Bayesian Network-Driven Risk Assessment and Reinforcement Strategy for Shield Tunnel Construction Adjacent to Wall–Pile–Anchor-Supported Foundation Pit

Abstract

With the increasing demand for urban rail transit capacity, shield tunneling has become the predominant method for constructing underground metro systems in densely populated cities. However, the spatial interaction between shield tunnels and adjacent retaining structures poses significant engineering challenges, potentially leading to excessive ground settlement, structural deformation, and even stability failure. This study systematically investigates the deformation behavior and associated risks of retaining systems during adjacent shield tunnel construction. An orthogonal multi-factor analysis was conducted to evaluate the effects of grouting pressure, grout stiffness, and overlying soil properties on maximum surface settlement. Results show that soil cohesion and grouting pressure are the most influential parameters, jointly accounting for over 72% of the variance in settlement response. Based on the numerical findings, a Bayesian network model was developed to assess construction risk, integrating expert judgment and field monitoring data to quantify the conditional probability of deformation-induced failure. The model identifies key risk sources such as geological variability, groundwater instability, shield steering correction, segmental lining quality, and site construction management. Furthermore, the effectiveness and cost-efficiency of various grouting reinforcement strategies were evaluated. The results show that top grouting increases the reinforcement efficiency to 34.7%, offering the best performance in terms of both settlement control and economic benefit. Sidewall grouting yields an efficiency of approximately 30.2%, while invert grouting shows limited effectiveness, with an efficiency of only 11.6%, making it the least favorable option in terms of both technical and economic considerations. This research provides both practical guidance and theoretical insight for risk-informed shield tunneling design and management in complex urban environments.

1. Introduction

The rapid development of urban underground transportation infrastructure has become an effective solution to urban surface traffic congestion. Among various tunneling techniques, shield tunneling has become the mainstream method for metro construction due to its advantages of safety, efficiency, and environmental friendliness [1,2,3]. However, with increasingly complex geological and construction conditions, the excavation of shield tunnels near existing foundation pits has introduced significant risks [4,5,6]. These include disturbance of the in situ stress equilibrium in the surrounding soil, leading to deformation of adjacent strata and retaining structures, and, in extreme cases, ground collapse and support instability [7,8,9,10]. Therefore, strict settlement control of both the foundation pit and the surrounding soil during shield tunneling is essential.

When a shield tunnel passes adjacent to a diaphragm wall–pile–anchor-supported pit, it is critical to ensure that settlements of the retaining system remain within serviceability limits [11,12]. Current practice often relies on settlement control theory to formulate construction control schemes, with grouting-based ground improvement used as a primary countermeasure [13,14,15,16]. Common grouting methods include high-pressure jet grouting, sleeve-valve pipe grouting, and MJS (multi-directional jet grouting) [17,18,19]. Studies have shown that combining radial grouting inside the tunnel with sleeve-valve surface grouting can reduce wall settlement by up to 44% [20,21,22]. Moreover, numerical analyses have demonstrated that increasing vertical grouting depth is more effective in reducing surface settlement than expanding the circumferential injection angle.

Due to the multiplicity of risk sources in shield construction, various management science techniques have been adopted for risk assessment. These include the Analytic Hierarchy Process (AHP), fuzzy logic theory, and fault tree analysis [21,23]. However, these methods often fail to capture the stochastic and uncertain nature of multiple interacting risk factors, limiting their effectiveness in dynamic risk warning [24,25,26,27]. With the advancement of intelligent technologies, Bayesian networks have emerged as powerful tools for risk assessment due to their ability to incorporate prior knowledge and update probabilities in real time [28,29,30].

Recent studies have applied dynamic Bayesian networks to assess shield tunneling risks beneath existing structures, incorporating monitoring data into predictive frameworks [31,32]. For example, Chen [33] used Bayesian models to predict pre-construction risks; Wang [34] combined Bayesian networks with fuzzy evaluation to assess underground construction risks; Xiang [35] integrated fault tree analysis with Bayesian inference to evaluate pipeline damage risks from nearby excavation. Despite their advantages, these studies primarily focus on special geotechnical conditions or tunneling near existing tunnels and utilities, with limited application to shield tunneling adjacent to retaining pits. Moreover, there is a lack of research integrating risk identification with practical mitigation strategies.

