Deformation Analysis of Existing Buildings Affected by Shield Tunnels Based on Intelligent Inversion and Measured Data

Abstract

In the construction of urban underground shield tunnels, uneven deformation can easily occur when the shield passes through soft soil and other poor strata. Such deformation has a significant impact on surface settlement and may cause potential safety hazards to the surrounding existing buildings, directly affecting the safety of urban operation. When simulating and predicting surface settlements, the small-strain soil hardening model can more accurately characterize the mechanical parameters of soil. Nevertheless, its parameters are numerous and complicated to determine accurately, so parameter inversion is needed to determine the accurate parameters of the soft soil layer in order to more accurately predict the surface settlement. This study uses the EFAST method to analyse the sensitivity of the HSS model parameters of soft soil strata. It is determined that the parameters that have the most significant impact on the surface settlement are the reference tangent modulus, rebound modulus, and effective cohesion. Then, XGBoost’s fast calculation speed and high precision of SSA inversion are used to inverse and optimize the parameters with high sensitivity. Finally, according to the parameters of the soft soil layer obtained from inversion and measured data, the settlement deformation and safety behaviour of existing buildings are analysed. Combined with the actual shield tunnel project in a city along a river, the inversion calculation shows that the overall average error of the transverse monitoring section is 1.04 mm, and the average maximum error of each monitoring point in the overall shield process is 2.87 mm. The prediction effect is significantly improved compared with the original parameters. The accuracy of the inversion of soil layer parameters is verified from the perspective of time and space. The average settlement of the river embankment foundation is 2.5 mm. Compared with the original parameter data, the prediction results have been greatly improved, and the settlement deformation results are more consistent with the measured data.

1. Introduction

With the rapid development of the economy and the continuous growth of urban populations, the density of urban buildings is also increasing, and underground space development has gradually become popular in major cities [1]. At the same time, this may also cause some potential safety hazards to the surrounding existing buildings. Many pipelines, including urban underground tunnel projects, such as water conveyance, transportation, communication, and power [2], need to be buried underground. To make rational use of underground space, various underground pipelines should be integrated to create intensive and multifunctional underground tunnels, which can alleviate not only urban traffic pressure but also achieve multidimensional collaborative integration of urban space. However, it is inevitable that existing buildings on the ground may be impacted when underground tunnel projects are carried out in cities. Such impacts are mainly caused by ground settlements that occur due to the shield tunnelling process. In tunnel construction methods, the shield tunnelling method is widely used in urban underground tunnel construction because of its strong adaptability, small settlement impact, low cost, and short construction period compared with other methods. In some coastal cities, underground tunnel projects often encounter situations of soft soil interlayers. Due to the poor parameters of the soft soil stratum, difficulties in determining mechanical parameters, and more significant disturbances of the stratum generated by shield tunnelling, large-scale collapse of the soft soil stratum is prone to occur [3], resulting in substantial surface subsidence that poses significant safety hazards to the surrounding buildings on the surface [4,5]. Therefore, it is of great practical significance to invert the mechanical parameters of the soft soil layer in numerical simulations to more accurately predict the impacts of shield tunnels on surface settlements and surrounding buildings.

Shield construction is a highly complex, multi-effect coupling underground construction process. The distribution of the soil layer and its mechanical parameters, construction parameters, lining support assembly method, tunnel burial depth, and other factors all act on the ground and affect the surface settlement deformation, affecting the existing buildings on the surface. When analysing the existing buildings, it is necessary to first study the surface settlement. At present, there are four main research methods with regards to surface settlement caused by shield construction: empirical methods, analytical solutions [6,7,8], model test methods [9,10,11], and numerical simulation methods [12,13,14,15]. The famous Peck formula was first proposed by R.B. Peck [16]. This formula, which is based on actual engineering data, is used to express the general law of surface subsidence. However, empirical methods can only express the qualitative law of surface subsidence, with limited prediction ability for actual complex engineering. Regarding the analytical solution, Wei Gang [17] combined the tangent soil loss model with the focal point movement coordinate to analyse the surface settlement and obtained a general solution for the surface settlement. However, the derivation process of the analytical solution is complex, and the number of parameters considered is too few, which restricts its application in practical engineering. Regarding the model test method, Zhang Zixin et al. [10] analysed the impact of construction parameters on surface settlement through model tests and obtained the optimal values of the grouting amount, grouting pressure, and other parameters. Boonyarak [18], Marshall [19], and Siyue He [20] successively studied the response of pile groups caused by shield construction through model tests. The deformation law can be obtained through the model test method, which also provides a reference for practical projects. However, the model test cost is high and easily affected by various factors, resulting in excessive errors; thus, it can only be used as a regular guide for practical projects. Regarding the numerical simulation method, Zhu Caihui et al. [21] conducted a numerical simulation of shield tunnelling through saturated loess strata and obtained a parameter range that meets the control value of surface settlement. Lv Jianbing et al. [22] conducted a construction simulation of two closely connected shield tunnels and determined that setting isolation piles for reinforcement can effectively reduce lining deformation and surface settlement. The numerical simulation method can quickly and efficiently predict the ground deformation of shield construction and is also widely used in the deformation analysis of existing buildings [23,24]. However, the parameters significantly affect the numerical simulation method, and its prediction accuracy will also be substantially affected when the soft soil layer’s parameters are difficult to determine accurately. Therefore, it is necessary to build an intelligent algorithm to inverse the mechanical parameters of soft soil to improve the accuracy of the simulation prediction.

