Modeling the effects of rice husk ash and cassava peel ash on the California bearing ratio (CBR) of Agbani soils

2.1. Soil index property prediction

Research has investigated the relationship between CBR and soil index characteristics. In their investigation of this relationship for Ethiopian subgrade soils, Abdella, Abebe, and Quezon [1] discovered strong relationships between CBR and characteristics such as maximum dry density (MDD) and plasticity index (PI). They created regression models, one of which was a multiple linear regression model that showed noticeably better predictive power:

CBR = 5.34MDD + 0.026F − 0.069PI, ($R^2=$ 0.973).

Using multiple linear regression models, Nwaogazie and Irokwe [2] also concentrated on creating models to estimate the CBR of soil from its index parameters along the Ogbia-Nembe road in Nigeria. The following were determined to be statistically significant using linear, quadratic, and multiple linear regression models:

– CBR = −69.89 + 54.944MDD, ($R^2=$0.82).

– CBR = 38.676 − 1.386OMC, ($R^2=$ 0.93).

– CBR = −820.11 + 926.06MDD − 252.49MDD², ($R^2=$ 0.89).

2.2. Stabilization with Rice Husk Ash (RHA) and Cassava Peel Ash (CPA)

Ishola et al. [3] and Diugwu and Ike [4] particularly concentrated on using RHA to stabilize lateritic soil in order to enhance its engineering qualities. Their research showed that adding RHA raised the CBR of Agbani soil up to an ideal mix ratio. RHA's ability to alter the engineering characteristics of expansive soils (black cotton soil) was examined by Jain et al. [5]. According to the study, CBR dramatically rose as RHA content increased, reaching a peak at 20 % RHA with a 6.19-fold improvement over untreated soil. A regression model was also developed by Ike and Ike [6] to forecast the CBR of lateritic soil stabilized with RHA. In order to forecast the California bearing ratio (CBR) of lateritic soil stabilized with rice husk ash, he developed an equation using Scheffe's simplex lattice design or the regression model, which is written as a second-degree polynomial:

where ${\beta }_1=Y_1=$ 21, ${\beta }_2=Y_2=$ 19, ${\beta }_3=Y_3=$ 30, ${\beta }_{12}=$ –8, ${\beta }_{13}=$ –30, ${\beta }_{23}=$ –18. So:

where $Z_1$, $Z_2$, $Z_3$ are the proportions of the lateritic soil, rice husk ash and water respectively.

${\beta }_{12}$, ${\beta }_{13}$, ${\beta }_{23}$ are interaction coefficients between the components.

$Y_1$: This is the CBR value of the mixture when component 1 ($X_1$) is used at 100 % (i.e., it is the only material in the mix) in this study.

$Y_2$: This is the CBR value of the mixture when component 2 ($X_2$) is used at 100 %.

$Y_3$: These values are used as the linear blending coefficients in Scheffe’s quadratic model and are also part of the interaction term calculations (${\beta }_1$${\beta }_2$${\beta }_3$).

These figures represent the contributions of water, rice husk ash (RHA), and soil, in that order. The CBR value is predicted by equation number 94 using the mix proportions of water, RHA, and soil. The changes in CBR, MDD, and OMC as a percentage are: Bearing Ratio for California (CBR): In comparison to the control mix without RHA, which had a CBR of 21 %, the ideal mix (1:1.70:0.25 for soil, RHA, and water) attained a CBR of 30 %, a 42.86 % increase. Additionally, Alhassan [7] assessed the stabilization of A-7-6 lateritic soil with RHA and found that while high RHA content decreased unconfined compressive strength (UCS), optimal RHA amount (6-8 %) enhanced CBR. For improved stabilization, the study suggested mixing RHA with lime or cement. There is little thorough study that focuses especially on the combined or comparative impacts of RHA and CPA on Agbani soil, despite the fact that data on their separate application for soil stabilization is already available. When it comes to predictive modeling for important geotechnical factors like CBR, this disparity is very noticeable. Fewer research have developed and validated reliable mathematical models for predicting these soil qualities when treated with agro-waste ashes, while the majority of the literature currently in publication focuses on experimental investigations. By creating and verifying predicting models for CBR of Agbani soil stabilized using different ratios of RHA and CPA, this study seeks to close this gap.

