**3.2 Consistency limits**

A wide range of plasticity (**Figure 2**) characterized the inorganic silty clayey soils in the area. The liquid limit varied between 13.4 and69% with a lower range experienced in PCG derived soils (<32.4%), while plastic limit and plasticity

**Figure 2.** *Casagrande chart of plasticity-liquid limit relationship.*

*Multivariate Assessment of California Bearing Ratio with Contrasted Geotechnical Properties… DOI: http://dx.doi.org/10.5772/intechopen.93523*

index at the PCB unit ranged between 2.2–50% and 1.62–39%, with mean values of 28.4, 19.0, and 9.4%, respectively (**Table 1**). The Casagrande plasticity chart revealed majority of the soils from the migmatite-gneiss origin placed above the A-line, indicating that they are composed of inorganic clay material and exhibited low to medium plasticity, implying low to medium swelling and compressibility. The moderate plasticity suggests low to medium dry strength, which could easily crumble under load thus leading to pavement failure and possible erosion under climatic threat. The distribution of the soil samples on the chart portrayed the variability in soil plasticity characteristics.

Moreover, free swell (Fsw) varied from 1.8 to 28.4% in PCB, 2.8–19.6% in PCM and 3.2–4.67% in PCG with mean values ranging from 6.4, 7.1, and 4.04%, respectively; while soil activity with mean values oscillated between 0.09–8.5 (1.1), 0.17–7.85 (0.9), and 0.2–5.08 (1.2) within the 3 units. The weighted plasticity index (wPI) value ranged between 0.25–31.9% (5.1%), 0.92–25.3% (5.8%), and 0.87–7.3% (3.5%) with mean from the 3 units. In PCB soils, activity tends to be higher than normal (8.5), high weighted plasticity index (wPI), plasticity ratio (PIr), and swelling potential (SP) indicating that the soils are active. The result of natural moisture content (NMC) (2.6–22.7%) is fairly high, considering the time of sample collection. This indicates the soil potential for water retention, which is a property of fine-grained soils. The high water content also suggests the presence of high water table earlier reported by Adams et al. [12]. These observations correspond with Bayamack et al. [13]. The derived plasticity parameters (wPI, PIr, SP, and LLr) represent the effective contribution of the plasticity of fines to the performance of the entire soil materials, depending on the amount of fines.

#### **3.3 Compaction and California Bearing Ratio**

The maximum dry density (MDD) of the soils from PCB area (**Table 1**) increases with mean to 2.6 mg/m3 (1.77 mg/m3 ) at 25% (13%) optimum moisture contents (OMC). These values are higher than those obtained in metasediment (PCM) and older granite (PCG) units with 2.1 mg/m3 (1.6 mg/m3 ) MDD and 22.5% (15%) OMC. The low density-moisture relationship implies low strength instigated by loose soils that are susceptible to erosion. The interaction of the subgrade with water greatly reduces strength and therefore promotes continuous failure of the overlying pavement. Few examples of soil compaction curves (**Figure 3**) illustrate distinct peak of maximum dry density at optimum moisture content.

The CBR values at 95% OMC after 48 hours of immersion varied between 10 and 56.4% for PCB, 11 and 45% for PCM and 12.1 and 37.2% for PCG soils (**Table 1**). The mean values within the three lithological units varied between 28.8, 23.6, and 27.8%, respectively. For unsoaked condition, the CBR varied in a higher rate from 12.5 to 75.0% within the 3 units. The result showed a reduction in strength due to soaking suggesting a probable drastic reduction in strength by more than half during wet condition and the penetration resistance becomes reduced due to excessive moisture. These values are similar to those found along Ado Ekiti-Akure road (27–100%) by Adams and Adetoro [14]. The low mean CBR value (<30%) suggests that the soils may not withstand ground vibrations when vehicular load is applied and reinforces its susceptibility to erosion. Soil improvement measures are therefore, envisaged for the stability of soils for adequate strength.

