Evaluation of Shear Stress in Soils Stabilized with Biofuel Co-Products via Regression Analysis Methods

Abstract

In recent years, the employment of artificial neural networks (ANNs) has risen in various engineering fields. ANNs have been applied to a range of geotechnical engineering problems and have shown promising outcomes. The aim of this article is to enhance the effectiveness of estimating unfamiliar intermediate values from existing shear stress data by employing ANNs. Artificial neural network modelling was undertaken through the Regression Learner program that is integrated with the Matlab 2023a software package. This program offers a user-friendly graphical interface for developing AI models absent of the need for any coding. The validation and training of the ANNs were executed by relying on shear box test data which had been conducted at the Geotechnical Laboratory situated at Iowa State University. The objective of these experiments was to explore the potential of biofuel co-products (BCPs) in soil stabilization. The data should be structured with input and output parameters in columns and samples in rows. The dataset comprises a 216 × 6 matrix. The data columns provide information on soil type (pure soil—unadulterated; and 12% BCP-adulterated soil), time (1, 7, and 28 days), normal stress (0.069-DS10, 0.138-DS20, and 0.207-DS30 MPa), moisture content (OMC−4%, OMC%, and OMC+4%), and corresponding shear stress (σ, MPa) values. The AI predictions for the test data output provide an outstanding R² score of 0.94. This indicates that employing ANN to teach shear test data facilitates gaining a large quantity of data more efficiently, with fewer experiments and in less time. Such an approach seems encouraging for geotechnical engineering.

1. Introduction

In recent years, artificial neural networks (ANNs) have proven to be effective in addressing a wide range of complex challenges in geotechnical engineering [1]. The engineering properties of soil and rock exhibit diverse and uncertain behaviors as a result of the intricate and imprecise physical processes involved in their formation. To cope with the complexity of geotechnical behavior and the spatial variability of these materials, conventional engineering design models are understandably simplified [2]. The methodology known as artificial neural networks (ANNs) is particularly well suited to modelling complex problems characterized by an unknown relationship between the model variables [3]. Artificial neural networks (ANNs) represent a computational emulation of the physiological structure and mechanisms of the human brain. This machine learning technique differs from conventional approaches of signal reasoning and logical thinking. Artificial neural networks (ANNs) are proficient in tackling challenges associated with incomplete associative memory, faulty pattern recognition, and autonomous learning. These networks provide three main benefits—high computational speed, robust fault-tolerant capabilities, and proficiency in addressing problems characterized by intricate solution rules [4].

A comprehensive literature review shows the successful application of artificial neural networks (ANNs) in a wide range of geotechnical disciplines, including pile capacity prediction, soil behavior modelling, site characterization, analysis of earth retaining structures, settlement assessment of structures, slope stability analysis, design of tunnels and underground openings, assessment of liquefaction susceptibility, determination of soil permeability and hydraulic conductivity, evaluation of soil compaction, investigation of soil welling phenomena, and soil classification [5].

Goh [5] developed an artificial neural network to predict the settlement of vertically loaded pile foundations in a uniform soil stratum. Goh [6,7] introduced an artificial neural network model to estimate the frictional capacity of piles in clayey soil. All technical term abbreviations are explained at their first usage to ensure comprehensibility. Later, Goh [8,9] developed a new neural network model aimed at estimating the ultimate load-bearing capacity of driven piles in cohesionless soil environments. Chan et al. [10] created an artificial neural network as an alternative to conventional pile driving formulas. The network was trained using identical parameters to those in the simplified Hiley formula [11], including factors like elastic compression of both the pile and soil, pile set, and energy applied during pile driving. Lee and Lee [12] also utilized neural networks for predicting the ultimate bearing capacity of piles. They simulated the problem using data from model pile load tests conducted in a calibration chamber and results from in situ pile load tests. Abu-Kiefa [13] presented three different neural network models for predicting the capacity of driven piles in cohesionless soils.

Sivakugan et al. [14] investigated the feasibility of using neural networks to predict settlement in shallow foundations on granular soils. Similarly, Shahin et al. [15] carried out a similar investigation for the prediction of settlement in shallow foundations on cohesionless soils.

