Safety assessment and Long short-term memory-Attention-based deformation prediction for existing tunnels during shield tunnelling undercrossing

Abstract

As underground space continues to be developed, tunnels are inevitably affected by new tunnel construction, threatening operational safety. This study adopts numerical simulation to study the longitudinal response of existing tunnels under different spatial positions and evaluate the tunnel safety of bearing capacity. Then, based on measured data, a long short-term memory (LSTM)-Attention model was developed as a predictive model for safety control throughout the construction process. The importance of tunnelling parameters was quantified, and their dynamic nonlinear influence mechanisms revealed. Results show that there are complex coupling effects during the construction of the new twin tunnels, and the LSTM-Attention model achieves 96.42% prediction accuracy for invert deformation prediction. The main tunnelling parameters (chamber pressure (CY), propulsion speed (SP), and synchronous grouting volume (ZJ)) exhibit strong interaction effects (0.8), while the distance between the tunnel face and the monitoring point (DS) exhibits weaker interaction effects (0.3). The total sensitivity index for input parameters is approximately 0.8, with the order DS > CY > ZJ > SP. In practical tunnel undercrossing projects, the CY should be prioritized during the construction stage, with coordinated adjustments to other parameters to ensure tunnel safety.

Graphical abstract

Keywords

shield tunnel undercrossing / structural safety / LSTM-Attention-based model / tunnel deformation prediction / tunnelling parameters

1 Introduction

The shield tunnels inevitably influenced by unfavorable disruptive activities during long-term operation [1], such as the adjacent engineering disturbances, including tunnelling and excavation. In these projects, the stress change and displacement in surrounding soils inevitably occurs [2], triggers uneven settlement, segment misalignment, spalling and water leakage [3,4], affecting the tunnel structure safety and normal operation. In particular, the construction of twin tunnel would cause complex coupling effects in different spatial relationship between new and existing tunnels [5,6]. Considering the response mechanism of existing tunnels is fundamental for controlling construction safety and costs [7], and the intelligent methods have become the mainstream approach in current research. Therefore, understanding the response mechanism of existing tunnels under adjacent construction disturbances and developing reliable prediction methods are crucial for ensuring construction safety and controlling engineering costs.

Researchers have conducted extensive investigations through field monitoring and model tests [8–10], theoretical analyses [11,12], and numerical simulations [13,14]. Among these approaches, the disturbance of shield tunnelling undercrossing was investigated deeply, and the primary deformation of the existing tunnel induced by shield tunnelling undercrossing predominantly manifests as vertical settlements [2], which exhibit as a characteristic “U-shaped”. More recently, several researchers have also investigated the effects of soil parameter uncertainties [15,16]. Beyond the final failure state after construction, numerous studies have been conducted on the deformation and internal force evolution of existing tunnels during the construction process [17,18]. Furthermore, there are comprehensive and mature theoretical method for the deformation analysis of tunnels under adjacent construction disturbances regardless of whether construction control measures are implemented. For instance, Avesani Neto [19] has been introduced a two-layer system theory to calculate of settlements and vertical stress propagation in soil reinforcement with geocell, which could be used to verify the effectiveness of safety control measures. Additionally, the theoretical method considered the critical factors which influence the response of existing tunnel more rapid, including the construction method [20,21], the construction sequences of new multi-tunnel, cross-sectional geometries, the boundary conditions [6], and the structural stiffness of existing tunnels [22]. These researches also help understand how the space position between new and existing tunnels influence their interactions [23], and how the tunnel stresses characteristics developed.

Furthermore, the safety of existing tunnels has also been studied, such as the early warning system based on Timoshenko beam [24] and the probabilistic assessment to predict deformation risks under volume loss conditions. Based on the results of safety analysis, several construction control methods were implemented, among which grouting stands out as the most representative [25–28], and is highly effective in controlling and mitigating structural deformations [29]. Additionally, adjustments to tunnelling parameters serve as an effective measure for controlling structural deformation [30], collectively contributing to ensuring safety in adjacent shield tunnelling projects. Delisio and Zhao [31] analyzed operational data to establish a TBM performance prediction model. Mahdevari et al. [32] applied mathematical statistical methods and support vector regression (SVR) models to study the correlation between shield machine parameters and surrounding geotechnical parameters, achieving predictions of shield tunnelling speed. Hou et al. [33] developed a machine learning model to predict construction risks and proposed an intelligent decision-making method for control of tunnelling parameters based on multi-objective optimization. These studies have advanced the intelligent control of tunnelling parameters in various geological conditions. However, they primarily focus on newly constructed tunnels and surrounding geotechnical conditions, giving less attention to the impact of construction parameters on existing structures, and always overlook the time-varying effects of shield excavation on existing tunnels [34,35]. Given the uncertainty of tunnelling parameters and the cumulative effect of twin tunnel construction disturbances on existing tunnels, numerical simulations for analyzing the impact of tunnelling parameters on existing tunnels require substantial computational effort. The hybrid frameworks combining numerical simulation with machine learning have been proposed to maintain prediction accuracy while reducing computational costs [36]. Recent advances in deep learning have demonstrated promising performance in tunnel deformation prediction, with Transformer-based surrogate models being developed for deformation simulation [37]. However, such models are heavily dependent on large-scale datasets, limiting their applicability in engineering scenarios with limited monitoring data. Therefore, intelligent time-series methods are well-suited to address the challenge of predicting existing tunnel deformation under construction disturbance. Long short-term memory (LSTM) models, with inherent memory functionality, are particularly applicable to the shield tunnelling construction which involves cumulative effects over time.