#### **3.4 Simple linear regression**

High statistically significant correlation (R > 0.70) is recorded among 13 soil attributes pairs (**Table 2**) such as gravel, coarse sand (CS), medium sand (MS), fine

#### **Figure 3.**

*Compaction curves of selected soil samples.*


#### **Table 2.**

*Pearson significant correlation of soil properties.*

sand (FS), silt, clay, fines, swelling potential (SP), free swell (Fsw), liquid limit (LL), plasticity index (PI), dry density (DD) and maximum dry density (MDD) which raises the issue of multi-collinearity. However, other parameters exhibit low *Multivariate Assessment of California Bearing Ratio with Contrasted Geotechnical Properties… DOI: http://dx.doi.org/10.5772/intechopen.93523*

correlations (R < 0.50) including sand, activity (Ac), plastic limit (PL), moisture content (MC) and optimum moisture content (OMC).

This could be attributed to the presence of high fine fractions and potential influence from environmental factors. The result corroborates with the observations obtained on gneiss derived laterite in Central Cameroun [15] and reaffirms the views of the earlier scholars that geotechnical properties of laterites depends on the parent materials, climate, vegetation, topography and duration of the laterization phenomenon [16].

### **3.5 Multivariate analysis of soil properties**

### *3.5.1 Principal component analysis*

Among the multivariate analysis techniques, principal component analysis is the most frequently used because it is the starting point in data mining which aims at minimizing the dimensionality of the data. Seven principal components (PCs) were extracted with eigenvalues >1 which accounted for 83.8% of the total variance of data (**Table 3**).

However, the first five PCs accounted for >70% of variability in measured soil properties. While PC1 explained 33.4% of the total variance with fines as the major contributing variable (R = 0.87), PC2 accounted for additional 14.7% of the total variance with plasticity index (PI) as the second major contributing variable (R = 0.70). In PC3, 11.4% was accounted for, with coarse sand (CS) contributing more (R = 0.67). Other components accounted for <15% and as such were removed as they explained less variance than individual variable in the dataset [8].

Based on the communality estimates, the five factors explained more than 90% of variance in MDD, PI, LL, DD, BD, FS, CS, SP, fines and gravel; > 80% in wPI, PL, Fsw, Wr, LLr, NMC, sand, silt and clay; > 70% in MS, MC, CBRu, and Dr.; above 60% in PIr, OMC, and Ac; and 53% in CBRs (**Table 4**). According to Johnson and Wichern [17], a high communality suggests that a high proportion of the variability is explained by the factor with a higher preference over a low communality estimate. By implication, the factors fairly explained the variance in soaked CBR and as such required a regression model to predict the property. The values obtained are similar to those obtained by Shukla et al. [18].

The coefficient of linear correlation between the variables and their factors (**Table 4**) give a meaning to the principal components. The parameters are well represented and explained by the factorial axes on the correlation circle (**Figure 4**).


**Table 3.** *Eigenvalues and proportions of variance explained by PCA.*


#### **Table 4.**

*Proportion of variance and communality estimates of soil variables.*

This graph shows three groups of variables, suggesting the existence of correlation between them.

PC1 positively correlates (> 0.84) with SP, PI, LL, Fsw, wPI and MC, NMC, PL, CBRu (**Table 4**) and is termed plasticity parameters. PC2 demonstrated very high positive correlation with soil densities (MDD, DD, BD) (> 0.93) and negatively correlated with moisture contents (MC, OMC) (<−0.6) and is termed moisturedensity or compaction parameters since the variables are important functions of soil moisture density. It also showed moderate positive loading from CBRs (0.37) resulting from significant correlation between MDD and OMC. Similarly, PC3 defined as fine gradation parameters showed highest positive correlation (0.72) with clay and NMC; FS, silt and fines (0.53, 0.61, 0.67); and negatively correlated (>0.75) with activity and liquid limit ratio (LLr). These variables are a function of fine soil texture. PC4 and PC5 are positively correlated (>0.70) with coarse materials (gravel, coarse and medium sand), referred to as coarse soil texture.

*Multivariate Assessment of California Bearing Ratio with Contrasted Geotechnical Properties… DOI: http://dx.doi.org/10.5772/intechopen.93523*
