Field-Validated Hyperbolic Model Predicts Load Displacement of Untested Grouted Railway Piles

ABSTRACT Current design codes for grouted piles focus exclusively on bearing capacity improvements (β factors) and lack reliable methods for displacement prediction, creating significant risks for settlement-sensitive railway infrastructure. To address this gap, this study proposes a hyperbolic τ–s/σ–s constitutive model that integrates both stiffness (α) and resistance (β) enhancement factors. The test piles were constructed by the slurry-drilled method, leaving a filter cake on the borehole wall that was subsequently addressed by postgrouting. Detailed intermediate derivation steps for converting two-level bidirectional test data to top-loading scenarios are provided, providing a critical foundation for the model’s development. Based on 10 full-scale field tests on the Ninghuai Intercity Railway, grouting was found to improve initial stiffness by 19–94 % (with αs=1.19−1.48 and αb=1.94 in clay; αb=1.39 in silty sand) and increase ultimate resistance by 22–109 % (βs=1.22−1.66 and βb=2.09 in clay; βs=1.76 in silty sand). When validated against untested piles from the same project, the model achieved prediction errors of only 6 % for pre-grouted test piles and 12 % for fully untested piles. This demonstrates its capability to provide reliable settlement forecasts in the absence of site-specific load tests. These findings support future code revisions by incorporating stiffness-based displacement criteria, bridging the gap between theoretical models and the practical design of railway pile foundations.