Ellis et al. [16] formulated an artificial neural network (ANN) model tailored to sands based on grain size distribution and stress history. Sidarta and Ghaboussi [17] used an artificial neural network (ANN) model in conjunction with finite element analysis to infer geometric constitutive behavior from inhomogeneous material tests. Penumadu and Jean-Lou [18] used neural networks to simulate the behavior of both sand and clay soils. Ghaboussi and Sidarta [19] used neural networks to simulate both drained and undrained behavior of sandy soils under triaxial compression-type tests. Penumadu and Zhao [20] also used ANNs to model the stress–strain and volume change behavior of sand and gravel under drained triaxial compression test conditions. Cal [21] used a neural network model to generate a quantitative soil classification based on three primary factors: plastic index, liquid limit, and clay content. Najjar et al. [22] demonstrated the effectiveness of neural network based models in accurately assessing soil swelling. Their research highlighted the significant improvements in prediction accuracy achieved by neural network models compared to statistical models. Agrawal et al. [23], Gribb and Gribb [24], and Najjar and Basheer [25] all used neural network methods to estimate the permeability of clay liners. Basheer and Najjar [26] presented neural network approaches to analyze soil compaction.

The applications of artificial neural networks (ANNs) extend beyond those mentioned above; there are several notable studies in the field of soil mechanics where ANNs have been used. These include the modelling of the mechanical behavior of medium to fine sands [27], the investigation of the rate-dependent behavior of clay soils, as carried out by Penumadu et al. [28], simulating the uniaxial stress–strain constitutive behavior of fine-grained soils under both monotonic and cyclic loading conditions [29,30], characterizing the undrained stress–strain response of Nevada sand subjected to triaxial compression and extension loading paths [31,32], predicting the axial and volumetric stress–strain behavior of sand during loading, unloading and reloading phases [33], and estimating the anisotropic stiffness of granular materials using standard repeated loading triaxial tests [34].

Of particular note is the work of Basheer [35], where soil data were used, and the results obtained using hysteresis modelling achieved an impressively high R-squared value of 0.99. These results highlight the importance of ANNs as a powerful tool for understanding and predicting various complex issues in soil mechanics.

Two additional studies [36,37] have harnessed cone penetration test (CPT) data to assess both soil liquefaction potential and resistance. Furthermore, Najjar and Ali [38] have employed neural networks in their research endeavors, aiming to comprehensively characterize soil liquefaction resistance. Their investigations are based on extensive field data collected from diverse earthquake-prone regions worldwide.

Basheer et al. [38] have outlined the usefulness of neural networks in accurately mapping and predicting changes in soil permeability. The objective of this application is to identify landfill borders and aid in the establishment of waste landfill sites. Similarly, Rizzo et al. [39] introduced a novel site characterization technique known as SCANN (site characterization using artificial neural networks). Neural networks enhance site characterization processes by mapping discrete spatially distributed fields, which SCANN leverages. Additionally, further contributions to the field are presented by Najjar and Basheer [39] and Rizzo and Dougherty [40], who offer additional applications utilizing neural network capabilities. Additionally, Goh and colleagues [41] have developed a neural network model that specifically provides initial estimations of maximum wall deflections in the context of braced excavations within soft clay. Ni et al. [42] have further proposed a novel methodology that combines fuzzy sets theory and artificial neural networks, presenting an approach for evaluating slope stability.

In the area of tunnel engineering, Shi et al. [43] carried out an extensive study on the use of neural networks to predict settlement phenomena in tunnels. Additionally, Lee and Sterling [44] have made considerable advancements in the field with their development of a neural network model designed to identify potential failure modes for underground openings. Their approach utilizes historical case history information to improve predictive capabilities. Expanding upon this groundwork, Sterling and Lee [45] have broadened the application of neural networks by integrating them into a knowledge-based expert system. This imbued system aims to proffer substantial assistance throughout the intricate process of tunnel design. Similarly, Moon et al. [46] have utilized artificial neural networks (ANNs) along with an expert system to provide a pioneering methodology towards the preliminary design facet of tunnel projects.

In Güllü et al. [47], the input parameters in the network model were size, distance, and soil condition, and the output parameter was the maximum ground acceleration. In the training phase of the network, the correlation coefficient between the predicted maximum ground accelerations and measured accelerations was found to be 92% and 64% in the test phase. Compaction of coarse- and fine-grained soils, as well as physical properties, was used by Sinha and Wang [48] to determine the permeability properties (R² = 0.92). By using a compression test in uniform sands, Sezer et al. [49] estimated the maximum dry unit volume weight with an R² of 0.98.

In engineering, artificial neural networks (ANNs) are increasingly used to formalize and synthesize data obtained from finite element (FE) modelling studies. These studies commonly utilize a standard set of input parameters. These crucial factors include wall stiffness, the ratio of soil layer thickness to excavation width, the actual excavation width, soil unit weight, un-drained shear strength of the soil, excavation height, and the ratio of undrained soil modulus to shear strength. These parameters must be considered for excavation purposes [50,51].

