Modal Parameter Variation of an Earthquake Damaged Building

  • Antonio A. Aguilar
  • Ruben L. Boroschek
  • Leonardo M. Massone
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


On February 27, 2010 one of the largest magnitude earthquake ever registered occurred in Chile. Although, several tall buildings suffered damage without collapse, the response of these buildings, in general, has been considered a success. Several studies have been carried out to understand the seismic response of these damage buildings, in order to develop appropriate retrofit strategies. We have selected one building located in the coastal city of Viña del Mar for instrumentation. This area suffered strong shaking with peak ground acceleration close to 0.35 g and more than 180 s of motion. The structure is a residential shearwall building with 17 stories and one basement level. The main structural system was damaged at the basement and first floor levels. The main damage was concrete crushing of walls, along with longitudinal reinforcement buckling at wall boundaries and severe cracking of slabs and lintel beams. An array of 12 accelerometers was deployed in the building to evaluate its modal properties variations, recording five aftershocks. This publication presents the structural damage in the building and the preliminary system identification results from strong motion records. Variations of the modal parameters are correlated with motion amplitudes and compared with ambient vibration conditions.


SHM Chile earthquake Damping System identification 


\( \left\{ {{x_k}} \right\} \)

State vector on k.

\( \left[ A \right] \)

Discrete system matrix.

\( \left[ C \right] \)

Output matrix.

\( \left\{ {{w_k}} \right\} \)

Process noise vector

\( \left\{ {{v_k}} \right\} \)

Measurement noise vector.

\( i \)

i-th mode.

\( {\lambda_i} \)

Eigen value from continuous system matrix.

\( {\mu_i} \)

Eigen value from discrete system matrix.

\( \Delta t \)

Sample time.

\( {\omega_i} \)

Angular frequency.

\( {\xi_i} \)

Damping ratio.

\( \left[ \phi \right] \)

Modal shape.

\( \left[ \Psi \right] \)

Eigen vector from discrete system matrix.

\( a{g_j}(t) \)

Recorded base acceleration. Direction j.

\( {L_{{i,j}}} \)

Modal participation ratio for base acceleration in direction j.

\( {\phi_{{i,p}}} \)

Modal shape vector at position p.

\( {y_i}(t) \)

Modal response.

\( {a_p}(t) \)

Estimated acceleration of MIMO algorithm at position p.

\( E \)

MIMO goodness of fit error.

\( {\alpha_p} \)

Weight coefficient at position p in MIMO goodness of fit error.


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Copyright information

© The Society for Experimental Mechanics, Inc. 2012 2012

Authors and Affiliations

  • Antonio A. Aguilar
    • 1
  • Ruben L. Boroschek
    • 1
  • Leonardo M. Massone
    • 1
  1. 1.Civil Engineering DepartmentUniversity of ChileSantiagoChile

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