The commonly used constitutive models in the numerical simulation of shield tunnel construction are the Mohr–Coulomb model (the M–C model) and the small-strain soil hardening model (the HSS model), which have been widely considered in recent years. Compared with other constitutive models, the HSS model can obtain more accurate calculation results in foundation pit excavation and shield tunnel simulation, due to its more reasonable consideration of the small strain characteristics of soil [25,26]. Liu Dawei [27] and others have used the HSS model for the numerical simulation of deep foundation pit projects. Fan Pengcheng [28] and Zhu Hongxi [29] have used the HSS model in shield tunnelling projects, verifying the model’s accuracy. There have been in-depth studies on selecting the HSS model parameters in foundation pit projects in many regions [30,31,32]. When selecting the HSS model for calculation, many parameters need to be input, the inversion of all parameters is relatively complex, and it is not easy to ensure the accuracy of inversion under the influence of many parameters. Therefore, sensitivity analysis is prioritized to determine the parameters that have the most significant impact on surface subsidence, providing a basis for parameter inversion.

In summary, an actual urban shield tunnel project that contains a typical shield section with a soft soil layer is studied, a global sensitivity analysis on the parameters of the soft soil layer is conducted, the parameters of the soft soil layer that are most sensitive to the surface settlement under the effect of multiparameter coupling are determined, and their accurate values are obtained by constructing an intelligent algorithm for parameter inversion. Finally, finite element software is used to carry out refined modelling and to simulate the whole process of shield excavation, and the impact of the shield construction process on the surface settlement and the deformation of surrounding buildings is analysed based on measured data.

2. Constitutive Model and Algorithm Principle of the Shield Tunnel

2.1. Small-Strain Soil Hardening Model

The HSS model is a constitutive soil model proposed by Benz [33], based on the soil hardening model (the HS model), which can consider the small strain characteristics and unloading characteristics of the soil. It has been widely used in the analysis of foundation pit engineering in soft soil areas, but it is rarely used in the study of shield tunnel engineering. In practical engineering, the range of soil stiffness showing complete elasticity is very small. With the expansion of the strain range, most of them will show nonlinear attenuation, and the attenuation is usually less than 1/2 of the initial state modulus. In tunnel engineering, the strain range of soil mostly belongs to the range of small strain [34], as shown in Figure 1. Therefore, compared with the M–C model, the HSS model, which considers the small strain characteristics of soil, has a higher prediction accuracy in the model prediction with soft soil strata. Corresponding research has been conducted and verified in practical projects in many places, such as Shanghai [35], Ji-nan [36], and Bei**g [37].

The HSS model contains 11 parameters based on the HS model, and two parameters are added on the basis of the HS model to describe the small strain stiffness. Some parameters under the standard triaxial drainage test are calculated as follows:

$$E_{50}=E_{50}^{ref}{\left(\frac{c\cos \phi -{\sigma }_3^{\prime }\sin \phi }{c\cos \phi +p^{ref}\sin \phi }\right)}^m$$

(1)

$$E_{oed}=E_{oed}^{ref}{\left(\frac{c\cos \phi -\frac{{\sigma }_3^{\prime }}{K_0^{nc}}\sin \phi }{c\cos \phi +p^{ref}\sin \phi }\right)}^m$$

(2)

$$E_{ur}=E_{ur}^{ref}{\left(\frac{c\cos \phi -{\sigma }_3^{\prime }\sin \phi }{c\cos \phi +p^{ref}\sin \phi }\right)}^m$$

(3)

where $E_{50}^{ref}$ is the corresponding reference secant modulus when the reference confining pressure is $p_{ }^{ref}$ = 100 kPa, $E_{oed}^{ref}$ is the corresponding reference linear modulus when the confining reference pressure is $p_{ }^{ref}$ = 100 kPa, $E_{ur}^{ref}$ is the reference Young’s modulus for unloading and reloading, ${\sigma }_3^{\prime }$ is the confining pressure of the triaxial test, $c$ is the cohesive force of soil, $\phi$ is the internal friction angle of soil, and $m$ is the degree of stress correlation.