2.3. Research gaps and novelty

There is a dearth of comprehensive numerical models that can predict the California bearing ratio (CBR) of Agbani lateritic soil when treated with the combined effects of RHA and CPA, despite existing research on the individual use of RHA and CPA for soil stabilization. The majority of existing literature focuses on experimental investigations, with fewer studies developing and validating robust mathematical models, particularly for the combined RHA and CPA mixture. Several research gaps were identified based on the reviewed literature, including a limited focus on Agbani soil and insufficient investigation of the interaction effects between RHA and CPA.

By offering a thorough analysis and creating reliable predictive models utilizing Multiple Linear Regression for the CBR of Agbani soil stabilized with different fractions of RHA and CPA, this work seeks to close these gaps. Despite earlier studies on soil stabilization, nothing is known about the precise impacts of RHA and CPA on Agbani lateritic soil, and there are no predictive models for its essential characteristics. In particular, there is a dearth of thorough numerical models that can forecast the CBR of Agbani lateritic soil treated with RHA and CPA, as well as little thorough study focusing on their combined or compared impacts on Agbani soil. This study tackles this issue by examining and simulating these impacts in order to offer alternatives for economical and sustainable road building in the area.

This study aims to model how the California Bearing Ratio (CBR) of Agbani lateritic soils is affected by rice husk ash and cassava peel ash. The precise goals of this study are as follows: 1) To evaluate the effects of cassava peel ash and rice husk ash on the California Bearing Ratio (CBR) values of Agbani soil using laboratory tests. 2) To create a mathematical model that uses multiple linear regression (MLR) techniques to forecast the CBR of Agbani lateritic soil treated with rice husk ash and cassava peel ash.

3.1. Materials

Lateritic soil samples were collected from Agbani, Enugu State, Nigeria, at fifteen different locations within the study area. Cassava peels and rice husks were obtained from agricultural processing sites in Abakaliki, Ebonyi State.

3.2. Production of rice husk ash and cassava peel ash

Rice husks and cassava peels were first air-dried to remove moisture. The dried materials were then calcined in a controlled open furnace at temperatures ranging between 600 °C and 700 °C to obtain ash with sufficient pozzolanic reactivity. After cooling, the ashes were sieved through a 75 µm sieve to remove unburnt particles and ensure uniform fineness suitable for soil stabilization.

3.3. Sampling strategy and mix design

From the fifteen sampling locations, three soil samples were obtained at each location, giving a total of forty-five samples. Laboratory test results from each location were averaged to yield fifteen representative data points used for analysis. The soil was blended with RHA (0-25 %) and CPA (0-35 %) by dry weight of soil. Fifteen mix proportions were designed to examine both individual and combined effects of RHA and CPA. An experimental design along with a thorough statistical and data analysis methodology were used in the study. The USCS and AASHTO methods were used to classify the soil. An experimental design along with a thorough statistical and data analysis methodology were used in the study. The USCS and AASHTO methods were used to classify the soil. Atterberg limits, particle size distribution, compaction, and CBR values were among the characteristics of both treated and untreated soil samples that were tested in the lab. A total of fifteen samples were made with different ratios of CPA (0 % to 35 %) and RHA (0 % to 25 %). The mix ratios taken into account during the investigation were: 100S:0RHA:0CPA; 95S:5RHA:0CPA; 90S:5RHA:5CPA; 85S:10RHA:5CPA; 80S:15RHA:5CPA; 75S:20RHA:5CPA; 70S:25RHA:5CPA; 95S:0RHA:5CPA; 90S:0RHA:10CPA; 85S:5RHA:10CPA; 80S:5RHA:15CPA; 75S:5RHA:20CPA; 70S:5RHA:25CPA; 65S:5RHA:30CPA; 60S:5RHA:35CPA.

3.4. Laboratory testing

Laboratory tests conducted included particle size distribution, Atterberg limits, compaction characteristics, and soaked CBR tests. Testing procedures followed relevant standard specifications. All tests on treated soils were conducted after adequate mixing and curing to ensure uniformity.

