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Review

The Application of Machine Learning Techniques in Geotechnical Engineering: A Review and Comparison

by
Wei Shao
1,
Wenhan Yue
1,
Ye Zhang
2,
Tianxing Zhou
2,
Yutong Zhang
2,
Yabin Dang
1,
Haoyu Wang
1,
Xianhui Feng
3,* and
Zhiming Chao
1,4,5,6,*
1
College of Ocean Science and Engineering, Shanghai Maritime University, Shanghai 201306, China
2
Mentverse Ltd., 25 Cabot Square, Canary Wharf, London E14 4QZ, UK
3
School of Civil and Resources Engineering, University of Science and Technology Beijing, Beijing 100083, China
4
Institute of Water Sciences and Technology, Hohai University, Nanjing 211106, China
5
Shanghai Estuarine and Coastal Science Research Center, Shanghai 201201, China
6
Failure Mechanics and Engineering Disaster Prevention, Key Laboratory of Sichuan Province, Sichuan University, Chengdu 610065, China
*
Authors to whom correspondence should be addressed.
Mathematics 2023, 11(18), 3976; https://doi.org/10.3390/math11183976
Submission received: 18 August 2023 / Revised: 6 September 2023 / Accepted: 11 September 2023 / Published: 19 September 2023
(This article belongs to the Special Issue Advances in Mathematical, Numerical and Artificial Intelligence Methods in Rock Engineering Applications)
Browse Figures
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Abstract

:
With the development of data collection and storage capabilities in recent decades, abundant data have been accumulated in geotechnical engineering fields, providing opportunities for the usage of machine learning approaches. Thus, a rising number of scholars are adopting machine learning techniques to settle geotechnical issues. In this paper, the application of three popular machine learning algorithms, support vector machine (SVM), artificial neural network (ANN), and decision tree (DT), as well as other representative algorithms in geotechnical engineering, is reviewed. Meanwhile, the applicability of diverse machine learning algorithms in settling specific geotechnical engineering issues is compared. The main findings are as follows: ANN, SVM, and DT have been widely adopted to solve a variety of geotechnical engineering issues, such as the classification of soil and rock types, predicting the properties of geotechnical materials, etc. Based on the collected relevant research, the performance of random forest (RF) in sorting soil types and assessing landslide susceptibility is satisfying; SVM has high precision in classifying rock types and forecasting rock deformation; and backpropagation ANNs and Hopfield ANNs are recommended to forecast rock compressive strength and soil settlement, respectively.
Keywords:
geotechnical engineering; rock; soil line
MSC:
68T01

1. Introduction

Correctly evaluating the properties of geomaterials is the key to the operation and safe construction of geotechnical engineering facilities such as landfills, foundations, dams, etc. [1,2,3,4,5]. Carrying out physical tests is a vital approach to determining the properties of geomaterials [6,7,8]. However, conducting physical tests is expensive and time-consuming, and the specific material to be adopted on engineering sites is usually selected well after the design stage; thus, there is a clear need to construct predictive models to assess the properties of geomaterials.
Since the properties of geomaterials, including rock and soil, are significantly nonlinear, the majority of the assessing models built based on traditional fitting or analytical approaches have a relatively low precision in predicting the characteristics of geomaterials [9,10,11]. Especially for geomaterials subjected to multiple impact factors, the traditional modeling approaches are not able to fully describe the influence of multiple factors on the nonlinear characteristics of geomaterials, causing predictive errors [12,13,14,15,16,17]. Artificial intelligence techniques can avoid the weaknesses of traditional modeling methods in describing the complicated relationships between multiple parameters effectively. Thus, a rising number of scholars have applied machine learning approaches to address a variety of geotechnical issues [18,19], such as classifying soil types [20], classifying rock types, forecasting landslide susceptibility [21], predicting rock deformation [22], forecasting soil settlement [23,24], assessing rock compressive strength [25], etc.
The algorithm is the key to machine learning modeling [26]. With the rapid progress in machine learning techniques, the number of available machine learning algorithms has risen significantly [27]. Different machine learning algorithms have diverse features which can be applied to different geotechnical issues [28,29]. For a specific geotechnical issue, different machine learning algorithms have diverse predictive performance, and selecting suitable algorithms can remarkably improve the forecasting accuracy [30]. However, to date, a summary of the applicability of different machine learning algorithms in solving certain geotechnical engineering issues has not been reported. Hence, a comprehensive summary of the existing usage of machine learning techniques in geotechnical engineering is required to contrast the forecasting accuracy of different machine algorithms in specific geotechnical areas. This is vital for the more effective utilization of machine learning methods in geotechnical engineering. The aim of this paper is to conduct an in-depth investigation and summary of the current application of machine learning techniques in geotechnical engineering. It also involves a comparative analysis of the performance of various machine learning algorithms in specific geotechnical fields. This paper can provide a comprehensive reference for professionals and researchers in the field of geotechnical engineering, allowing them to gain a better understanding of the potential and limitations of machine learning methods. Additionally, it seeks to offer guidance to engineers and researchers in selecting suitable machine learning algorithms for specific issues, ultimately enhancing the accuracy and efficiency of predictions.
In this paper, firstly, the existing research related to the usage of machine learning approaches in geotechnical engineering is summarized; after that, a comparison of the performance of diverse machine learning algorithms in solving specific geotechnical engineering issues is presented.

