A tunnel excavation grouting support construction method for water-rich fine sand strata

By combining ground grouting, full-section grouting and advance small conduit grouting in water-rich fine sand formations, the problem of poor performance of traditional grouting support methods in water-rich sand formations is solved, and the problem of further improvement is achieved Efficient support and safer tunnel excavation process.

CN118933889BActive Publication Date: 2025-02-11北京住总集团有限责任公司
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Patent Information

Application Number
CN202411211037.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-08-30
Publication Date
2025-02-11
Estimated Expiration
2044-08-30

AI Technical Summary

Technical Problem

When tunnel excavation is carried out in water-rich fine sand formations, the traditional grouting support method is not effective and is prone to collapse risk.

Method used

The tunnel excavation process is supported by combining three grouting support methods: ground grouting, full-section grouting and advance small conduit grouting. The specific steps include formation detection, ground grouting, full-section grouting and advance small conduit grouting. By adjusting the construction parameters and the ratio of grouting liquid, the grouting strengthening process is optimized.

Benefits of technology

Through the combination of three grouting methods, the support strength is significantly improved, the risks of collapse and water permeability are reduced, and the safety and construction quality of tunnel excavation are ensured.

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Abstract

The present invention discloses a tunnel excavation grouting support construction method applied to water-rich fine sand strata. Aiming at the characteristics of water-rich strata and combining on-site construction conditions, a method combining three grouting support methods, namely ground grouting, full-section grouting and advanced small-duct grouting, is adopted to support the tunnel excavation process, and the tunnel strata are strengthened from three dimensions and three directions to avoid the dangers of collapse, water seepage and the like during the tunnel excavation process, thereby greatly improving the support strength and meeting the requirements of the preliminary design, thus realizing the engineering application of safely and efficiently excavating tunnels in water-rich fine sand strata. In the advanced small-duct grouting construction, strong wind pressure is used for blowing holes, which is easier to form holes and less prone to collapse than drilling rod drilling, and is faster and more efficient than drilling holes with a drilling machine, thereby improving the overall construction progress, being not restricted by the on-site environment and the depth of dark excavation, and having high construction efficiency.
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Description

Technical Field

[0001] The invention relates to the technical field of grouting in underground tunneling projects, and in particular to a tunnel excavation grouting support construction method applied to a water-rich fine sand stratum. Background Art

[0002] With the rapid development of infrastructure construction in my country, especially the increasing development of highways, railways and urban underground space, tunnel engineering, as a key infrastructure construction project, has increasingly higher requirements for construction technology and safety. In tunnel construction, especially when passing through soft and broken strata, shallow buried sections, sandy sections, portal biased sections, fault fracture zones and gravel sections and other unfavorable geological conditions, how to ensure the stability of the surrounding rock during tunnel excavation has become a technical problem that needs to be solved urgently.

[0003] According to the impact of water inflow and water pressure on construction safety and construction difficulty in engineering practice, in general, the water-rich stratum has a pressurized water head height of 2m~4m and a water inflow of 50m³ / d, which can be called a water-rich stratum; such stratum changes into a water-conducting structure. Once it is enriched with high-pressure groundwater, the stability of the soil itself is extremely poor. When the tunnel passes through pressurized water, it is easy to produce water and mud inrush, which brings great risks to construction safety; when excavating tunnels in soft and broken surrounding rocks with a short self-stabilization time or even under fine sand geological conditions, grouting support is required, but because of the characteristics of fine sand itself, it is loose, has low cohesion, and is prone to collapse, which brings great difficulties to the support work.

[0004] Therefore, in strata with high water content, the presence of pressurized water but low head of pressurized water, high water inflow, high sand content and poor geological conditions, the use of traditional technology and a single grouting support method is not enough to play the role of pre-support reinforcement. Summary of the invention

[0005] The present invention provides a tunnel excavation grouting support construction method applied to water-rich fine sand strata, which is used to solve the technical problems such as poor effectiveness of traditional grouting support methods and the risk of collapse during excavation when carrying out tunnel excavation construction in water-rich strata.

