A study of the Newmark sliding block displacement functions

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.