To address these gaps, this study adopts an orthogonal experimental design to analyze the influence and significance levels of shield tunneling parameters on settlement control. A Bayesian network model is then used to assess the probabilistic risk of settlement-related failures when a shield tunnel is constructed near a diaphragm wall–pile–anchor-supported pit. The key influencing factors are identified, and numerical simulations are employed to evaluate the effectiveness of grouting reinforcement around the tunnel. A practical and economically viable control strategy is proposed to reduce the risk of settlement-induced failures, thereby offering technical guidance for safer shield tunneling adjacent to foundation pits.

2. Methodology

2.1. Finite Element Numerical Model

Finite element modeling was conducted using MIDAS GTS/NX 2024R1 to simulate the ground and structural response during adjacent shield tunnel construction [36,37]. The primary purpose of this numerical analysis was twofold: (1) to quantitatively evaluate the influence of different construction parameters (e.g., grouting pressure, soil properties) on surface settlement and support system performance and (2) to generate representative physical data that supports the conditional probability structure within the Bayesian network model developed in this study [38,39]. The overall model dimensions are 120 m in length, 120 m in width, and 50 m in height. The soil mass and segmental lining were modeled using 3D hexahedral solid elements. The shield shell and diaphragm wall were modeled using 2D shell elements. The struts and piles were represented by 1D beam elements, while the anchors were simulated using 1D embedded truss elements. In the meshing process, a balance between simulation accuracy and computational efficiency was considered, and a uniform mesh size of 1.0 m was selected for model analysis.

In the FEM model, the soil was assumed to be a homogeneous elastoplastic material, with all soil layers uniformly distributed across the construction site. The diaphragm wall, piles, capping beams, anchor bolts, and tunnel segments were modeled as linear elastic elements. To account for the mechanical behavior of segmental joints, the structural strength of the tunnel segments was reduced by 15%. The initial stress field considered only self-weight-induced stress, and the interface friction between the shield machine and the surrounding soil was neglected. The groundwater table was modeled as a stable confined aquifer located 10.8 m below the ground surface.

In the numerical model, the long side of the excavation pit is aligned parallel to the X-axis, the short side is parallel to the Y-axis, and the Z-axis is oriented vertically. Boundary conditions are applied as follows: the bottom surface is fully constrained in the X, Y, and Z directions; all vertical side surfaces are constrained in the direction normal to each respective face; and the top surface remains free without any constraints. For the one-dimensional (1D) structural elements in the model, rotational degrees of freedom are restrained to prevent torsional effects. During the tunnel excavation process, grouting is simulated by modifying the material properties of the soil elements within the grouting zone using the “attribute modification” function, thereby reflecting the improvement effect of grouting on the mechanical behavior of the surrounding soil.

To improve computational efficiency, a 2D finite element model was employed to perform an orthogonal experimental analysis of shield tunneling adjacent to a diaphragm wall–pile–anchor-supported excavation. Figure 1 presents the 2D finite element model, while Figure 2 illustrates the 3D counterpart. The comparison of results between the 2D and 3D models is shown in

Table 1. Comparison between 2D and 3D finite element model results.

Model/Deformation	2D Simulation Result	3D Simulation Result	Error
Maximum ground surface settlement outside the excavation (mm)	10.6	10.0	6%

. The difference in computed values was within 6%, indicating that the deviation was minor. It should be noted that the maximum surface settlement outside the excavation zone was selected as the primary index for comparing the 2D and 3D models, mainly due to its critical role in engineering practice. This parameter is highly sensitive and commonly used as a key control criterion in risk evaluation and surface deformation monitoring during shield tunnel construction [40,41,42]. It should also be noted that the maximum surface settlement outside the excavation zone was selected as the primary index for comparing the 2D and 3D models, mainly due to its critical role in engineering practice. This parameter is highly sensitive and commonly used as a key control criterion in risk evaluation and surface deformation monitoring during shield tunnel construction.

2.2. Model Parameter Design

2.2.1. Soil Parameters

In the modified Mohr–Coulomb [43] constitutive model, the required soil parameters include unit weight, internal friction angle, cohesion, Poisson’s ratio, secant stiffness from triaxial tests ($E_{50}^{ref}$), tangent stiffness from oedometer tests ($E_{oed}^{ref}$), and unloading–reloading stiffness ($E_{ur}^{ref}$). In the model parameterization process, the geotechnical properties of the soil, such as unit weight, cohesion, internal friction angle, compression modulus, and Poisson’s ratio, were primarily derived from the geotechnical investigation report of the project site. Based on this, a series of laboratory soil tests were conducted to obtain the parameters of each soil layer, as summarized in

Table 2. Geotechnical properties of soil layers.

