# Compression Index Regression of Fine-Grained Soils with Machine Learning Algorithms
## 1 Introduction  
The compressibility of fine-grained soils is critically important across multiple fields of study. In civil engineering, the compression characteristics of fine-grained soils under a load affects the stability of structures such as buildings and roads; therefore, engineers must carefully account for this property to prevent issues like differential settlement and structural damage. In addition, in environmental engineering, understanding soil's low permeability due to its compressibility helps in designing effective barriers against contaminant migration in groundwater [1; 2; 3]. This knowledge is vital for safeguarding water resources and managing hazardous waste disposal sites. Moreover, soil compressibility influences soil fertility, water retention, and drainage, directly impacting crop growth in agriculture [4; 5; 6]. Farmers adapt their irrigation and drainage practices to optimize agricultural productivity and prevent soil erosion. Additionally, in soil science, soil's compressibility is integral to soil classification systems and understanding soil behavior under different conditions. This knowledge supports land use planning, environmental assessments, and sustainable soil management practices. Overall, a comprehensive understanding of the compressibility of soils enhances our ability to address challenges in infrastructure stability, environmental protection, agricultural productivity, and soil conservation across various disciplines. Consolidation is a process applied to fine-grained soils. It involves slowly compressing the water in these soils under a load and removing it through drainage. Fine-grained soils, particularly clay, exhibit unique characteristics such as high compressibility, which play crucial roles across various disciplines. In the engineering field, this process increases the load carrying ability of the ground and minimizes long-term settlement, significantly affecting structural strength. Consolidation is particularly critical in fine-grained soils like clay because they react more slowly to the movement of water under a load. The compressibility of soils is quantified using the compression index (\(C_{c}\)), an important measurement for understanding settlement behavior. The compression index indicates the logarithmic amount of settlement per unit load increment and is typically determined in the laboratory through consolidation tests. This parameter is crucial in engineering applications for predicting soil behavior and developing appropriate foundation designs [7]. In geotechnical engineering, the evaluation and prediction of soil behavior under various loading conditions are critical for the stability and longevity of civil engineering structures. Key soil properties influencing such behavior include the liquid limit (LL), plastic limit (PL), water content (\(w\)), plasticity index (PI), specific gravity (\(G_{s}\)), and initial void ratio (\(e_{0}\)), all of which are integral to calculating the compression index of soils. The liquid limit (LL) denotes the water content level at which the soil transitions from liquid to plastic, while the plastic limit (PL) marks the shift from plastic to semi-solid, essential for characterizing soil plasticity [8]. Water content directly impacts soil's consistency and compressibility and is pivotal in soil behavior analysis [9]. The plasticity index, derived from the difference between the LL and PL, provides a comprehensive measure of soil plasticity, influencing its mechanical properties [7]. The initial void ratio (\(e_{0}\)), expressing the volumetric relationship between soil voids and solids, significantly determines the soil compression and settlement potential under a load ([PERSON], 1980). Furthermore, specific gravity (\(G_{s}\)), evaluating the particle density of soil relative to water, is crucial for understanding soil compressibility and stress behavior [10]. These parameters collectively contribute to determining the \(C_{c}\) value, a critical metric for predicting soil compression under loading [11].