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Analytical evaluation and experimental validation on dynamic rocking behavior for shallow foundation considering structural response

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Abstract

The challenge in the practical application of rocking foundations is the estimation of its performance, particularly the rotation angle, during a strong earthquake. In this study, the dynamic rocking behavior for a shallow foundation considering structural response was evaluated through two analytical approaches: the conventional soil-foundation-structure interaction (SFSI) governing equation of a single-degree-of-freedom (SDOF) structure on a rocking shallow foundation, and the Housner rocking model (i.e., a rocking rigid block on a rigid base). Both approaches were validated with dynamic centrifuge tests. The test models consisted of a soft soil deposit, a shallow rectangular foundation, and an SDOF structure dominated by a bending behavior. A total of 11 foundation-structure systems and six seismic waves, including recorded earthquake signals and sinusoidal waves, were utilized. The results showed that the conventional SFSI equation well predicted the maximum rotation during strong earthquakes. However, this method was less accurate regarding the rotational phase information and maximum rotation of the foundation during weak earthquakes. On the other hand, although the modified Housner’s rocking model required five parameters relevant to a soil-foundation-structure system, it overestimated the maximum rotation of the foundation when compared with the results from dynamic centrifuge tests.

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References

  • Allmond JD and Kutter BL (2014), “Design Considerations for Rocking Foundations on Unattached Piles,” Journal of Geotechnical and Geoenvironmental Engineering, 140(10): 04014058.

    Article  Google Scholar 

  • Anastasopoulos I, Gazetas G, Loli M, Apostolou M and Gerolymos N (2010), “Soil Failure can be Used for Seismic Protection of Structures,” Bulletin of Earthquake Engineering, 8(2): 309–326.

    Article  Google Scholar 

  • Anastasopoulos I and Kontoroupi T (2014), “Simplified Approximate Method for Analysis of Rocking Systems Accounting for Soil Inelasticity and Foundation Uplifting,” Soil Dynamics and Earthquake Engineering, 56: 28–43.

    Article  Google Scholar 

  • Anastasopoulos I, Kourkoulis R, Gelagoti F and Papadopoulos E (2012), “Rocking Response of SDOF Systems on Shallow Improved Sand: An Experimental Study,” Soil Dynamics and Earthquake Engineering, 40: 15–33.

    Article  Google Scholar 

  • Anastasopoulos I, Loli M, Georgarakos T and Drosos V (2013), “Shaking Table Testing of Rocking—Isolated Bridge Pier on Sand,” Journal of Earthquake Engineering, 17(1): 1–32.

    Article  Google Scholar 

  • Apostolou M, Gazetas G and Garini E (2007), “Seismic Response of Slender Rigid Structures with Foundation Uplifting,” Soil Dynamics and Earthquake Engineering, 27(7): 642–654.

    Article  Google Scholar 

  • Craig JRR and Kurdila AJ (2006), Fundamentals of Structural Dynamics, John Wiley & Sons, Inc., New Jersey, USA.

    Google Scholar 

  • DeJong MJ (2012), “Amplification of Rocking Due to Horizontal Ground Motion,” Earthquake Spectra, 28(4): 1405–1421.

    Article  Google Scholar 

  • Deng L and Kutter BL (2012), “Characterization of Rocking Shallow Foundations Using Centrifuge Model Tests,” Earthquake Engineering and Structural Dynamics, 41(5): 1043–1060.

    Article  Google Scholar 

  • Deng L, Kutter BL and Kunnath SK (2012), “Centrifuge Modeling of Bridge Systems Designed for Rocking Foundations,” Journal of Geotechnical and Geoenvironmental Engineering, 138(3): 335–344.

    Article  Google Scholar 

  • Deng L, Kutter BL and Kunnath SK (2014), “Seismic Design of Rocking Shallow Foundations: Displacement-Based Methodology,” Journal of Bridge Engineering, 19(11): 04014043.

    Article  Google Scholar 

  • Di Egidio A, Zulli D and Contento A (2014), “Comparison Between the Seismic Response of 2D and 3D Models of Rigid Blocks,” Earthquake Engineering and Engineering Vibration, 13(1): 151–162.

    Article  Google Scholar 

  • FEMA-356 (2000), Prestandard and Commentary for the Seismic Rehabilitation of Buildings, Rep., Building Seismic Safety Council (BSSC), Washington D.C., USA.

    Google Scholar 

  • Gajan S and Kayser M (2019), “Quantification of the Influence of Subsurface Uncertainties on the Performance of Rocking Foundations During Seismic Loading,” Soil Dynamics and Earthquake Engineering, 116: 1–14.

    Article  Google Scholar 

  • Gajan S, Kutter BL, Phalen JD, Hutchinson TC and Martin GR (2005), “Centrifuge Modeling of Load-Deformation Behavior of Rocking Shallow Foundations,” Soil Dynamics and Earthquake Engineering, 25(7): 773–783.

    Article  Google Scholar 

  • Gajan S and Kutter BL (2008), “Capacity, Settlement, and Energy Dissipation of Shallow Footings Subjected to Rocking,” Journal of Geotechnical and Geoenvironmental Engineering, 134(8): 1129–1141.

