The physical characterization of the soil includes the determination of the specific gravity of solid grains, bulk density, in-situ void ratio, saturated water content, Atterberg limits, and optimal compaction parameters.

3.1.1. Particle Density and Specific Weight

The specific weight or unit weight ( γ s ) of a soil is used in civil engineering to determine the weight of a structure designed to support specific loads while remaining intact and within its deformation limits. Its laboratory determination is based on the measurement of the particle density (or real density) ρ s of the

Figure 1. Location of the sampling site.

soil’s solid grains (NF-EN-ISO-17892-3, 2015). The experimental setup and key laboratory procedure steps are illustrated in Appendix A (Figure A2).

The test was conducted on a single specimen. The values obtained for the particle density ( ρ s ) and specific gravity ( γ s ) are recorded in Table 1. The determined value of ρ s is close to the standard particle density value typically used for soils when measurements are unavailable, namely 2650 kg∙m⁻³.

Table 1. Particle density and specific weight.

3.1.2. Atterberg Limits

Atterberg limits, or soil consistency limits, are used to identify and classify the soil. They also allow for the prediction of its behavior during earthwork phases and/or when subjected to mechanical stress (allowable stress, modulus of elasticity). Standard NF-EN-ISO-17892-12 (2018) specifies the methods for their determination, namely the liquid limit ( w L ) and the plastic limit ( w P ). These are determined on the fine fraction of the material passing through a 0.4 mm sieve. The plasticity index I P of the soil corresponds to the difference between w L and w P . It indicates the extent of the plastic range and is commonly used to characterize soil clayiness. Table 2 summarizes these three soil parameters. Based on the obtained values, the studied soil, with an I P between 12 and 22, is classified as moderately clayey [27].

Table 2. Atterberg limits of the soil.

3.1.3. Methylene Blue Value of the Soil

The methylene blue value (MBV), which characterizes the clayiness of a soil, is determined according to standard NF-EN-933-9 (1999). The test data and the resulting VBS are recorded in Table 3. According to the GTR classification system [27], which uses the VBS for soil identification, the studied material is classified as a low-plasticity clayey sand.

Table 3. Methylene blue value of the soil.

3.1.4. Proctor Characteristics

The Proctor characteristics of the soil are presented below. Figure 2 shows the Proctor curves obtained according to standard NF-P94-093 (2014). The 80% and 100% saturation curves (zero air voids curves) are also illustrated. Table 4 summarizes the optimal compaction characteristics of the studied soil.

Figure 2. Proctor curves.

The curves, which are relatively flat, reveal a wide range of compaction water contents that allow the material to achieve optimal mechanical performance. The optimal characteristics of this soil (Table 4) are virtually identical to those reported by Savadogo et al. [24]. Furthermore, the Modified Proctor dry density ( ρ OPM ) is in the same range as those measured by Mbengue et al. [21]. In contrast, the optimal water content ( w OPM ) obtained for this soil is slightly lower, indicating a higher clay particle content in the studied soil.

Table 4. Proctor characteristics of the soil.

The particle size distribution (PSD) of the soil is determined according to standard NF-EN-ISO-17892-4 (2018). The described methodology employs both sieve analysis (for particles larger than 80 μm) and hydrometer analysis (for those smaller than 80 μm). The soil’s grading curve is presented in Figure 3. Table 5 summarizes the results of the particle size analysis of the studied soil.

Table 5. Morphological characteristics of the soil.

a. United States Department of Agriculture.

Figure 3. Granulometric curve of soil.

The grain size classification of the soil was performed in accordance with the USDA classification system. The coefficient of uniformity C u provides an indication of grain size homogeneity: C u > 2 corresponds to a well-graded (extended) distribution, while C u < 2 indicates a uniform distribution. The grading is considered well-graded if 1 < C c < 3 , and poorly graded otherwise. Based on the values in Table 5, the studied material has an extended but poorly graded particle size distribution. The proportion of material passing through the 63 μm sieve is essential for classification according to GTR [27]. This proportion is 39.50%. Being higher than the 35% threshold established by GTR [27], this indicates that the material’s behavior is governed by its fine fraction (i.e., particles smaller than 63 μm).