Layer Number and Soil Type	Unit Weight γ (kN/m)	Cohesion c (kPa)	Internal Friction Angle ϕk (°)	Compression Modulus E(1–2) (MPa)	Poisson’s Ratio v
Layer 1 (Miscellaneous Fill)	19.1	15	15	3.0	0.37
Layer 2 (Silty Clay)	20	32	18	7.5	0.32
Layer 3 (Silty Clay)	19.5	30	20	7.2	0.33
Layer 4 (Silt)	20.6	28	24	10.5	0.31
Layer 5 (Silty Sand)	21.6	1	35	12	0.29
Layer 6 (Silty Clay)	20.3	30	27	8	0.32

. The physical and mechanical properties of the soil are listed in Table 2, and the thicknesses of the soil layers are provided in

Table 3. Assigned soil layer thicknesses in the numerical model.

Formation Name	Thickness of Soil Layer in the Model (m)
Layer 1 (Miscellaneous Fill)	2
Layer 2 (Silty Clay)	3
Layer 3 (Silty Clay)	3
Layer 4 (Silt)	5
Layer 5 (Silty Sand)	10
Layer 6 (Silty Clay)	17

.

2.2.2. Structural Material Parameters

The diaphragm wall, piles, and struts are composed of C35 concrete, while the tunnel segments are made of C50 concrete. To account for the effect of segmental joint staggering, a stiffness reduction factor of 0.85 is applied to the tunnel segments. The mechanical properties of all structural materials used in the model were obtained through laboratory testing, and the test results are presented in

Table 4. Material properties for structural elements.

Structural Elements	Elastic Modulus E (MPa)	Density ρ (kg/m3)	Poisson’s Ratio μ
Shield shell	2.1 × 105	8 × 103	0.30
Wall, pile, and tie beam	3.15 × 104	2.35 × 103	0.25
Ground anchor	2.0 × 105	7.7 × 103	0.2
Tunnel segment	2.93 × 104	2.35 × 103	0.25

.

2.2.3. Simulation of Ground Loss

In this study, ground loss is simulated using equivalent layers and controlled grouting parameters. The configuration of the equivalent layer is illustrated in Figure 3. It is modeled as a three-dimensional solid element with a thickness calculated using Equation (1) [44,45], and a value of 10 cm is adopted.

$$\delta =\eta \cdot \Delta$$

(1)

where Δ is the tail void (half of the difference between the shield outer diameter and the segment outer diameter, taken as 0.15 m in this study), and η is the reduction factor, ranging from 0.7 to 1.5, with 0.7 used herein.

The equivalent layer is filled with grout. To simulate the curing process, different material parameters are assigned according to the number of rings behind the shield tail [46,47]. Specifically, the 1st ring uses 0-day grout, the 2nd ring uses 1-day grout, the 3rd to 4th rings use 2-day grout, the 5th to 10th rings use 7-day grout, and rings beyond the 10th use 28-day grout. In addition, considering the performance requirements of grouting materials during actual shield tunneling operations, a series of laboratory-prepared grouting samples were tested to determine their physical and mechanical properties at different curing ages. The corresponding results are shown in

Table 5. Physical and mechanical parameters of grouting material in equivalent gap layers at different curing ages.

Grout Curing Age (d)	Density (kg/m3)	Poisson’s Ratio	Elastic Modulus (MPa)	Thickness (cm)
0	1600	0.45	5	10
1	1660	0.4	25	10
2	1700	0.35	50	10
7	1800	0.25	300	10
28	2100	0.2	400	10

.

3. Orthogonal Experimental Design

Key experimental factors selected for this study include grouting pressure, elastic modulus of the grouting layer after 28 days of hardening (400 MPa), and the cohesion and internal friction angle of the soil above the tunnel. The levels of each factor were determined based on engineering experience. The orthogonal experimental factors and their corresponding levels are presented in

Table 6. Orthogonal test factors and levels.

Factors	Levels
	1	2	3	4
Grouting pressure, P (kPa)	300	375	450	525
Elastic modulus of the grouting layer, Ea (MPa)	E	1.25 E	1.5 E	1.75 E
Cohesion of the soil above the tunnel, c (kPa)	0	5	10	15
Internal friction angle of the soil above the tunnel, φ (°)	10	15	20	25

.

