
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

72384
10.1038/s41598-024-72384-1
Article
Study of the static response and zoning of the existing tunnel adjacent to the suspension bridge's tunnel-type anchorage
Li Ruihan 1
Zhou Jiamei tmzjm@home.swjtu.edu.cn

1
Qin Qingsong 3
Yuan Song 2
Cui Kaiqi 1
Yue Feixiang 14
Song Songke 2
Xue Zhibin 1
1 https://ror.org/00hn7w693 grid.263901.f 0000 0004 1791 7667 College of Civil Engineering, Southwest Jiaotong University, Chengdu, 610031 China
2 Sichuan Communication Surveying and Design Institute Co, Ltd, Chengdu, 610031 China
3 Yunnan Institute of Transportation Planning and Design, Kunming, 650299 China
4 https://ror.org/00hn7w693 grid.263901.f 0000 0004 1791 7667 Present Address: State Key Laboratory of Intelligent Geotechnics and Tunnelling, Southwest Jiaotong University, Chengdu, Sichuan China
13 9 2024
13 9 2024
2024
14 2140224 4 2024
6 9 2024
© The Author(s) 2024
2024
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Due to the ability to utilize the strength of the surrounding rock to enhance bearing capacity, tunnel-type anchorages have been consistently utilized in suspension bridges. Nevertheless, a close interaction occurs between the tunnel and the tunnel-type anchor when a highway tunnel is connected to a suspension bridge. This study employed numerical simulation and theoretical analysis based on the G317 Line Huangjiayuan tunnel and Zipingpu Bridge tunnel-type anchorage project, focusing on this specific type of adjacent engineering. Firstly, the discriminant degree of adjacent influence suitable for the interaction between the tunnel-type anchorage and the tunnel structure is established. The calculation conditions are distinguished by the influencing factors determined in the discriminant. The interaction law between tunnel-type anchorage and pre-built tunnel structure is further obtained. Using the method of curve regression, based on the criterion of proximity influence degree, the partition of mutual influence degree between the tunnel-type anchorage and the tunnel structure is obtained. At the same time, it is concluded that under the original design condition, the displacement degree of the tunnel structure will be greatly affected, and the tunnel structure is located in the strong influence area. According to the partition result, under the benchmark engineering geological condition, it is suggested that the angle of intersection between tunnel anchorage and tunnel structure should be increased to 3.3° and the anchor body inclination should be increased to 44°.

Keywords

Tunnel-type anchorage
Adjacent engineering
Static influence zoning
Existing tunnel structure
Subject terms

Civil engineering
Computational science
Sichuan Communication Surveying and Design Institute Co., LtdNo.232022003-2 No.232022003-2 No.232022003-2 No.232022003-2 No.232022003-2 No.232022003-2 No.232022003-2 No.232022003-2 Li Ruihan Zhou Jiamei Qin Qingsong Yuan Song Cui Kaiqi Yue Feixiang Song Songke Xue Zhibin issue-copyright-statement© Springer Nature Limited 2024
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pmcWhen crossing valleys and rivers, the suspension bridge has the most robust spanning ability1. The tunnel anchorage of the suspension bridge can fully use the surrounding rock's clamping force and friction resistance to improve the bearing capacity2. However, when the suspension bridge connects with the highway tunnel, the tunnel-type anchorage will have a close interaction with the highway tunnel, and the excavation and construction process of the tunnel-type anchorage will impact the structure of the adjacent tunnel.

In the research field of tunnel-type anchorage of suspension bridges, most scholars used numerical simulation, in-situ scale tests, and field monitoring to study the time–space effect of deformation of tunnel anchorage3 and the failure mode of tunnel anchorage4,5. The ultimate bearing capacity and mechanism of tunnel-type anchorage were studied6, and the results showed that the maximum bearing capacity of tunnel-type anchorage is closely related to the strength of the surrounding rock. The failure mode of anchorage is an inverted cone-shaped failure extending to the interior of the surrounding rock.

In the field of research on the interaction between the tunnel-type anchorage and the existing tunnel, Wang et al.7 systematically analyzed the influence of tunnel construction on the surrounding rock of tunnel-type anchorage. The research status indicates a limited number of studies on tunnel-type anchorage in the adjacent field, and there is a need for a reference regarding the influence of tunnel-type anchorage construction on existing adjacent tunnels. The influence of the adjacent construction of the underpass tunnel on the settlement of the anchor plug body of the overlying suspension bridge tunnel is studied by Liang et al.8 It is found that the settlement of the tunnel vault and the settlement of the bottom of the anchor plug body is affected by the change of the buried depth of the tunnel. They also found that the change of anchor tunnel spacing has little effect on the settlement of the tunnel vault but greatly influences the settlement of the anchor plug. Based on the actual project, Liu et al.9 carried out the indoor model test of the tunnel-anchor approach, which showed that the spandrel and vault of the tunnel would be greatly affected. There are few studies on the interaction between tunnel anchorage and tunnel structure, and most scholars focus on the bearing capacity of tunnel anchorage. The influence law of tunnel-type anchorage on existing close-distance tunnel structures must be carried out urgently.

