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Modal-based ground motion selection procedure for nonlinear response time history analysis of dual wall-frame structures

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Abstract

The dual wall-frame structure consists of a structural wall system and a rigid frame system, and there is a strong interaction between the frame and wall systems in the top and bottom of structures. Therefore, the structural response of the dual wall-frame structures is entirely different from that of the single structural system. This paper presented a modification on the modal-based ground motion selection (MGMS) procedure for concerning the distinct structural behaviour of wall-frame structures to properly consider the effect of frequency contents combination in the time domain (FCCTD) of input ground motion (IGMs) in selecting IGMs for the nonlinear response time history analysis (NLRHA) of the structure. The MGMS procedure for wall-frame structures (MGMS-WF) employed a pseudo-first mode with a uniformly distributed mode shape and selected IGMs that induced the most significant interaction of the first three modes or the pseudo-first, second and third modes from a suite of seed IGMs for the NLRHA of wall-frame structures. A comprehensive case study was conducted involving four reinforced concrete (RC) wall-frame structures with different heights and combinations of wall and frame. To verify the capability of the MGMS-WF in consistently selecting proper IGMs for the NLRHA of wall-frame structures, design spectra and conditional mean spectra with various construction conditions were employed as target spectra to select and scale seed IGMs. The results show that the seismic demands of wall-frame structures computed using the MGMS-WF-IGMs have high yet consistent reliability.

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Abbreviations

CMS:

Conditional mean spectrum

CM-UW:

Uniformly weighted closest spectra matching procedure

CM-VW:

Variably weighted closest spectra matching procedure

DS:

Design spectrum

FCCFD:

Frequency contents combination in the frequency domain

FCCTD:

Frequency contents combination in the time domain

HPR:

Hinge plastic rotation

IDR:

Inter-storey drift ratio

IGMs:

Input ground motions

MGMS:

Modal-based ground motion selection

MGMS-WF:

Modal-based ground motion selection for wall-frame structure

MSE:

Mean computed weighted mean squared error

NL-ESDOF:

Nonlinear equivalent single-degree-of-freedom system

NLRHA:

Nonlinear response time history analysis

SDOF:

Single-degree-of-freedom system

\(\mathbf{u}\) :

Displacement vector of floor

\({a}_{n}(\mathrm{t})\) :

Normalised top displacement time history of mode n

\(\overline{{d }_{ijk}}\) :

Benchmark demands ith storey of wall-frame k for motion set j

\({d}_{M}^{ijk}\) :

Seismic demands at ith storey of wall-frame k calculated using IGMs from selection method M for motion set j

\({D}_{n}\) :

Peak displacement of mode n

\({d}_{n}\) :

Displacement of ESDOFs of mode n

\({D}_{n}(t)\) :

Top displacement time history of the mode n

\({d}_{ny}\) :

Yield displacement of ESDOFs of mode n

\({F}_{sn}\) :

Restoring force of ESDOFs of mode n

\({F}_{sny}\) :

Yield force of ESDOFs of mode n

\(\mathbf{i}\) :

Influence vector

\({L}_{n}\) :

Modal excitation factor of mode n

m, c and k :

Mass, damping, and stiffness matrices

\({M}_{n}\) :

Generalised mass of mode n

\({S}_{aj}(T)\) :

Spectrum acceleration value of motion j at period T

\({S}_{a}^{t}(T)\) :

Spectrum acceleration value of target spectra at period T

\({S}_{d1}\) :

Design spectrum acceleration at 1.0 s

\({S}_{ds}\) :

Design spectrum acceleration at 0.2 s

\({t}_{k}\) :

Any time point within the duration of IGM

\({T}_{j0}\) :

Duration of motion j

\({T}_{L}\) :

Long-period transition period

\({T}_{n}^{*}\) :

Vibration period of NL-ESDOF of mode n

\(\widehat{{u}_{jn}}\) :

The maximum displacement of NL-ESDOF of mode n under motion j

\({u}_{jn}({t}_{k})\) :

