Research Progress of Machine Learning in Deep Foundation Pit Deformation Prediction

Abstract

During deep foundation pit construction, slight improper operations may lead to excessive deformation, resulting in engineering accidents. Therefore, how to accurately predict the deformation of the deep foundation pit is of significant importance. With advancements in artificial intelligence technology, machine learning has been utilized to learn and simulate complex nonlinear relationships among various factors influencing foundation pit deformation. Prediction accuracy is significantly improved, and the dynamic trend of foundation pit deformation is accurately grasped to curb the risk of safety accidents. This paper systematically reviews the current applications of machine learning in deep foundation pit deformation prediction. The fundamental principles of machine learning models, including neural networks, support vector machines, and Bayesian networks, are elaborated in the context of their application to deep foundation pit deformation prediction. The application effects of various machine learning models in predicting deep foundation pit supporting structure deformation, surrounding surface settlement, and assessing foundation pit risks are summarized. The limitations and future development prospects of current machine learning models for deformation prediction in deep foundation pit construction are discussed. The research results offer valuable insights for the application and advancement of machine learning in the deep foundation pit deformation prediction field.

1. Introduction

In recent years, rapid economic growth has led to the saturation of ground space utilization. Therefore, higher requirements have been proposed for the development of underground space, leading to the emergence of a significant number of deep foundation pit projects [1]. Due to the increasing depth of building foundations, the construction environment of deep foundation pit projects has become more complex. Even minor errors during the construction process may result in excessive deformation of the deep foundation pit. Once the deformation of the foundation pit exceeds the safe range, it is highly likely to trigger a series of accidents, including foundation pit collapse, building inclination, and even structural collapse [2,3,4]. Such incidents significantly compromise construction safety and the surrounding environment, leading to direct economic losses. Therefore, accurate prediction of deformation is particularly critical during the construction of deep foundation pits. By predicting the deformation of deep foundation pits, construction personnel can promptly take targeted preventive measures to effectively decrease the probability of accidents.

With rapid advancements in computational capabilities and theoretical breakthroughs in artificial intelligence, machine learning has been increasingly implemented in the construction industry. These applications include materials optimization design [5,6,7], performance prediction of construction materials [8,9,10], and structural damage identification [11,12]. Currently, machine learning has been gradually infiltrated and applied to foundation pit engineering [13,14,15]. The primary research methods for predicting deep foundation pit deformation include theoretical analysis [16,17,18,19,20], numerical simulation [21,22,23,24,25], and machine learning [26,27,28], among others. Theoretical analysis relies on numerous assumptions, making it difficult to fully capture the complexity of the actual situation. Numerical simulations are unable to fully simulate the nonlinear characteristics of soil and do not adequately account for the effects of time and space on deformation. Compared with other research methods, machine learning exhibits strong applicability and high prediction accuracy. It can effectively simulate and predict the complex nonlinear relationships among multiple influencing factors, which are difficult to express using traditional explicit functions. Research on machine learning for deep foundation pit deformation prediction primarily focuses on the following two aspects. The first aspect is model optimization. To enhance prediction accuracy and minimize errors in machine learning when dealing with complex nonlinear relationships, time series, and high-dimensional data in deep foundation pit deformation, optimization algorithms and data processing techniques are implemented to improve model performance [29,30]. The second aspect involves model selection and application. Different machine learning models exhibit distinct advantages and limitations in deformation prediction. Therefore, suitable models are selected and applied based on specific requirements in practical engineering.

In light of the aforementioned aspects, numerous scholars have conducted extensive research and achieved significant results. Machine learning has demonstrated success in practical engineering applications. This paper first summarizes the commonly used machine learning prediction models and their optimization strategies in the field of deep foundation pit engineering. Subsequently, research advancements in various machine learning models in the field of deep foundation pit deformation prediction are summarized. Detailed introductions are provided regarding the application of machine learning in deformation of supporting structures, surrounding surface settlement, soil parameter analysis, and risk assessment. Furthermore, the applicability of different machine learning models across various application domains is summarized, and measures to optimize the prediction performance are proposed. Finally, the future development direction and prospects of machine learning in the field of deep foundation pit deformation prediction are elaborated. This offers insights and guidance for future research on deep foundation pit deformation prediction.

2. Machine Learning Model

With the increasing application of machine learning in deep foundation pit engineering, optimizing individual prediction models is of significant importance to further enhance the accuracy and performance of machine learning-based deformation predictions. Based on the fundamental principles of machine learning models, this paper systematically reviews optimization measures addressing the limitations of these models and analyzes the impact of such measures on the prediction accuracy. The aim is to provide a reference for the optimization of prediction models.

2.1. Neural Network

The neural network consists of neurons and synaptic connections. The connection strength and threshold between neurons are determined through learning from existing training samples [31]. Currently, back propagation (BP) neural networks, Elman recurrent neural networks, and long short-term memory (LSTM) neural networks are extensively studied in the field of deep foundation pit deformation prediction.

2.1.1. BP Neural Network

The structure of the BP neural network primarily comprises an input layer, one or more hidden layers, and an output layer, with full connections between these layers [32]. Its topology is illustrated in Figure 1.

Due to issues associated with BP neural networks, such as the tendency to fall into local optima, slow convergence speed, or even non-convergence, the prediction error for deep foundation pit deformation has increased. Consequently, many scholars have conducted extensive research on optimizing BP neural networks for deep foundation pit deformation prediction. Currently, the optimization of machine learning models such as BP neural networks can be categorized into two types. The first approach is to utilize data processing technology for optimizing monitoring data. The second approach involves optimizing the network structure and parameters. An optimization diagram for BP neural networks (or other machine learning models) is presented in Figure 2.

