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A vector-valued ground motion intensity measure incorporating normalized spectral area

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Abstract

A vector-valued intensity measure is presented, which incorporates a relative measure represented by the normalized spectral area. The proposed intensity measure is intended to have high correlation with specific relative engineering demand parameters, which collectively can provide information regarding the damage state and collapse potential of the structure. Extensive dynamic analyses are carried out on a single-degree-of-freedom system with a modified Clough–Johnston hysteresis model, using a dataset of 40 ground motions, in order to investigate the proposed intensity measure characteristics. Response is expressed using the displacement ductility, and the normalized hysteretic energy, both of which are relative engineering demand parameters. Through regression analysis the correlation between the proposed intensity measure and the engineering demand parameters is evaluated. Its domain of applicability is investigated through parametric analysis, by varying the period and the strain-hardening stiffness. Desirable characteristics such as efficiency, sufficiency, and statistical independence are examined. The proposed intensity measure is contrasted to another one, with respect to its correlation to the engineering demand parameters. An approximate procedure for estimating the optimum normalized spectral area is also presented. It is demonstrated that the proposed intensity measure can be used in intensity-based assessments, and, with proper selection of ground motions, in scenario-based assessments.

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Abbreviations

EDP :

Engineering demand parameter

IM :

Intensity measure

M :

Moment magnitude

N :

Sample size

NHE :

Normalized hysteretic energy

R :

Distance from fault

R y :

Yield reduction factor

\( S_{a} \left( {T_{1} } \right) \) :

Spectral acceleration at period T 1

\( S_{d} \left( {T_{1} } \right) \) :

Spectral displacement at period T 1

\( S_{dN} \left( {T_{1} ,T_{2} } \right) \) :

Normalized spectral area

SD :

Significant duration

T 1 :

Natural period of system

T 2 :

Elongated period of system

T eq :

Equivalent natural period

T N :

Normalizing constant

V S30 :

Shear wave velocity in the top 30 m of the ground

f y :

Yield strength

f 0 :

Maximum elastic force

k e :

Elastic stiffness

k eq :

Secant stiffness

k s :

Strain-hardening stiffness

m :

Mass

u :

Response displacement

\( \dot{u} \) :

Response velocity

\( {\ddot{u}} \) :

Response acceleration

\( {\ddot{u}}_{g} \left( t \right) \) :

Ground acceleration

u m :

Maximum displacement demand

u y :

Yield displacement

u 0 :

Maximum elastic displacement

α :

Strain hardening coefficient

α s :

Significance level

ε :

Epsilon

\( \zeta \) :

Viscous damping ratio

\( \zeta_{eq} \) :

Equivalent damping ratio

\( \mu_{d} \) :

Displacement ductility factor

\( \lambda \left( x \right) \) :

Mean annual frequency of exceeding variable x

ρ :

Correlation coefficient

ω n :

Natural circular frequency

Δ mean :

Mean spectral displacement

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, GU2 7XH, UK

    Aris-Artemis I. Theophilou & Marios K. Chryssanthopoulos

  2. Department of Civil Engineering, School of Mathematics, Computer Science and Engineering, City University London, London, EC1V 0HB, UK

    Andreas J. Kappos

Authors
  1. Aris-Artemis I. Theophilou
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  2. Marios K. Chryssanthopoulos
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  3. Andreas J. Kappos
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Correspondence to Aris-Artemis I. Theophilou.

Appendix

Appendix

Table 1 presents the dataset of 40 records used in the dynamic analyses.

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Theophilou, AA.I., Chryssanthopoulos, M.K. & Kappos, A.J. A vector-valued ground motion intensity measure incorporating normalized spectral area. Bull Earthquake Eng 15, 249–270 (2017). https://doi.org/10.1007/s10518-016-9959-7

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