Preliminary Study on Double Lining Support Design for Water Plugging of Highway Tunnel under High Water Pressure in Mountain Area Based on Limited Drainage

Abstract

In the water-rich karst regions, high water and mud outbursts are common geological disasters in tunnel construction. To ensure the safe and smooth construction of tunnel projects, it is necessary to consider anti-water pressure, water inrush prevention and geological disasters during the design of tunnels. Based on the Yongfutun Tunnel Project, this paper studies the application and effect of radial grouting and curtain grouting, which involves those in high-water-pressure tunnels under double-layer support conditions. To obtain the effects and parameters of radial grouting and curtain grouting, the influences of different grouting ranges on the tunnel’s surrounding rocks and supporting structures were analyzed and the finite difference method was adopted. The results show that the radial grouting of the surrounding rock can notably improve the initial support of the tunnel, but the impact is less obvious when the grouting range exceeds 4 m. The design of radial grouting is recommended to be 4.0 m to 4.5 m. Curtain grouting can effectively reduce the external water pressure of the tunnel lining. The external water pressure of the grouting area is 23% greater than that without curtain grouting. Curtain grouting can slow down the infiltration of external water pressure. This is beneficial to the stress of the tunnel lining structure, but the improvement in initial support force is slight. Moreover, curtain grouting improves the safety reserve of the secondary lining by strengthening the self-stability ability of the surrounding rock. Meanwhile, the double-layer primary support can effectively share the external water pressure and surrounding rock pressure. This study provides a certain reference for the lining design of high-water-pressure tunnels.

1. Introduction

After years of transportation construction, China’s total highway mileage had reached 5,198,100 km by 2020, including 21,316 road tunnels with a linear length of 21.9993 million meters. There are 2249 more tunnels, with an increase of 3.0327 million linear meters. Among them, 1394 extra-long tunnels have a total length of 6,235,500 linear meters, and 5541 long tunnels have a total length of 9.6332 million linear meters [1]. Tunnel construction is gradually developing in remote areas with complex topography and geology. During the construction, high-pressure and water-rich tunnels are the most common and prominent sites of geological disasters. Sometimes, they cause huge economic losses and even casualties [2,3]. Water control often follows the guidance of “water plugging coordinated with limited drainage” [4]. For the safety of people’s lives and property, curtain grouting, radial advance grouting, and other grouting techniques are recommended as the common solutions to these challenges. These techniques have become the main construction measures to deal with the problem of high water pressure in tunnels based on the construction concept of NATM [5,6,7,8,9,10,11,12,13]. The tunnel’s surrounding rocks, reinforced by advanced grouting, can bear part of the water pressure and block the passage of groundwater flowing into the tunnel. However, regarding both curtain grouting and radial grouting, the influence of grouting scope on the construction of water-rich tunnels has not been specifically discussed. Technicians often use experience and judgment in the design, and the determination of grouting parameters has become a major task. Due to the thick anti-water-pressure lining, the construction can be inconvenient and difficult, and the tunnel cannot bear water pressure in time. Based on the engineering practice of double-layer initial support to control the large deformation of the tunnel [14,15,16,17,18,19,20], a double-layer initial support (two-layer shotcrete and steel arch combined structure) is proposed to bear the high-water pressure, reduce the thickness of the secondary lining, and enhance the waterproof effect. However, previous designs adopted a single measure of grouting, without considering the damage and stress of the initial support. The research shows that the rich water in the later tunnel still has a great impact on the initial support. Therefore, the scheme of double-layer initial support design plus curtain grouting is proposed to support the surrounding rock area with high water pressure.

In previous tunnel construction cases, curtain grouting was used for the construction of water-rich tunnels. Although curtain grouting initially alleviated the risk of water inrush and gushing of the tunnel, the large seepage water pressure in the construction acted on the initial support, so engineers often used strong initial support, and later also used a thick secondary lining structure to control deformation and bear water pressure, which increased the construction investment to a certain extent. Referring to the deformation control technology of double-layer initial support used in the construction of soft rock tunnels, the authors adopts a strategy to bear the external load of the surrounding rock step by step and make full use of the support system formed by the surrounding rock and lining. The first layer of initial support bears the main load, and the second layer of initial support carries out reinforcement and offers a safety guarantee, so as to reduce the secondary lining structure, effectively speed up the project’s progress, and reduce investments. Therefore, based on the previous experience of water-rich tunnel treatment, this paper creatively puts forward the structural type of “curtain grouting + double-layer initial support” to provide the stability of the anti-water-pressure lining and improve the efficiency of water-rich tunnel construction. To obtain the effect of tunnel radial grouting and curtain grouting based on double-layer initial support, the finite difference method is adopted in this paper to analyze the radial grouting and curtain grouting technologies. These technologies are used in the Yongfutun tunnel of the Guilin–Liuzhou expressway. This paper aims to obtain the stress variation law of the surrounding rock deformation, shotcrete, and secondary lining under the operating conditions of different grouting ranges. The conditions can be with or without curtain grouting when the anti-seepage grade is P8 (according to 10.2.3 of “Specifications for Design of Highway Tunnels, Section 1 Civil Engineering” [21], the impermeability grade of concrete should not be less than P8; P8 is used for fortification in this study). The research results can provide a reference for the grouting and lining support design of tunnels with high water pressure.

In general, this article summarizes the main construction measures of water-rich tunnels used in the past, and, combined with the large deformation control technology of soft rock, the structural type of “curtain grouting + double-layer initial support” is proposed to provide the stability of the anti-water-pressure lining and improve the efficiency of water-rich tunnel construction.

1.1. Tunnel Overview

The left line and the right line of the Yongfutun tunnel are located in Siding Town, Rong’an County, Liuzhou City, Guangxi. Their lengths are 5640 m and 5647 m, respectively. Their longitudinal slopes are −2.37% one-way slopes. As a separated extra-long tunnel, the Yongfutun tunnel zone belongs to the geomorphic area of tectonic dissolution with a peak-cluster depression and valleys, with a maximum buried depth of approximately 301 m. According to the drilling and geological mapping results, at the tunnel site, with a relatively thin overburden, the lithology of the underlying bedrock is dolomitic limestone of upper Liujiang formation (D3) and middle Donggangling formation (D2D) of the Devonian system. The dominating tunnel surrounding rocks are of Grade III and Grade IV. The unfavorable geology in the tunnel area is mainly karst. Several sinkholes were found in the tunnel during the survey, while geophysical exploration showed that the tunnel may have karst fissures, karst caves, and underground rivers, etc.