In addition to the above soil hardening parameters, the HSS model also needs to consider two additional small strain parameters: $G_0^{ref}$ and ${\gamma }_{0.7}^{ }$. The main factors affecting these two parameters are the material’s stress state and void ratio.

$$G_0=G_0^{ref}{\left(\frac{c\cos \phi -{\sigma }_1^{\prime }\sin \phi }{c\cos \phi +p^{ref}\sin \phi }\right)}^m$$

(4)

$$G_0^{ref}=\frac{{\left(2.79-e\right)}^2}{1+e}33[MPa]$$

(5)

$${\gamma }_{0.7}\approx \frac{1}{9G_0}\left[2c^{\prime }\left(1+\cos \left(2{\phi }^{\prime }\right)\right)-{\sigma }_1^{\prime }\left(1+K_0\right)\sin \left(2{\phi }^{\prime }\right)\right]$$

(6)

where $e$ is the void ratio, $K_0$ is the coefficient of static side pressure, $c^{\prime }$ is the effective cohesion of the soil mass, ${\phi }^{\prime }$ is the adequate internal friction of soil mass, ${\sigma }_1^{\prime }$ is the effective vertical stress, and ${\gamma }_{0.7}$ is the corresponding shear strain when the shear modulus decays to 70% of the initial shear modulus.

2.2. EFAST Global Sensitivity Analysis Method

The extended Fourier amplitude sensitivity test (EFAST) is a global sensitivity analysis method that Saltelli et al. [38]. developed by combining the Sobol method and the FAST method. The EFAST method based on variance decomposition is used to analyse the Fourier series spectrum curve obtained by the Fourier transform and obtain the impact of each parameter coupling on the output. The first-order sensitivity and global sensitivity of each parameter can be obtained by calculating the model variance. The first-order sensitivity indicates the impact of a single parameter change on the model, and the global sensitivity suggests the effect of a parameter on the model under overall parameter coupling. Its calculation formula is briefly introduced as follows:

$$V_i={\displaystyle \sum _{p\in \Sigma }{\Lambda }_p}{\omega }_i=2{\displaystyle \sum _{p=1}^{\infty }{\Lambda }_p}{\omega }_i$$

(7)

$${\Lambda }_p=A_p^2+B_p^2$$

(8)

where $V_i$ is the model output variance caused by changes in the parameters $x_i$; ${\omega }_i$ is the oscillation frequency of the parameters $x_i$, $i$ = 1,2, …, $m$; $A_p$ and $B_p$ are the Fourier amplitudes; and $p\in Z=\{-\infty ,\cdots ,-1,1,\cdots ,+\infty \}$.

2.3. EFAST Global Sensitivity Analysis Method

2.3.1. Basic Principle of SSA

The sparrow search algorithm [39] (SSA) is inspired by the sparrow’s foraging and anti-predation behaviour. Its overall idea is to divide different roles in the sparrow population according to the evaluation of fitness values. Those with high fitness values are called producers and are responsible for searching for food, while those with low fitness values are called beggars and follow the producers to obtain food. When an individual sparrow finds a predator, it will immediately produce an alarm. The producer will quickly lead the population to a safe area to continue searching for food. The algorithm has the advantages of a good search accuracy, fast convergence speed, and strong robustness.

The specific process of the algorithm is as follows: (1) initialize the population, set the number of iterations and the proportion of producers and beggars; (2) calculate and sort the initial fitness; (3) update the location of the producers, beggars, and predators; (4) calculate the new fitness value and determine whether to carry out the iterative operation according to the fitness value; and (5) stop the iteration after the specified number of iterations or certain conditions are met and determine the optimal value.

2.3.2. Basic Principles of XGBoost

Extreme gradient boosting (XGBoost) is a tree-based model. It improves accuracy by building a set of multiple decision trees. Its goal is to improve the generalization ability of the model by improving its accuracy. XGBoost is different from traditional gradient boosting. It uses more technologies to improve the training speed and model accuracy. The three features of XGBoost are as follows:

(1)

Loss function: XGBoost uses the loss function to measure the model’s accuracy. It uses the mean square error (MSE) as the default loss function, but other loss functions can also be used if there are first and second derivatives.

(2)

Learning objective: XGBoost uses the gradient of the minimization loss function to learn the model. In each iteration, the loss function is expanded by a second-order Taylor expansion. In the next iteration, both the first derivative and the second derivative are considered to speed up model learning.

(3)

Regularization: XGBoost uses regularization to prevent overfitting. It uses L1 and L2 regularization to reduce the complexity of the model.

The advantage of XGBoost is that it can train models faster, and the accuracy of models is higher than that of traditional gradient boosting. It can also process a large number of features and can automatically detect the correlation between features to improve the accuracy of the model.