An orthogonal experimental matrix was constructed according to standard orthogonal array design principles, and numerical simulations were performed [48]. The maximum surface settlement outside the excavation zone was chosen as the evaluation index, as it directly reflects the intensity of the shield tunnel excavation effect. The results of each test scenario are summarized in

Table 7. Orthogonal test design and results.

Factors	P (kPa)	Ea (MPa)	C (MPa)	φ (°)	Maximum Ground Settlement Outside the Excavation (mm)
Test 1	300	E	0	10	10.2
Test 2	300	1.25 E	5	15	5.9
Test 3	300	1.5 E	10	20	5.6
Test 4	300	1.75 E	15	25	5.0
Test 5	375	E	5	20	5.0
Test 6	375	1.25 E	0	25	8.5
Test 7	375	1.5 E	15	10	4
Test 8	375	1.75 E	10	15	3.7
Test 9	450	E	10	25	3.5
Test 10	450	1.25 E	15	20	3.3
Test 11	450	1.5 E	0	15	7.1
Test 12	450	1.75 E	5	10	3
Test 13	525	E	15	15	2.9
Test 14	525	1.25 E	10	10	2.6
Test 15	525	1.5 E	5	25	2.7
Test 16	525	1.75 E	0	20	6.6

.

The experimental results reveal clear trends. Lower grouting pressure and zero soil cohesion (e.g., Test 1) resulted in the highest observed settlement of 10.2 mm, while the smallest deformation (2.6 mm) was achieved under high pressure (525 kPa) and moderate soil strength (Test 14). As grouting pressure and soil cohesion increased, settlement generally decreased, reflecting enhanced soil confinement and load redistribution. Notably, although E_a and φ exhibited marginal influence compared to P and C, tests with elevated E_a (e.g., 1.75 E in Test 4 and 12) consistently showed improved performance in settlement reduction. These results indicate that soil cohesion and grouting pressure are dominant control parameters. This lays the foundation for subsequent variance analysis and multi-objective optimization of reinforcement strategies, as discussed in the following sections.

4. Results and Discussion

4.1. Analysis of Influencing Factors of Ground Settlement During Shield Tunneling

4.1.1. Analysis of Range

Table 8. Range analysis of maximum ground settlement outside the pit (mm).

Levels	P	Ea	c	φ
Mean 1	6.675	5.400	8.100	4.950
Mean 2	5.300	5.075	4.150	4.900
Mean 3	4.225	4.850	3.850	5.125
Mean 4	3.700	4.575	3.800	4.925
Range (R)	2.975	0.825	4.300	0.225
Rank	2	3	1	4

presents the range analysis of the maximum surface settlement. It indicates that grouting pressure and soil cohesion exhibit the largest range of values, suggesting a stronger influence on surface settlement. In contrast, the elastic modulus of the grouting layer and the internal friction angle have smaller range values, indicating a weaker effect. As shown in Figure 4, the steeper the slope of the response curve, the greater the factor’s influence on surface settlement. Based on the test data, the factors influencing are ranked in descending order of significance as follows: cohesion (c), grouting pressure (P), elastic modulus of the grouting layer (E_a), and internal friction angle (φ).

4.1.2. Analysis of Variance

To further evaluate the significance of each factor, an analysis of variance (ANOVA) was conducted using the maximum surface settlement as the response variable. A confidence level of 95% was adopted. The ANOVA results are shown in

Table 9. ANOVA of maximum ground settlement outside the pit (mm).

Factors	Degrees of Freedom	Sum of Squares of Deviations from the Mean	Mean Square	F-Value	p-Value
P	3	20.735	6.9117	1382.33	0.000
Ea	3	1.465	0.4883	97.67	0.002
c	3	52.370	17.4567	3491.33	0.000
φ	3	0.250	0.0417	8.33	0.058
Error	3	0.015	0.005

. The result presents the ANOVA for surface settlement. The F-values of grouting pressure and soil cohesion are 1382.33 and 3491.33, respectively, which are significantly higher than those of the other factors. This demonstrates that these two parameters have the most prominent effect on surface settlement. Therefore, under a 95% confidence level, soil cohesion and grouting pressure are identified as the primary influencing factors.

4.2. Bayesian Network Evaluation of Construction Risks for Shield Tunneling near Wall–Pile–Anchor-Supported Excavations

To control deformation-related failures during shield tunneling adjacent to pile–anchor-supported foundation pits, it is essential to conduct a thorough risk assessment prior to construction [49,50]. In this study, a Bayesian network Model is employed to quantitatively analyze the probability of deformation-induced failures in such scenarios [22,35,51].

