Twelve soil samples known for their mud bricks were collected in 7 localities in the departments of Lékoumou, Bouenza and Niari in the south of the Republic of Congo. In these localities, there are several quarries of materials that differ in soil texture and color, which varied from yellow, grey and red. Samples were taken from the different horizons used by the brick makers, to determine the properties of soils. At each collection site, a representative sample of about 10 kg of clay soil was taken.

From the physical and chemical properties of grains, the soils are classified according to the AASHTO T88-70, (NF P-11300) and USCS classifications [13] [14] .

Origin Pro 2019b software was used in the process of developing correlations between the intrinsic properties of soils. The correlation selected is the one with the highest coefficient of determination.

The granulometry represents the percentage distribution of solid grains according to their dimensions. For particle separation, two types of tests were performed by: sieving for grains of the size φ > 80 μm according to NF P94-056 [15] and the sedimentation for the grains of diameter φ ≤ 80 μm according to NF P94-057 [16] . The grain size fraction is deduced from the recommendations of grain size nomograms, considering clays as particles < (0.002 mm), silts (0.002 - 0.06 mm) and sands (0.06 - 2 mm).

The Atterberg limits are determined by the Casagrande method, in accordance with NF P 94-051 [17] . The plasticity index characterizes the extent of the water content range in which soils behave plastically. The limits of liquidity (LL) and plasticity (PL) are determined on the fraction of soil (mortar) passing a 0.40 mm sieve. The plasticity index (PI) is expressed by the following relationship:

$\text{PI}=\text{LL}-\text{PL}$ (1)

The measurement of methylene blue adsorption capacity of a soil consists of measuring the quantity of methylene blue adsorbed by the 0/5 mm fraction of material suspended in water. This test makes it possible to characterize the clay content (or cleanliness) of a soil. It is a quantity that is directly linked to the specific surface of soil and reflects the overall quantity and quality (activity) of the clay fraction. The methylene blue value of a soil (BVS) is determined by the standard NF P 94-068 [18] .

Specific surface area (SSA) refers to the actual surface area of a soil particle as opposed to its apparent surface area. It is of great importance for phenomena involving surfaces, such as water adsorption and absorption. This parameter allows the interpretation of physical characteristics such as shrink-swell potentials. Depending on the geotechnical properties, the specific surface is determined by the following formula:

$\text{SSA}=20.93\ast \text{SBV}$ (2)

SSA (m²/g)—specific surface, BVS (g/100g)—Blue value of a soil.

The cation exchange capacity is the number of cations in the double layer that can be easily replaced or exchanged by other cations per 100 grams of soil. It is determined by the formula:

$\text{CEC}=\frac{\text{BVS}\ast 1000}{374}$ (3)

CEC (meq/100)—cation exchange capacity; BVS (g/100g)—blue value of a soil.

The “Ac” activity characterizes the mineral constituting the fine particles. When the clay content is sufficiently high, grains larger than two micrometers are embedded in the clay and barely touch each other. The activity can be related to the mineralogy and geology of the soil and defined as the ratio between the plasticity index PI and the clay content CF [1] :

$\text{AC}=\frac{\text{PI}}{\text{CF}\left(\text{\%}\right)<0.002\text{mm}}$ (4)

Ac—activity, PI—plasticity index, CF—clay fraction.

The relative activity is the ratio of the plasticity index to the specific surface area, which defines the role of the specific surface area on the plasticity of soil [19] :

$\text{RA}=\frac{\text{PI}}{\text{SSA}}$ (5)

RA—relative activity, PI (%)—plasticity index, SSA (m²/g)—specific surface area.

Kaolinite and Illite minerals are defined according to the surface activity Sc which is the ratio of the specific surface area to the clay fraction CF, defined by the following formula:

$\text{Sc}=\frac{\text{SSA}}{\text{CF}}$ (6)

Sc (m²/g*10²)—surface activity, SSA (m²/g)—specific surface area, CF (%)—clay fraction.

