In the field of civil engineering, swelling and shrinkage phenomena are the cause of numerous disorders in both surface structures (buildings, surface foundations, retaining structures, embankments, etc.) and buried structures (tunnels, piles, pipes, deep foundations, etc.). There are many examples of disorders linked to the presence of swelling clays [3] . The disorders associated with foundation movement generally manifest themselves in the appearance of cracks on the house [4] . These cracks due to the shrink-swell phenomenon generally appear at the end of a dry period when the soil shows maximum settlement. They evolve according to climatic conditions: they enlarge during dry periods and may tend to close during wet periods.

When swelling clay soils are subjected to variations in water content, they undergo major deformations known as shrink-swell phenomena, which can cause damage to structures built on them.

In general, there are two possible solutions for preventing building damage caused by the risk of geotechnical drought, as quoted [2] .

- adapting the building structure to soil movements, by taking into account practical constructive measures.

- adapting the soil to the structure by trying to modify its behavior. This is called stabilization. The main purpose of soil stabilization is to alter the geotechnical properties of natural soils to meet specific engineering purposes. The soil’s geotechnical properties can be improved by enhancing the shear strength parameters, increasing the tensile strength, and improving stiffness. It also aims to reduce plasticity, and minimize volumetric changes in expansive or fine-grained soils caused by moisture variability [5] .

Stabilization techniques frequently used in civil engineering projects include the following: mechanical stabilization, thermal stabilization, chemical stabilization (using additives), stabilization by adding sand. In this work the chemical stabilization called lime stabilization is used. It is a well-established practice to utilize lime to enhance the engineering behavior of expansive clayey soils. Generally, fine-grained treated with exhibit decrease plasticity, enhancement of workability, and decrease volume variations characteristics. The three kinds of limes utilized to enhance the soil parameters include hydrated lime (calcium hydroxide-Ca(OH)₂, hydrated lime slurry, and quicklime (calcium oxide-CaO) [6] . Figure 1 shows the chemical stabilization methods.

The reaction diagram illustrates the process of stabilizing expansive soils using quicklime (calcium oxide, CaO). When quicklime is mixed with water (H₂O), it undergoes a reaction to form calcium hydroxide (Ca(OH)₂) a compound that is highly alkaline.

Quicklime is obtained by calcination given in Equation (1)

CaCO₃ + 50 kcal $\to$ CaO + CO₂ (1)

It reacts in contact with water with a strong release of heat, then transforms into a white powder called slaked lime given in Equation (2)

CaO + H₂O $\to$ Ca(OH)₂ + Heat(2)

In the presence of carbon dioxide, slaked lime can carbonate and become limestone again, according to this following chemical reaction following Equation (3)

Ca(OH)₂ + CO₂ $\to$ CaCO₃ + H₂O(3)

Several methods are used to treat soils prone to swelling using lime. Among them, lime column technique. The lime column technique was introduced in Sweden in 1967 as a new type of foundation for light building (Breddenberg and Broms in [7] . The lime column technique has been applied successfully in recent years to improve the physical and mechanical properties of the soils [8] . Lime columns are constructed in-situ using a tool that functions like a giant “egg beater” ( Figure 2 ). The principle is to screw down the tool into the soil in the required depth of the column. In the desired depth, the rotation of the tool is reversed and unslaked lime is forced under compression through openings placed just above the blades of the tool [8] .

The material is extracted in Diamniadio, a town located approximately 30 km southeast of Dakar, more precisely in the department of Rufisque. The site is located next to the Diamniadio soccer field. The samples were collected using hand-dug wells approximately 1 m deep. Three (03) wells were dug and distributed around the site around the reference point: Latitude: 14.738931, Longitude: −17.232519 ( Figure 3 ).

Figure 4 shows experimental procedure for soil stabilization.

Physical, Mechanical and chemical tests were carried out on the sample in order to determine the characteristics of the soil.

To determine the water (moisture) content $w$ defined by Equation (4), three samples were used and Table 1 shows the water content average.

Where $m_w$ and $m_d$ are respectively the water mass evaporated during drying and the solid grains mass

$w=m_w/m_d$(4)

The particle size analysis by sieving was carried out using the wet method in accordance with standard NF P 94-056, and the sedimentological analysis was carried out in accordance with standard NF P 94-057 ( Figure 5 ). Table 2 shows $C_u$ (uniformity coefficient) and $C_c$ (curvature coefficient) values derived from the particle size distribution curve.

In accordance with standard NF P 94-051, tests to determine the Atterberg limits were carried out, giving the values shown in Table 3 .

With a plasticity index $I_p$ of 27.4 between 15 and 40, the soil sample is considered plastic. The test according to standard NF P94-054 determined the specific weight ${\gamma }_s$ to be 2.6 g/ml, which corresponds to clay soil. With regard to chemical tests, standard NF P 94-048 enabled the VBS methylene blue value to be calculated from two tests ( Table 4 ).

A pH value of 8.15 was determined using a pH meter in the chemistry department laboratory at Alioune Diop University in Bambey (Senegal).

The oedometer test according to standard NF P94-090-1 was also performed in order to plot the compressibility curve of untreated clay ( Figure 6 ). This curve corresponds to the evolution of the void ratio as a function of the vertical stress applied to the clay.

Thanks to the compressibility curve, the compression index $C_c$ defined by the equation and the swelling index $C_G$, were determined

$C_c=\left(-\Delta e\right)/\Delta \left(\log {{\sigma }^{\prime }}_z\right)$ (5)

By analyzing the compressibility curve, we observe that the swelling index of the clay is 0.038. As $C_G$ is lower than 0.05, we can conclude that the clay has low swelling properties. Furthermore, with a $C_c$ value of 0.386, the clay in question is characterized by high compressibility.