To investigate the structural response of existing tunnels induced by undercrossing shield construction, numerical simulation is employed not only to identify the key factors governing existing tunnel deformation, but also to characterize the time-series evolutionary patterns of deformation at critical cross-sectional positions, which collectively inform the selection of input features for the predictive model. Building upon these mechanistic insights, an LSTM-Attention-based deformation prediction model is subsequently developed to enable real-time safety control throughout the construction process. Section 2 outlines the project overview and research methodology, followed by Section 3 which investigates the impact of spatial position on tunnel performance and safety. Section 4 presents an LSTM-Attention-based approach for construction control measures and introduces the LSTM model without attention mechanisms and an SVR method for comparison to validate the accuracy and practicality of the proposed model. Section 5 provides a comprehensive summary and discussion.

2 Project profile and research methodology

2.1 Project profile

2.1.1 Engineering geology and site conditions

The South Xizang Road River-Crossing tunnel undercrossing Metro Line 8 project is divided into the east and west shield propulsion sections. The outer diameter of the South Xizang Road River-Crossing tunnel segment is D = 11.36 m, the inner is d = 10.36 m, the center ring width is 1.5 m. The M8 line adopts reinforced concrete segment, and the outer diameter is D₁ = 6.2 m, the inner is d₁ = 5.5 m, the ring width is 1.2 m. The clear distance between the east and west lines of South Xizang Road River-Crossing tunnel is about L = 11.4 m, and the distance between the upper and lower lines of the M8 tunnel is 4.6 m. The two pairs of tunnels intersect in a well shape, and the intersection angle of the center lines in the crossing area is about 56°. The vertical clear distance between the South Xizang Road River-Crossing tunnel and M8 tunnel is about S = 2.8 m. and the relative position of the two tunnels is shown in Fig. 1. During the undercrossing, the soil excavated by the shield consisted of yellowish-brown sandy silt and grayish-yellow fine sand. At this point, Line M8 had a primary soil layers in the section comprising gray silty clay and dark green silty clay, interbedded with a 1.1–2.3 m layer of dark green silty clay. In order to ensure the orthogonal test conditions, the engineering geology of each operation condition in the subsequent orthogonal test is consistent with the project.

2.1.2 Measurement points

Automated settlement monitoring was conducted using electronic leveling rods, supplemented by manual monitoring with a Leica NA2 precision level to ensure mutual validation. Centered at the intersection of the new and existing tunnels, 30 monitoring points were arranged at 4 m intervals within a 55 m range on both sides along Metro Line M8, covering a total monitoring range of 120 m for both the uplink and downlink tunnels. Settlement measurement points were located on the tunnel invert and track bed (Fig. 2). Field data indicate that the disturbance caused by shield tunnelling primarily manifests as vertical displacement, and this study focuses on analyzing the vertical displacement of the existing tunnel.

2.2 Research methodology

Construction disturbance differs from sudden disasters like earthquakes and floods in that it is a controllable and preventable type of engineering interference. Therefore, this study adopted a deep learning model (LSTM-Attention), which is a control method that dynamically adjusts key construction parameters by integrating monitoring data. The sensitivity of existing tunnel performance to various parameters in underpass engineering were revealed, and effective safety control schemes were proposed, which provides a reference for ensuring structural safety and reducing maintenance costs. The research framework is shown in Fig. 3.

2.2.1 Simulation of tunnel undercrossing

Numerical simulation can be used to study the longitudinal response of existing tunnels under different spatial positions, clarify the response mechanism, and find the most dangerous location. The clear distance (S) between new tunnel and existing tunnel, and the spacing (L) of new twin tunnel are selected as variables, then the orthogonal experimental design method is adopted as shown in the following Table 1.