4.2.1. Identification and Analysis of Risk Factors

It is acknowledged that the input parameters used in the Bayesian network model, particularly the conditional probabilities, are primarily derived from expert elicitation due to the lack of comprehensive field monitoring data. While this approach facilitates the construction of a functional and interpretable causal model, it inevitably introduces a degree of subjectivity. Therefore, the present model is intended primarily for qualitative trend analysis and identification of dominant risk factors. In projects involving shield tunneling near existing pile–anchor-supported pits, the structural safety of the tunnel and pit is influenced by multiple factors, including the construction environment, construction plan, construction technique, and construction management. Based on field investigations, expert consultations, literature review [27,31,35], and simulated construction processes, the main risk sources were identified and classified into basic events, as listed in

Table 10. Risk sources and basic events of shield tunneling adjacent to diaphragm wall–pile–anchor-supported pit.

Serial Numbers	Risk Source	Basic Events
1	Construction environment	Climatic conditions, stratigraphic conditions, and groundwater stability
2	Construction scheme	Geological investigation, shield tunneling design, and monitoring plan
3	Construction technology	Shield steering correction, reinforcement of wall–pile–anchor support, segment installation, and tail grouting
4	Construction management	Contractor experience, construction team management system, and emergency response plan

.

The top event of the Bayesian network model is defined as the occurrence of a “shield tunneling failure,” denoted as node T. The full Bayesian network structure is shown in Figure 5. Once the basic events are determined, prior probabilities for each node are calculated using an expert weight-based evaluation method. Specifically, before construction, experts assess the likelihood of each basic event by assigning it a risk level, as specified in Table 10. These assessments are based on relevant documentation or personal experience. The final prior probability for each event is calculated as the weighted average of expert opinions, with results presented in

Table 11. Classification criteria for likelihood of risk occurrence.

Risk Levels	Likelihood	Probability
I	Frequent	[0.1, 1]
II	Probable	[0.01, 0.1)
III	Occasional	[0.001, 0.01)
IV	Rare	[0.0001, 0.001)
V	Impossible	[0, 0.0001)

.

A total of six experts in geotechnical and tunneling engineering contributed to the assessment of prior probabilities for the basic events in the Bayesian network. The weighting assigned to each expert is listed in

Table 12. Weight assignment for expert judgment.

Classification	Description	Weight	Number of Experts
I	Experts (Category I)	1	2
II	Experts (Category II)	0.8	4

, while the index and prior probability of each basic event are provided in

Table 13. Prior probabilities of basic events related to shield tunnel accidents.

No.	Basic Events	Experts (Category I)		Experts (Category II)				Prior Probability
		1	2	3	4	5	6
X11	Climatic conditions	0.053	0.046	0.04	0.08	0.05	0.07	0.056
X12	Stratigraphic conditions	0.185	0.2	0.17	0.12	0.15	0.13	0.163
X13	Groundwater stability	0.1	0.13	0.14	0.12	0.11	0.14	0.123
X21	Geological investigation	0.03	0.04	0.05	0.048	0.04	0.05	0.042
X22	Shield tunneling design	0.01	0.012	0.006	0.01	0.006	0.007	0.009
X23	Monitoring plan	0.002	0.003	0.001	0.003	0.002	0.003	0.002
X31	Shield steering correction	0.055	0.064	0.1	0.075	0.08	0.085	0.075
X32	Reinforcement of wall–pile–anchor support	0.09	0.1	0.1	0.12	0.13	0.1	0.106
X33	Segment installation	0.07	0.068	0.035	0.05	0.05	0.045	0.055
X34	Tail grouting	0.007	0.005	0.005	0.008	0.006	0.007	0.006
X41	Contractor experience	0.037	0.043	0.025	0.03	0.035	0.03	0.034
X42	Construction team management	0.045	0.055	0.09	0.06	0.085	0.06	0.065
X43	Emergency response plan	0.002	0.005	0.003	0.002	0.001	0.003	0.003

.

Conditional probabilities are defined as the probability that a child event occurs, given that the parent event has failed. For example, if the conditional probability of X₁ is 0.55, it indicates that, given an unfavorable construction environment, the probability of failure in the shield tunneling adjacent to the pile–anchor-supported pit is 55%. These probabilities are calculated by weighted averaging of expert evaluations, as shown in

Table 14. Conditional probabilities of shield tunnel accident events.