Romero and Pamukcu [52] have demonstrated the efficacy of neural networks in effectively characterizing and estimating the shear modulus of granular materials. Sivrikaya et al. [53] conducted a study in which they achieved notable results. They obtained R-squared (R²) values of 0.78 and 0.81 in two similar artificial neural network (ANN) models. These models were developed to predict the undrained shear strength (c_u) and incorporated variables such as water content (w_n), liquid limit (w_L), plasticity index (PI), effective stress (σ_v′), as well as SPT N_field and N₆₀. Zhu et al. [54,55] used neural networks to model the shear behavior of fine-grained residual soil, dune sand, and Hawaiian volcanic soil.

2. Materials and Methods

2.1. Materials

Soil stabilization involves the application of agents, energy, or a combination of both to bind soil particles together, primarily aimed at enhancing shear strength and reducing compressibility [56].

A comprehensive laboratory experimental test program was performed, comparing the shear strength of BCP treated on four different representative Iowa soil types. The engineering properties of the soil samples are shown in

Table 1. Engineering properties for four types of soils [57].

Property	Soil 1	Soil 2	Soil 3	Soil 4
Classification
AASHTO (group index)	A-6 (2)	A-4 (2)	A-4 (1)	A-4 (0)
USCS group symbol	SC	CL-ML	CL-ML	ML
USCS group name	Clayed sand	Sandy Silty with clay	Sandy Silty with clay	Sandy Silty
Grain Size Distribution
Gravel (4.75 mm), %	7.1	0.1	5.2	3.8
Sand (0.075–4.75 mm), %	54.9	37.2	41.7	45.3
Silt and clay (0.075mm), %	38.0	62.7	53.1	50.9
Atterberg Limits
Liquid limit (LL), %	32.8	29.1	27.5	17.2
Plasticity limit (PL), %	17.4	22.9	22.2	15.1
Plasticity index (PI), %	15.4	6.20	5.30	2.10
Proctor Test
Optimum moisture content (OMC), %	14.4	18.2	13.5	12.0
Maximum dry unit weight (γd max), kg/m3 (pcf)	1.728 (107.9)	1.631 (101.8)	1.818 (113.5)	1.839 (114.8)

.

Considering that lignin widely exists as a large fraction of plant biomass, use of sulfur-free lignin in soil stabilization has been previously proposed by researchers at Iowa State University (ISU) for deriving potential new economic benefits from lignocellulosic bio-refineries treated sandy lean clay (CL) soil with two different BCPs containing sulfur-free lignin, a black liquid type, and a yellow powder type. They added each of these two BCPs to soil with up to 15% dry unit weight at three different moisture levels: dry side (OMC−4%), optimum moisture content (OMC), and wet side (OMC+4%). After 1-day and 7-day curing, they reported that maximum strength improvement (UCS) was achieved on both specimens containing 12% of the two BCPs. They also conducted UCS tests for specimens under both saturation and half-saturation and reported significant strength improvement with these two BCP treatments, especially with the liquid-type treatment [58].

Puppala [59] and Puppala et al. [60] used two other BCPs containing sulfur-free lignin containing up to 15% by dry soil weight to treat silt soil. They also reported that a 12% application rate for both these BCPs could achieve the highest strength improvement after 1-day, 7-day, and 28-day curing. They also carried out XRD and SEM analyses to verify physical bonds as the mechanism of sulfur-free lignin for soil stabilization. These results indicated that sulfur-lignin can play a positive role in soil stabilization at a recommended application rate of 12% by dry soil weight.

The unconsolidated undrained direct shear test (DST) was conducted following the ASTM standard [61], with a consistent displacement shearing rate of 0.35 mm per minute applied to all specimens. The DST aimed to assess the shear properties of two categories of samples: pure soil and soil treated with a 12% concentration of BCP. Various normal stress levels, namely 0.069 MPa (DS 10), 0.138 MPa (DS 20), and 0.207 MPa (DS 30), were applied. Additionally, three different moisture content levels (OMC−4%, OMC, and OMC+4%) were examined in conjunction with three distinct curing periods (1, 7, and 28 days). Detailed DST parameters are provided in

Table 2. DST results (MPa) at different moisture contents: Soil-1; Soil-2; Soil-3; Soil-4 [62].

