⚡ electrical engineering

Investigation of Full-Process Settlement Behavior and Prediction Models for Long-Short Pile Composite Foundations

This paper proposes a hybrid prediction model integrating empirical models (Weibull and modified Poisson) with intelligent algorithms (EMD and LS-SVM) to accurately characterize the "S-shaped" settlement evolution and predict the full-process settlement of long-short pile composite foundations, as validated by the Seoul Park project.

Original authors: Yang Liu, Guobo Han, Lihua Zhang, Xuemei Tian, Changjin Zhang, Hongbo Qu, Lili Zhang

Published 2026-08-08

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CC BY 4.0

Original authors: Yang Liu, Guobo Han, Lihua Zhang, Xuemei Tian, Changjin Zhang, Hongbo Qu, Lili Zhang

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are building a giant sandcastle on a beach that is slowly sinking. You don't just want to know how deep the hole is right now; you want to know exactly how much it will sink tomorrow, next month, and next year. This is the daily challenge for engineers building skyscrapers on soft ground. They use special "composite foundations," which are like a team of long and short wooden stakes driven into the mud to hold the building up. But the ground doesn't just sink in a straight line; it behaves like a living thing, reacting to the weight of the building, the rain, and the construction workers in a messy, unpredictable way. To keep the building safe and straight, engineers need to predict this sinking behavior perfectly. If they guess wrong, the building could tilt or crack. This paper is about finding the best "crystal ball" to predict exactly how much these special foundations will settle over time.

The researchers in this study, led by Yang Liu and colleagues, tackled the problem of predicting the "full-process settlement" (the total sinking from start to finish) of these long-short pile foundations. They knew that simple math formulas often struggle because the ground's movement is messy and changes speed over time. To fix this, they tried three different approaches. First, they used two classic mathematical shapes called the Weibull model and a Modified Poisson model. Think of these like trying to fit a smooth, pre-made curve over a bumpy hiking trail. They found that while these curves could describe the general "S-shape" of the sinking (starting slow, speeding up, then slowing down again), they sometimes missed the little bumps and wiggles caused by construction noise or sudden load changes. The Modified Poisson model was a bit better at bending to fit the curve, but it still had limits.

To get a truly accurate prediction, the team invented a smarter, hybrid method called EMD-LS-SVM. They treated the settlement data like a complex song full of different instruments playing at once. First, they used a technique called Empirical Mode Decomposition (EMD) to separate the "song" into its individual instruments: the deep, slow bass notes (the long-term sinking trend), the mid-range melodies (the steady building of floors), and the high-pitched, scratchy noise (sudden jitters from construction work). Then, they used a powerful AI tool called Least Squares Support Vector Machine (LS-SVM) to predict the future of each instrument separately. Finally, they mixed these predictions back together.

The results, tested on a real building called Building B27 in a residential project in China, showed that this new hybrid method was the clear winner. While the simple curve-fitting models were okay, the hybrid model was incredibly precise. It predicted the final settlement at 600 days to be -27.5430 mm, with a maximum error of only 0.4760 mm. This is a huge improvement, cutting the error of the older models by more than half. The study suggests that by breaking the problem down into smaller, simpler pieces and then reassembling them, engineers can get a much clearer picture of how the ground will behave, helping them keep buildings safe and stable without the guesswork.

Technical Summary: Investigation of Full-Process Settlement Behavior and Prediction Models for Long-Short Pile Composite Foundations

Problem Statement
The accurate prediction of full-process settlement in long-short pile composite foundations is critical for ensuring the safety and serviceability of structures built on soft ground. However, existing prediction methods face two primary limitations:

Empirical Model Constraints: Conventional empirical models (e.g., standard Weibull and Poisson models) often rely on parameter estimation methods like cubic spline interpolation or nonlinear regression, which are sensitive to initial values and sample sizes, leading to limited parameter identification accuracy and robustness.
Complexity of Settlement Behavior: Foundation settlement is a complex, non-stationary process influenced by increasing superstructure loads, soil consolidation, and pile-soil interaction. It exhibits pronounced nonlinearity and multi-scale characteristics. Single empirical models struggle to simultaneously capture the long-term evolutionary trend and local fluctuations caused by construction disturbances and environmental variations.