3.5. Statistical modeling

Multiple linear regression (MLR) analysis was employed to model the relationship between CBR and stabilizer contents. The general polynomial form included linear, interaction, quadratic, and cubic terms for RHA and CPA. Higher-order terms were introduced to capture observed nonlinear trends in CBR response. Model performance was evaluated using the coefficient of determination ($R^2$), adjusted $R^2$, and analysis of variance (ANOVA). Given the relatively small dataset ($n=$ 15), model complexity and potential overfitting were critically assessed. Multiple Linear Regression was the main statistical method used in the study to create mathematical models. Multiple Linear Regression Calculator-Statistics Kingdom, Multiple Linear Regression-Stats Blue, and Microsoft Excel 2013 were the tools utilized. Because of its capacity to model a dependent variable (CBR) as a linear function of several independent variables (RHA and CPA contents, including their higher-order and interaction terms), the MLR technique was chosen. Up to the third degree, the polynomial MLR model used has the following general form:

The dependent variable is the California Bearing Ratio (CBR); the independent variables are the percentages of Rice Husk Ash and Cassava Peel Ash, respectively; the intercept is ${\beta }_0$; the regression coefficients are ${\beta }_1$ to ${\beta }_7$; and the error term is epsilon. The Fisher’s F-statistic and Analysis of Variance (ANOVA) were used to verify the model’s overall reliability and significance, while the Student's t-test was used to evaluate the significance of individual coefficients. The explanatory power of the model was assessed using both the coefficient of determination ($R^2$) and the adjusted coefficient of determination ($R_{Adj}^2$).

4.1. Basic properties of Agbani lateritic soil

According to Table 1, the basic physical characteristics of the soil samples under investigation were fine-grained, plastic, reddish brown in color, and had 1.15 % passing sieve No. 200. The soil samples were classified as A-2-6 by AASHTO [8] and as SC by UCSC. The mean particle size distribution graph of the soil samples is shown in Fig. 1.

Fig. 1Mean particle size distribution of Agbani soil

4.2. Effect of RHA and CPA on CBR

The addition of RHA and CPA resulted in a consistent improvement in CBR up to an optimum stabilizer content. Initial strength gains are attributed to improved particle packing and the onset of pozzolanic reactions between ash constituents and soil minerals. The maximum CBR value of 33.69 % was obtained at a mix proportion of 70 % soil, 25 % RHA, and 5 % CPA. Beyond this optimum, CBR values decreased, likely due to excess ash particles disrupting soil matrix continuity.

The Grande Mean findings of laboratory tests on the characteristics of Agbani Soil treated with Cassava Peel Ash and Rice Husk Ash from Stations 1 through 15 are displayed in Table 2. The various stations’ results are also displayed. Fig. 2 also displays the correlations between the California Bearing Ratio (CBR) in accordance with ASTM [9], Maximum Dry Density (MDD), Optimum Moisture Content (OMC) values of Agbani soil, and the different mix proportions of Laterite, Rice Husk Ash, and Cassava Peel Ash. The results are presented in Table 2 and illustrated in Fig. 2.

The range of CBR values for the different mix proportions was 21.5909 % to 33.6880 %. The control (natural soil without any additives) had the lowest CBR value (21.5909 %), demonstrating the soil’s inherent low bearing potential and the necessity of modification.

The addition of RHA and CPA raised the CBR values. The CBR increased by 6.18 % to 22.9233 % with just 5 % RHA (95S:5RHA:0CPA). 70S:25RHA:5CPA was the ideal mix proportion, with an average CBR of 33.6880 %. The high silica levels of RHA and CPA, which cause cementitious compounds to gradually develop in the soil, are responsible for this notable improvement. The observed decrease in plasticity indices and rise in the angle of internal friction and cohesion provide more evidence for this chemical process. The CBR values significantly decreased beyond the ideal range, indicating that too many additives took up space in the soil matrix and weakened the connection.

