Deep Learning Method on Deformation Prediction for Large-Section Tunnels

Abstract

With the continuous development of engineering construction in China, more and more large-section highway tunnels have emerged. Different geological engineering environments determine the diversity of construction plans. The determination of construction plans and the prediction of tunnel deformations have always been the key points of engineering construction. In this paper, we use numerical simulations to determine specific construction parameters in the context of actual highway tunnel projects, and then use deep learning methods to predict deformation during tunnel construction, thus providing guidance for construction. We have found that: (i) Different excavation sequences and excavation depths have different effects on the surrounding rock deformation around the tunnel. The optimal excavation sequence through numerical simulation in this study is symmetrical excavation, and the excavation depth is 2 m. (ii) Numerical simulation based on Long Short-Term Memory (LSTM) algorithm is used to predict the tunnel deformation. It is found that the prediction results of the LSTM algorithm are more consistent with the actual monitoring data. (iii) Multi-step prediction is more important for engineering guidance, and three-step prediction can be considered during the process of engineering construction. Therefore, the machine learning algorithm provides a new method for engineering prediction.

1. Introduction

As highway tunnel engineering can shorten mileage, improve alignment, reduce travel time, and effectively improve the economic efficiency, it plays an increasingly important role in infrastructure engineering construction. China’s geological conditions are complex, and more and more projects need to be built in unfavorable geological bodies such as groundwater enrichment areas, fault structural belts, and karst. Especially in the western region of China, the rock mass in the shallowly buried crushed area where the highway tunnel is located is loose and weak, the surrounding rock is complex and generally biased, and the tunnel may pass through some unfavorable geological areas, such as faults and dangerous rocks. These comprehensive factors greatly increase the difficulty of tunnel design and construction. The slightest carelessness will lead to the occurrence of safe construction such as landslides, which may cause serious economic and social impacts. Therefore, under adverse geological conditions, selecting appropriate construction scheme, accurately predicting the deformation of the tunnel, and taking protective measures in advance are the keys to ensure the safety of the tunnel project.

Many scholars have studied the construction method and deformation prediction of highway tunnels. The construction methods of highway tunnels mainly include double side heading method, cross diaphragm (CrD) method, layered pilot pit, and so on [1,2,3,4,5,6,7], Jin et al. [8] have established a three-dimensional calculation model to study the effect of tunnel excavation on the ground. Through comparative analysis, the double side heading method, which was selected as the tunnel construction plan, can better control the surface deformation and has relatively higher construction efficiency. Sun et al. [9] have used three-dimensional numerical simulation to study the deformation laws of different construction methods on the large-section loess tunnels during the construction process. The results show that: (i) the CrD method is better, when the surrounding rock converges substantially; (ii) the twin-side heading method is better, when the surface subsidence is relatively large. Cao et al. [10] has studied the deformation characteristics during the construction of shallow tunnels with soft surrounding rock. The results show that an excavation footage of 0.5 m can effectively control the settlement of highway pavement. These construction methods mainly can be divided into symmetrical excavation and asymmetrical excavation. Since the tunnel section is generally symmetrical, tunnel structure is more table under the symmetrical excavation [7]. The deformation prediction caused by highway tunnel construction is mainly divided into the empirical formula method and numerical simulation method [11,12,13,14,15]. Zhang et al. [16] studied the deformation characteristics of the super-large tunnels using the experiments to obtain the smallest reasonable spacing for a large section highway tunnel in surrounding rock. Kavvadas et al. [17] adopted the two-dimensional and three-dimensional finite element models to predict the longitudinal deformation during tunneling in soil. Gao et al. [18] introduced short-range repulsive force into peri-dynamic equation of motion and simulated the tensile and compression failure characteristics of rock materials, which can predict the excavation damage zone and tunnel deformation. Zhou et al. [19] predicted the tunnel deformation based on [BQ] method and FLAC3D software. Finally, engineering monitoring was carried out to verify the feasibility of the method. Hoek [20] has classified the deformation of soft rock tunnels into non-extrusion deformation, slight extrusion deformation, moderate extrusion deformation, severe extrusion deformation, and extremely severe extrusion deformation based on the strain rate. According to the above index, Singh et al. [21] have classified the compression deformation degree of surrounding rock into weak compression, moderate compression, and high compression. Hoek et al. [22] have proposed to classify large deformations into five classes using the dual index of strength-stress ratio and tunnel strain rate: no support problem, slight extrusion, severe extrusion, very severe extrusion, and extremely severe extrusion.