FLAC^3d numerical simulation software is used to simulate the tunnelling process of the new tunnel. To avoid boundary effects, the model dimensions are set as 140 m × 60 m × 100 m. Meanwhile, the model comprised approximately 152060 elements. the tunnel segment, grouting layer, shield shell and soil stratum are simulated by solid element. The segment and the grouting layer adopt the elastic constitutive model. The soil profile in the undercrossing section primarily consists of sandy silt, fine sand, gray silty clay, and dark green silty clay. Given the presence of soft cohesive soil layers with complex stratification, the Modified Cam-Clay model was adopted as the soil constitutive model, as it is capable of capturing the elastoplastic deformation behavior and stress-path dependency of such soils under construction disturbance, which cannot be adequately represented by the Mohr-Coulomb model with its linear elastic assumption. The model parameters, including the compression index, swelling index, and critical state stress ratio, were determined based on laboratory triaxial compression tests, field geotechnical investigation results, and existing research [38]. The shield tunnelling process (the calculation parameters are determined according to the laboratory triaxial compression tests and field geotechnical investigation results) and the comparison between the simulated and measured data are shown in Fig. 4, and the coefficient of determination (R²) = 0.9762, root mean square error (RMSE) = 0.8998, indicating that the simulated and measured data show consistent trends. Although certain numerical deviations exist, they are acceptable for engineering applications, confirming the rationality of the adopted simulation approach. The support pressure at the tunnel face is set according to the hydrostatic pressure at the corresponding depth, and frictional contact between the tunnel lining and surrounding soil is incorporated to simulate the resistance during shield advancement. It can be seen that the measured data are consistent with the simulated data, the numerical simulation method is reasonable.

2.2.2 Long short-term memory-Attention for construction control

2.2.2.1 Long short-term memory neural network

The LSTM network is a recurrent neural network that effectively addresses the issues of vanishing and exploding gradients in traditional recurrent neural network (RNN) models caused by long time spans, making it well-suited for processing significant events with long-term temporal dependencies [39,40]. The gating mechanism, consisting of an input gate, forget gate, and output gate, was introduced to enable the LSTM model to selectively process and retain information, enhancing its information processing capability (Fig. 5). However, when the input sequence is excessively long, the LSTM may encounter issues with attention dispersion, making it challenging for the model to assess the importance of the input sequence for the current prediction. To address this issue, an attention mechanism was incorporated.

2.2.2.2 Attention mechanism

The attention mechanism is a data processing approach that selectively focuses on critical information while disregarding less relevant information. It has been effectively applied in various machine learning tasks, including natural language processing, image recognition, and speech recognition. Existing methods incorporate the attention mechanism by using weight information to reflect the degree of focus on different information, implemented as a multilayer perceptron composed of a query matrix, key, and weighted average. The attention mechanism involves performing a weighted sum of the value in the source, with the weights of the corresponding Values calculated using Query and Key, as illustrated in Fig. 6. In the context of predicting tunnel deformation based on tunnelling parameters of new shield tunnels, the distance between the excavation face and monitoring points, and historical data from monitoring points, the issue of attention dispersion in the LSTM model is particularly pronounced. The developed LSTM-Attention model demonstrates effective application in addressing this problem.

To accurately evaluate the predictive performance of the model, the RMSE was selected to assess the magnitude of prediction errors (Eq. (1)), while the R² was used to evaluate the goodness of fit between predicted and actual values. In cases of significant data noise (Eq. (2)), the mean absolute error (MAE) was employed to verify the robustness (Eq. (3)).

(1)RMSE=\sqrt{\frac{1}{n}\sum _{i=1}^n{\left(y_i-{\overline{y}}_i\right)}^2},

(2)R^2=1-\frac{{\displaystyle \sum _{i=1}^n{\left(y_i-{\overline{y}}_i\right)}^2}}{{\displaystyle \sum _{i=1}^n{\left(y_i-y_m\right)}^2}},

(3)MAE=\frac{1}{n}\sum _{i=1}^n\left|y_i-{\overline{y}}_i\right|,

where n represents the sample size, y_i denotes the observed value at time i, {\overline{y}}_i represents the predicted value corresponding to time i, and y_m indicates the mean value.

2.2.2.3 Shapley additive explanations and Sobol method

To further analyze the prediction mechanism of the LSTM-Attention model and the importance of tunnelling parameters on the deformation of existing tunnels, a combined analysis method of Shapley additive explanations (SHAP) analysis and Sobol global sensitivity was adopted, and an analysis framework of model interpretation-parameter control was established. SHAP analysis is used to interpret the prediction mechanism of machine learning models. By quantifying the marginal contribution of each input feature to the predicted deformation prediction value, the inherent prediction logic and decision-making basis will be revealed, the interpretability and credibility of the prediction model will be ensured. The basic principle of Sobol global sensitivity analysis method is variance decomposition, primarily used to rank the sensitivity of tunnelling parameters to deformation. During this process, the contribution of each input parameter and its interaction effects to system uncertainty will be quantified.

