Accurate settlement prediction for high-speed railway (HSR) soft foundations remains challenging due to the irregular and dynamic nature of real-world monitoring data, often represented as non-equidistant and non-stationary time series (NENSTS). Existing empirical models lack clear applicability criteria under such conditions, resulting in subjective model selection. This study introduces a Monte Carlo-based evaluation framework that integrates data-driven simulation with geotechnical principles, embedding the concept of symmetry across both modeling and assessment stages. Equivalent permeability coefficients (EPCs) are used to normalize soil consolidation behavior, enabling the generation of a large, statistically robust dataset. Four empirical settlement prediction models—Hyperbolic, Exponential, Asaoka, and Hoshino—are systematically analyzed for sensitivity to temporal features and resistance to stochastic noise. A symmetry-aware comprehensive evaluation index (CEI), constructed via a robust entropy weight method (REWM), balances multiple performance metrics to ensure objective comparison. Results reveal that while settlement behavior evolves asymmetrically with respect to EPCs over time, a symmetrical structure emerges in model suitability across distinct EPC intervals: the Asaoka method performs best under low-permeability conditions (EPC ≤ 0.03 m/d), Hoshino excels in intermediate ranges (0.03 < EPC ≤ 0.7 m/d), and the Exponential model dominates in highly permeable soils (EPC > 0.7 m/d). This framework not only quantifies model robustness under complex data conditions but also formalizes the notion of symmetrical applicability, offering a structured path toward intelligent, adaptive settlement prediction in HSR subgrade engineering.

Accurate prediction of post-construction settlement in high-speed railway (HSR) soft foundations is critical for operational safety yet challenging due to the non-equidistant and non-stationary nature of observation data. This study systematically evaluated the robustness and accuracy of settlement prediction models using a Monte Carlo simulation approach. A numerical model incorporating the permeability characteristics of soft foundations was established to simulate stochastic system responses. Furthermore, an innovative multi-metric evaluation framework was constructed using the entropy weight method, integrating goodness-of-fit, prediction accuracy (systematic error), and stability (random error). Four classical empirical models—Hyperbolic, Exponential Curve, Asaoka, and Hoshino—were assessed. The results indicate that: (1) The Hyperbolic Method significantly outperformed other models ($p<0.01$) in goodness-of-fit (mean correlation coefficient: 0.983 ± 0.006) and accuracy (systematic error: 3.2% ± 1.1%); (2) The Hoshino Method exhibited optimal stability, characterized by the lowest random error (3.8 ± 2.0 mm); and (3) Model performance showed a significant positive correlation with the permeability coefficient ($R^2>0.92$). Validated by five distinct engineering cases, the comprehensive performance ranking was determined as: Hyperbolic > Hoshino > Exponential Curve > Asaoka. These findings provide a scientific strategy for model selection under non-stationary conditions and offer theoretical support for refining railway deformation monitoring standards.

In the small-deformation scenario of high-speed railway (HSR) rigid pile–raft composite foundations, the coupled effects of non-equidistant and non-stationary (NENS) characteristics in observational data significantly affect the system response of prediction models. Existing research has predominantly focused on single evaluation metrics or large-deformation scenarios, lacking a comprehensive evaluation system for the multidimensional performance of these models under small-deformation conditions. NENS time-series data were generated via Monte Carlo simulation. The coupled effect was quantified through a process involving “theoretical curve extraction–non-equidistant sampling–random disturbance injection”. Parameters such as pile length, displacement ratio, and pile–soil modulus ratio were normalized using the composite modulus (CMA) method to uniformly characterize the influence of foundation stiffness on time-varying settlement characteristics. A robust entropy-weighted method was then used to construct a comprehensive evaluation index (CEI), which integrates goodness-of-fit (36%), prediction accuracy (26%), and stability (38%) to systematically assess four empirical models: the hyperbolic method, exponential curve method, Asaoka method, and Hoshino method. The results indicate that when CMA ≤ 100 MPa, settlement curves exhibit nonlinearity, and the Hoshino and hyperbolic methods perform optimally. Between 100 and 1000 MPa, pile–soil interaction intensifies, highlighting the Hoshino method’s superior stability. When CMA ≥ 1000 MPa, pile–soil interaction becomes load-dominated, with the Hoshino method remaining optimal while the hyperbolic and exponential curve methods exhibit significantly increased errors. The proposed NENS time-series simulation–multi-criteria coupling evaluation framework resolves model selection challenges in small-deformation scenarios and provides robust decision support for HSR settlement prediction.