    Article  Google Scholar 

  • Gajan S and Kutter BL (2009b), “Effects of Moment-to-Shear Ratio on Combined Cyclic Load-Displacement Behavior of Shallow Foundations from Centrifuge Experiments,” Journal of Geotechnical and Geoenvironmental Engineering, 135(8): 1044–1055.

    Article  Google Scholar 

  • Gavras AG, Kutter BL, Hakhamaneshi M, Gajan S, Tsatsis A, Sharma K, Kouno T, Deng L, Anastasopoulos I and Gazetas G (2020), “Database of Rocking Shallow Foundation Performance — Dynamic Shaking,” Earthquake Spectra, 36(2): 960–982.

    Article  Google Scholar 

  • Gazetas G (2015), “4th Ishihara Lecture: Soil-Foundation-Structure Systems Beyond Conventional Seismic Failure Thresholds,” Soil Dynamics and Earthquake Engineering, 68: 23–39.

    Article  Google Scholar 

  • Ha JG, Ko KW, Jo SB, Park HJ and Kim DS (2019), “Investigation of Seismic Performances of Unconnected Pile Foundations Using Dynamic Centrifuge Tests,” Bulletin of Earthquake Engineering, 17(5): 2433–2458.

    Article  Google Scholar 

  • Hakhamaneshi M, Kutter BL, Moore M and Champion C (2016), “Validation of ASCE 41–13 Modeling Parameters and Acceptance Criteria for Rocking Shallow Foundations,” Earthquake Spectra, 32(2): 1121–1140.

    Article  Google Scholar 

  • Housner GW (1963), “The Behavior of Inverted Pendulum Structures During Earthquakes,” Bulletin of the Seismological Society of America, 53(2): 403–417.

    Article  Google Scholar 

  • Kavvadias IE, Papachatzakis GA, Bantilas KE, Vasiliadis LK and Elenas A (2017), “Rocking Spectrum Intensity Measures for Seismic Assessment of Rocking Rigid Blocks,” Soil Dynamics and Earthquake Engineering, 101: 116–124.

    Article  Google Scholar 

  • Khanmohammadi M and Mohsenzadeh V (2018), “Effects of Foundation Rocking and Uplifting on Displacement Amplification Factor,” Earthquake Engineering and Engineering Vibration, 17(3): 511–525.

    Article  Google Scholar 

  • Kim DK, Lee SH, Kim DS, Choo YW and Park HG (2015), “Rocking Effect of a Mat Foundation on the Earthquake Response of Structures,” Journal of Geotechnical and Geoenvironmental Engineering, 141(1): 04014085.

    Article  Google Scholar 

  • Kim DK, Park HG, Kim DS and Lee H (2020), “Nonlinear System Identification on Shallow Foundation Using Extended Kalman Filter,” Soil Dynamics and Earthquake Engineering, 128: 105857.

    Article  Google Scholar 

  • Ko KW, Ha JG, Park HJ and Kim DS (2018a), “Comparison Between Cyclic and Dynamic Rocking Behavior for Embedded Shallow Foundation Using Centrifuge Tests,” Bulletin of Earthquake Engineering, 16: 5171–5193.

    Article  Google Scholar 

  • Ko KW, Ha JG, Park HJ and Kim DS (2018b), “Soil Rounding Effect on Embedded Rocking Foundation via Horizontal Slow Cyclic Tests,” Journal of Geotechnical and Geoenvironmental Engineering, 144(3): 04018004.

    Article  Google Scholar 

  • Ko KW, Ha JG, Park HJ and Kim DS (2019), “Centrifuge Modeling of Improved Design for Rocking Foundation Using Short Piles,” Journal of Geotechnical and Geoenvironmental Engineering, 145(8): 04019031.

    Article  Google Scholar 

  • Ko KW, Ha JG, Park HJ and Kim DS (2021), “Investigation of Period-Lengthening Ratio for Single-Degree-of-Freedom Structures Using Dynamic Centrifuge Test,” Journal of Earthquake Engineering, 25(7): 1358–1380.

    Article  Google Scholar 

  • Kokkali P, Abdoun T and Anastasopoulos I (2015), “Centrifuge Modeling of Rocking Foundations on Improved Soil,” Journal of Geotechnical and Geoenvironmental Engineering, 141(10): 04015041.

    Article  Google Scholar 

  • Kourkoulis R, Anastasopoulos I, Gelagoti F and Kokkali P (2012), “Dimensional Analysis of SDOF Systems Rocking on Inelastic Soil,” Journal of Earthquake Engineering, 16(7): 995–1022.

    Article  Google Scholar 

  • Kutter BL, Moore M, Hakhamaneshi M and Champion C (2016), “Rationale for Shallow Foundation Rocking Provisions in ASCE 41-13,” Earthquake Spectra, 32(2): 1097–1119.

    Article  Google Scholar 

  • Makris N and Konstantinidis D (2003), “The Rocking Spectrum and the Limitations of Practical Design Methodologies,” Earthquake Engineering and Structural Dynamics, 32(2): 265–289.