Thermal conductivity is used to describe the thermal behavior of the soil. This parameter is essential for modeling heat transfer within the soil to optimize the design and durability of structures subjected to thermal stresses. The thermal conductivities of the soil in dry ( λ dry ) and saturated ( λ sat ) states were measured in the laboratory following standard ASTM-D5334-22 (2022). The specimens used were compacted at optimal conditions: w = w OMC = 9.4 % and ρ d = ρ d OMC = 1.98   g ⋅ cm − 3 . The dry specimen was prepared in a Proctor mold (Height H = 116.5 mm and Diameter D = 101.5 mm) and subsequently demolded. To ensure uniform and complete drying, it was exposed to ambient air at an average daily temperature of approximately 35˚C for 30 days. It was carefully drilled using a power drill to accommodate the sensor. As for the saturated specimen, it was prepared in an oedometer ring (Height H = 20 mm and Diameter D = 70 mm) and then submerged for 96 hours to achieve full saturation. The KD2 Pro measurement system equipped with the RK-1 sensor, along with the dry and saturated specimens, are shown in Figure A3 of Appendix A. The RK-1 sensor, with a diameter of 3.9 mm and a length of 6 cm, measures thermal conductivities ranging from 0.10 W∙m⁻¹∙K⁻¹ to 6.00 W∙m⁻¹∙K⁻¹ with an accuracy of ±10%. In accordance with the user manual¹, the sensor was inserted into a hole carefully drilled in each specimen. A reading time of 15 min was set for each of the three (03) measurements performed. The measurement results and the average values are summarized in Table 6.

Table 6. Thermal conductivity (W∙m⁻¹∙K⁻¹) of the soil in dry and saturated states.

The results show a ratio of approximately 4 (i.e., 1.826/0.458). This discrepancy between λ dry and λ sat is due to the replacement of air (an insulator, λ air ≈ 0.024 W∙m⁻¹∙K⁻¹) with water (a conductor, λ water ≈ 0.6 W∙m⁻¹∙K⁻¹) within the pores during saturation, thereby creating “thermal bridges” between the solid grains. Furthermore, the saturated value of 1.826 for λ sat is consistent with soils having a dominant sandy fraction [28]">">[28].

The intrinsic permeability k of a soil depends on its geometry as well as the distribution and size of its constituent pores. It is related to the saturated hydraulic conductivity K sat by Equation (1).

where:

K sat [ m ⋅ s − 1 ] is the saturated hydraulic conductivity of the soil; k [ m 2 ] is the intrinsic permeability of the soil; ρ [ kg ⋅ m − 3 ] is the fluid density; g = 9.81   m ⋅ s − 2 is the acceleration due to gravity; μ [ kg ⋅ m − 1 ⋅ s − 1 ] is the dynamic viscosity of the fluid.

Direct measurement of intrinsic permeability is complex [29]. Therefore, saturated hydraulic conductivity K sat , which is directly linked to k (Equation (1)), is generally used instead. Experimental laboratory or in-situ measurement methods are proposed in the literature for estimating K sat . In this study, K sat is determined using a falling-head permeameter and through a consolidated undrained (CU) triaxial test.

4.2.1. Falling-Head Permeameter Method

Standard NF-X30-441 (2008) specifies the laboratory experimental procedure. The hydraulic conductivity is obtained using Equation (2):

where:

Δ t [ s ] is the time taken by the water to cover the distance h 0 − h 1 [ m ] ( h 0 and h 1 being the initial and final hydraulic heads, respectively); s and S are the cross-sectional areas of the standpipe and the specimen, respectively [in m²]; L [ m ] is the height of the specimen.

4.2.2. Triaxial Test

The triaxial procedure [30] utilizes Darcy’s law (Equation (3)), which expresses the volumetric flow rate Q [m³∙s⁻¹] (or the filtration velocity of water through the soil column) as a function of the cross-sectional area A [m²] of the specimen and the hydraulic gradient i = Δ h / L :

where Δ h [m] is the head loss. Figure 4 shows the evolution of the volume of water injected into the soil specimen during the test at a pressure of 79 kPa. The volumetric flow rate Q corresponds to the slope of the resulting linear trend line. The measurement characteristics for K sat are presented in Table 7.

Table 7. Permeability measurement characteristics.

Figure 4. Variation of water volume as a function of time.

