Strong seismic motions estimated from a one direction-three components ("1d-3c") approach, application to the city of rome, italy

Strong seismic motions in soils generally lead to both a stiffness reduction and an increase of the energy dissipation in the surficial layers. In order to study such phenomena, several nonlinear constitutive models were proposed and were generally implemented for 1D soil columns. However, one of the main difficulties of complex rheologies is the large number of parameters needed to describe the model. In this sense, the multi-surface cyclic plasticity approach, developed by Iwan in 1967 but linked to Prandtl or Preisach theoretical work, is an interesting choice: the only data needed is the modulus reduction curve. Past studies have generally implemented such models for one-directional shear wave propagation in a “1D” soil column considering one motion component only (“1C”). Conversely, this work aims at studying strong motion amplification by considering seismic wave propagation in a “1D” soil column accounting for the influence of the 3D loading path on the nonlinear behavior of each soil layer. In the “1D-3C” approach, the three components (3C) of the outcrop motion are simultaneously propagated into a horizontally layered soil for which a three-dimensional constitutive relation is used (Finite Element Method). The alluvial site considered in this study corresponds to the Tiber River Valley, close to the historical centre of Rome (Italy). The computations are performed considering the waveforms referred as the 14th October 1997 Umbria-Marche earthquake, recorded on outcropping bedrock. Time histories and stress-strain hysteretic loops are computed all along the soil column. The octahedral stress, the strain-depth profiles and the transfer functions in acceleration (surface/outcrop spectral ratios) are estimated for the 1D-1C and the 1D-3C approaches, evidencing the influence of the three-dimensional loading path.

💡 Research Summary

The paper introduces a novel “1D‑3C” methodology for simulating strong‑motion amplification in layered soils, extending the conventional one‑dimensional, single‑component (1D‑1C) approach by simultaneously propagating all three components of an incident seismic wave through a 1‑D soil column. The authors adopt Iwan’s multi‑surface cyclic plasticity model (1967), which is linked to the Prandtl‑Preisach framework and requires only the shear‑modulus reduction curve as input, thereby drastically reducing the number of material parameters compared with more complex rheologies.

Numerically, the problem is solved with the Finite Element Method (FEM). Although the geometry remains one‑dimensional (horizontal layering), each element is assigned a three‑dimensional constitutive law, allowing the soil layers to experience the full three‑axis stress path generated by the incoming motion. The input motion is taken from the outcrop recordings of the 14 October 1997 Umbria‑Marche earthquake, measured on the underlying bedrock near the Tiber River Valley, close to historic Rome.

Two sets of simulations are performed: the traditional 1D‑1C case (single shear component) and the proposed 1D‑3C case (all three components). Results are presented as time histories, octahedral stress and strain profiles, hysteresis loops, and acceleration transfer functions (surface‑to‑outcrop spectral ratios). The comparison reveals several key findings. First, the 1D‑3C model exhibits stronger high‑frequency attenuation and a more pronounced low‑frequency amplification relative to the 1C model, indicating that the three‑dimensional loading path intensifies both stiffness degradation and energy dissipation. Second, octahedral stress and strain depth profiles show that, in addition to shear deformation, compressive and tensile strains develop simultaneously, producing a more complex stress state throughout the column. Third, hysteresis loops in the 3C case are significantly wider, confirming increased nonlinear damping.

These outcomes demonstrate that the conventional 1D‑1C framework may underestimate the nonlinear amplification that occurs under realistic three‑component seismic loading, especially in urban settings with shallow, heterogeneous deposits such as Rome’s historic center. The Iwan model’s reliance on a single modulus‑reduction curve makes it attractive for field applications, as it can be calibrated from standard laboratory or in‑situ tests without extensive parameter identification. Consequently, the 1D‑3C approach offers a practical yet more physically realistic tool for seismic hazard assessment and engineering design. Future work suggested by the authors includes extending the method to two‑ and three‑dimensional wave propagation, incorporating spatial heterogeneity, and validating the approach against recorded strong‑motion data from other sites.