It can be seen that the research on the construction method and deformation prediction of highway tunnels has achieved rich results, but there are still some areas that can be improved: (1) China’s vast geographical area determines the diversity of geological conditions, so it is difficult to obtain the widely used construction method, thus the selection of tunnel construction method and specific construction steps need to be studied for specific projects; (2) The deformation prediction of the tunnel mainly relies on empirical formula and numerical software, the accuracy of which is often unsatisfactory, thus cannot effectively guide the construction of the project; (3) Monitoring data contains a lot of information; however, it can always be neglected. Machine learning can extract the data characteristic, which can provide guidance for the project construction.

2. Proposed Methodology

In this paper, a case study of a highway tunnel in the western China is presented. First, the project overview and construction plan are discussed. Then, the numerical simulation is used to model the tunnel construction scheme, and then the optimal construction scheme is determined. Finally, Long Short-Term Memory (LSTM) algorithm is used to predict the deformation of the tunnel and guidance for construction is provided.

3. Project Overview and Construction Plan

3.1. Project Overview

The tunnel project is located in Lanzhou, China, which is a key infrastructure project in Lanzhou City. The project not only can effectively enhance the transportation connection between Lanzhou regions, but also can effectively connect the vast northwest region, and promote regional economic development and cultural exchanges, which has great economic and political significance. From the perspective of the project itself, the tunnel project is characterized by its large scale, high technical content, unique geographical location, complex geological conditions, sensitive surrounding environment, high risk of construction period control, and difficult project management.

The project tunnel has six lanes in both directions, 3645 m long in the east line, and 3735 m long in the west line. The south entrance of the west line is a 130-m-long span section with eight lanes in both directions, with a cross-section width of 23.44 m and a height of 14.05 m. The large cross-section of the V-level fenestration section, many guide holes and many processes increased the difficulty of construction organization on site. The structure of the fault and extrusion belt has a great influence on the construction of tunnel engineering. The tunnel section is large and the geological section is unfavorable; therefore, choosing a suitable construction plan is the key to ensure the safety, reliability, quality, and completion of the project. The relevant experience can provide a practical reference for similar projects.

The buried strata in the tunnel site are mainly Quaternary slope residual layers, and the underlying bedrock is granite and quartz amphibole. The strata in the site are described in order from top to bottom as follows: Silty clay; fully weathered granite; highly weathered granite; moderately weathered granite; slightly weathered granite; fully weathered quartz diorite; highly weathered quartz diorite; moderately weathered quartz diorite; slightly weathered quartz diorite, as shown in Figure 1.

3.2. Construction Plan

The current stage of the crustal movement in this area is basically upward movement as the main trend, accompanied by the differential lifting movement of fault blocks; that is, the fault-uplift area continues to rise intermittently, while the fault-depression basin continues to decline, the crustal movement is still very active, and there are high-temperature hot springs in the southwest and northeast. The construction methods mainly include: full-section method, step method, three-step temporary invert method, middle partition (CD) method, cross middle partition (CRD) method, and double side heading method. The surrounding rock and initial support are allowed to have a certain deformation, and the design excavation section should be appropriately expanded. The general provisions are as follows: the II surrounding rock is 3 to 5 cm, the III surrounding rock is 5 to 8 cm, the IV surrounding rock is 8 to 10 cm, and the V surrounding rock is 10 to 15 cm. The double side heading method is suitable for the excavation of driving tunnels under the condition of the V surrounding rock at the entrance of the tunnel with poor surrounding rock. In the construction of shallow buried long-span tunnels, the use of the double side heading method can control the surface subsidence and maintain the surface stability, safety and reliable. The tunnel project crossing area is mainly composed of moderately weathered and slightly weathered mica granite, with unfavorable geological conditions such as grade IV and V surrounding rocks, and consider that the characteristics of the stratum deform during tunnel construction. Moreover, the tunnel construction method is determined based on comprehensive consideration of factors such as engineering geological and hydrogeological conditions, the size of the excavation section, the burial depth, the difficulty of construction method conversion, the configuration of mechanical equipment and environmental constraints. Therefore, the double side heading method is selected for excavation construction.