4.2.3. Results

The measurement results for the soil’s hydraulic conductivity are presented in Table 8. The obtained experimental values of K sat are relatively close, with a mean relative difference of 2.09%. These values, on the order of 10⁻⁸ m∙s⁻¹, are typical of a clayey to silty clay soil.

Table 8. Hydraulic conductivity and intrinsic permeability of the soil.

The ability of a soil to retain or release its pore water is characterized by the determination of the soil-water characteristic curve (SWCC). It is typically represented in an ( S r , s ) or ( w , s ) plane for a given void ratio e 0 . The experimental setup for measuring suction at a given water content differs for low and high suction ranges. A synthesis of the challenges regarding the experimental and numerical (modeling) determination of the characteristic curve is presented in [29], with an emphasis on determination across the entire water content range: from the saturated state to the near-dry state. The WP4C chilled-mirror dewpoint potentiometer (Figure A4 of Appendix A) was used in our study. Unlike other methods such as the pressure plate apparatus (Richards pressure chamber), this device measures total soil suction over a range from 100 kPa to 3∙10⁵ kPa. The experimental procedure complies with the standard ASTM-D6836-16 (2016). Its operating principle is based on measuring the relative humidity of air at the dew point inside a sealed chamber containing the soil specimen at equilibrium García Fernández et al. [31]. Kelvin’s law (Equation (4)) is then applied to estimate the total soil suction Ψ (the sum of a matric component Ψ m due to the porous matrix and capillary forces, and an osmotic component Ψ O due to solute concentration in the pore fluid). In this study, osmotic effects were neglected because at low water contents, the measured suction is dominated by capillary and matric effects; furthermore, demineralized water was used in specimen preparation, thereby limiting the presence of soluble salts [32][33]. Consequently, the suction measured by the WP4C is assumed to be the matric suction ( Ψ m ≈ Ψ = − s ).

where:

s [ MPa ] is the matric suction; R = 8.3143   J ⋅ K − 1 ⋅ mol − 1 is the ideal gas constant; T [ K ] is the absolute temperature; M w = 0.01801   kg ⋅ mol − 1 is the molar mass of water; ρ w = 998   kg ⋅ m − 3 is the density of pure water at 293 K; and;RH [/] is the relative humidity.

Figure 5 presents the experimental retention curves alongside those estimated by the numerical model (Equation (5)) of Van Genuchten [34] (the most widely used in the literature). Discrepancies between the experimental and simulated curves are observed for water contents exceeding 50%. These gaps are explained by the inaccuracy of suction measurements in this range, as the WP4C is particularly suited for high suctions. The model calibration parameters (Equation (5)) and the associated statistical test results (R² and Root Mean Square Error: RMSE) are presented in Table 9.

where:

S e [ / ] is the effective degree of saturation of the soil; S l [ / ] is the liquid (water) saturation; S max [ / ] is the maximum saturation; S min [ / ] is the minimum (or residual) saturation; s [ MPa ] is the matric suction; P [ MPa ] and λ [ / ] are constant parameters to be determined from the experimental curve.

Figure 5. Soil-water characteristic curve.

Table 9. Van Genuchten model parameters [34] for the characteristic curve.

The discrepancy between P dry = 1.85   MPa and P wet = 1.03   MPa indicates that the soil releases its water more with more difficulty than it reabsorbs it. This behavior is conventionally attributed to changes in the contact angle during the drying-wetting cycle. The higher value of P dry suggests a degree of hydraulic inertia during desiccation episodes.

From a practical standpoint, this property could be a potentially favorable factor for embankment stability under alternating dry and wet seasons. Indeed, since desaturating the material is more difficult ( P dry > P wet ), the suction variations induced by climatic cycles could be limited—and consequently, variations in effective stress—thereby reducing the risk of shrink-swell behavior. However, it should be emphasized that in situ stability cannot be captured by the retention curve alone, as it depends on several other parameters (geometry, drainage conditions, cohesion, friction angle, and dynamic loading). The work of Kocaman et al. [35] and Luo et al. [36] indicates that pores associated with higher values of P or suction (several hundred kPa) fall within the range of micropores and ultramicropores, which are typical of fine-grained structures. A parameter P of 1.85 MPa thus indicates fine pores, confirming the presence of the clay fraction identified earlier.