[0006] To achieve the above object, the present invention adopts the following technical solution:

[0007] The present invention provides a tunnel excavation grouting support construction method applied to a water-rich fine sand stratum, comprising the following steps:

[0008] S1, formation detection: first sample the formation, detect the formation particle composition and the distribution of fine sand formation, and adjust the relevant construction parameters according to the detection results;

[0009] S2, Ground Grouting:

[0010] S21, positioning: mark the grouting hole points on the ground, and the grouting hole points are arranged in a plum blossom shape;

[0011] S22, drilling: according to the positioning, use a drilling rig to drill underground, with the drill rod pointing vertically downward, using the interval drilling method, and stop drilling after drilling 50cm below the bottom of the arch foot;

[0012] S23, grouting: after drilling, the boreholes are grouted backwards, using the skip-drilling grouting method, grouting one hole at a time, and entering S3 after the ground grouting is completed;

[0013] S3, full section grouting:

[0014] S31, positioning: Use measuring instruments to locate and stake out the holes at the section of the tunnel primary lining excavation and 1.5m outside the side walls, bottom plate and arch of the excavation profile. The holes are arranged in a plum blossom shape in the tunnel section;

[0015] S32, drilling: drilling is done by drilling rig, with the drill rod arranged perpendicular to the tunnel section. The order of drilling is first up and then down, first outside and then inside. The same circle of holes is drilled at intervals;

[0016] S33, grouting: perform backward grouting on the drilled holes in sections, grouting one hole at a time, and enter S4 after the full-section grouting is completed;

[0017] S4, advanced small tube grouting:

[0018] S41, positioning: locate and stake out the holes, arrange them 10 cm in a circumferential direction outside the tunnel arch excavation contour line, and mark the layout points of the advance small guide tubes with red paint;

[0019] S42, erecting a small conduit: the worker holds the small conduit with the tip of the small conduit facing the tunnel arch, fixes the small conduit firmly, and determines the angle between the small conduit and the tunnel arch surface;

[0020] S43, air blowing and drilling: start the power supply, conduct a trial run first, and after the trial run is normal, start the power supply, run the air compressor, maintain the air pressure at 0.3MPa, and the worker inserts a small catheter back and forth into the tunnel vault surface to form a hole at the marked position of the tunnel vault. Repeat the above operation until the hole that meets the design requirements is completed, then stop the air supply, continue to repeat the above operation, and drill holes for the remaining marked points in turn;

[0021] S44, grouting: before grouting, water test is first performed to ensure that the pipeline is unobstructed and the sealing is checked; first, a sealing plug is installed on the grouting nozzle, and then the grouting nozzle is inserted into the small conduit to start grouting. When the small conduit is filled with slurry, the pressure is stabilized for a period of time to ensure the penetration range of the slurry and then stop grouting in this hole; repeat the above operation and grout the remaining holes in turn;

[0022] S5, strength test: After the slurry solidifies, core samples are taken from the three grouting locations and a compressive strength test is performed. If the strength is not less than 0.6MPa, it is qualified.

[0023] Preferably, in S1, after sampling the stratum, BIM modeling is performed based on the collected data to simulate the stratum structure, the grouting strengthening process is simulated by changing the stratum parameters, and the effects of the drilling depth, angle, density and grouting amount of ground grouting, full-section grouting and advanced small-tube grouting on the stratum strength are tested to obtain the optimal drilling depth, drilling angle, drilling density and grouting amount.

[0024] Preferably, in S1, the relevant construction parameters include the length, diameter, number, distribution spacing, angle between the grouting holes and the structural surface, and grouting time of the grouting holes.

[0025] Preferably, the grouting liquid in S2~S4 adopts cement-water glass double liquid slurry, the water-cement ratio of the cement slurry is 1:1; the concentration of the water glass stock slurry is 40 degrees Baume, and the modulus is 2.4~3.0; the volume ratio of the water glass stock slurry and water is 1:1, and the water glass dilution liquid is prepared, and the volume ratio of the cement slurry and the water glass dilution liquid is 1:1.

[0026] Preferably, in S21, three rows of grouting holes are arranged horizontally, and the distribution spacing of the holes is 80 cm; in S31, the spacing of the full-section grouting holes is 80 cm; in S41, the spacing of the holes is 30 cm.

[0027] Preferably, in S23, the grouting pressure is 0.3 MPa; in S33, the grouting pressure does not exceed 0.5 MPa; in S44, the grouting pressure is controlled at 0.2-0.5 MPa, and the stabilizing pressure is maintained at 0.5 MPa.