Methodology
The study proposes a hybrid prediction framework that integrates empirical statistical modeling with intelligent data-driven algorithms. The methodology is structured in three phases:

Optimized Empirical Modeling:
- Weibull Model: Established to characterize the "S-shaped" settlement evolution. An optimization-based parameter identification method was developed to minimize the sum of squared errors between measured and predicted values, subject to a maximum absolute error constraint of 1 mm.
- Modified Poisson Model: A shape-modification parameter ( $c_4$ ) was introduced to the conventional Poisson model. This enhancement increases the model's flexibility to capture asymmetric settlement evolution and significant variations in settlement rates, which are common in long-short pile systems due to stress redistribution.
Hybrid Intelligent Prediction (EMD-LS-SVM):
- Empirical Mode Decomposition (EMD): The raw settlement monitoring data is decomposed into multiple Intrinsic Mode Functions (IMFs) and a residual component. This adaptive process separates the signal into distinct time scales: high-frequency components (short-term fluctuations/noise), medium-frequency components (stage-wise loading effects), and low-frequency/residual components (long-term consolidation trends).
- Least Squares Support Vector Machine (LS-SVM): An independent LS-SVM model is constructed for each decomposed component. LS-SVM is chosen for its ability to handle small-sample, nonlinear regression problems efficiently by transforming the quadratic programming problem into a system of linear equations.
- Weighted Reconstruction: The final prediction is generated by optimally reconstructing the predicted components using weighting coefficients determined by the minimum prediction error criterion.
Engineering Validation:
- The models were validated using field monitoring data from Building B27 in the Seoul Park Residential Development (Hebei, China). The foundation utilized a Cement Fly-ash Gravel (CFG) long-short pile system (long piles: 21.45 m; short piles: 11.90 m) in silty clay soil.

Key Results

Settlement Evolution Pattern: The full-process settlement of the composite foundation follows a typical "S-shaped" evolution pattern, characterized by an initial development stage, a rapid growth stage (where the settlement rate peaks), and a stable consolidation stage.
Empirical Model Performance: Both the optimized Weibull and modified Poisson models successfully captured the overall settlement trend with maximum absolute errors under 1.0 mm. The modified Poisson model demonstrated superior flexibility and predictive performance during stages with rapid changes in settlement rate due to its additional shape parameter.
Multiscale Characteristics: EMD successfully separated the settlement signal into distinct physical mechanisms. IMF1 captured short-term construction disturbances; IMF2 reflected stage-wise loading and pile-soil interaction; and the residual component represented the long-term soil consolidation trend.
Hybrid Model Superiority: The EMD-LS-SVM combined model significantly outperformed the single empirical models.
- It achieved a maximum absolute error of 0.4760 mm at 158 days, representing a reduction of over 50% compared to the maximum errors of the empirical models.
- At 128 days, the model achieved an error of 0.0000 mm.
- It effectively captured both the global evolution trend and local fluctuations, particularly during periods of rapid settlement rate changes where empirical models showed deviations.

Significance and Claims
The paper claims that the proposed hybrid approach addresses the limitations of traditional methods by:

Enhancing Parameter Identification: Utilizing optimization algorithms to improve the accuracy and robustness of empirical model parameters.
Decomposing Complexity: Leveraging EMD to transform a complex, non-stationary time series into simpler, stationary components, thereby reducing the difficulty of nonlinear mapping for the LS-SVM.
Improving Prediction Accuracy: Providing a theoretical basis and technical reference for settlement monitoring and safety control. The study asserts that the EMD-LS-SVM model offers a more reliable solution for the intelligent prediction of composite foundation settlement, capable of handling the coupled effects of construction loading, pile-soil interaction, and time-dependent consolidation.

The authors conclude that while empirical models are sufficient for capturing general trends, the combined EMD-LS-SVM model is necessary for high-precision prediction in complex engineering conditions where local fluctuations and multi-scale behaviors are significant.

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