The Application of Machine Learning in Geotechnical Engineering

1. Introduction

Geotechnical engineering is civil engineering constructed in rock and soil and includes three main types: underground, foundation, and slope engineering. Because rock and soil are typical natural geological bodies, their mechanical properties and internal structures are very complex [1]. They are characterized by complicated physical, mechanical, and chemical behaviors, and their structure is a three-phased system which changes depending on water content and environmental conditions in a highly non-linear manner. Moreover, rock and soil are anisotropic and heterogeneous by nature owing to differences in their origins and formation processes. Therefore, most geotechnical engineering problems involve the coupling of multiple fields and multiple phases; generally, they cannot be solved easily. Moreover, unsafe geotechnical engineering will bring about serious disasters, such as landslides and surface subsidence, which cannot be solved well by traditional (e.g., theoretical, numerical, and experimental) methods. However, the development of artificial intelligence has supported the development of better solutions to geotechnical engineering problems. Machine learning methods have been applied widely to this end and have gained prominence in current research trends [2,3]. The first study to use machine learning in geotechnical engineering was conducted by Stanford in 1983 [4] and addressed the potential applications of expert systems in the domain of slope engineering specifically. From that moment on, machine learning methods have been gaining increasingly widespread use in the field of geotechnical engineering. Because geomechanics are the foundation of geotechnical engineering, nowadays, there are numerous studies on the applications of machine learning methods in geomechanics. These include two main aspects: geotechnical parameters and geotechnical constitutive models [5,6]. Numerous studies have also explored using machine learning methods in the three main types of geotechnical engineering: underground engineering [7,8], foundation engineering [9], and slope engineering [10]. Moreover, machine learning methods have been used to solve specific geotechnical engineering problems, including soil–structure interactions [11] and seepage of dams [12]. In addition, machine learning methods have been employed to predict geotechnical engineering disasters, such as ground surface settlements [13], landslides [14], rock bursts [15], etc. Currently, machine learning methods have become prevalent in the development of boring machines for underground engineering: the construction of integrated management systems for tunnel boring machine operations [16], the safety prediction of shield tunnel construction [17], the prediction of shield attitudes [18], and main drive torque estimation in shield tunnelling [19] are some of the areas in which they have proven useful. Therefore, nowadays, machine learning methods have been applied in most, if not all, fields of geotechnical engineering and geomechanics. Almost all types of machine learning methods have been employed in this field; examples include expert systems, fuzzy systems, artificial neural networks, deep learning methods, swarm intelligence, evolutionary algorithms, big data analysis, biological computation, nature-inspired computation, support vector machine, and Gaussian process regression. Out of these, the use of artificial neural networks has been the most extensive.

This Special Issue presents new applications of machine learning methods in the field of geotechnical engineering, from planning and design to construction. It contains 19 articles, which I will briefly describe in the next section. It is not the purpose of this Editorial to elaborate on each of the papers, but rather to encourage the reader to explore them on their own.

2. An Overview of the Published Papers

In the study by Elsawy et al. (contribution 1), the undrained shear strength of sensitive alluvial soft clay located in northern areas of the Nile River, Egypt, is determined using the machine learning approach. This analysis is key to assessing the stability of foundation engineering in this type of soil. Generally, the main method to determine the undrained shear strength of soil is through laboratory tests. However, this is costly and time-consuming. Moreover, extracting undisturbed samples of sensitive clay from construction sites it extremely difficult. Therefore, based on a dataset of 111 geotechnical testing points from laboratory and field tests, Elsawy et al. use several machine learning models (including linear regression, Gaussian process regression, regression trees, ensembles of regression trees, and support vector machine) to determine the undrained shear strength of sensitive alluvial soft clay according to the soil’s key features, which include water content, liquid limit, dry unit weight, plasticity index, consistency index, void ratio, specific gravity, and pocket penetration shear. The performance of each machine learning model is assessed through its coefficient of determination. The results show that the most accurate model is the support vector regression model.