The minerals Illite and Montmorillonite are defined according to the Cation Exchange Capacity Activity CECA which is the ratio of the cation exchange capacity to the clay fraction is defined by the following formula:

$\text{CECA}=\frac{\text{CEC}}{\text{CF}}$ (7)

CECA—cation exchange capacity activity, CEC (meq/100)—cation exchange capacity, CF (%)—clay fraction.

Figure 1 shows the grain distribution of the twelve soils.

From Figure 1 , the clay, silt and sand fractions contained in Table 1 are extracted.

Table 1 shows the particle size fractions of the twelve soils with a clay fraction of CF (32.82% - 70.54%), a silt fraction of SF (14.48% - 24.72%) and a sand fraction of SF (7.35% - 47.03%).

Table 2 presents the results of the laboratory tests. These are: LL—liquidity limit, PL—plasticity limit, PI—plasticity index, BVS—blue value of a soil, SSA—specific surface area, CEC—cation exchange capacity.

Figure 2 shows the characterization of the plasticity of twelve soils.

In Figure 2 , eight clayey soils of medium plasticity can be distinguished, despite their clay fraction CF (32.82% - 59.91%). Three low plasticity clayey sands, with clayey fractions of CF (61.81% - 70.54%) and one very plastic clayey soil with a clay content of CF (69.13%).

Figure 3 shows the swelling potential of twelve soils (variation in linear volume of the soil due to water absorption).

From Figure 3 , the swelling potential of the soils is composed as follows: ten soils have a medium swelling potential and liquidity limits of LL (31% - 64%). Two swelling soils have liquidity limits of LL (35% - 40%).

According to Table 3 , the soils are composed of clays of classes A₂, A₃ or A-7 and clayey sands of classes A₂ and A-2 according to the USCS, GTR 92 and AASHTO classifications [13] [14] .

Table 4 presents the results of the activities obtained after calculation on the basis of the geotechnical properties contained in Table 1 and Table 2 . These are: Ac—activity, Sc (m²/g*10²)—surface activity, RA—relative activity, CECA—cation exchange capacity activity, Ac/Sc—relationship between activity and surface activity.

Figure 4 shows the activities of active, normal and inactive soil.

Nine clayey soils and one clayey sand are inactive, in fact their activities are lower than 0.75. The Yengola clayey sand has a normal activity, higher than 0.75, but lower than 1.75. The rouge Bilinga clayey sand has an activity close to 0.75, that is it has a normal activity.

Figure 5 shows the relative activity that defines the role of the specific surface on soil plasticity.

The relative activity values of 0.2, 0.3, and 0.4 represent the geology of soils sampling sites. These soils have geological formations that change from one sampling site to another. The relative activity depends on the mineralogy of soil.

Figure 6 shows the relationship between activity [1] and surface activity [5] .

Figure 8 shows the relationship between activity Ac [1] and the surface activity Sc [8] used to delineate mineralogy, which is another way of defining relative activity [7] . Indeed, three soils (Nzaou, Kingoué 2, Bilinga rouge) have an activity Ac = 0.005*Sc. In other words, these three soils fall on the C-line [8] , that is, they have mineralogy close to marine clays [8] .

Figure 7 shows the Sc surface activities of the twelve soils for the determination of minerals kaolinite and illite.

Using the specific surface area as a function of the clay fraction, the new activity values can be defined. Most natural soils, generally composed of mixed mineral layers, would fall somewhere between the Sc values.

The twelve soils have surface activities Sc above 0.5, but below 3, that is, they contain the mineral kaolinite.

Figure 8 shows the cation exchange capacity normalized by the clay fraction for the determination of the minerals illite and montmorillonite.