Fig. 2Correlation between CBR, MDD, OMC and mix proportions

4.3. Regression model interpretation

The developed MLR model exhibited strong predictive capability, with $R^2$ values of approximately 0.92 and adjusted $R^2$ of about 0.84. Statistical significance testing revealed that CPA and its quadratic term were more influential predictors of CBR than RHA. This suggests that CPA contributes more effectively to cementitious bonding in the studied soil. Although cubic terms improved model fit, their inclusion increases the risk of overfitting; hence, the model is best suited for preliminary estimation rather than definitive design.

Multiple Linear Regression was used in the statistical analysis to determine how RHA and CPA affected the CBR of Agbani soil. The input data required to create the model, including the higher-order and interaction terms, is displayed in Table 3.

The Multiple Linear Regression study performed with Microsoft Excel 2013 is summarized in Tables 4, 5.

The effects of rice husk ash and cassava peel ash on the California Bearing Ratio (CBR) of Agbani soils were modeled using three predictive models: Multiple Linear Regression Stats Blue, Multiple Linear Regression Calculator Statistics Kingdom, and Microsoft Excel 2013.

Multiple Linear Regression (Stats Blue): CBR = 22.6276 − 0.1727RHA + 1.054CPA − 0.0392(RHA·CPA) + 0.0207RHA² − 0.0476CPA² + 0.0002RHA³ + 0.0007CPA³, $R^2=$ 0.9219, $R_{adj}^2=$ 0.8438.

Multiple Linear Regression Calculator – Statistics Kingdom: CBR = 22.722708 + 0.769023CPA − 0.0786941(RHA·CPA) + 0.027286RHA² − 0.0114589CPA², $R=$0.940197, $R^2=$ 0.88397, $R_{adj}^2=$ 0.837558.

Microsoft Excel 2013: CBR = 22.63 − 0.173RHA + 1.054CPA − 0.039(RHA·CPA) + 0.021RHA² − 0.048CPA² + 0.00019RHA³ + 0.00069CPA³, $R^2=$ 0.921886, $R_{adj}^2=$ 0.843772, $R=$0.960149.

The anticipated and actual CBR values show a strong linear relationship according to the MLR models. for both the Excel and Stats Blue models, the multiple correlation coefficient ($R$) was consistently strong at roughly 0.96. At roughly 0.92, the coefficient of determination ($R^2$) values were likewise high. This shows that a significant portion of the variability in CBR roughly 92.2 % is explained by the models. The robustness of the MLR models was confirmed by the modified $R^2$ values, which take into consideration the number of predictors and were roughly 0.8438. With a high F-value of 11.80181 and a low p-value of 0.002122, the Excel ANOVA results validated the regression model’s statistical significance. This demonstrates how well the model explains the variance in CBR dependent on additions of RHA and CPA. The relative impact of the additives is highlighted by the individual coefficient analysis. the control CBR value (21.5909 %), which is the CBR when both RHA = 0 and CPA = 0, is quite near to the intercept coefficient (22.62764). the in the Excel model, it was determined that the CPA term (1.054) and the CPA2 term (0.04757) were statistically significant (p values are roughly 0.003 and 0.048, respectively). This implies that, in comparison to RHA, CPA has a more noticeable and reliable impact on CBR. in the Excel model, the RHA coefficient (–0.17275) was not statistically significant ($p$ value of 0.668). the relative impact of the additives is highlighted by the individual coefficient analysis. the control CBR value (21.5909 %), which is the CBR when both RHA = 0 and CPA = 0, is quite near to the intercept coefficient (22.62764). in the Excel model, it was determined that the CPA term (1.054) and the CPA2 term (–0.04757) were statistically significant (p values are roughly 0.003 and 0.048, respectively). This implies that, in comparison to RHA, CPA has a more noticeable and reliable impact on CBR. in the Excel model, the RHA coefficient (–0.17275) was not statistically significant (p value of 0.668). in contrast to CPA, RHA’s lack of statistical significance in some models indicates that RHA’s impact on CBR is more strongly associated with its interaction with CPA and the higher-order polynomial variables [10] than with its straightforward linear contribution. Mathematical methods are useful for evaluating the CBR of Agbani soil stabilized by agro-waste ashes, as demonstrated by the MLR models, especially the Excel and Stats Blue versions, which successfully established a predictive link.