4. Determination of Construction Scheme Based on Numerical Simulation

Based on the above chapters on the basis of the tunnel construction scheme, this chapter simulates the construction of the tunnel using the finite difference software FLAC3D, analyzes the deformation of the tunnel structure caused by excavation under the different construction schemes, and selects the optimal construction scheme for engineering construction.

4.1. Choice of Construction Parameters

Based on the analysis of the rock strata of the tunnel excavation section and experts’ demonstration, it is decided to divide the section into seven excavation sections. According to the literature [23,24], the excavation sequence of section of the tunnel and the length of the excavation steps are important factors affecting the deformation of the surrounding rock around the tunnel. Therefore, in order to study the influence of different excavation sequence and excavation step length on the deformation of surrounding rock, three excavation sequences and three excavation lengths are selected in this section through literature studies [25,26,27] to study the effects of different excavation schemes on the deformation characteristics of surrounding rock through numerical simulation. The excavation plans are shown in

Table 1. Different excavation sequence.

Excavation Schemes	Excavation Sequence
1	Ⅰ → Ⅱ→ Ⅲ→ Ⅵ→ Ⅶ→ Ⅳ→ Ⅴ
2	Ⅳ→ Ⅵ→ Ⅴ→ Ⅶ→ Ⅰ → Ⅱ→ Ⅲ
3	Ⅳ→ Ⅴ→ Ⅵ→ Ⅶ→ Ⅰ → Ⅱ→ Ⅲ

and

Table 2. Different excavation step length.

Excavation Schemes	Excavation Step Length
1	1 m
2	2 m
3	3 m

.

4.2. The Establishment of Three-Dimensional Numerical Model

Based on the actual situation, a three-dimensional finite difference model is established in this paper, as shown in Figure 2. Considering the influence range of the model boundary effect, the model excavation surface is 100 m horizontally, 500 m longitudinally, and 50 m vertically. In the model, the tunnel excavation direction is the Y-axis direction, and the vertical direction is the Z-axis positive direction. This model has a total of 112,400 grid elements and 120,399 nodes. According to the actual situation, the boundary condition of the top surface of the model is set as a free boundary, and other interfaces are set according to the normal constraint. The rock and soil mass are simulated by the Mohr–Coulomb constitutive model. The tunnel lining adopts the Liner structural unit, and the tunnel anchor adopts the Cable structural unit. The physical and mechanical parameters of rock and soil mass and other structural element parameters are shown in

Table 3. Parameters of the surrounding rock and soil.

Layer	Name	ρ/(kg/m−3)	c/(kPa)	ϕ/°	E/(GPa)	υ
1	Silty clay	19.8	25	20	2.1	0.38
2	Fully weathered granite	20	10	32	4.2	0.25
3	Strongly weathered granite	21	30	32	6.4	0.28
4	Medium weathered granite	23	100	39	7.6	0.31
5	Micro-weathered granite	24	200	44	8.1	0.34
6	Fully weathered quartz diorite	23	26	28	4.8	0.35
7	Strong weathered quartz diorite	27.7	28	30	7	0.32
8	Medium weathered quartz diorite	28.9	5.5 × 103	41	4	0.30
9	Breeze quartz diorite	30.0	7.0 × 103	42	6.5	0.23

,

Table 4. Tunnel lining support parameters.

Structural Unit	ρ/(kg/m−3)	Thickness/(m)	E/(GPa)	υ	Normal Coupling Stiffness/(Gpa)	Tangential Coupling Stiffness/(Gpa)
Liner	2000	1	30	0.25	9.77	9.77

and

Table 5. Tunnel bolt support parameters.

Structural Unit	ρ/(kg/m−3)	Cross-Sectional Area/(cm2)	E/(GPa)	c/(kPa)	Grouting Perimeter/(m)	ϕ/°
Cable	2000	5.9	200	50	0.157	35

.