The study by Zheng et al. (contribution 2) is focused on the back analysis of surrounding rock parameters of underground engineering. For the construction of large-span arch cover metro stations, the determination of the surrounding rock parameters is very important. In this paper, to obtain the surrounding rock parameters of Shikui Road station, located on Dalian Metro Line Five, an intelligent back analysis method, called the Gaussian process differential evolution co-optimization algorithm (GP-DE algorithm), is proposed. In this method, based on the data obtained by the FLAC3D finite element model using the orthogonal scheme for numerical results, the relationship between monitoring data (displacement and stress) and the surrounding rock parameters is constructed by the Gaussian process model. Based on data measured in real-life engineering, through the optimization of the differential evolution algorithm, suitable surrounding rock parameters can be obtained. Finally, by using the forward calculation of FLAC3D, the accuracy of the inversion parameters is verified. The results show that the forward calculation results obtained using the inversed parameters are in good agreement with those obtained in real life, and the accuracy of this back analysis method is very high.

The third article in this Special Issue is also focused on the back analysis of geomaterial mechanical parameters of underground engineering. In this study, a novel back analysis method combining a reduced-order model (ROM) and grey wolf optimization (GWO) has been proposed. In this method, the ROM is adopted to construct a surrogated model between the response of the underground structure and the surrounding rock parameters based on a numerical model, and GWO is used to optimize the surrounding rock parameters based on the ROM. The proposed method is applied to determine the surrounding rock parameters of two tunnels. The results show that the obtained surrounding rock parameters are in excellent agreement with the actual parameters, and the deformation results computed based on those parameters are consistent with the theoretical deformation results.

In the fourth article in this collection, the synthetic aperture radar (SAR) and optical image registration are studied. The SAR and optical images collect rich spectral information for ground objects, but their qualities are seriously affected by atmospheric attenuation and weather conditions. Therefore, improving the quality of these images is crucial to improving geotechnical engineering surveys. In this study, a novel method for SAR and optical image registration is proposed. In the new method of feature point extraction, phase consistency intensity screening and scale space grid division are combined to obtain stable and uniform feature points from images, and in feature description, the extended phase consistency method is applied to calculate the gradient amplitude and direction of the images. The experimental results showed the superior matching performance of the new method compared with current state-of-the-art methods.

The study by Zhan et al. (contribution 5) is also focused on the back analysis of surrounding rock parameters of underground engineering. In this study, based on data from a numerical model established based on a fluid–solid coupling finite element model, a surrogated model between the response of the surrounding rock (displacement and pore water pressure distribution) and surrounding rock parameters is constructed by the Gaussian process. According to the measured displacement and pore water pressure of the surrounding rock, this surrogated model searches for the suitable rock parameters using differential evolution. Therefore, the study proposes a new intelligent back analysis method for fluid–solid coupling of surrounding rock in tunnels in water-rich areas. Finally, this new back analysis method is verified by comparing the inversion parameters with the ones measured in real-life.

In the next paper, by Li and Dias (contribution 6), the assessment of rock elasticity modulus is conducted using four hybrid random forest models. The study proposes a data-driven method based on the hybrid random forest for the determination of rock elasticity modulus, which is vital for rock engineering design and cannot be solved using traditional methods such as experimental analysis and empirical formulas. In this new method, four metaheuristic optimization algorithms (backtracking search optimization algorithm, multi-verse optimizer, golden eagle optimizer, and poor and rich optimization algorithm) are used to optimize the random forest, thus enabling the construction of four hybrid random forest models. Based on the collected database consisting of 120 rock samples, the hybrid random forest models are applied to predict the rock elasticity modulus according to four factors (porosity, P-wave velocity, Schmidt hammer rebound number, and point load index). Moreover, the performance of the four hybrid random forest models is evaluated according to four indices (root-mean-square error, mean absolute error, determination coefficient, and Willmott’s index). The results show that the prediction accuracy of the hybrid random forest model based on the poor and rich optimization algorithm is the best, and that porosity is the most important factor.