Displacement of NL-ESDOF of mode n under motion j at time tk

\({u}_{rn}\) :

Roof displacement of mode n

\({V}_{bn}\) :

The base shear force of mode n

\({\alpha }_{i}\) :

Modal mass coefficient of mode i

\({\beta }_{j}\) :

Maximum modal combination factor of motion j

\({\beta }_{jk}\) :

Maximum modal combination factor of motion j at time tk

\({\Gamma }_{n}\) :

The modal participating factor of mode n

\({\updelta }_{M}^{ijk}\) :

The relative difference between the benchmark demands of motion set j and demands computed using IGMs from selection method M at the ith storey of wall-frame k

\({\phi }_{n}\) :

Mode shape of mode n

\({\phi }_{rn}\) :

Mode shape value at the roof of mode n

References

  • Abrahamson NA, Silva WJ (2008) Summary of the Abrahamson & Silva NGA ground motion relations. Earthq Spectra 24(1):67–97

    Google Scholar 

  • Ansal A, Tönük G, Kurtuluş A (2018) Implications of site specific response analysis. ECEE 2018. Geotechnical, Geological and Earthquake Engineering, vol 46. Springer, Cham

    Google Scholar 

  • ASCE (2017) Minimum design loads for buildings and other structures (ASCE/SEI 7-17). American Society of Civil Engineering, Reston, VA

    Google Scholar 

  • Baker J (2011) Conditional mean spectrum: Tool for ground-motion selection. J Struct Eng 137(3):322–331

    Google Scholar 

  • Baker J, Cornell C (2005) A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon. Earthq Eng Struct Dyn 34:1193–1217

    Google Scholar 

  • Baker J, Cornell C (2006) Spectral shape, epsilon and record selection. Earthq Eng Struct Dyn 35(9):1077–1095

    Google Scholar 

  • Baker J, Lee C (2018) An improved algorithm for selecting ground motions to match a conditional spectrum. J Earthq Eng 22:708–723

    Google Scholar 

  • Barbosa A, Ribeiro F, Neves L (2018) Influence of earthquake ground-motion duration on damage estimation: application to steel moment resisting frames. Earthq Eng Struct Dyn 46:27–49

    Google Scholar 

  • Bhanu V, Chandramohan R, Sullivan TJ (2021) Influence of ground motion duration on the dynamic deformation capacity of reinforced concrete frame structures. Earthq Spectra. https://doi.org/10.1177/87552930211033879

    Article  Google Scholar 

  • Boore DM, Atkinson GM (2008) Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5% damped PSA at spectral periods between 0.01 s and 10.0 s. Earthq Spectra 24(1):99–138

    Google Scholar 

  • Campbell KW, Bozorgnia Y (2008) NGA ground motion model for the geometric mean horizontal component of PGA, PGV, PGD and 5% damped linear elastic response spectra for periods ranging from 0.01 to 10 s. Earthq Spectra 24(1):139–171

    Google Scholar 

  • CEN (2004) Eurocode 8: design of structures for earthquake resistance-Part 1: general rules, seismic actions and rules for buildings. European Committee for Standardization, Brussels

    Google Scholar 

  • Chiou BSJ, Youngs RR (2008) A NGA ground motion relations for the geometric mean horizontal component of peak and spectral ground motion parameters. Earthq Spectra 24(1):173–215

    Google Scholar 

  • Chopra A (2017) Dynamics of structures: theory and applications to earthquake engineering, 5th edn. Pearson Prentice Hall, Upper Saddle River, NJ

    Google Scholar 

  • Chopra AK, Goel RK (2002) A modal pushover analysis procedure for estimating seismic demands for buildings. Earthq Eng Struct Dyn 31:561–582

    Google Scholar 

  • CSI SV. 18 (2018) Integrated finite element analysis and design of structures basic analysis reference manual. Computers and Structures Inc, Berkeley, CA

    Google Scholar 

  • Du W, Ning C, Wang G (2019) The effect of amplitude scaling limits on conditional spectrum-based ground motion selection. Earthq Eng Struct Dyn 48:1030–1044