4.3. Steps of Numerical Simulation

Firstly, the effects of different excavation sequences on the deformation of surrounding rock are studied, and the construction schemes are shown in Table 1 and Table 2. In the study of the effects of different excavation sequences on the deformation of surrounding rock, the excavation depths under the three schemes are the same (2 m), in order to avoid the influence of excavation depth on the results; then, the optimal excavation sequence was obtained by numerical simulation. Next, the effects of different excavation depths on the deformation of surrounding rock are investigated.

The steps of the numerical simulation are as follows: (i) The initial in-situ stresses of the model are calculated, and the displacement field is cleared. (ii) A complete construction step includes the completion of one guide hole excavation followed by on-time construction of the lining and anchors. The tunnel deformation caused by construction is calculated. (iii) Then, the next guide hole is excavated, and the lining and anchors are constructed on time. The tunnel deformation caused by construction is calculated. (iv) The above construction steps are repeated until the excavation of the tunnel section is completed.

4.4. Results Discussion

4.4.1. Different Excavation Sequence

Figure 3 is the deformation cloud diagrams of the surrounding rock around the tunnel after one excavation sequence is completed under three different excavation sequences. During the excavation, settlement occurred at the tunnel vault, and a certain uplift occurred at the tunnel bottom. Comparing the settlement values of the three schemes, it can be found that the maximum settlement values of the first, second, and third scheme are 1.1 mm, 0.78 mm and 1.56 mm, respectively, after the tunnel section is excavated. Figure 4 and

Table 6. Tunnel deformation under different excavation sequence (mm).

Excavation Schemes	1	2	3	4	5	6	7
1	0.13	0.29	0.45	0.59	0.74	0.91	1.1
2	0.1	0.17	0.28	0.37	0.54	0.62	0.78
3	0.16	0.31	0.62	0.89	1.15	1.28	1.56

show the deformation of the tunnel vault in each excavation sequence. It can be seen that with the progress of the excavation sequence, the deformation value of the tunnel vault gradually increases, indicating that the excavation of the tunnel will affect the deformation of the surrounding rock, and the deformation will gradually accumulate with the excavation time. At the same time, it can be seen intuitively that the tunnel vault deformation caused by the second excavation sequence is the smallest, the deformation caused by the first excavation sequence is the second, and the deformation caused by the third excavation sequence is the largest. It is indicated that the second excavation has the least disturbance to the surrounding rock, and the second scheme is selected as the construction plan for the project.

4.4.2. Different Excavation Step Length

Figure 5 shows the deformation cloud diagrams of the surrounding rock around the tunnel after one excavation step is completed under three different excavation depths. It can be seen that during the excavation, settlement occurred at the tunnel vault, and a certain uplift occurred at the tunnel bottom. Comparing the settlement values of the three schemes, it can be found that the maximum settlement values of the first, second, and third scheme are 0.47 mm, 0.78 mm, and 6.85 mm, respectively, after the tunnel section is excavated. Figure 6 and

Table 7. Tunnel deformation under different excavation depth (mm).

Excavation Schemes	1	2	3	4	5	6	7
1	0.07	0.11	0.15	0.21	0.29	0.36	0.46
2	0.1	0.17	0.28	0.37	0.54	0.62	0.78
3	0.21	0.89	2.43	3.69	4.74	5.42	6.85

show the deformation of the tunnel vault during each excavation step. It can be seen that with the progress of the excavation sequence, the deformation value of the tunnel vault gradually increases, while it can be visualized that the smallest deformation of the tunnel vault is caused at an excavation depth of 1 m, the second largest at an excavation depth of 2 m, and the largest at an excavation depth of 3 m. It can be seen that with the increase of the length of the excavation step, the settlement value of the surrounding rock is larger. This is mainly because the longer the excavation length, the greater the disturbance to the surrounding rock. Therefore, it is recommended to adopt the excavation method of “short footage and quick support” during the excavation process. In addition, it can be found that under the conditions of excavation depth of 1 m and 2 m, the difference in the deformation of the tunnel vault is small. Therefore, in the actual project, considering other factors such as the construction period and project cost, these two construction schemes can be selected. According to the above numerical simulation research, the final construction plan is: the excavation sequence is the second scheme, and the excavation step length is 2 m.