The water inflow section is located at the tunnel exit. The rock mass joints and fissures around the tunnel site are developed. There are two groups of main joint fissures at the exit. The occurrence of L1 is 250° ∠ 86°, closed, with an extension length of 2–3 m and a density of 1–2 pieces/m; L2 occurrence is 320° ∠ 80°, closed, with an extension length of 3–4 m and a density of 2–3 strips/m. Dissolution depression L42 is found at 175 m to the right of K66+450 and dissolution depression L43 is found at 210 m to the left of ZK66+643.

The geostructure of the tunnel site is located in the first Indosinian substructure (Devonian system). There is no tertiary stratum in the area. According to the development of quaternary river terraces and karst caves, the Himalayan movement involves mainly upward movement, which is manifested in terraces and karst cave layers of different heights at all levels. The underground water in the tunnel site area is mainly supplied by atmospheric rainfall and discharged in vein and linear form to the low-lying depression along with the pores, bedrock fissures, and dissolution fissures. The amount of karst water is controlled by the degree of karst development and supply source, and the seasonality is obvious. In particular, the surface flow formed in the rainy season easily infiltrates rapidly along the dissolution fissure and water drop tunnel, and the groundwater flow increases sharply, which has an important impact on tunnel construction.

On 17 June 2019, a mud outburst and water inrush disaster occurred at the K66+490 palm surface on the right line of the tunnel. This disaster was caused by a hidden cavern triggered by blasting construction. As of 30 June 2019, the cumulative amount of water and mud inrush reached 10,000 cubic meters (see Figure 1 and Figure 2).

1.2. Treatment Scheme Design

To ensure the construction progress and safety, the standard section lining was adjusted to a water-pressure-resistant lining. To optimize the thickness of the lining, a double-layer initial support scheme was designed (see Figure 3). Two rows of Φ42 mm grouting with a small conduit were used as advance support, being 4.5 m in length. The extrapolation angles of the first and the second rows were 10° and 20°, respectively; the systematic bolts adopted Φ42 grouting small conduits, being 6 m in length. The spacing of the bolts was 50 × 50 mm, and they were in a quincunx arrangement; the initial support was a combined structure of C25 shotcrete (28 cm) + reinforcement mesh (Φ8, 20 × 20 cm) + I-beam steel frame (i22b, 50 cm/bay); the secondary lining was C40 reinforced concrete.

2. Design of Radial Grouting Range

2.1. Calculation Model and Parameters

In this paper, FLAC3D software is used for simulation, and the numerical method is based on the nodal finite difference equation of the fluid continuity equation.

The numerical model sized 92 × 127 × 1 m is designed to study the support of radial grouting range on the water-rich tunnel under high water pressure. The distances from the left and right boundaries to the tunnel are both 40 m, and the distances from the upper and lower boundaries to the tunnel are 95 m and 23 m, respectively (Figure 4). The surrounding rock, grouting area, and initial support are all simulated by solid elements, and the secondary lining is simulated by shell elements. Mohr–Coulomb (M-C) was adopted to obtain the constitutive relationship between the surrounding rock and grouting area, and other materials are all elastic; the initial support includes shotcrete and steel arches, and the material parameters are obtained according to the equivalent stiffness method. In terms of mechanical boundaries, the front, rear, left, and right boundaries are applied with normal constraints, while the lower boundary is applied with a fixed constraint; as for the seepage boundary, its bottom is impermeable, and the other boundaries are permeable. The initial stress only considers self-weight stress in the calculation, and the fluid–solid coupling effect is considered in the construction simulation. The fluid–solid coupling model involves indirect coupling. In other words, the flow switch is turned off during static calculation, and the static switch is turned off during flow calculation.

See

Table 1. Values of relevant parameters.

Material	E/GPa	μ	γ/(kg·m−3)	φ/(°)	c/(MPa)	k	EI	k0
Surrounding rock	1.5	0.3	2400	30	0.3	4.3 × 10−4	/	0.43
Grouting area *	2.2	0.3	2400	45	0.45	1.0 × 10−5	/	0.45
Initial support	28	0.25	2400			2.61 × 10−9	7.84 × 109	/
Secondary lining	32	0.20	2500				25.6 × 109	/

* 1. The materials in the grouting area shall be increased by 1.5 times the surrounding rock materials, and the permeability coefficient shall be obtained according to the on-site sampling test.

for the calculation parameters obtained from the test and literature [13].

According to the design specifications, in this calculation, the thickness of the double-layer lining is 80 cm. During calculation, the double-layer initial support is used with an anti-seepage grade of P8. Models are established for the four operating conditions with grouting ranges of 0 m, 2 m, 4 m, and 6 m (

Table 2. Calculation conditions.

Calculation Condition	Initial Support Form	Anti-Seepage Grade	Infiltration Coefficient/(×10−9 cm/s)	Grouting Range	Shotcrete Thickness/(m)	Secondary Lining Thickness/(m)
1	Double-layer initial support	P8	2.61	0 m	0.28	0.8
2	Double-layer initial support	P8	2.61	2 m	0.28	0.8
3	Double-layer initial support	P8	2.61	4 m	0.28	0.8
4	Double-layer initial support	P8	2.61	6 m	0.28	0.8

).

