Selected AI optimization techniques and applications in geotechnical engineering

Abstract

In an age of depleting earth due to global warming impacting badly on the ozone layer of the earth system, the need to employ technologies to substitute those engineering practices which result in emissions contributing to the death of our earth has arisen. One of those technologies is one that can sufficiently replace overdependence on laboratory activities where oxides of carbon and other toxins are released. Also, it is one technology that brings precision to other engineering activities especially earthwork design and construction thereby reducing to lower ebb the release of carbon oxides due to inexact utilization of materials during geotechnical practices. In this review, the use of artificial intelligence techniques in geotechnics has been explored as a precise technique through which geotechnical engineering works don’t impact on our planet due to precision. The intelligent learning algorithms of ANN, Fuzzy Logic, GEP, ANFIS, ANOVA and other nature-inspired algorithms have been reviewed as they are applied in the prediction of geotechnical and geoenvironmental problems and system. It is a complex exercise to conduct experimental protocols during the design and construction of earthwork infrastructures. Most times, such experimental exercises don’t meet the required condition for sustainable design and construction. At other times, certain errors as a result of experimental set up or human misjudgment may mar the accuracy of measurements and release unexpected emissions. The employment of the evolutionary learning methods has solved most of the lapses encountered in repeated laboratory measurements. So, in this review work, the relevant computational intelligent techniques employed at different times, under different laboratory protocols and utilizing different materials, have been presented as a comprehensive guide to future researchers in this innovative and evolving field of artificial intelligence. With this extensive review, a researcher would not have to look far to get a technical and state of the art guide in the utilization of various intelligent techniques that would enable engineering models in a more efficient, precise and more sustainable approach to forestall multiple practices that release carbon emissions into the environment.

Keywords:

• Computational intelligence
• soft computing
• artificial intelligence
• eco-friendly geomaterials optimization
• machine learning
• geotechnics and earthworks
• precision optimization

1. Introduction

With the increasing growth in the use of science and technology in solving everyday life problems, the need for methods that understand complex and ambiguous problems becomes greatly inevitable. Soft computing is an emerging collection of various methodologies aimed at finding a balance to poor precision, uncertainty, and unclear truth by applying a collection of statistical, probabilistic, and optimization tools in analyzing sets of data, classify the data, identify new patterns and predict next trends within the shortest convenient time. Soft computing has three main branches which are artificial neural networks, genetic algorithms, and fuzzy logic; these branches tend to build intelligent and wiser machines that behave like the human mind and can answer questions explicitly and not just provide answers. The application of soft computing in branches of civil engineering such as geotechnics has been a breakthrough of the 21st century with these techniques helping solve different cumbersome mathematical problems in a space of seconds. Geotechnics is one of the most relevant branches of civil engineering, which deals with the study of the engineering behavior of the earth materials using the principles of soil mechanics and material engineering in finding lasting solutions to earth problems. The complexity accompanying geotechnical engineering has further led to the need to apply these soft computing techniques in solving earth problems such as swelling potentials of soils as recorded by Alaneme et al. (2020) in the modeling change in volume properties of hydrated lime activated rice husk ash modified soft soil using artificial neural network. This study x-rays the application of ANN model in estimation of the swelling and shrinkage potential and consistency indices of the stabilized soil by adopting the soil HARHA replacement ratio and corresponding Atterberg limit responses as the network input variables while the shrinkage, clay activity, and swelling characteristics were utilized as the network output parameters using Levernberg Marquardt (LM) training and feed—forward back-propagation algorithm with 5-9-6 network architecture. He recorded that the application of the ANN model in his research saved cost, made the best use of research materials, and was time efficient. Kayadelen et al. (2009) studied a model for the swelling potential of compacted soils, adaptive neuro-fuzzy model was applied on compacted soils sourced within Nigde, Turkey, parameters such as the coarse grain fraction ratio, and fine-grained fraction ratio, plasticity index, and maximum dry density were presented to the model as input. The results obtained showed that the ANFIS model is a more reasonable model for predicting the swelling potential of soils. Furthermore, soft computing in geotechnics have been applied in the determination of mixture designs, predicting shallow foundations, predicting and modeling soil behaviors, study of pile cap resistance, etc. At the moment soft computing-based techniques are becoming more popular in the field of geotechnics with several works on the application of neural networks and fuzzy logic and little work done on the application of genetic algorithms in this field.

2. Soft computing optimization techniques

2.1. Artificial neural network (ANN)

2.1.1. Background

In the past two decades, artificial neural network (ANN) has been one of the major interests in structural engineering, environmental and water resources engineering, traffic engineering and geotechnical engineering. ANNs represent a class of robust, non-linear models applicable for solving a wide variety of complex engineering problems. Engineering problems that involve highly nonlinear functional approximations could be solved using ANNs. Artificial neural networks (ANNs) may be defined as a structure of tightly interconnected adaptive simple processing elements (named artificial neurons or nodes) which are able to perform large-scale parallel computations for data processing and knowledge representation (Huang et al., 2019). In 1943, McCulloch and Pitts (1943) proposed the first artificial neuron model (MP model), which adopted simplified signal propagation mechanism to imitate some basic functions of human brain neurons, thus laying the foundation for the development of early neural computing. Adeli and Yeh (1989) published one of the first journal articles on the civil/structural engineering applications of neural networks. Since then, neural network has been widely used in civil engineering. ANN is a kind of technical reconstruction of biological neural network in a simplified sense. Its main task is to build a practical artificial neural network model according to the principle of biological neural network and the need of practical application, design corresponding learning algorithm, and simulate some intelligent activities of human brain. Finally, it is implemented technically to solve practical problems. An artificial neural network (ANN) is a computational model which tries to simulate the functional aspects of biological neural networks. ANNs consist of connected artificial neurons and process information using a connectionist approach. ANNs are used to correlate inputs and outputs by continuously enhancing links weights according to inputs—outputs. They can be used to model complex relationships between inputs and outputs or to find patterns in data (Salahudeen et al., 2020). Complicated relationships between outputs and inputs could be discovered by changing model architect and links weights. Although apart from these advantages, ANNs have a major disadvantage; they do not generate a closed form formula. Developing process of ANN model has six steps. These are: selecting variables (input & output), collecting of database and divide it into training and validating groups, determining the network architect, optimizing of links weights, ending of training based on predefined criteria and validating of the accuracy of the ANN.

Artificial neural networks (ANNs) are a form of artificial intelligence which attempt to mimic the behavior of the human brain and nervous system. The common architect of ANN includes two layers (input & output) and number of hidden layers between them. Input layer has a number of nodes equal to the input variables, output layer has a number of nodes equal to the output variables, while each hidden layer has a selected number of nodes depends on the complexity of the relationship. Each node sums its inputs from the linked nodes from the previous layer multiplied by the weight of each link, nonlinear activation function is applied to that sum to generate the output of the node which will be the input of the linked nodes in the next layer. Information propagates off in the ANN from the input layer to the output layer through the hidden layers. During training (learning) process, the weights of the links are optimized to minimize the prediction error using the training database. After training process, the accuracy of the trained ANN must be tested using independent validation database. ANNs learn from data examples presented to them and use these data to adjust their weights in an attempt to capture the relationship between the model input variables and the corresponding outputs. Consequently, ANNs do not need any prior knowledge about the nature of the relationship between the input/output variables, which is one of the benefits that ANNs have compared with most empirical and statistical methods. The ANN modelling philosophy is similar to a number of conventional statistical models in the sense that both are attempting to capture the relationship between a historical set of model inputs and corresponding outputs. ANNs can form the simple linear regression model by having one input, one output, no hidden layer nodes and a linear transfer function. ANNs adjust their weights by repeatedly presenting examples of the model inputs and outputs in order to minimize an error function between the historical outputs and the outputs predicted by the ANN model.

Artificial Neural Networks take their name from the networks of nerve cells in the brain. Although they represent a much-simplified version of the human brain, yet these computational models inspired by biological neural network may provide new directions to solve complex problems (Chandwani et al., 2014). In contrast to digital computers, which offer sequential processing of information, ANNs parallel processing inspired by working of a human brain, gives computers an additional advantage to simultaneously process large volumes of data. ANNs are well suited for problems whose solutions require knowledge that is difficult to specify but for which there are enough data or observations. The neural network’s ability to learn from experience without seeking prior knowledge about the governing relationships and to generalize when presented with unseen data forms the backbone of its modelling ability, with which it approximates any functional relationship with reasonable accuracy. It has been reported that the ANN has the ability to extract the patterns in phenomena and overcome the difficulties due to the selection of the model form, such as linear, power, or polynomial. The common features of some of these successful applications of ANNs in prediction and modelling are that the quantities being modelled are governed by multivariate interrelationships and the data available.

Haykin (2009) defined neural networks as a massively parallel distributed processor made up of simple processing units, which has a natural propensity for storing experiential knowledge and making it available for use. Neurons are the basic units used for computation in the brain, and their simplified abstract models are the basic processing units of ANNs. In addition to the processing elements called “neurons”, the neural networks comprise the connections between the processing elements. The connections carry a “weight” parameter signifying the importance of the link between the neurons. The synaptic weights store the knowledge of the neural networks and therefore in the training phase with a continuous flow of information, there is a gradual reorganization of weights within the neural network and subsequent comparison of target and predicted values in an attempt to reduce the network error to a minimum. The continuous updating of synaptic weights is undertaken by a learning algorithm called error back-propagation. Back-propagation provides a computationally efficient method for changing the weights in a feed forward network, with differentiable activation units to learn a training set of input-output examples.

ANN is classified as “black box system”, because its links weights, parameters and processes are hidden from users (Goh et al., 2005). Besides that, insufficient database may cause a poor generalization. Backpropagation ANN was used to estimate the residual friction angle of clay using its consistency limits (LL, PI, CF and ΔPI), also, the relative importance of each input was evaluated. The developed ANN model was presented by drawing the ANN structure with links weights values.

2.1.2. The artificial neuron basics

Much remains unknown concerning the way brain trains itself to deal with information, and related theories. Within the human brain, a typical nerve cell (neuron) collects signals from neighbor cells through a number of fine paths known as dendrites (see Figure 1) (Park, 2011). The neuron sends out spikes of electrical activity through a long, skinny stand referred to as associate nerve fiber that splits into thousands of branches. At the top of every branch, a structure called a conjunction converts the activity from the axon into electrical effects that inhibit or excite activity from the axon into electrical effects that inhibit or excite activity within the connected nerve cells. Once a neuron receives excitant input that’s sufficiently giant compared with its repressing input, it sends a spike of electrical activity down its axon. Learning happens by dynamical the effectiveness of the synapses in order that the influence of 1 neuron on another changes. A man-made neuron could be a device with several inputs and one output. The neuron has two modes of operation; the utilizing mode and also the training mode. Within the training mode, the neuron may be trained to fireplace (or not), for specific input patterns. Within the using mode, when an educated input pattern is detected at the input, its associated output becomes this output. If the input pattern doesn’t belong within the educated list of input patterns, the firing rule is employed to work out whether or not to triggered or not.