Proximity engineering is an important research topic in tunneling and underground engineering. Most scholars have carried out extensive research in the field of large-scale proximity engineering and obtained some conclusions. For the influence of foundation pit excavation on the existing tunnel structure, some scholars have studied the impact of parameters such as stratum elastic modulus, excavation depth, and excavation geometry on the current tunnel response using theoretical analysis and numerical simulation10 and established a simplified evaluation and calculation method for the existing tunnel structure11–13. The interaction mechanism of the foundation pit supporting structure-soil-tunnel has been revealed14, and the pre-reinforcement measures for the existing tunnel structure were given for the influence range of foundation pit excavation15.In urban underground space engineering, the problems of proximity between new tunnels and existing tunnels often occur. Most scholars have conducted relevant research through numerical analysis and theoretical methods and established a theoretical calculation model of structural deformation caused by the new excavating tunnel in the existing tunnel16. The results showed that when the distance between the two tunnels is less than the tunnel’s diameter, the new tunnel will significantly impact the existing tunnel17. The above scholars have conducted in-depth research on adjacent engineering through theoretical and numerical calculation methods and formed some systematic theories and consensus on the macro level. Research on classifying strong and weak influences in adjacent engineering has emerged as the prominent research direction.

Existing research on approaching engineering has developed specific system theories. However, the impact of the approach varies significantly depending on the approaching engineering, and there are various sensitivity factors. At the same time, the existing system theory has limited applicability when studying the impact of approaching tunnel and tunnel-type anchorage. Further research is needed to deepen the understanding of the interaction laws between the tunnel and the tunnel-type anchorage. While exploring the static response in adjacent projects, specific projects have successfully investigated the zoning of static construction influence. However, further research is required to obtain more relevant results regarding the zoning of static response between the tunnel and the adjacent tunnel-type anchorage.

This study employed numerical simulation and theoretical analysis based on the G317 Line Huangjiayuan tunnel and Zipingpu Bridge tunnel-type anchorage project, focusing on this specific type of adjacent engineering. Firstly, the discriminant degree of adjacent influence suitable for the interaction between the tunnel-type anchorage and the tunnel structure is established. The calculation conditions are distinguished by the influencing factors determined in the discriminant. The interaction law between tunnel-type anchorage and pre-built tunnel structure is further obtained. Using the method of curve regression, based on the criterion of proximity influence degree, the partition of mutual influence degree between the tunnel-type anchorage and the tunnel structure is obtained.

Adjacent partition criterion of tunnel and tunnel-type anchorage

(1) Generalized proximal partition criterion.

The concept of proximity effects has been introduced in underground engineering to quantitatively assess the adverse impact on adjacent existing projects, aiming to provide an intuitive representation of the degree of mutual influence18. The n-dimensional influence factor of the proximity influence degree is divided into regions, known as proximity partitions, based on the relationship between the value of the proximity influence degree.

The partition is based on the quantification of influence. For the criterion of reasonably quantifying the influence degree, Qiu.19 proposed a generalized calculation formula for quantifying the influence degree of adjacent engineering, which consists of three categories and six subcategories, as shown in Table 1.Table 1 Discrimination criterion of proximity engineering influence degree.

Categories of criteria	Subcategories	
I. Criteria for strata discrimination	1. Stress criterion	
2. Plastic zone criterion	
3. Displacement criterion	
II. Criteria for existing structures	4. Strength criterion	
5. Stiffness criterion	
III. Combinational decision rule	6. Combination of 1–5	

(2) Static partition criterion and threshold of the tunnel and adjacent tunnel-type anchorage.

① Stiffness criterion of pre-built tunnel.

According to the national standard in China20, Table 2 shows the corresponding relationship between the frequency of support displacement measurement and its displacement rate during construction.Table 2 Relationship between the displacement rate of the tunnel lining structure and measurement frequency.

Rate of displacement(mm/d)	Measurement rate	
 ≥ 5	2–3times/d	
1–5	One-time/d	
0.5–1	One-time /(2–3) d	
0.2–0.5	One-time/3d	
 < 0.2	One-time /(3–7) d	

Assuming that the single construction footage of the post-built anchor tunnel is 3.5 m and the construction time of each cycle is 1 d. The displacement difference between the adjacent anchor tunnel construction steps is the lining displacement rate in mm/d. This paper quantifies the stiffness criterion using the displacement difference between adjacent tunnel-type anchorage construction steps. Combined with the displacement rate threshold in Table 2, the displacement increment partition threshold value is shown in Table 3.Table 3 Threshold of existing structural stiffness criterion for tunnel and adjacent tunnel-type anchorage.

Single-step support displacement increment(mm)	Divisional situation	
 ≥ 1	strong influence area	
0.5–1	weak influence area	
 ≤ 0.5	unaffected area	

②Strength criterion of pre-built tunnel.

According to the national standard in China20, the stress level of the tunnel structure is evaluated based on the ratio of the measured value to the allowable value. When the ratio reaches 0.8, the surrounding rock is unstable, and appropriate countermeasures must be implemented. Previous studies on the proximity of underground engineering primarily focus on the increase in principal stress within the tunnel lining structure to describe the negative impact of the post-built structure on the pre-built structure's strength21. In the case of a pre-built tunnel, the initial stress levels vary across different locations before the construction of the post-built project. Consequently, the precise magnitude of the principal stress increment at each location has varying implications for the safety of the tunnel structure. To effectively characterize the impact of the post-construction project on the strength of the pre-construction project, this study introduces the concept of the principal stress increase ratio, as a measure of the post-construction project's influence on the pre-construction project's strength. The expression is shown in Eq. (1).1 l=MaxΔσ10.8ft-σ01,Δσ10.8fc-σ03

In which Δσ1 is the maximum change value of the maximum principal stress of the measuring point in the construction process of the post-construction project, compared with the non-construction of the post-construction project; Δσ3 is the maximum change value of the minimum principal stress of the measuring point in the construction process of the post-construction project, compared with the non-construction of the post-construction project; ft is the design value of axial tensile strength of concrete; fc is the design value of axial compressive strength of concrete.