No.	Basic Events	Experts (Category I)		Experts (Category II)				Conditional Probability
		1	2	3	4	5	6
X1	Climatic conditions	0.52	0.58	0.6	0.48	0.55	0.57	0.55
X2	Stratigraphic conditions	0.36	0.4	0.41	0.37	0.35	0.45	0.39
X3	Groundwater stability	0.36	0.4	0.3	0.45	0.35	0.3	0.36
X4	Geological investigation	0.44	0.5	0.45	0.33	0.35	0.43	0.42
X11	Shield tunneling design	0.18	0.16	0.2	0.11	0.15	0.16	0.16
X12	Monitoring plan	0.6	0.5	0.6	0.43	0.5	0.55	0.53
X13	Shield steering correction	0.52	0.5	0.45	0.54	0.6	0.45	0.51
X21	Reinforcement of wall–pile–anchor support	0.24	0.3	0.32	0.37	0.3	0.35	0.31
X22	Segment installation	0.33	0.35	0.35	0.45	0.37	0.33	0.36
X23	Tail grouting	0.15	0.19	0.2	0.27	0.25	0.22	0.21
X31	Contractor experience	0.20	0.22	0.15	0.22	0.3	0.23	0.22
X32	Construction team management	0.18	0.24	0.25	0.15	0.2	0.1	0.19
X33	Emergency response plan	0.55	0.5	0.54	0.48	0.55	0.6	0.54
X34	Climatic conditions	0.52	0.5	0.5	0.35	0.4	0.47	0.46
X41	Stratigraphic conditions	0.16	0.2	0.2	0.27	0.25	0.22	0.21
X42	Groundwater stability	0.45	0.4	0.44	0.39	0.5	0.32	0.42
X43	Geological investigation	0.21	0.2	0.25	0.23	0.3	0.2	0.23

. Taking the “construction environment” node X₁ as an example, its conditional probabilities are defined as shown in

Table 15. Conditional probability table of construction environment X₁ (%).

X11	X12	X13	X1 = S	X1 = D
S	S	S	100	0
S	S	D	49	51
S	D	S	47	53
S	D	D	23	77
D	S	S	84	16
D	S	D	41	59
D	D	S	39	61
D	D	D	19	81

. In this context, X₁₁ = S denotes favorable weather conditions, X₁₁ = D denotes adverse weather, X₁₂ = S represents favorable geological conditions, X₁₂ = D represents poor geological conditions, X₁₃ = S indicates stable groundwater, and X₁₃ = D indicates unstable groundwater. The parent node X₁ = S indicates a generally safe construction environment, whereas X₁ = D implies a hazardous condition. When all three influencing factors are favorable, i.e., X₁₁ = S, X₁₂ = S, and X₁₃ = S, the conditional probability of X₁ = S is assigned a value of 1.0 (or 100%). This assignment is based on an idealized modeling assumption, indicating that under the optimal combination of weather, geology, and groundwater conditions, the construction environment can be considered highly reliable. It should be noted that this value does not imply absolute certainty in real-world conditions, but rather, it represents the maximum confidence output of the system under this specific input configuration.

4.2.2. Risk Factor Evaluation

Using the Bayesian network software NETICA V5.18, the construction risk associated with shield tunneling adjacent to pile–anchor-supported foundation pits was quantitatively assessed. The calculation results, shown in Figure 6, indicate that the probability of engineering failure is 13.1% when no effective construction control measures are implemented. In the model, “S” denotes the safe state and “D” denotes the dangerous state; all probabilities are expressed in percentage terms.

Subsequently, the backward inference function of the Bayesian network was applied. Assuming that the engineering failure has already occurred (i.e., the top node T is set to state D with a probability of 100%), the posterior probabilities of all basic events were calculated, as illustrated in Figure 7. The results of the maximum causal chain analysis reveal that the geological condition (X₁₂) is the primary contributing factor to failure during shield tunneling adjacent to the pile–anchor-supported pit. In addition, groundwater stability (X₁₃), along with construction-related technical factors, including shield deviation correction (X₃₁), pile–anchor support reinforcement (X₃₂), segmental lining assembly (X₃₃), tail void grouting (X₃₄), and construction team management practices (X₄₂), also significantly influence construction safety.

The posterior probabilities of each basic event under the condition of engineering failure are presented in

Table 16. Posterior probabilities of basic events.