[0028] Preferably, in S4, a small catheter needs to be made before the hole is formed. First, a three-axial tube punching machine is used to punch holes in the small catheter in the upper, left and right directions at the same time. Then, a split small catheter tip machine is used to process the small catheter. The small catheter is placed in a heating ring. After heating, the feeding rack automatically feeds the material into the tip shrinking mold for compression molding.

[0029] Preferably, in S41, the connection triangulation method is adopted, and the ground control points are led to the underground tunnel using the surveying instrument total station, and the control points are arranged in a solid position with good visibility. The center line of the tunnel is laid out using the total station, and as the tunnel is excavated, the control points are continuously introduced forward to locate and lay out the hole positions.

[0030] Preferably, in S42, the angle between the small conduit and the tunnel vault surface is 15°~30°.

[0031] Preferably, both S2 and S3 use a drill rod with an outer diameter of 50 mm, and each section of the drill rod is 0.8 m long.

[0032] The beneficial effects of the present invention are embodied in:

[0033] 1) The present invention provides a tunnel excavation grouting support construction method for water-rich fine sand strata. In view of the characteristics of water-rich strata and combined with on-site construction conditions, a method combining three grouting support methods, namely ground grouting, full-section grouting and advanced small-duct grouting, is adopted to support the tunnel excavation process, and the tunnel strata are strengthened from three dimensions and three directions to avoid the dangers of collapse, water seepage and the like during the tunnel excavation process, thereby greatly improving the support strength, ensuring the construction quality, reducing the safety risk, meeting the preliminary design requirements, and realizing the engineering application of safely and efficiently excavating tunnels in water-rich strata;

[0034] 2) The present invention provides a tunnel excavation grouting support construction method applied to water-rich fine sand strata. After sampling the strata, BIM modeling is performed based on the collected data to simulate the stratum structure. The grouting strengthening process is simulated by changing the stratum parameters, and the effects of the hole depth, angle, density and grouting amount of ground grouting, full-section grouting and advanced small-duct grouting on the stratum strength are tested to obtain the optimal hole depth, hole angle, hole density and grouting amount, so that different stratum structures can be specially treated during each grouting, so that the grouting can play the maximum reinforcement and support role, play a sufficient stabilizing effect, and greatly reduce the risk of soil collapse and sudden water and mud.

[0035] 3) The present invention provides a tunnel excavation grouting support construction method applied to water-rich fine sand strata. In the advanced small-duct grouting construction, strong wind pressure is used to blow holes. Compared with drilling holes with drill rods, it is easier to drill holes and less likely to collapse. It is faster and more efficient than drilling holes with drilling machines, which improves the overall construction progress and is not restricted by the on-site environment and the depth of underground excavation. Both blowing and grouting are carried out using small ducts, which are easy to operate and have high construction efficiency.

[0036] Other features and advantages of the present invention will be set forth in the following description, and in part will become apparent from the description, or may be understood by practicing the present invention; the main purpose and other advantages of the present invention may be realized and obtained through the solutions particularly pointed out in the description. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a front view of the grouting hole for ground grouting of the present invention.

[0038] Figure 2 It is a top view of the grouting holes for ground grouting of the present invention.

[0039] Figure 3 It is a front view of the grouting hole for full-section grouting of the present invention.

[0040] Figure 4 It is a front view of the grouting hole for the advanced small-duct grouting of the present invention. DETAILED DESCRIPTION

[0041] The technical solution of the present invention is described in detail below through examples. The following examples are merely exemplary and can only be used to explain and illustrate the technical solution of the present invention, but cannot be interpreted as limiting the technical solution of the present invention.

[0042] Embodiment, this embodiment takes a certain tunnel construction project as an example, in which tunnel excavation is carried out in a water-rich fine sand stratum. The water-rich stratum has a large amount of water gushing, there is pressurized water but the water head is low, and the high fine sand content makes it easy to collapse, and the support work is difficult. Under such harsh geological conditions, a comprehensive grouting support method is provided, first grouting is carried out on the ground, then full-section deep hole grouting is carried out on the heading face, and then advanced small-duct grouting is carried out during frame construction. The combination of the three grouting methods is safer for underground tunneling projects. The three methods do not interfere with each other and work together to make them flexible and convenient to use, with fast construction speed and high efficiency. They are not restricted by on-site geological conditions, can greatly improve construction efficiency, and obtain good economic benefits. They have good application prospects in tunnel excavation projects in water-rich strata.