SOIL TYPE			OMC −4			OMC			OMC +4
			DS 10	DS 20	DS 30	DS 10	DS 20	DS 30	DS 10	DS 20	DS 30
SOIL-1	PURE	1 day	19.30	25.00	32.50	16.50	23.00	29.80	11.00	17.00	24.50
		7 day	21.00	24.70	31.00	15.50	21.00	28.20	9.90	16.00	21.00
		28 day	20.20	25.30	31.30	17.70	22.90	28.30	11.10	16.80	22.40
	12% BCP A	1 day	33.50	37.00	52.70	23.50	27.20	44.90	16.00	23.50	33.00
		7 day	28.50	38.30	44.50	23.00	29.00	36.30	16.50	29.00	32.00
		28 day	33.60	39.30	48.00	20.20	29.80	36.50	15.80	22.60	28.50
SOIL-2	PURE	1 day	10.00	15.50	22.70	7.90	14.80	22.00	6.70	12.40	19.50
		7 day	10.20	16.30	22.50	9.00	15.50	21.30	8.50	13.00	20.50
		28 day	10.50	16.00	23.00	8.80	14.60	21.00	7.50	12.80	19.00
	12% BCP A	1 day	19.50	23.80	28.50	13.70	17.50	21.50	11.50	15.20	19.00
		7 day	18.00	24.50	31.30	13.40	18.10	23.70	10.60	14.50	17.00
		28 day	16.10	22.50	27.50	12.00	17.00	23.10	10.30	14.10	19.20
SOIL-3	PURE	1 day	18.50	27.00	32.10	14.60	18.80	25.00	8.80	14.40	18.50
		7 day	17.20	26.00	32.00	12.60	18.20	24.10	9.90	15.00	18.00
		28 day	14.80	24.00	30.00	12.30	18.00	25.30	9.00	14.60	17.20
	12% BCP A	1 day	37.00	43.00	47.20	25.00	30.20	37.00	18.00	23.00	26.70
		7 day	40.00	45.00	51.00	23.50	26.90	33.80	17.50	22.70	28.00
		28 day	30.00	35.50	40.20	18.30	24.10	29.20	15.60	20.90	23.00
SOIL-4	PURE	1 day	14.70	20.50	27.50	9.50	16.00	22.90	7.40	14.00	20.00
		7 day	18.50	22.50	30.00	13.50	20.30	27.70	10.90	17.30	25.90
		28 day	17.00	21.70	27.50	12.80	19.60	27.00	10.80	16.90	24.50
	12% BCP A	1 day	32.00	40.50	45.00	23.80	28.00	35.00	15.00	18.80	24.70
		7 day	28.30	37.50	49.00	22.00	27.00	34.50	15.90	22.50	25.50
		28 day	25.10	32.00	41.00	18.80	24.50	28.70	13.00	18.00	20.80

.

The results are shown graphically in Figure 1.

The shear stress values examined within the scope of the article have been reorganized to create a dataset in the form of a 216 × 6 matrix. In the data columns, the following are presented in the following order: soil type (Soil-1, Soil-2, Soil-3, Soil-4), BCP (pure soil—unadulterated; 12% BCP-adulterated soil), time (1, 7, and 28 days), normal stress (0.069-DS10; 0.138-DS20; 0.207-DS30 MPa), moisture content (OMC−4%, OMC%, and OMC+4%); and in the corresponding output data column, shear stress values (MPa) are provided.

2.2. Methods

Neural Networks, biological or artificial, represent interconnected systems of neurons. Biological neural networks consist of natural neurons, while artificial neural networks, constructed with artificial nodes, address artificial intelligence challenges. Neurons’ connections are mimicked as weights in artificial networks, with positive values denoting excitatory links and negative values indicating inhibitory ones [63]. Inputs are linearly combined through these weights, and an activation function modulates output amplitudes, typically falling within a range of 0 to 1 or −1 to 1.

Artificial neural networks find application in predictive modeling, adaptive control, and data-driven training, allowing them to self-learn and draw conclusions from complex information. Inspired by the human brain’s structure and function, scientists have developed artificial neuron and network models, leading to the emergence of the field of artificial neural networks (ANN) [64]. An ANN is a system inspired by the human brain’s neural structure, capable of fulfilling specific functions. Figure 2 shows a general block diagram of an ANN.

In Figure 2, the “bias” error/deviation is the value reflecting the distance between the data predicted as a result of modelling and the actual data. “Weight” corresponds to inputs values.

