A Semi-Empirical Model for the Stress Reduction Factor Incorporating Soil Plasticity and Random Vibration Theory

This study presents a physics-informed semi-empirical formulation for the stress reduction factor (rd) that integrates random vibration theory with nonlinear soil behavior and plasticity-dependent attenuation. The model incorporates depth, effective stress ratio, normalized shear modulus, and Plasticity Index (PI) within a unified analytical framework, enabling representation of frequency-dependent seismic stress attenuation. A synthetic dataset comprising approximately 3600 realizations was generated using physically consistent constraints based on spectral attenuation and modulus reduction relationships, in which the target rd values represent hybrid responses derived from random vibration theory and calibrated empirical trends. Model parameters were optimized using a global calibration procedure, improving predictive performance from an initial R2 ≈ 0.31 to R2 = 0.914. Validation was conducted by comparing the model with established empirical models and by independent evaluation using real earthquake records (Chi-Chi, Kobe, and Kocaeli), demonstrating the model’s ability to capture variations in seismic frequency content and energy distribution. Although direct field measurement of rd is inherently limited, the agreement with multiple independent seismic datasets and widely accepted empirical relationships provides strong indirect validation of the model’s physical reliability. Global sensitivity analysis using Sobol indices confirms that the effective stress ratio is the dominant controlling parameter, while soil plasticity influences rd primarily through interaction effects. The proposed model offers an interpretable and computationally efficient alternative to conventional approaches for seismic site response and liquefaction assessment.