5. Tunnel Deformation Prediction Based on LSTM Algorithm

With the rapid development of machine learning technology, it has gradually started to be applied in the field of engineering, providing a new method for engineering prediction [28,29,30,31,32,33,34,35,36,37,38,39,40]. Machine learning focuses on training the data, extracting the internal features of the data, mining the trends of the data, and then predicting the future changes of the data. Deep learning is an important branch of machine learning [41,42,43,44,45,46]. Deep learning is designed to learn the intrinsic patterns and representation levels of sample data. The information obtained from these learning processes has a great impact on the interpretation of data such as text, images, and sounds. Its ultimate goal is to enable machines to have the same analytical and learning capabilities as humans. Deep learning is a complex machine learning algorithm that has already achieved results in speech and image recognition, and it has far surpassed previous related techniques. In this section, the deep learning method is mainly used to predict the tunnel deformation and to provide guidance for the subsequent construction.

5.1. Long Short-Term Memory (LSTM)

A recurrent neural network (RNN) is a structure that recurs over time. It has a wide range of applications in natural language processing (NLP), image recognitions, and other fields. The main difference between RNN network and other networks is that RNN can achieve a certain “memory function”, which is one of the best choices for time series analysis. However, for long-term sequence learning, there are problems of gradient disappearance and gradient explosion. Some scholars have improved the RNN structure and proposed the LSTM algorithm. LSTM is a special network structure with three “gate” structures, namely forget gate, input gate, and output gate. LSTM relies on the “gate” structure to make information selectively affect the state of each moment in the neural network. The “gate” structure is an operation that uses a sigmoid neural network combined with a bitwise multiplication, as shown in Figure 7. It has been shown that the LSTM algorithm outperforms traditional machine learning models in terms of prediction performance. Since the excavation of a tunnel is a sequential process, and the construction period of highway tunnels is usually long, this section uses the LSTM neural network to predict the deformation of the tunnel.

(1)

The calculation formulas for the input gate, forget gate, and output gate are:

$$I_t=\sigma \left(W_{xi}{x}_t+W_{hi}{h}_{t-1}+b_i\right)$$

(1)

$$F_t=\sigma \left(W_{xf}{x}_t+W_{hf}{h}_{t-1}+b_f\right)$$

(2)

$$O_t=\sigma \left(W_{xo}{x}_t+W_{ho}{h}_{t-1}+b_o\right)$$

(3)

where $W_{xi},W_{xf},W_{xo}$ are the weight values of the input parameter $x_t$ and gate units, respectively; $W_{hi},W_{hf},W_{ho}$ are the weight values of the input parameter $h_{t-1}$ and gate units; $b_i,b_f,b_o$ are bias vectors of three gate units; and $\sigma$ is a sigmoid function, with values from 0 to1;

(2)

The update status in the neural unit cell is:

$$s_t^{\ast }=\tanh (W_{xc}{x}_t+W_{hc}{h}_{t-1}+b_c)$$

(4)

$$s_t=F_t{c}_{t-1}+s_t^{\ast }{I}_t$$

(5)

where $x_t$ is the input value at the current moment; $h_{t-1}$ is the output of the previous neural unit; $W_{xc}$ is the weight value of the input parameter $x_t$ and the memory unit; $W_{hc}$ is the weight value of the $h_{t-1}$ and the memory unit; $b_c$ is the bias vector; and $s_{t-1}$ is the stored value at the previous moment.

(3)

The output value of the LSTM unit is:

$$h_t=O_t\tanh \left(s_t\right)$$

(6)

where $h_t$ is the output value of the neural unit at the current moment.

5.2. Tunnel Deformation Prediction

5.2.1. Data Preparation

The first step in predicting tunnel deformation using machine learning methods is to select the appropriate input parameters. There are many parameters involved in tunnel deformation, and the relationship between the parameters is complex. In this section, based mainly on existing related studies [47,48], the input parameters selected are rock uniaxial compressive strength, confining pressure, in situ stress, rock humidity, joint spacing, and joint dip. The output parameters are the deformation of the tunnel vault and bottom, as shown in

Table 8. Experiment parameters.

