Probabilistic Fractional-Order Modeling Driven by Bayesian Neural Networks Captures Long-Term Creep in Peat

Peat soils present formidable challenges in geotechnical engineering due to extreme compressibility and pronounced secondary creep. Because conventional deterministic models struggle to predict this time-dependent deformation accurately while quantifying inherent uncertainties, this study introduces a novel hybrid numerical framework combining a fractional-order poro-viscoplastic model with a Bayesian Neural Network (BNN). Methodologically, the constitutive model integrates Modified Cam Clay (MCC) theory with a Caputo fractional derivative to capture the hereditary memory of peat creep. To overcome the limitations of circular calibration, this study proposes a rigorous Simulation-Based Inference (SBI) framework. The BNN is trained exclusively on 10,000 synthetic data points generated via forward fractional FEM simulations. Subsequently, empirical posterior inference is conducted using a dedicated laboratory dataset comprising 5000 observations from 50 independent oedometer creep tests on undisturbed Kampung Gajah peat. Finally, actual field monitoring data from a full-scale trial embankment is employed exclusively for independent predictive validation. Results demonstrate that the calibrated fractional order (α = 0.48) acts as a critical rheological interpolator; higher values (α = 0.8) simulate sustained viscous flow, whereas lower values (α = 0.2) trigger rapid elastic deceleration. Unlike standard integer-order frameworks like the Soft Soil Creep (SSC) model, this fractional formulation rigorously propagates the inferred epistemic uncertainties to generate a robust 2D long-term settlement forecast bounded by a 95% credible interval. Ultimately, this integration of probabilistic machine learning with fractional mechanics offers a highly robust, risk-informed forecasting tool for sustainable peatland infrastructure design.