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Bulletin of Earthquake Engineering

, Volume 16, Issue 7, pp 3031–3056 | Cite as

Fragility analysis of the nave macro-element of the Cathedral of Santiago, Chile

  • Wilson Torres
  • José Luis Almazán
  • Cristián Sandoval
  • Fernando Peña
Original Research Paper
  • 257 Downloads

Abstract

This paper presents the fragility analysis of a typical nave macro-element of the Metropolitan Cathedral of Santiago, Chile. The analysis is carried out by using the rigid body spring model approach, in which rigid elements are connected to each other by means of axial and shear springs. The 2D model generated is initially verified by comparing modes with a 3D finite element model previously calibrated in DIANA software. The methodology used in this study is based on a set of eleven real seismic records corresponding to four major earthquakes that have affected Santiago city. Nonlinear incremental dynamic analyses together with a damage index based on stiffness degradation, which considers the relation between shear at the base and deformation of the macro-element, are used to generate the fragility curves. As a result of this study, the probability of exceedance for different damage states has been obtained based on a possible peak ground acceleration of the site. In particular, the results of the study demonstrate that the proposed damage index satisfactorily describes the damage suffered by some of the nave transverse sections of the Cathedral after the 2010 Maule earthquake (PGA 2.11 m/s2—Santiago Centro station).

Keywords

Heritage buildings Fragility analysis Nonlinear analysis Masonry building Rigid body spring model (RBSM) 

List of symbols

Ao

Effective acceleration for the site

bx

Distance between the axial and shear springs in a vertical interface

by

Distance between the axial and shear springs in an horizontal interface

C

Random variable representing the limit state of the structure

dY

Yielding displacement

dU

Ultimate displacement

Ebm

Young’s modulus of brick masonry

Erm

Young’s modulus of reinforced brick masonry

Esm

Young’s modulus of stone masonry

E0

Elastic Young’s modulus of axial stress in the interface

E*

Non elastic Young’s modulus for loading and unloading of axial stress in the interface

G0

Elastic shear modulus in the interface

G*

Non elastic shear modulus for loading and unloading in the interface

ik

Stiffness degradation index

ik2

Stiffness degradation index based on change of frequency of modes

kA

Spring stiffness values for compression loading

kA*

Spring stiffness values compression unloading

khQ

Stiffness of shear springs in horizontal direction

kvQ

Stiffness of shear springs in vertical direction

kxA

Stiffness of axial spring in X direction

kyA

Stiffness of axial spring in Y direction

mpi

Modal mass participation of the ith mode

p

Value for generation of Chilean spectrum

Pc

Probability of event C that has full compliance given a PGA value of x

Q

Variable related to the level of seismic intensity expressed in terms of PGA

Ti

Periods for generation of Chilean spectrum. Where, i could be a, b, c, or d

wf

Weighting factor based on natural frequency error

wi

Weighting factor for each mode

wϕ

Weighting factor based on modal shape error

x

PGA for which the cumulative probability is calculated

Z

Factor of seismic zonification

αJJ

Factors for generation of Chilean spectrum. Where, J could be A, V, or D

β

PGA logarithmic standard deviation for compliance with the limit state C

εAc

Strain at peak compression strength

εAr

Strain at the start of the residual stage in tension

εAt

Strain at peak tension strength

εQ*

Maximum strain reached by the shear spring

εQc

Strain at peak shear strength

φ[]

Normal cumulative distribution

ΔVb

Change in the base shear for each cycle

Δδ

Displacement of control point for each cycle

μ

PGA for which the structure reaches 50% of the cumulative probability

σAc

Peak compression strength

σAr

Strength at the start of the residual stage in tension

σAt

Peak tension strength

ωio

Frequency of the ith mode before the earthquake

ωif

Frequency of the ith mode after the earthquake

DM

Damage measure

EDP

Engineering demand parameter

MAC

Modal assurance criterion

RBSM

Rigid body spring model

Notes

Acknowledgements

The first author acknowledges the support of the Secretary of Higher Education, Science, Technology and Innovation of Ecuador (SENESCYT), through contract number 20120011. Additionally, the first author also wants to thank the financial support given by the Vicerrectoría de Investigación (VRI) of the Pontificia Universidad Católica de Chile for his research stage at the Engineering Institute, UNAM, of Mexico.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  • Wilson Torres
    • 1
  • José Luis Almazán
    • 2
  • Cristián Sandoval
    • 2
    • 3
  • Fernando Peña
    • 4
  1. 1.Faculty of EngineeringPontificia Universidad Católica del EcuadorQuitoEcuador
  2. 2.Department of Structural and Geotechnical EngineeringPontificia Universidad Católica de ChileSantiagoChile
  3. 3.School of ArchitecturePontificia Universidad Católica de ChileSantiagoChile
  4. 4.Instituto de IngenieríaUniversidad Nacional Autónoma de MéxicoMexico CityMexico

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