The SHAP model is an interpretive framework based on Shapley values from game theory. The core concept is treat each feature as a participant in a game, calculating the marginal contribution of these feature across all possible feature sequences (Eq. (4)), then averaging to determine the SHAP baseline value, quantifying the impact on the prediction result.

(4){\psi }_i=\sum _{S\subseteq \{x_1,\dots ,x_n\cup x_i\}}\frac{\left|s\right|!\left(p-\left|S\right|-1\right)!}{p!}\left[f_x\left(S\cup \left\{x_j\right\}-f_x\left(S\right)\right)\right],

where \{x_1,\dots ,x_p\} represents the set of inputs, p represents the number, \{x_1,\dots ,x_n\}/\{x_j\} represents the set of all inputs exclude the \{x_j\}, f_x\left(S\right) represents the prediction of feature subset S, {\displaystyle \frac{\left|s\right|!\left(p-\left|S\right|-1\right)!}{p!}} represents the probability weight of the marginal contribution.

The Sobol method is a variance-based Monte Carlo simulation approach, primarily used to evaluate the impact of uncertainty in model input parameters on the output values. This method decomposes the model into combinations functions of individual and multiple input variables, calculating the impact of single and multiple input variables on the total output variance (Eq. (5)), and the sensitivity coefficient (Eqs. (6) and (7)). The sensitivity coefficient reflects the parameters contribution to output variance, enabling parameter importance ranking and providing a basis for formulating reasonable construction parameter control recommendations.

(5)

(6)S_i=\frac{V_i}{V\left(Y\right)},

(7)TSI=\frac{E_{X_{\sim i}}[V_{X_i}\left(Y|X_{\sim i}\right)]}{V(Y)}=1-\frac{V_{X_{\sim i}}[V_{X_i}\left(Y|X_{\sim i}\right)]}{V(Y)},

where p represents the number of input parameters, V(Y) represent total output variance of Y, V_i represents the main effect variance of parameter x_i, V_ij represents the interaction effect variance between parameters x_i and x_j, S_i represents the first-order sensitivity index of the ith input parameter, and TSI represents the total effect sensitivity index of the ith input parameter. E_{X_{\sim i}}[V_{X_i}\left(Y|X_{\sim i}\right)] represents the expectation of other parameters under the condition that X_i is fixed.

3 Impact of spatial position on tunnel safety

According to the existing research [7,41], Orthogonal intersection of tunnels is safer than oblique, and the extreme values of additional internal forces occur at the crown, invert and sidewall on the cross section of the existing tunnel. Therefore, the four key points were analyzed in this research, and the results obtained in this study based on orthogonal conditions represent a conservative scenario.

3.1 Deformation of tunnel under varying spatial relationship

Figure 7 shows the settlement variation of the crown, invert, and sidewalls of the existing tunnel cross-section during single-tunnel construction. It can be seen that a larger clear distance S between the new and existing tunnels leads to smaller settlement of the existing tunnel. The deformation at the invert and sidewalls of the existing tunnel is affected the stronger than crown, almost reaching the warning limit of −10 mm specified by the code.

Figure 8 shows the settlement variation of crown, invert and sidewall of existing tunnel cross-section under twin tunnel construction. It can be seen that a larger spacing L between the new tunnels results in smaller settlement of the existing tunnel under the twin-tunnel construction disturbance. Meanwhile, a larger clear distance S between the new and existing tunnels leads to greater deformation of the existing tunnel when clear distance S is small. Also, the deformation patterns of the four key locations are similar.

To investigate the deformation of the existing tunnel under different construction stages, taking Condition 1 as an example, and the deformation of the existing tunnel invert under the scenario of a new single tunnel undercrossing (ignoring the coupling effect of double-tunnel undercrossing) is selected for analysis, as shown in Fig. 9. It can be observed that the blue curves represent the settlement values of the existing tunnel at different times. The intervals from zuo-19 to zuo-23 and from zuo-23 to zuo-27 both correspond to the construction of four ring segments. However, the settlement differences between these intervals are not consistent. This indicates that during shield tunnelling, the previously constructed segments produce a cumulative effect, which influences the deformation of the existing tunnel.