2. Applying Machine Learning Techniques in Geotechnical Engineering

SVM, ANN, and DT are some of the most dominant machine learning techniques used in geotechnical engineering. This is because of two reasons: firstly, the algorithms have normalized steps for their usage [31]; and secondly, the algorithms can describe the complex nonlinear relationships between multiple influence factors accurately [32]. Thus, in the following, details of the application of SVM, ANN, and DT in solving geotechnical issues, and the utilization of other machine learning algorithms, are introduced.

2.1. SVM

SVM is widely adopted in geotechnical fields [33,34]; it is able to effectively handle regression and pattern recognition problems [35]. SVM has three main strengths: (1) It is able to conduct nonlinear mappings from raw low-dimensional spaces to higher-dimensional spaces based on kernel functions, as shown in Figure 1. (2) It is able to carry out accurate forecasting based on few specimen data points. (3) Its computational cost is low [36].
Many researchers have adopted SVM to implement the classification of geotechnical materials, including rock and soil, etc. Regarding the classification of soil, Kovačević et al. [37] first used linear and non-linear SVM to classify soil types. The results indicated that non-linear SVM has higher precision in identifying kinds of soil than linear SVM. Then, Heung et al. [38] further studied the effects of kernel functions on the accuracy of soil classification by comparing the performance of four SVM models with different kernel functions, and pointed out that the SVM model with the radial basis function model has the highest accuracy. In terms of rock classification, Seng and Chen [39] first integrated a rough set into SVM to classify rock ores, and Seng pointed out that the established model has a fast operation speed and high precision. Then, Qiu et al. [40] adopted a genetic algorithm (GA) to raise the precision of SVM in classifying rock, and the outcomes demonstrate that the GA-SVM model can effectively sort the types of soil.
SVM is extensively used in analyzing landslide susceptibility. Yao et al. [41] first applied SVM techniques to predict landslide susceptibility according to landslide records. Then, Xu et al. [42] examined the efficiency of SVM-based models with various kernel functions in predicting landslide susceptibility under earthquakes. The highest forecasting accuracy was obtained from the SVM model related to the radial basis kernel function. After that, Pham et al. [43] carried out comparison research on SVM and DT in forecasting rainfall-induced landslides. The research indicates that the predictive results gained via adopting SVM are closest to the measured values. Subsequently, Pham et al. [44] further applied five different predictive methods, SVM, logistic regression, linear discrimination analysis, Bayesian network, and naïve Bayes, to evaluate the susceptibility to landslides. The results indicate that SVM has the highest predictive accuracy among the five approaches.