The study by Yang et al. (contribution 7) is also focused on estimating the undrained shear strength of clay. In this study, based on the collected database of 202 Finnish clay samples, a CatBoost–Bayesian hybrid model adaptively coupled with modified theoretical equations is constructed to determine the undrained shear strength of clay according to 11 main parameters (organic content, clay content, void ratio, natural water content, liquid limit, plastic limit, effective overburden pressure, preconsolidation pressure, overconsolidation ratio, compression index, and sensitivity). The CatBoost–Bayesian hybrid model, in which the Bayesian optimization algorithm is used to optimize the CatBoost algorithm, is employed to obtain the feature importance level of the 11 parameters and is adaptively coupled with the theoretical equation of undrained shear strength derived from the modified Cambridge model. The constructed model is verified using the experimental samples of Finnish clay. The results indicate that the established model can successfully estimate the undrained shear strength of isotropically consolidated clays.

The next study, by Lee et al. (contribution 8), uses machine learning for the prediction of ground subsidence risk in urban areas in Korea. Because ground subsidence in urban areas, caused by damage to underground utilities, can cause serious disasters, Lee et al. construct a machine learning-based ground subsidence risk prediction model based on the collected attribute information and historical ground subsidence data on six types of underground utility lines (water supply, sewage, power, gas, heating, and communication). Firstly, the target area is divided into a square grid from which the attribute information and historical ground subsidence data are extracted. Twenty-four datasets are developed, including single-type attribute information, merged by six types of underground utility lines, and three risk levels, categorized from the number of ground subsidence occurrences. Then, based on the datasets, three machine learning models (random forest, extreme gradient boosting, and light gradient boosting machine) are applied to classify ground subsidence risk levels. The results show that the new method can successfully predict risk levels in the target region.

The study by Chala and Ray (contribution 9) is focused on comparing four machine learning-based soil classification methods using cone penetration test data. In this study, the four machine learning methods include artificial neural network, random forest, support vector machine, and decision trees. The database used is collected from the International Society for Soil Mechanics and Geotechnical Engineering (ISSMGE) database and includes 232 cone penetration test (CPT) datasets, and soil is classified according to Robertson’s soil behavioral types. Moreover, the quantitative metrics used to evaluate the machine learning methods include overall accuracy, sensitivity, precision, F1_score, and confusion matrices. The results show that all machine learning methods can accurately classify most soils, and most evaluation metrics of the four machine learning methods indicate high scores. Moreover, the support vector machine and random forest have outstanding performance on both majority and minority soil classes and can be applied for rapid and accurate soil classification.

The article by Lendo-Siwicka et al. (contribution 10) is focused on the determination of the damping ratio of clay soils. In this study, to ease the difficulty of determining the properties of soils, which are affected by many complex factors, a new method to determine the value of the clay soil damping ratio using an artificial neural network model is proposed. Based on a dataset consisting of 1227 examples from the testing 15 soil samples in the Resonance Column, the damping ratio of clay soils affected by seven factors (shear strain, normalized shear modulus, liquid limit, mean effective stress, silt content, plasticity limit, and clay content) is predicted. Moreover, a comparison of the new artificial neural network model with empirical formulas is conducted. The results show that the new method boasts a much higher prediction accuracy and a more flexible application.

The next study, by Cheng et al. (contribution 11), is focused on the prediction of undrained bearing capacity of skirted foundation in spatially variable soils. The bearing capacity of the skirted foundation, widely used in offshore and subsea engineering, is seriously affected by variabilities in soil undrained shear strength. To predict its uniaxial bearing capacity factors under pure horizontal and moment loads, an efficient machine learning method using a two-dimensional convolutional neural network is proposed. In this new method, datasets with 600 samples from the random finite element numerical simulation are used; the input is a random field data matrix for the soil domain in a numerical model, and the output is the corresponding bearing capacity factor. The results show that the prediction performance of the new method is satisfactory in terms of the variation coefficients and the fluctuation scale in two directions, with a high determination coefficient and low root-mean-square error.