Figure 1. Biological neuron.

ANNs are a type of AI that aims to mimic the performance of the human brain associated nervous system. Though the idea of ANNs was initially introduced in 1943 by McCulloch and Pitts (1943), analysis into applications of ANNs has blossomed since the introduction of the back-propagation coaching algorithmic rule for feed-forward multilayer perceptron (MLPs) in 1986 by Rumelhart et al. (1986). Typically, the design of ANNs consists of a series of process components (PEs), or nodes, that are sometimes organized in layers: an input layer, an output layer, and one or additional hidden layers, as shown in Figure 2.

Figure 2. Typical structure and operation of artificial neural networks (Ebid, 2020).

2.1.3. ANN model

Setting the ANN architect means determining hidden layers number and how many nodes in each layer. Using nonlinear activation function allows ANN to simulate the complicated performance of the considered system. Input & output layers have number of nodes equal to input and output variables respectively. Choosing of optimum number of nodes for each hidden layer can be done by iteration. Using few nodes will affect the prediction accuracy, while using too many of them will lead to over fitting (memorization).

2.1.4. Choosing the suitable inputs and outputs

In the current years, artificial neural networks have been largely used in modeling a wide range of engineering issues related to their nonlinearity and the proven advantage over their extraordinarily reliable predictive ability. In contrast to statistical modeling, ANN is an information-based technique and as a result no longer requires a prior understanding of the fundamental relationships of variables (Shahin et al., 2002). Moreover, those nonlinear parametric models are able to approximate any non-stop relationship between input and output (Onoda, 1995). The technique of the unusual maximum in selecting information inputs in geotechnical engineering is mainly based on prior understanding of the machine in question. Therefore, the I/O variables of ANN shapes are determined by way you deal with the underlying elements that have an effect on the behavior of the target variable.

2.1.5. Division of Dataset

In nearly all geotechnical models using ANN, usually, cross-validation is used in order to prevent criterion, which calls for the whole dataset to be divided into three subsets: (1) training dataset, (2) testing dataset, and (3) validation dataset. The distribution ratio between the three subsets may also have a substantial effect on version performance (Shahin et al., 2004).

Therefore, it’s far essential to divide the dataset into three subsets in this sort of manner that they constitute the identical statistical populace showing comparable statistical characteristics (Salahudeen & Sadeeq, 2019).

2.1.6. Network architecture

Defining network architecture involves choosing the architecture of the model and the way information propagate in the ANN. Although there are many types of ANN, but the “Multi-layered Preceptron” (MLP) trained using back propagation algorithm was used for both forecasting & prediction. So far, “Feed-Forward Network” FFN was successfully used in different geotechnical issues (Günaydin, 2009; Kuo et al., 2009; Salahuddin et al., 2020).

2.1.7. Optimization of Model

Model optimization, which includes comparing the most fitting weights for the ANN connections, is typically completed the usage of the back-propagation set of rules (Shahin & Jaksa, 2006). They are the most popular optimization rules in “Feed-Forward Network” FFN and were efficaciously carried out a lot in geotechnical problems (Pooya Nejad et al., 2009). The back-propagation rules are primarily based on the “First Order Gradient Descent Rule” and have the ability to escape local minima (Maier & Dandy, 1998).

2.1.8. Ending criteria

Stopping criteria defines when to stop the training stage of the artificial neural network model. Validation stage must be carried out after training to ensure that overfitting did not happen or occur. Accordingly, the collected database should be divided into 3 sub datasets: 1) training, 2) testing and 3) validation. The first dataset is used to optimize the weights of the links during training. ANN is considered trained when the predicting error of this dataset is minimal. The developed ANN is considered generalized (not over fitting) when the error of both training and testing datasets are almost the same, this is when the training should be stopped. Continuing the training after this point will increase the error of the testing dataset due to overfitting (Maier & Dandy, 2000).

2.1.9. Validation & behaviour evaluation

After finishing the training stage, ANN must be validated using independent database to ensure the ANN’s generalizability. The trained ANN should illustrate the non-linear behavior between inputs& outputs, rather than remembers the trained dataset (Shahin et al., 2003). Because the ANN is scored against an invisible dataset, the results are meaningful for evaluating network performance. The metrics commonly used to assess the prediction performance of networks are the “Mean Square Error” (MSE), the “Mean Absolute Error” (MAE), and the “Correlation of Determination” (R²). Using MSE pays much more attention to larger errors than smaller errors, while MAE gives an indication of the size of the error. The (R²) is used to measure the fitness quality &the correlation between predicted and experimental results

2.1.10. Application of ANN in geotechnical problems

Engineering characteristics of soil and rock present complex & uncertain behavior because of due to the micro formations of these materials (Jaksa, 1995). This is unlike most construction materials, such as concrete, steel & timber, which show more isotropy & homogeneity. To simulate the complex behavior soil, and its uncertainty, conventional design methods are approximated and simplified. Another approach is the (AI) techniques like ANN which showed great success with distorted, incomplete and noisy data, accordingly, it is ideal to predict the complicated, nonlinear behavior of soil (Hubick, 1992).

ANNs have been applied successfully in many geotechnical engineering areas. Thisincludes pile capacity prediction, settlement of foundations, soil properties and behaviour, liquefaction, site characterisation, earth retaining structures, slope stability and the design of tunnels and underground openings. Perhaps the most successful and well-established applications are the capacity prediction of driven piles, liquefaction and theprediction of soil properties and behaviour. Other applications like settlement of structures need to be treated with caution until further understanding of the mechanism is ensured. There are also several areas in which the feasibility of ANNs has yet to be tested, such as bearing capacity prediction of shallow foundations, capacity of bored piles, design of sheet pile walls and dewatering, among others.

In the last two decades, ANNs have been used in many geotechnical engineering applications. The important component of this simulation is the novel structure of the information processing system which consists of a huge amount of well interconnected processing elements (neurons) focused on solving a particular problem (Maizir & Kassim, 2013; Shahin et al., 2001). Just as it is the case in human beings, ANNs also learn by training. An ANN is developed for a distinct application. These applications include data classification and/or patterns recognitions during the training process. ANN has many types with different applications, like data association, prediction, classification, conceptualization and filtering (Salahudeen et al., 2020). Usually, ANN has three main layers: input, hidden and output. “Multi-Layer Networks” make use of several types of training techniques; back-propagation is the most popular one (Eidgahee et al., 2015; Fakharian et al., 2018).

Because rock and soil properties exhibit significant nonlinearity and plasticity, traditional geotechnical methods unable to predict the nonlinear behavior of rock and soil accurately. Accordingly, there are urgent needs to predict the complex behavior of soil and rock (Chao et al. 2018). “Machine Learning” (ML) techniques can effectively deal with rock and soil nonlinear and plastic behavior and avoid the disadvantages of conventional methods. (ML) techniques are algorithms allow computer system to self-learn and figure out trends & patterns in huge databases and use them to create predictive models. There are many types of (ML) algorithms. ANN is the most popular (ML) techniques especially in geoengineering problems. The ANN can effectively deal with incomplete and noisy data, it has 3 advantages: First, it has high computational speed. Second, it has strong fault tolerance ability. Third, he is adept at tackling problems with complicated resolution rules.

2.1.11. Application to geotechnical site characterization

Site characterization is a field concerned with the analysis and interpretation of geotechnical site investigation data. Ranasinghe et al. (2017) applied artificial neural networks (ANNs) to forecast the efficiency of dynamic rolling pressure (RDC) using (CPT) data with respect to a “four-sided impact cylinder”. This was done using the computer program NEUFRAME. The model, which is based on a Multilayer Perspective (MLP), includes four inputs, measurement depth, initial tip resistance and sleeve friction of CPT, and number of passes, while the output is the final tip resistance at considered depth after compaction. The architecture of the developed ANN is 4-4-1. The ANN model is developed using the algorithm defined by Maier et al. (2010). The developed ANN was presented as an equation that yielded reliable prediction results with respect to the validation data set. It was concluded that the developed ANN can accurately predict enhanced tip resistance after compaction. Sensitivity analysis determined that soil type and DCP primes were the dominant parameters.

In a detailed review on ANN applications on pile foundations, Fatehnia and Amirinia (2018) listed 25 researches regarding using ANN in piled foundation, 38 different parameters were used as inputs. Length of pile was the most used parameter in 21 research, while cross section area of pile came in the second rank. Generally, properties of pile were the most repeated parameters then soil properties (Hammer/SPT/CPT) and lastly the loading history. It was recommended to include soil-pile inter action in that future ANN studies.

Besawa et al. (2006) present a subsurface characterization methodology that integrates multiple types of data using a modified counter propagation artificial neural network (ANN) to provide parameter estimates and define groundwater contamination at a leaking landfill. The results of this research illustrate the feasibility of combining principal component analysis (used to reduce data dimensionality) with the counter propagation ANN and traditional geo-statistical methods (kriging) to estimate subsurface contamination. The study demonstrates the potential for applying this ANN estimation technique (as an alternative to kriging) to delineate the leachate contaminated groundwater and evaluate water quality associated with subsurface contamination at a full-scale site. These results suggested that the counter propagation ANN is a promising parameter estimation method when integrating multiple data types to enhance prediction accuracy and reduce uncertainty.

Ikizler et al. (2009) present an ANN model to predict the effect of both vertical and lateral swelling pressure on retaining structure. They collected a database for the experimentally measured swelling pressures (lateral & vertical) on a vertical layer of geofoam placed between swilling soil and vertical rigid steel plate. The collected database was divided into training and validation subsets. Then ANN was trained using the training subset to predict the two swelling pressures values against the retaining structure. The results of both subsets illustrated that the developed ANN can satisfactorily predict both vertical and lateral swilling pressure values.

Next, Ikizler et al. (2012) introduced a new estimation model for stress prediction as described in Ikizler et al. (2009) using empirical data. An experimental test results database was collected using new test setup consisting of steel box equipped to measure swelling in both horizontal and vertical directions. A predictive hyper ANN—fuzzy model (ANFIS) were developed. First, both swelling pressures (lateral & vertical) were recorded. Then, ANN and ANFIS techniques were developed using the collected test results. The obtained results showed that the prediction based on the ANN and the ANFIS approach can be satisfactorily used for estimating the lateral and vertical swell stresses transferred for extended soils.

Benali et al. (2013) used ANNs to simulate the mechanical behaviour of an axially loaded pile and more particularly the prediction of the bearing capacity. The ANNs used were MLPs that were trained with the back-propagation algorithm. The study was aimed at showing the efficacy of the approach to estimate the total pile capacity in cohesionless soils. A database containing 120 records of experimental values for capacity was used to develop and verify the ANN model. The optimum network architecture was with 6 nodes in the hidden layer, the internal parameters were found to be as follows: learning rate of 0.3; a momentum of 0.01; a Tan-sigmoidal and pure-line activation functions for hidden and output layers respectively. The importance of each factor was determined using sensitivity analysis. This study showed that the SPT, the overburden the pressure at the pile point, the pile slenderness, and the internal angle of friction, the penetration depth, the roughness of the pile/soil interface, the pile diameter and the over-consolidation ratio are most important factors affecting pile capacity in cohesionless soils. ANN results when compared with the experimental ones and with those from other conventional methods showed that the ANN model can accurately predict the pile capacity without need of using table or charts. Like other AI models, the outputs of the ANN model are valid within the trained range only. Despite of these limitations, the results of this study indicate that ANNs have a number of significant benefits that make them a powerful and practical tool for pile capacity prediction in cohesionless soils.

