Contents lists available at ScienceDirect Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn Reduction of peak ground velocity by nonlinear soil response – I: Excitation by SH pulse Vlado Gičev a , Mihailo D. Trifunac b, ⁎ a Univ. Goce Delčev, Dept. of Computer Science, Tošo Arsov 14, 2000, Štip, Macedonia b Univ. Southern California, Dept. of Civil Eng, Los Angeles, CA, 90089-2531, USA ARTICLEINFO Keywords: Reductionofpeakgroundvelocitybynonlinear site response Strain localization as a barrier for transfer of seismic wave energy ABSTRACT WestudythereductionofpeakvelocityonthegroundsurfaceofasoilvalleyforexcitationbyanSHhalf-sine pulse.Thisreductioniscausedbythelossofwaveenergyduringpropagationaccompaniedbylargenonlinear strains and strain localizations in the soil medium. Our aim is to fnd a physically plausible explanation for observed spatial variations of damaged buildings, which suggests that damage is signifcantly larger in areas where the soil experiences little or no nonlinear deformations. In order to create simple and manageable calculations, we work with the most elementary representation of the soil valley (fnite soil box) and assume the soil to behave like an elasto-plastic material. Our work belongs in the category of Gedanken numerical experiments. 1. Introduction Observations of the response of buildings to strong earthquake groundshakinghaveshownthatdamagecanbereducedbyanonlinear response in the soil [1,2]. Combined mapping of areas of damaged buildings, and of areas with broken water pipes, have confrmed this trend and demonstrated how, spatially, it can be correlated with properties of shallow soil deposits [3,4]. The reduction of building damage results from the dissipation of incident wave energy by a nonlinearsiteresponsethatleadstoareductioninavailableenergythat canreachandexcitethestructures.Examplesofsuchdamagereduction in California have been described following the earthquakes in Long Beach (1933) [5], San Fernando (1971), and Northridge (1994) [4,6–8]. Fig. 1 shows the areas where buildings were damaged (within the gray zones) in the San Fernando Valley (north-western region in Los Angeles metropolitan area), as well as broken pipes following the Northridge 1994 earthquake. The fgure illustrates that in instances of no broken water pipes (no large strains and no permanent soil de- formations) buildings were damaged; while in the areas that experi- enced a nonlinear site response (with breaks in the water pipes), there werealmostnodamagedbuildings.Damagedbuildingsin Fig.1 arethe buildings, which received red tags after the earthquake, that is, they weredeterminedtobeunsafeforoccupancy[6].Thepopulationofred- tagged buildings includes a broad spectrum of diferent building types and, thus indicates the strong motion amplitudes in a broad frequency range. Thegeographiclocationandshapeofthegrayzonesin Fig.1 canbe adjusted to also include the distribution of damaged buildings during the Feb. 9, 1971 earthquake in the San Fernando Valley [8]. This im- plies that the spatial distribution of gray areas, and the areas which experienced a nonlinear site response, may not have changed sig- nifcantly over a period of two decades and possibly a much longer time. Fig. 2 shows the distribution of damaged buildings (shown by open triangles, squares, and circles of diferent colors) and the breaks in water pipes (solid black dots) following the earthquake of March 10, 1933, in Long Beach, California. At frm sites (also sites with low and verylowliquefactionsusceptibility)thebuildingsweredamaged,while in areas where the sites responded in a nonlinear manner (high lique- faction susceptibility), damage to buildings was sparse; however, many water pipes were broken. Many studies have addressed various aspects of the nonlinear re- sponse of soils and have confrmed, both directly and indirectly, that nonlinear soil response does occur. The nonlinear response of soils has also been shown indirectly by a reduction in recorded peak accelera- tions recorded at sites with “softer” surface deposits (e.g. Ref. [3], a prolongation of site periods for larger amplitudes of strong motion [10–12] and by documented changes in the system frequencies of the soil-structure interaction for buildings (e.g. Refs. [13–15]. However, https://doi.org/10.1016/j.soildyn.2019.105810 Received 12 June 2019; Received in revised form 7 August 2019; Accepted 9 August 2019 ⁎ Corresponding author. E-mail address: trifunac@usc.edu (M.D. Trifunac). Soil Dynamics and Earthquake Engineering 127 (2019) 105810 0267-7261/ © 2019 Published by Elsevier Ltd. T