2.2. Result Analysis

2.2.1. Deformation Analysis of Surrounding Rock

Figure 5 shows the four operation conditions. Their settlements are 13.72 mm, 13.62 mm, 13.52 mm, and 13.50 mm, respectively. They have a small difference in settlement values. Water plugging is the main purpose of surrounding rock grouting in the tunnel. Under high water pressure, it is necessary to improve the anti-seepage performance of the surrounding rock. During its reinforcement in the tunnel excavation, most surrounding rock is deformed. Therefore, the surrounding rock grouting after excavation has little impact on the surrounding rock deformation. At the same time, according to the displacement nephogram analysis, the increase in the grouting circle radius can improve the local self-supporting capacity of the surrounding rock within a certain range, but the overall deformation of the surrounding rock is less affected by the lining thickness. Therefore, the authors believe that the deformation is not the decisive factor to control the grouting parameters, and it is necessary to select an economic and reasonable grouting radius according to the stress control index of the lining structure.

2.2.2. Stress Analysis on Initial Support

As shown in

Table 3. Minimum and maximum principal stress of initial support with different grouting ranges.

Grouting Range (m)	First-Layer Initial Support		Second-Layer Initial Support
	Min Principal Stress (MPa)	Max Principal Stress (MPa)	Min Principal Stress (MPa)	Max Principal Stress (MPa)
0	3.26	0.69	4.38	0.69
2	2.15	0.48	2.88	0.48
4	1.24	0.28	1.48	0.29
6	1.12	0.24	1.34	0.25

, when no grouting is conducted for water plugging and reinforcement, the minimum and maximum principal stress of the first-layer initial support are 4.38 MPa and 0.69 MPa, respectively. When the grouting is conducted within 2 m around the tunnel, the minimum and maximum principal stress of the first-layer initial support are 2.88 MPa and 0.48 MPa, respectively. It represents a decrease of 34.25% and 30.43%, respectively. When the grouting is conducted within 4 m around the tunnel, the minimum and maximum principal stresses of the first-layer initial support are 1.48 MPa and 0.29 MPa, respectively. The figures are reduced by 48.61% and 39.58%, respectively. When the grouting is conducted within 6 m around the tunnel, the minimum and maximum principal stresses of the first-layer initial support are 1.34 MPa and 0.25 MPa, respectively, and the figures are reduced by 9.46% and 13.79%, respectively.

The stress analysis on the second-layer initial support shows that when no grouting is conducted for water plugging and reinforcement, the minimum and maximum principal stress of the second-layer initial support are 3.26 MPa and 0.69 MPa, respectively; when the grouting is conducted within 2 m around the tunnel, the minimum and maximum principal stresses of the second-layer initial support are 2.15 MPa and 0.48 MPa, respectively. The figures are reduced by 34.05% and 30.43%, respectively. When the grouting is conducted within 4 m around the tunnel, the minimum and maximum principal stresses of the second-layer initial support are 1.24 MPa and 0.28 MPa, respectively, and they decrease by 42.33% and 41.67%, respectively. When the grouting is conducted within 6 m around the tunnel, the minimum and maximum principal stresses of the second-layer initial support are 1.12 MPa and 0.24 MPa, respectively. They are reduced by 9.68% and 14.29%, respectively. The stress comparison between the first layer and the second layer’s initial support shows that the grouting range around the tunnel exceeding 4 m has an impact on the surrounding rock, and the radial grouting range on the first-layer initial support is reduced.

2.2.3. Internal Force Analysis of Secondary Lining

The surrounding rock’s radial grouting plays an important role in the internal force of the tunnel’s secondary lining (see

Table 4. Minimum and maximum internal forces of secondary lining with different grouting range.

Grouting Range (m)	Bending Moment (kN.m)	Axial Force (kN)
0	219	1602.26
2	148	1079.51
4	85.4	614.95
6	75.3	531.43

). According to the design scheme, with the tunnel lining anti-seepage grade of P8, the thickness of the double-layer initial support is 80 cm. Without radial grouting, the maximum values of bending moment and axial force are 219 kN.m and 1602.26 kN, respectively. When the radial grouting range is 2 m, the maximum bending moment and axial force become 148 kN.m and 1079.51 kN, respectively. These figures are 32.42% and 32.63% lower than those without radial grouting. When the radial grouting range is 4 m, the maximum bending moment and axial force are 85.4 kN.m and 614.95 kN, respectively. These figures are 42.30% and 43.03% lower than those with the radial grouting range of 2 m. As for the radial grouting range of 6 m, the maximum bending moment and axial force are 75.3 kN.m and 531.43 kN, respectively. They are 11.83% and 13.58% lower than those with the radial grouting range of 4 m. Therefore, the radial grouting range has a small impact on the internal force of the secondary lining after exceeding 4 m.

As indicated by the analysis above, radial grouting of the surrounding rock can effectively assist the initial support in bearing the peripheral stress and reduce the stress on the initial support. However, when the radial grouting range exceeds 4 m, there is less influence on the grouting range. Therefore, radial grouting within the range of 4.0 m to 4.5 m has to be controlled during design.

Radial grouting is used for surrounding rock reinforcement in water-rich tunnels under high water pressure. Curtain grouting is also adopted for water plugging in front of the palm surface. Such design is further studied in the following section.

3. Design Analysis of Curtain Grouting

3.1. Calculation Model and Operating Conditions

Curtain grouting uses medium and low pressure to inject pressure. The pressure of grouting slurry enters the fractures, cracks, and voids of the broken rock stratum, soft sand rock layer, and other strata. Meanwhile, certain water will permeate through the advanced grouting holes on the working face. After solidification, the rocky soil or particles are cemented into a whole to form a plugging layer of grouting water. The Yongfutun tunnel section with the stake number of YK66+490 is selected for the establishment of the 3D model. The 3D model is divided into element grids according to the 1 m element size. The solid elements are hexahedrons, and the grids are set in combination with the calculation steps. The surrounding rock, grouting area, and initial support are simulated by the solid elements, and the secondary lining is simulated by the shell element. With Mohr–Coulomb (M-C) adopted as the constitutive relationship between the surrounding rock and grouting area, other materials are all elastic. The material parameters of the initial support, which are composed of shotcrete and a steel arch frame, are obtained by the equivalent stiffness method (E₁I₁ = E₂I₂). As for the mechanical boundaries (see Figure 6), the front, rear, left, and right boundaries are applied with normal constraints. The lower boundary is applied with a fixed constraint. The bottom of the seepage boundary is impermeable, and the other boundaries are permeable. The model is a 3D finite element stratum model. Its width is 45 m in the X direction, 45 m in the Y direction, and 130 m in the Z direction. The net height and net width of the simulated tunnel are 10.02 m and 6.44 m, respectively (symmetrical); 4.41 times the maximum span of the tunnel is taken in the X direction. The tunnel height (approximately 30 m) is taken 3 times vertically downward and 130 m of the tunnel height is taken vertically upward. Moreover, the simulated hydrostatic head is 90 m.