2.1.12. Application to geotechnical soil parameters prediction

In recent times, artificial neural networks (ANNs) have been applied to many geotechnical engineering tasks and have demonstrated some degree of success (Shahin et al., 2002). Ozer etal. (2008) applied ANN for the estimation of compression index of clay soils anddetermined that ANN has a better estimation performance than regression equations. The performance of widely used empirical equations for the estimation of swell index of fine-grained soils using regression equations and artificial neural networks was assessed by Nihat (2009) using a database consisting of 42 laboratory test data. The study used ANN with one hidden layer and eight hidden layer nodes. Back propagation algorithm was used to train the network. Results indicate that artificial neural networks have significant advantages over traditional regression methods such as being more flexible and being able to discover more complex relationships with less effort.

Kolay et al. (2008) investigated the effectiveness of neural network simulation application in predicting the compression index of tropical soft soil based on the geotechnical characteristics of different borehole data collected from Geospec Sdn Bhd, Kuching Sarawak, Malaysia. Based on the neural network testing results it was concluded that the network trained with Levenberg-Marquardt algorithm and BFGS Quasi-Newton consistently simulates the most accurate results and the Networks trained with Polak-Ribiére Update algorithm simulate the least accurate results. It was also observed that smaller number of neurons in the hidden layer yield better results than simulation with a greater number of neurons and a learning rate of 0.1 and 2 neurons in the hidden layer yielded an accuracy of 92% for compression index prediction. In a study by Kalantary and Kordnaeij (2012), the performances of widely used single andmulti-variable empirical equations for the estimation of the compression index were evaluated using a database consisting of 400 wide-ranging samples obtained from 125 construction sites in the Mazandaran Province of Iran. Using the same database, new single and multi-variable empirical equations were developed using ANN. Furthermore, compression index was predicted using neural network simulation. Based on the regression analysis, it was concluded that the models using parameters of the void ratio and natural water content show better performance than other models.

Iyeke et al. (2016) developed models for predicting the shear strength parameters (cohesion and angle of friction) of lateritic soils in central and southern areas of Delta State of Nigeria using artificial neural network modelling technique. A total of eighty-three (83) soil samples were collected from various locations in the study area. The optimum artificial neural network architecture used for cohesion was 3-9-1, while the angle of friction had optimal network geometry of 3–11-1. The results of the coefficient of determination and root mean square showed that the artificial neural network method outperforms some selected empirical formulae in the prediction of shear strength parameters. A Pearson correlation analysis was carried out to study the relative relationship of the factors that affect shear strength parameters. The correlation analysis indicated a high level of relationship between plastic limit, liquid limit and plasticity index. Hence only the plasticity index was used in the modelling exercise. The results between the predicted and measured shear strength parameters obtained by utilizing ANNs were compared with three traditional methods. The results obtained demonstrated that the ANN method outperforms the empirical methods considered.

Das and Basudhar (2008) proposed a neural network model to predict the friction angles supported clay fraction and consistency limits. Totally different sensitivity analysis was created to figure out the important parameters poignant the friction angle. it had been finished that the ANN model with clay fraction and physical property index as input parameters was the most effective model, based on statistical parameters, efficiency and correlation coefficients, for both testing & training datasets. These analyses illustrated that both correlation coefficient, Garson’s method and links weight, the plasticity index is that the most significant item.

Salahudeen and Sadeeq (2019) developed (ANNs) to estimate the (CBR) values of Nigerian black clay. Multilayer perceptron (MLPs) ANNs use the back-propagation set of rules to simulate soaked and un-soaked CBR of cement kiln dust-modified black clay. Eight input & output variables had been used for the developed ANN. The used input variables are the Gs, SL, Cu, Cc, LL, PL, OMC and MDD. The output variables are the soaked and un-soaked CBR. Both MSE and R² had been used as measurements for acceptability of performance. ANN 8-8-1 model was the best for soaked CBR, while ANN 8–17-1 model was the optimum for un-soaked CBR. The results showed strong correlation between measured and predicted soaked and un-soaked CBR values.

2.1.13. Application to geotechnical soil properties and behaviour

Soil properties and behavior is an area that has attracted many researchers to modelling using ANNs. Developing engineering correlations between various soil parameters is an issue of major importance in geotechnical engineering. The design of foundations is generally controlled by the criteria of bearing capacity and settlement, but the settlement often governs the design. The problem of estimating the settlement of foundations is very complex and uncertain. This fact encouraged some researchers to apply the ANN technique to settlement prediction. Based on the method of back-propagation neural network, Feng et al. (2014) established a foundation settlement prediction model for a railway subgrade in HeFei area of China. In the model, field monitoring data was used as the training sample and then settlement was predicted. The model was used for four test sections of the railway subgrade. The results showed that for the four test sections, the predicted settlement in the developed model were consistent with the field monitoring values. It was established that the back-propagation neural network prediction model can predict the final settlement of railway foundation commendably which provided a reliable reference for railway design, construction operation management and maintenance.

Shahin et al. (2000) carried out similar work for predicting the settlement of shallow foundations on cohesionless soils. In this work, 272 data records were used for modelling. The input variables considered to have the most significant impact on settlement prediction were the footing width, the footing length, the applied footing pressure and the soil compressibility. The results of the ANN were compared with three of the most commonly used traditional methods. The results show that ANNs were able to predict the settlement well and outperform the traditional methods. The ANN produced high coefficients of correlation, r, low root mean squared errors, RMSE, and low mean absolute errors, MAE, compared with the other traditional methods.

Salah El-Din et al. (2018) applied ANN approach trained using a back-propagation feedback algorithm, to simulate (OMC) and (MDD) of black cotton soil stabilized with cement kiln dust. Ten sets of input and output data were used to develop the ANN model. The (MSE) and R² values were used as the criterion for accepted behavior. ANN 10-5-1 and ANN 10-7-1 were used for OMC and MDD in order. They showed the minimum MSE value & the maximum R² value. A strong correlation between experimental and predicted OMC and MDD values as reported.

Recently, Salah El-Din et al. noted that (ANN) have not been efficiently extended to the topic of soil stabilization. (2020) used Multilayer Artificial Neural Networks trained on a back-propagation back-feeding algorithm to simulate the (UCS) of dust-treated expanded Nigerian clay in cement kilns. For each one of the three developed ANN models, 8 inputs & one output datasets were used. (MSE) & R² values were used evaluate the performance. ANN 8–11-1 had the minimum MSE value & maximum R² value. All obtained simulation results were reported to be satisfactory and a good correlation was reported between predicted and experimental UCS values .

Tizpa et al. (2014) presented artificial neural network prediction models that link properties of pressure, permeability, and shear strength of soil with soil index properties. A dataset containing 580 records was collected.

Results of particle size distribution, consistency limits, and permeability were measured at different levels of stress using triaxial compression tests. Comparing experimental and predicted results indicated that the predictions are within a 95% confidence interval. According to the sensitivity analysis performed, consistency limits and fines content (silt & clay) are the most effective variables in predicting MDD& OWC. Another coherent aspect of sensitivity analysis is the great importance of the degree of stress in predicting the coefficient of permeability. Also, it has been observed that the effective shear friction angle is mainly dependent on the bulk density of the soil.

2.1.14. Application in seismic and earthquakes

Goh (1994) used neural networks to model the complex relationship between seismic and soilparameters in order to investigate liquefaction potential. The neural network used in this work was trained using case records from 13 earthquakes that occurred in Japan, United States and Pan-America during the period 1891–1980. The study used eight input variables of SPT-value, the fines content, the mean grain size, the total stress, the effective stress, the equivalent dynamic shear stress, the earthquake magnitude and the maximum horizontal acceleration at ground surface. The output variable was only one which was assigned a binary value of 1 for sites with extensive or moderate liquefaction, and a value of 0 for marginal or no liquefaction possibility. The results obtained by the neural network model were compared with the method of Seed et al. (1985). The study showed that the neural network gave correct predictions in 95% of cases, whereas Seed et al. (1985) gave a success rate of 84%.

Goh (1996) also used neural networks to assess liquefaction potential from cone penetration test (CPT) resistance data. The data records were taken for sites of sand and silty sand deposits in Japan, China, United States and Romania, representing five earthquakes that occurred during the period 1964–1983. A similar neural network modelling strategy, as used in Goh (1994), was used for this study and the results were compared with the method of Shibata and Teparaksa (1988). The neural network showed a 94% success rate, which is equivalent to the same number of error predictions as the conventional method by Shibata and Teparaksa (1988).

Blasting has been widely used as an economical and cheap way of rock breakage in mining and civil engineering applications. An optimal blast yields the best fragmentation in a safe, economic and environmentally friendly manner. The degree of fragmentation is vital as it determines to a large extent the utilization of equipment, productivity. Explosive energy, besides rock fragmentation, creates health and safety issues such as ground vibration, air blast, fly rock, and back breaks among others. As a result, the explosive energy impacts structures and buildings located in the vicinity of the blasting operation, and cause human annoyance, as well as exposes operators in the field to hazardous conditions. There is therefore a need to develop a model to predict blast-induced ground vibration (PPV), air-blast (AOp), and rock fragmentation. Artificial neural network (ANN) technique is preferred over empirical and other statistical predictive methods as it is able to incorporate the numerous factors affecting the outcome of a blast. To this end, Tiile (2016) developed a simultaneous integrated prediction model for rock fragmentation, ground vibration and air blast using artificial neural network system based on 180 monitored blast records taken from a gold mining company in Ghana using a three-layer, feed-forward back-propagation ANN. Based on the results obtained from the study, ANN model with architecture of 7–13-3 was found optimum having the least root mean square error. Optimum ANN model was observed to have improved the efficiency of the blast operation by reducing ground vibration and air-blast values below company limits. Rock fragments were within the desired range. There was a 31% and 37% improvement in crusher and excavator productivities respectively. Crusher availability went up by 11% while excavator availability increased by 10% following the application of the ANN model. Artificial neural network (ANN) model proved to be more effective compared to empirical equations and multivariate regression (MVR) matching their respective RMSE and—value.

2.1.15. Application of ANNs in construction and civil engineering materials

There are several applications of ANNs to civil engineering materials and construction works. Subasi (2009) applied ANN for the prediction of mechanical properties of cement containing class C fly ash. In a recent study, El-Khoja et al. (2018) developed artificial neural network (ANN) models to predict the compressive strength of rubberized concrete (RuC). A trained and tested ANN was developed using a comprehensive database collected from different sources in the literature. The ANN model developed used five input parameters that include: coarse aggregate (CA), fine aggregate (FA), w/c ratio, fine rubber (Fr), and coarse rubber (Cr). The ANN outputs were the corresponding compressive strengths. A parametric study was also conducted to study the effects of various RuC constituents on the compressive strength of RuC. ANN models reasonably predicted the compressive strength of RuC. ANN method can be used as an accurate and quick tool for estimating the compressive strength of any RuC.It was however observed that for more efficient training of the developed ANNs, the database should be increased for the model to yield better results.