When the maximum or minimum principal stress of concrete reaches the ultimate stress of the material, the tunnel structure risks cracking and instability. At this time, the closed value is 1. Referring to the ratio of the substantial influence threshold and the secure value of the structural strength criterion21, the partition threshold of the structural strength criterion is shown in Table 4.Table 4 Strength criterion threshold of the existing tunnel structure.

Principal stress increase ratio	Divisional situation	
 ≥ 0.67	Strong influence area	
0.33–0.67	Weak influence area	
 < 0.33	Unaffected area	

(3) Control factors of proximity influence between tunnel and tunnel-type anchorage.

The control factors and their relationship governing the degree of influence vary for different types of adjacent projects. The parameters determining the degree of mutual effect are summarized below, depending on the particular form of tunnel-type anchorage adjacent to the existing tunnel.

①Relative position relationship between tunnel and tunnel-type anchorage.

To characterize the size of the net distance of the adjacent project, Zheng.22 proposed the ratio of the net distance between the new and existing structures to the equivalent size of the adjoining project as a measure of geometric proximity.

In the project, the tunnel-type anchorage can only move around the main cable saddle of the suspension bridge in the vertical plane or horizontal plane after the main tower position of the suspension bridge is determined. Therefore, the relative position relationship between the cable saddle of the suspension bridge and the tunnel can be determined by the inclination angle and intersection angle between the tunnel and the tunnel-type anchorage. This paper represents the angle between the tunnel-type anchorage and the horizontal plane by α. The intersection angle between the tunnel-type anchorage and the tunnel in the horizontal plane is represented by β, as shown in Fig. 1. bi1 is defined to reflect the proximity influence degree from the spatial point of view, which can be expressed as a function of α and β.Fig. 1 The relative position relationship between the tunnel-type anchorage of Zipingpu Bridge and Huangjiayuan Tunnel(The map data comes from Gaode open platform, http://datav.aliyun.com/portal/school/atlas/area_selector).

②Rock condition.

Surrounding rock condition is one of the essential factors affecting the mechanical response of adjacent engineering, and tunnel-type anchorage is usually applied to surrounding rock with good engineering characteristics2. The factors of geological conditions in the expression of the degree of influence of the tunnel-type anchorage adjacent to the existing tunnel are expressed by parameter bi2. In engineering practice, it is necessary to use multiple engineering mechanical parameters to characterize the surrounding rock conditions. To determine the value of bi2, this paper modifies the primary quality index of surrounding rock [BQ] to reflect the characteristics of the surrounding rock.

③Terrain and buried depth.

As the depth of the tunnel-type anchorage is shorter than the tunnel length, the tunnel affected by the tunnel-type anchorage is typically the shallowly buried part. The term bi3 is established in this study to reflect the variation in the tunnel's buried depth with the distance from the tunnel portal.

④Engineering response measures.

In adjacent projects, three directions exist to control the interaction between projects15. One is to reinforce the existing structure to prevent excessive deformation during construction and operation, the other is to reduce the disturbance of surrounding rock, and the third is to strengthen the surrounding rock. The parameter bi4 represents the response measures, where a higher degree of surrounding rock reinforcement corresponds to a smaller value of bi4.

⑤Calculation formula of the criterion for judging the proximity of tunnel and tunnel-type anchorage.

In this project, the new Austrian tunneling method (NATM) is used for construction, and different section construction schemes and footage depths have been considered in the parameters of the countermeasures, so the parameters representing the construction mode in the generalized criterion quantitative expression can be omitted. The tunnel and its adjacent tunnel-type anchorages are constructed nearly simultaneously in this project, thereby allowing the degree of structural deterioration to be disregarded. Hence, the parameters that represent the deterioration degree of existing structures are excluded from the generalized criterion quantitative expression. In summary, a composite function with four variables can quantify each criterion's value for a tunnel-type anchorage adjacent to the existing tunnel in this project. Ji represents the value of the ith criterion, and Ki corresponds to the value of the ith criterion in the benchmark project. Referring to the generalized criterion calculation formula19, Ji can be expressed as2 Ji=Kibi1bi2bi3bi4

Establishment of the numerical calculation model

Based on the G317 Huangjiayuan tunnel project and its adjacent Zipingpu bridge tunnel-type anchorage, the minimum clear distance between the Huangjiayuan tunnel and the Zipingpu bridge tunnel-type anchorage is 5 m. The spatial relative position relationship is shown in Fig. 1.

(1) Calculation range and boundary conditions .

This paper uses the general finite element software ABAQUS for numerical simulation. The surrounding rock and tunnel lining structure are simulated by the C3D8 element. In the numerical simulation of underground engineering, the static calculation range is usually selected as three times the hole diameter. However, due to this project’s unique engineering proximity characteristics, stratum disturbance is increased. The calculation range of the model is 170 m (length) × 110 m (height) × 100 m (width), as shown in Fig. 2.Fig.2 Numerical model and the layout of the monitoring point.