2.2. ANN

A large number of researchers have utilized ANNs in geotechnical engineering, which include three main models: feed-forward, feed-back, and self-organizing competition models. BPANN, Hopfield ANN, and self-organizing map network (SOM) ANN are the most representative ANN algorithms used with the corresponding fundamental models, respectively.
The majority of ANN models that are used in geotechnical engineering employ the BPANN algorithm, whose typical structure is shown in Figure 2 [45]. A BPANN model to categorize soil textures was constructed by Zhai et al. [46], and their research shows that the BPANN algorithm has lower predictive accuracy if the data specimens are limited. Then, Wang et al. [47] established a BPANN model to assess the settlements of a soil embankment by integrating the momentum method and the self-adaptive learning rate. After that, Saito et al. [48] used BPANN to establish landslide susceptibility maps. The outcomes indicate that BPANN is a powerful tool in evaluating landslide susceptibility. Subsequently, Samui and Sitharam [49] developed BPANN models to evaluate the liquefication susceptibilities of soil after an earthquake. Afterward, BPANN was utilized by Ardakani and Kohestani [50] to forecast the liquefaction potential of soil under dynamic loading based on cone penetration test results. In the same year, Brungard et al. [51] used the BPANN technique to determine the types of soil and map the distribution of different types of soil. Cooner et al. [52] adopted machine learning techniques such as BPANN, SVM with a radial basis kernel function, and random forest (RF) for detecting the damages caused by the Haiti Earthquake. The study indicates that machine learning algorithms can be applied to assess earthquake damage.
Hopfield ANN is a symmetrical single-layer full-feedback neural network. It can be classified into the discrete Hopfield neural network (DHNN) and continuous Hopfield neural network (CHNN) according to different activation functions. Most of the usage related to Hopfield ANN in geotechnical engineering adopts the DHNN [53]. The DHNN has two main strengths: (1) it has favorable stability, and (2) it has a limited number of balancing points. Ambrožič and Turk [54] first applied the DHNN to foretell soil settlement, and the investigation demonstrated that the model can obtain satisfactory predictions. Then, Tiryaki [55] applied the DHNN to evaluate rock cuttability, and the predictive outcomes were verified by experiment results. After that, Yao et al. [56] proposed a DHNN model to predict the deformation of rock. Subsequently, Dagdelenler et al. [57] explored the applicability of DHNN in assessing the weathering degree of granitic rocks, and the results indicate that the developed model is efficient. Afterward, a DHNN model was established by Monjezi et al. [58] to forecast the uniaxial compressive strength of rock.
SOMANN is a competitive learning ANN algorithm without supervision, and it can map data from high-dimension spaces to low-dimension spaces. SOMANN consists of input and competitive layers, and the neurons in the input and competitive layers are interconnected [59]. SOMANN is widely adopted in geotechnical engineering to settle problems about prediction, categorization, and visualization. Firstly, a SOMANN model was established by Ferentinou and Sakellariou [60] to evaluate slope stability under static and dynamic loadings. The results show that the model can make precise estimations of the stability of slopes under different loadings. Then, Chauhan et al. [61] proposed that the SOMANN skill is useful in establishing 2D segmented pictures to analyze the microstructures of rock cores. Subsequently, Huang et al. [62] combined SOMANN and extreme learning machine (ELM) techniques to predict landslides. The investigation demonstrates that the combined model has higher accuracy in forecasting the susceptibility of landslides than the SOMANN or ELM models. Afterward, Mokarram et al. [63] proposed that SOMANN is a reliable tool to visualize data, and it can precisely categorize soil according to soil fertility evaluation results.

2.3. DT

The structure of DT, which can be used conduct classification and prediction operations, is composed of nodes and directed edges, as seen in Figure 3 [64]. There are three main strengths of DT: (1) its principle is easily understood; (2) the number of needed specimen data points for modeling is not many; and (3) the performance of DT is convenient to validate with static tests [65].
DT is extensively used in settling the issues of geomaterial categorization and pattern recognition. Juang et al. [66] first combined the analysis of fuzzy sets and DT to classify slope failure potentials for establishing a slope hazard map. The study demonstrates that the established model can evaluate the slope failure potentials precisely. Then, Scull et al. [67] applied DT to classify the types of soil, which was proved to be an effective method. After that, Shahriar et al. [68] employed DT to divide rock under different ground conditions on account of the tunnel boring machine data. The categorization outcomes were verified by the results of field tests, indicating that the established model can divide rock effectively. Subsequently, Jin et al. [69] researched the applicability of DT in dividing the types of soil according to the freeze states of soil, and the outcomes indicated that the precision of DT is high in recognizing the types of soil. Afterward, according to soil parent materials, Lacoste et al. [70] constructed a DT model to forecast and categorize soil parent materials. The outcomes indicate that the established soil parent material maps can represent superficial soil more precisely than the maps gained via conventional approaches. Afterwards, Gandomi et al. [71] established a DT model to evaluate soil liquefaction by adopting standard penetration test data. The outcomes indicate that the DT model has a higher accuracy than that of the model that was established by logistic regression. Following that, Liang et al. [72] adopted DT to classify rock according to rock strength, and the outcomes show that DT has a higher forecasting accuracy than that of multiple regressions.
DT is also extensively adopted in geotechnical engineering to settle problems related to complicated and non-linear modeling. Zmazek et al. [73] first used DT, linear regression, and instance regression to analyze soil radon data, and proposed that DT has a higher predictive accuracy than the other models. Then, Geissen et al. [74] applied DT to predict soil erosion, and the results show that the forecasting performance of DT is satisfactory. After that, Sikder and Munakata [75] combined the rough sets and the DT model to recognize the most significant variables of earthquake activity. The research indicates that the joint usage of rough sets and DT can obtain more precise forecasting results. Subsequently, Pham et al. [76] compared the performance of two machine learning skills, bagging-based DT and logistic regression, in constructing landslide susceptibility maps. The forecasting precision was verified using statistical approaches, and the outcomes show that the bagging-based DT model has a higher accuracy.