The special phenomenon above is related to the complex coupling effects during the construction of the new twin tunnels, and the effects mainly include the coupled influence induced by the excavation of the first tunnel and the cumulative effects of the preceding excavation stages. Moreover, the coupling effect gradually decreases as the clear distance S between the new and existing tunnels increases. Therefore, the coupling effect of the new twin tunnels undercrossing on the deformation of the existing tunnel is not only related to the spatial relationship of the new and existing tunnels, but also influenced by the cumulative effects of tunnel excavation.

3.2 Safety factor for bearing capacity

3.2.1 Internal forces under varying spatial position of new and existing tunnel

In the orthogonal state, the bending moment of the tunnel sidewall are negative, while crown and invert moments are positive, and all axial forces are negative (compression). As the clear distance (S/D) increases, the variation between maximum and minimum bending moments and axial forces decreases, and both become more uniform along the longitudinal direction, approaching the initial pre-construction state (see Figs. S1–S2 in Appendix A in Electronic Supplementary Material). These results indicate that increasing clear distance reduces disturbances from the first tunnel undercrossing (hereinafter FT undercrossing), evidenced by decreased additional loads and stress disturbances.

After the first and second shield tunnelling undercrossing (hereinafter FT undercrossing and ST undercrossing), bending moments at both sidewalls are similar. A larger twin tunnel spacing L leads to stronger internal forces, which becomes more pronounced with decreasing clear distance S (see Figs. S3–S4 in Appendix A in supplementary material). This can be attributed to the fact that as L increases, the disturbance zones induced by tunnel construction become more spatially separated, resulting in a wider affected range and more asymmetric stress redistribution. This effect is further amplified when S is small, as the existing tunnel (hereinafter ET) becomes more sensitive to ground disturbance from the undercrossing tunnels.

3.2.2 Safety analysis of tunnel under different spatial position

According to the existing literature [15], the safety factor F_s of the bearing capacity of the existing tunnel can be calculated by Eqs. (8) and (9), the variability of the safety factor (F_s) can be calculated by Eq. (10). If the minimum stress σ_min of existing tunnel liner is greater than 0, the safety factor F_s is calculated by Eq. (8), otherwise it can be calculated by Eq. (9).

(8)N=-\frac{\left|M\right|At}{2I}+\frac{{\sigma }_{\text{c}}A}{F_{\text{S}}},

(9)N=\frac{\left|M\right|At}{2I}+\frac{{\sigma }_{\text{t}}A}{F_{\text{S}}},

(10){\delta }_{F_{\text{S}}}=\frac{F_{\text{s}\left(\text{std}\right)}}{F_{\text{s}\left(\text{mean}\right)}},

where M represents the bending moment of the existing tunnel lining, N represents the axial thrust, σ_c and σ_t represent the compressive and tensile strength of the existing tunnel lining, respectively, A represents the cross-sectional area, t represents the lining thickness, I represents the moment of inertia. F_s(mean) and F_s(std) represent the mean and standard deviation of the safety factor of different cross sections, {\delta }_{F_{\text{S}}} is the coefficient of variation of the safety factor, indicating the spatial difference of the safety factor.

Taking the clear distance (S/D) and the spacing (L/D) as the variable, the variation of the safety factor at the crown, invert and sidewall of the existing tunnel under different operating conditions are analyzed, as shown in Fig. 10, the first three working conditions represent the safety factors of the existing tunnel under the influence of single-tunnel excavation at different clear distance S. The remaining nine working conditions correspond to the safety factors of the existing tunnel under twin-tunnel excavation. Figure 10(a) shows the mean value of existing tunnel safety factor under different working conditions, and Fig. 10(b) presents the coefficient of variation of the safety factor. After the second tunnel undercrossing, the mean value of the safety factor in the longitudinal direction at the crown, invert, and sidewall of the existing tunnel is lower than single tunnel undercrossing, while the differences are small, indicating that the twin-tunnel undercrossing has a minor impact on the bearing capacity of the existing tunnel. Meanwhile, the variability trend of the safety factor at the left and right sidewall is almost same, and the safety factors at the left and right sidewall are relatively low, indicating that the sidewalls have a lower bearing capacity. Therefore, under tunnel undercrossing disturbance, the bearing capacity of the existing tunnel can be ranked as crown > invert > left and right sidewalls.

4 Deformation prediction model based on LSTM-Attention

Based on the above study, the impact of the new tunnel undercrossing on the bearing capacity of the existing tunnel is relatively small, but it has a significant effect on the deformation of the existing tunnel, with the invert and left sidewall being the most critical (Fig. 7). When S = 0.5D, the maximum settlement of the existing tunnel is approximately 10 mm, reaching the warning value specified by the code. Since smaller clear distance S leads to greater settlement and deformation, and the new tunnel in this case is of large diameter (D = 11.36) with a small clear distance (S = 2.8 m) from the existing tunnel, implementing effective construction control measures is crucial.