A layered ANN architecture, inspired by the human nervous system, connects neurons in diverse topologies. Neural networks can be trained to perform functions by optimizing connection multiplier values. A neural node comprises input values, weights, addition, transfer functions, and output values. Similarly to the human brain, ANNs act as parallel processors, capable of receiving, storing, and generalizing information through inter-neuron weights. Learning involves algorithms that renew weights to achieve desired outcomes [65].

Figure 3 illustrates the elements of a neural network: R represents the number of inputs, p denotes input values, w is the weight multiplier for input-neuron connections, b signifies the neuron’s bias value, f represents the transfer function, and a is the output value. Input values undergo multiplication by weights, followed by summation and bias translation, resulting in an output through the transfer function, which can be linear or non-linear. This model establishes a mathematical relationship between inputs and outputs, with the need to optimize w and b values for the neuron to produce the desired output [66].

Regression methods describe the relationship or correlation between an output variable and one or more input variables. The toolboxes in the Matlab-R2023a software package allow us to define and use non-linear, generalized, and linear regression methods, including cascade and/or mixed models. These tools can be employed for model design, output prediction, model performance assessment, and visual representation.

The Regression Learner application in the Matlab software package also includes non-parametric methods to include more complex prediction curves without expressing the relationship between outputs and a predetermined predictor. After the training is finished, the trained model can make predictions using new data as the application is activated in the field.

Linear regression models are a statistical approach used to model the relationship between a system’s response and input variables. When dealing with a single input variable, it is termed as a simple linear regression, while scenarios involving multiple input variables are called multiple linear regressions. These models establish relationships through linear prediction functions derived from data [67].

In the realm of statistical modeling, linear regression is a fundamental tool for exploring the connection between a dependent variable, often denoted as ‘y’, and one or more independent variables, represented as ‘x’. ‘y’ serves as the response variable, indicating the variable of interest, while ‘x’ encompasses the independent variables, also known as explanatory or predictor variables, crucial for explaining variations in the response variable [68].

It is essential to distinguish two main types of independent variables within this framework. Continuous explanatory variables are referred to as covariates due to their measurable, continuous nature, whereas categorical independent variables are labeled as factors, reflecting their categorical and discrete characteristics. Additionally, the matrix ‘x’, containing observations related to predictor variables, is commonly termed the design matrix and plays a central role in formulating and executing linear regression models [69].

In statistics, R² (coefficient of determination), often represented as R² or r², measures the portion of variation in the dependent variable that can be predicted from independent variable(s). This statistic is essential in statistical models primarily used for forecasting future outcomes and testing hypotheses based on relevant information. It quantifies how accurately observed outcomes align with the model, based on the proportion of total outcome variation explained by the model. The R² value falls within the range of 0 to 1, with values closer to 1 indicating a lower error and better model fit [70,71].

3. Results and Discussion

In the direct shear test, we conducted a comparative analysis of shear strength results across three distinct optimum moisture contents (OMCs), with OMC−4% yielding the highest value, as depicted in Figure 3. Remarkably, the introduction of 12% (BCP) into the originally pure soil yielded a substantial and consistent increase in shear strength across all soil types. In fact, the shear strength values nearly doubled for each soil type. Notably, the fine particle content within the soils played a pivotal role in influencing their strength characteristics. Soil-1 consistently exhibited the highest strength capacity across all specimen types. This can be attributed to its notably lower clay content compared to the other soils. Conversely, Soil-2 consistently displayed the weakest shear strength results, primarily due to its significantly higher clay content. Interestingly, Soil-3 and Soil-4 showcased similar levels of fine particle content, resulting in comparable shear strength values.

The dataset given in the tables in

Table 3. The dataset used in the Regression Learner application in MATLAB for direct shear test (DST) values.