3. Sensitivity Analysis of the HSS Model’s Parameters

3.1. Construction of the Idedal Shield Model

When analysing the influence of the HSS model parameters on surface settlements, an ideal soil model composed of a single soil layer is established [37] to avoid the influence of other factors, such as soil layer distribution, and the effect of groundwater is not considered. Only the sensitivity of constitutive model parameters is considered. By changing the parameters of the HSS model and carrying out finite element numerical calculations, the corresponding surface settlement value is obtained to analyse the influence of the parameters of the soft soil layer on the surface settlement. To simplify the calculation, the overall model is a symmetrical half structure, and the model size is taken as 100 m along the excavation direction, 40 m perpendicular to the excavation direction, and 50 m below the surface. This size is sufficient to take into account the development of any possible failure mechanism and reduce the impact of model boundary effects. The 10-node tetrahedral element is used for the model, and the ground settlement monitoring point above the tunnel axis at Y = 30 m is selected. The ideal single soil layer model and the location of the ground settlement monitoring point are shown in Figure 2:

3.2. Determination of the Range of the HSS Model’s Parameters

Thirteen parameters are required for the HSS model, among which $G_0^{ref}$ and ${\gamma }_{0.7}^{ }$ are unique parameters that characterize the small strain characteristics of the soil mass, though these have been little research undertaken on them. The loading and unloading Poisson’s ratio ${\nu }_{ur}^{ }$ can be obtained in the model calculation, and its default value is 0.2. The static side pressure coefficient is $K_0$ = 1 − $\sin \phi$, and the reference confining pressure is $p_{ }^{ref}$ = 100 kPa. The value ranges of other parameters in this calculation are shown in

Table 1. HSS model parameters definition and experience value.

Parameter	Experience Value	Parameter Lower Limit	Parameter Upper Limit
$E_{50}^{ref}$	$E_{50}^{ref}$$\approx 1.02E_{\mathrm{s}1-2}$	2.0	50
$E_{oed}^{ref}$	$E_{oed}^{ref}$ ≈ 0.81$E_{\mathrm{s}1-2}$	1.6	48
$E_{ur}^{ref}$	$E_{ur}^{ref}$ = 3~5$E_{\mathrm{s}1-2}$	6.0	250
${\mathrm{c}}^{\prime }$	${\mathrm{c}}^{\prime }$ = −1.32 (${\phi }^{\prime }$ − 33)	0.0	50
${\phi }^{\prime }$	${\phi }^{\prime }$ = 26.9$e^{-0.72}$	10.0	30
$\psi$	$\psi$ = ${\phi }^{\prime }$ − 30, if ${\phi }^{\prime }$ < 30, $\psi$ = 0	-	-
$R_f$	0.5~0.95	0.5	0.95
$G_0^{ref}$	$G_0^{ref}$ = 6~12$E_{\mathrm{s}1-2}$	20.0	300
$m$	0.5~0.9	0.5	0.9
${\gamma }_{0.7}$	1~9 × 10−4	1 × 10−4	9 × 10−4

.

In addition to taking the default values of $K_0$, $p_{ }^{ref}$, ${\nu }_{ur}^{ }$ and $\psi$, to consider the coupling effect of multiple parameters, other parameters are taken as the target parameters during sensitivity analysis. A total of nine parameters are considered. Random sampling is performed within the parameter range to generate a multidimensional parameter set. The EFAST method stipulates that the sampling times must be 65 times greater than the number of parameters for the analysis results to be valid [40]. The more samples there are, the more reliable the results. Therefore, a sample group of 200 times the number of parameters is generated during sampling, and a total of 2000 groups of samples are generated after rounding. All parameter samples are evenly distributed. After verification by many documents, it was determined that a certain proportional range relationship exists between the selection of the modulus parameters $E_{50}^{ref}$, $E_{oed}^{ref}$, $E_{ur}^{ref}$, $G_0^{ref}$ and the compression modulus of soil $E_{s1-2}^{ }$. Therefore, $E_{s1-2}^{ }$ is sampled first. Then, appropriate proportions are set for the parameters that have a proportional range relationship with $E_{s1-2}^{ }$. The sampling method adopts Latin hypercube sampling (LHS) to sample and finally obtain the model parameter samples required for sensitivity analysis, while the corresponding surface subsidence samples are predicted through finite element calculation combined with the trained XGBoost model and finally obtain complete sensitivity analysis data.

3.3. Results of the Global Sensitivity Analysis of HSS Constitutive Model Parameters

The EFAST algorithm is used to calculate the first-order sensitivity and global sensitivity of the HSS model’s parameters to surface settlement. The first-order sensitivity represents the impact index of a single parameter change on the model, and the global sensitivity represents the impact index of a parameter on the model under the interaction of different parameter combinations containing it. The calculation results are shown in Figure 3 below.

Based on the sensitivity analysis results in Figure 3, the following conclusions are drawn. (1) Among the nine selected soil layer parameters, the parameter that has the greatest impact on surface settlements is $E_{50}^{ref}$, with the first-order sensitivity index of $E_{50}^{ref}$ being much higher than other parameters, indicating that the impact of $E_{50}^{ref}$ on surface settlements is mainly caused by its direct effect and is less affected by other parameters. (2) The impact of $E_{ur}^{ref}$ and ${\mathrm{c}}^{\prime }$ on surface subsidence is secondary, with a smaller first-order sensitivity index and a larger global sensitivity index, indicating that these parameters interact with other parameters to produce indirect effects on surface subsidence. (3) The first-order sensitivity indices and global sensitivity indices of other parameters are small, with values less than 0.2, which means that their impact on surface subsidence is minimal and can be regarded as negligible, and these indices can be substituted into empirical values in subsequent inversion.