Due to errors in the monitoring data of deep foundation pits, noise and outliers may be introduced into the training data, potentially compromising the training efficiency and prediction accuracy of the model. Many scholars [33,34,35] have utilized wavelet transform for denoising, decomposing, and reconstructing monitoring data. They further divide the monitoring data into trend term and error term. Based on this division, the prediction model has been established to predict both the trend term and the error term. Wavelet transform has a wide range of applicability and is not limited to BP neural network. It is often used in the data processing of various machine learning models [36,37,38,39,40]. This provides accurate and reliable data support for the training of machine learning models.

To obtain the optimal weights and thresholds of the BP neural network, a deep foundation pit deformation prediction model with stable performance has been constructed. Some scholars have utilized the global optimization capabilities of genetic algorithms, sparrow search algorithms, particle swarm optimization, and other optimization algorithms to optimize the weights and thresholds of BP neural networks [41,42,43,44,45,46]. Different optimization algorithms exhibit varying degrees of effectiveness in optimizing BP neural networks, and selecting an appropriate optimization algorithm is crucial for enhancing prediction performance. The genetic algorithm, artificial bee colony algorithm, and sparrow search algorithm exhibit strong global optimization capabilities, significantly enhancing the prediction performance of the BP neural network. In contrast, the whale optimization algorithm and bat algorithm demonstrate relatively poor optimization performance. Figure 3 illustrates the optimization performance of the BP neural network achieved by ten optimization algorithms. A coefficient of determination (R²) closer to 1 indicates better model performance, while a root mean square error (RMSE) closer to 0 suggests higher prediction accuracy. Additionally, existing optimization algorithms can be further enhanced to improve their optimization capabilities. Cui et al. [47] enhanced the supply and demand optimization algorithm. Experimental results demonstrated that the improved algorithm outperformed the genetic algorithm and the artificial bee colony optimization algorithm in optimizing BP neural network parameter selection. In the practical application of deep foundation pit engineering, it is essential to select an appropriate optimization algorithm based on the specific characteristics of the problem at hand. Alternatively, one may consider enhancing the existing algorithm to enhance the training effectiveness of the BP neural network.

The selection of feature vectors in the BP neural network significantly influences the model’s performance. Wang et al. [49], based on the engineering background of 30 foundation pit cases, employed quantitative theory III to analyze the influence of various factors on foundation pit deformation. The selected factors were utilized as the feature vectors for the BP neural network. Figure 4 presents a comparison between the prediction results of the BP neural network optimized using the feature vector and those of the unoptimized model. The selection of an appropriate feature vector set can significantly enhance the prediction accuracy and generalization capability of the model, while reducing errors in the prediction of deep foundation pit deformation. In addition, to simplify the network structure and enhance training efficiency, the BP neural network model is integrated with other models, such as the radial basis function (RBF) neural network [50] and the grey GM (1,1) model [51]. On this basis, the optimization algorithm can be integrated with data processing techniques to further enhance prediction performance [52,53].

2.1.2. Elman Recurrent Neural Network

The Elman recurrent neural network is supported by the BP neural network, with the context layer incorporated into the hidden layer. The number of neurons in the context layer is equal to that in the hidden layer. The context layer is designed to accept the feedback signal from the hidden layer through a one-step delay operator, thereby enabling memory functionality. This mechanism allows the neural network to adapt to time-varying characteristics [54]. The topological structure is shown in Figure 5.

Currently, feedforward neural networks such as the BP neural network are predominantly utilized in the field of deep foundation pit deformation prediction, and various combined models based on the BP neural network have been derived. Several researchers have applied the Elman recurrent neural network to the prediction of deep foundation pit deformation. Compared with the single BP neural network model, the Elman model demonstrates superior accuracy in medium- and long-term predictions [54].

Since the Elman recurrent neural network is supported by the BP neural network, its initialization weight threshold also exhibits a degree of blind randomness. Progress has been achieved in the selection of weights and thresholds for Elman recurrent neural networks.

Table 1. Optimization algorithm.

Document	Optimization Algorithm
Ren [55]	Sparrow search algorithm
Sun et al. [56]	Improved mind evolutionary algorithm
Zhang [57]	Sparrow search algorithm
Guo et al. [58]	Genetic algorithm
Zhou et al. [48]	Adaptive mutation–sparrow search algorithm

summarizes the research findings on weight and threshold selection for Elman recurrent neural networks. Figure 6 illustrates the optimization performance of the Elman model using different optimization algorithms. As demonstrated in Table 1 and Figure 6, the Elman model’s prediction performance is improved when optimized by the optimization algorithm. The sparrow search algorithm has been widely utilized in optimizing the Elman model and its improvement effect is better. However, optimization algorithms may converge to local optima when addressing certain problems. To enhance their global search capabilities and mitigate the risk of becoming trapped in local optima during the search process, numerous scholars have proposed improvements and innovations to these algorithms. Zhou et al. [48] employed adaptive mutation (AM) to enhance the sparrow search algorithm, thereby improving its search capability and stability. The optimization performance of the enhanced sparrow search algorithm is illustrated in Figure 7. In future research, advanced theories or methods could be integrated with the optimization algorithm to enhance its optimization capabilities, thereby improving the accuracy and stability of deep foundation pit deformation predictions.