    Google Scholar 

  • Du W, Yu X, Ning CL (2020) Influence of earthquake duration on structural collapse assessment using hazard-consistent ground motions for shallow crustal earthquakes. Bull Earthq Eng 18(7):3005–3023

    Google Scholar 

  • Han S, Ha S (2017) Assessment of ground motion selection criteria specified in current seismic provisions with an accurate selection algorithm. Bull Earthq Eng 15(10):1–20

    Google Scholar 

  • Hancock J, Bommer J (2007) Using spectral matched records to explore the influence of strong-motion duration on inelastic structural response. Soil Dyn Earthq Eng 27(4):291–299

    Google Scholar 

  • Huang K (2011) Continuum MDOF model for seismic analysis of wall-frame structures. Dissertation, Hong Kong University of Science and Technology

  • Kalkan E, Chopra A (2010) Modal-pushover-based ground-motion scaling procedure. J Struct Eng 137(3):298–310

    Google Scholar 

  • Katsanos E, Sextos A (2018) Structure-specific selection of earthquake ground motions for the reliable design and assessment of structures. Bull Earthq Eng 16:583–611

    Google Scholar 

  • Katsanos E, Sextos A, Manolis G (2010) Selection of earthquake ground motion records: a state-of-the-art review from a structural engineering perspective. Soil Dyn Earthq Eng 26:157–169

    Google Scholar 

  • Kayhan A, Korkmaz K, Irfanoglu A (2011) Selecting and scaling real ground motion records using harmony search algorithm. Soil Dyn Earthq Eng 31(7):941–953

    Google Scholar 

  • Kohrangi M, Kotha S, Bazzurro P (2018) Ground-motion models for average spectral acceleration in a period range: direct and indirect methods. Bull Earthq Eng 16:45–65

    Google Scholar 

  • Liu Y, Kuang JS, Huang Q (2018) Modified spectrum-based pushover analysis for estimating seismic demand of dual wall-frame systems. Eng Struct 165:302–314

    Google Scholar 

  • Liu Y, Kuang JS, Yuen Y (2020) Modal-based ground motion selection procedure for nonlinear response time history analysis of high-rise buildings. Earthq Eng Struct Dyn 49:95–110

    Google Scholar 

  • Mander JB, Priestley MJ, Park R (1988) Theoretical stress-strain model for confined concrete. J Struct Eng 114(8):1804–1826

    Google Scholar 

  • Mergos P, Sextos A (2019) Selection of earthquake ground motions for multiple objectives using genetic algorithms. Eng Struct 187:414–427

    Google Scholar 

  • Naeim F, Alimoradi A, Pezeshk S (2004) Selection and scaling of ground motion time histories for structural design using genetic algorithms. Earthq Spectra 20(2):413–426

    Google Scholar 

  • O’Donnell A, Kurama Y, Kalkan E (2017) Experimental evaluation of four ground-motion scaling methods for dynamic response-history analysis of nonlinear structures. Bull Earthquake Eng 15:1899–1924

    Google Scholar 

  • Palanci M, Kayhan A, Demir A (2018) A statistical assessment on global drift ratio demands of mid-rise RC buildings using code-compatible real ground motion records. Bull Earthq Eng 16:5453–5488

    Google Scholar 

  • Pan Y, Ventura CE, Finn WL, Xiong H (2019) Effects of ground motion duration on the seismic damage to and collapse capacity of a mid-rise woodframe building. Eng Struct 197:109451

    Google Scholar 

  • Papaspiliou M, Kontoe S (2013) Sensitivity of site response analysis on the number of ground motion records and implications for PSHA. Bull Earthq Eng 11:1287–1304

    Google Scholar 

  • PEER Ground Motion Database (2020) Pacific Earthquake Engineering Research Centre. University of California, Berkeley, CA

    Google Scholar 

  • Samanta A, Huang YN (2017) Ground-motion scaling for seismic performance assessment of high-rise moment-resisting frame building. Soil Dyn Earthq Engi 94:125–135