The shield tunnelling parameters and the spatial distance between the new and existing tunnels are important factors influencing the intensity of construction disturbance. As illustrated in Fig. 9, the deformation of the existing tunnel exhibits pronounced time-series evolutionary characteristics, indicating strong time-series dependency and nonlinear features simultaneously influenced by multiple construction parameters. While various deep learning models have demonstrated strong performance in engineering prediction tasks, their applicability varies depending on data characteristics and problem settings. Convolutional neural networks -based models lack the ability to capture dynamic inter-variable interactions in multivariate time-series tasks, and Transformer models are prone to overfitting under the limited data conditions of this study. In contrast, LSTM models are well-suited for time-series tasks through gating mechanisms, and the incorporation of an attention mechanism further enables adaptive focusing on the most contributive time steps. Therefore, an LSTM model integrated with an attention mechanism was adopted to investigate the relationship between existing tunnel deformation and construction parameters, providing a theoretical basis for controlling tunnel deformation through real-time adjustment of construction parameters.

4.1 Model training performance

4.1.1 Description of the dataset

The deformation values of monitoring point X19 during the construction of a new shield tunnel crossing the intersection area of new and old tunnels were selected as the training and validation sets for the LSTM-Attention model, split in an 8:2 ratio based on the time series, with the adjacent point X18 selected as the test set. To simplify the analysis conditions, this study selected five basic features: three key parameters of shield machine operation during new tunnel construction (chamber pressure (CY), propulsion speed (SP), and synchronous grouting volume (ZJ)), the distance between the tunnel face and the monitoring point (DS), and the deformation of monitoring point X19 (De). To leverage the temporal dependency of time series data, the basic features were expanded to 21 features, including temporal features, differential features, and lag features. The linear relationship strength between each feature and the target variable De was calculated using SelectKBest, and the 15 most important features were selected as model inputs, with the De as the output.

The basic features are the original input parameters, and parameter sensitivity analysis can effectively measure the impact of small changes in input parameters on the accuracy of prediction results. The Spearman correlation coefficient (SCC) was used to evaluate the relationship between each basic feature and the deformation of the existing tunnel. As shown in Fig. 11, CY and DS exhibit high correlation with the deformation, and should be closely monitored during the construction process.

(11){\rho }_{\text{sp}}={\displaystyle \frac{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left(R\left(x_i\right)-\overline{R\left(x\right)}\right)\cdot \left(R\left(y_i\right)-\overline{R\left(y\right)}\right)}}{\sqrt{\left({\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{\left(R\left(x_i\right)-\overline{R\left(x\right)}\right)}^2}\right)}\cdot \left({\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{\left(R\left(y_i\right)-\overline{R\left(y\right)}\right)}^2}\right)}}.

4.1.2 Long short-term memory-Attention model training process and the results

The LSTM model consists of two LSTM layers, each with a hidden size of 64, followed by a fully connected output layer. The time step was set to 5, meaning that each prediction is based on the preceding 5 consecutive time steps of construction parameter data. The mean squared error was used as the loss function. Since the training data in this study only included deformation values of the existing tunnel during the construction of the new tunnel in the intersection area, the dataset was relatively limited. To ensure model convergence and generalization performance, the model hyperparameters were configured as follows: Input-size = 15, Hidden-size = 64, Num-layers = 2, Dropout = 0.3, Sequence-length = 5, Learning-rate = 0.001, Batch-size = 32, and Num-epochs = 300. Throughout the training process, the convergence of the model was evaluated based on changes in the loss function value, as shown in Fig. 12(a), achieving stable convergence after 200 training iterations. The prediction results, as shown in Fig. 12(b), indicate MAE = 0.1223, RMSE = 0.2102, R² = 0.9642, demonstrating good prediction performance.

Figure 13 analyzes the relationship between observed and predicted values by density, scatter and residual plots. The density plot shows the distribution differences between the training and test sets, indicating that the distribution patterns of both datasets are generally consistent, with the model performing similarly on both sets. The scatter plot demonstrates a high correlation between predicted and observed values (R² close to 1). The residual plot reflects the distribution and pattern of prediction errors, showing that residuals are mostly centered around 0 and approximate a normal distribution, collectively indicating a good model fit.