Ten soils have a cation exchange capacity activity greater than CECA = 0.25 but, less than CECA = 1, ten soils contain the mineral Illite. In addition, the soils of Yengola and Bilinga red, have a cation exchange capacity activity CECA ≥ 1. The soils contain the minerals illite and montmorillonite. From Figure 6 , Figure 7 , for a given clay fraction, the specific surface area is proportional to the mineralogy following the order kaolinite < illite < montmorillonite [1] .

Figure 9 shows the correlation between the surface area activity and activity.

From Figure 9 , the evolution of surface activity as a function of activity is a sigmoidal fit of the slogistics model 1:

$\text{Sc}=\frac{a}{1+\exp \left(-k\ast \left(\text{Ac}-X_C\right)\right)}$ (8)

$a=0.36774\pm 0.03557$

$X_C=0.35148\pm 0.01429$

$K=9.8726\pm 3.84786$

$R^2=0.881$

Sc—surface activity, Ac—activity, R²—coefficient of determination.

Figure 10 shows the correlations between plasticity index and blue value of a soil in function of the specific surface area.

The plasticity index is closely related to the specific surface area. The evolution of the plasticity index as a function of the specific surface is a linear fit.

Plasticity index:

$\text{PI}=a+b\ast \text{SSA}$ (9)

$a=3.8475\pm 0.07801$

$b=1.42208\pm 0.00529$

$R^2=0.999$

Blue value of a soil

$\text{BVS}=a+b\ast \text{SSA}$ (10)

$a=3.84715\pm 0.07801$

$b=1.42208\pm 0.00529$

$R^2=0.999$

PI (%)—plasticity index, SSA (m²/g)—specific surface area, BVS—Blue Value of a Soil, R²—coefficient de détermination.

Figure 11 shows the correlations between relative activity and activity in function of the liquidity limit.

The evolution of relative activity as a function of the liquidity limit is a sigmoidal fit of the logistic model:

$\text{RA}=A_2+\frac{A_1-A_2}{1+{\left(\frac{\text{LL}}{X_0}\right)}^p}$ (11)

$A_1=1.95232\pm 0.23371$

$A_2=1.59978\pm 0.05258$

$X_0=37.91619\pm 8.69189$

$p=5.47909\pm 4.96906$

$R^2=0.859$

The evolution of activity as a function of the liquidity limit is an exponential fit in the Exp3P1 model:

$A_c=\exp \left(\frac{a+b}{\text{LL}+C}\right)$ (12)

$a=-0.7754\pm 0.03526$

$b=-0.08929\pm 0.11079$

$c=-40.31886\pm 0.42032$

$R^2=0.406$

RA—relative activity, A_C—Activity, LL (%)—liquidity limit.

Figure 12 shows the correlation between the blue value of a soil and the liquidity limit.

From Figure 11 , the evolution of blue value of a soil versus liquidity limit is a Sigmoidal fit of the Slogistic1 Model:

Blue value of a soil:

$\text{BVS}=\frac{a}{1+\exp \left(-k\ast \left(\text{LL}-X_C\right)\right)}$ (13)

$a=1.09246\pm 0.14855$

$X_C=38.55063\pm 4.0704$

$K=0.07019\pm 0.02226$

$R^2=0.923$

BVS (g/100g)—blue Value of a Soil, LL (%)—liquidity limit, R²—coefficient de détermination.

Figure 13 shows the correlations between specific surface area and cation exchange activity in function of the liquidity limit.

From Figure 12 , the evolution of specific surface area and cation exchange capacity versus liquidity limit is a Sigmoidal fit of the Slogistic1 Model:

$\text{SSA}=\text{CEC}=\frac{a}{1+\exp \left(-k\ast \left(\text{LL}-X_C\right)\right)}$ (14)

$a=2.92102\pm 0.39701$

$X_C=38.55063\pm 4.06915$

$K=0.07018\pm 0.02224$

$R^2=0.923$

SSA (m²/g)—specific surface area, CEC (meq/100)—cation exchange capacity, LL (%)—liquidity limit, R²—coefficient of determination.