During shield construction in sandy pebble stratum, due to the jacking and extrusion of shield machine and the shear friction between shield shell and soil, the equilibrium state of stratum is disturbed and destroyed, the soil particles move, and the initial stress of stratum changes and redistributes, causing stratum loss. The ground loss V _s is calculated as follows: V s = V s ′ π r 0 2 (1) where, V _s is ground loss in m², V _sˊ is ground loss ratio in % and r ₀ is outer diameter in m.

The loss of sandy gravel stratum caused by shield tunneling is usually the sum of the loss of excavation face, the periphery of shield machine and the tail of shield. When the shield top thrust is extruded during shield tunneling, the soil moves sideways and loosens up in a specific area in front of the excavation face, which is what causes the formation loss at the excavation face, as illustrated in Figure 2. Because the sand pebble stratum contains a lot of pebbles and they are strong, the cutter head and shield machine’s props frequently sustain significant wear. Additionally, when the cutter is replaced or the machine pauses when it runs into significant frontal obstructions, stratum loss occurs. During tunneling, the shield machine will produce varying degrees of friction, shear and extrusion with the surrounding sand pebbles, and a certain thickness of shear disturbance area will be formed around the shield, within which the soil mass will move and cause formation loss, as shown in Figure 3. Additionally, the gap between the outer diameter of the cutter head and the outside circumference of the shield shell and the overbreak of the shield brought on by the attitude adjustment during the tunneling of the shield machine would both result in the loss of the sandy gravel layer. At the shield’s tail, there is a small opening between the segment lining ring and the tunnel excavation wall. Deep soil disturbance and formation loss will result from the soil disturbed by friction shear moving to this gap. Because the sandy gravel stratum has such wide pores and a high permeability coefficient, grouting cannot be done effectively, which will impact the stability of the sandy gravel stratum tunnel later on.

According to the settlement mechanism, the stress state of the excavation surface, the gap between the soil and the shield shell, the over break caused by deviation correction, the grouting pressure at the tail of the shield and other influencing factors are related to the control of the shield construction parameters, mainly including the pressure of the Earth bunker, the tunneling speed, the total thrust of the shield, the torque and speed of the cutter head, the grouting pressure and amount in the same step, and the posture offset of the shield. The working pressure in the soil bin is not always consistent with the real situation due to the weak flow plasticity of sand and gravel, which will impair the stability of the excavation surface and, in severe circumstances, cause surface settlement and collapse. Large stones can easily remain in the soil bin during slag discharge or migrate about, which can impact the shield machine’s ability to maintain its position and attitude. The shield machine’s inability to go forward once obstructed will have an impact on the stability of the excavation surface. Another important aspect impacting surface settlement is the shield tunnel’s depth, which influences whether or not a pressure arch can be built on top of the tunnel to limit soil particle movement and minimize disturbance.

Based on deep learning algorithm based on statistical learning theory, LSSVM replaces quadratic programming optimization in support vector machine by solving linear equations. LSSVM model is an adaptive model, which can change the empirical risk from the first power to the second power, and replace inequality constraints with equality constraints (Lin et al., 2014; Zhang et al., 2022). Compared with the traditional support vector machine, its advantage is to improve the solution speed and simplify the complex calculation. GLSSVM model is based on LSSVM and Grey theory GM (1.1) to accumulate the original data, and then get new sequence data that is less affected by disturbance factors and has stronger regularity. The specific modeling process is as follows:

1) Original data sequence:

The Lagrangian operator is applied to optimize w and e, and the Lagrangian function is established: L ( w , b , e , α ) = J ( w , e ) − ∑ i = 1 n α i { w T φ ( x i ) + b + e i − y i } (6) Where, α _i is Lagrange multiplier, and the differential solution of Eq.4 is carried out. The linear equations are obtained according to the optimal conditions of KKT (Karush Kuhn Tucker): [ 0 E T E Q + I / γ ] [ b α ] = [ 0 y ] (7) Where, y = [y ₁, y ₂, … , y _i ]^T, E = [1, 1, … , 1]^T, α =[α ₁, α ₂, … , α _i ]^T, Q is kernel function for nonlinear mapping, which Q _ij = K (x _i , x _j ), i, j =(1, 2, … , n), and I is identity matrix. The regression model of LSSVM is obtained by solving the equations: f ( x ) = ∑ i = 1 n α i y i K ( x i , x j ) + b (8)