In terms of generalization ability, the training and test set metrics show close agreement (R²: 0.9842 vs. 0.9642; MAE: 0.1099 vs. 0.1224; RMSE: 0.1387 vs. 0.2103), indicating reliable predictive accuracy on unseen data without significant overfitting. The proposed LSTM-Attention framework is a data-driven approach that does not rely on geology-specific assumptions, and the input features (e.g., CY, SP, ZJ) and prediction target are physically meaningful and consistent across different shield tunnelling cases, confirming that the methodology is universally applicable to shield undercrossing scenarios with similar input-output relationships. However, the specific model parameters and trained weights are inherently tied to the engineering conditions of this case. When applied to projects with significantly different geological conditions or tunnels, the model would require retraining with site-specific monitoring data to ensure prediction accuracy. Future studies will explore transfer learning strategies to reduce the data requirements for model adaptation across different engineering scenarios, which will be pursued as important extensions of the present research.

4.1.3 Comparative analysis with other models

The LSTM model without attention mechanism and an SVR model were selected for comparative analysis with the proposed LSTM-Attention model. Figure 14(a) presents the comparison between predicted and measured values of the LSTM model without consider the attention mechanism on the test set. The overall trend of the prediction curve is consistent with the measured curve (MAE = 0.1513, RMSE = 0.2874, R² = 0.9320); however, notable prediction errors are observed at certain extreme values, indicating limited capability in capturing abrupt deformation features. Figure 14(b) shows the test set prediction results of the SVR model (MAE = 1.9757, RMSE = 1.9817, R² = 0.8580), where the prediction curve fails to track the continuous dynamic variations of the measured settlement, demonstrating that the SVR model is poorly suited for the strongly nonlinear time-series characteristics of shield construction-induced tunnel settlement. In contrast, the prediction curve of the LSTM-Attention model shows significantly higher agreement with the measured curve, demonstrating clear superiority in predictive performance.

Figure 15 shows that the LSTM model without attention mechanism achieves test R² = 0.9320, MAE = 0.1512, and RMSE = 0.2874, with notably higher scatter dispersion in the test set than the training set, indicating limited generalization ability. The SVR model performs considerably worse, with test R² = 0.8580, MAE = 1.9757, and RMSE = 1.9817, where test scatter points deviate severely from the y = x reference line with highly asymmetric residuals. In comparison, the LSTM-Attention model demonstrates comprehensive superiority in prediction accuracy, stability, and generalization ability, validating the effectiveness of the attention mechanism in improving settlement prediction performance.

The performance ranking of the three models is LSTM-Attention > LSTM > SVR. The SVR model performs worst due to its inability to effectively handle strongly nonlinear time-series features. Although the LSTM model without attention mechanism possesses certain time-series learning capability, it insufficiently utilizes information at critical time steps. By adaptively focusing on the time steps that contribute most significantly to prediction through the attention mechanism, the LSTM-Attention model achieves optimal results across all three metrics (MAE, RMSE, and R²), demonstrating the best overall predictive performance.

4.2 Model parameter description

4.2.1 Shapley additive explanations analysis of long short-term memory-attention model

Figure 16 illustrates importance of the 15 input features in model training and their correlation with the prediction results. The horizontal axis at the top represents the mean absolute SHAP value (indicating feature importance), while the vertical axis lists the input features, sorted by the absolute SHAP value from high to low, with blue bars reflecting the magnitude of feature importance. The horizontal axis at the bottom represents the SHAP value (indicating the impact of each feature on the model output), where positive values denote a positive impact, and larger absolute values indicate a more significant impact. The bee swarm plot scatters represent samples, with color coding reflecting feature value magnitudes (red for higher values and green for lower). The top five most important features account for 75.38% of the total importance, showing that decision-making of the model is dominated by historical data of deformation (X19), with importance decreasing from lag1 to lag3 (20.91% → 17.03% → 8.54%), consistent with the temporal decay pattern. For DS, green points (shorter distances) are distributed in the positive value region, while red points (longer distances) are in the negative value region, indicating that shorter distances between the new tunnel face and the predicted point contribute more positively to the prediction results, aligning with the spatial proximity effect. Features like CY and ZJ exhibit relatively complex nonlinear relationships, probably due to the regional variation effects, contributing less to the model. Thus, the model primarily relies on historical deformation, adjusted by spatial distance, forming an interpretable and intuitive prediction mechanism. Given the memory characteristics of LSTM, this model may perform better in predicting large-scale construction data, which should be further explored in future research.