In the finite element model, 1.5 m is selected as the cyclical footage. The bench length is 3.0 m. The longitudinal length of the tunnel is 36 m. The analysis model adopts the bench method according to the construction scheme; the upper bench is excavated every 1.5 m, and the analysis load step is gradually simulated and established according to the excavation and support conditions. The calculation is completed during simulation of one board lining and the secondary lining. The bench method includes the following procedures: firstly, the front soil is conducted with full curtain grouting for the construction of an advanced anchor bolt. After the excavation of the upper part, the arch of the upper bench is conducted with initial support (two series of initial support are carried out separately). In this case, the upper bench is 12 m long. The side walls are conducted with initial support during the lower bench excavation. In this way, initial support is implemented close to a ring. The secondary lining can be conducted when the heading face is pushed to a certain distance. This is carried out with a stable initial support. The displacement boundary and stress boundary are two parts of the setting for model boundary conditions. The displacement boundary condition is used in this simulation. In other words, the longitudinal displacement of the model is fixed at the front and back along the tunnel excavation. The horizontal displacement of the model is horizontally fixed on the left and right sides. The vertical displacement is fixed vertically on the lower surface. The upper surface of the model in the vertical direction is a free surface, which is not constrained. A map of the layout of the analytical measuring points is shown in Figure 7.

3.2. Result Analysis

3.2.1. Analysis of Pore Water Pressure

According to the analysis in

Table 5. Variation diagram of pore water pressure at arch bottom (Unit: MPa).

The Advance Progress of Heading Face (m)	0	3	6	9	12	15	18	21	24	27	30	33	36
A-1	0.91	0.42	0.33	0.30	0.27	0.33	0.41	0.45	0.48	0.49	0.50	0.51	0.51
B-1	0.91	0.59	0.46	0.35	0.30	0.26	0.23	0.31	0.42	0.46	0.48	0.49	0.50
C-1	0.91	0.73	0.64	0.54	0.44	0.34	0.28	0.25	0.24	0.23	0.38	0.43	0.46
D-1	0.91	0.81	0.73	0.66	0.59	0.51	0.43	0.34	0.28	0.25	0.23	0.21	0.32
E-1	0.91	0.85	0.78	0.73	0.67	0.61	0.54	0.48	0.41	0.34	0.27	0.23	0.22
A-2	0.91	0.40	0.40	0.39	0.37	0.35	0.40	0.48	0.53	0.57	0.60	0.63	0.65
B-2	0.91	0.61	0.59	0.53	0.47	0.39	0.31	0.34	0.42	0.50	0.56	0.60	0.63
C-2	0.91	0.77	0.77	0.76	0.73	0.62	0.51	0.43	0.36	0.29	0.41	0.49	0.56
D-2	0.91	0.84	0.84	0.84	0.84	0.83	0.79	0.71	0.59	0.48	0.40	0.31	0.39
E-2	0.91	0.88	0.88	0.87	0.87	0.87	0.87	0.86	0.84	0.77	0.64	0.52	0.44

Notes: A-1 represents the operating condition without grouting; A-2 represents the operating condition with curtain grouting (the same below).

and

Table 6. Variation diagram of pore water pressure outside the grouting range (Unit: MPa).

The Advance Progress of Heading Face (m)	0	3	6	9	12	15	18	21	24	27	30	33	36
A-1	0.91	0.00	0.22	0.27	0.28	0.39	0.44	0.47	0.49	0.49	0.50	0.50	0.51
B-1	0.91	0.52	0.34	0.00	0.13	0.25	0.28	0.38	0.44	0.47	0.48	0.49	0.50
C-1	0.91	0.69	0.59	0.50	0.37	0.09	0.00	0.22	0.26	0.30	0.41	0.45	0.46
D-1	0.91	0.77	0.69	0.63	0.56	0.48	0.38	0.23	0.00	0.16	0.23	0.26	0.37
E-1	0.91	0.80	0.75	0.69	0.63	0.58	0.51	0.45	0.38	0.28	0.00	0.00	0.20
A-2	0.91	0.00	0.18	0.20	0.22	0.38	0.44	0.51	0.55	0.58	0.60	0.62	0.64
B-2	0.91	0.54	0.45	0.00	0.13	0.24	0.24	0.39	0.48	0.54	0.58	0.61	0.63
C-2	0.91	0.72	0.72	0.71	0.64	0.17	0.00	0.24	0.26	0.31	0.48	0.54	0.59
D-2	0.91	0.80	0.80	0.80	0.80	0.78	0.73	0.50	0.00	0.22	0.27	0.27	0.46
E-2	0.91	0.83	0.83	0.83	0.83	0.83	0.83	0.82	0.79	0.65	0.00	0.00	0.27

, under the condition of no curtain grouting, the pore water pressure around the surrounding rock of the tunnel decreases significantly with the advance of the upper bench face outside the surrounding rock of the tunnel. The excavation is carried out on the palm surface of the tunnel upper bench for 3 m. As a result, the water pressure around the palm surface drops to 0.42 MPa. With the gradual excavation of the upper and lower bench, there is no role of the water-resistant grouting layer around the tunnel. The overall water pressure gradually decreases from the initial 0.91 MPa to 0.27 MPa. Next, the pore water pressure reaches a low point when excavation is carried out on the section of the measuring point. The figure rises when there is a certain distance between the palm surface and the section (i.e., the initial support is closed into a ring), and finally stabilizes at 0.5 MPa. With the adoption of the curtain grouting method, the excavation to the position of the measuring point causes another decrease in the water pressure of the palm surface, but the change is slight. The water pressure decreases from the initial 0.91 MPa to 0.33 MPa under the influence of palm surface excavation, and then rises to 0.65 MPa soon after the completion of the support. At the same time, through the analysis of water pressure at the same stage of driving footage, it is found that the periphery of the grouting circle bears the main water pressure under the curtain grouting condition, and the maximum difference between the two water pressures is 0.21 MPa, indicating that the curtain grouting construction can effectively improve the water environment of tunnel construction and ensure the safety of tunnel construction.

