## 1 Introduction  
The compression index (\(C_{c}\)) is a crucial parameter in geotechnical engineering for predicting the settlement behavior of clayey soils under consolidation. Its accurate estimation is fundamental for foundation design and soil stability analysis. Conventionally, \(C_{c}\) is empirically estimated using correlations based on soil index properties (e.g., the liquid limit, the plasticity index) or determined directly through laboratory consolidation tests [1,2]. While these traditional methods provide useful estimations, they are often limited by regional soil characteristics and laboratory constraints [3]. Recent advancements in machine learning (ML) have enabled more accurate, adaptable predictions of geotechnical parameters like \(C_{c}\)[4]. Many empirical models have been developed to correlate \(C_{c}\) with soil properties such as the natural water content, the liquid limit, and the void ratio. [PERSON] [2] proposed one of the earliest models, correlating \(C_{c}\) with the liquid limit for normally consolidated clays. In 1944, [PERSON] [2] proposed an empirical formula to estimate the \(C_{c}\) of remolded clay based on their liquid limit (LL):  
\[C_{c}=0.007\times(\text{LL}-10) \tag{1}\]  
This equation suggests that the compression index increases linearly with the liquid limit. For normally consolidated clays, [PERSON] and [PERSON] [1] recommended a similar relationship with a slightly higher coefficient:  
\[C_{c}=0.009\times(\text{LL}-10) \tag{2}\]  
These correlations provide a straightforward method to estimate the compressibility of clays using their liquid limit. Other studies have since refined these relationships and incorporated more variables for improved accuracy [5,6]. However, empirical models are often highly dependent on soil-specific characteristics and lead to less reliable predictions across diverse soil profiles [7]. Table 1 shows the main empirical correlations for determining \(C_{c}\). A recent study developed a novel gene expression programming (GEP) model to predict the compression index (\(C_{c}\)) of fine-grained soils using the liquid limit (LL), the plastic limit (PL), and the initial void ratio (\(e_{0}\)) and provide a cost-effective and time-efficient alternative to conventional methods while demonstrating superior performance in terms of \(R^{2}\), the RMSE, and the MAE [12]. Another study utilized single and MLR analyses to predict the compression index (\(C_{c}\)) of fine-grained remolded soils using basic soil properties, such as the liquid limit (LL), the plasticity index (PI), the optimum moisture content (OMC), the maximum dry density (MDD), and the DFS. The best-propos \begin{table}
\begin{tabular}{c c c c} \hline
**Reference** & **Inputs** & **Type of Soil** & **Formula** \\ \hline Skempton [2] & Liquid Limit (LL) & Normally Consolidated Clays & \(C_{c}=0.007\times(\text{LL}-10)\) \\ [PERSON] and Peck [1] & Liquid Limit (LL) & Normally Consolidated Clays & \(C_{c}=0.009\times(\text{LL}-10)\) \\ [PERSON] [6] & Liquid Limit (LL) & Normally Consolidated Clays & \(C_{c}=0.0046\times(\text{LL}-9)\) \\ [PERSON] et al. [8] & Natural Water Content (\(w\)) & Clayey Soils & \(C_{c}=0.3\times w-0.05\) \\ [PERSON] [9] & Initial Void Ratio (\(e_{0}\)) & Normally Consolidated & \(C_{c}=0.15\times e_{0}\) \\ [PERSON] and [PERSON] [10] & Liquid Limit (LL) & General & \(C_{c}=0.012\times\text{LL}\) \\ [PERSON] and [PERSON] [11] & Liquid Limit (LL), Plastic Limit (PL) & General & \(C_{c}=0.0042\times(\text{LL}-\text{PL})\) \\ \hline \end{tabular}
\end{table} 
Table 1: Empirical correlations to determine \(C_{c}\). \(R^{2}\) of 0.95 and an average variation of \(-13.67\%\) to +9.62%, making it a reliable tool when combined with engineering judgment [13]. Furthermore, a study evaluated the accuracy of an artificial neural network (ANN) model for predicting the compression index (\(C_{c}\)) by comparing it to laboratory values and models proposed by [PERSON] and [PERSON] [14].