2.4. Other Machine Learning Algorithms

Except for the aforementioned three machine learning techniques, other machine learning algorithms have been extensively adopted in geotechnical areas, regarding the classification and prediction of the characteristics of soil. Firstly, Bhattacharya and Solomatine [77] and Bhargavi and Jyothi [78] used constraint clustering and classification to classify the type of soil. The outcomes were verified by the results of physical tests. The study indicates that the established approach can classify the kind of soil efficiently, which is consistent with the experimental results. Then, Bhargavi and Jyothi [75] classified the type of agricultural soil according to naïve Bayes and conventional statistic approaches. The research indicates that machine learning skills can classify the type of soil when sufficient data are available, and that the predictive precision is higher than that for conventional methods. Regarding dividing and forecasting the properties of rock, Simpson and Priest [79] established a GA-based model to recognize the maximum discontinuity frequency inside complex rock structures. The outcomes demonstrate that the constructed model can obtain the optimum solution, and the predicted accuracy is high. For the usage of machine learning skills in earthquake analysis, firstly, with the aim of earthquake early warning, Oh et al. [80] used the Bayesian learning technique with an automatic relevance determination prior to categorize earthquake ground motion data into near and far sources. The outcomes show that the established model has superior classification precision to that of conventional approaches, with superior generalizing. Then, Alimoradi and Beck [81] constructed a model according to Gaussian regression to conduct analysis and carry out the simulation of the ground motion under an earthquake. The outcomes demonstrate that the established model can effectively assess the ground motion, particularly in regions that are well instrumented.

3. Comparing Diverse Machine Learning Algorithms

The algorithm is the key to machine learning techniques, and every machine learning algorithm has its own superior and inferior fields because of the inherent structure features of different algorithms. For a specific geotechnical issue, it is vital to determine the applicable machine learning algorithms, which can remarkably improve the prediction performance. Thus, this section summarizes comparison studies regarding the applicability of diverse machine learning algorithms in settling different geotechnical problems, and for a given matter the corresponding best-matched algorithm is given.

3.1. Soil Classification

Soil categorization is significant for the design, building, and maintenance of geotechnical engineering applications. The comparative research about the use of machine learning algorithms in classifying soil types is summarized in Table 1.
Table 1 shows six different comparison studies about machine learning algorithms in soil classification, which all involve the usage of SVM. Among them, there are four studies conducted by Ahmad et al. [82], Heung et al. [38], Ardakani and Kohestani [50], and Kovačević et al. [37] that show that SVM has the optimal performance in the classification of soil types. The other two comparison studies implemented by Duro et al. [83] and Brungard et al. [51] involve the comparison of SVM and RF, indicating that RF has better classification accuracy than SVM. Thus, based on the collective relevant research, SVM has higher precision than ANN, DT and MLR in sorting soil types, but when compared with RF, the accuracy of SVM is lower.

3.2. Rock Classification

Rock classification is also a significant study area in geotechnical engineering. Some comparative research has been conducted in this research area to explore the applicability of different machine learning algorithms, as listed in Table 2.
Table 2 lists four different comparison studies about the use of machine learning modeling in sorting rock types. Three of the studies involve the usage of BPANN and SVM, conducted by Qiu [40], Seng and Chen [39], and Chauhan et al. [84], respectively, all showing that SVM has better classification performance when compared with BPANN, MNB, and SOMANN. Thus, based on the collective studies, compared with BPANN, MNB, and SOMANN, it is recommended to adopt SVM to sort rock types.