The most common application of ANNs in the construction management area is prediction. Margaret et al. (2002) developed neural network cost models using data collected from nearly 300 building projects. The models based on linear regression techniques can be used as a benchmark for evaluation of the neural network models. The results showed that the major benefit of the neural network approach was the ability of neural networks to model the nonlinearity in the data. Murat (2003) developed and tested a model of cost estimation for the RC structural systems buildings in the early design phase using ANN. This model helps the designers to select the optimum decisions at the concept phase. Dataset from 30 projects was used to develop the ANN.8 parameters were utilized to estimate the cost of one square meter of RC residential building of 4–8 storeys in Turkey, an average cost estimation accuracy of 93% was achieved. Assaf, et al. , investigated the overhead cost practices of construction companies in Saudi Arabia. They show how the unstable construction market makes it difficult for construction companies to decide on the optimum level of overhead costs that enablesthem to win and efficiently administer large projects.

ElSawy et al. (2011) uses Artificial Neural Network (ANN) approach to develop a parametric cost-estimating model for site overhead cost in Egypt by taking fifty-two actual real-life cases of building projects constructed in Egypt. Seyed et al. (2008) presented application of Artificial Neural Network (ANN) to forecast actual cost of a project based on the earned value management system (EVMS) by selecting some projects randomly based on the standard data set. They compared between real and forecasted data and showed the better performance which was based on the mean absolute percentage error (MAPE) criterion. Their approach could be applicable to better forecasting the project cost and result in decreasing the risk of project cost overrun, and therefore it is beneficial for planning preventive actions. Yu-Ren et al. (2009) build two credible models linking pre-project planning and project success by employing neural networks. To enhance the performance of the neural networks model, bootstrap aggregation and boosting algorithms are incorporated in the model development process. Then they examined the results from these two neural network models. Sodikov (2005) developed more accurate estimation technique for highway projects in developing countries at the conceptual phase using artificial neural networks and showed ANN to be an appropriate tool to help solve problems which come from a number of uncertainties such as cost estimation at the conceptual phase.

Alireza et al. (2007) introduced and employed ANN to plan the breakdown works in structural projects of limited domain. Primary bases of the “Andishevaran Methodology of Project Management” (AMPM), including “Project Control Work Breakdown Structure” (PCWBS), “Functional Work Breakdown Structure” (FWBS) and “Relational Work Breakdown Structure” (RWBS), were used to develop the ANN model. The developed model was validated using out of domain samples, the results illustrated that the breakdown structures & its activities meet the requirements regardless of the level of validity. Hence, outputs of the model can be considered as the preliminary plan of project structures that may be enhanced by some updating. Tarek et al. developed neural network application for optimum mark-up estimation and discussed potential applications in construction engineering and management. Kima et al. applied a hyper technique of “Back Propagation Network” (BPN) and “Genetic Algorithms” (GAs) to estimate project cost. GA was to figure out the BPN variables and to enhance the precision of project cost estimation. A collected database for the cost of 530 residential buildings projects in Korea, constructed in the period (1997–2000) was help in training and testing the accuracy of the developed model. They reported that the developed hyper model was more precise than the BPN model using conventional trial & error.

Chester et al. (2005) developed an ANN model to estimate the cost of highway projects in terms of cost index. That includes the cost of material, equipment & labor. Results showed that the developed model was can predict the cost of highways in Louisiana accurately. Another set of highways cost were predicted using the developed ANN considering future forecasting, the predictions indicated that Louisiana highway costs will be doubled during (1998–2015). Chua et al. (1997) developed an ANN determine the parameters that have major impact on projects budget. A database was collected contains project performance parameters and the corresponding budget. As (AI) model, the developed ANN was able to correlate inputs& outputs even if there is no clear relation defined. Eight project parameters were considered as inputs namely: number levels from “Project Manager” PM to craftsmen, PM experience, and budget of control system, is the design completed before construction, program constructability, and control meetings frequency, turnover rate of project team and budget updates frequency. The developed model showed good predictions even if there unseen or incompletedata on the main parameters. The model is able to examine different managementconcepts and hence save resources and enhance the project management.

The potential surface settlement is one of the most dangerous factors in infrastructuretunnel excavations, so accurate prediction of surface maximum settlement (MSS) is thekey to reduce the risk of surface failure. Hasanipanah et al. (2016) proposed an artificial neural network (ANN) hybrid model based on particle swarm optimization (PSO) to predict MSS caused by tunnelling along subways. It was concluded that in order to minimize the total cost, bridges should be designed with safety and durability. Garcia-Segura et al. (2017) presented an integrated multi-objective harmony search with artificial neural networks (ANNs) to reduce the computational time of finite element model used in deck analysis. The optimal design of the post-tensioned concrete box girder road bridge was carried out for the purpose of the cost, the overall safety factor and the initial corrosion time. Fiber Reinforced Polymers (FRPs) are widely adopted in passive confinement to Reinforced Concrete (RC) for improving compressive strength and ductility.

Casardi et al. presented a model based on artificial neural network (ANN) for the prediction of FRP-constrained concrete compressive strength. Compared with the general models, the proposed one establishes an analytical relationship without considering traditional effectiveness parameter. Compared with reinforced concrete products, glass fiber-reinforced polymer (GFRP) bar reinforced concrete structures have higher durability. The evaluation of the bonding properties of GFRP bars to concrete is of great significance to the design and implementation of the polymer-matrix composites (PMCs). Yan et al. (2017) proposed a hybrid model to predict the bond strength of GFRP bars to concrete by using the strong nonlinear mapping ability of artificial neural network (ANN) with the global searching ability of genetic algorithm (GA). Improper structural design may lead to sudden collapse of multistory reinforced concrete buildings, which needs proper analysis of all factors that affects the structure. Because the traditional neural network model has poor convergence under the training of local search optimization algorithm, which cannot achieve the expected learning effect, Chatterjee et al. (2017) proposed a model based on neural network-particle swarm optimization (NN-PSO) to predict the structural failure of a multistoried reinforced concrete building.

The promotion of recycled aggregate concrete (RAC) can effectively reduce constructionwaste, and different techniques have been used to predict and evaluate the properties ofRAC in recent years. Naderpour et al. (2018) applied ANN model trained by 139 sets of existing data to predict the compressive strength of RAC. The proposed ANN model has 6 input features, such as water-cement ratio, water absorption rate, fine aggregate, natural coarse aggregate, recycled coarse aggregate, and water-total material ratio. The ANNs perform well on some tasks while poorly on others. Specifically, they are suitable for tasks involving incomplete data sets, fuzzy or incomplete information, and for highly complex and ill-defined problems where human decisions are often made intuitively (Kalogirou, 2001). After decades of development, neural networks have been widely used in various fields of civil engineering, including structural optimization, structural condition assessment and health monitoring, structural control, structural material characterization and modelling, construction engineering, highway engineering, etc. (Adeli, 2001). In recent years, deep learning has become a hot area of research in neural networks and made great breakthroughs in speech recognition, image recognition, natural language processing and other fields.

Lastly, a huge collection of test results on “FRP-confined concrete” was collected by Naderpour et al. (2010). The developed ANN predicts the compressive strength of “FRP-confined concrete” using six inputs, which are, specimen dimensions, FRP thickness, FRP hoop tensile strength, FRP Young’s modulus, unconfined concrete compressive strength. The results of the trained ANN were compared to 3 existing strength models (linear, nonlinear & 2nd order). Both ANN and existing models showed an average error of 9% and 13% respectively. That indicates that the developed ANN model is successful predicted the “FRP-confined concrete” compressive strength.

The current results showed that ANN better than or at least the same level of accuracy of the considered traditional methods. The high complexity of most geotechnical issues and the lack of physical understanding are limiting the applicability and the accuracy of the theoretical, mathematical and numerical models. In such cases, (AI) techniques, which depend only on data, are the best choice. ANN models could be trained using database of test results to minimize the prediction error without physical understanding, simplifications or assumptions. On the other hand, ANN has some disadvantages such as that the developed models do not have a physical bases and they are valid only within the input values ranges that used in training process. However, previous reviews indicated that ANN was successfully used in many engineering fields such as construction optimization, civil engineering, decision systems, geotechnical problems and risk analysis.

2.2. Fuzzy Logic (FL)

2.2.1. Background

Any process or methodology undertaken in making the best or most effective use of a situation or source could be termed as optimization. It could be described as a search for another way with the utmost attainable performance under a set of specified constraints by maximizing preferred variables and minimizing unwanted variables in order to attain the needed maximum outcome without regard to cost or expense (Rani and Kumar, 2015). Nature inspired/artificial intelligence techniques (biomimetics) extensively do not describe the physical procedures for the problems being investigated. Mathematical computations have been used over the years for engineering optimization processes. For any algorithm optimization to work effectively three conditions must be met; there has to be: (1) an objective function. (2) Constraints and (3) A set of data to test the algorithm. However, due to saturation in the use of these methods, and because of the complexity associated with civil engineering problems, researchers explored the use of nature inspired/artificial intelligence optimization algorithms in applications such as earthquake engineering (Akhani et al., 2019), structural engineering (Bekdaş et al., 2019), geotechnical engineering (Z.Y. Yin et al., 2018; Gandomi et al. 2017; Gandomi & Kashani, 2018; Kashani et al., 2019), transportation engineering (Khorshidian et al., 2019), pavement management (Olowosulu et al., 2020), construction management (Panwar & Jha, 2019; Sahib & Hussein, 2019), and water resources engineering (Afshar et al., 2015; Azizi et al., 2017).For almost four (4) decades, artificial intelligence studies have increased almost at an exponential rate. Some of the nature inspired/artificial intelligence optimization algorithms that have been reported in the literature are Artificial Neural Network (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), Genetic Algorithm (GA), Genetic Programming (GP), Expert System (ES), Fuzzy Logic (FL), Support Vector Machine (SVM), Evolutionary Polynomial Regression (EPR), Particle Swarm Optimization (PSO), Bacterial Foraging Optimization (BFO) and Smell Agent Optimization (SAO). However, the FL algorithm is the second most used technique (Ebid, 2020). Haghshenas et al. (2017a, 2017b) reported that FL is a powerful modeling tool for multiple issues especially under conditions of uncertainty, associated with geotechnical engineering

2.2.2. Fuzzy Logic Applications

Generally, geotechnical engineering problems are filled with undefined, ambiguous and incomplete information. In most cases, such problems are successfully solved through knowledge and experience of relevant specialists. Artificial intelligence has been used to imitate the decision-making procedures similar to that of human brain to aid the geotechnical specialist’s choice of solution to practical problems involving the construction of retaining walls and estimation for duration of slurry walls (M-Y. Cheng et al., 2008; Chandwani, et al. 2013). The Fuzzy Logic (FL) which is based on a natural language that is theoretically stress-free to understand could be flexible and lenient on imprecise data. It can also model non-linear functions of random complexity in geotechnical problems (T. Mohamed et al., 2012).