Input Parameters	Output Parameters
rock uniaxial compressive strength	the deformation of the tunnel vault and bottom
confining pressure
in situ stress
rock humidity
joint spacing
joint dip

. According to the study in the literature [49], with the continuous excavation of the tunnel, the maximum deformation of the tunnel is usually located at the excavation hole, so the selected deformation points are located at the excavation hole. These data are mainly obtained from the monitoring system and geological exploration reports. The monitoring frequency of the monitoring system is 10 min per group, with a total of 34,000 groups of data. Through the experiments, eighty percent of the data in each dataset are used as the training set, and the remaining data are used as the test set.

The RMSE (root mean square error), MAE (mean absolute error), and R² (coefficient of determination) of the test set are used as the model evaluation indicators:

$${\alpha }_{MAE}=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|y_i-\stackrel{\wedge }{y_i}\right|}$$

(7)

$${\alpha }_{RMSE}={\left[\frac{1}{n}{\displaystyle \sum _{i=1}^n{\left(y_i-{\stackrel{\wedge }{y}}_i\right)}^2}\right]}^{1/2}$$

(8)

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

(9)

To improve the prediction accuracy of the model and speed up the convergence speed of the model training, this paper first normalizes the raw data:

$$x^{\ast }=\frac{x-x_{\min }}{x_{\max }-x_{\min }}$$

(10)

where $x$ is the raw data and $x_{\max }, x_{\min }$ are the maximum and minimum values of the raw data, respectively.

5.2.2. Model Training

The hyperparameters of the model have a great impact on the prediction performance of the model. However, there is no mature theory and method to guide the selection of hyperparameters. Therefore, this paper mainly adopts the method of repeated experiments to select the hyperparameters of the model [50]. The experiment environment is shown in

Table 9. Experiment configuration.

Parameters	Notes
Operation system	windows 10
CPU	IntelI CoITM) i7-10710U CPU @ 1.10 GHz
GPU	GeForce MX350
Python	3.9
PyTorch	1.9.1

. The final hyperparameters of the model are shown in

Table 10. The parameters of the model.

The Model Parameters	LSTM Layers	Units	Dense	Batch_size	Epoch	Activate Function	Optimizer	Loss
Number/Type	3	64	1	100	150	Relu	Adam	Mse

below.

5.2.3. Model Prediction

In order to ensure the accuracy of the prediction, this paper adopts a single-step rolling prediction method, and the time step determined by the experiment is 60, i.e., the predicted value of the 61st group can be obtained by the data of the 1st to the 60th group. After the real value of the 61st group is obtained, it will be combined with the previous real data to form a new data set, which is trained by the LSTM model, and then predict the value of the 62nd group through the data of the 2nd to 61st groups, and so on. The time series prediction of tunnel deformation is achieved by continuously updating the dataset by adding real values until the tunnel is penetrated.

5.2.4. Baseline Model

In order to verify the prediction accuracy of the LSTM model, two widely used prediction models, namely, Random Forest (RF) and Recurrent Neural Network (RNN), are introduced for comparison with the LSTM algorithm. In each experiment, the model performance is analyzed on the training dataset to adjust the hyperparameters, and the predictive accuracy are finally verified on the test dataset. In order to analyze the prediction performance of the LSTM algorithm, numerical simulation is also introduced for comparison with the LSTM algorithm.

5.3. Results Discussion

5.3.1. Performance of LSTM Algorithm

As can be seen from Figure 8, the loss value of the model gradually decreases with the increase of the number of iterations and finally stabilizes, which indicates that the prediction error becomes smaller and smaller as the model is continuously trained. The final loss value on the test set is 0.14, which indicates that the prediction has a high prediction accuracy. Comparing the two curves, we can see that the difference between the two values is not large, which indicates that the LSTM model can avoid the overfitting problem during the training process and has good generalization ability.

5.3.2. Prediction Performance of LSTM Algorithm

In order to ensure the rationality of the results, the optimal hyperparameters of the RF and RNN algorithms are selected by training. The optimal parameters of the algorithms are shown in the

Table 11. Optimal hyperparameters of different algorithms.