The study by Daghistani and Abuel-Naga (contribution 12) is also focused on the prediction of soil behavior using machine learning methods. In this study, based on a dataset from 1068 tests on sand (including microscopy, direct shear, oedometer, and specific gravity tests), a machine learning model for evaluating the influence of sand particle morphology on shear strength is constructed. Two machine learning methods—multiple linear regression and random forest regression—are applied and compared. The features of sand particle morphology considered by the two machine learning models include mean particle size, uniformity coefficient, curvature coefficient, dry density, normal stress, and particle regularity. The results show that the prediction accuracy of both models is very high compared to the experimental results, and the most important factor affecting the shear strength of sand is mean particle size.

The next study, by Chala and Ray (contribution 13), is focused on the prediction of soil shear wave velocity, which is an essential parameter in evaluating the seismic response in foundation engineering. In this study, based on a collected dataset with 1000 cone penetration test data, four machine learning methods (random forest, support vector machine, decision trees, and extreme gradient boosting) are employed to predict soil shear wave velocity according to four features: cone tip resistance, sleeve friction, friction ratio, and soil depth. Moreover, to improve the performance of the four machine learning methods, their hyperparameters are optimized using Bayesian optimization with the k-fold cross-validation method. Eight metrics (root-mean-square error, mean absolute error, mean absolute percentage error, coefficient of determination, performance index, scatter index, uncertainty analysis at 95% confidence level, and proportion of samples that fall within ±10% deviation from the predicted values compared with the target value) are used to evaluate the performance of the proposed machine learning methods. The results show that the performance of the random forest is the best, achieving the highest accuracy and the lowest level of errors.

The study by Ma et al. (contribution 14) focuses on the application of the multi-objective optimization method for the optimization of the foundation pit dewatering scheme, which is very important for the safety of foundation engineering. Using the foundation pit dewatering theory and the multi-objective optimization algorithm of the non-dominated sorting genetic algorithm (NSGA-II), the authors optimize the foundation pit dewatering scheme for a foundation pit dewatering project at an inverted siphon section of the Xixiayuan canal head. This multi-objective optimization has three objectives, which are minimum total cost of dewatering, minimum amount of land subsidence caused by dewatering, and maximum drawdown of water level in the center of the foundation pit. Using this new method, a Pareto-optimal solution set with uniform distribution is obtained, and the optimization scheme is applied to the solution set to produce multiple feasible schemes for real dewatering. The results show that the obtained foundation pit dewatering scheme meets the requirements for water level and settlement control.

The article by Almasoudi et al. (contribution 15) focuses on the effects of dry density and moisture content on kaolin–brass interfacial shear adhesion. In this study, to evaluate the interface shear adhesion between compacted kaolin clay and a metallic surface, a new testing method is proposed. Compacted kaolin clay specimens with various energy levels and moisture contents are used to determine the interface shear adhesion strength between reconstituted kaolin clay and a metallic surface. The results show that to provide the highest density and divide the compaction curve into dry and wet sides, the optimum moisture content is 30%, and as the clay’s dry density increases, the interface shear adhesion strength increases too. Moreover, as the moisture content rises on the wet side of the compaction curve, the strength decreases significantly.

The next article, by Abed et al. (contribution 16), focuses on the accurate estimation of soil compaction parameters. In this study, based on a collected dataset with 226 entries, the multivariate adaptive regression splines model algorithm is used to predict essential soil compaction parameters, including optimum water content and maximum dry density, according to six factors (liquid limit, plastic limit, compaction energy, sand content, fines content, and gravel content). The hyperparameter of the multivariate adaptive regression splines model is searched for using the grid search approach with cross-validation strategies. To evaluate the performance of the proposed machine learning method, three metrics (root-mean-square error, mean absolute error, and coefficient of determination) are applied. The results show that the performance of the proposed model is excellent, with a high coefficient of determination and a low root-mean-square error and mean absolute error. Thus, the model’s robustness and reliability in predicting soil compaction parameters are all very high.

