Source-linked AI summary
Prediction of Compression Index of Fine-Grained Soils Using a Gene Expression Programming Model
Danial Mohammadzadeh, Seyed-Farzan Kazemi, Amir Mosavi, Ehsan Nasseralshariati, Joseph H. M. Tah
TL;DR
Estimating Cc for fine-grained soil settlement is costly, time-consuming, and technician-intensive. The paper develops a GEP closed-form equation from LL, PL, and e0 using 108 data points, and reports better R2, RMSE, and MAE performance than other models.
Problem
Estimating Cc for fine-grained soil settlement is costly, time-consuming, and requires skilled technicians.
Method
The study develops a GEP-based closed-form equation predicting Cc from LL, PL, and e0 using 108 soil data points.
Results
The GEP model achieved R2 values of 0.8231, 0.8603, and 0.8320 for training, validation, and the entire dataset, respectively, with low RMSE values.
Takeaways & Limitations
The developed model provides a practical Cc prediction approach based on simpler soil parameters and showed good performance compared with previous models.
Abstract
from arXiv · showhide
In construction projects, estimation of the settlement of fine-grained soils is of critical importance, and yet is a challenging task. The coefficient of consolidation for the compression index (Cc) is a key parameter in modeling the settlement of fine-grained soil layers. However, the estimation of this parameter is costly, time-consuming, and requires skilled technicians. To overcome these drawbacks, we aimed to predict Cc through other soil parameters, i.e., the liquid limit (LL), plastic limit (PL), and initial void ratio (e0). Using these parameters is more convenient and requires substantially less time and cost compared to the conventional tests to estimate Cc. This study presents a novel prediction model for the Cc of fine-grained soils using gene expression programming (GEP). A database consisting of 108 different data points was used to develop the model. A closed-form equation solution was derived to estimate Cc based on LL, PL, and e0. The performance of the developed GEP-based model was evaluated through the coefficient of determination (R2), the root mean squared error (RMSE), and the mean average error (MAE). The proposed model performed better in terms of R2, RMSE, and MAE compared to the other models.
1. Introduction
Fine-grained soil settlement requires accurate compression-index estimation, but existing statistical and soft-computing approaches have important limitations. The study therefore investigates GEP for producing a closed-form Cc prediction equation from simple soil tests.
- Accurate Cc estimation is critical for calculating fine-grained soil-layer settlement, where low permeability makes compressibility especially important.
- Traditional empirical equations can suffer from low correlation between input and output parameters.
- Common soft-computing methods often predict well statistically but do not provide a closed-form prediction equation.
- The study develops a GEP-based Cc equation using the liquid and plastic limits as simple soil-test inputs.
2. GEP
GEP evolves multiple gene-based programs into closed-form prediction models. Its structure combines fixed-length chromosomes, expression trees, selected functions, and fitted coefficients.
- GEP evolves multiple genes, or subprograms, to construct complex prediction models from fixed-length character strings.
- Unlike conventional GP, GEP converts chromosomes into expression trees with varied sizes and shapes while preserving genetic diversity through chromosome operators.
- The sample model uses inputs, arithmetic and nonlinear functions, and least-squares-fitted coefficients to produce a closed-form solution.
3. Modeling of Cc for Fine-Grained Soils
The study models Cc from LL, PL, and e0 using 108 soil records and evaluates the resulting GEP equation with standard fit and error metrics. These inputs were selected because they are easier to determine than Cc through consolidation testing.
- 3.1. Data Collection: The model uses 108 data points containing LL, PL, e0, and Cc values for individual fine-grained soil samples.
- 3.2. Model Structure and Performance: LL, PL, and e0 were selected because they are straightforward to determine compared with consolidation tests that directly measure Cc.
- 3.2. Model Structure and Performance: The GEP formulation treats Cc as a function of LL, PL, and e0 and evaluates predictions using R2, RMSE, and MAE.
t h RMSE
The GEP model was trained and validated on divided data, evaluated with multiple statistical criteria, and compared with existing prediction models. It achieved strong fit and low errors, while outperforming regression models in comparison but not matching the lowest RMSE and MAE of several AI methods.
- Model development: The database was split into training and validation subsets to reduce overfitting, and candidate models were selected using simplicity and performance criteria.The GEP algorithm was run with varied parameter combinations, including trial-and-error settings for influential parameters.
- Model performance: R2 values exceeded 0.8 for the training, validation, and entire datasets, while RMSE and MAE remained relatively low across all sets.The reported evaluation used measured-versus-predicted Cc values for the training, validation, and complete datasets.
- Additional evaluation: The model met all listed acceptance criteria for additional statistical performance measures.These criteria and results are presented in Table 4.
- Comparison with existing models: The GEP model achieved higher R2 than existing AI methods, although MEP, ANNs, and MGGP produced lower RMSE and MAE.The comparison included regression equations and AI methods such as MEP, ANNs, and MGGP.
- Comparison with existing models: The GEP model outperformed regression models by combining varied base functions without assuming a predefined solution shape.The authors attribute this comparison to GEP’s ability to represent complex interactions among LL, PL, e0, and Cc.
5. Conclusions
The study developed a GEP model and closed-form equation to estimate Cc from LL, PL, and e0 using 108 data points. The model showed acceptable predictive performance and nonlinear parameter interactions, with e0 positively correlated with Cc and LL and e0 more influential than PL.
- 5. Conclusions: The model used 108 data points to estimate Cc from LL, PL, and e0, producing a closed-form prediction equation.The authors developed the model using tuned calibration parameters selected through trial and error.
- 5. Conclusions: The closed-form equation was used to create surface charts predicting Cc from LL and PL for a specified e0.The authors anticipate savings in time and cost compared with determining Cc through conventional testing.
- 5. Conclusions: R2 was 0.8231, 0.8603, and 0.8320 for the training, validation, and entire datasets, respectively, while RMSE was 0.0269, 0.0237, and 0.0262.The authors interpreted the high R2 and low error as indicating highly acceptable model performance.
- 5. Conclusions: The GEP model showed highly nonlinear behavior, with e0 positively correlated with Cc and LL and e0 more influential than PL.The conclusion contrasts this behavior with classical regression-based models.