3.3. Forecasting the Deformation of Rock

The deformation of rock has a large impact on the safety of engineering applications. However, the deformation of rock has remarkable non-linearity and plasticity, which makes it highly difficult to predict via adopting conventional approaches. Thus, a rising number of scholars have used machine learning approaches to address these kinds of issues. The existing relevant research compares the applicability of DT, SVM, and BPANN in predicting the deformation of rock, which is summarized in Figure 4 [85].
In Figure 4, if the predictive points fall on the black straight line (y = x), this represents that the observed value equals the predictive value. Thus, the distance between the data points and the line reflects the predictive accuracy. Based on Figure 4, in general, the data points obtained by SVM are closer to the black line. To conduct quantitative analysis and draw comparisons on the prediction precision for the three machine learning approaches, the data points gained by adopting diverse approaches, as shown in Figure 1, are fitted by Equation (1) to obtain the regression coefficients, as shown in Table 3.
y = A x + B
where A and B are constants, respectively.
As listed in Table 3, the regression coefficients of the three machine learning algorithms are all above 0.90. Among them, the regression coefficient of SVM is highest, at 0.99. Thus, based on the collective research, compared to DT and BPANN, it is recommended to adopt SVM to forecast the deformation of rock.

3.4. Predicting the Compressive Strength of Rock

Correctly evaluating the compressive strength of rock determines the stability of the engineering applications that are built on rock foundations. Since there are multiple influencing factors affecting the compressive strength of rock, it is tough to use traditional methods to predict the compressive strength. Thus, several investigators have utilized machine learning techniques to assess compressive strength. The existing research compared the applicability of BPANN, Hopfield ANN, and DT in predicting the compressive strength of rock, which is summarized in Figure 5 [86].
As above, in Figure 5, the black straight line (y = x) indicates that the observed value equals the predicted value. In general, the data points obtained by BPANN are closer to the line. To analyze and compare the forecasting precision of the three machine learning algorithms, the data points in Figure 2 were fitted by using Equation (1) to obtain the regression coefficients, as listed in Table 4.
According to Table 4, the regression coefficients of the three machine learning algorithms are all above 0.90. Among them, the regression coefficient of BPANN is the highest, at 0.99. Thus, based on the collective research, compared to Hopfield ANN and DT, it is recommended to adopt BPANN to assess the compressive strength of rock.

3.5. Landslide Susceptibility

The analysis of landslide susceptibility can offer guidance for geotechnical engineers to adopt steps to prevent landslides happening and protect the safety of the public. Some researchers compared the applicability of different machine learning techniques in analyzing the susceptibility of landslides, as listed in Table 5.
Table 5 lists six different comparison studies about the applicability of diverse machine learning algorithms in predicting landslide susceptibility, five of which involve the usage of SVM. The comparison investigations conducted by Yao et al. [87], Pham et al. [88], Marjanović et al. [89], and Huang and Zhao [90] all show that SVM has the best performance in forecasting landslide susceptibility when compared with linear regression, BPANN, and DT. However, the comparison research implemented by Micheletti et al. [91], and Zhang et al. [92] indicates that compared with RF, SVM has a lower predictive accuracy. Overall, based on the collective research, SVM has a higher precision than DT and BPANN in assessing landslide susceptibility, but when compared to RF, the forecasting accuracy of SVM is lower.
Table 5. The performances of machine learning algorithms in forecasting landslide susceptibility.
Table 5. The performances of machine learning algorithms in forecasting landslide susceptibility.
Authors’ NameTimeAlgorithmPredictive Performance
Yao [87](2007) Predictive precision
SVM90.39%
Linear regression77.29%
Micheletti [91](2014) Predictive accuracy
SVM92%
RF93%
Marjanović [89](2011) Kappa statistics κ
SVM0.43
Linear regression0.23
DT0.34
Pham [88](2016) Predictive accuracy
SVM79.65%
DT79.10%
Huang [90](2017) Predictive accuracy
BPANN84.25%
SVM87.37%
Pham [88](2017) Predictive accuracy
Linear regression88%
DT90%

3.6. Prediction of Soil Settlement

Some researchers have compared the performance of diverse machine learning algorithms in forecasting soil settlement. The existing research compared the applicability of Hopfield ANN and multiple layer perceptron (MLP) models in assessing soil settlement, which is shown in Figure 6 [93,94,95,96,97,98].
As above, in Figure 6, the black straight line (y = x) indicates that observations equal predictions. In general, the data points obtained by Hopfield ANN are closer to the black line. To conduct quantitative analysis and draw comparisons on the prediction precision for the two machine learning methods, Equation (1) is used to fit the data points in Figure 6; the regression coefficients are listed in Table 6.
According to Table 6, both of the regression coefficients for the two machine learning algorithms are above 0.90. Compared to MLP, Hopfield ANN has a higher regression coefficient, at 0.99, indicating the more accurate results obtained by using Hopfield ANN. Thus, based on the collective research, Hopfield ANN is recommended to predict soil settlement over MLP.