Due to the influence of the construction environment, the monitoring data of deep foundation pits exhibit significant fluctuations and non-stationarity, resulting in poor prediction performance. To address the issue of poor prediction performance caused by the influence of monitoring data on the Elman recurrent neural network, Zhao et al. [59] introduced phase space reconstruction technology to reconstruct the monitoring data sequence of the foundation pit. This approach significantly enhanced the prediction accuracy of the Elman recurrent neural network model. Xu [60] applied empirical mode decomposition to filter field monitoring data. The data were decomposed and reconstructed to obtain stable monitoring results. Sun et al. [56] utilized variational mode decomposition to decompose the time series of foundation pit displacement into trend, periodic, and random terms and analyzed the rationality of the decomposition for each sub-displacement sequence. The Elman model was employed to predict the trend, periodic, random terms, and decomposition error, and the prediction results were superimposed to obtain the total displacement prediction.

2.1.3. LSTM Neural Network

The LSTM neural network is a specialized type of recurrent neural network within the domain of deep learning. It incorporates a memory cell unit within its hidden layer, which consists of a cell state and three regulatory gates: the input gate, the forget gate, and the output gate [61]. These gates are designed to protect and regulate the cell state, enabling the network to perform functions such as memorization and forgetting. The architecture of the LSTM neural network is illustrated in Figure 8. X_t is the input at time t. i_t, f_t, and o_t are input gate, forget gate, and output gate, respectively. C_t and C_t−1 are the cell state at time t and t − 1, respectively (long-term memory). $\widetilde{C_t}$ is the candidate state. h_t and h_t−1 are the hidden states at t and t − 1, respectively (short-term memory). σ and tanh are sigmoid function and tanh function, respectively. + and × represent the addition and multiplication of vectors, respectively.

The LSTM neural network model is capable of accurately capturing the long-term dependencies between temporal and spatial sequences while effectively mitigating the issue of gradient vanishing commonly encountered in traditional recurrent neural networks [63,64,65]. Due to the complex spatiotemporal characteristics and highly nonlinear nature of deep foundation pit data, the data capacity for feature extraction is constrained. As a result, nonlinear and non-stationary sequences are not adequately handled. To accurately predict the nonlinear and complex time series in deep foundation pit engineering, Zhang et al. [66] employed the pole symmetric mode decomposition algorithm to identify and decompose the monitoring data at multiple scales. They reconstructed the multi-dimensional phase space based on the fuzzy entropy theory. An LSTM neural network model optimized by the artificial jellyfish search algorithm was developed, and this model was utilized to predict the reconstructed subsequences. Ma et al. [67] employed bidirectional long short-term memory networks to predict the time series of deformation monitoring, achieving more comprehensive feature analysis. They also utilized attention mechanisms to enable the neural network to focus on learning the important features of the data.

Some scholars [68,69,70] have found that the convolutional neural network (CNN) model could effectively extract input features and integrate them with the LSTM model to construct the CNN-LSTM model. Based on the aforementioned research results, Li et al. [71] proposed a method to further optimize the utilization of computing resources and enhance prediction accuracy. This approach involved increasing the depth of data mining by integrating LSTM and an attention mechanism, building upon CNN-based data space feature extraction. This integration took into account data temporality and weight characteristics. Separately, Fang et al. [72] utilized variational mode decomposition to address the nonlinear and non-stationary issues inherent in the original time series data, providing a more stable data foundation for the CNN-LSTM model.

In addition, the complexity of constructing LSTM prediction models and the substantial amount of long-term data required for model training have limited the research and application of the model in the deep foundation pit deformation prediction field. Cho et al. [73] proposed a simplified version of the LSTM model in 2014, known as the gated recurrent unit (GRU) model. In the context of deep foundation pit deformation prediction, the GRU model exhibits fewer structural parameters and higher prediction accuracy compared with the LSTM model [74,75]. Currently, the research on the application of LSTM models for deep foundation pit deformation prediction remains insufficient. Future studies could further explore the potential of deep learning techniques, such as LSTM neural networks, and combine them with advanced technologies like optimization algorithms and big data to enhance their applicability in this field.

2.2. Support Vector Machine

The support vector machine (SVM) is a machine learning method designed for small-sample scenarios, grounded in statistical learning theory [76]. In SVM classification tasks, determining the optimal decision boundary is crucial. The optimality of the decision plane is evaluated based on whether the distance between the decision boundary and the nearest data points from both classes is maximized, as illustrated in Figure 9.

In the deep foundation pit deformation prediction study, the SVM model’s prediction accuracy depends on the appropriateness of its basic parameters and the relevant parameters of the kernel function. Consequently, optimizing the SVM model involves selecting the optimal parameter combination. With the emergence of swarm intelligence optimization algorithms and other optimization techniques, an effective approach has been provided to optimize the parameter selection of SVM models. This approach has garnered increasing attention from researchers. Table 2 presents the optimization algorithms employed by scholars and the corresponding parameters of the SVM model.

Suykens et al. [77] proposed the least squares support vector machine (LSSVM) method, which represents an extension of the standard support vector machine. LSSVM obtains the decision function by solving least squares linear equations, thereby avoiding complex quadratic programming problems. The LSSVM model based on this method demonstrates good reliability and practicability in the deep foundation pit deformation prediction field [78,79]. However, the LSSVM model’s prediction accuracy remains dependent on the selection of its parameters, which is largely dependent on experience and trial calculations. Currently, there is no uniform rule for determining these parameters [80]. In addition, the irregularity of training data can lead to model overfitting. To address this issue, some scholars have conducted research on parameter optimization and data processing techniques for LSSVM. Table 3 summarizes the optimization algorithms and data processing methods employed by researchers in the deep foundation pit deformation prediction field using the LSSVM model.