Algorithms	Hyperparameters
RF	Max_Features = 400, Max_Depth = 6, N_Estimators = 70, Min_Sample_Leaf = 2, Min_Sample_Split = 2, Random_State = 10
RNN	RNN layer = 3, Number of the RNN units = 64, Each batch = 64, Iteration = 200, Dense = 1, Dropout rate = 0.1, Optimizer = Adam, Loss function = MSE, Activation function = ReLu

.

As shown in

Table 12. Model evaluation (tunnel vault).

Algorithms	Dataset	MAE	RMSE	R2
LSTM	Train	0.104	0.171	0.946
	Test	0.225	0.238	0.928
RF	Train	0.321	0.472	0.801
	Test	0.346	0.498	0.784
RNN	Train	0.256	0.386	0.843
	Test	0.286	0.402	0.822

and

Table 13. Model evaluation (tunnel bottom).

Algorithms	Dataset	MAE	RMSE	R2
LSTM	Train	0.111	0.178	0.958
	Test	0.246	0.231	0.931
RF	Train	0.335	0.480	0.793
	Test	0.363	0.503	0.762
RNN	Train	0.267	0.391	0.836
	Test	0.291	0.433	0.817

, for both the vault or the bottom of the tunnel, the MAE and RMSE values of the LSTM algorithm on both the training set and the test set are smaller than RF and RNN algorithms, R² value are larger than RF and RNN algorithms, indicating that the LSTM algorithm has achieved good performance on the training set and the test set than RF and RNN algorithms, the reason is that LSMT networks are better suited for time series data. Furthermore, the MAE and RMSE values of the LSTM algorithm on both the training set and the test set are small, it shows that the LSTM model has good generalization ability. In order to further evaluate the prediction effect of the LSTM model, the actual monitoring data of the tunnel vault and bottom for 24 days, the LSTM model prediction data, and the numerical simulation data are selected, as shown in Figure 9 and Figure 10. It can be seen that the change trend of the prediction results of the numerical simulation and the LSTM model are all consistent with the actual monitoring data. With the continuous excavation of the tunnel, the deformation of the tunnel gradually increases, so monitoring should be strengthened in the actual construction. In addition, compared with the numerical simulation results, it can be clearly seen that the prediction results of the LSTM model are more consistent with the actual monitoring data, and the error is smaller, which can fully prove the effectiveness of the machine learning model.

5.3.3. Multi-Step Prediction Result

In practical engineering, the prediction information provided by single-step prediction is limited, and the response time of engineers is also short, so multi-step prediction is more important for engineering guidance. Therefore, this section mainly studies the multi-step prediction effect of the LSTM model on the tunnel vault settlement, and selects 1, 2, 3, 4, and 5 steps, respectively. The results are shown in Figure 11. It can be seen that with the increase of the number of steps, the MAE value and RMSE value gradually increase, while the R² value gradually decreases. It indicates that the accuracy of the model prediction gradually decreases, which is mainly because the multi-step prediction has the phenomenon of error accumulation compared to the single-step prediction. As the number of steps increases, the accumulated error value also increases. However, it can be seen that the errors of one-step, two-step, and three-step are small, and the error value gradually increases after the step 3. Therefore, the method of three-step prediction can be considered during the process of engineering construction.

6. Conclusions

In this paper, a highway tunnel under complex geological conditions was studied, and the different excavation sequences and excavation depths were investigated by numerical simulation. The optimal construction scheme was symmetrical excavation (the second scheme), and the excavation depth was 2 m. Then, the LSTM model was selected to predict the tunnel deformation in actual construction. It was found that the MAE value of the model in the tunnel vault and tunnel bottom test set are 0.225 and 0.246, RMSE value are 0.238 and 0.231, the MAE and RMSE value are all small, and the R² values exceeded 90%, indicating that the LSTM model has good generalization ability. By comparing with the actual value and the numerical simulation value, it was found that the trends of the prediction results of both the numerical simulation results and the LSTM model were all consistent with the actual monitoring data. However, the prediction results of the LSTM model were more consistent with the actual monitoring data, and the error is smaller, which can fully prove the effectiveness of the machine learning model. Multi-step prediction can cause accumulation of errors compared with the single-step prediction. However, multi-step prediction is more important for engineering guidance, and three-step prediction can be considered during the process of engineering construction. How to further improve the prediction accuracy of the multi-steps predictions is our next work.