SOIL TYPE	BCP (0–12%)	DAY (1–7,28)	DS (10,20,30 Mpa)	OMC (−4, 0, +4)	OUTPUT (MPa)	SOIL TYPE	BCP (0–12%)	DAY (1–7,28)	DS (10,20,30 Mpa)	OMC (−4, 0, +4)	OUTPUT (MPa)	SOIL TYPE	BCP (0–12%)	DAY (1–7,28)	DS (10,20,30 Mpa)	OMC (−4, 0, +4)	OUTPUT (MPa)
1	0	1	10	−4	19.30	2	0	1	10	0	7.90	3	0	1	10	4	8.80
1	0	7	10	−4	21.00	2	0	7	10	0	9.00	3	0	7	10	4	9.90
1	0	28	10	−4	20.20	2	0	28	10	0	8.80	3	0	28	10	4	9.00
1	1	1	10	−4	33.50	2	1	1	10	0	13.70	3	1	1	10	4	18.00
1	1	7	10	−4	28.50	2	1	7	10	0	13.40	3	1	7	10	4	17.50
1	1	28	10	−4	33.60	2	1	28	10	0	12.00	3	1	28	10	4	15.60
1	0	1	20	−4	25.00	2	0	1	20	0	14.80	3	0	1	20	4	14.40
1	0	7	20	−4	24.70	2	0	7	20	0	15.50	3	0	7	20	4	15.00
1	0	28	20	−4	25.30	2	0	28	20	0	14.60	3	0	28	20	4	14.60
1	1	1	20	−4	37.00	2	1	1	20	0	17.50	3	1	1	20	4	23.00
1	1	7	20	−4	38.30	2	1	7	20	0	18.10	3	1	7	20	4	22.70
1	1	28	20	−4	39.30	2	1	28	20	0	17.00	3	1	28	20	4	20.90
1	0	1	30	−4	32.50	2	0	1	30	0	22.00	3	0	1	30	4	18.50
1	0	7	30	−4	31.00	2	0	7	30	0	21.30	3	0	7	30	4	18.00
1	0	28	30	−4	31.30	2	0	28	30	0	21.00	3	0	28	30	4	17.20
1	1	1	30	−4	52.70	2	1	1	30	0	21.50	3	1	1	30	4	26.70
1	1	7	30	−4	44.50	2	1	7	30	0	23.70	3	1	7	30	4	28.00
1	1	28	30	−4	48.00	2	1	28	30	0	23.10	3	1	28	30	4	23.00
1	0	1	10	0	16.50	2	0	1	10	4	6.70	4	0	1	10	−4	14.70
1	0	7	10	0	15.50	2	0	7	10	4	8.50	4	0	7	10	−4	18.50
1	0	28	10	0	17.70	2	0	28	10	4	7.50	4	0	28	10	−4	17.00
1	1	1	10	0	23.50	2	1	1	10	4	11.50	4	1	1	10	−4	32.00
1	1	7	10	0	23.00	2	1	7	10	4	10.60	4	1	7	10	−4	28.30
1	1	28	10	0	20.20	2	1	28	10	4	10.30	4	1	28	10	−4	25.10
1	0	1	20	0	23.00	2	0	1	20	4	12.40	4	0	1	20	−4	20.50
1	0	7	20	0	21.00	2	0	7	20	4	13.00	4	0	7	20	−4	22.50
1	0	28	20	0	22.90	2	0	28	20	4	12.80	4	0	28	20	−4	21.70
1	1	1	20	0	27.20	2	1	1	20	4	15.20	4	1	1	20	−4	40.50
1	1	7	20	0	29.00	2	1	7	20	4	14.50	4	1	7	20	−4	37.50
1	1	28	20	0	29.80	2	1	28	20	4	14.10	4	1	28	20	−4	32.00
1	0	1	30	0	29.80	2	0	1	30	4	19.50	4	0	1	30	−4	27.50
1	0	7	30	0	28.20	2	0	7	30	4	20.50	4	0	7	30	−4	30.00
1	0	28	30	0	28.30	2	0	28	30	4	19.00	4	0	28	30	−4	27.50
1	1	1	30	0	44.90	2	1	1	30	4	19.00	4	1	1	30	−4	45.00
1	1	7	30	0	36.30	2	1	7	30	4	17.00	4	1	7	30	−4	49.00
1	1	28	30	0	36.50	2	1	28	30	4	19.20	4	1	28	30	−4	41.00
1	0	1	10	4	11.00	3	0	1	10	−4	18.50	4	0	1	10	0	9.50
1	0	7	10	4	9.90	3	0	7	10	−4	17.20	4	0	7	10	0	13.50
1	0	28	10	4	11.10	3	0	28	10	−4	14.80	4	0	28	10	0	12.80
1	1	1	10	4	16.00	3	1	1	10	−4	37.00	4	1	1	10	0	23.80
1	1	7	10	4	16.50	3	1	7	10	−4	40.00	4	1	7	10	0	22.00
1	1	28	10	4	15.80	3	1	28	10	−4	30.00	4	1	28	10	0	18.80
1	0	1	20	4	17.00	3	0	1	20	−4	27.00	4	0	1	20	0	16.00
1	0	7	20	4	16.00	3	0	7	20	−4	26.00	4	0	7	20	0	20.30
1	0	28	20	4	16.80	3	0	28	20	−4	24.00	4	0	28	20	0	19.60
1	1	1	20	4	23.50	3	1	1	20	−4	43.00	4	1	1	20	0	28.00
1	1	7	20	4	29.00	3	1	7	20	−4	45.00	4	1	7	20	0	27.00
1	1	28	20	4	22.60	3	1	28	20	−4	35.50	4	1	28	20	0	24.50
1	0	1	30	4	24.50	3	0	1	30	−4	32.10	4	0	1	30	0	22.90
1	0	7	30	4	21.00	3	0	7	30	−4	32.00	4	0	7	30	0	27.70
1	0	28	30	4	22.40	3	0	28	30	−4	30.00	4	0	28	30	0	27.00
1	1	1	30	4	33.00	3	1	1	30	−4	47.20	4	1	1	30	0	35.00
1	1	7	30	4	32.00	3	1	7	30	−4	51.00	4	1	7	30	0	34.50
1	1	28	30	4	28.50	3	1	28	30	−4	40.20	4	1	28	30	0	28.70
2	0	1	10	−4	10.00	3	0	1	10	0	14.60	4	0	1	10	4	7.40
2	0	7	10	−4	10.20	3	0	7	10	0	12.60	4	0	7	10	4	10.90
2	0	28	10	−4	10.50	3	0	28	10	0	12.30	4	0	28	10	4	10.80
2	1	1	10	−4	19.50	3	1	1	10	0	25.00	4	1	1	10	4	15.00
2	1	7	10	−4	18.00	3	1	7	10	0	23.50	4	1	7	10	4	15.90
2	1	28	10	−4	16.10	3	1	28	10	0	18.30	4	1	28	10	4	13.00
2	0	1	20	−4	15.50	3	0	1	20	0	18.80	4	0	1	20	4	14.00
2	0	7	20	−4	16.30	3	0	7	20	0	18.20	4	0	7	20	4	17.30
2	0	28	20	−4	16.00	3	0	28	20	0	18.00	4	0	28	20	4	16.90
2	1	1	20	−4	23.80	3	1	1	20	0	30.20	4	1	1	20	4	18.80
2	1	7	20	−4	24.50	3	1	7	20	0	26.90	4	1	7	20	4	22.50
2	1	28	20	−4	22.50	3	1	28	20	0	24.10	4	1	28	20	4	18.00
2	0	1	30	−4	22.70	3	0	1	30	0	25.00	4	0	1	30	4	20.00
2	0	7	30	−4	22.50	3	0	7	30	0	24.10	4	0	7	30	4	25.90
2	0	28	30	−4	23.00	3	0	28	30	0	25.30	4	0	28	30	4	24.50
2	1	1	30	−4	28.50	3	1	1	30	0	37.00	4	1	1	30	4	24.70
2	1	7	30	−4	31.30	3	1	7	30	0	33.80	4	1	7	30	4	25.50
2	1	28	30	−4	27.50	3	1	28	30	0	29.20	4	1	28	30	4	20.80