From Table 1 and Table 2, it is evident that the limited variety of optimization algorithms for SVM parameter selection constrains the potential of SVM in deep foundation pit deformation prediction. In future research, it would be beneficial to explore the integration of advanced optimization algorithms, such as the zebra optimization algorithm and the spider monkey optimization algorithm, with the SVM model. Additionally, combine SVM with deep learning models, such as CNN and LSTM. By leveraging the strengths of deep learning in feature extraction and complex pattern recognition, along with SVM’s robust capabilities in classification and regression tasks, a more intelligent and accurate prediction model is constructed.

Table 2. Optimization algorithm and optimization parameters.

Document	Optimization Algorithm	Optimization Parameter	Annotation
Jin et al. [81]	Differential evolution algorithm	g, c	G, g, and σ are radial basis kernel function parameters. ε is insensitive loss factor. c is penalty parameter. f(x) is decision function.
Cui et al. [82]	Differential evolution algorithm	f(x)
Chen et al. [83]	Ant colony optimization algorithm	σ, ε, c
Shi et al. [84]	Genetic algorithm	σ, c
Liu [85]	Particle swarm optimization algorithm	c, g
Song et al. [86]	Simulated annealing algorithm–particle swarm optimization algorithm	G, c
Niu et al. [87]	Genetic algorithm	g, c

Table 2. Optimization algorithm and optimization parameters.

Document	Optimization Algorithm	Optimization Parameter	Annotation
Jin et al. [81]	Differential evolution algorithm	g, c	G, g, and σ are radial basis kernel function parameters. ε is insensitive loss factor. c is penalty parameter. f(x) is decision function.
Cui et al. [82]	Differential evolution algorithm	f(x)
Chen et al. [83]	Ant colony optimization algorithm	σ, ε, c
Shi et al. [84]	Genetic algorithm	σ, c
Liu [85]	Particle swarm optimization algorithm	c, g
Song et al. [86]	Simulated annealing algorithm–particle swarm optimization algorithm	G, c
Niu et al. [87]	Genetic algorithm	g, c

Table 3. Optimization algorithm and data processing.

Document	Optimization Algorithm	Optimization Parameter	Data Processing Technique	Annotation
Xu et al. [88]	Grid search algorithm	γ, σ	/	γ and C are regularization parameters. C and d are penalty parameters. σ, g, and σ2 are radial basis kernel function parameters. μ is kernel function width. “/” represents no special processing of the data.
Cao et al. [89]	Particle swarm optimization algorithm	σ, c	Phase space reconstruction theory
Li et al. [90]	Particle swarm optimization algorithm	σ, d	Local mean decomposition
Xie et al. [91]	Fruit fly algorithm	σ, C	Phase space reconstruction theory
Jia et al. [92]	Improved Skyhawk algorithm	γ, g	/
Liu et al. [93]	Particle swarm optimization–genetic algorithm	σ, γ	Adaptive noise-complete ensemble empirical mode decomposition

Table 3. Optimization algorithm and data processing.

Document	Optimization Algorithm	Optimization Parameter	Data Processing Technique	Annotation
Xu et al. [88]	Grid search algorithm	γ, σ	/	γ and C are regularization parameters. C and d are penalty parameters. σ, g, and σ2 are radial basis kernel function parameters. μ is kernel function width. “/” represents no special processing of the data.
Cao et al. [89]	Particle swarm optimization algorithm	σ, c	Phase space reconstruction theory
Li et al. [90]	Particle swarm optimization algorithm	σ, d	Local mean decomposition
Xie et al. [91]	Fruit fly algorithm	σ, C	Phase space reconstruction theory
Jia et al. [92]	Improved Skyhawk algorithm	γ, g	/
Liu et al. [93]	Particle swarm optimization–genetic algorithm	σ, γ	Adaptive noise-complete ensemble empirical mode decomposition

2.3. Bayesian Network

The Bayesian network (BN) integrates the probability theory and statistical methods, employing graphical representations to analyze problems and predict outcomes through the use of network nodes, directed edges, and conditional probability tables [94]. The network nodes represent variables, the directed edges represent conditional dependencies between nodes, and the conditional probability tables define the relationships from parent nodes to child nodes [95]. For event L, set the set of all variables that affect its occurrence as X = (X₁, X₂, X₃, ⋯, X_n). The Bayesian inference formula is then expressed as:

$$P(X_i\left|L\right)={\displaystyle \frac{P\left(L\right|X_i\left)P\right(X_i)}{P\left(L\right)}}={\displaystyle \frac{P\left(L\right|X_i\left)P\right(X_i)}{{\Sigma }_{j=1}^{ n}P\left(L\right|X_i\left)P\right(X_j)}}$$

where $X_i$ represents the risk factor in set X, $P(X_i)$ denotes the prior probability, $P\left(L\right|X_i)$ is the conditional probability, $P\left(L\right)$ is the probability of event L, and $P(X_i\left|L\right)$ represents the posterior probability.

