Stable soil conditions are essential for the construction of structures such as earthen dams and embankments. To achieve this stability, the soil must be compacted to a certain degree. Furthermore, the soil must meet specific permeability requirements. Permeability is influenced by the compaction parameters of the soil, so the Maximum Dry Density (MDD) and Optimal Moisture Content (OMC) are critical factors in the design of compacted earthworks.
Numerous studies have been conducted to establish a correlation between soil permeability and compaction parameters. Key physical properties considered in these analyses include plasticity characteristics such as the liquid limit, plastic limit, shrinkage limit, and plasticity index, as well as specific gravity and grain size distribution. Researchers have developed several correlations by employing various methodologies, including regression analysis, neural networks, and artificial neural networks (ANN), to predict maximum dry density (MDD), optimal moisture content (OMC), and permeability. However, it has been noted that there exists a significant gap in terms of a general correlation between permeability and soil gradation. Moreover, it is essential to consider a comprehensive range of grain size distributions alongside factors such as density and void ratio of the soil mass to establish a robust correlation.
In response to this need for improved predictive models, a study has been undertaken by a team of researchers from the University of Exeter, UK, focusing on the prediction of compaction characteristics (OMC and MDD) and soil permeability. This study employs the Evolutionary Polynomial Regression (EPR) algorithm to develop its predictive models. EPR is a sophisticated hybrid data-mining technique that combines genetic algorithms and least-squares regression to identify polynomial structures that accurately represent complex soil behaviours. This approach addresses certain limitations associated with artificial neural networks, including issues of interpretability and the necessity for pre-defined network structures. Mathematically, EPR can be expressed as y = F(X,Φ), where y signifies the output, X and Φ represent the input variables, F is a function in an m-dimensional space, and m denotes the number of inputs.
The data on compaction and permeability was derived from a soil mixture composed of four components: gravel, sand, limestone dust, and bentonite. The bentonite utilised in this study primarily consisted of Na-montmorillonite as its key clay mineral. The limestone dust was sourced as a by-product from limestone quarrying, characterised by a grain size ranging from 0.002 to 0.047 mm. The sand component featured well-graded fine aggregate suitable for the production of Portland cement concrete, with grain sizes between 0.074 and 4.76 mm. The gravel served as a coarse aggregate, exhibiting a particle size range of 4.76 to 10.05 mm. An EPR model was developed for each output parameter—maximum dry density (MDD), optimum moisture content (OMC), and permeability—taking into account distinct sets of input variables. Furthermore, the performance of the model was assessed using the coefficient of determination (COD).
For Maximum Dry Density (MDD), the following inputs were considered: dry density of the solid phase (gs) expressed in kg/m³, fineness modulus (Fm), effective grain size (D10) expressed in mm, plastic limit (PL) expressed as a percentage, and liquid limit (LL). The model achieved a coefficient of determination (COD) of 96%, indicating a strong correlation between the variables. An increase in MDD correlates with a rise in soil grain density, while an increase in fineness modulus suggests coarser soil, both resulting in higher maximum dry density values. Conversely, higher liquid and plastic limits indicate finer soil, which leads to a reduction in maximum dry density values. This aligns with the predictions of the model.
In the analysis of OMC (Optimum Moisture Content), the key inputs considered were fineness modulus (Fm), coefficient of uniformity (U), and plastic limit (PL), all expressed as percentages. The model achieved a coefficient of determination (COD) of 94%, indicating a strong correlation within the data. The findings suggest that as the fineness modulus increases, resulting in coarser soil grains, there is a corresponding decrease in the specific surface area of these grains. This decrease contributes to a reduction in optimum moisture content, which the model accurately captures. Furthermore, the influence of the coefficient of uniformity on optimum moisture content reveals that a higher coefficient signifies a broader range of particle sizes within the soil, ultimately leading to lower optimum moisture content. These results are consistent with previous research, underscoring the accuracy and reliability of this model. Additionally, it is noteworthy that while the fineness modulus and coefficient of uniformity significantly affect optimum moisture content, the plastic limit appears to exert a lesser influence.
In the context of soil permeability, several key parameters have been analyzed, including the coefficient of permeability (measured in m/s), degree of compaction (P) expressed as a percentage, mean grain size (D50) presented in millimeters, effective grain size (D10) in millimeters, plastic limit (PL) as a percentage, and liquid limit (LL) also as a percentage. The developed EPR model demonstrates a coefficient of determination (COD) of 92%, indicating its capacity to effectively predict soil permeability. This model performs favourably in comparison to experimental data and other existing models. Key findings from the parametric study highlight several critical relationships: increased compaction results in reduced void volume, thereby lowering permeability. Initially, larger effective grain sizes contribute to increased permeability; however, this increase stabilizes after reaching a certain threshold. Additionally, a higher plasticity index, which signifies greater fine content, significantly reduces permeability. It is noteworthy that the plasticity index exerts the most substantial influence on soil permeability, while the degree of compaction and effective grain size show moderate effects.
The models developed in this study were rigorously compared with traditional neural networks to assess their performance and efficacy. The coefficient of determination (COD) for the models capturing Moisture-Dependent Density (MDD) stands at an impressive 98%, while the models for Optimal Moisture Content (OMC) and Permeability exhibit CODs of 92% and 90%, respectively. These results underscore the robustness of the EPR models.
This research shows that EPR models accurately predict soil compaction parameters, such as moisture-dependent density and optimal moisture content, and provide valuable insights into soil permeability. A significant advantage of EPR models is their transparency and interpretability, which often pose challenges in the more complex architectures of neural networks.
Furthermore, these proposed models are designed with user-friendliness in mind, allowing practitioners in the field to apply them with relative ease. They also have the potential for continuous improvement as more data becomes available, enhancing their reliability and accuracy over time. This makes EPR models especially beneficial for various applications within geotechnical engineering, providing valuable tools for engineers in their assessments and decision-making processes.
Reference
Ahangar-Asr, A., Faramarzi, A., Mottaghifard, N., & Javadi, A. A. (2011). Modeling of permeability and compaction characteristics of soils using evolutionary polynomial regression. Computers & Geosciences, 37(11), 1860-1869.
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