    Google Scholar 

  • Shakeri K, Khansoltani E, Pessiki S (2018) Ground motion scaling for seismic response analysis by considering inelastic response and contribution of the higher modes. Soil Dyn Earthq Eng 110:70–85

    Google Scholar 

  • Stafford B, Coull A (1991) Tall building structures: analysis and design. Wiley, New York

    Google Scholar 

  • Standard C (2008) Code for seismic design of buildings (GB 50011-2010). Chinese Building Press, Beijing

    Google Scholar 

  • Tarbali K, Bradley B (2016) The effect of causal parameter bounds in PSHA-based ground motion selection. Earthq Eng Struct Dyn 45:1515–1535

    Google Scholar 

  • Wang G (2011) A ground motion selection and modification method capturing response spectrum characteristics and variability of scenario earthquakes. Soil Dyn Earthq Eng 31(4):611–625

    Google Scholar 

  • Zerbin M, Aprile A, Spacone E (2020) New formulation of ductility reduction factor of RC frame-wall dual systems for design under earthquake loadings. Soil Dyn Earthq Eng 138:106279

    Google Scholar 

  • Zhang R, Wang DS, Chen XY, Li HN (2019) Weighted scaling and selecting method of ground motions in time-history analysis considering influence of higher modes. China Civil Eng J 52(9):53–68

    Google Scholar 

  • Zhu TJ, Tso WK, Heidebrecht AC (1988) Effect of peak ground A/V ratio on structural damage. J Struct Eng 114(5):1019–1037

    Google Scholar 

Download references

Acknowledgements

The financial supports from the National Natural Science Foundation of China under Grant No. 52108454, Research Start-up Fund for High-level Talents of Huaqiao University under Grant No. 20191XD042 are gratefully acknowledged.

Author information

Authors and Affiliations

  1. College of Civil Engineering, Huaqiao University, Xiamen, China

    Yang Liu, Qunxian Huang, Yang Liu, Zixiong Guo & Hao Kang

  2. Key Laboratory of Structural Engineering and Disaster Prevention of Fujian Province, Xiamen, China

    Yang Liu, Qunxian Huang, Yang Liu & Zixiong Guo

  3. Faculty of Science and Technology, The Technological and Higher Education Institute of Hong Kong, Hong Kong, China

    Xueying Wang

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  1. Yang Liu
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Contributions

Y.L.: methodology, conceptualization, writing—original draft, funding acquisition, project administration, writing—review & editing. Q.H.: conceptualization, methodology, writing—original draft. Y.L.: conceptualization, writing—review & editing, Z.G.: supervision, conceptualization, writing—review & editing. H.K.: writing—review & editing, investigation. X.W.: writing—review & editing, investigation.

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Correspondence to Yang Liu.

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Appendix

Appendix

See Figs. 11, 12, 13, 14 and 15.

Fig. 11
figure 11

Mean spectra of IGMs of different selection of motion set 1 and set 2

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Fig. 12
figure 12

Mean spectra of IGMs of different selection of motion sets 3 and 7

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Fig. 13
figure 13

Mean spectra of IGMs of different selection of motion sets 4 and 8

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Fig. 14
figure 14

Mean spectra of IGMs of different selection of motion sets 5 and 9

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Fig. 15
figure 15

Mean spectra of IGMs of different selection of motion sets 6 and 10

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See Table 7, 8, 9, 10 and 11.

Table 7 Information of seed IGMs of motion sets 1 and 2
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Table 8 Information of seed IGMs of motion sets 3 and 7
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Table 9 Information of seed IGMs of motion sets 4 and 8
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Table 10 Information of seed IGMs of motion sets 5 and 9
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Table 11 Information of seed IGMs of motion sets 6 and 10
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Liu, Y., Huang, Q., Liu, Y. et al. Modal-based ground motion selection procedure for nonlinear response time history analysis of dual wall-frame structures. Bull Earthquake Eng 20, 765–793 (2022). https://doi.org/10.1007/s10518-021-01264-0

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