The behavior of laterally loaded pile groups is usually accessed by beam-on-nonlinear-Winkler-foundation (BNWF) approach employing various forms of empirically derived p-y curves and p-multipliers. Averaged p-multiplier for a particular pile group is termed as the group effect parameter. In practice, the p-y curve presented by the American Petroleum Institute (API) is most often utilized for piles in granular soils, although its shortcomings are recognized. In this study, we performed 3D finite element analysis to develop p-multipliers and group effect parameters for 3 × 3 to 5 × 5 vertically squared pile groups. The effect of the ratio of spacing to pile diameter (S/D), number of group piles, varying friction angle (φ), and pile fixity conditions on p-multipliers and group effect parameters are evaluated and quantified. Based on the simulation outcomes, a new functional form to calculate p-multipliers is proposed for pile groups. Extensive comparisons with the experimental measurements reveal that the calculated p-multipliers and group effect parameters are within the recorded range. Comparisons with two design guidelines which do not account for the pile fixity condition demonstrate that they overestimate the p-multipliers for fixed-head condition.

Hyperbolic type nonlinear models used in 1D site response analysis are reported to predict favorably the nonlinear soil response at small strains, but may provide poor fits at large strains. It has been shown to result in unrealistic site response for deep and soft sites particularly in regions of high seismicity, where implied strength correction is demonstrated to be important. In this study, the importance of the implied strength correction for shallow sites at a region of moderate to low seismicity is investigated. This paper uses a quadratic/hyperbolic model that can capture the stress-strain response at large strains in addition to the small strain stiffness dependence. A total of fifteen measured site profiles are used and a suite of 1D site response analyses are performed using a range of input motions. The strength correction is shown to be relevant even for shallow sites and moderate intensity ground motions. The difference between non-corrected and corrected analyses is conditional on the site period. The overall difference is demonstrated to be more prominent in soft sites. A quantitative estimate of the difference between two types of analyses is presented.

The Makran Subduction Zone (MSZ) is a tectonic plate boundary where the Arabian Plate is subducting beneath the Eurasian Plate. This study investigated the dynamic response in the Gwadar region, located in the eastern part of the MSZ. A suite of seismic records compatible with the Building Code of Pakistan (BCP:2021) rock design spectrum was used as the input ground motions at the bedrock. The amplification characteristics were assessed through a series of one-dimensional (1D) site response analyses utilizing a non-linear (NL) approach. The results revealed significant de-amplification in soft soils at short spectral periods. A general depth-wise decrease in the shear stress ratio and peak ground acceleration values was observed, influenced by shear-strain-induced effects and shear wave velocity reversals within the site profiles. The code spectra, compared to the proposed design spectra, underestimated the site amplification for stiff soils (i.e., Site Class D) for periods of less than 0.32 s and overestimated it for soft soils (i.e., Site Class E) across all periods. These findings underscore the necessity for site-specific ground response analyses, particularly within the framework of the China–Pakistan Economic Corridor (CPEC).

This study investigates the site amplification factors in Islamabad, Pakistan, as per seismic regulations of a newly enacted Building Code of Pakistan (BCP, 2021). Using a series of 1D non-linear site response analyses, the study evaluates these factors for the Islamabad region. Nineteen representative profiles were selected from a dataset of 125 site profiles, classified according to the Code. The representative profiles were subjected to a combination of thirteen ground motions that are compatible with site class B of the BCP, 2021, and 1D nonlinear seismic site response analyses were performed. Calculated response spectra and amplification factors are compared with design estimates provided by the code spectra. The study finds that while the Code-based design spectrum aligns with the current study’s findings for periods greater than 0.5 seconds, it underpredicts the response for shorter periods for both SC and SD site classes. These findings highlight the need for a more refined approach in the seismic provisions for Islamabad to ensure accurate seismic hazard assessments and improved earthquake safety.