2) Calculation Parameters .

The surrounding rock of the Huangjiayuan Tunnel is mainly limestone, and the rock mass adopts the Mohr–Coulomb yield criterion. The primary lining of the Huangjiayuan tunnel and the tunnel-type anchorage adopt C25 shot concrete. The secondary lining of the tunnel structure adopts C30 molded concrete. The secondary lining of the tunnel-type anchorage and the anchor plug body adopt C40 fiber impermeability concrete. Concerning the national standard in China23, the mechanical parameters of the surrounding rock and tunnel lining structure are shown in Table 5. The buried depth of the tunnel is 31 m, and the excavation is carried out using the ring reserved core soil method. The slope angle is 42°, and the pile-anchor support is carried out on the slope of the tunnel entrance before excavation. The tunnel and the tunnel-type anchorage are new projects, and the tunnel is constructed before the tunnel-type anchorage.Table 5 Physical and mechanical parameters of surrounding rock and tunnel lining structure.

Medium	ρ(kg/m)	E (GPa)	ν	c (MPa)	φ(°)	
Moderately weathered rock	2250	5.4	0.305	0.6	37	
Strong ~ moderately weathered rock	1900	1.65	0.42	0.16	21	
The primary lining of the tunnel(C25)	2600	28	0.2	–	–	
The secondary lining of the tunnel(C30)	2600	32.5	0.2	–	–	
The primary lining of tunnel–type anchorage (C25)	2600	28	0.2	–	–	
The secondary lining of tunnel–type anchorage (C40)	2600	33.5	0.2	–	–	
Anchor plug(C40)	2600	33.5	0.2	–	–	

3) Numerical model and the layout of the monitoring point .

The Huangjiayuan Tunnel is excavated a cycle length of 3.5 m. Due to the relatively small cross-section size, the tunnel-type anchorage adopts full-section excavation, and the excavation cycle footage is 3.5 m. The numerical model diagram and monitoring point layout are shown in Fig. 2.

Analysis of the influence of tunnel-type anchorage construction on the pre-built tunnel

Depending on the project, tunnel construction is done before tunnel-type anchorage construction. The change in the influence of the tunnel-type anchorage construction process on the adjacent tunnel is the key to the countermeasures in the project. According to the stiffness and strength criteria of the pre-built tunnel determined above, the influence of tunnel-type anchorage construction on the lining structure of the pre-built tunnel is studied.

1) Stiffness effect.

According to the numerical simulation results, taking the distance from the tunnel portal as the horizontal axis and the tunnel-type anchorage construction step as the vertical axis, the single-step displacement increment distribution of each measuring point is drawn, as shown in Fig. 3. The unit of single-step displacement increment is mm/d.Fig. 3 Single-step displacement increment isoline of each measuring point.

In Fig. 3, the displacement increment to the inside of the tunnel is positive. For the construction steps of tunnel-type anchorage, 1 ~ 22 steps are tunnel-type anchorage’s excavation and support, 23 ~ 24 steps are scattering saddle excavation and construction, 25 ~ 26 steps are pouring anchor body, and 27 ~ 28 steps are pre-stressing and cable loading. The statistics of the affected range of each measuring point and the maximum value of single-step displacement increment are shown in Table 6.Table 6 The affected range of measuring points and the maximum value of single-step displacement increment.

Measuring point position	Weak influence range(m)	Strong influence range(m)	The maximum value of single step displacement increment(mm/d)	
Arch crown	57.7 ~ 112.00	–	0.86	
Inverted arch	63.85 ~ 103.2	76.1–83.1	1.04	
Left spandrel	65.6 ~ 110.2	–	0.94	
Right spandrel	63.85 ~ 109.3	91–92	1.00	
Left haunch	80.47 ~ 92.09	–	0.71	
Right haunch	60.35 ~ 95.35	–	0.73	
Left arch springer	59.97 ~ 105	69.97–95.35	1.25	
Right arch springer	61.22 ~ 105.8	72.6–97.97	 − 1.28	

The influence range of the arch crown is the most extensive among the monitoring points of the supporting structure. The measured points in the inverted arch, tunnel right spandrel, tunnel right Springer, and tunnel left springer exceed the threshold for strong influence. Among them, the strong influence range of the tunnel right springer is the most widely distributed, and the strong influence range is 72.6 m ~ 97.97 m, accounting for 90.6% of the strong influence range of the tunnel. The maximum value of displacement increment in a single step occurs at a distance of 90.97 m from the tunnel right springer, with a magnitude of 1.28 mm/d. Compared to the measuring points on the left side of the tunnel, the affected range of the right side is more comprehensive and more affected.

From the perspective of tunnel-type anchorage construction, the steps that impact the tunnel structure are steps 15 to 22 and step 28. These steps involve excavating the anchor plug body, the back section of the front anchor chamber, and tension the main cable. Specifically, steps 18 to 21, which focus on excavating the anchor plug body, strongly influence the tunnel structure.

2) Strength effect.

Figure 4 shows the maximum and minimum principal stress increase ratio change curves, taking the distance from the tunnel portal as the horizontal axis and the principal stress increase ratio defined above as the vertical axis.Fig. 4 The increased ratio of the maximum principal stress.