The three parameters that have the greatest impact on surface subsidence are selected, and a three-dimensional scatter diagram of their impact on surface subsidence is drawn, as shown in Figure 4. The coordinate axes in Figure 4 represent the three most sensitive parameters, and the data point colour represents the surface subsidence size. The results show that the smaller the three influence parameters are, the larger the settlement deformation value is, and vice versa. The reference secant modulus $E_{50}^{ref}$ has the most significant impact on the surface settlement, which is consistent with the sensitivity analysis results. Through sensitivity analysis, nine formation parameters to be determined in the HSS model were reduced to three important parameters, which narrowed the calculation range for subsequent constitutive model parameter inversion and improved the purpose and accuracy.

4. Construction of the Material Parameter Inversion Model Based on SSA-XGBoost

When sensitivity analysis and parameter inversion of soil layer HSS constitutive model parameters are carried out, many constitutive model parameter samples must be calculated. However, the traditional finite element model has limited computing power and cannot complete the deformation calculation of a shield tunnel with many samples in a short time. The XGBoost model is used instead of the finite element model to predict the deformation of the shield tunnel to achieve rapid and efficient acquisition of surface settlement.

The core of XGBoost is the engineering implementation of the gradient-optimized GBDT algorithm. The GBDT algorithm has been greatly optimized and improved [41] so that it can process a large amount of data at an extremely fast speed while ensuring a high accuracy. Regular items have been added to XGBoost [42], the overfitting phenomenon of the model is well controlled, and the calculation efficiency and versatility are improved. In addition, XGBoost’s flexible scalability and portability greatly improve the computer’s machine learning ability. Therefore, XGBoost has a stronger fitting ability than ANN, RF, and LR models [43,44]. However, XGBoost has a poor ability to process ultrahigh-dimensional feature data, and many parameters need to be adjusted in the algorithm. Some parameters have a greater impact on the calculation results. The aim of this paper is to solve the complex problem of adjusting the algorithm parameters by using the Sparrow Search Algorithm (SSA) to automatically optimize the internal parameters of XGBoost to achieve a better model fitting and prediction ability. Then, XGBoost is used as the proxy calculation model, SSA is used again to inverse and optimize the parameters of the constitutive soil model, and a certain number of iterations are set to ensure the accuracy of the inversion results. The inversion analysis steps established in this paper are as follows:

(1)

Through the sensitivity analysis results, the most sensitive soil layer parameters to the surface subsidence are obtained and are taken as the inversion target. Moreover, their variation ranges are determined. Then, the LHS method is used for sampling to form a set of parameters to be inverted;

(2)

The finite element calculation model of shield tunnel excavation is established, and the ground settlement corresponding to the set of parameters to be inverted is calculated;

(3)

The parameter set to be inverted and the corresponding surface subsidence are used as training and test samples for the XGBoost model, and SSA is used to optimize the parameters of the algorithm model to determine whether the required accuracy is achieved based on the prediction results of the test group. Finally, a finite element calculation proxy model is constructed;

(4)

The SSA algorithm is used for parameter optimal value inversion, and the inversion result is determined by determining whether the fitness is optimal;

(5)

The inversion parameters are used to simulate and predict the existing buildings within the influence range of shield tunnelling and analyse and compare the calculated values of the inversion parameters with the actual settlement values.

The overall process of constructing the SSA-XGBoost model for parameter inversion based on the sensitivity analysis results is shown in Figure 5 below.

5. Engineering Example

5.1. Introduction to a Shield Tunnel Project

To optimize the layout of water plants in the main urban area and improve the demand for urban water supply capacity, a city needs to lay water transmission pipelines along the riverside roads before the relocation of the original water plants, complete the water supply and promote high-quality water resources into the main urban area. At the same time, to make comprehensive planning and rational use of urban underground space, the water conveyance gallery also undertakes the function of underground transportation to release the vitality of ground space, enhance the vitality of the city, and shape the integration of the river and the city. The water transmission pipe gallery is located in the core section north of the riverbank and is an important hub to connect the scenic spots nearby. The project is 6.3 km long, and the open-cut method and shield method are used for construction, of which the shield section is 3.6 km long. Moreover, the tunnel runs along the river. The overall project is shown in Figure 6:

The west shield section mainly passes through the moderately weathered argillaceous siltstone section. After the statistical analysis of the surface settlement data, the surface deformation value is small, and the deformation range is within ±5 mm, which is less than the surface deformation control value. This indicates that the geological engineering conditions are relatively good. At the same time, the shield tunnel is deeply buried, which has little impact on the surface settlement. However, in some shield sections, the soil layer containing a soft soil interlayer (muddy silty clay) is crossed. The mechanical properties of the soft soil layer are poor, and it is vulnerable to the impact of shield tunnelling. Relevant research shows that shield tunnels containing a soft soil layer are prone to uneven settlement [3]. The existing monitoring data also show that its surface subsidence is significantly increased. The extreme value of surface subsidence is far greater than the data with regards to crossing the moderately weathered sandstone section. Therefore, in this paper, the soft soil to the interbed section is selected for numerical simulation analysis. The shield section selected for this calculation mainly crosses six types of strata: gravel fill, silty clay with gravel, muddy silty clay, and siltstone. According to the geological exploration data and HSS constitutive model experience, some of the original parameters that need to be inverted are shown in

Table 2. Original parameters of the soil mass.

Soil Layer Name	Severe g/kN/m3	Reference Secant Modulus E50/MPa	Modulus of Resilience Eur/MPa	Effective Cohesion c′/kPa
Gravel fill	19.3	15	4.0	2
Sandy silt	18.5	13	6.0	25
Silty siltstone	17.2	9	2.2	13
Completely weathered argillaceous siltstone	19.3	16	6.0	40
Strongly weathered argillaceous siltstone	20.3	26	18.0	24
Moderately weathered argillaceous siltstone	25.0	35	40.0	230

:

5.2. Numerical Model Construction and Simulation Method of the Shield Tunnel

The soil mass of the selected shield section belongs to the typical soft soil layer in this area, and the soil layer distribution in this section is relatively uniform. After the weighted average treatment of the soil layer thickness near it, the uniform thickness stratum is taken for modelling. The central buried depth of the selected monitoring section shield tunnel is 21.67 m, and the thickness of the overlying soil layer is 14.42 m. The shield tunnel adopts the form of a single round section with an inner tunnel diameter of 13.3 m. The lining is poured in a single layer, with a lining thickness of 600 mm and an outer diameter of 14.5 m. In the shield tunnel project, it is considered that the influence range of the construction process on the surrounding soil is 2~3 times the tunnel diameter. Since the stratum is distributed axially, the finite element model is constructed as an axisymmetric structure along the centreline of the tunnel diameter to simplify the model and reduce the calculation time. To eliminate the influence of end shield excavation, the overall finite element model size is 100 m × 40 m × 48 m, and the thickness of each soil layer is taken as the weighted average of the adjacent borehole data. The shield machine body is a steel structure, simulated by plate elements, with a thickness of 0.17 m and a weight of 247 kN/m³. The tunnel lining is made of C60 concrete, and the lining is simulated by the solid element. The friction displacement between the soil and the lining is not considered in the simulation. The overall mesh is divided by a 10-node tetrahedral element. The model includes 68,223 nodes and 42,788 grid cells. The overall model is divided into 50 rings, and the monitoring section is at the 25th ring with Y = 50 m. The finite element model and monitoring point locations of the selected shield project section are shown in Figure 7:

Since the construction process of a tunnel shield is a complex dynamic process, each excavation link contains many construction links. To ensure the accuracy and efficiency of the calculation, the main links are simplified in the finite element numerical simulation as follows: (1) freeze the soil mass of the excavation ring and simulate the excavated soil mass; (2) apply surface load on the excavation face to simulate the pressure of the tunnel face to balance the earth pressure, and apply circumferential uniform load on the shield tail to simulate the impact of grouting pressure on the soil during grouting; (3) apply a uniform load opposite to the shield direction on the lining to simulate the process of jack thrust pushing the shield machine to excavate the next ring; and (4) repeat the above steps for the next shield. In this simulation, the variation law of ground settlements with time is considered. Each forward excavation of the shield machine is an excavation step, and 42 excavation steps are set. The whole tunnel excavation simulation process is shown in Figure 8:

5.3. Analysis of the Back Analysis Results of Shield Tunnel Parameters Based on the SSA-XGBoost Algorithm

In the third part, the sensitivity analysis of the HSS model parameters of soft soil stratum containing muddy silty clay is carried out, and the three parameters with the highest global sensitivity, that is, the maximum impact on surface settlements, are $E_{50}^{ref}$, $E_{ur}^{ref}$ and ${\mathrm{c}}^{\prime }$. On this basis, SSA’s better parameter inversion capability and XGBoost’s high-precision fitting and prediction capability are used to invert the three most sensitive parameters above. The optimal formation parameters are obtained through continuous fitting and iterative calculation. The final calculation results are shown in

Table 3. Parameter inversion results of HSS constitutive model based on SSA-XGBoost.

