Probabilistic NTH Calibration for Friction-Angle Inference Across Diverse Clay States

Abstract

The accurate determination of the effective friction angle in fine-grained soils remains a foundational challenge in geotechnical engineering and site characterization. Traditional deterministic methods relying on in-situ penetration testing often fail to account for the complex internal state variables of clays, such as the overconsolidation ratio, stress history, and spatial variability. This paper introduces a comprehensive framework utilizing Probabilistic Normalized Tip Heuristics (NTH) calibration to infer the effective friction angle across highly diverse clay states. By integrating advanced probabilistic techniques with normalized penetration parameters, the proposed NTH methodology provides a robust quantification of epistemic and aleatory uncertainties inherent in sub-surface investigations. The research meticulously details the transition from deterministic empirical correlations to a rigorously structured probabilistic inference model based on Bayesian updating principles. Through the analysis of extensive field penetration data coupled with high-quality laboratory triaxial baseline testing, the model successfully captures the nonlinear response of clays across normally consolidated and heavily overconsolidated domains. The findings demonstrate that probabilistically calibrated NTH parameters yield a significantly higher predictive reliability compared to traditional deterministic transformation models. Furthermore, this research elucidates the specific boundary conditions under which friction angle inference transitions from a robust physical correlation to a highly uncertain extrapolation, offering practitioners a calibrated confidence interval for engineering design. The methodology fundamentally advances the integration of statistical learning paradigms into traditional critical state soil mechanics.