There are two main methods to determine the Bayesian network structure [96]. The first approach involves establishing causal relationships between nodes based on domain experts’ prior knowledge. The second approach involves constructing the structure of the Bayesian network through data-driven learning. This method requires collecting a sufficient number of deep foundation pit deformation samples and performing multiple iterative learnings. The construction of the network structure limits the application of BN. Tang et al. [97] proposed a method to derive all conditional probability data from partial data. However, this method did not address the issue of BN structure construction. Several scholars [98,99,100] have conducted research on the complex issue of BN model construction. By transforming fault tree models into BN models, the structural construction obstacles are circumvented. The model diagrams of the fault tree and Bayesian network are illustrated in Figure 10.

Due to the influence of traditional probability methods on BN, uncertainty reasoning based on precise probability still faces limitations [101]. The acquisition of precise probability relies on extensive statistical data from historical failure cases. However, owing to the unique nature of deep foundation pit engineering, historical data for many nodes are often scarce or entirely unavailable. Some scholars [99,100] have integrated the fuzzy theory with Bayesian networks to estimate the probabilities of nodes in the network, thereby partially overcoming the limitations of traditional probability methods. By incorporating the time factor, the Bayesian network (BN) model can be extended to a dynamic Bayesian network (DBN). Shen et al. [95] employed the fuzzy set theory and an improved similarity aggregation method to determine the prior and conditional probabilities of network nodes in the DBN model. Furthermore, Lei et al. [102] combined a fuzzy dynamic Bayesian network with an enhanced evidence theory to address uncertainties in complex scenarios.

In addition, some scholars [103,104] have integrated the pair–copula theory, commonly used in financial forecasting, with Bayesian network models to establish the PCBN model. This model combines the flexibility of pair–copula in handling complex and variable data with the ability of Bayesian networks to address uncertainty.

3. Application Research of Deep Foundation Pit Deformation Prediction Based on Machine Learning

Machine learning can accurately predict the deformation of deep foundation pits during construction, including surrounding surface settlement and the displacement of supporting structures. Additionally, machine learning can effectively identify potential safety hazards based on deformation predictions, conduct risk analysis, and enhance the stability and safety of deep foundation pit engineering.

3.1. Displacement Prediction of Supporting Structure (Building Envelope)

3.1.1. Underground Continuous Wall

In the early stages of deformation prediction for underground diaphragm walls, many scholars established traditional machine learning models, such as BP neural networks [105,106] and SVM models [107], to predict horizontal displacement. However, with advancements in artificial intelligence technology, the variety of machine learning methods has significantly increased. Consequently, deep learning concepts, such as CNN and recurrent neural network (RNN), have been proposed and applied to the deformation prediction of underground diaphragm walls.

To evaluate the deep learning model’s predictive performance for the horizontal displacement of underground diaphragm walls, Wang et al. [27] developed a genetic algorithm–generalized regression neural network (GA-GRNN) model. This model was used to predict the horizontal displacement of underground diaphragm walls in deep foundation pit engineering within soft soil areas at various depths and construction stages. The results demonstrated that the GA-GRNN model exhibited superior accuracy and stability compared with the genetic algorithm–BP (GA-BP) model. Zhang et al. [64] investigated the deformation prediction of underground diaphragm walls using different neural network models under foundation pit excavation conditions. The study revealed that the BP neural network exhibited better prediction accuracy during the initial stages of excavation. However, as time progressed, its prediction performance deteriorated. In contrast, the LSTM prediction model demonstrated stable performance, with errors fluctuating between −2.5 mm and 1.5 mm throughout the excavation period. The overall error was stable, the trend was consistent, and the prediction accuracy was satisfactory. The comparative predictions of the two models during the excavation period are illustrated in Figure 11. Xu et al. [75] investigated the deformation prediction of supporting structures at different stages and found that LSTM and GRU models are capable of capturing the temporal dependencies in the input data. This is because these models account for the influence of time-series inputs on the output, which aligns more closely with the actual deformation behavior of supporting structures during foundation pit excavation. Consequently, these models demonstrate superior prediction performance. The findings suggest that deep learning models, such as LSTM neural networks, are more powerful and better aligned with actual conditions in predicting the deformation of underground continuous walls compared with traditional machine learning models.

The research has shown that the selection of training samples is crucial when constructing machine learning models for predicting the deformation of underground continuous walls. Given the large volume of monitoring data available for underground continuous walls, some scholars have selected factors that significantly influence the supporting structure as training samples. Xu et al. [50] used soil cohesion, internal friction angle, height of the underground continuous wall, foundation pit excavation depth, and measuring point depth as input variables for a BP-RBF prediction model. Zeng et al. [108] selected the construction period, excavation depth, groundwater level, and daily temperature as inputs for the BP neural network model, with deformation as the output. During the construction process, numerous factors contribute to the deformation of the underground continuous wall, some of which are critical, such as the timing of support construction [109]. By reasonably quantifying these key factors and combining them with actual deformation monitoring data as training samples, dynamic training, adjustment, and updating of machine learning models can be achieved. This approach can further enhance the prediction accuracy, generalization ability, and robustness of the underground continuous wall deformation prediction mode.

3.1.2. Supporting Pile

In the supporting pile’s prediction deformation, many scholars have utilized machine learning to predict the pile’s horizontal displacement. Currently, research on the supporting pile’s displacement prediction primarily focuses on bored piles. Among the methods employed, the BP neural network model [110,111] and the GA-BP neural network model [41,112] have been widely used. The implementation process of the BP neural network optimized by the genetic algorithm is illustrated in Figure 12. When the GA-BP neural network is applied to predict the horizontal displacement of bored piles at various depths, the deviation of the predicted displacement values meets the requirements for construction safety, providing an accurate reference for engineering applications. The distribution of the horizontal displacement prediction errors of the GA-BP neural network at different depths is presented in Figure 13.