and created within the scope of the thesis was modelled using the Regression Learner application in the Matlab 2023a software package. The experiments were carried out on a desktop computer with an Intel i5 processor with 8GB memory.

The Matlab Regression Learner application artificial intelligence models to be created without writing code via a simple graphical user interface. The application screen can be opened by giving the Regression Learner command to the Matlab console. After the application is opened, a new experiment is started with the New Session command. The previously prepared dataset should be loaded into the Matlab Workspace.

The data format should be organized in such a way that there are input and output parameters in columns and records (samples) in rows. Table 3 shows the dataset, application interface, input, and output selection screens. The dataset is a 216 × 6 matrix, and the columns contain, respectively, the following: soil type, additive (pure soil, 12% BCP-amended soil), time-day (1, 7, 28 days), normal stress (0.069-DS10, 0.138-DS20, and 0.207-DS30 MPa), and water content (OMC−4%, OMC%, and OMC+4%), and shear stress (MPa).

When working on a dataset with artificial intelligence methods, the entire dataset is not used in training in order to test the performance of the model created. In practice, 90% or 80% of the randomly selected part of the dataset is usually used in the training phase, and the remaining 10% or 20% of the data are used for testing the trained model. Test data is also called validation data. The Matlab Regression Learner application supports k-fold cross validation. When k is taken as 5, the dataset is divided into five sections and experiments are performed five times. In each execution phase, four sections are used for training and one section is used for testing. The training and testing phases of the dataset are completed by shifting the partitions sequentially. The error metrics obtained are the average of five experiments. In the experiments given in this section, k = 5 is taken. Therefore, training was performed with 80% of the data and testing was performed with 20% of the data.