3.2.2. Deformation Analysis of Surrounding Rock

Arch crown settlement reflects the impact of curtain grouting in a direct way, and the settlement analysis on the measuring point at the arch crown (

Table 7. Settlement deformation trend of arch crown (Unit: mm).

The Advance Progress of Heading Face (m)	0	3	6	9	12	15	18	21	24	27	30	33	36
A-1	−11.3	−12.3	−13.0	−13.5	−14.0	−14.4	−14.7	−14.9	−15.2	−15.3	−11.3	−12.3	−13.0
B-1	−9.0	−10.5	−11.7	−12.4	−13.0	−13.4	−13.8	−14.1	−14.3	−14.5	−9.0	−10.5	−11.7
C-1	−4.8	−6.1	−8.3	−10.3	−11.5	−12.2	−12.8	−13.2	−13.5	−13.8	−4.8	−6.1	−8.3
D-1	−4.3	−4.7	−5.3	−6.1	−8.2	−11.2	−12.6	−13.3	−13.9	−14.3	−4.3	−4.7	−5.3
E-1	−4.2	−4.6	−4.9	−5.3	−5.7	−6.2	−7.7	−9.6	−11.3	−12.2	−4.2	−4.6	−4.9
A-2	−5.5	−6.3	−7.2	−7.8	−8.4	−8.8	−9.2	−9.6	−9.9	−10.2	−5.5	−6.3	−7.2
B-2	−3.4	−5.1	−6.2	−7.0	−7.7	−8.3	−8.8	−9.2	−9.5	−9.8	−3.4	−5.1	−6.2
C-2	−0.3	−0.8	−2.3	−5.1	−6.5	−7.4	−8.1	−8.6	−9.1	−9.5	−0.3	−0.8	−2.3
D-2	−0.2	−0.2	−0.5	−0.9	−2.0	−5.3	−7.1	−8.1	−8.9	−9.5	−0.2	−0.2	−0.5
E-2	−0.2	−0.2	−0.4	−0.5	−0.8	−1.1	−1.8	−3.7	−6.2	−7.5	−0.2	−0.2	−0.4

) shows that the tunnel arch crown settlement gradually increases with the palm surface excavation of the tunnel upper bench. For measuring point A, under the condition of no curtain grouting, its initial settlements are 8.89 mm. After the tunnel is excavated to 36 m, the maximum displacement is 15.3 mm. Its initial and final settlements are 3.38 mm and 10.2 mm, respectively. This is under the condition of curtain grouting. The results prove that curtain grouting can effectively control tunnel arch crown settlement. Secondly, the adoption of the curtain grouting scheme leads to the obvious deformation of surrounding rocks. This is most notable when the excavation of the upper bench palm surface reaches the measuring point. In comparison, in the scheme with no grouting, the surrounding rocks are already partially deformed under the water pressure and empty palm surface. The deformation exceeds approximately 3 mm. Thirdly, according to the analysis of the measuring points, the tunnel arch crowns with the adoption of grouting are smaller than those without grouting. This proves that curtain grouting can effectively strengthen the self-stability of surrounding rocks and it controls the deformation settlement by around 33%.

This paper has analyzed the extraction of characteristic points of the arch bottom. It aims to study the tunnel arch bottom uplift during excavation (

Table 8. Settlement deformation trend of the arch bottom (Unit: mm).

The Advance Progress of Heading Face (m)	0	3	6	9	12	15	18	21	24	27	30	33	36
A-1	0.00	0.18	1.87	2.66	3.07	4.52	5.36	5.59	5.67	5.69	5.68	5.64	5.61
B-1	0.00	−1.81	−0.78	0.60	1.87	2.83	3.26	4.12	4.98	5.29	5.38	5.40	5.39
C-1	0.00	−2.46	−2.48	−2.34	−1.65	−0.41	0.99	2.12	2.71	3.22	4.27	4.76	4.92
D-1	0.00	−2.48	−2.69	−2.89	−3.02	−2.99	−2.60	−1.41	0.18	1.54	2.34	2.80	3.69
E-1	0.00	−2.47	−2.71	−2.94	−3.16	−3.37	−3.52	−3.50	−3.19	−2.25	−0.80	0.72	1.80
A-2	0.00	1.60	3.63	4.97	5.88	7.32	7.86	8.23	8.48	8.63	8.71	8.75	8.76
B-2	0.00	0.32	1.12	2.68	4.42	5.73	6.49	7.35	7.97	8.32	8.53	8.64	8.70
C-2	0.00	0.13	0.13	0.38	0.95	2.16	3.86	5.36	6.25	6.95	7.80	8.23	8.49
D-2	0.00	0.11	0.00	0.00	0.04	0.13	0.42	1.32	3.02	4.73	5.84	6.62	7.51
E-2	0.00	0.10	−0.01	−0.05	−0.09	−0.17	−0.23	−0.21	0.00	0.62	2.02	3.91	5.29

). The groundwater flows through the pores to the un-grouted part of the arch bottom. The arch bottom uplift under the curtain grouting condition is approximately 40% higher than that without grouting. The difference in the final uplift of the arch bottom at 30 m from the palm surface is 3.5 mm. This proves that completing the inverted arch closure in time during the construction process is necessary.

3.2.3. Stress Analysis of Initial Support

(1)

Stress analysis on the first-layer initial support

For the double-layer lining structure, the initial support of the first layer needs to stabilize the surrounding rock even after the construction is completed. This paper has analyzed the minimum principal and maximum principal stresses under the grouting condition and the non-grouting conditions, as shown in

Table 9. Minimum principal stress trend of the first-layer initial support (Unit: MPa).