With regard to mechanical testing, the direct shear test in accordance with standard NF P94-071-1 was used to evaluate the shear strength of soils, focusing mainly on cohesion and friction angle. Figure 7 shows the Mohr-Coulomb diagram, which indicates that the clay has a cohesion of 27.495 kPa and a friction angle of 7.744.

The simple compression test according to standard NF P94-077 was used to determine the simple compressive strength using Equation (6), which corresponds to a value of 0.69 MPa.

$R_C=F_{\max }/S$ (6)

The material was treated with lime, whose chemical and physical characteristics are given in Table 5 and Table 6 , respectively.

This part of the paper present the results of soil stabilization regarding to the percentage of used lime.

The pH value of the Diamniadio clay studied in this article, which is initially 8.15, increases after the gradual addition of lime to a value of 12.27 corresponding to 2% lime. For a lime percentage above 2%, the pH value stabilizes despite the continuous addition of lime ( Figure 8 ). Thus, we can conclude that the initial percentage for stabilizing Diamniadio clay soil is 2%. The starting dosage of 2% is retained because it is at this threshold that the pH reaches approximately 12.3 and stabilizes, conditioning pozzolanic activation, with a simultaneous decrease in Atterberg limits (and therefore plasticity) and swelling indicators.

Figure 9 shows a decrease in the liquidity limit from 51.1% for untreated clay to 40.7% when the proportion of lime reaches 8%. The curve shown in Figure 10 illustrates the change in the plasticity limit as lime is added. The curve shows an increase in the plasticity limit as the percentage of lime increases, from 23.6% in the absence of lime to 36.9% when the percentage of lime reaches 8%.

The curve shows a reduction in the plasticity index as the percentage of lime increases, from 27.4% without lime to 3.1% when the lime content reaches 8%.

As for the swelling coefficient, it decreases as the percentage of lime increases, reaching a minimum of 0.0094 at 4% lime. Above this proportion, the swelling potential begins to increase again in proportion to the addition of lime ( Figure 11 ).

Figure 12 shows the evolution of undrained cohesion as a function of the lime addition rate. These results show an improvement in cohesion until the percentage of lime added reaches 4%. However, above this concentration, cohesion decreases.

Figure 13 shows the evolution of the internal friction angle as a function of the increase in the rate of lime addition.

Figure 14 illustrates the significant change in tensile strength following the addition of lime during a 28-day curing period. The observation shows that incorporating lime into clay soils makes them more resistant to compression. By gradually increasing the percentage of lime in the mixture (lime and clay), increased resistance is observed up to a threshold of 4%.

This section of the article presents a numerical analysis of the stabilization of the swelling clay soil in Diamniadio using lime columns to reduce settlement. PLAXIS 3D CE V20 was used.

Based on the lithology of the Diamniadio site, we observe a layer of black clay on the surface, followed by a layer of marl-limestone at depth ( Figure 15 ). Therefore, for modeling purposes, the HSM model for the clay and marl-limestone layer was used to account for the swelling effect. Table 7 and Table 8 show the parameters for the clay and marl layers, respectively.

$E_{ur}^{ref}$ the unloading/reloading elastic modulus (by default $E_{ur}^{ref}=3E_{50}^{ref}$), $E_{50}^{ref}$: the reference secant modulus in a triaxial situation, $E_{oed}^{ref}$ the reference tangent modulus under edometric stress, C: cohesion, $\phi$: friction angle et, $R_f$ le ratio de rupture (par défaut $R_f$ = 0.9), ${\nu }_{ur}$: elastic Poisson’s ratio (by defaut ${\nu }_{ur}$ = 0.2), $K_0^{NC}$: $K_0$-consolidation (by defaut $K_0^{NC}=1-\sin \varphi$).

For this study, a circular column with a diameter B of 0.8 m, a length L of 12 m, and a thickness E of 1.2 m was used. Table 9 shows the Mohr Coulomb parameters for the column.

The foundation in this study is a concrete raft slab with a length L of 2.5 m, a width l of 2.5 m, and a thickness E of 0.45 m, a long-term modulus of elasticity of concrete E_b = 10 GPa, a Poisson’s ratio υ_p = 0.15, and a density of concrete γ_d = 24 kN/m³. The applied load is a surface load of 55.9 kN/m resulting from the descent of loads from a four-story building.

As part of this study, four calculation stages were taken into account:

• Phase 1: corresponding to the application of a load on the foundation without swelling

• Phase 2: corresponding to the application of a load on the foundation with a column without swelling

• Phase 3: corresponding to the application of a load on the foundation with swelling and a group of columns without swelling

• Phase 4: corresponding to the application of a load on the foundation with swelling

Soil treatment with lime columns indicates that the use of lime reduces soil settlement. Less settlement is observed when columns are installed compared to the footing alone under load, as shown in Figures 16-18 .

The obtained results are summarized in Table 10 . We can see how the use of lime column impacted the settlement of the foundation when the swelling is not taken account (settlement from 1.584 mm to 1.511 mm) and also when the swelling is taken account.

The impact of column diameter on settlement was analyzed. The results obtained are shown in Figure 19 .

A study of the influence of spacing on settlement between columns was also carried out. The results obtained are presented in Table 11 .

The results indicate that settlement decreases as the columns get closer together, resulting in less settlement when the spacing between columns is 1 m.

The numerical analysis carried out on the stabilization of the swelling clay soil in Diamniadio using lime columns demonstrates the beneficial effect of lime on reducing soil settlement, which decreases from 1.85 mm for the base on the swelling soil to 1.054 mm after treating the soil with lime columns. Following the application of volumetric deformation to integrate swelling, settlement decreased from 1.511 mm to 1.322 mm. This reduction in settlement is due to the swelling of the clay soil, which was reduced by the lime column.