The graphical representation of the test data’s system output (ideal shear stress) values and the graphical representation of the artificial intelligence predictions are provided in Figure 4.

In Model 2.23, the training results of the neural network show that the deviation of data points from the expected linear trend yields an R² value of 0.94. This R² value is exceptionally high, signifying an outstanding level of model accuracy.

The error amounts for the test data are visualized in Figure 5. It can be observed that there are errors around −6 and +6 in some examples. Considering that the ideal shear stress values are given in the range of 0 to 60 (Mpa), it is observed that there is a small amount of prediction error for a few examples.

The numerical results for the test data, ranging from the best to the worst, are presented in

Table 4. The error metrics of artificial intelligence regression models created in Matlab for the test data.

Models	Mean Absolute Error (MAE)	R2	Root Mean Square Error (RMSE)
Neural Network	1.7086	0.94	2.3392
Neural Network	1.8556	0.93	2.4935
Neural Network	1.9968	0.93	2.5564
Neural Network	2.2091	0.90	2.8976
Ensemble	2.1707	0.89	3.1066
Gaussian Process Regression	2.2678	0.89	3.1533
Gaussian Process Regression	2.4867	0.86	3.5070
Gaussian Process Regression	2.4873	0.86	3.5214
SVM	3.0506	0.80	4.2134
Neural Network	3.1330	0.76	4.5570
SVM	3.4090	0.76	4.5582
Stepwise Linear Regression	3.7873	0.73	4.8896
Linear Regressiom	3.7219	0.72	4.9538
SVM	3.6584	0.72	4.9576

. The best result was achieved using the neural network method. In the model created with neural networks, the error metrics were calculated as follows: MAE (mean absolute error) was 1.7086, R² (R-Squared) was 0.94, and RMSE (root mean square error) was 2.3392. With an average error of approximately 1.7, the model successfully predicted rupture values within the range of 0–60. In this form, the proposed model has been evaluated as usable and successful.

In Figure 6, the output parameter (blue) of the artificial intelligence regression model trained with the shear stress value for all data after training is depicted along with the difference (orange) between them. As is evident from Figure 6, for many examples, the errors are quite low and nearly identical.

4. Conclusions

This study examined the reliability of ANN outputs after training on existing shear stress data using artificial neural networks (ANNs). At the Geotechnical Laboratory of Iowa State University, shear box test data, emphasizing the utilization of biofuel by-products (BCPs) in soil stabilization, were employed to train and validate an Artificial Neural Network (ANN). The final concluding statements of this study are as follows:

• The data format should be organized so that there are input and output parameters in columns and records (samples) in rows. The dataset consists of a 216 × 6 matrix.
• The input parameters for the dataset were selected as soil type, additive ratio, time, and optimum moisture content, all derived from direct shear stress parameters. The output parameter was the shear stress values obtained from the experiments.
• Simulations conducted using the Regression Learner application in the Matlab software package compared 27 different regression methods using k = 5 cross-validation. The top 13 methods, ranked by success, are summarized in Table 3.
• The best test results were obtained using the neural network method. In the model created with neural networks, the error metrics were calculated as follows: MAE 1.7086, R² 0.94, and RMSE 2.3392.

In summary, the utilization of artificial intelligence, as exemplified by an impressive R² value of 0.94 that signifies a robust correlation, has yielded excellent results in predicting the system output values for the test data. This achievement holds significant promise for the field of geotechnical engineering, particularly in the context of experiments that are often time-consuming and require a multitude of trials. The demonstrated success of employing artificial neural networks (ANN) to interpret shear test data suggests that researchers can benefit substantially from this approach. By doing so, it becomes possible to acquire a substantial amount of data more efficiently, with the need for fewer experimental trials and a considerably shorter timeframe.

This application of ANN not only enhances the predictive accuracy but also serves as a valuable resource for geotechnical engineering research, reducing the labor-intensive and resource-demanding nature of traditional experimentation. The findings underscore the potential for AI-driven solutions to revolutionize data collection and analysis in geotechnical engineering and offer a more streamlined and expedited approach to obtaining meaningful insights for future projects in this field. As technology continues to advance, it is expected that the integration of AI methodologies will play a pivotal role in shaping the future of geotechnical research and practice.