The research focuses on so-called coherency functions, statistical tools that quantify how strongly ground motions at two separated points on the ground surface are correlated as a function of frequency and distance. When waves propagate through the heterogeneous Earth, scattering, differences in arrival times known as wave passage effects, and local site conditions all erode this correlation, particularly at high frequencies. Because engineers cannot know the exact ground motion at every foundation point in advance, they rely on empirical coherency models fitted to dense instrument arrays, such as the SMART-1 array in Taiwan and the Lotung large-scale seismic experiment, to generate statistically consistent sets of spatially varying ground motion time histories for analysis.

A central motivation of the study is to validate the spectral correction factors recommended in ASCE Standard 4-98, the American Society of Civil Engineers standard for the seismic analysis of safety-related nuclear structures, and the coherency model developed by Norman Abrahamson in 2005 for the Electric Power Research Institute. These corrections account for the fact that the motion actually experienced by a large foundation is smoother, and generally weaker at high frequencies, than the free-field motion recorded in the soil away from the structure. This averaging effect, sometimes called the foundation input motion reduction, depends on the size and stiffness of the foundation, the properties of the underlying soil, and the assumed degree of incoherency in the incoming wave field.

To carry out the investigation, the team implemented several widely used coherency functions in code_aster, the open-source finite element software developed by EDF for advanced structural analysis. The models compared include classical formulations such as the Harichandran-Vanmarcke model, the Hao-Oliveira-Penzien model, the Der Kiureghian model and the Abrahamson and co-workers empirical functions derived from the Lotung experiment. Using these functions, the researchers generated ensembles of spatially varying ground motions compatible with target free-field response spectra for both rock and soil site profiles, following established simulation techniques for multivariate stochastic processes.

In the first part of the study, the authors analysed a rigid square foundation subjected to spatially varying ground motion that includes wave incoherency. From the computed foundation motions they derived foundation response spectra, which describe the maximum response a single-degree-of-freedom oscillator would experience at the base of the structure. By comparing these spectra with the corresponding free-field response spectra, they determined reduction factors, that is, ratios quantifying how much the foundation motion is attenuated relative to the free field at each frequency. These numerically derived factors were then benchmarked against the spectral corrections prescribed in the EPRI 2005 methodology and ASCE Standard 4-98.

The results reveal a striking sensitivity: the foundation response spectra can change considerably depending on which coherency model and which ground motion parameters are assumed. Because each empirical model was calibrated on different arrays, site conditions and frequency ranges, they do not produce identical descriptions of the wave field, and these differences propagate directly into the computed reduction factors. For practitioners, this means that the choice of incoherency model is not a technical detail but a decision that can materially influence the seismic demand calculated for safety-critical structures, particularly in the frequency range above a few hertz where incoherency effects are strongest.

The second part of the paper extends the analysis to a full reactor building of a nuclear power plant, coupling the spatially varying excitation with a soil-structure interaction model. Soil-structure interaction refers to the mutual influence between the flexibility of the supporting soil and the dynamic response of the structure: soft soils can lengthen the effective period of the building system and dissipate energy through radiation damping, while the massive foundation filters and averages the incoming wave field. When the ground motion is also spatially incoherent, these two mechanisms interact, and the resulting structural response can differ substantially from what a conventional analysis with identical motion at all support points would predict.

The findings show that the effect of incoherency is remarkable for secondary systems within the reactor building that are sensitive to frequencies larger than 10 hertz. Secondary systems include piping, cable trays, equipment and other components anchored to the structure, whose response is governed by the floor motion spectra at their attachment points rather than by the ground motion itself. Because incoherency predominantly suppresses high-frequency content in the foundation input motion, floor response spectra at these higher frequencies can be reduced, which may ease the design burden for high-frequency equipment, but the magnitude of this reduction depends again on the coherency model selected.

The work was carried out within an international collaborative framework, with support from the German Academic Exchange Service (DAAD), the European Commission’s METIS program under Horizon 2020, and the German Federal Ministry for the Environment, Nature Conservation, Nuclear Safety and Consumer Protection through the CRUAS-19 project. This combination of academic and industrial partners reflects the practical stakes of the research: nuclear regulators and operators in Europe and elsewhere are increasingly requiring that wave incoherency be explicitly accounted for in site-specific seismic assessments, and reliable, validated modelling tools are essential for that task.

For the earthquake engineering community, the study delivers a clear message about uncertainty and standardisation. The spectral corrections embedded in ASCE Standard 4-98 and the EPRI methodology represent decades of accumulated empirical knowledge, but the new results show that they should be applied with an awareness of the sensitivity of the outcome to the underlying coherency assumptions. As dense seismic arrays continue to record data worldwide, and as site-specific coherency functions are developed for individual nuclear sites, the authors’ open-source implementation in code_aster offers a transparent pathway for engineers to test alternative models, quantify the spread of predicted foundation and floor response spectra, and ultimately make more robust safety decisions for the large semi-rigid structures that society depends upon most.

Subject of Research: Effect of spatial ground motion coherency models on soil-structure interaction analysis of large semi-rigid structures such as nuclear reactor buildings

Article Title: Influence of different spatial coherency models in soil-structure interaction analyses of large semi-rigid structures

Article References: Soyluk, K., Zouatine, M., Sadegh-Azar, H., Zentner, I., Kudawoo, D., & Khemakhem, A. (2026). Influence of different spatial coherency models in soil-structure interaction analyses of large semi-rigid structures. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02664-w

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02664-w

Keywords: spatial variability, soil-structure interaction, coherency model, nuclear power plant, reactor building, seismic analysis, ground motion, wave incoherency, foundation response spectra, ASCE Standard 4-98, code_aster, earthquake engineering