The Advance Progress of Heading Face (m)	0	3	6	9	12	15	18	21	24	27	30	33	36
A-1	−2.97	0.00	−5.55	−7.24	−8.41	−8.71	−9.53	−10.1	−10.4	−10.6	−10.7	−10.8	−11.0
B-1	−2.97	−4.23	−3.39	0.00	−4.16	−5.81	−6.66	−7.13	−7.82	−8.19	−8.41	−8.54	−8.68
C-1	−2.97	−3.63	−3.86	−4.60	−2.87	0.00	−3.39	−4.58	−5.38	−5.86	−6.51	−6.81	−6.99
D-1	−2.97	−3.58	−3.63	−3.74	−4.02	−4.77	−2.91	−1.79	−4.83	−5.73	−6.22	−6.68	−7.23
E-1	−2.97	−3.58	−3.60	−3.63	−3.69	−3.83	−4.11	−4.94	−1.12	−3.25	−5.68	−6.42	−6.82
A-2	−2.41	0.00	−6.14	−8.08	−9.13	−9.17	−9.93	−10.5	−10.7	−10.8	−10.9	−11.0	−11.1
B-2	−2.41	−3.12	−3.91	0.00	−4.95	−6.46	−6.86	−6.87	−7.63	−7.96	−8.14	−8.26	−8.36
C-2	−2.41	−3.03	−3.14	−3.41	−4.34	0.00	−3.74	−5.03	−5.24	−5.18	−5.97	−6.28	−6.44
D-2	−2.41	−3.03	−3.06	−3.12	−3.25	−3.61	−3.93	−2.32	−5.79	−6.64	−6.68	−6.80	−7.43
E-2	−2.41	−3.05	−3.06	−3.08	−3.11	−3.19	−3.33	−3.76	−2.33	−4.03	−6.78	−7.59	−7.55

and

Table 10. Maximum principal stress trend of the first-layer initial support (Unit: MPa).

The Advance Progress of Heading Face (m)	0	3	6	9	12	15	18	21	24	27	30	33	36
A-1	−1.56	−1.17	−0.55	−0.40	−0.36	−0.13	0.02	0.18	0.27	0.34	0.40	0.44	0.46
B-1	−1.56	−1.21	−0.95	−0.56	−0.41	−0.24	−0.18	−0.09	−0.02	0.06	0.11	0.15	0.18
C-1	−1.56	−1.60	−1.40	−1.13	−0.88	−0.52	−0.34	−0.23	−0.13	−0.08	−0.01	0.06	0.08
D-1	−1.56	−1.73	−1.66	−1.55	−1.35	−1.08	−0.82	−0.51	−0.31	−0.22	−0.08	−0.06	0.04
E-1	−1.56	−1.77	−1.72	−1.68	−1.62	−1.52	−1.35	−1.07	−0.78	−0.50	−0.30	−0.20	−0.03
A-2	−1.27	−1.20	−0.83	−0.66	−0.60	0.31	0.78	0.85	0.76	0.63	0.51	0.48	0.51
B-2	−1.27	−1.15	−0.80	−0.57	−0.52	−0.43	−0.15	0.30	0.55	0.56	0.48	0.37	0.31
C-2	−1.27	−1.34	−1.26	−1.08	−0.75	−0.55	−0.49	−0.42	−0.13	0.30	0.52	0.52	0.42
D-2	−1.27	−1.40	−1.39	−1.35	−1.26	−1.05	−0.71	−0.52	−0.47	−0.39	−0.06	0.29	0.49
E-2	−1.27	−1.42	−1.42	−1.42	−1.40	−1.35	−1.25	−1.05	−0.69	−0.53	−0.48	−0.38	−0.04

. According to the results, similar principal stress under the grouting and non-grouting conditions indicates large compressive stress. The compressive stress is produced under the external water pressure and the action of the self-weight of the surrounding rock’s broken-rock zone, which increases from the initial maximum of 2.41 MPa to 11.03 MPa, with the maximum principal stress changing from −1.56 MPa compressive stress into 0.50 MPa tensile stress; thus, it is concluded that after the tunnel excavation, the initial support mainly bears the self-weight stress produced by the broken-rock zone, rather than the external water pressure.

(2)

Stress analysis of the second-layer initial support

Table 11. Minimum principal stress trend of the second-layer initial support (Unit: MPa).

The Advance Progress of Heading Face (m)	0	3	6	9	12	15	18	21	24	27	30	33	36
A-1	−2.97	0.00	−1.43	−1.84	−2.11	−2.19	−2.40	−2.56	−2.64	−2.70	−2.74	−2.77	−2.81
B-1	−2.97	−4.31	−2.82	0.00	−1.05	−1.48	−1.69	−1.83	−2.01	−2.11	−2.17	−2.21	−2.25
C-1	−2.97	−3.64	−3.88	−4.71	−2.22	0.00	−0.88	−1.16	−1.36	−1.51	−1.68	−1.76	−1.82
D-1	−2.97	−3.58	−3.63	−3.75	−4.05	−4.75	−1.87	−0.41	−1.20	−1.41	−1.54	−1.69	−1.84
E-1	−2.97	−3.58	−3.60	−3.63	−3.69	−3.83	−4.14	−4.80	−0.80	−0.80	−1.43	−1.61	−1.73
A-2	−2.41	0.00	−1.44	−1.88	−2.12	−2.16	−2.34	−2.46	−2.50	−2.53	−2.56	−2.58	−2.60
B-2	−2.41	−3.14	−3.88	0.00	−1.17	−1.51	−1.60	−1.62	−1.81	−1.88	−1.93	−1.96	−1.98
C-2	−2.41	−3.03	−3.15	−3.45	−4.06	0.00	−0.89	−1.18	−1.23	−1.24	−1.43	−1.50	−1.54
D-2	−2.41	−3.03	−3.06	−3.12	−3.27	−3.67	−3.22	−0.44	−1.26	−1.45	−1.47	−1.52	−1.67
E-2	−2.41	−3.05	−3.06	−3.08	−3.12	−3.20	−3.35	−3.85	−1.86	−0.90	−1.55	−1.74	−1.75

and

Table 12. Maximum principal stress trend of the second-layer initial support (Unit: MPa).

