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A study of the Newmark sliding block displacement functions

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Abstract

The Newmark sliding block displacement function, the curve showing the relation between the sliding response and the critical acceleration ratio, is important because its applications have been widespread in seismic designs of earth structures. The aims of this article are twofold: (a) to give a new point of view on the related abscissa parameter, and (b) to provide a new methodology for better understanding the displacement functions. Regarding the new methodology, the study of the properties of the displacement functions is divided into two parts: one is the property of the amplitude at a specific abscissa, and the other is the shape property. After derivations, validations and calibrations, the authors have obtained a simple expression for the characteristic slippage. Simple expressions have also been obtained for the shapes of the displacement functions using observations and derivations. The authors compare their results for the characteristic slippage predictions and for the shapes of displacement functions with related previous studies. Finally, empirical attenuation relationships of the characteristic slippage for different ground types are developed.

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Acknowledgments

The authors thank Professor Woei-Lih Jeng, Professor Ming-Lang Lin, Professor Ken Palmer, Dr. Ton Kloks, Dr. David B. Chandler, Dr. Yuriy V. Tokovyy, Dr. Ming-Wey Huang, and Dr. Po-Shen Lin for valuable discussions and helpful suggestions. The author (GSH) is grateful to Professor Chien-Ching Ma for providing financial support from the Grants NSC94-2811-E-002-051, NSC95-2811-E-002-027, NSC96-2811-E-002-032, NSC97-2811-E-002-039, NSC98-2811-E-002-086, NSC99-2811-E-002 -093, NSC100-2811-E-002-054 and NSC101-2811-E-002-052. Also, we appreciate the English language assistance from Lt. Col. Joseph F. Melichar, U.S. Air Force retired, and from Lecturer Marc Anthony.

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Taiwan University, Room 406, Engineering Complex Building, Sec. 4, No. 1, Roosevelt Rd., Taipei 106, Taiwan

    Gwo-Shyang Hwang

  2. Department of Civil Engineering, National Taiwan University, Taipei, Taiwan

    Cheng-Hsing Chen

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  1. Gwo-Shyang Hwang
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  2. Cheng-Hsing Chen
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Correspondence to Gwo-Shyang Hwang.

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Hwang, GS., Chen, CH. A study of the Newmark sliding block displacement functions. Bull Earthquake Eng 11, 481–502 (2013). https://doi.org/10.1007/s10518-012-9403-6

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  • DOI: https://doi.org/10.1007/s10518-012-9403-6

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