Through calculation, the predicted value of the cumulative sequence is obtained: y _n+k (k = 1, 2, … , n). The prediction model of the original data sequence is obtained by progressive reduction: x ¯ 1 = y n + k + 1 − y n + k (9)

The choice of kernel function has an important impact on the accuracy and accuracy of the prediction results of GLSSVM regression model. GLSSVM regression model usually uses Gaussian radial basis kernel function K (x _i , x _j ) to analyze nonlinear sample data, as follow: K ( x i , x j ) = exp [ − 1 σ 2 ‖ x i − x j ‖ 2 ] (10)

In order to correctly predict unknown data without a priori reference value, the fault-tolerant penalty coefficient of kernel function must be γ and kernel parameters σ ² adjust the two parameters. At present, GA and PSO algorithms are commonly used for parameter optimization, but neither of them can guarantee the optimal solution. If the operator of GA algorithm is embedded into PSO algorithm, and the GA algorithm with excellent change ability is added to the memory ability of PSO algorithm, the whole population can converge rapidly towards the global optimization (Huang et al., 2022). Suppose a group of particles in D-dimensional space, each particle corresponds to a position X and velocity V that can characterize its attributes. When the dth particle swarm iteration is updated, the iteration of motion velocity V _i and motion position X _i of particle i is updated as follows: V i d = ω V i d − 1 + c 1 r 1 ( p B e s t i − X i d − 1 ) + c 2 r 2 ( g B e s t i − X i d − 1 ) (11) X i d = X i d − 1 + V i d (12) Where, ω is inertia weight, i =(1, 2, … , m), d =(1, 2, … , D), and m is number of particles, D is search dimension, c ₁ and c ₂ are acceleration factors, and their values determine the optimization time, which is usually positive, pBest _i is optimal position of particle i, r ₁ and r ₂ are random constants between [0, 1].

The value of the inertia weight ω has a direct impact on both the global and local optimization outcomes. The inertia weight is determined as follows to better balance the local and global search capabilities: ω = ω max − t ⋅ ω max − ω min t max (13) Where, ω max is maximum inertia weight, ω min is minimum inertia weight, ω min is maximum iterations, t is current iterations. It can be seen that the combination of PSO and GA for parameter optimization has the advantages of global convergence of GA algorithm and rapid convergence of PSO algorithm. The topological structure diagram of prediction model for the Earth pressure in chamber is shown in Figure 4, and the prediction process is shown in Figure 5.

The key to build the GA-PSO-GLSSVM bunker pressure prediction model is to choose which tunneling parameters are the input variables to predict the bunker pressure. According to the EPB shield’s affecting elements, there is a strong correlation between Earth bunker pressure and the total thrust, cutter head torque, cutter head speed, propulsion speed, screw machine speed, grouting volume, and grouting pressure (Liu et al., 2010; Yu et al., 2020; Shen et al., 2022). However, under different geological conditions, the relationship between bunker pressure and tunneling parameters is also quite different. It is necessary to determine the tunneling parameters as input variables through correlation analysis according to the actual engineering conditions, and build the bunker pressure prediction model. The correlation between the soil pressure within the chamber and different tunneling parameters is quantitatively described in this study using the Pearson correlation coefficient (PCC): v = ∑ f = 1 p ( Y f − Y ¯ ) ( Z f − Z ¯ ) ∑ f = 1 p ( Y f − Y ¯ ) 2 ∑ f = 1 p ( Z f − Z ¯ ) 2 (14) where, v is Pearson correlation coefficient, Y and Z are parameters to be analyzed and p is number of data groups.