The FL technique involves knowledge-based models which use human intuitive reasoning considered as being biased and imprecise (Olowosulu et al., 2020). Artificial intelligence has been used in geotechnical engineering applications that include: the correlation of soil properties, soil classification and profiling, detailed rock properties (e.g., shear, tensile and compressive strength, elastic modulus and density as well as electrical conductivity), slope stability, soil compaction, soil-water interaction, soil behaviour and modelling under loads, prediction of the deformations beside braced deep excavation, estimating the stability of retaining structures, selection of optimum shoring technique, prediction of settlement due to tunnelling, soil liquefaction, appraising the ultimate bearing capacity for shallow and deep foundation, etc. (Ebid, 2020)

Moisture content: A little increase in soil water content can result in substantial reduction in stiffness or resilience modulus of the soil. Van Schelt et al. (1994) reported that earlier in situ water content measuring devices that provide exact results, extended equipment lifespan, and constant monitoring were not available. Mohamed and Hawas (2004) developed a neuro-fuzzy logic model to estimate water content in sandy soil and reported that most points of the predicted water content and the actual were within 95 % confidence level. The authors also stated that the same procedure could be used for soils with different properties. Additionally, the model developed could be applied for the monitoring of fluctuations in water content under foundations, in slopes, subgrade materials and contaminant transportation in leachates beneath waste containment systems.

Waste containment application: The management of municipal solid waste (MSW) is been one of the key difficulties experienced by city planners globally, which has attracted the attention of researchers in the last three decades. Landfill has been reported to be the most popular, economical and environmentally appropriate way for MSW disposal because of its ease of operation in both industrialized and developing areas of the world (Eberemu et al., 2013; Li et al., 2017; Oluremi et al., 2019; K. Yin et al., 2016). Site characteristics are key factors considered in the location of waste containment systems. It is a complex as well as time-consuming procedure that entails the evaluation of several factors. The conventional method of obtaining a reliable result to meet regulatory/environmental requirements for decision making is through site investigation, screening/characterization. Aydi et al. (2013) as well as Chamchali and Ghazifard (2020) suggested important points to be considered in the minimization of environmental risk through multi-criteria selection of landfill site by means of FL models. The selection procedure is centred on the application of fuzzy set principle, analytic hierarchy process and the weighted linear combination. The final MSW site will further require detailed geotechnical and hydrogeological analysis targeted at protecting the ground as well surface water from contamination. The uncertainty of MSW characteristics and complex nature of landfill processes have led to the use of knowledge-based techniques such as FL for modelling such complex systems. FL can be used to solve challenging operational problems in modern landfills at a specific time based on measurable properties of leachate produced and the biogas production (A. Mohamed et al., 2011)

Geotechnical site characterization: In geotechnical engineering operations, site characterization is one of the first and important steps used in tackling the problem. A model of the subsoil condition is a pre-requisite for an effective analysis. Huang and Siller (1997) used fuzzy sets to signify data gathered from site to deduce the subsoil profile. The resultant fuzzy system created a novel way of developing subsurface profiles and better site characterization. Diamalddine et al. (2011) use FL to adequately characterize a site and made estimate for a common project. The authors concluded that FL could be used by geotechnical engineers as a support tool in systematic choice making for site characterization problems.

Tunnelling: The use of soft computing methods in tunnelling is mainly with respect to approximation of outward settlement (Ahangari et al., 2015; Bouayad & Emeriault, 2017). Studies related to tunnelling reported in the literature present numerous capabilities and responses when soft computing methods are used for the optimum use of tunnel boring machine (TBM). Ahangari et al. (2015) as well as Bouayad and Emeriault (2017) reported the used of FL to estimate the approximate settlement resulting from tunnelling. Kohestani et al. (2017) demonstrated the use of machine learning (ML) for the approximation of the highest surface settlement initiated by earth pressure. Isam and Wengang (2019) reviewed studies on the use of soft computing methods in TBM with emphasis on the programmes learned and made recommendations for their best. Although advances have been made with regard to TBM and checking techniques, substantial advancement has also been recorded in the use of soft computing methods for optimization targeted at the decrease in disturbance related to tunnelling, engineers are still faced with hitches in making the best decision when soft computing practice is used to resolve the composite problems relating to boring operation with TBM (Isam & Wengang, 2019).

Embankment/slope stability analysis: The major problem encountered in geotechnical engineering is the analysis of slope/embankment stability, therefore the result of faulty stability analysis of slope will be a huge disaster. The stability of a slope is dependent on the factor of safety (FOS). This is usually explained as the proportion of ultimate shear strength to the mobilized shear stress at initial failure, the FOS in the stability of slope is today a major subject of discussion in geotechnical engineering due to indecisions connected with it. Marandi et al. (2016) reported that the uncertainties are linked to the shear strength parameters of the soil, the complex method of numerical analysis, etc. The authors observed that the highest uncertainty in the FOS was associated with the presence of groundwater, while absence of groundwater gave the least ambiguity. These assemblies are often used in several construction schemes such as embankments, highways, tunnelling, mines, etc.

The FL system was used by T. Mohamed et al. (2012) to predict the stability of a slope. Parameters peculiar to the slope such as unit weight of the soil, angle, height, soil cohesion and angle of internal friction were used as input factors; while the FOS was the output factor. The study showed that the prediction made using FL was quite exact and nearby to the targeted data. Wang (2010) also used FL to evaluate the stability of a slope. The author highlighted the basic principles of the Fuzzy set theory and the progress made in its application to slope stability problems.

Soil stabilization/pavement works: Before this discovery and use of geosynthetic materials, conventional soil stabilization had been used to increase the strength properties of weak soils for over a century (Azura & Adnan, 2019). Geogrid is a geosynthetic material frequently used in the past four decades for the improvement of subgrade layer of unpaved roads to meet the required specification and at the same time speeding the road construction process on weak subgrade soils (Singh et al., 2020). Two FL algorithms were developed by Singh et al. (2020) for the prediction of reinforced geogrid subgrade behaviour using maximum dry density (MDD), optimum moisture content (OMC), liquid limit (LL), plastic limit (PL), plasticity index (PI),, soaked/un-soaked condition, reinforced/unreinforced segment, depth of reinforcement and California bearing ratio (CBR) as input factors. The results obtained revealed significant increase in the CBR values for the geogrid-reinforced subgrade soil mainly attributed to the addition of geogrid. The optimal range of improvement in goegrid reinforcement was obtained for 36 to 60 % of the soil layer thickness thus underscoring the effectiveness of the algorithm.

2.3. Adaptive Neuro Fuzzy Inference System (ANFIS) and its Application in Civil Engineering

2.3.1. Background

Adaptive Neuro-Fuzzy Inference System (ANFIS) technique was developed in the early 1990s and it is a form of artificial neural network (ANN) based on the Takagi—Sugeno fuzzy inference system (Takagi & Sugeno, 1985). ANFIS is a member of hybrid system called neuro fuzzy networks (Jang, 1993). It fits to a group of adaptive networks that integrate mutually the linguistical principles of fuzzy logic (FL) and ANN to produce an outcome of relatively higher accuracy and performance for a given established input variables (Armaghani & Asteris, 2020; Cabalar et al., 2012; Fani & Basil, 2020; Neha et al., 2016). ANNs generally are controlled learning (CL) algorithms which make use of a past dataset to predicting future values (Pramanik & Panda, 2009; Sadrmomtazi et al., 2013). On the other hand, FL achieves the generation of control signals from firing the rule base obtained from past/historical random data (Neha et al., 2016). Having a rule base being random data suggests that the controller’s output is equally random, which thus affect optimum results. The application of ANFIS overcomes the challenges associated with optimal results mentioned earlier by choosing a rule base that is more favourable and adaptive to give optimum results (Neha et al., 2016).Using the ANFIS approach, the rule base is carefully chosen using the neural network methods by means of the back propagation algorithm (Fani & Basil, 2020; Muzzammil, 2010). To increase ANFIS performance, the features of FL (i.e., using IF-THEN rules to estimate a non-linear function incorporated in the modelling procedure) is used. This incorporated procedure makes ANFIS a widespread acceptable estimator (Kusagur et al., 2010; Neha et al., 2016). As stated earlier, ANFIS combines the properties of FL and ANN, which is exemplified. In the study carried out by Neha et al. (2016) in which the authors proposed a fundamental structure of ANFIS mostly consisting of fuzzification, inference engine, rule base and defuzzification blocks as presented in Figure 3.

Figure 3. Block diagram of ANFIS controller.

The crisp input signal for the ANFIS controller using the membership function was transformed to fuzzy inputs (Neha et al., 2016). The Gaussian membership function application was used for the ANFIS model. Gaussian membership function alongside the fuzzy inputs was imputed into the neural network interface. The verbal output generated from the ANN interface is at that point transformed to crisp output using the defuzzifier unit (Sugeno & Kang, 1988). The structural system of ANFIS encompasses diverse adaptive layers. Every single layer has nodes of linked network of transfer functions via which the fuzzy inputs are managed (Ahmad et al., 2018; Behfarnia & Khademi, 2017; Khademi et al., 2017; Neha et al., 2016). The adaptive network structural arrangement consists of five network layers 1 to layer 5 (by way of nodes as well as connections) as presented in Figure 4. For a system defined by inputs x₁ and x₂, one output z and fuzzy set A₁,A₂,B₁,B₂; therefore, for a first order Takagi–Sugeno (1985) fuzzy model, with two IF-THEN rules in the common rule set, can be expressed mathematically with equations (1)(1) $f_1=p_1{x}_1+q_1{x}_2+r_1\mathit{\hspace{0.17em}}$(1) and (2(2) $f_2=p_2{x}_1+q_2{x}_2+r_2\mathit{\hspace{0.17em}}$(2) ) (Celikyilmaz & Türksen, 2009):

Rule 1: if $x_1\mathit{\hspace{0.17em}}\mathit{is}\mathit{\hspace{0.17em}}{A}_1\mathit{\hspace{0.17em}}\mathit{and}\mathit{\hspace{0.17em}}{x}_2\mathit{\hspace{0.17em}}\mathit{is}\mathit{\hspace{0.17em}}{B}_1$ Then

(1) $f_1=p_1{x}_1+q_1{x}_2+r_1\mathit{\hspace{0.17em}}$(1)

Rule 2: if $x_1\mathit{\hspace{0.17em}}\mathit{is}\mathit{\hspace{0.17em}}{A}_2\mathit{\hspace{0.17em}}\mathit{and}\mathit{\hspace{0.17em}}{x}_2\mathit{\hspace{0.17em}}\mathit{is}\mathit{\hspace{0.17em}}{B}_2$ Then

(2) $f_2=p_2{x}_1+q_2{x}_2+r_2\mathit{\hspace{0.17em}}$(2)

Figure 4. Takagi–Sugeno type ANFIS Architecture for a first order two rule

(Source: Neha et al., 2016).