4. Conclusions

This paper reviews the applications of machine learning techniques in geotechnical engineering, and a comparison of the applicability of different machine learning algorithms in settling special geotechnical issues is summarized. The following are the main conclusions: Firstly, ANN, SVM, and DT are among the most popular machine learning algorithms used in geotechnical engineering, addressing various geotechnical issues. Based on collective research, RF is recommended for soil type classification over SVM, ANN, and DT. Additionally, SVM is preferred for rock type classification and deformation prediction over BPANN and DT. Moreover, BPANN is recommended for assessing rock compressive strength over HPANN and DT, as shown in Table 7. Lastly, for soil settlement prediction, Hopfield ANN is favored over MLP, as indicated by the collective research.
In the future, researchers can choose appropriate machine learning algorithms and perform model parameter tuning to find the best models. Consideration can also be given to using ensemble learning methods to improve model performance and enhance prediction accuracy. Furthermore, researchers should explore the potential of deep learning techniques in geotechnical engineering, utilizing deep learning algorithms such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs) for more complex problem modeling and prediction. Attention should also be given to research on the interpretability of machine learning models, allowing engineers and decision-makers to understand the models’ prediction results and reasoning processes.

Author Contributions

Conceptualization, W.S.; investigation, W.Y. and Y.Z. (Ye Zhang); resources, Z.C. and X.F.; data curation, W.S. and W.Y.; writing—original draft, Z.C. and X.F.; writing—review and editing, Z.C., H.W. and W.Y.; visualization, W.S., T.Z. and Y.Z. (Ye Zhang); software, W.Y., X.F. and Y.Z. (Yutong Zhang), supervision, Y.D. and X.F.; funding acquisition, Z.C. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the consistent support of the National Natural Science Foundation of China (No. 52301327). The paper is also sponsored by the 2022 Open Project of Failure Mechanics and Engineering Disaster Prevention, Key Lab of Sichuan Province (No. FMEDP202209), and the Shanghai Sailing Program (No. 22YF1415800, No. 23YF1416100). Finally, this project is also funded by the Shanghai Natural Science Foundation (No. 23ZR1426200), the China Postdoctoral Science Foundation (No. 2023M730929, No. 2023TQ0025), the Shanghai Soft Science Key Project (No. 23692119700), the Key Laboratory of Ministry of Education for Coastal Disaster and Protection, Hohai University (No. 202302), and the Key Laboratory of Estuarine & Coastal Engineering, Ministry of Transport (No. KLECE202302).

Data Availability Statement

In this paper, all data, models, and code used during the study appear in the submitted article.

Conflicts of Interest

The authors declare no conflict of interest.

