Prediction of the intensity of earthquake-induced motions at the ground surface attracts extensive attention from the geoscience community due to the significant threat it poses to humans and the built environment. Several factors are involved, including earthquake magnitude, epicentral distance, and local soil conditions. The local site effects, such as resonance amplification, topographic focusing, and basin-edge interactions, can significantly influence the amplitude-frequency content and duration of the incoming seismic waves. They are commonly predicted using site effect proxies or applying more sophisticated analytical and numerical models with advanced constitutive stress-strain relationships. The seismic excitation in numerical simulations consists of a set of input ground motions compatible with the seismo-tectonic settings at the studied location and the probability of exceedance of a specific level of ground shaking over a given period. These motions are applied at the base of the considered soil profiles, and their vertical propagation is simulated using linear and nonlinear approaches in time or frequency domains. This paper provides a comprehensive literature review of the major input parameters for site response analyses, evaluates the efficiency of site response proxies, and discusses the significance of accurate modeling approaches for predicting bedrock motion amplification. The important dynamic soil parameters include shear-wave velocity, shear modulus reduction, and damping ratio curves, along with the selection and scaling of earthquake ground motions, the evaluation of site effects through site response proxies, and experimental and numerical analysis, all of which are described in this article.

This paper presents a site-specific seismic ground response evaluation through convolution-deconvolution analysis in the Balaroa-Petobo area during the 2018 Palu-Donggala Indonesia earthquake. The equivalent-linear ground response analysis for the earthquake time history recorded at Balaroa was carried out using DEEPSOIL software. The results of the analysis indicate that the EW component of the earthquake motion was amplified more severely (amax) than was the NS component, as it propagated to the Petobo surface. The amplification of the bedrock motion on the Petobo surface was more serious than that on the Balaroa surface, which appears to be due to the differences in the subsurface stratification and material properties of the two sites. The Fourier spectrum and response spectra also showed greater maximum spectral accelerations (Sa,max) and maximum Fourier amplitudes (Af) at the Petobo site than at the Balaroa site. The frequency of surface soil both the Petobo and Balaroa sites computed by using comparison between response spectra analysis and the local modes analysis VS/4*H was indicated the potential decline of surface soil stiffness at Petobo area appear to account for the structural damage and liquefaction flow slides during the 2018 incident.

Railway embankments in seismically active areas are prone to earthquake-induced damage. In many instances globally, such damage has led to substantial economic losses. Serviceability assessment of these embankments is pivotal in ascertaining better performance during earthquakes. This work presents a physics-based approach to assess the serviceability of railway embankments subjected to strong ground motions. A series of nonlinear dynamic analyses are performed to evaluate the failure mechanism, progression of the failure plane, accumulation of plastic strain, and deformations of a railway embankment using the framework of smoothed particle hydrodynamics (SPH). The embankment and its underlying foundation are treated as a layered domain, and peak acceleration within each layer is determined through the site-specific nonlinear ground response analysis. The vulnerability assessment of the embankment is carried out considering the vertical displacement of the crest, accumulation of plastic strain, and post-failure scenario under site-specific ground motion characteristics. The vulnerability of the embankment is further quantified through fragility analysis by considering various damage levels. Fragility analysis is carried out using incremental dynamic analysis (IDA) against peak ground acceleration (PGA) of input ground motions as the key hazard indicator. The robustness of the developed vulnerability evaluation framework is also scrutinized through a sequence of stochastic analyses, considering the variability in ground conditions to enhance engineering assessment. The embankment is seen to experience a maximum vertical deformation of 0.05 m at the crest when initial signs of plastic strain development are observed, with deformation increasing to around 0.1 m for moderate damage levels and reaching up to 0.2 m at the point of slope failure. Fragility curves reveal that the right edge of the embankment reaches the first damage level at a PGA of approximately 0.12 g, followed by higher damage levels at PGA's as high as 0.8 g, for a 100% probability of extensive damage. Stochastic analysis shows that the probability of maximum vertical displacement exceeding deterministic values is about 78.47%, with maximum deviations of 2.599 m. For plastic strain, the probability of exceeding deterministic values is 78.49%, with maximum deviations of 13.08. These findings underscore the importance of considering site-specific conditions and the variability of soil properties in seismic assessments to ensure accurate and reliable serviceability evaluations of railway embankments.

Evaluating soil nonlinearity during cyclic loading is one of the most significant challenges in ground response analysis, especially when dealing with the inverse problem of deconvolution. Different schemes have already been developed for dynamic ground response analysis, both in the time and the frequency domain. The most accurate method to account for soil nonlinearity is the nonlinear dynamic analysis in the time domain. This approach is based on nonlinear constitutive models capable of accurately simulating highly nonlinear problems like soil liquefaction. However, the time-domain analysis is suitable only for the convolution analysis to define the ground motion at the free surface of a soil deposit from the bedrock motion. The frequency-domain analysis is the most common solution for the inverse problem called deconvolution, which is used to define the bedrock motion from the free surface ground motion. A well-known approach developed in the frequency domain for ground response analysis is the equivalent-linear method (EQL). This approach adopts an iterative procedure to define elastic shear modulus and damping ratio compatible with the induced strain level. Still, it presents some limitations, especially for highly nonlinear soil response, due to the use of strain-compatible but constant soil properties. This article presents a new scheme to conduct truly nonlinear dynamic analysis in the frequency domain based on the new concept of the short-time transfer function. Unlike the EQL method, which uses a constant transfer function, the proposed approach, called the Equivalent-Nonlinear method (EQNL), defines a soil transfer function evolving in time, depending on the shear stress and strain demands. The EQNL method approximates the response of a nonlinear system as an incrementally changing viscoelastic system and could represent a valuable tool for nonlinear deconvolution. This article shows the analytical formulation and the first set of validations of the EQNL approach, with detailed comparisons with the EQL and NL methods and vertical array data. These comparisons show the potentialities of the EQNL approach to reproduce the results of the nonlinear dynamic analysis. The EQNL approach has been implemented in MATLAB, and the source code is provided as supplementary material for this article. A more comprehensive validation is underway, aiming to better characterize the limitations and the capabilities of the method.