As shown in Figs. 4 and 5, from the position of the peak value of the increment of each measuring point, the peak value of the maximum principal stress increment mostly appears near 70 m from the tunnel portal, and the peak value of the minimum principal stress mostly appears near 60 m from the tunnel portal. According to the method of judging the maximum increment of stress21, the maximum increment of the maximum principal stress of the tunnel lining structure is 0.544 MPa. The maximum increment of the minimum principal stress is 1.575 MPa, which does not reach the weak influence threshold, and the construction influence of the tunnel-type anchorage can be ignored. However, the inverted arch has a high level of maximum principal stress before excavating the tunnel-type anchorage. During the construction of the tunnel-type anchorage, the stress increment reaches 65% of its safety reserve, which exceeds the weak influence threshold of 3%. The construction of the tunnel-type anchorage will have a certain degree of adverse impact on the tunnel structure. Therefore, when considering the mutual influence of the adjacent project, it is essential to consider not only the principal stress increment value but also the original stress safety reserve of the supporting structure.Fig. 5 Increase ratio of the minimum principal stress.

3) The influence of the anchor body on the tunnel structure under different inclination angles (α) and intersection angles (β).

In the existing project2, the anchor body's inclination angle varies from 35° to 45°, while the angle of intersection between the anchor body and the tunnel is mostly 2° ~ 3°. Under different inclination and intersection angles, the influence of tunnel-type anchorage construction on the tunnel structure must be studied and analyzed in depth. This paper establishes 25 working conditions, as shown in Table 7, to further investigate the impact of the anchor body's inclination and intersection angles on the tunnel structure.Table 7 Inclination and intersection modes of tunnel-type anchorage and tunnel.

Intersection angle	Inclination angle	
33°	36°	39°	42°	45°	
1.5°	mode1	mode 2	mode 3	mode4	mode5	
2.0°	mode6	mode7	mode8	mode9	mode10	
2.5°	mode11	mode12	mode13	mode14	mode15	
3.0°	mode16	mode17	mode18	mode19	mode20	
3.5°	mode21	mode22	mode23	mode24	mode25	

①Stiffness criterion.

In the previous study, it was observed that the right arch springer exhibited the most significant single-step displacement increment among all the measuring points. This finding suggests that the right arch springer can be an appropriate control point for assessing the stiffness criterion. The curve of the maximum value of the single-step displacement increment of the right arch springer with the distance from the tunnel portal is shown in Fig. 6.Fig. 6 The maximum single-step displacement of the right arch springer under each working condition.

Tables 8 and 9 count the maximum values of single-step displacement and the strong influence range of stiffness in the above modes, respectively.Table 8 The maximum single-step displacement of each mode.

Intersection angle	Inclination angle	
33°	36°	39°	42°	45°	
1.5°	1.35	1.84	1.71	1.24	0.89	
2.0°	1.23	1.54	1.47	1.11	0.74	
2.5°	1.17	1.29	1.26	0.99	0.86	
3.0°	1.00	1.11	1.08	0.89	0.38	
3.5°	0.86	0.66	0.95	0.80	0.34	

Table 9 Strong influence area of stiffness criterion.

Intersection angle	Inclination angle	
33°	36°	39°	42°	
1.5°	87.8–113.4	81.0–96.8	74.3–96.8	73.2–87.9	
2.0°	96.9–110.8	83.0–104.1	76.0–95.1	76.0–85.2	
2.5°	97.0–110.5	84.61–100.5	77.5–93.5	–	
3.0°	103.1–103.3	86.97–97.3	80.85–90.0	–	

Combined with Fig. 6 and Table 8, it can be observed from the analysis of the maximum single-step displacement increment values under various modes with the same intersection angle that there is an initial increase followed by a decrease when the inclination angle ranges from 33° to 45°. The range of 36° to 39° represents the most unfavorable inclination angle. Additionally, when analyzing the single-step displacement increment under the same inclination angle, an increase in the intersection angle leads to a decrease in the maximum single-step displacement increment. Furthermore, the maximum value curve trend for each single-step displacement increment becomes more consistent. The maximum single-step displacement increment occurs at an inclination angle of 36° for all intersection angles except for 3.5°. Conversely, the minimum single-step displacement increment occurs at an inclination angle of 45° for each intersection angle.

Table 9 shows further analysis of the maximum single-step displacement increment's location and the strong influence interval distribution. As the intersection angle increases, the location of the maximum value does not change, but its strong influence interval decreases with the increase of the intersection angle.

②Strength criterion.

For the strength criterion, the maximum principal stress of the inverted arch has a small safety reserve, making it highly susceptible to the construction of the tunnel-type anchorage. Consequently, the stress level during construction frequently exceeds the limit value. Therefore, the inverted arch is chosen as the control point for the strength criterion. The maximum principal stress increase ratio of the inverted arch varies with the distance from the entrance under each mode, as shown in Fig. 7.Fig. 7 Distribution of principal stress increase ratio.

The maximum value of the principal stress increase ratio and the strong influence range under the strength criterion in the above modes are respectively counted in Table 10 and Table 11.Table 10 The maximum value of the principal stress increase ratio in each mode.