    Article  Google Scholar 

  • Makris N and Roussos YS (2000), “Rocking Response of Rigid Blocks Under Near-Source Ground Motions,” Geotechnique, 50(3): 243–262.

    Article  Google Scholar 

  • Mavroeidis GP and Papageorgiou AS (2003), “A Mathematical Representation of Near-Fault Ground Motions,” Bulletin of the Seismological Society of America, 93(3): 1099–1131.

    Article  Google Scholar 

  • Mergos PE and Kawashima K (2005), “Rocking Isolation of a Typical Bridge Pier on Spread Foundation,” Journal of Earthquake Engineering, 9(sup2): 395–414.

    Article  Google Scholar 

  • Paolucci R, Shirato M and Yilmaz MT (2008), “Seismic Behaviour of Shallow Foundations: Shaking Table Experiments vs Numerical Modelling,” Earthquake Engineering and Structural Dynamics, 37(4): 577–595.

    Article  Google Scholar 

  • Pecker A (2006), “Enhanced Seismic Design of Shallow Foundations: Example of the Rion Antirion Bridge,” Proceedings of the 4th Athenian Lecture on Geotechnical Engineering, Athens, Greece, pp.1–23.

  • Pelekis I, Madabhushi GSP and DeJong MJ (2018), “Seismic Performance of Buildings with Structural and Foundation Rocking in Centrifuge Testing,” Earthquake Engineering and Structural Dynamics, 47: 2390–2409.

    Article  Google Scholar 

  • Priestley MJN (1993), “Myths and Fallacies in Earthquake Engineering-Conflicts Between Design and Reality,” Bulletin of the New Zealand Society for Earthquake Engineering, 26(3): 329–341.

    Article  Google Scholar 

  • Priestley MJN (2000), “Performance Based Seismic Design,” Bulletin of the New Zealand Society for Earthquake Engineering, 33(3): 325–346.

    Article  Google Scholar 

  • Priestley MJN, Calvi GM and Kowalsky MJ (2007), Displacement-Based Seismic Design of Structures, IUSS Press, Pavis, Itally.

    Google Scholar 

  • Ther T and Kollár LP (2017), “Refinement of Housner’s Model on Rocking Blocks,” Bulletin of Earthquake Engineering, 15(5): 2305–2319.

    Article  Google Scholar 

  • Tsatsis A and Anastasopoulos I (2015), “Performance of Rocking Systems on Shallow Improved Sand: Shaking Table Testing,” Frontiers in Built Environment, 1(9): 1–19.

    Google Scholar 

  • Vetr MG, Nouri A R and Kalantari A (2016), “Seismic Evaluation of Rocking Structures Through Performance Assessment and Fragility Analysis,” Earthquake Engineering and Engineering Vibration, 15(1): 115–127.

    Article  Google Scholar 

  • Xia X, Wu S, Shi J, Jia J, Chen X and Ma H (2020), “Seismic Response of Rocking Isolated Railway Bridge Piers with Sacrificial Components,” Earthquake Engineering and Engineering Vibration, 19(4): 1005–1015.

    Article  Google Scholar 

  • Yim CS, Chopra AK and Penzien J (1980), “Rocking Response of Rigid Blocks to Earthquakes,” Earthquake Engineering and Structural Dynamics, 8(6): 565–587.

    Article  Google Scholar 

  • Zhang J and Makris N (2001), “Rocking Response of Free-Standing Blocks Under Cycloidal Pulses,” Journal of Engineering Mechanics, 127(5): 473–483.

    Article  Google Scholar 

  • Zhang J, Xie Y and Wu G (2019), “Seismic Responses of Bridges with Rocking Column-Foundation: A Dimensionless Regression Analysis,” Earthquake Engineering and Structural Dynamics, 48(1): 152–170.

    Article  Google Scholar 

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Acknowledgement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean Government (Ministry of Science and ICT) (No. 2017R1A5A1014883).

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, UC Berkeley, California, 94720, USA

    Kil-Wan Ko

  2. Advanced Structures and Seismic Safety Research Division, 111, Daedeok-daero 989 Beon-gil, Yuseong-gu, Daejeon, 34057, Korea

    Jeong-Gon Ha

  3. Department of Civil and Environmental Engineering, KAIST, Daejeon, 34141, Korea

    Dong-Soo Kim

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  1. Kil-Wan Ko
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  2. Jeong-Gon Ha
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Correspondence to Jeong-Gon Ha.

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National Research Foundation of Korea (NRF) Grant funded by the Korean Government (Ministry of Science and ICT) under Grant No. 2017R1A5A1014883

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Ko, KW., Ha, JG. & Kim, DS. Analytical evaluation and experimental validation on dynamic rocking behavior for shallow foundation considering structural response. Earthq. Eng. Eng. Vib. 21, 37–51 (2022). https://doi.org/10.1007/s11803-022-2075-6

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  • DOI: https://doi.org/10.1007/s11803-022-2075-6

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