The mean absolute error (MAE), root mean square error (RMSE), coefficient of determination (R ²), and relative error (MAPE) can be used to calculate the discrepancy data and the actual monitoring data in order to assess the accuracy of the prediction model. The prediction result of the prediction model is more accurate and the prediction impact is stronger if the value of the two error indicators approaches 0. The Earth pressure in chamber prediction model’s topological structure, prediction method, and model validity test are as follows: MAE = 1 p ∑ f = 1 p | q f − z f | (15) RMSE = 1 p ∑ f = 1 p ( q f − z f ) 2 (16) R 2 = 1 − ∑ f = 1 p ( q f − z f ) 2 ∑ f = 1 p ( z f − z ¯ ) 2 (17) MAPE = 1 p ∑ f = 1 p ( | q f − z f | z ¯ ) × 100 (18) where, q f is parameter prediction value of group f data, z f measured values of parameters of group f data and z ¯ is average of all measured values.

The starting point of the tunnel between the fifth municipal hospital station and Fengxi station in Chengdu Metro Line 17 is located at the intersection of the north section of Fengxi Avenue and Xifeng street. It is arranged along the north-south direction of Fengxi Avenue, and double track tunneling is accomplished using an Earth pressure balancing shield machine. The left line tunnel is 1610.186 m long, the right line tunnel is 1611.485 m long, and each of the left and right lines uses a separate EPB shield machine. In this segment, the tunnel mostly travels through dense pebble soil layer. The tunnel’s minimum plane curve radius is 450 m, and its longitudinal slope gradient is 10.063‰. The tunnel’s inner diameter is 7500 mm, its outer diameter is 8300 mm, the top of the tunnel is buried at a minimum depth of approximately 9.5 m and a maximum depth of about 20 m in this section. The mechanical properties of the sandy gravel strata are exceedingly complicated, and it exhibits low cohesion and a big gap between its particles. Shield machine tunneling disturbs the stratum significantly, hence it is important to precisely manage the tunneling parameters. During shield tunneling, one set of monitoring data can be obtained for each ring of excavation. The data set is composed of total thrust, cutter head torque, propulsion speed, screw machine speed, screw machine torque, grouting volume and soil pressure. According to the actual monitoring data, there are 1033 groups of data in this section, and a total of 900 groups of data from 101–1000 rings are taken for statistical analysis. In Table 1, the statistical distribution is displayed.

A total of 635 groups of data from 220 to 855 rings are selected for research. Because the shield parameters do not reflect the general conditions of normal tunneling due to the fact that the shield attitude has not yet been adjusted to the normal position at the beginning of shield tunneling, and also during the shield exit., as shown in Figure 6, and the distribution of the Earth pressure in chamber is shown in Figure 7.

The association between the soil pressure inside the chamber and different tunneling parameters is expressed by the Pearson correlation coefficient, and the results of Pearson correlation coefficient is shown in Table 2. The calculations show that the Earth pressure within the chamber is positively correlated with the speed of the cutter head, the propulsion speed, the torque of the screw, and the grouting volume and negatively correlated with the total thrust, the cutter head torque, and the screw speed.

Test the calculated correlation coefficient according to requirement that the two factors are at the confidence level ɑ when |r|≥r _ɑ . The following correlation shows that screw speed, torque, and cutter head speed are all significantly correlated with Earth pressure in the chamber at the level of 0.01, while total thrust, propulsion speed, and grouting volume are significantly correlated at the level of 0.1, and the correlation between screw torque and Earth pressure in the chamber is negligible. Therefore, the cutter head torque, speed, screw speed, grouting volume, propulsion speed, and total thrust are the input variables for the prediction model for the Earth pressure in the chamber.

The training set consists of the first 535 of the 635 groups of data, while the test set consists of the last 100. GM (1.1) model accumulation preprocessing is performed on the learning sample set data, and GLSSVM model is established. The crossover operator and genetic operator of GA algorithm are embedded in PSO algorithm, and the fault-tolerant penalty coefficient of GLSSVM model kernel function is calculated γ and kernel parameters σ ² optimize. The population size is 30, the number of iterations is 300, the crossover rate is 0.6, the variation rate is 0.1, the value range for the two optimization parameters is [0.01, 1000], and the maximum and lowest values of the inertia weight are 0.9 and 0.4, respectively. Local search capability and global search capability c ₁=c ₂ =1.49445. GA-GLSSVM, PSO-GLSSVM and GA-PSO-LSSVM are used to predict and analyze the data set respectively. The change law of fitness MSE is shown in Figure 8.