[0043] This embodiment provides a tunnel excavation grouting support construction method applied to a water-rich fine sand stratum, comprising the following steps:

[0044] S1, stratum detection: firstly, the stratum was sampled to detect the stratum particle composition and the distribution of fine sand stratum. The fine sand particles of 0.25~0.075mm in the stratum accounted for ≥47%, which was a fine sand stratum. The water head height of the stratum was 2.8m, and the water inflow was 53m³ / d. Therefore, the stratum was determined to be a water-rich fine sand stratum. In order to ensure the support quality, it was necessary to adopt a combination of three grouting methods for all-round support. Firstly, BIM modeling was carried out based on the collected data to simulate the stratum structure. By changing the ground The grouting strengthening process is simulated by using layer parameters, and the effects of the hole depth, angle, density and grouting amount of ground grouting, full-section grouting and advanced small-duct grouting on the stratum strength are tested; then the relevant construction parameters are adjusted according to the results of the test to obtain the optimal hole depth, hole angle, hole density and grouting amount. The relevant construction parameters include the length, diameter, number, distribution spacing of the grouting holes, the angle between the grouting holes and the structural surface, and the grouting time. The specific construction parameters are obtained according to the calculation formula of the grouting amount. The calculation formula of the grouting amount is:

[0045] Q1=πR 2 Lnαβ,

[0046] Among them, R is the slurry diffusion radius, L is the grouting length, n is the porosity, α is the formation filling coefficient, and β is the slurry consumption coefficient.

[0047] The specific construction steps and construction parameter settings are as follows:

[0048] S2, Ground Grouting:

[0049] S21, positioning: mark the grouting hole points on the ground. The grouting hole points are arranged in a plum blossom shape. According to the optimal construction parameters simulated in S1, three rows of grouting holes are arranged horizontally, and the distribution spacing of the holes is 80 cm;

[0050] S22, drilling: according to the positioning, use a drilling rig to drill underground, use a drill rod with an outer diameter of 50mm, each section of the drill rod is 0.8m long, the drill rod is vertically downward, and the holes are drilled at intervals. Stop drilling after drilling 50cm below the bottom of the arch foot. Refer to Figure 1 and Figure 2 ;

[0051] S23, grouting: after drilling, the borehole is grouted backwards, the grouting pressure is 0.3MPa, and the skip-drilling grouting method is adopted. Grouting is performed one hole at a time, and after the ground grouting is completed, enter S3;

[0052] S3, full section grouting:

[0053] S31, positioning: Use measuring instruments to locate and stake out the holes at the section of the tunnel primary lining excavation and 1.5m outside the side wall, bottom plate and arch of the excavation profile. The holes are arranged in a plum blossom shape in the tunnel section. According to the optimal construction parameters simulated in S1, the hole spacing is 80cm, referring to Figure 3 ;

[0054] S32, drilling: The holes are drilled by a drilling rig, using a drill rod with an outer diameter of 50 mm. Each section of the drill rod is 0.8 m long. The drill rod is arranged perpendicular to the tunnel section. The drilling sequence is first up and then down, first outside and then inside. The holes in the same circle are drilled at intervals.

[0055] S33, grouting: perform backward segmented grouting on the boreholes, with the grouting pressure not exceeding 0.5 MPa, grouting one hole at a time, and enter S4 after the full-section grouting is completed;

[0056] S4, advanced small tube grouting:

[0057] S41, positioning: positioning and staking out the hole positions. The specific operation is as follows: using the connection triangulation method, use the surveying instrument total station to lead the ground control points to the underground tunnel, arrange the control points in a solid position with good sight, use the total station to stake out the tunnel centerline, and as the tunnel is excavated, continue to introduce the control points forward to position and stake out the hole positions. Arrange them 10 cm in a circle along the excavation contour line of the tunnel arch. According to the optimal construction parameters simulated in S1, the small guide tube uses a 2.25m long, Ф32×3.25 steel pipe. The small guide tube is inserted into the hole to a depth of 2m and exposed 25cm. The arrangement spacing of the holes is 30cm, and the number is 10. After confirmation, use red line paint to mark the arrangement points of the leading small guide tubes. Refer to Figure 4 ;

