Research Paper

Evolutionary Framework with Bayesian Calibration for Probabilistic Maximum Seismic Shear Strain Estimation in Nonlinearly Responding Layered Geological Profiles

Dehghanian K., and Yılmaz M.T.

J. Civil Eng. Urban., 16(1): 01-12, 2026; pii:S225204302600001-16

DOI: https://dx.doi.org/10.54203/jceu.2026.1 

Abstract
Estimating maximum seismic shear strain in layered geological profiles is critical for the safety of underground infrastructure. However, traditional simplified methods often rely on stationary excitation assumptions and equivalent linear soil models (EQL) that fail to capture the non-stationary nature of ground motions and significant soil nonlinearity. This study introduces an evolutionary framework that replaces standard stationary power spectral density (PSD) with an evolutionary representation (EPSD) derived from Short-Time Fourier Transform decomposition. To enhance accuracy at high strain levels, the framework integrates a hyperbolic constitutive model using Darendeli parameterization. Furthermore, the depth normalization coefficients within the random vibration theory (RVT) were updated using Bayesian Markov Chain Monte Carlo calibration based on 312 records from the NGA-West2 database. Validation against nonlinear time-domain site response analyses demonstrates that the proposed framework reduces the root mean square error by 43% compared to original formulations, effectively eliminating systematic bias. The practical utility of the model is illustrated through fragility surfaces, which reveal that current design guidelines for soft clay may underestimate seismic shear strain demands by 1.5 to 2.5 times. These findings provide a more robust probabilistic tool for the seismic assessment of underground structures in complex geological settings.
Keywords: Evolutionary power spectral density, Maximum seismic shear strain, Bayesian calibration, Hyperbolic soil model.

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