The Advance Progress of Heading Face (m)	0	3	6	9	12	15	18	21	24	27	30	33	36
A-1	−1.56	−0.99	−0.41	−0.30	−0.26	0.03	0.09	0.16	0.20	0.24	0.26	0.28	0.29
B-1	−1.56	−1.15	−0.94	−0.50	−0.33	−0.19	−0.13	0.07	0.10	0.11	0.13	0.15	0.17
C-1	−1.56	−1.60	−1.40	−1.11	−0.87	−0.46	−0.27	−0.19	−0.11	0.09	0.11	0.11	0.12
D-1	−1.56	−1.73	−1.66	−1.56	−1.37	−1.06	−0.80	−0.45	−0.25	−0.18	−0.09	0.10	0.11
E-1	−1.56	−1.76	−1.72	−1.68	−1.63	−1.53	−1.36	−1.04	−0.75	−0.44	−0.25	−0.16	−0.07
A-2	−1.27	−1.09	−0.62	−0.50	−0.45	0.04	0.08	0.11	0.14	0.18	0.22	0.25	0.28
B-2	−1.27	−1.12	−0.72	−0.46	−0.42	−0.34	−0.09	0.05	0.08	0.10	0.11	0.13	0.16
C-2	−1.27	−1.33	−1.26	−1.07	−0.70	−0.45	−0.40	−0.33	−0.07	0.05	0.09	0.11	0.11
D-2	−1.27	−1.40	−1.39	−1.35	−1.26	−1.05	−0.67	−0.44	−0.39	−0.31	−0.04	0.06	0.09
E-2	−1.27	−1.42	−1.42	−1.41	−1.40	−1.35	−1.25	−1.05	−0.65	−0.45	−0.40	−0.30	−0.04

show the stresses on the second-layer initial support in the double-layer support and the compressive stresses borne by the second-layer initial support under the condition of no grouting. The result of no grouting is around 10% higher than that with curtain grouting. This indicates that the surrounding rock with grouting under the curtain grouting condition can bear a certain pressure, and the two working conditions are similar.

3.2.4. Axial Force Analysis of Steel Arch Frame

The steel plays a major role in the support. The initial support bears the main surrounding rock load and has to quickly bear the main acting force after the support construction. The variation analysis of the steel support’s axial force in the first-layer initial support (

Table 13. Axial force trend of the first-layer steel support (Unit: kN).

The Advance Progress of Heading Face (m)	6	9	12	15	18	21	24	27	30	33	36
A-1	−95.8	−117.2	−130.6	−125.5	−134.3	−140.7	−141.7	−142.0	−142.3	−142.4	−142.6
B-1	0.0	−96.7	−119.2	−127.3	−120.6	−128.5	−133.4	−134.9	−135.6	−135.6	−136.0
C-1	0.0	0.0	−99.6	−117.4	−128.2	−121.0	−128.1	−133.5	−134.9	−135.5	−135.8
D-1	0.0	0.0	0.0	−101.1	−118.0	−128.4	−121.3	−128.6	−134.0	−135.7	−136.3
E-1	0.0	0.0	0.0	0.0	−91.3	−111.6	−120.3	−112.8	−120.3	−125.6	−127.1
A-2	−79.5	−105.4	−120.1	−119.9	−131.6	−138.6	−141.5	−143.8	−144.9	−145.9	−147.2
B-2	0.0	−80.3	−105.2	−117.6	−115.9	−126.7	−133.2	−135.7	−137.5	−138.5	−140.0
C-2	0.0	0.0	−81.5	−104.3	−115.7	−115.9	−125.9	−131.5	−133.7	−135.0	−136.2
D-2	0.0	0.0	0.0	−82.2	−99.9	−115.5	−113.6	−123.2	−129.7	−131.5	−132.4
E-2	0.0	0.0	0.0	0.0	−74.8	−101.3	−113.1	−111.0	−120.6	−126.1	−128.1

) shows that after the upper bench excavation, the steel support’s axial force in the initial support stage with no curtain grouting is around 10 kN larger than that with curtain grouting. The final stable bearing capacity of the steel support is approximately 160 kN, but with similar axial force values for the two conditions. This is consistent with the performance of initial support stress; meanwhile, the variation in the steel support’s axial force in the second-layer initial support (

Table 14. Axial force trend of the second-layer steel support (Unit: kN).

The Advance Progress of Heading Face (m)	6	9	12	15	18	21	24	27	30	33	36
A-1	−111.6	−138.0	−152.1	−149.5	−155.3	−163.7	−165.8	−167.0	−168.1	−168.7	−169.3
B-1	0.0	−114.3	−143.7	−150.9	−145.4	−151.1	−158.2	−161.1	−162.0	−162.6	−163.5
C-1	0.0	0.0	−118.0	−141.5	−151.3	−145.0	−150.7	−157.3	−159.7	−161.2	−161.9
D-1	0.0	0.0	0.0	−122.5	−141.9	−152.4	−146.0	−151.6	−158.8	−161.2	−162.4
E-1	0.0	0.0	0.0	0.0	−112.1	−134.9	−142.5	−136.3	−141.0	−148.4	−150.7
A-2	−93.3	−120.5	−131.9	−132.4	−142.7	−151.1	−154.9	−157.9	−159.6	−160.9	−162.5
B-2	0.0	−93.3	−118.0	−130.4	−129.5	−139.3	−147.1	−150.4	−152.7	−154.1	−155.7
C-2	0.0	0.0	−95.2	−122.0	−131.0	−131.5	−140.2	−147.6	−150.4	−152.2	−153.6
D-2	0.0	0.0	0.0	−95.9	−116.7	−129.0	−128.6	−137.2	−144.9	−147.3	−148.7
E-2	0.0	0.0	0.0	0.0	−87.7	−115.6	−124.7	−124.0	−132.0	−138.9	−141.6

) shows that the steel support’s axial force under the condition of no curtain grouting is around 20 kN larger than that under the condition of curtain grouting, which is mainly because the capability of the surrounding rock around curtain grouting to further carry out cementation makes the overall stability of surrounding rock better, with smaller external water pressure; thus, the stress is relatively small. The comprehensive analysis shows that the first layer of the steel support first bears the surrounding rock pressure and water pressure caused by surrounding rock deformation, the second layer of steel support bears the internal force after deformation coordination, and the two-layer steel support meets its material characteristics.