4.2.2 Parameters sensitivity and tunnel safety analysis

The Sobol sensitivity analysis results for the input parameters CY, SP, ZJ, DS, and the output parameter De is shown in Fig.17. Figure 17(a) shows that the total sensitivity index (TSI) for input parameters are high (approximately 0.8), with the order DS > CY > ZJ > SP. The first-order sensitivity index (S1) for DS is about 0.6, indicating a direct influence of DS on the variance of the output parameter De. However, this value is lower than its TSI (S1 = 0.6 < TSI = 0.8), suggesting that part of DS variance effect is contributed by interaction effects with other variables (CY, SP, ZJ). Figure 17(b) indicates strong interaction effects among CY, SP, and ZJ (approximately 0.8), while DS exhibits weaker interaction effects (approximately 0.3), suggesting that DS has a relatively independent influence on tunnel deformation compared to the other parameters. As SP increases, faster shield tail retreat elevates the risk of ground loss, necessitating a proportional increase in ZJ to control settlement, forming a strong operational coupling between SP and ZJ. Meanwhile, CY must be dynamically adjusted in response to SP variations to maintain excavation face stability. Furthermore, changes in CY alter the stress state ahead of the excavation face, indirectly influencing the required grouting pressure and volume, establishing an indirect coupling between CY and ZJ. Therefore, CY, SP, and ZJ are inherently interdependent parameters that collectively govern the deformation response of the existing tunnel to construction disturbance, which constitutes the intrinsic reason for their pronounced interactive effects. This further demonstrates that the proposed model has effectively learned the underlying patterns of practical engineering behavior. Figure 17(c) illustrates the trend of cumulative S1 and cumulative TSI as the number of variables increases. The cumulative TSI rises rapidly to 3.5, while the S1 shows minimal growth. This suggests that the distance between the excavation face and the monitoring point has the greatest impact on the deformation of the existing tunnel, followed by shield machine cabin pressure and grouting volume. Moreover, the interactions among input variables have a greater influence on monitoring point deformation than the individual variables themselves.

In practical shield undercrossing construction, field monitoring data are continuously collected and fed into the trained LSTM-Attention model for real-time settlement prediction. When the predicted settlement exceeds the warning threshold, an alert is triggered to assist construction personnel in adjusting key parameters. Given that the spatial distance between the excavation face and the existing tunnel cannot be controlled in real time, priority should be given to adjusting earth CY, while simultaneously optimizing the combination of CY and ZJ to account for their strong interaction effects, thereby achieving proactive and dynamic control of existing tunnel deformation.

5 Conclusions

Based on practical engineering, a deep learning model (LSTM-Attention) was adopted to investigate the influence of tunnelling parameters, and its prediction accuracy and generalization capability for existing tunnel deformation were validated through comparative experiments with a LSTM model without attention mechanism and an SVR model. The main conclusions are as follows.

1) A larger spacing L results in smaller settlement of the existing tunnel, and a greater clear distance S between the new and existing tunnels leads to larger deformation of the existing tunnel under twin tunnel construction when S < D. This phenomenon is related to the complex coupling effects during the construction of the new twin tunnels, and the coupling effect is not only related to the spatial relationship of the new and existing tunnels, but also related to the cumulative effects of the preceding excavation stage.

2) The mean value of the safety factor in the longitudinal direction at the crown, invert, and sidewall of the existing tunnel under twin tunnel construction is lower than single tunnel, while the differences are small, the twin-tunnel undercrossing has a minor impact on the bearing capacity of the existing tunnel. Meanwhile, the variability of the safety factor at the left and right sidewall is almost the same, and the values are smaller than the invert and crown, indicating that the sidewalls have a lower bearing capacity.

3) A temporal correlation model was established to analysis the relationship of tunnel deformation and the critical excavation parameters. The LSTM method with an attention mechanism is particularly capable of capturing temporal features to reveal the coupling effects of twin tunnel construction, and it was trained using measured data. The model demonstrates excellent performance with R² = 0.9642, indicating that the LSTM-Attention model is acceptable to predict the tunnel deformation.

4) The distance between the excavation face and the monitoring point has the greatest impact on the tunnel deformation, followed by CY and ZJ. The interactions among input variables have a greater influence on monitoring point deformation than the individual variables themselves. In practical tunnel construction, priority should be given to adjusting CY while optimizing SP and grouting volume based on their interactions, with deformation prediction using the proposed LSTM-Attention model to ensure construction safety.

This study integrates numerical simulation, machine learning, and interpretability analysis into a mechanism-driven and data-driven unified framework, providing a novel approach for safety assessment and deformation prediction in shield undercrossing construction. The proposed method enables real-time deformation prediction and parameter sensitivity analysis, facilitating the transition from experience-based to data-driven decision-making in tunnel construction, which holds significant reference value for advancing the intelligent development of underground engineering. With the continued development of monitoring technologies and artificial intelligence, the framework is expected to be extended to more complex underground engineering scenarios, contributing to smart construction site implementation and technological progress in the industry.

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