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Mathematics 11 03976 g001
Figure 1. The mapping from low-dimensional spaces to high-dimensional spaces: (A) low-dimensional space; (B) high-dimensional space.
Figure 1. The mapping from low-dimensional spaces to high-dimensional spaces: (A) low-dimensional space; (B) high-dimensional space.
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Figure 2. The typical structure of BPANN.
Figure 2. The typical structure of BPANN.
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Figure 3. The typical structure of decision trees.
Figure 3. The typical structure of decision trees.
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Figure 4. The comparison of DT, SVM, and BPANN in forecasting the deformation of rock.
Figure 4. The comparison of DT, SVM, and BPANN in forecasting the deformation of rock.
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Figure 5. The comparison of BPANN, Hopfield ANN, and DT in forecasting the rock compressive strength.
Figure 5. The comparison of BPANN, Hopfield ANN, and DT in forecasting the rock compressive strength.
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Figure 6. The comparison of Hopfield ANN and MLP in predicting soil settlement.
Figure 6. The comparison of Hopfield ANN and MLP in predicting soil settlement.
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Table 1. The performances of different machine learning algorithms in categorizing soil.
Table 1. The performances of different machine learning algorithms in categorizing soil.
Authors’ NameTimeAlgorithmClassification Performance
Kovačević et al. [37](2009) Kappa statistics κ
SVM0.52
Multinomial Naïve Bayes (MNB)0.51
Ahmad et al. [82](2009) Fitting of degree R2
SVM 0.51
BPANN0.42
Multinomial Logistic Regression (MLR)0.39
Duro et al. [83](2011) Regression coefficient
SVM89.26%
RF89.67%
DT87.6%
Heung et al. [38](2015) Classification accuracy
DT67%
k-nearest neighbor72%
MLR37%
BPANN26%
RF68%
SVM72%
Brungard et al. [51](2014) Kappa statistics κ
RF0.55
MLR0.37
DT0.27
SVM0.46
BPANN0.41
Ardakani et al. [50](2015) Classification accuracy
BPANN97.2%
SVM100%
DT96.3%
Table 2. The performances of machine learning approaches in categorizing rock.
Table 2. The performances of machine learning approaches in categorizing rock.
Authors’ NameTimeAlgorithmPerformance Parameters
Qiu et al. [40](2010) Classification accuracy
SVM100%
BPANN67.7%
Seng et al. [39](2009) Classification accuracy
MNB95%
BPANN96%
SVM99%
Chauhan et al. [84](2016) Classification accuracy
SOMANN95%
BPANN97%
SVM90%
Liang et al. [72](2016) R2
DT0.801
MNB0.77
Table 3. Regression coefficients (DT, SVM, and BPANN).
Table 3. Regression coefficients (DT, SVM, and BPANN).
AlgorithmDTSVMBPANN
R0.960.990.92
Table 4. Regression coefficients (Hopfield ANN, DT, and BPANN).
Table 4. Regression coefficients (Hopfield ANN, DT, and BPANN).
AlgorithmHopfield ANNDTBPANN
R0.960.920.99
Table 6. Regression coefficients (Hopfield ANN and MLP).
Table 6. Regression coefficients (Hopfield ANN and MLP).
AlgorithmHopfield ANNMLP
R0.990.90
Table 7. The strengths and weaknesses of three ML techniques (ANN, SVM, and DT).
Table 7. The strengths and weaknesses of three ML techniques (ANN, SVM, and DT).
AlgorithmStrengthWeakness
ANN
  • Wide applicability, suitable for various types of problems such as image recognition, regression analysis, etc.
  • Capable of learning complex nonlinear relationships, excels in handling complex data and tasks.
  • Can utilize parallel computing to accelerate the training process.
  • High training complexity.
  • Difficulty in selecting hyperparameters.
  • Risk of overfitting when data are insufficient.
SVM
  • Performs well with high-dimensional data and is suitable for tasks such as text classification and image classification.
  • Different kernel functions can be used to adapt to various types of data.
  • Overfitting can be controlled by adjusting the regularization parameter.
  • For large-scale datasets, SVMs have high training time and memory requirements.
  • Multiclass problems require the use of a one-vs.-all or one-vs.-one strategy.
  • Performance is highly dependent on parameter selection, necessitating processes such as cross-validation for tuning.
DT
  • Easy to visualize and explain.
  • Capable of handling numerical and categorical features.
  • Exhibits a certain level of robustness against missing data or outliers.
  • Pruning and other methods are needed to reduce the risk of overfitting.
  • There is instability, as minor changes in data may lead to the generation of different tree structures.
  • The process of generating decision trees uses a greedy algorithm, which may lead to getting stuck in local optimal solutions.
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Shao, W.; Yue, W.; Zhang, Y.; Zhou, T.; Zhang, Y.; Dang, Y.; Wang, H.; Feng, X.; Chao, Z. The Application of Machine Learning Techniques in Geotechnical Engineering: A Review and Comparison. Mathematics 2023, 11, 3976. https://doi.org/10.3390/math11183976

AMA Style

Shao W, Yue W, Zhang Y, Zhou T, Zhang Y, Dang Y, Wang H, Feng X, Chao Z. The Application of Machine Learning Techniques in Geotechnical Engineering: A Review and Comparison. Mathematics. 2023; 11(18):3976. https://doi.org/10.3390/math11183976

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Shao, Wei, Wenhan Yue, Ye Zhang, Tianxing Zhou, Yutong Zhang, Yabin Dang, Haoyu Wang, Xianhui Feng, and Zhiming Chao. 2023. "The Application of Machine Learning Techniques in Geotechnical Engineering: A Review and Comparison" Mathematics 11, no. 18: 3976. https://doi.org/10.3390/math11183976

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