[0058] S42, erecting a small conduit: the worker holds the small conduit with the tip facing the tunnel arch and fixes the small conduit firmly. The angle between the small conduit and the tunnel arch surface is 20°;

[0059] S43, air blowing and drilling: start the power supply, conduct a trial run first, and after the trial run is normal, start the power supply, run the air compressor, maintain the air pressure at 0.3MPa, and the worker inserts a small catheter back and forth into the tunnel vault surface to form a hole at the marked position of the tunnel vault. Repeat the above operation until the hole that meets the design requirements is completed, then stop the air supply, continue to repeat the above operation, and drill holes for the remaining marked points in turn;

[0060] S44, grouting: Before grouting, test the water to make sure the pipeline is unobstructed and check the sealing performance; install the sealing plug on the grouting nozzle first, then insert the grouting nozzle into the small conduit and start grouting. The grouting pressure is controlled at 0.2~0.5MPa. When the small conduit is filled with slurry, stabilize the pressure for 5 minutes. The stabilization pressure is maintained at 0.5MPa. After ensuring the penetration range of the slurry, stop grouting in this hole; repeat the above operation and grout the remaining holes in turn;

[0061] S5, strength test: after the slurry solidifies, core samples are taken from the three grouting locations, and a compressive strength test is performed. If the strength is not less than 0.6MPa, it is qualified. If the strength is less than 0.6MPa, the grouting operation is increased by increasing the density of grouting holes, increasing the grouting pressure or extending the grouting time until the strength of the consolidated body meets the standard.

[0062] Furthermore, the grouting liquid in S2~S4 adopts cement-water glass double liquid slurry, the water-cement ratio of the cement slurry is 1:1; the concentration of the water glass original slurry is 40 degrees Baume, and the modulus is 2.4~3.0; the volume ratio of the water glass original slurry and water is 1:1, and the water glass diluted liquid is prepared, and the volume ratio of the cement slurry and the water glass diluted liquid is 1:1.

[0063] Furthermore, the advanced small-tube grouting requires the production of a small tube before drilling, and the method for producing the small tube includes the following steps: first, a three-axial tube punching machine is used to simultaneously punch holes in the small tube in the upper, left, and right directions, and then a split-type small-tube tip machine is used to process the small tube, and the small tube is placed in a heating ring. After heating, the feeding rack automatically feeds the material into the tipping mold for compression molding.

[0064] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that a technician familiar with the technical field can think of within the technical scope disclosed in the present invention should be covered within the protection scope of the present invention.