Layer 1: The layer 1 is referred to as fuzzification layer. In this layer, crisp input signal is served to the node i, which is linked to the linguistic label Ai or Bi −2.

Therefore, the membership function (MF) O₁, _i(X) controls the membership level of a certain input. The output of every single node was computed by means of equations (3)(3) ${\mathrm{O}}_{1,\mathit{i}}={\mu }_{A_i}\left(x_1\right),\mathit{for}\mathit{i}=1,\mathit{\hspace{0.17em}}2\mathit{\hspace{0.17em}}$(3) and (4(4) ${\mathrm{O}}_{1,\mathit{i}}={\mu }_{{\mathit{B}}_{\mathit{i}-2}}\left(x_2\right),\mathit{for}\mathit{i}=3,4$(4) ) correspondently. Neha et al. (2016) used.O₁, i(X) as the universal Gaussian formed MF.

(3) ${\mathrm{O}}_{1,\mathit{i}}={\mu }_{A_i}\left(x_1\right),\mathit{for}\mathit{i}=1,\mathit{\hspace{0.17em}}2\mathit{\hspace{0.17em}}$(3)

(4) ${\mathrm{O}}_{1,\mathit{i}}={\mu }_{{\mathit{B}}_{\mathit{i}-2}}\left(x_2\right),\mathit{for}\mathit{i}=3,4$(4)

Layer 2: In layer 2, nodes are immovable and considered as O₂, i. The output of every single node is the product of the entirely incoming signals as presented in equation (5)(5) ${\mathrm{O}}_{2,\mathit{i}}=w_1={\mu }_{A_i}\left(x_1\right){\mu }_{B_i}\left(x_2\right),\mathit{for}\mathit{i}=1,\mathit{\hspace{0.17em}}2$(5) .

(5) ${\mathrm{O}}_{2,\mathit{i}}=w_1={\mu }_{A_i}\left(x_1\right){\mu }_{B_i}\left(x_2\right),\mathit{for}\mathit{i}=1,\mathit{\hspace{0.17em}}2$(5)

Every node output denotes the firing power of a rule. Moreover, it is also called membership layer which acts on the input parameters from layer 1 as MF to symbolize them respectively in fuzzy sets.

Layer 3: In layer 3 every node computes the ratio of a single rule firing power to the entire summation of all rules firing powers as presented in equation (6)(6) ${\mathrm{O}}_{3,\mathit{i}}=\overline{w_i}=\frac{w_i}{w_1+w_2}\mathit{for}\mathit{i}=1,2$(6) . $\overline{w_i}$ is for the normalized firing power. Therefore, layer 3 is named rule layer.

(6) ${\mathrm{O}}_{3,\mathit{i}}=\overline{w_i}=\frac{w_i}{w_1+w_2}\mathit{for}\mathit{i}=1,2$(6)

Layer 4: Layer 4 is referred to as defuzzification layer. This layer computes individual output values y beginning from the inferring of rules to the rule base. Discrete nodes of this layer are joined to the corresponding normalization node in layer 3 and likewise obtain the input signal. Every node of layer 4 is adaptive in their nature with the node function expressed as equation (7)(7) ${\mathrm{O}}_{4,\mathit{i}}=\overline{w_i}{f}_i=\overline{w_i}(p_i{x}_1+q_i{x}_2+r_i\mathit{\hspace{0.17em}}$(7) in which p_i,q_i,r_iis a set of subsequent rule i parameters.

(7) ${\mathrm{O}}_{4,\mathit{i}}=\overline{w_i}{f}_i=\overline{w_i}(p_i{x}_1+q_i{x}_2+r_i\mathit{\hspace{0.17em}}$(7)

Layer 5: Layer 5 is referred to as output layer. Layer 5 has only one node and it computes the summation of the entire outputs upcoming from defuzzification layer nodes to generate the complete ANFIS output as presented in equation (8)(8) $\mathit{Overall}\mathit{output}={\mathrm{O}}_{5,\mathit{i}}=\mathit{\hspace{0.17em}}\sum _i\overline{w_i}{f}_i=\frac{\sum _i{w}_i{f}_i}{\sum _i{w}_i}$(8) :

(8) $\mathit{Overall}\mathit{output}={\mathrm{O}}_{5,\mathit{i}}=\mathit{\hspace{0.17em}}\sum _i\overline{w_i}{f}_i=\frac{\sum _i{w}_i{f}_i}{\sum _i{w}_i}$(8)

This entire design of the adaptive network was utilised to generate the ANFIS model used by Neha et al. (2016).

2.3.2. Applications of ANFIS in geotechnical engineering

Rock mechanics: ANFIS has been successfully applied in civil engineering and other fields of engineering. For example, Gokceoglu et al. (2004) used the ANFIS model for appraisal of the deformation modulus in rock mass and obtained satisfactory results. Also, Kayadelen et al. (2009a) used ANFIS on the shear strength parameter of soil to establish the relationship between φ and the soil properties (i.e., soil plasticity properties, grading and the soil density). Results of the study obtained using ANFIS were compared with laboratory values, which showed some acceptable level of agreement. Neuro-Fuzzy system was used by Rangel et al. (2005) for tunnel stability analysis during field construction to confirm the effectiveness of the model on two specific tunnels. The result of the analysis showed that the use of Neuro-Fuzzy (NF) system gave better approximation when compared with other generally used techniques.

Deep foundation: ANFIS was used by Zounemat-Kermani et al. (2009) to predict the current-induced scour depth around pile groups in a bridge foundation. The ANFIS model gave a better estimate when compared with the results obtained using other conventional methods.

The use of ANFIS model was recommended by Kalkan et al. (2008) for the estimation of unconfined compressive strength (UCS) of compacted granular soils. Results of the study showed that ANFIS gave better predicted UCS of granular soils when compared with the results obtained using other conventional techniques. Also, ANFIS was used by Kayadelen et al. (2009b) to study the swelling potential of soils and established that the estimates are in agreement with the corresponding test results.

Soil permeability: Permeability estimations are used in decision making during geotechnical engineering construction works. The ANFIS model was used by Sezer et al. (2010) to predict permeability of sand. A comparison of the ANFIS results with non-linear multiple regression analyses results showed that ANFIS structure is reasonably effective in estimating permeability using grading properties and particle shape information.

Slope stability: The ANFIS modelling approach was used by Pradhan et al. (2010) to produce regional landslide susceptibility maps. The output is beneficial and useful in regional landslide susceptibility studies.

Intrinsic soil properties: The use of ANFIS in geotechnical engineering was reported by Cabalar et al. (2012). The authors considered the forecast of damping ratio and shears modulus of different sand–mica mixes with respect to stress, mica content as well as strain using Neuro-Fuzzy (NF) approach. Nine undrained consolidated torsional resonant column tests carried out on different mica and Leighton Buzzard sand mixtures were used for the ANFIS modelling. All round pressures between 350 and 450 kPa and pore pressure of 300 kPa were used. The forecasts produced by NF models individually for damping ratio (R² = 0.99) and shear modulus (R² = 0.99) were relatively accurate when compared with test results.

2.4. Gene Expression Programming (GEP)

2.4.1. Background

GEP is a type of evolutionary algorithms inspired by biological systems; the system is a full-fledged genotype/phenotype system with expression trees of various sizes and shapes encoded in linear chromosomes of fixed length. Though almost like GAs and GPs, GEP chromosomes are multi-genic, encoding multiple expression trees or sub-programs which will be organized into a far more complex program with operational flowchart presented in Figure 5. So, just like the DNA/protein system of life on earth, the genes/trees system of GEP can not only explore all the paths of the solution space but it is also absolving to explore higher levels of organization.

GEP has two main players; the chromosomes and also the expression tree (ET), these can further be classified as genotype and phenotype respectively. The genotypes are chromosomes which are simple entities; linear, compact, relatively small, easy to manipulate genetically while the phenotypes are exclusively the expression of their respective chromosomes. They are the entities upon which selections acts and according to fitness they are selected to reproduce with modification. The interplay of chromosomes (genotype) and expression trees (phenotype) in GEP implies an unequivocal translation system for translating the language of chromosomes into the language of expression trees (ETs) (Ferreira, 2001)

Figure 5. Flowchart of GEP model.

The application of GEP permits that the chromosome can have more than one gene. These genes contain two types of information, the first type is stored in the head of the gene containing the data which is employed in producing the overall GEP model and the second is stored in the tail of the gene and used to generate future GEP models (see Equation 9)(9) $\mathit{t}=\mathit{h}\mathit{\hspace{0.17em}}\left(\mathit{n}-1\right)+1$(9) .For every problem, the length of the head h is chosen, whereas the length of the tail t is a function of h and the number of arguments n of the function with more arguments (also called maximum arity) and is evaluated by the equation:

(9) $\mathit{t}=\mathit{h}\mathit{\hspace{0.17em}}\left(\mathit{n}-1\right)+1$(9)

The process as shown in Figure 5 starts with randomly generating chromosomes of a certain number of individuals (initial population). Then these chromosomes are expressed, and therefore the fitness of every individual is evaluated against a collection of fitness cases. Then, the individuals are selected in line with their fitness to reproduce with modification. These new individuals are subjected to identical developmental processes such as expression of the genomes, confrontation of the selection environment, selection, and reproduction with modification. The process is repeated for a certain number of generations or until a good solution is found (Ferreira, 2001, 2006). The terminal set consists of the independent variables that are considered as input variables of the model. So, the first step to use the GEP method is to define the terminal set. An evolutionary process is applied in the GEP method for finding the optimum program and individual chromosomes are modified and optimized in each iteration based on the fitness function and genetic operators like the genetic algorithm. This process is repeated until the convergence criteria are achieved.

The technique known as Gene Expression Programming (GEP) makes use of population in this case population of models and solutions, selects and reproduces them according to fitness, and introduces genetic variation using one or more genetic operators such as mutation or recombination (Mitchell, 1998). Though the GEP can be likened to the GA and GP as the two still operates on the principle of population, the fundamental distinction among the three algorithms is dependent on the nature of the individuals or models or solutions as the case may be; in GA the individuals are symbolic strings of fixed chromosomes, in GP the individuals are non-linear entities of different sizes and shapes while in GEP the individuals are encoded in symbolic strings of fixed chromosomes which are expressed as GPs, this means that GEP is a combination of GA and GP.

