This paper proposes a frequency wavenumber-finite element hybrid method with kinetic source model for dynamic analysis of pile founded nuclear island from fault to structure. This method benefits from the effective synthesis of broadband ground motions by the fault source model, the realism of frequency wavenumber for earthquake simulation from fault to the site and the mesh refinement capabilities of the finite element in modeling the nuclear structure and the near soil. This method achieves the expression of source rupture, wave propagation, site response, soil-structure interaction, soil nonlinearity and structure response accurately, which solves the multi-scale problem from crustal layer to nuclear structure. Under finite-fault excitation, the correctness of the proposed method is validated by comparing with the frequency wavenumber method. Then, a full process seismic simulation of a pile founded nuclear island built on a non-rock site is conducted. The influence of source parameter and soil-structure interaction is studied. Results indicate that the change of source parameter can lead to difference nuclear island failure direction. With the increase of dip angle, the appearance of maximum stress is in advance. The soil nonlinearity could greatly amplify the soil-structure interaction effect and the loads on piles. The connection between the containment vessel and the raft is vulnerable and the piles on the edge of the raft is prone to damage. This hybrid method could accomplish an appropriate seismic evaluation of the nuclear structures and the conclusions may provide reference for seismic design of nuclear structure.

As the monopile supported offshore wind turbine (OWT) is a dynamic sensitive structure, one of the major challenges in its design is the assessment of the natural frequency to avoid resonance during the lifetime. Since the characteristics of OWTs under dynamic loading and their long-term behavior are not fully understood, to study their natural frequency considering soil-monopile interaction, a series of scaled model tests in sand were performed. The first part was about the initial resonant frequency subjected to different forcing amplitudes and the second part was about the change of the natural frequency under long-term horizontal cyclic loadings. Based on the test results, the effects of pile-soil interaction, related to the loading amplitude, embedment depth, soil density, and cyclic numbers, on the natural frequency of OWTs are presented by a non-dimensional group based on the explanation of the governing mechanism. As the soil nonlinearity leads to a degradation in the natural frequency of monopile supported OWTs in the sand and the cyclic loading results in an increase, the choice of the natural frequency closer to the upper limit of the 1P band is suggested in practice based on the tradeoff of the two above effects.

This study established a numerical model for soil-structure interaction (SSI) to examine the effects of the spatial incidence angle of SV waves and soil nonlinearity, utilizing viscoelastic artificial boundaries (VAB) and equivalent nodal force (ENF) method. Both the foundation's and superstructure's torsion and rocking responses were then analyzed. The findings indicate that subjected to spatially oblique incident SV waves, the rectangular foundation primarily has the rocking response while the torsional response is negligible. Furthermore, the maximum torsional and rocking angles about the x-axis at each frame floor are significantly enlarged by comparison with the perpendicular incident case. Moreover, the soil nonlinearity could increase the foundation's rocking angle and enlarge the maximum torsion and rocking responses of the structure's floors. Consequently, structural seismic damage assessment requires considering both the soil nonlinearity and incident seismic wave angles.

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.