Other machine learning models demonstrate better prediction performance for bored piles, with their accuracy meeting engineering requirements. For instance, the LSSVM model [78] achieves an average relative error of less than 2%, while the random forest model yields a minimum relative error of 2.09% [113]. Figure 14 illustrates the relationship curve between the predicted and measured values of the bored pile’s horizontal displacement. It is evident that there is no absolute optimal machine learning model for bored pile deformation prediction. However, with advancements in machine learning technology, the accuracy of deformation prediction for bored piles is expected to continue improving.

In the aforementioned research, the constructed model primarily focuses on the short-term prediction of horizontal displacement in bored piles. However, given the long-term nature of deep foundation pit engineering, the machine learning model faces challenges in achieving effective long-term predictions for bored pile deformation in practical applications. Niu et al. [87] developed a combined SVM–autoregressive moving average model utilizing both one-step prediction and multi-step rolling prediction methods to predict the short-term and long-term horizontal displacement of bored piles. The average relative errors for one-step prediction were −0.15%, 0.24%, and −1.70%, while those for multi-step rolling prediction were −3.02%, 7.14%, and −9.54%. Li et al. [71] proposed a CNN-LSTM model incorporating the attention mechanism (AM) to study the long-term maximum deformation values of three different supporting piles in deep foundation pits in Beijing. Furthermore, the accuracy of machine learning models is highly dependent on the quantity and quality of the training samples. During the early stages of foundation pit construction, monitoring data for supporting piles are often limited, which can reduce the generalization capability of the model and consequently diminish its long-term prediction performance. In the future, a large number of deep foundation pit engineering cases could be collected to establish a database and data analysis platform for data sharing and machine learning model training. However, it is worth noting that the current research remains predominantly focused on bored piles, while the exploration and research on other types of piles, such as pipe piles, are still insufficient.

3.2. Prediction of Surrounding Surface Subsidence

To improve the accuracy and efficiency of surface subsidence prediction around deep foundation pits, many scholars have developed prediction models based on machine learning, achieving significant research progress. Over the past few decades, numerous models have been widely applied in the field of surface subsidence prediction. These include the random forest model [114,115], BP neural network model [116,117], SVM model [92,93], XGBoost model [118,119], extreme learning machine [120,121,122], RBF neural network [123], and recurrent neural network [124], among others.

Some scholars have integrated different models and algorithms to leverage their respective advantages, thereby better capturing the linear and nonlinear relationships in settlement data. Qiao et al. [125] proposed a novel gray wolf optimization–extreme learning machine model for training and predicting surface subsidence data. Zhang et al. [126] combined an optimized gray Verhulst model with a BP neural network model to construct a hybrid model. Liu et al. [127] optimized the RBF neural network using the K-means clustering algorithm, developed a prediction model for the maximum surface settlement around foundation pits, and achieved advanced prediction prior to construction. Zhang et al. [128] established an improved random wavelet network foundation pit surface settlement prediction model with water level drawdown, compression modulus, thickness, consolidation degree, and monitoring point orientation of the soil layer as input parameters and total settlement of the foundation pit as an output parameter. Qin et al. [129] proposed a multi-model fusion method for land subsidence prediction based on stacking ensemble learning. This approach integrates multiple models, including random forest, SVM, and artificial neural networks. A schematic diagram of the stacking ensemble model is presented in Figure 15.

With the rapid development of artificial intelligence, numerous deep learning methods have emerged, such as LSTM neural network, GRU neural network, and CNN. Many scholars have applied these methods to the field of surface settlement prediction around deep foundation pits. To more accurately predict the temporal characteristics of settlement data in foundation pit engineering, Tang et al. [69] proposed hybrid time-series neural network models, namely CNN-LSTM and CNN-GRU. Li et al. [130] employed a modal decomposition method to decompose settlement data into different sequences and established a GRU model to predict each sequence. The final settlement prediction value was obtained by summing the predictions of these individual sequences. The settlement monitoring data in deep foundation pit engineering are related in time dimension and space dimension. Some scholars have observed that existing surface subsidence prediction models primarily focus on the temporal correlation of single-point data while neglecting the spatial correlation between adjacent monitoring points. To address this issue, Zhang et al. [131] proposed a method that combines CNN to capture the spatial characteristics of settlement data with the GRU neural network to analyze the temporal patterns of settlement data. Additionally, the self-attention mechanism is employed to capture the internal correlations within the settlement data, enabling the simultaneous extraction of spatial and temporal features to predict settlement values. Compared with other deep learning models, this approach demonstrates higher prediction accuracy and better stability. The performance metrics of various deep learning models for predicting surface subsidence deformation are presented in Figure 16. The results indicate that a well-designed combination of different deep learning models can significantly enhance the settlement prediction accuracy and improve the model’s generalization capability.

3.3. Research Progress of Soil Parameters

The theoretical analysis of deep foundation pit deformation relies on accurate soil parameters, which are typically obtained through laboratory tests. However, due to factors such as sampling disturbance, instrument accuracy, and soil heterogeneity, the test parameters often deviate from actual field conditions. In practical engineering, these uncertainties can lead to significant errors in the analysis results. With the increasing application of machine learning in various fields, many researchers have utilized its nonlinear mapping capabilities to describe the relationship between soil parameters and displacement in displacement back analysis. By inverting these parameters, more accurate soil properties can be obtained for theoretical analysis or numerical simulations of deformation prediction. This approach helps reduce errors in the analysis results and ensures that they better reflect the actual conditions of the project.