2.4.2. Geotechnics

Evaluation of soil liquefaction using the GEP model approach was studied by Goharzay et al. (2017). GEP was applied to develop different deterministic models to evaluate the occurrence of soil liquefaction in terms of liquefaction field performance indicator (LI) and factor of safety (Fs) in logistic regression and classification concepts. The results of their study encourage the use of GEP as a green decision-making tool in engineering design to quantitatively assess the liquefaction triggering thresholds. Armaghani et al. developed a GEP model for the prediction of uniaxial compressive strength; this research studied the feasibility of GEP in the indirect determination of UCS values of sandstone rock samples. Several models were developed based on multiple inputs and the best model selected, it was further recorded that the GEP model is superior to linear multiple regression (LMR) in terms of applied performance indices. Mohammadzadeh et al. (2019) utilized a GEP model to predict the compression index of fine-grained soils; GEP was employed to develop a model for estimating Cc using LL, PL, and e0. The study analyzed 108 data points containing Cc, LL, PL, and e0 and used same to train and validate the model, contrary to other models used in the estimation of Cc, the GEP model revealed highly nonlinear behavior and included a complex combination of influential input parameters furthermore revealing its good performance. Johari A et al. trained a GEP approach to the prediction of the maximum lateral displacement of retaining wall in granular soil. The input parameters of the model consist of the effective period of adjacent structure, horizontal and rocking stiffness of the foundation of adjacent structure, density, Young’s modulus, and friction angle of granular soil as well as the thickness and height of retaining wall, the results from the model predictions were compared to the actual data and it showed a good performance for prediction of lateral displacements of structures in granular soils. Johari and Hooshmand predicated soil-water characteristics using GEP, the model was developed in two phases for control and validation. The model prediction indicated a reasonable accuracy, both for the results employed in the first phase, and results in the validation phase. The model prediction had some discrepancies compared to the actual test data; however, a comparison of the results from the proposed model with traditional methods indicated its superior performance for the prediction of soil water characteristics. Uysal (2020) compared the GEP model to actual experimental values and regression model in the prediction of collapse potential of soils, GEP was observed that GEP-based models are detected to be simpler methods to estimate the collapse potential. Armaghani (2016) studied the settlement of the rock socketed piles through a technique based on gene expression programming; the results demonstrated the feasibility of the GEP-based predictive model on the settlement. Coefficients of determination (CoD) values of 0.872 and 0.861 for training and testing datasets of the GEP equation respectively show the prevalence of this model in predicting pile settlement. This soft computing approach has proven to be very useful within the field of geotechnics because it generally fits in and thrives where other models have failed or have restricted abilities hence, this study aims to effectively explore GEP around all corners of geotechnics engineering, how the language of genotypes is translated to that of the phenotypes with reference to geotechnics engineering and therefore the evaluation of sensitivity analysis and parametric study using the developed model.

2.4.3. Tunnel Coverage

In recent years in the cities, underground spaces are becoming increasingly important. In regard of this, the need is increasing for underground spaces utilization and, consequently, the excavation of these spaces has increased significantly. There are serious risks and many uncertainties that are associated with the excavation of underground spaces. As the tendency for reduction of the excavated area due to change in the initial stresses, convergence of tunnel is constantly monitored, in order to observe the construction safety and to estimate the design, construction and behavior of the tunnel when in use. Research has also been conducted aiming to previously efforts have been made towards predicting convergence of tunnel by means of computational intelligence techniques (Mahdevari et al., 2013, 2012). Hajihassani et al. (2019) proposed a model equation derived by the GEP approach, with the purposes to forecast convergence of tunnels excavated that meets the requirement of the New Austrian Tunneling Method (NATM). To achieve this primary aim, a database was obtained from laboratory experiments, consisting of 6 predictors and one target (dependent variable). The predictors (independent variables) were depth of tunnel, cohesion, angle of internal friction, soil unit weight, Poisson’s ratio, and modulus of elasticity, while the total convergence predicted parameter. GEP model configurations were evaluated by means of trial-error procedure and finally an optimized model was generated and proposed. Furthermore, a mathematical model was derived from the forecasted GEP model. There was a very good agreement between the GEP-proposed model results and the values measured in the laboratory. This demonstrated the GEP modeling strength to evaluate the tunnel convergence in a more reliable manner and with flexibility.

2.4.4. Ground Movement/Vibrations Resulting from Blasting

In the estimation of blasting operations impact on nearby structures and infrastructures, peak particle velocity is a very critical parameter that calls for attention. Blasting design requires that an exact evaluation of the magnitude of PPV from blasting operation and correlation with the allowable values forms an integral part. By employing GEP and Monte Carlo model techniques, Mahdiyar et al. (2020) studied four quarry sites in Malaysia and modeled PPV. 149 data points from blasting operations were collected and utilized in the GEP model exercise. 10, 000 iterations were performed to ensure that predictor variables combinations were accurately considered. The forecast results produced PPV in the range of between 1.13 mm/s and 34.58 mm/s for the minimum and maximum magnitude respectively. The PPV proposed model was exposed to sensitivity analysis and proposed a method valid for the four case studies and the present technique which can be applied to the same application with different field variables. Ground vibration is one of the critical situations faced with blasting operations through which rock fragmentation is achieved. This is a dangerous environmental effect from opencast mines and tunneling engineering. In order to identify safety grounds, accurate and effective forecasting of ground movements or vibrations induced by blasting is essential for design and performance monitoring. A model to take care of blast induced movements was predicted through the intelligent learning of GEP by Faradonbeh et al. (2016) and this was carried out in a granite quarry in Malaysia. A total of 102 blast exercises were studied and blasting parameters relevant to this study were measured in the field operation. The measured predictors in this model were burden to spacing ratio, depth of hole, stemming, powder factor, maximum charge per delay and distance from blast face. As a base regression model, the nonlinear multiple regression (NLMR) was conducted on the datasets to correlate the parameters relationship with each order in the model operation. The GEP training and testing outcomes for the coefficient of determination showed values of 0.914 and 0.874 against 0.829 and 0.790 respectively for NLMR. GEP showed its superiority in modeling the ground movement or vibration induced by blasting.

2.5. Analysis of Variance (ANOVA)

2.5.1. Description of ANOVA

Analysis of variance (ANOVA) is tool used for statistical analysis which separates an observed aggregate variability found inside a data set into random and systematic factors. The random factors do not influence a given data set statistically, while the systematic factors do. Thus, analysts in diverse field of study make use of the ANOVA test for the determination of the effect that independent variables have on the dependent variable in a statistical regression study. The variables that are measured are called the dependent variables whereas; the variables that are controlled/manipulated are called independent variables or factors. ANOVA is an extension of the t—and z-tests and it is also called the Fisher analysis of variance. It is used to investigate if significance difference exists between the mean of two or more groups. The assumptions used in ANOVA are that the fundamental distributions are normally distributed and that the variances of the distributions being compared are analogous (Smith, 2018). The formula for ANOVA is given as:

(10) $\mathit{F}=\frac{\mathrm{MSE}}{\mathit{MST}}$(10)

Where:

F = ANOVA coefficient

MST = Mean sum of squares between the groups due to treatment

MSE = Mean sum of squares within the groups due to error

ANOVA is usually used to generate the F-value and p-value from the data set of an experimental sample. The F-value and p-value are used to test the significance of the selected regression models at a 95% significance level. When there is no real difference existing between the tested groups, which is called the null hypothesis, the result of the ANOVA’s F-ratio statistic will be close to 1. In ANOVA analysis, p-value is an important parameter to consider because it indicates the probability that the results of the analysis could have occurred by chance. When the p-value is greater than 0.05, the null hypothesis would be accepted whereas, if the p-value is less than 0.05, the null hypothesis would be rejected and the alternative hypothesis would be accepted as indicated in Table 1.

Table 1. Interpretation of p-value in ANOVA analysis

p-value	Null Hypothesis	Result Interpretation
≥ 0.05	Do not reject the null hypothesis	Result is not statistically significant
< 0.05 but ≥ 0.01	Reject the null hypothesis	Result is significant
≤ 0.01	Reject the null hypothesis	Result is highly significant

ANOVA analysis can be conducted using statistical software like Microsoft Excel and Minitab. The sums of squares in the result of ANOVA analysis is separated into different components which describe the variation due to different sources when Minitab software is used.

2.5.2. Classifications of ANOVA and Need for its Use

The ANOVA is classified into two types: one-way and two-way ANOVA. The number of independent variables in the analysis of variance test determines whether the ANOVA is one-way or two-way. A one-way ANOVA is used to evaluate the impact of a single factor on an individual response variable. Hence, it determines whether all the samples are the same. The one-way ANOVA is employed in determining whether there are any statistically significant differences existing between the means of three or more independent (unrelated) groups. However, a two-way A NOVA is an extension of the one-way ANOVA. The major difference between one-way ANOVA and two-way ANOVA is that in a one-way ANOVA, there is only one independent variable affecting a dependent variable whereas, in a two-way ANOVA, there are two independents variables. For instance, a Civil Engineer can utilize a two-way ANOVA to compare the effects of two independent variables such as water content and cement content on the strength of concrete or mortar. Thus, a two-way ANOVA indicates the interaction between the two independent factors (water content and cement content) and also tests the effects of the two independent factors on the dependent factor (concrete or mortar). The ANOVA test is the preliminary step applied in the investigation of the factors that affect a given set of data in an experimental setup. ANOVA is comparable to multiple two-sample t-tests and it is useful for testing three or more variables. It gives fewer type I errors and is suitable for a variety of problems. ANOVA makes use of comparison of mean of each group to assemble differences existing between the groups as well as distributing the variance into various sources. It is utilized in diverse subjects, test groups, within groups and between groups. The number of factors considered determines the type of ANOVA test to be employed for the statistical analysis of an experimental data. ANOVA is appropriate for small sample sizes and the sample sizes are uniform for the various factor level combinations in an experimental design.

2.5.3. Application of ANOVA in the Optimization of Civil Engineering Properties

Analysis of variances (ANOVA) is a statistical tool used for the investigation of the differences between all of the variables used in an experimental setup. As part of the design of experimental process, the evaluation of ANOVA is usually with respect to a particular model. These models can be linear, non-linear or mixed models (Obianyo et al., 2020). In Engineering, insufficient data and variability of data always lead to the presence of uncertainty (Ang et al. 2006). Hence, the need for the application of statistical analysis tool such as ANOVA in the analysis of experimental data. There has been diverse application of ANOVA in the optimization of various civil Engineering properties such as compressive strength, impact strength, shear strength, durability, fracture toughness and flexural strength (Obianyo et al., 2020; Uysal et al., 2020). In a construction application, for example, a researcher in the field of Civil Engineering would test two different processes of producing concrete using ANOVA test to see if one process is better than the other in terms of strength and cost efficiency. Various researchers have worked on using ANOVA and other statistical tools for the optimization of Civil Engineering properties. The effects of individual factors on the compressive strength of stabilized lateritic bricks were investigated using two-way ANOVA and regression analysis (Obianyo et al., 2020). ANOVA analysis was used for the optimization of the durability properties of the concretes containing fly ash as partial replacement of cement (Uysal et al., 2020). ANOVA analysis was also used by Jafari et al. (2018) for the optimization of the mixture design of polymer concrete. The ANOVA had been used to optimize the use of stone dust as fine aggregates replacement in improving the compressive strength of concrete (Andrade et al. 2018). In this study, the ANOVA was used to verify the statistical effect of the different replacement levels and mix design proportioning in the corresponding compressive strength obtained from the experimental data. The result of the analysis shows that the compressive strength of concrete with 30% level of replacement gave similar behavior to the reference concrete indicating that the stone dust content and the mix design proportioning has significant effect on the compressive strength of the concrete. The F-test in the ANOVA analysis was used to determine the existence of significant differences between the properties examined. When the p-value of the F-test is less than 0.05, there is significant effect of the factor/variable over the properties investigated at a confidence level of 95% and vice versa. Thus, ANOVA was a useful analytical tool for the evaluation of the effect of the factors in the response of an experiment as shown in Table 2.