Event Risk Levels	Basic Events
I	X12, X13, X31, X32, X33, X34, X42
II	X11, X21, X22, X41
III	X23, X43
IV
V

. Based on the results of the Bayesian inference, key risk factors in the construction of shield tunnels adjacent to pile–anchor-supported foundation pits were identified. These include unfavorable geological conditions, unstable groundwater, insufficient control of construction techniques, and inadequate management systems. Corresponding mitigation measures should be implemented for each critical factor identified in the assessment, with the aim of minimizing the probability of failure and ensuring the safety and reliability of the tunneling operation.

4.3. Analysis of Soil Reinforcement Control for Shield Tunneling near Wall–Pile–Anchor Support

4.3.1. Grouting Reinforcement Scheme for the Surrounding Soil of the Tunnel

During the construction of a shield tunnel passing through a foundation pit supported by wall–pile–anchor systems, grouting reinforcement around the tunnel is often required to improve local ground conditions and control ground settlement outside the pit. Prior to grouting, it is necessary to determine the appropriate size and location of the reinforcement zone. To define the optimal reinforcement extent, a series of single-factor parametric analyses were conducted based on the numerical model presented [52]. A schematic diagram of the grouting reinforcement area surrounding the tunnel is shown in Figure 8, and the mechanical parameters of the grouted soil are listed in

Table 17. Mechanical parameters of grouted soil.

Cement Content	γ (kN/m3)	${\mathit{\varphi }}_{\mathit{k}}(°)$	${\mathit{E}}_{50}^{\mathit{r}\mathit{e}\mathit{f}}(\mathbf{M}\mathbf{P}\mathbf{a})$	${\mathit{E}}_{\mathit{o}\mathit{e}\mathit{d}}^{\mathit{r}\mathit{e}\mathit{f}}(\mathbf{M}\mathbf{P}\mathbf{a})$	${\mathit{E}}_{\mathit{u}\mathit{r}}^{\mathit{r}\mathit{e}\mathit{f}}(\mathbf{M}\mathbf{P}\mathbf{a})$	C (kN/m2)
15%	17.8	51.2	250.1	175.1	750.3	447.6

.

To assess the effectiveness of different reinforcement positions and ranges, the maximum surface settlement outside the excavation before and after reinforcement was used as the primary control index [53]. In comparing various reinforcement strategies, two indicators were introduced to evaluate the settlement reduction effect and economic feasibility, including grouting improvement ratio W and grouting efficiency Z [50,54]. The grouting improvement ratio W is calculated using Equation (2). A higher value of W indicates a more effective reinforcement outcome. In this study, the reinforcement ratio W is defined as a dimensionless index that quantifies the relative effectiveness of grouting in reducing the maximum surface settlement. It is calculated as the percentage reduction in maximum settlement after reinforcement compared to the unreinforced condition. This index quantifies the proportional effectiveness of the reinforcement measure in controlling settlement, allowing for a direct and comparable evaluation across different reinforcement schemes. By expressing performance improvements in percentage terms, it also facilitates the integration of technical effectiveness with cost–benefit analysis for decision-making. The grouting efficiency Z, defined by Equation (3), reflects the settlement control effect per unit reinforcement width; the larger the value of Z, the greater the economic benefit of the grouting reinforcement schemes.

$$W={\displaystyle \frac{S-S^{\prime }}{S}}\times 100$$

(2)

where W is the grouting reinforcement ratio, S is the maximum surface settlement caused by shield tunneling without reinforcement, and S′ is the maximum surface settlement caused by shield tunneling after reinforcement.

$$Z={\displaystyle \frac{W}{B}}\times 100$$

(3)

where B is the width of the reinforced soil, in meters (m); Z is the grouting reinforcement efficiency, expressed in inverse meters (m⁻¹).

4.3.2. Analysis of the Effect of Grouting Reinforcement on the Surrounding Tunnel Soil

(1) Soil reinforcement on both sides of the tunnel spring line

To simulate the effect of grouting reinforcement, the mechanical properties of the soil within the reinforcement zones were modified. The lateral reinforcement widths on each side of the tunnel were set to 1 m, 1.5 m, 2 m, and 2.5 m, resulting in total widths B of 2 m, 3 m, 4 m, and 5 m, respectively. The corresponding surface settlement curves after tunneling are shown in Figure 9. The maximum surface settlements for reinforcement widths of 2 m, 3 m, 4 m, and 5 m were 8.48 mm, 7.81 mm, 7.25 mm, and 6.98 mm, respectively. Increasing the reinforcement width effectively reduces surface settlement. The location of maximum settlement remains directly above the tunnel centerline and does not shift with reinforcement width. The reinforcement ratio and efficiency for lateral grouting are shown in Figure 10. The result illustrates that as the lateral reinforcement width increases from 2 m to 5 m, the reinforcement ratio increases from 15.1% to 30.2%, while the reinforcement efficiency decreases from 7.6% to 6.0%. This indicates that although expanding the reinforcement zone improves settlement control, it yields diminishing economic returns.