Wang et al. [132] performed a back analysis based on the measured maximum horizontal displacement of an underground continuous wall. They trained a BP neural network using the calculation parameters from FLAC forward analysis as target values and subsequently back analyzed the mechanical parameters of key soil layers in the project using the measured data. He et al. [133] employed a BP neural network as a forward modeling tool, replacing the finite element method, to describe the nonlinear mapping between soil parameters and support displacement. They also utilized a clonal selection algorithm as an inversion tool to determine the soil parameters of a deep foundation pit through inversion analysis. Liu et al. [134] and Xiao et al. [135] employed the displacement back analysis method based on a BP neural network to analyze the sensitivity of key physical and mechanical parameters of the soft soil layer. Forward numerical calculations were performed using the parameters obtained through inversion. The error between the calculated horizontal displacement of the retaining pile and the monitored values was less than 5%. The derived soil parameters can serve as reference values for similar projects in local deep soft soil layers. A comparison between the inverted values and the monitored values of the horizontal displacement of the retaining pile is presented in Figure 17.

Zou et al. [136] employed finite difference numerical simulation and a BP neural network algorithm to invert the elastic modulus, Poisson’s ratio, cohesion, and internal friction angle of the Quaternary overburden and bedrock. The inverted elastic modulus of the Quaternary overburden was 23.0 MPa, with a Poisson’s ratio of 0.31, a cohesion of 37.5 kPa, and an internal friction angle of 26.8°. For the bedrock, the inverted elastic modulus was 2214.2 MPa, with a Poisson’s ratio of 0.28, a cohesion of 470.8 kPa, and an internal friction angle of 33.8°. The reasonableness and reliability of the inverted parameters were confirmed through verification using the typical cross-section enclosure structure of the foundation pit.

The aforementioned research indicates that, in the field of soil parameter inversion, machine learning studies predominantly focus on BP neural networks. Furthermore, the soil parameters obtained through machine learning inversion can not only be utilized for investigating deep foundation pit deformation but can also be applied to evaluate the internal forces and bending moments of supporting structures. This enhances the applicability and practicality of machine learning in soil parameter inversion for deep foundation pits. With the recent advancements in deep learning, future research could explore its application in soil parameter inversion to further improve the accuracy and efficiency of the inversion process.

3.4. Risk Analysis

3.4.1. Risk Management

With the increasing scale and complexity of deep foundation pit engineering projects, the risk and potential losses caused by foundation pit deformation have also risen significantly. To control construction risks and ensure the successful completion of such projects, effective risk management for foundation pit projects is particularly crucial. Yin et al. [54] integrated deformation data from deep foundation pit monitoring with an Elman neural network to predict the third monitoring data after the construction monitoring day. Based on this prediction, they calculated the corresponding risk level, enabling construction personnel to formulate appropriate preventive measures. Wang et al. [98] combined event tree and fault tree analyses to construct the BN model for the SMW supporting structure. They analyzed the probability of foundation pit accidents and identified the main basic events contributing to such accidents. Zhou et al. [137] developed the SVM prediction model to classify and predict the risks associated with deep foundation pits. This model does not require a large amount of data and can provide highly accurate predictions, enabling better risk control and management. Zhou et al. [138] proposed a risk prediction model for subway deep foundation pits based on the random forest algorithm and applied the model to a foundation pit engineering project at a subway station.

To mitigate the subjectivity in evaluation results, several scholars have investigated the subjectivity, dynamic changes, and randomness associated with the risk assessment of deep foundation pits. Song et al. [139] comprehensively took into account the subjectivity in experts’ cognition, the dynamic nature of the evaluation process, and the randomness of indicators. Utilizing the data envelope method, they calculated the index weights and, in conjunction with the BP neural network method, conducted dynamic evaluations of the deep foundation pit’s construction safety in subway stations. Wang et al. [100] proposed a method for evaluating the collapse risk of deep foundation pits based on a multi-state fuzzy Bayesian network. This method enables real-time dynamic risk analysis during foundation pit construction, allowing for a scientifically sound and reasonable assessment of collapse risks and the key risk factor’s identification. Ma et al. [140] established risk transfer nodes and observation nodes and introduced the noisy-max hypothesis to optimize the expert experience method in constructing the DBN risk analysis model. This approach accurately predicts the dynamic changes in confined water risk throughout the entire process of deep foundation pit construction.

3.4.2. Safety Analysis of Supporting Structure

The safety of deep foundation pit support structures and their impact on the surrounding environment have become increasingly significant. If the deformation of the support structure exceeds the safety threshold, it may lead to construction accidents. To address this, some scholars have converted monitoring and prediction data into risk metrics by predicting the deformation of each structural component in deep foundation pits. This approach enables the evaluation of the foundation pit’s safety status and facilitates risk classification. Xia et al. [141] developed an LSTM-based deep foundation pit deformation safety risk early warning model to predict the deformation of foundation pit supporting structures, surrounding roads, underground pipelines, and other related structures. By integrating a risk assessment method based on monitoring data, they dynamically evaluated the safety risks of deep foundation pits and determined the corresponding warning levels. Wei et al. [142] employed wavelet analysis, artificial neural networks, and Copula correlation analysis to establish a horizontal deformation prediction model for foundation pits, taking into account the influence of rainfall. This model was applied to predict the deformation of an actual deep foundation pit, enabling the issuance of risk warnings in advance.