Claims

1. A tunnel excavation grouting support construction method applied to water-rich fine sand strata, characterized in that: The steps include: S1, formation detection: first sample the formation, detect the formation particle composition and the distribution of fine sand formation, and adjust the relevant construction parameters according to the detection results; In S1, after sampling the stratum, BIM modeling was performed based on the collected data to simulate the stratum structure. The grouting strengthening process was simulated by changing the stratum parameters, and the effects of the drilling depth, drilling angle, drilling density and grouting amount of ground grouting, full-section grouting and advanced small-pipe grouting on the stratum strength were tested to obtain the optimal drilling depth, drilling angle, drilling density and grouting amount. S2, Ground Grouting: S21, positioning: mark the grouting hole points on the ground, and the grouting hole points are arranged in a plum blossom shape; S22, drilling: according to the positioning, use a drilling rig to drill underground, with the drill rod pointing vertically downward, using the interval drilling method, and stop drilling after drilling 50cm below the bottom of the arch foot; S23, grouting: after drilling, the boreholes are grouted backwards, using the skip-drilling grouting method, grouting one hole at a time, and entering S3 after the ground grouting is completed; S3, full section grouting: S31, positioning: Use measuring instruments to locate and stake out the holes at the section of the tunnel primary lining excavation and 1.5m outside the side walls, bottom plate and arch of the excavation profile. The holes are arranged in a plum blossom shape in the tunnel section; S32, drilling: drilling is done by drilling rig, with the drill rod arranged perpendicular to the tunnel section. The order of drilling is first up and then down, first outside and then inside. The same circle of holes is drilled at intervals; S33, grouting: perform backward grouting on the drilled holes in sections, grouting one hole at a time, and enter S4 after the full-section grouting is completed; S4, advanced small tube grouting: S41, positioning: locate and stake out the holes, arrange them 10 cm in a circumferential direction outside the tunnel arch excavation contour line, and mark the layout points of the advance small guide tubes with red paint; S42, erecting a small conduit: the worker holds the small conduit with the tip of the small conduit facing the tunnel arch, fixes the small conduit firmly, and determines the angle between the small conduit and the tunnel arch surface; S43, air blowing and drilling: start the power supply, conduct a trial run first, and after the trial run is normal, start the power supply, run the air compressor, maintain the air pressure at 0.3MPa, and the worker inserts a small catheter back and forth into the tunnel vault surface to form a hole at the marked position of the tunnel vault. Repeat the above operation until the hole that meets the design requirements is completed, then stop the air supply, continue to repeat the above operation, and drill holes for the remaining marked points in turn; S44, grouting: before grouting, water test is first performed to ensure that the pipeline is unobstructed and the sealing is checked; first, a sealing plug is installed on the grouting nozzle, and then the grouting nozzle is inserted into the small conduit to start grouting. When the small conduit is filled with slurry, the pressure is stabilized for a period of time to ensure the penetration range of the slurry and then stop grouting in this hole; repeat the above operation and grout the remaining holes in turn; In S4, a small tube needs to be made before forming a hole. First, a three-axial tube punching machine is used to punch holes in the small tube in the upper, left and right directions at the same time. Then, a split small tube tipping machine is used to process the small tube. The small tube is placed in a heating ring. After heating, the feeding rack automatically feeds the material to the tipping mold for compression molding. S5, strength test: After the slurry solidifies, core samples are taken from the three grouting locations and a compressive strength test is performed. If the strength is not less than 0.6MPa, it is qualified.

2. A tunnel excavation grouting support construction method applied to water-rich fine sand strata as claimed in claim 1, characterized in that: In S1, the relevant construction parameters include the length, diameter, number, distribution spacing, angle between the grouting holes and the structural surface, and grouting time of the grouting holes.

3. The tunnel excavation grouting support construction method applied to water-rich fine sand strata according to claim 1, characterized in that: The grouting liquid in S2~S4 adopts cement-water glass double liquid slurry, the water-cement ratio of cement slurry is 1:1; the concentration of water glass original slurry is 40 degrees Baume, and the modulus is 2.4~3.0; the volume ratio of water glass original slurry and water is 1:1, and the water glass diluted liquid is prepared, and the volume ratio of cement slurry and water glass diluted liquid is 1:

1.

4. The tunnel excavation grouting support construction method applied to water-rich fine sand strata according to claim 1, characterized in that: In S21, three rows of grouting holes are arranged horizontally, and the spacing between the holes is 80 cm; in S31, the spacing between the grouting holes in the entire section is 80 cm; in S41, the spacing between the holes is 30 cm.

5. The tunnel excavation grouting support construction method applied to water-rich fine sand strata according to claim 1, characterized in that: In S23, the grouting pressure is 0.3 MPa; in S33, the grouting pressure does not exceed 0.5 MPa; in S44, the grouting pressure is controlled at 0.2~0.5 MPa, and the stabilizing pressure is maintained at 0.5 MPa.

6. The tunnel excavation grouting support construction method applied to water-rich fine sand strata according to claim 1, characterized in that: In S41, the connection triangulation method is adopted, and the ground control points are led to the underground tunnel with the surveying instrument total station. The control points are arranged in a solid position with good visibility. The center line of the tunnel is laid out with the total station. As the tunnel is excavated, the control points are continuously introduced forward to locate and lay out the hole positions.

7. The tunnel excavation grouting support construction method applied to water-rich fine sand strata according to claim 1, characterized in that: In S42, the angle between the small duct and the tunnel vault surface is 15°~30°.

8. The tunnel excavation grouting support construction method applied to water-rich fine sand strata according to claim 1, characterized in that: Both S2 and S3 use drill rods with an outer diameter of 50 mm and each section of drill rod is 0.8 m long.

Citation Information

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