(2) Soil reinforcement below the tunnel invert

Subsequently, the bottom reinforcement depth was set to 1 m, 1.5 m, 2 m, and 2.5 m. Figure 11 presents the corresponding settlement curves. The maximum surface settlements were 9.38 mm, 9.21 mm, 9.02 mm, and 8.90 mm, respectively. Although deeper bottom reinforcement reduces settlement, the control effect remains limited. By replacing the reinforcement width B in Equation (3) with the bottom reinforcement depth, the corresponding reinforcement ratio and efficiency were calculated (Figure 12). As depth increases from 1 m to 2.5 m, the reinforcement ratio increases from 6.2% to 11.6%, while the efficiency decreases from 6.2% to 4.2%. This demonstrates that bottom reinforcement contributes little to settlement control and exhibits lower cost-effectiveness.

(3) Soil reinforcement above the tunnel crown

The top reinforcement height varied as 1 m, 1.5 m, 2 m, and 2.5 m. The post-construction settlement curves are shown in Figure 13. The maximum surface settlements were 8.34 mm, 7.63 mm, 7.03 mm, and 6.53 mm, respectively. These results confirm that top reinforcement significantly reduces surface settlement.

By substituting the top reinforcement height into Equation (3), the reinforcement ratio and efficiency were computed (Figure 14). As the height increases from 1 m to 2.5 m, the ratio increases from 16.6% to 34.7%, while the efficiency decreases from 16.6% to 13.9%. This indicates that grouting above the tunnel is highly effective in controlling surface settlement with strong economic performance. In conclusion, considering both settlement control and cost efficiency, grouting above the tunnel should be prioritized, followed by lateral grouting. Bottom reinforcement proves less effective and can be excluded. The extent of reinforcement should be selected based on allowable settlement thresholds and simulation outcomes, as indiscriminately expanding the zone may lead to unnecessary economic loss.

5. Conclusions

This study integrates numerical simulation, experimental design, and Bayesian probabilistic inference to systematically investigate the deformation behavior and risk control strategies associated with deep excavations supported by wall–pile–anchor systems adjacent to shield tunnels. The research identifies key parameters influencing ground surface settlement and proposes a technical framework for deformation risk control under such complex urban tunneling scenarios. The following conclusions are drawn:

• Range and variance analyses based on maximum surface settlement outside the excavation indicate significant differences in the impact of influencing parameters. Soil cohesion and grouting pressure are identified as the most critical variables, jointly accounting for over 72% of the variance in settlement response, followed by the elastic modulus of the grouted layer and the internal friction angle of the soil.
• A Bayesian network model was established to represent and infer causal relationships among various risk sources by integrating expert knowledge and field data. The results indicate that unfavorable geological conditions, unstable groundwater, insufficient shield steering correction, inadequate support reinforcement, and weak construction management are the primary causes of failure. Posterior inference further confirms the leading role of geology and construction control in ensuring project safety, providing a scientific basis for pre-construction risk mitigation.
• The effectiveness and cost-efficiency of different grouting reinforcement strategies around the tunnel were evaluated through parametric simulation. The results show that top grouting increases the soil reinforcement ratio to 34.7% and achieves the highest reinforcement efficiency (13.9%), offering the best performance in settlement control and economic return. Sidewall grouting provides a reinforcement efficiency of approximately 6.0%, serving as a supplementary measure. In contrast, invert grouting yields a low efficiency of only 4.2%, indicating limited effectiveness and cost performance.
• This study provides a systematic modeling framework and quantitative analysis method for addressing deformation response and risk control associated with adjacent shield tunneling in complex urban environments. However, the research is constrained by idealized boundary conditions and the static nature of the model. Future work may focus on integrating real-time monitoring data and machine learning techniques to enable dynamic model updating and enhance the broader applicability of the proposed approach.