Intersection angle	Inclination angle	
33°	36°	39°	42°	45°	
1.5°	0.964	0.591	0.661	0.719	0.430	
2.0°	0.893	0.722	0.783	0.673	0.598	
2.5°	0.823	0.668	0.708	0.625	0.552	
3.0°	0.720	0.686	0.642	0.583	0.501	
3.5°	0.630	0.536	0.576	0.533	0.064	

Table 11 Strong influence area under the strength criterion.

Intersection angle	Inclination angle	
33°	36°	39°	42°	
1.5°	118.1–132.1	–	–	98.2–109.9	
2.0°	118.1–132.1	108.5–120.2	76.0–95.1	98.2–109.9	
2.5°	118.1–131.0	–	107.8–110.0	–	
3.0°	118.7–120.5	–	–	–	

Combined with Fig. 7 and Table 10, it can be seen that with the increase of the inclination angle of the anchor body, the peak position of the stress increment ratio gradually moves forward. When the intersection angle of the anchor body changes, the changing trend of the stress increment ratio is the same, but its peak value and influence range will vary. In general, as the inclination angle of the anchor body increases from 33° to 45°, the principal stress increment ratio tends to decrease. On the other hand, as the intersection angle of the anchor body increases from 1.5° to 3.5°, the principal stress increment ratio typically initially increases and then decreases. The most unfavorable intersection angle is around 2.0°.

The maximum principal stress increase ratio of the tunnel support structure is 0.964, observed at an intersection angle of 1.5° and an inclination angle of 33°, located 119.6 m away from the tunnel portal. This signifies that the increment in the maximum principal stress equals its safety reserve value, indicating a potential risk of instability within the tunnel lining structure.

4) Influence of tunnel-type anchorage construction on tunnel structure under different surrounding rock conditions.

The tunnel-type anchorage incorporates the surrounding rock into the bearing structure. Based on this engineering characteristic, five kinds of surrounding rock modes were selected for research. The mechanical parameters of the surrounding rock are shown in Table 12.Table 12 Mechanical parameters of the surrounding rock.

Number of working conditions	Rock classification	γ(kN/m3)	E(MPa)	ν	c(MPa)	φ(°)	[BQ]	
26	III2	23.5	8850	0.28	0.9	41.5	375.5	
27	IV1	22.5	5400	0.305	0.6	37	333	
28	IV2	21.5	3100	0.32	0.4	32.5	300	
29	IV3	20.5	1850	0.34	0.25	28.5	267.5	
30	V1	19	1650	0.42	0.16	21	230.5	

①Stiffness criterion.

Figure 8 shows the curve of the maximum single-step displacement increment of the tunnel lining structure with the distance from the tunnel portal under different surrounding rock conditions.Fig. 8 Trend of single-step displacement increment ratio under different surrounding rock conditions.

From the stiffness criterion, the tunnel lining structure will likely be strongly affected under V1 and IV3 surrounding rock conditions. It will be weakly affected under the condition of IV2 surrounding rock. Under the conditions of IV1 and III2 surrounding rock, the tunnel lining structure will not be affected by tunnel-type anchorage construction. Regardless of the surrounding rock conditions, the maximum single-step displacement increment of the tunnel support structure exhibits a consistent trend. The peak value occurs at 88.28 m from the tunnel entrance, gradually decreasing from 1.467 mm to 0.164 mm.

②Strength criterion.

The maximum principal stress increment ratio of the tunnel structure under different surrounding rock conditions is shown in Fig. 9. According to the strength criterion, the tunnel structure is strongly affected under the condition of V1 surrounding rock, and the tunnel is weakly affected under the conditions of IV3 and IV2 surrounding rock. When the tunnel and tunnel-type anchorage are in IV1 and III2 surrounding rock, the tunnel structure will not be affected by tunnel-type anchorage’s construction. The maximum principal stress increment ratio decreased from 0.783 in V1 to 0.119 in III2. Different from the position where the maximum value of the single-step displacement increment ratio appears when the surrounding rock levels are V1, IV3, and IV2, the maximum principal stress increment ratio appears at 109.3 m from the tunnel portal, which is 0.783, 0.503, and 0.421, respectively. When the surrounding rock grades are IV1 and III2, the maximum principal stress increment ratio appears at 91.85 m from the hole, which is 0.225 and 0.115, respectively.Fig. 9 Trend of the maximum principal stress increment ratio under different surrounding rock conditions.

Research of tunnel and tunnel-type anchorage adjacent partition

In the previous paper, the expression of the criterion for the proximity of the tunnel and tunnel-type anchorage is determined, and the criterion values under various working conditions are obtained by the numerical simulation method. In this section, according to the value of the criterion under discrete working conditions, the criterion of the proximity influence is reasonably combined. Furthermore, the static influence zoning of the tunnel and tunnel-type anchorage is obtained.

(1) Formula of static stiffness criterion .

From Eq. (2), the influence degree calculation formula is obtained by correcting the value of the influence criterion of the reference working condition by a certain proportion. The value of each correction coefficient in the criterion is determined as follows.

①K1-comprehensive influence coefficient.

The comprehensive influence coefficient represents the benchmark case's criterion value. Based on the project's determined working condition (intersection angle α = 2.0°, inclination angle β = 39°, surrounding rock condition is V1), the maximum single-step displacement increment is 1.47 mm, that is, K1 = 1.47.

