# Compression Index Regression of Fine-Grained Soils with Machine Learning Algorithms
## 1 Introduction
\begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **Empirical Equation** & **Soil Type** & **Reference** \\ \hline (5) & \(C_{c}=0.009(\mathrm{LL}-10)\) & Normally consolidated clays & [PERSON] et al. [11] \\ \hline (6) & \(C_{c}=0.83(\mathrm{LL}-0.09)\) & Weald clay & Schofield and Wroth [16] \\  & & Kaolin & \\ \hline (7) & \begin{tabular}{c} Soft silty clays \\ \(C_{c}=0.0024\mathrm{LL}+0.071\) \\ \(C_{c}=0.261e_{0}-0.04\) \\ \end{tabular} & \begin{tabular}{c} \begin{tabular}{c} Soft silty clays \\ (from the lowlands of Santos) \\ Clay and silty clays \\ (from Sao Paulo) \\ \end{tabular} & Ozdikmen [17] \\ \hline (8) & \begin{tabular}{c} \(C_{c}=0.4(e_{0}+0.1001w_{n}-0.25)\) \\ \(C_{c}=0.006(\mathrm{LL}-9)\) \\ \(C_{c}=0.01(w_{n}-5)\) \\ \(C_{c}=0.4(e_{0}-0.25)\) \\ \end{tabular} & Clay & [PERSON] et al. [18] \\ \hline (9) & \begin{tabular}{c} \(C_{c}=0.01w_{n}\) \\ \(C_{c}=0.009w_{n}+0.005\mathrm{LL}\) \\ \(C_{c}=0.2343(\mathrm{LL}/100)G_{s}\) \\ \(C_{c}=0.2343w_{n}G_{s}\) \\ \end{tabular} & Cohesive soils & [PERSON] [19] \\ \hline (10) & \begin{tabular}{c} \(C_{c}=0.2343(\mathrm{LL}/100)G_{s}\) \\ \(C_{c}=0.2343w_{n}G_{s}\) \\ \end{tabular} & Clay & Nagaraj and Murthy [20] \\ \hline (11) & \begin{tabular}{c} \(C_{c}=0.003\mathrm{LL}(1+e_{0})\) \\ \(C_{c}=-0.165+0.411e_{0}+0.00058\mathrm{LL}\) \\ \end{tabular} & Colloidal-size particle soils & Al-Khafaji and Andersland [22] \\ \hline (13) & \begin{tabular}{c} \(C_{c}=0.008(\mathrm{LL}-12)\) \\ \(C_{c}=0.007(\mathrm{PI}+18)\) \\ \(C_{c}=0.014(\mathrm{PI}+3.6)\) \\ \end{tabular} & \begin{tabular}{c} Low-plasticity clays \\ Low-plasticity silts \\ Highly plastic silts \\ \end{tabular} & [PERSON] et al. [23] \\ \hline (14) & \begin{tabular}{c} \(C_{c}=0.0103w_{n}\) \\ \end{tabular} & Soft clays & Nagaraj and Miura [24] \\ \hline (15) & \begin{tabular}{c} Low-plasticity clays \\ Highly plastic clays \\ Normally consolidated clays \\ Over-consolidated clays \\ \end{tabular} & Lav and Ansal [25] \\ \hline (16) & \
\begin{tabular}{c} \(C_{c}=\\ -0.404+0.341e_{0}+0.006w_{n}+0.004\mathrm{LL}\) \\ \end{tabular} & Marine clays & Yoon and Kim [26] \\ \hline (17) &
\begin{tabular}{c} \(C_{c}=0.013w_{n}-0.115\) \\ \(C_{c}=0.49e_{0}-0.11\) \\ \(C_{c}=2.926(\mathrm{LL}/100)G_{s}\) \\ \(C_{c}=0.014\mathrm{LL}-0.168\) \\ \(C_{c}=0.013w_{n}+0.168\) \\ \end{tabular} & Clay & [PERSON] and [PERSON] [27] \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._improve risk assessments, streamline construction processes, and increase the reliability of engineering solutions [35]. Studies have been published in the literature that accurately predict the compression index using various machine learning methods. Utilizing an artificial neural network (ANN), a machine learning technique, researchers predicted the compression index using a dataset that included parameters like \(w\), LL, PI, and \(G_{s}\)[27]. [PERSON] et al. [36] used ANN models, genetic programming, and multiple regression analysis to estimate the compression index on a dataset that contained LL, \(w\), FCs (fine contents), P\({}_{h}\) (wet density), PI, \(e_{0}\), and soil types. In addition, [PERSON] et al. [37] employed machine learning techniques like extreme gradient boosting and random forest models on a dataset comprising \(e_{0}\), \(w\), LL, PI, and \(G_{s}\) to predict the compression index. Also, [PERSON] et al. [38] utilized random forest (RF) and gradient boosting tree (GBT), tree-based machine learning techniques, with input parameters including LL, \(e_{0}\), PL, and moisture content (MC) to determine the value of \(C_{c}\). Lastly, [PERSON] et al. [39] predicted the compression index using an ANN model, a form of deep learning, on a dataset containing \(w\), PI, LL, and the compression index (\(C_{c}\)). Artificial intelligence methods are increasingly being used in various soil and rock analyses in geotechnical engineering, yielding successful results. [PERSON] et al.