According to the fitness curves of each model, GA-GLSSVM model has stronger global search ability and PSO-GLSSVM model has faster convergence speed. Embedding GA operator into PSO algorithm can not only realize the global optimization advantage of GA algorithm, but also give play to the advantage of PSO to accelerate the convergence speed and improve the goodness of fit of the model. When calculating the fitness, the Grey theory GM (1,1) is used to accumulate the original data, and the new sequence data with less influence of disturbance factors and stronger regularity can be obtained. Gray superposition can significantly increase the model’s prediction accuracy when compared to GA-PSO-LSSVM and GA-PSO-GLSSVM. The optimal parameter combinations of different models is shown in Table 3.

The optimized parameters of each model are brought into LSSVM model for prediction and analysis. The data accumulated by GM (1,1) model will get the accumulated sequence prediction value, and the prediction value is restored, that is, the original data and the prediction data. The predictions’ outcomes are displayed in Figure 9.

When compared, it can be seen that the PSO-GLSSVM model’s prediction data is comparatively steady and fluctuates only little, although the predicted result is lower than the actual value. The GA -GLSSVM prediction results fluctuate relatively large in the late stage, and the prediction results are larger than the actual value. The benefits of the aforementioned two models are taken into consideration in the GA-PSO-GLSSVM model, and the forecast outcomes are quite similar to the actual values. The GA-PSO-LSSVM model’s predictions have low accuracy and great volatility. After removing certain huge data points from the learning sample set, the distribution of the remaining 524 data is displayed in Figure 10 to demonstrate the model’s correctness.

In order to further verify the effectiveness of the anti-volatility capability of the GA-PSO-GLSSVM model and to illustrate the shortcomings of the GA-PSO-LSSVM model with weak anti-volatility capability, the prediction results of the GA-PSO-LSSVM model before and after removing the volatile data are compared here. Make the model parameters unchanged, take the first 424 data as the training set and the last 100 data as the test samples for GA-PSO-LSSVM prediction, and the results are shown in Figure 11.

After excluding certain big values, the model’s prediction data have less fluctuation and are more accurate when compared to the GA-PSO-LSSVM prediction results in Figure 9. For the original data samples, GM (1.1) accumulation processing of the sample data in GA-PSO- GLSSVM model can effectively reduce the impact of the fluctuation of the original data and improve the prediction accuracy.

Due to its strong water permeability and poor self stability, sandy pebble stratum is easy to cause stratum loss when disturbed. Therefore, there are many factors affecting the pressure of the soil during the excavation process, especially when encountering large-size pebbles or poor slag discharge, it is easy to cause abnormal fluctuations in the pressure of the soil. Through comparison study, it can be found that the GA-GLSSVM, PSO-GLSSVM, and GA-PSO-LSSVM initial prediction accuracy and effect are all rather excellent. The difference between the projected value of the soil pressure in the chamber and the observed value is significant when encountering fluctuating data. As can be observed, the prediction model’s learning effect is negatively impacted by the quick shift in the tunneling scenario, which significantly reduces forecast accuracy. The GA-PSO-GLSSVM model weakens the influence of data fluctuation on the prediction model, and it has significant applicability to predict the pressure parameters of EPB shield in complex strata such as sand and gravel.

The root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and the coefficient of decision (R ²) are used as assessment indicators to assess the accuracy of the prediction model in order to further examine the model’s dependability and accuracy. Table 4 displays a comparison of each model’s prediction accuracy. The GA-PSO-GLSSVM model has superior stability, fitting accuracy, and result accuracy than other models. As can be shown, the GA-PSO-GLSSVM algorithm predicts the Earth pressure in the EPB shield chamber accurately, and the effect of the prediction after GM (1.1) pretreatment is superior to that of the conventional prediction model.