②b11-correction coefficient of relative position relationship between anchor and tunnel.

The value of b11 depends on the intersection and inclination angles. According to the proportion between the single-step displacement increase value under the reference working condition and the maximum single-step displacement increment value for working conditions 1–25, the value of b11 under different intersection angles and inclination angles can be obtained, as shown in Table 13.Table 13 The value of b11 under various modes.

Intersection angle	Inclination angle	
33°	36°	39°	42°	45°	
1.5°	0.918	1.252	1.163	0.844	0.605	
2.0°	0.837	1.048	1.000	0.755	0.503	
2.5°	0.796	0.878	0.857	0.673	0.585	
3.0°	0.680	0.755	0.735	0.605	0.259	
3.5°	0.585	0.449	0.646	0.544	0.231	

The horizontal axes depict the intersection angle and inclination angle of the anchor body, while the vertical axis represents the influence coefficient b11. Figure 10 illustrates the distribution of the correction coefficient b11 in three-dimensional space and its regression surface.Fig. 10 Regression surface of coefficient b11.

The regression formula of b11 about α and β is as follows:3 b11=1.83α+3.08β-0.0035α2-0.19αβ+0.125β2-27.78

③ b12-surrounding rock condition correction coefficient.

The value of b12 is determined by the surrounding rock correction [BQ]. According to the ratio of the maximum single-step displacement increment value of working conditions 26–30 to the single-step displacement increment under the reference working condition, the value of b12 under different correction [BQ] values can be obtained, as shown in Table 14.Table 14 The value of coefficient b12 under different modes.

[BQ]	230.5	267.5	300	333	375.5	
b12	1	0.721	0.556	0.325	0.114	

Taking the modified [BQ] value as the horizontal axis and the influence coefficient b12 as the vertical axis, the distribution of each discrete point b12 and its regression curve are shown in Fig. 11.Fig. 11 Regression curve of coefficient b12.

The b12 regression formula for [BQ] is as follows:4 b12=12.96exp(-0.01097·[BQ])

④ b13-buried depth and its change trend correction coefficient.

In this paper’s influence zoning calculation simulation, the slope and the tunnel depth are consistent with the supporting project, so b13 = 1.

⑤b14-Countermeasure correction coefficient.

This paper’s influence degree and calculation simulation use conventional measures, so b14 = 1.

Based on the coefficients above, the calculation formula for the stiffness criterion can be determined as follows:5 J1=1.47·(1.83α+3.08β-0.0035α2-0.19αβ+0.125β2-27.78)·2.96exp(-0.01097·[BQ])

(2) Formula of static strength criterion.

Similar to the static stiffness criterion, the comprehensive influence coefficient K2 = 0.7836, b23 = 1, and b24 = 1 can be determined based on the working condition 8. The following will determine the values of b21 and b23.

b21-correction coefficient of relative position relationship between tunnel-type anchorage and tunnel.

According to the proportion between the principal stress increase ratio value under the reference working condition and the working conditions of 1 ~ 25, the value of b21 under different intersection angles and inclination angles can be obtained, as shown in Table 15.Table 15 The value of b21 under various modes.

Intersection angle	Inclination angle	
33°	36°	39°	42°	45°	
1.5°	1.23	0.75	0.84	0.92	0.55	
2.0°	1.14	0.92	1.00	0.86	0.76	
2.5°	1.05	0.85	0.90	0.80	0.70	
3.0°	0.92	0.88	0.82	0.74	0.64	
3.5°	0.80	0.68	0.74	0.68	0.08	

The horizontal axes represent the intersection angle and inclination angle of the anchor body, while the vertical axis represents the influence coefficient b21. The distribution of the correction coefficient b21 in the three-dimensional space and its regression surface are shown in Fig. 12.Fig. 12 Regression surface of coefficient b21.

The regression formula of b21 about α and β is as follows:6 b21=-7.18α-9.83β+0.17α2+0.44αβ+0.63β2+100.8

%1%1b22-surrounding rock condition correction coefficient.

The value of b22 is determined by the surrounding rock correction [BQ]. According to the proportion between the principal stress increase ratio value under the working conditions of 26 ~ 30, the value of b22 under different correction [BQ] values can be obtained, as shown in Table 16.Table 16 The value of coefficient b22 under different modes.

[BQ]	230.5	267.5	300	333	375.5	
b22	1	0.642	0.538	0.287	0.147	

Taking the modified [BQ] value as the horizontal axis and the influence coefficient b22 as the vertical axis, the distribution of each discrete point b22 and its regression curve are shown in Fig. 13.Fig. 13 Regression curve of coefficient b22.

The b22 regression formula for [BQ] is as follows:7 b22=12.96exp(-0.0114·[BQ])

According to the values of the above coefficients, the calculation formula of the stiffness criterion can be determined as follows:8 J2=0.783·(-7.18α-9.83β+0.17α2+0.44αβ+0.63β2+100.8)·12.96exp(-0.0114·[BQ])

(3) Combination of static criteria and static partition .

The initial sections provide the definitions of the strength criterion and stiffness criterion. This paper comprehensively considers the surrounding rock conditions and engineering safety in the tunnel and tunnel-type anchorage project. The strength and stiffness criteria are combined based on the principle of 'once a strong is strong, double weak is weak.' The project is considered to be significantly affected if any criterion shows a strong influence. In contrast, it is considered mildly affected only when both criteria indicate a weak influence.