Table 2. ANOVA for Compressive strength (Andrade et al. 2018)

Source of Variation	DF	SS	MS	F-test	P value
Stone dust	2	594.25	297.13	879.88	0
Age	2	1799.18	899.59	2663.97	0
Mix proportioning	2	1681.4	840.7	2489.57	0
Stone dust x age	4	7.25	1.81	5.37	0.001
Stone dust x Mix proportioning	4	65.13	16.28	48.22	0
Age x Mix proportioning	4	132.41	36.1	98.03	0
Stone dust x Mix proportioning x age	8	36.85	4.61	13.64	0
Error	54	18.24	0.34

*DF = Degree of Freedom; SS = Sum of Squares; MS = Mean Square.

The p-value for all the factors examined were found to be less than 0.05 and this implies that all the factors have significant effect on the compressive strength of the concrete.

The effect of natural fibres (sponge gourd, coir and jute fibres) on the impact strength of reinforced epoxy resin-based composites had been investigated using ANOVA (Yusuf et al. 2020).

For all the factors examined, the p-value is greater than 0.05 as shown in Table 3. Thus, the null hypothesis is accepted and this implies that all the factors have no significant effect on the impact strength of Fiber Reinforced Composites. ANOVA can also be used to check the adequacy of models in order to identify if there is a strong correlation between the model control results and experimental results. In other words, it can be used to test the significance of selected regression models used for the analysis of experimental results. This was explored by Attah et al. (2020) in the application of ANOVA to verify if there is significant difference between the experimental results and the model results for predicting the compressive strength of rice husk ash blended cement concrete.

Table 3. Results of ANOVA test for Blaine fineness (Kaplan et al., 2018)

Blaine fineness	P value	Significance
Cement chemical	0.987	NS
Dosage of chem. additive	0.548	NS
Fly ash	0.000	S

*NS = Not significant; S = Significant.

The null hypothesis of the analysis of variance is rejected if F > F_crit. Based on the results of the analysis, F_crit> F as shown in Table 4 and thus, the null hypothesis is accepted. This implies that there was no significant difference between the experimental results and the model results. Therefore, the model is satisfactory for use in predicting the compressive strength of rice husk ash blended cement concrete. One-way ANOVA was used to compare the feasibility of three indexes (density index, strength index and combined index) used for the assessment of the damage of masonry buildings in seismic-prone zones (Su et al., 2017). The differences of the influences of the three indexes on the potential damage category of the masonry buildings were investigated using one-way ANOVA. The ANOVA was also used to test for the Blaine fineness for the Optimization of Calcareous Fly Ash-Added Cement Containing Grinding Aids and Strength-Improving Additives (Kaplan et al., 2018). The result of the analysis is presented in Table 3.

ANOVA results shown in Table 5 indicated that the type and dosage of cement chemical used do not have significant effect on the Blaine fineness as their p-values are greater than 0.05. However, it was found that the ratio of fly ash used have a significant effect on Blaine fineness.

In all these scholarly documented applications of ANOVA in the optimization of various Civil Engineering properties, the influence of the investigated factors on the corresponding Civil Engineering properties was verified statistically. Hence, ANOVA is a powerful analytical tool with useful applications in predicting models for Civil Engineering properties.

2.6. Nature Inspired Optimization Algorithms

Bacteria foraging optimization (BFO): BFO is among the group of nature-inspired optimization algorithms. The BFO method has some benefits above other optimization methods such as: (1) it has minimal time for computing of results, (2) it is a derivative-free algorithm, and (3) it does not rest on the preliminary solution to begin its reiteration process (Hasanien & Ali, 2015).

The BFO algorithm system was adopted by Gadzama (2020) as well as Yohanna et al. (2020) in their studies using modelling software called Gene Expression Programming (GEP). The authors used GeneXpro tools 5.0 developed by Ferreira (2001) to optimize the generated hydraulic conductivity data of lateritic soil treated with Sporosarcina pasteurii and Bacillus coagulans, respectively, in municipal solid waste (MSW) containment application. The results obtained depicted the properties of a solid rock by recording 0 m/s after little iteration.

In the cited studies, the law of no free lunch (which states that in computational complexity and optimization there is certainly no recognized individual nature inspired optimization technique proficient of resolving all optimization difficulties) was tested by developing two additional algorithms namely, Particle Swarm Optimization (PSO) Algorithm and the Smell Agent Optimization (SAO) Algorithm. The results obtained from the PSO and SAO algorithms were similar to those obtained for BFO. Thus, based on the generated data, the three optimization algorithms can be ranked as follows: PSO > SAO > BFO.

Tunnelling:The PSO and FL were used by Mikaeil et al. (2019) to evaluate the geotechnical risk of tunnelling. The algorithms are comparatively fast and have suitable convergence and difference when compared with other optimization methods. Also, they are able to resolve most optimization difficulties like pattern recognition, training of neural network, robotic motion control and routing. The cited authors reported three major geotechnical risks associated with tunnelling namely, the instability of areas surrounding the tunnel, inflow of groundwater, and squeezing as being the utmost important hazards based on the views of field experts.

Embankment/slope stability analysis: Several studies on the analysis of slope using nature inspired algorithms mostly PSO have been reported (Li et al., 2005, 2007; Cheng et al., 2007a&b; C. Wang et al., 2007; Tian et al., 2009). The considerations of the authors are compatible with heterogeneous soils in soil slopes which produced more accurate solutions to the problems. On the other hand, Kashani et al. (2020) adopted the method reported by Cheng (2003) to produce a valid slip surface and appraisal of the FOS of every likely failure surface. Also, the minimization of the overall costs of projects and the quantity of materials to be used becomes easier with the application of nature inspired optimization algorithms; this is because it can accommodate several variables at a time.

Retaining structures: Several studies have been reported in the literature (e.g., Kaveh & Soleimani, 2015; Gandomi et al., 2017; Gandomi and Kashan, 2018; Ian et al., 2020; Kalemci et al., 2020; Kaveh et al., 2020).where different nature inspired algorithms to optimize geotechnical engineering problems relating to retaining structures: Concrete retaining wall is an important structure in geotechnical engineering due to its wide choice of application. However, it becomes a source of concern whenever the retaining structure is located on a natural trench that is unstable during construction. Also, because of the additional huge cost caused by these structures in related projects, it is necessary that much effort be made to produce optimal designs of such structures. The design criteria to be satisfied in order to guarantee the strength of the structure include: the geotechnical and structural strength characteristics, the FOS for overturning, the FOS for sliding and the FOS for bearing capacity. All the studies cited above used multi design variables in the algorithms to reflect site specifics.

2.7. Other optimization techniques

Shallow foundations studies: In geotechnical engineering practice, economic and safe design of structure is of great concern. These can be achieved using an optimization technique, which is an integral section of engineering practice. Optimization problems can be tackled through either deterministic or experimental methods. Also, similar to the variables used in the conventional design of footings, the following are the design variables considered in the formulation of the optimization algorithm: Footing length, footing width, footing thickness, embedment depth, length of longer direction of reinforcement bars and length of shorter direction of reinforcement bars (Khajezadeh et al., 2011).

The efficiency of some algorithms: evolution strategy (ES), differential algorithm (DE) and biogeography-based optimization algorithm (BBO) were developed by Kashani et al. (2020) to evaluate the cost of shallow foundation design and optimization. The authors first formulated the objective function that met the ACI 318–05 (ACI, 2005) requirements. Although BBO and WDE demonstrated adequate performance in most cases, however, no algorithm was more effective than the other in addressing the problem considered which also confirms the “no free lunch theory” defined earlier.

Soil erosion studies: Soil erosion is a natural process, which negatively affects natural resources, disturbs ecological systems; it destroys landscapes and quality of water, agricultural activities, ecosystems, diminishes environmental quality and increases hazards (Saha et al., 2019). Soil erosion becomes a threat to sustainability when it is bigger than the rate of soil formation (Rodrigo-Comino & Cerdà, 2018). Therefore, any management approach targeted to address these problems for sustainability is a necessity. Generally, engineering practice is incorporated in the above listed problems, and as such, engineering approach in addressing any of these challenges should be viewed as a breakthrough.

Four different algorithms using machine learning (ML) techniques namely, Gradient Boosted Regression Tree (GRBT), Random Forest (RF), Tree Ensemble (TE) and Naïve Bayes Tree (NBT) were developed by Saha et al. (2020) for the prediction of the spatial Gully Erosion Susceptibility (GES) using fourteen gully erosion condition variables. The study focused not only the ability of the model to predict the susceptibility to gully erosion, but also compared its ability and the most suitable among the tested models.

The findings showed that RF recorded the most exceptional output and was recommended to model the GES, not only for the area studied, but also for areas with similar geo-environmental conditions. From the recommended model, rainfall and elevation contributed the most vital factors to gully erosion. Similarly, Seyed et al. (2020) used four different algorithms namely, Logistic Ratio (LR), Frequency Ratio (FR), Imperialist Competitive Algorithm (ICA) and Ensemble of radial Basis Function (RBF) to evaluate a developed gully erosion susceptibility map (GESM). The authors considered twelve (12) variables as factors affecting gully erosion which were prepared in Geographic Information System (GIS) environment. The results showed that LR model was the best among the models considered and slope aspect factor was the most critical factor that caused gully erosion, while lithology is the least critical factor that caused gully erosion.

Also, Gholami et al. (2020) conducted a similar study to predict hazard on land exposure to wind erosion using sixteen (16) advanced ML regression-based algorithms. The results showed that five (5) out of the 16 models; Monotone Multi-Layer Perception Neural Network (MMLPNN), Spline Generalized Additive Model (SGAM), Cforest, Boosting Generalized Additive Model (BGAM) and Stochastic Gradient Boosting (SGB) are proficient in giving high estimation accuracy for land vulnerability to wind erosion threats.

3. Conclusions

Although The literature acknowledges that geotechnical engineering problems are complex, undefined, ambiguous and with incomplete information, however, these challenges have been successfully overcome by proffering solution based on knowledge and experience of experts backed with field results. The intelligent precision with which geotechnics processes are proposed and utilization of geomaterials with the aim to reduce carbon footprint during earthworks are optimized through the application of artificial intelligence and machine learning techniques. Also, through these state-of-the-art techniques, the contribution to global warming of earthwork protocols would be reduced to its lowest ebb. The use of artificial intelligence in conjunction with nature-inspired algorithm (biomimetic or metaheuristics) to solve some of these complex problems is beneficial to geotechnical engineering and civil engineering in general and the ecosystem at large and can be considered as a breakthrough in zero carbon footprints in geoenvironmental engineering.

Disclosure statement

No potential conflict of interest was reported by the author(s).