between the model and the recordings from 1755, which indicates that a linear

analysis, as the one made here, is not enough to verify the safety of the building. This kind of analysis

does not take into account the non-linear behaviour of the materials nor the soil/structure interaction.

In Figure 8 can be seen the areas in the building that were in compression in seismic simulation as

indicated in the areas red and orange.

Figure 8 – Minim stress (σ), under seismic combination, view from below.

Nevertheless, although simple, the model is valid to reveal the main parts in tension within the

cathedral’s structure (as indicated by the blue and green areas in the simulation results, Figure 9).

Figure 9 – Maxim stress (σ), under seismic combination, view from below.

PRESENT TIME versus 1755

During the last two centuries, the cathedral underwent different repair operations which

consisted in restoring its characteristics before the great earthquake. The only differences between the

building as we know at present and the building of 1755 were the inexistence of the room above the

sacristy and of two floors above the bell tower.

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These modifications did not cause any relevant changes on what the modelation is concerned. Figure

10 shows a seismic simulation on the actual structure and on the structure of 1755.

Figure 10 – Maxim stress (σ) at a longitudinal section of the Sé, under seismic simulation, at

present (left) and in 1755 (right).

The simulation of a seismic situation, both for 1755 and today, showed that the parts with the highest

cracking probability were the connections of the bell tower to the nave and transept, and the

connections of the front towers to the nave. The simulations are in agreement with what happened in

1755.

4. CONCLUSIONS

It was possible to obtain a model of the structural behaviour of the "Sé de Lisboa" for the present

situation and according to the building natural frequencies.

Under dead-loads and variable imposed loads, the model shows that the safety of the cathedral is

assured for the ultimate limit states.

There is a discrepancy between the model and the recordings from 1755, which indicates that a linear

dynamic analysis is not sufficient to evaluate the safety of the building in case of earthquake, since, for

instance, it does not take into account the nonlinear behaviour of materials nor the soil/structure

interaction. However, this model provides valid information on the monument parts where the cracking

probability will be greater in case of occurrence of an earthquake with the characteristics as defined by

RSA.

A detailed non-linear analysis, including the soil-structure interaction, should be considered in the near

future.

In this context, it would also be important to perform a new campaign for better characterization of

modal frequencies in situ

5. ACKNOLEDGEMENTS

I would like to express my gratitude to Dean of Chapter Canon Manuel Alves Lourenço, Prof. Carlos

Sousa Oliveira and Ana Bicho

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6. LITERATURE

Castilho, J. (1936) Lisboa Antiga, Bairros Orientais Vol. V e VI, 3ª Edição revista e ampliada com

anotações Eng. Augusto Vieira da Silva, Câmara Municipal de Lisboa, Lisboa.

Dionísio, M. A. A. R. (2002) Degradação da pedra em edifícios históricos. O caso da Sé de Lisboa,

Tese apresentada à Universidade Técnica de Lisboa para obtenção do grau de Doutor em

Engenharia de Minas, Lisboa.

Oliveira, C.S. (1997) Frequências próprias de estruturas com base em medições in–situ, 3ª

Conferência Nacional de Engenharia Sísmica, Instituto Superior Técnico, Lisboa.

Oliveira, C.S. (2003) Seismic Vulnerability of Historical Constructions: A Contribution, Bulletin of

Earthquake Engineering, Vol. I, pp37-82, Kluwer Academic Publishers.

Pereira de Sousa, F.L. (1923) O terramoto de 1 de Novembro de 1755 em Portugal, Um Estudo

Demográfico, Vol. I-IV, Serviços Geológicos de Portugal, Lisboa.

Reis, A. C., Farinha M. B., Farinha, J.P. B. (2006) Tabelas Técnicas, Edições Técnicas E.T.L., Lda.

Lisboa.

RSA (1983) Regulamento de Segurança e Acções para Estruturas de Edifícios e Pontes. Decreto-Lei

nº 235/83 de 31 de Maio.

SAP 2000 (2005), Integrated finite element analysis and design of structures basis analysis reference

manual v10, CSI Computers and Structures Inc.

Sucena, E. (2004) A Sé Patriarcal de Lisboa, História e Património, Ed. Sete Caminhos, Lisboa.

Tassios, T.P. (2010) Seismic Engineering of Monuments, Chapter 1, Garesky e Ansal (editors)

Earthquake Engineering in Europe, Springer, pp.1-42.

Van de Winckel, M. (1964) Atribuição de data a edifícios antigos pelo método das siglas lapidares,

aplicação deste método à Sé de Lisboa, Boletim Municipal, Nº 100, Lisboa, pp.64-68.

http://www-monumentos.pt