After combining the strength criterion with the stiffness criterion, when the surrounding rock condition is consistent with the benchmark project, the influence degree area is divided by the anchor body’s inclination angle and intersection angle plane, as shown in Fig. 14(a). If the relative position relationship between the tunnel and the tunnel-type anchorage matches that of the reference project, the partition of the surrounding rock correction [BQ] is shown in Fig. 14(b).Fig. 14 Partition diagram of static interaction between tunnel and tunnel-type anchorage.

Discussion

Based on the Huangjiayuan tunnel project and its adjacent Zipingpu bridge tunnel-type anchorage project, this paper uses the research methods of data investigation, theoretical analysis, and numerical simulation to carry out the influence of the symmetrically arranged tunnel-type anchorages’ structure on the near-junction highway tunnel. Firstly, a discriminant for the proximity influence degree of tunnel anchorage and tunnel structure is proposed. Based on the relevant influencing factors in the discriminant, the calculation conditions are divided, and the interaction law between tunnel anchorage and tunnel structure is explored. Based on the discriminant, the interaction partition between tunnel anchorage and tunnel structure is given by curve regression.

Liang et al.8 studied the influence of the new tunnel on the settlement of the existing tunnel-type anchorage. The analysis variables are the buried depth of the tunnel structure and the spacing between the tunnel and the tunnel-type anchorage. The results show that the change in the buried depth of the tunnel structure has the most significant influence on the settlement of the tunnel-type anchorage. Through the test method, Liu et al.9 explored the influence of the construction process of the underpass tunnel on the existing tunnel anchorage and put forward the critical construction steps. Compared with the above scholars' research conclusions, the spacing between tunnel anchorage and tunnel structure is smaller in this paper. Not only is the mutual position relationship between tunnel and tunnel anchorage taken as the research variable, but the strength of the surrounding rock is also introduced as the influencing factor variable in this paper. The influence zoning of tunnel-type anchorage and tunnel structure is proposed based on the above research variables.

Concerning the research conclusions of the above scholars, combined with the research in this paper, the following design and construction suggestions can be put forward for the project. According to the zoning results, under the benchmark engineering conditions, the stiffness of the tunnel structure will be strongly affected, and the strength of the tunnel structure will be weakly affected. Therefore, according to the partition result, it is suggested that the angle between the tunnel anchorage and the tunnel axis should be adjusted to 3.3°, and the intersection angle should be adjusted to 44°. For the tunnel structure, measures such as increasing the thickness of the lining locally and increasing the concrete grade can be adopted. At the same time, static blasting can be used when excavating the tunnel anchorage to reduce the vibration impact on the existing tunnel structure. For the rock and soil mass between the existing tunnel and the tunnel-type anchorage, the soil can be improved by grouting, freezing, and other measures. At the same time, the anchorage pile, steel sheet pile, and other structures can separate the tunnel-type anchorage from the existing tunnel structure.

Conclusion

This paper used the research methods of theoretical analysis and numerical simulation to carry out the influence of the tunnel-type anchorages’ structure on the near-junction highway tunnel. The main conclusions were as follows:

(1)Four factors influencing the proximity of tunnels and tunnel-type anchorages were summarized: relative position relationship, surrounding rock conditions, buried depth and topography, and engineering countermeasures. Based on the proximity of the associated projects, the calculation formula for the generalized proximity criterion was refined to derive a criterion suitable for this project type. The stiffness and strength of the pre-built tunnel were selected as criteria to assess the influence of tunnel-type anchorages, and thresholds for determining strong and weak influence zones of the relevant index were established.

(2)The pre-built tunnel lining's stiffness and strength evaluated the degree and range of the tunnel-type anchorage construction’s effect on the pre-built tunnel. Under the reference working condition, the construction of tunnel-type anchorage weakened the tunnel’s strength while substantially impacting its stiffness. Under various inclination angles, intersection angles, and surrounding rock conditions, the effect of tunnel-type anchorage construction on the pre-built tunnel was examined. Subsequently, the strength and stiffness criteria values were determined for each working condition.

(3)The regression curve (surface) for each discrete point was determined based on the value of the static criteria in each specific circumstance. The combination of stiffness and strength criteria was proposed, and the control parameters were segmented into areas in multi-dimensional space. Further research was conducted to identify the spatial zoning of static effects on the tunnel and adjacent tunnel-type anchorage in multi-dimensional space.

Acknowledgements

This work is supported by Sichuan Communication Surveying and Design Institute Co., Ltd Consulting Project--Research on bearing capacity of bridge tunnel anchor in high intensity earthquake area and seismic technology of adjacent highway tunnel (No.232022003-2).

Author contributions

J.Z., R.L. and Q.Q. contributed to the conception of the study; R. L. and Q.Q. contributed to the formal analysis; S. Y. and S. S. contributed to the funding acquisition; Q. Q. , F. Y. and K. C. contributed to the investigation of the study; K.C. and F. Y. contributed to the methodology; J. Z., S. Y. and S. S. contributed to the administration of the project; R. L., Z. X. and Q. Q. performed the data analyses and wrote the manuscript; J. Z., R. L. and F. Y contributed to the review & editing of the manuscript.

Data availability

All data, models, and code generated or used during the study appear in the submitted article.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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