The following article, by Gajan (contribution 17), predicts the acceleration amplification ratio of rocking shallow foundations. In this study, based on a dataset from 140 rocking foundation experiments comprising a total of 9 series of centrifuge and shaking table experiments, the maximum acceleration transmitted to structures on rocking shallow foundations during earthquake loading is predicted by various machine learning models (including artificial neural network, k-nearest neighbors regression, support vector regression, random forest, adaptive boosting regression, and gradient boosting regression models) according to three non-dimensional rocking system capacity parameters (critical contact area ratio of the rocking foundation, slenderness ratio of the rocking structure, and rocking coefficient of the soil–foundation structure system) and two earthquake loading demand parameters (peak horizontal ground acceleration of earthquake shaking and arias intensity of earthquake). Here, the acceleration amplification ratio is defined as the maximum acceleration at the gravity center of a structure by the peak ground acceleration of the earthquake. To evaluate the performance of the machine learning models, two metrics (mean absolute percentage error and mean absolute error) are applied. The results show that the artificial neural network model is the most accurate and most consistent.

The study by Yang et al. (contribution 18) focuses on the prediction of the advanced rate of dual-mode shield tunneling in complex strata. In this study, based on the geological and on-site monitoring parameters of dual-mode shield tunneling collected from the left tunnel of Shenzhen Metro Line 13 (China), the advanced rate of shield tunneling is predicted using a long short-term memory recurrent neural network. To this end, the influence factors of advanced rate of shield tunneling, including tunneling parameters, shield tunneling mode, and strata parameters, are used. Moreover, the original data are preprocessed by the isolation forest algorithm and the improved mean filtering algorithm to obtain steady-state phase parameters. Meanwhile, the hyperparameters of the long short-term memory recurrent neural network are optimized using the particle swarm optimization, genetic algorithm, differential evolution, and Bayesian optimization algorithms. The performance of the optimized long short-term memory recurrent neural network is evaluated using the evaluation metrics of mean absolute error, root-mean-square error, and mean absolute percentage error, according to which the Bayesian optimization–long short-term memory recurrent neural network achieves superior performance. Finally, by combining the dropout algorithm and five-fold time series cross-validation with the best model, a multi-algorithm-optimized recurrent neural network model for tunneling speed prediction is constructed. The results show that the new prediction model has high prediction accuracy and operational efficiency under different excavation modes.

The last paper, by Gao et al. (contribution 19), focuses on the prediction of utility tunnel performance in soft foundations during operation periods. In this study, based on a total of 15,376 data collected from field tests on utility tunnel engineering in Suqian City, Jiangsu Province, China, utility tunnel performance in soft foundations during operation periods, represented by the main structure responses (displacement and stress), is predicted using deep learning according to five main disturbance factors (four vehicle operating load parameters and one operating time parameter). The deep belief network is applied to treat big data. To improve the network’s performance and optimize its hyperparameters, the whale optimization algorithm is applied, resulting in the construction of a new deep learning model. To evaluate the prediction accuracy of the proposed model, three evaluation indexes (root-mean-square error, mean absolute error, and correlation coefficient) are applied. The results show that the new deep learning model can accurately predict the performance of utility tunnels during operation periods, with suitable applicability.

