Vol.15, No.2 EARTHQUAKE ENGINEERING AND ENGINEERING VIBRATION June, 2016 Earthq Eng & Eng Vib (2016) 15: 341-356 DOI: 10.1007/s11803-016-0326-0 Site response of heterogeneous natural deposits to harmonic excitation applied to more than 100 case histories Reza Jamshidi Chenari † and Shirin Aminzadeh Bostani Taleshani ‡ Department of Civil Engineering, University of Guilan, Guilan, Rasht 3756, Iran Abstract: Variation of shear-wave propagation velocity (SWV) with depth was studied by analyzing more than one hundred actual SWV profiles. Linear, power, and hyperbolic variation schemes were investigated to find the most representative form for naturally occurred alluvial deposits. It was found that hyperbolic (asymptotic) variation dominates the majority of cases and it can be reliably implemented in analytical or analytical-numerical procedures. Site response analyses for a one-layer heterogeneous stratum were conducted to find an equivalent homogeneous alternative which simplifies the analysis procedure but does not compromise the accuracy of the resonance and amplification responses. Harmonic average, arithmetic average and mid-value equivalents are chosen from the literature for investigation. Furthermore, full and partial depth averaging schemes were evaluated and compared in order to verify the validity of current practices which rely upon averaging shallow depths, viz., the first 30 m of the strata. Engineering bedrock concept was discussed and the results were compared. Keywords: heterogeneity; site response; transfer function; equivalent homogeneous; deterministic variation of shear wave propagation velocity Correspondence to: Reza Jamshidi Chenari, Department of Civil Engineering, University of Guilan, Guilan, Rasht 3756, Iran Tel: +98-13-33690270 E-mail: jamshidi_reza@guilan.ac.ir † Associate Professor; ‡ M.Sc. Graduate Received May 24, 2014; Accepted June 16, 2015 1 Introduction Site response analysis denotes the quantification of the response of a soil site given an earthquake excitation at the bedrock. Site response analysis is primarily performed for two purposes: To estimate the seismic hazard at a given site and for given bedrock motion, and as a precursor to soil-structure interaction analysis. Most of the current site response analysis methods were developed for seismic hazard applications rather than for soil-structure interaction. Site response analysis methods are either frequency domain programs that use an “equivalent linear” approximation to treat the nonlinear soil behavior or nonlinear time-domain programs that model nonlinear soil behavior using constitutive models. For relatively weak input motion (low strain levels) site response may be in the linear range, so both analyses can provide rational estimates of ground response. For problems where strain levels are high, nonlinear analyses are more reliable (Kramer, 1996; Semblat and Pecker, 2009). Traditional site response analysis methods perform 1D analysis by simplifying the earthquake shaking to vertically propagating shear waves as opposed to a 3D wave field. The heterogeneous alluvial deposits are idealized as strata of homogeneous layers, with constant properties within each layer, and further simplification introduced as necessary to make analytical solutions possible (e.g., Dobry et al., 1976). For thick and soft soil deposits, the conventional analysis procedures may underestimate the soil amplification with respect to the actual response of a continuously inhomogeneous medium, depending primarily on the frequency content of the input motion. Recently, attention has focused on a more realistic variation profile of the dynamic parameters of natural alluvial deposits. Towhata (1996) incorporated a nonlinear variation pattern for shear modulus, and he concluded that more energy can reach the ground surface than that given by the conventional approach. Extensive research on the ground dynamic response of continuously heterogeneous soils under vertically propagating shear waves has enabled closed-form solutions for salient features of a natural deposit. Following the early work of Ambraseys (1959), Seed and Idriss (1969), and Dobry et al. (1971) studied the dynamic response of inhomogeneous soils with shear wave propagation velocity conforming to the asymptotic power form. Travasarou and Gazetas (2004) assumed a specific asymptotic form of soft sediments in a part of their investigation of seismic response. Heterogeneity has also been taken into account by many other researches, considering different types of waves. Vardoulakis (1984) studied torsional wave propagation in an inhomogeneous