In addition, the application of the reliability theory to address safety concerns in deep foundation pit support structures has garnered increasing attention. A series of studies have been conducted to tackle the issues of low computational efficiency and the difficulty in ensuring accuracy associated with traditional methods. Mao et al. [143] employed an artificial neural network model combined with the Monte Carlo method to analyze the overall displacement control reliability of rock-socketed support structures in two super-large and ultra-deep foundation pits. Their findings indicate that the target reliability index for foundation pit support structures can be appropriately reduced compared with that of permanent structures. Zhu et al. [144] proposed a Bayesian correction method for reliability analysis, which addressed the displacement monitoring reading errors caused by the insufficient burial depth of the inclinometer. Wu et al. [104] conducted a reliability analysis of deep foundation pit supporting structures using the PCBN model. Their study revealed that the reliability of the supporting structures was most significantly influenced by the vertical displacement of the pile top, the horizontal displacement of the pile body, and the deep horizontal displacement of the pile, while the groundwater level had the least impact.

4. Model Reliability Analysis

Table 4. Performance comparison of predictive models based on machine learning.

Prediction Model	Advantage	Insufficient
BP model	(1) Strong nonlinear mapping capabilities. (2) High prediction accuracy for short-term surrounding surface subsidence deformation. (3) A certain degree of fault tolerance.	(1) Prone to converge with local minima. (2) Long-term deformation prediction accuracy is relatively low. (3) Blind randomness of parameter selection.
Elman model	(1) Effectively process time series data. (2) Captures the time-dynamic characteristics of foundation pit deformation. (3) Storage and utilization of historical information.	(1) Less training data, easy to overfit. (2) Blind randomness of parameter selection.
LSTM model	(1) Effectively processing and memorizing long-term sequence data. (2) Avoids the problem of gradient disappearance or gradient explosion. (3) Analysis of deformation prediction under the combined action of multiple factors.	(1) Less training data, lower prediction accuracy. (2) Needs a lot of data and calculation data to train. (3) Key parameters are difficult to determine.
SVM model	(1) Solves the problem of high dimension. (2) Completes theoretical basis and system. (3) Small sample data prediction accuracy is high.	(1) Difficult to handle large-scale data. (2) Difficult to deal with unbalanced data. (3) Difficult to select kernel functions and related parameters.
BN model	(1) Graphic visualization, easy to understand. (2) Effectively deals with uncertainty for risk analysis.	(1) Dependence on prior probability. (2) Structure is more complex.
Combinatorial model	(1) Suitable for high-precision requirements of the project. (2) Effectively deals with outliers and noise, the stability and robustness of the model are high. (3) The principle of the partial optimization algorithm is simple, and the parameters are set lower.	(1) The model is complex and the parameter tuning is difficult. (2) The partially optimized model still has the risk of overfitting. (3) Partial optimization algorithms only consider the local optimum, not the global optimum.

presents a performance comparison of various machine learning prediction models. Based on the above application studies, it can be observed that current machine learning models exhibit distinct performance characteristics in predicting deep foundation pit deformation. Specifically, SVM demonstrates strong generalization capabilities when handling small sample datasets. However, its processing efficiency for large-scale data is relatively low. Neural network models, particularly deep learning models, exhibit significant advantages in capturing complex data relationships. Nevertheless, their training processes are time-consuming and prone to overfitting. Bayesian networks are commonly applied to risk analysis in deep foundation pit deformation. While combined models achieve high precision, they are often complex and require extensive training time. Therefore, when selecting a machine learning prediction model, it is essential to comprehensively consider the specific requirements of deep foundation pit engineering, data availability, and computational resources.

5. Conclusions and Prospects

This study provides a systematic review of machine learning applications in deep foundation pit deformation prediction. The fundamental principles and application outcomes of neural networks, support vector machines, and Bayesian networks are comprehensively analyzed. Furthermore, this paper investigates the critical role of optimization algorithms and data processing technologies in enhancing model performance. Building on the current status and future development of machine learning in deformation prediction for deep foundation pits, the following conclusions are summarized:

(1)

In recent years, machine learning models in the deep foundation pit deformation prediction field have transitioned from single models to complex combined models, demonstrating a trend toward interdisciplinary integration. Optimizing these machine learning models can significantly enhance prediction accuracy and performance. Recently, new optimization algorithms have been proposed. Future research could explore the extent to which these algorithms improve the prediction models.

(2)

Machine learning needs to further adapt to the requirements of deep foundation pit deformation prediction in ultra-deep and extreme environments. In the fields of deformation prediction for deep foundation pit support structures and surrounding surface settlement, it is necessary to explore cutting-edge deep learning models, such as GRU. These advancements aim to provide innovative solutions to address the complex and polytropic challenges associated with deep foundation pit deformation prediction.

(3)

Given that the machine learning prediction accuracy hinges on the quality and scale of samples, it is essential to collect a large number of deep foundation pit engineering cases and process the data systematically. Machine learning can be integrated with other advanced technologies, such as the Internet of Things and big data, to establish a comprehensive database for deep foundation pit engineering, which would enable intelligent and automated deformation prediction.

(4)

The types of machine learning models used in the deep foundation pit deformation prediction field have become increasingly diverse, offering more reliable technical support for the development and utilization of urban underground spaces. Each machine learning model has its own unique advantages in terms of algorithm design, data processing, computational efficiency, and prediction accuracy. Scientific and rational model selection and optimization are critical to ensuring accurate and efficient predictions.