3. Conclusions

The papers collated in this Special Issue encompass the applications of machine learning methods across almost all geotechnical engineering disciplines, including underground and foundation engineering and cover a variety of stages, including planning and design, construction, and operation. This indicates that machine learning can be used across all stages of geotechnical engineering—that is, its applications can cover the full geotechnical engineering lifecycle. Moreover, machine learning methods can prove useful in the field of geomechanics, e.g., in the evaluation of the physical and mechanical parameters of geomaterials (including soil and rock). In addition, this collection covers numerous machine learning methods, including regression methods (Gaussian process regression, regression trees, ensembles of regression trees, support vector machine, reduced-order model, random forest, extreme gradient boosting, light gradient boosting machine, artificial neural network, decision tree, multivariate adaptive regression splines model, k-nearest neighbors regression, adaptive boosting regression, and CatBoost algorithm); intelligent optimization methods, from swarm intelligence and evolutionary algorithms to nature-inspired computation (differential evolution algorithm, grey wolf optimization, backtracking search optimization algorithm, multi-verse optimizer, golden eagle optimizer, poor and rich optimization algorithm, Bayesian optimization algorithm, non-dominated sorting genetic algorithm (NSGA-II), particle swarm optimization, genetic algorithm, and whale optimization algorithm); and even some deep learning methods (two-dimensional convolutional neural network, long short-term memory recurrent neural network, and deep belief network). Many of the studies presented here construct data-driven models with the aid of machine learning methods. For these studies, the key is to obtain a suitable dataset. Various methods are employed to achieve this goal, including field tests, laboratory tests, numerical simulation, previous studies, etc. Some of those datasets can be called big data.

In terms of the subjects covered by this Special Issue, the application of machine learning methods in geomechanics emerges as the main discussion topic, with eight papers. In seven of these, the research object is obtaining the properties of soil, as this can easily be achieved by tests. Of those seven papers, three focus on estimating mechanical parameters, another three on estimating physical parameters, and only one on soil classification. The final paper in this group of eight analyzes the mechanical parameters of rock. In these studies, information about the property parameters of geomaterials generally comes from laboratory tests.

The next main topic in this Special Issue is the application of machine learning methods in underground engineering, and there are six papers in this field. Among them, the most popular research object is the construction stage of engineering, which is the focus of four papers. Three of these are on the back analysis of tunnels and one on ground subsidence risks for underground utilities. Engineering during the design stage is the research object of one paper, which determines shield tunneling parameters. Finally, there is one paper whose research object is engineering during the operation period. It analyzes utility tunnel performance in soft foundations affected by operation factors.

The third major topic in this Special Issue is the application of machine learning methods in foundation engineering, which is discussed in four papers. The majority are concerned with engineering during the construction stage, with three papers covering three different research objects—the undrained bearing capacity of skirted foundations, the interaction between soil and structure, and the dynamic response of rock foundations. In the remaining paper, the research object is engineering during the design period. In this study, the optimization of a foundation pit dewatering design is conducted.

The last topic in this Special Issue is the application of machine learning methods in the planning of geotechnical engineering, with only one paper concentrating on this area. This paper focuses on the identification of geophysical prospecting information.

From the above analysis, it is evident that the geomechanics subjects in this compilation of articles are almost exclusively the parameters of geomaterials, and that one main geomechanics subject is lacking, namely the constitutive model of geomaterials. Moreover, in terms of geotechnical engineering subjects, a major area, namely slope engineering, is equally missing from this Special Issue. On top of the subjects mentioned above, machine learning methods can also be applied in the study of engineering disasters related to geotechnical engineering. Therefore, the papers in this Special Issue are only some of the new developments in the application of machine learning in geotechnical engineering, and should be seen not only as new results, but also as starting points, inviting readers to conduct future studies on the themes explored here.

As a final note, I would like to highlight the particularity that all papers in this Special Issue are on the construction of data-driven models, which is the main application of machine learning methods in geotechnical engineering. However, datasets obtained in geotechnical engineering, no matter what method is used (including field tests, laboratory tests, and numerical simulations), are not complete datasets, and their number is very limited; that is, these datasets only describe very limited, partial properties of real engineering. Therefore, purely data-driven models will run into essential problems. However, the properties of real engineering can partly be described by mechanical models on the soil and rock mechanics. Therefore, in order to apply machine learning in geotechnical engineering, mechanical models should be included as well, as is the case in physics-based machine learning [20]. Moreover, to obtain more big datasets, the development of modern monitoring technology is another way that will promote the application of machine learning in geotechnical engineering.