	Reference Secant Modulus E50/MPa	Modulus of Resilience Eur/MPa	Effective Cohesion c′/kPa
Laboratory test value	2.2	6.6	13
Parameter variation range	1–10	3–30	0.25
Inversion optimal value	1.83	5.50	10.13

below:

The shield excavation process can be divided into three stages: the early stage of shield crossing, the period of shield crossing, and the period of shield tail pulling out. Before the shield is excavated to Rings 5~10 of the monitoring section, it is generally the early stage of shield crossing. In this period, the surface settlement typically changes very little and will be slightly uplifted due to the influence of the tunnel face pressure. The period from the shield excavation to the first 5~10 rings of the monitoring section to the back 5~10 rings of the monitoring section is generally the shield crossing period, during which the shield tunnelling process has the greatest disturbance on the stability of the stratum. Generally, more than 90% of the deformation occurs in this period. After the shield is excavated to the 5th to 10th ring behind the monitoring section, the tail of the shield comes out. During this period, the lining construction is completed, the stratum gradually returns to stability, and the surface settlement also tends to fluctuate near a stable value.

The constitutive model parameters obtained from inversion are substituted into the finite element model, and the surface settlement amount is calculated under the optimal inversion parameters. Figure 9 shows the comparison of the time distribution of the surface settlement amount with the excavation process. The monitoring points in Figure 9a are the surface monitoring points above the shield excavation axis and are also the monitoring points with the largest surface settlement. Figure 9f is the monitoring point farthest from the tunnel axis, and the others are the intermediate monitoring points. The overall settlement trend of the monitoring points and the excavation process are more consistent with the actual monitoring values, but the numerical accuracy differs greatly. After the SSA-XGBoost algorithm inversion, the calculated parameters are more consistent with the actual monitoring data than the original parameters. In the shield tunnelling period, the surface settlement calculated by numerical simulation is occurs earlier than in the actual situation. The time for the surface settlement to enter the stable period is also faster. At the same time, the settlement calculated by numerical simulation is greater than the actual settlement value, which is considered the lag of the grouting pressure calculation in the finite element calculation process. The calculated settlement values tend to be stable during the shield tail exfoliation period. The maximum settlement value is located at the monitoring point above the tunnel axis. The measured settlement value is 17.54 mm, the calculated settlement value of the original parameter is 13.52 mm, and the calculated settlement value of the parameter after inversion is 16.72 mm. The difference between the calculated value after inversion and the measured value is only 0.82 mm. The stability value of the inversion parameter calculation results is closer to the actual monitoring data.

Figure 10 shows the comparison of the spatial distribution of the horizontal surface settlement on the selected monitoring section, and Figure 10a shows the slight uplift generated in the early stage of shield crossing. Figure 10b shows the shield crossing period, during which the ground settlement data are quite different. Because the shield crossing period of the numerical simulation is shorter than that of the actual ground settlement, the numerical simulation calculation values of both the inversion parameters and the original parameters are larger than the measured values in this period. Figure 10c shows the stable period of surface subsidence after the shield tail is removed. The overall error between the surface subsidence calculated by the original parameters and the actual monitoring value is 3.63 mm, and the maximum error is 5.04 mm. The overall error between the calculated parameters and the actual value after inversion is 1.04 mm, and the maximum error is 2.24 mm. From the above analysis, it can be seen that in terms of the spatial distribution of surface subsidence, the surface subsidence amount recalculated by inversion parameters is more consistent with the actual monitoring value, and the overall subsidence trend is more consistent with the actual situation.

Figure 11 shows the error comparison analysis chart of the original parameter calculation results and the inversion calculation results. Taking a total of 20 groups of data between the ground surface deformation at the early stage of shield tunnelling at each monitoring point and the stable ground settlement after the shield tail is pulled out as an example, the average absolute error (MAE), root mean square error (RSME), and average percentage error (MAPE) are calculated. The a–f axis in the Figure 11 corresponds to each monitoring point in Figure 9. Among them, the monitoring point located at the tunnel axis has the largest surface settlement value, resulting in large errors. The calculated errors of the parameters at each monitoring point after inversion are less than the calculation errors of the original parameters, which verifies that the parameters of the constitutive model obtained after inversion through the SSA-XGBoost model built in this paper are closer to the actual data. The accuracy of the surface settlement calculation through numerical simulation is greatly improved, and the capability of predicting the surface settlements for subsequent projects is optimized.

5.4. Deformation Prediction of the Existing Building Based on Inversion Results

The shield project is built along the river. There is an embankment on the riverbank. The minimum horizontal clear distance between the shield tunnel and the embankment is approximately 20 m, which is within the influence range of shield construction. Moreover, the height difference between the soil layers on both sides of the river embankment is close to 8 m. Due to the influence of surface settlement caused by shield excavation and unloading, the river embankment may have horizontal displacement and tilt, especially in the shield section with a soft soil layer. It is more likely to have a large displacement. In this section, the results of the parameter inversion are used to model and analyse the river embankment with a soft soil layer. Other soil layer parameters are provided in Table 2. The river embankment material is C20 concrete. To eliminate the influence of the model size, the model is 100 m along the shield direction, 140 m wide and 70 m deep, and the monitoring section is taken as Y = 50 m in the middle of the model. After the completion of shield excavation and crossing, the vertical displacement nephogram of the embankment finite element model and monitoring section is shown in Figure 12 below:

Figure 13 shows the comparison of the variation in the river embankment settlement with the excavation process under different parameters. The measured river embankment settlement data show that with the progress of shield excavation, the river embankment gradually produces settlement. When the shield excavation passes through the monitoring section, the river embankment settlement is relatively obvious. After the shield machine tail is far from the monitoring section, the river embankment settlement gradually becomes stable, and the final settlement is stable at approximately −2.3 mm. The final settlement of the embankment calculated by parameter inversion is stable at 2.5 mm, while the final settlement of the embankment calculated by the original parameter is stable at −1.6 mm. Compared with the original parameter settlement, the settlement predicted by parameter inversion is more consistent with the actual monitoring value, which proves that the calculation of the intelligent inversion model built in this paper is accurate. It can better reflect the material characteristics of muddy silty clay strata and lay a foundation for the accurate prediction of the surface settlements and deformations of existing buildings.

According to the finite element calculation and analysis, the riverside embankment has uneven settlement due to the influence of shield excavation, and the dike is slightly inclined to the shield excavation side (inner side) as a whole. Taking the foundation plane of the river embankment as the standard, the parameter inversion calculation shows that an uplift of 0.8 mm is generated on the riverside and that a vertical settlement of 4.4 mm occurs at the excavation side of the shield. The top of the dike has a horizontal displacement of 9.6 mm towards the riverside, and the foundation plane of the dike has a horizontal displacement of 13.5 mm towards the riverside. Due to shield excavation, the river embankment has an overall inclination of 0.046°. According to the calculation of the original parameters, an uplift of 0.75 mm is generated at the riverside side, and a vertical settlement of 3.75 mm is generated at the shield excavation side. The top of the embankment has a horizontal displacement of 8 mm to the riverside, and the foundation plane of the embankment has a horizontal displacement of 11.3 mm to the riverside. Affected by shield excavation, the river embankment has an overall inclination angle of 0.038°. The settlement results show that the calculation results of the original parameters are too small to accurately reflect the safety form of the existing buildings. Therefore, it is necessary to carry out an inversion of the parameters of the soft soil layer in this study. Cloud diagrams of the embankment deformation and displacement are shown in Figure 14 and Figure 15.

Figure 16 shows the distribution diagram of the effective principal stress of the river embankment. In the diagram, the tensile stress is a positive value, and the compressive stress is a negative value. In the calculation results of the inverse parameters, a maximum tensile stress of 0.63 MPa and a maximum compressive stress of 0.43 MPa are generated due to the uneven settlement of the embankment. In the calculation results of the original parameters, the maximum tensile stress of 0.34 MPa and the maximum compressive stress of 0.34 MPa are generated due to the uneven settlement of the embankment. The maximum tensile stress is located at the excavation side of the river embankment toe shield, which is less than the tensile strength of C20 concrete. The settlement deformation and stress of the river embankment caused by shield excavation meet the river embankment safety control standards.

6. Conclusions

Shield sections with soft soil interlayers are prone to large ground settlements during shield construction. Therefore, in this paper, a sensitivity analysis of the soil parameters of the soft soil interlayer is performed. Moreover, the goal of this study is to accurately determine the soil parameters in the HSS constitutive model. The SSA-XGBoost algorithm is built to inverse the parameters with the highest sensitivity to ground settlement to obtain more accurate soil parameters; the accuracy of the numerical simulation is improved. Finally, the settlement deformation of the river embankment beside the shield tunnel is calculated and analysed by using the parameters obtained from the inversion. The main conclusions are as follows.

(1)

The EFAST method is used to analyse the influence of various soil layer parameters on surface settlement, and the reference secant modulus is set as the soil layer parameter with the highest sensitivity to surface settlement deformation in the HSS constitutive model, $E_{50}^{ref}$. The modulus of resilience is $E_{ur}^{ref}$ and the effective cohesion is ${\mathrm{c}}^{\prime }$.

(2)

The SSA-XGBoost algorithm is constructed to carry out parameter inversion for the three parameters that have the greatest impact on the surface settlement, and the optimal soil parameters are obtained. The reference secant modulus is 1.83 MPa, the rebound modulus is 5.50 MPa, and the effective cohesion is 10.13 kPa.

(3)

The rationality and accuracy of the optimal soil layer parameters obtained from parameter inversion of the SSA-XGBoost algorithm are verified from the perspective of time and space, and the accuracy of the surface settlement prediction is improved.

(4)

The river embankment of the existing building adjacent to the shield tunnel project was affected by the shield excavation, resulting in an uneven settlement, and at the same time, slightly inclined to the shield side. This resulted in a maximum settlement of 4.4 mm near the shield side. The overall deformation and settlement value of the river embankment is within the control range.