3.2.5. Internal Force Analysis of Secondary Lining

The internal force of the secondary lining is an important indicator for analyzing and evaluating the safety of the structure. The axial force diagram of the secondary lining arch crown (

Table 15. Axial force trend of secondary lining arch crown (Unit: kN).

The Advance Progress of Heading Face (m)	18	21	24	27	30	33	36
A-1	9.27	39.45	42.84	41.98	40.81	39.43	38.78
B-1	0.00	20.35	31.00	33.51	32.09	31.61	30.96
C-1	0.00	0.00	18.63	30.20	33.15	32.30	31.98
D-1	0.00	0.00	0.00	19.35	31.48	34.27	33.95
E-1	0.00	0.00	0.00	0.00	19.81	31.78	35.62
A-2	9.27	29.59	32.13	31.48	30.61	29.57	29.09
B-2	0.00	15.26	23.25	25.13	24.06	23.71	23.22
C-2	0.00	0.00	13.97	22.65	24.86	24.23	23.99
D-2	0.00	0.00	0.00	14.51	23.61	25.71	25.46
E-2	0.00	0.00	0.00	0.00	14.85	23.83	26.71

) shows that when the secondary lining concrete reaches the design strength, the axial force of the lining structure will increase significantly after bearing the remaining surrounding rock pressure. Under the conditions of no curtain grouting and curtain grouting, respectively, the maximum axial forces reach 42.84 kN and 29.09 kN. When the measuring point of the arch crown is more than 21 m away from the palm surface, the axial force area tends to be stable, with a slight decrease generally valued at approximately 4 kN. Secondly, the maximum difference between the axial force of the secondary lining under the condition of no curtain grouting and the axial force of the arch crown under the condition of curtain grouting is around 10 kN, with a difference in the axial force values under the two conditions of approximately 25%, thus indicating the ability of curtain grouting to comprehensively enhance the secondary lining’s safety reserve or improve the secondary lining stress.

Table 16. Bending moment trend of secondary lining arch crown (Unit: kN).

The Advance Progress of Heading Face (m)	18	21	24	27	30	33	36
A-1	25.34	30.53	34.16	38.39	33.85	32.89	34.12
B-1	0.00	16.77	5.80	5.04	12.96	12.76	11.53
C-1	0.00	0.00	25.26	26.86	29.98	39.71	33.58
D-1	0.00	0.00	0.00	22.82	22.44	25.03	30.88
E-1	0.00	0.00	0.00	0.00	16.04	21.30	19.43
A-2	20.27	24.43	27.33	30.71	27.08	26.31	27.30
B-2	0.00	13.62	4.71	4.10	10.53	10.37	9.37
C-2	0.00	0.00	20.52	21.82	24.35	32.26	27.28
D-2	0.00	0.00	0.00	18.26	17.95	20.03	24.70
E-2	0.00	0.00	0.00	0.00	12.83	17.04	15.55

shows the variation in the bending moment stress at each measuring point of the secondary lining arch crown. The certain similarity in the stress trend between the secondary lining bending moment and the axial force is reflected as follows: the secondary lining bending moment under the condition of no curtain grouting firstly reaches the maximum at 38.39 kN.m and then slightly decreases to 34.12 kN.m. Meanwhile, the secondary lining bending moment with curtain grouting firstly reaches the maximum of 30.72 kN.m, and then slightly decreases to 27.30 kN.m. Secondly, the maximum difference between the bending moment of the secondary lining without curtain grouting and the bending moment of the arch crown with curtain grouting is around 7.67 kN. The difference in bending moment values under the two conditions is around 20%. Therefore, the curtain grouting scheme can effectively increase the safety reserve of the secondary lining support and ensure the stability and durability of the tunnel lining structure.

According to the lining structure safety calculation and analysis in 9.2.11 and 9.2.12 of the “Specification for Design Highway Tunnels Section 1 Civil Engineering” (JTG 3370.1-2018) [21] (Figure 8), the minimum safety factor for the secondary lining is 1.54 under no grouting conditions, which does not meet the safety factor requirements of the specification (specification safety factor 2.4); the final lining safety factor is approximately 2.95, and the minimum safety factor under curtain grouting conditions is 2.66, which meets the safety factor requirements of the specification; the final lining safety factor is around 3.79. According to the overall analysis of the safety factor, the safety factor of the lining structure under the curtain grouting condition is around 20% to 25% higher than that under the no grouting condition, which improves the safety reserve of the secondary lining.

4. Conclusions

(1)

Surrounding rock radial grouting can significantly improve the tunnel’s initial support. The effects decrease when the grouting range exceeds 4 m. Therefore, the radial grouting should be controlled within the range of 4.0 m to 4.5 m during the design.

(2)

Curtain grouting effectively reduces external water pressure, and the external water pressure of the grouting area is 23% greater than that without curtain grouting. Therefore, curtain grouting benefits the stress of the tunnel lining structure by slowing down the infiltration of external water pressure.

(3)

Curtain grouting can effectively strengthen the self-stability of surrounding rocks and control the deformation settlement by approximately 33%. However, there is no significant change in the stress of the initial support.

(4)

If without curtain grouting, the safety reserves of the secondary lining are 25% and 20%, respectively. These are higher than those with curtain grouting in terms of axial force and bending moment.

(5)

When curtain grouting is adopted, the initial support of the first layer and the initial support of the second layer have different pressure-sharing proportions to the surrounding rock. When the water pressure has not increased, the sharing proportion of the initial support for the first layer is large, and after the water pressure increases, the initial support of the second layer increases by a large proportion.