Crushed rock-soil body mountain ridge tunnel portal cover arch and pipe shed structure

By introducing components such as adjustment racks, adjustment discs and drive plates into the arch structure, the problem of easy interference in the installation angle of the orifice pipe is solved, and the stability and support effect of the arch and pipe shed structure are improved.

CN223035051UActive Publication Date: 2025-06-27SHANXI MECHANIZATION CONSTRUCTION GROUP CO LTD
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Patent Information

Application Number
CN202422057897.3
Authority / Receiving Office
CN · China
Patent Type
Utility models(China)
Current Assignee / Owner
Filing Date
2024-08-23
Publication Date
2025-06-27
Estimated Expiration
2034-08-23

AI Technical Summary

Technical Problem

During the construction process of the existing arch and pipe shed structure, due to the complex geological conditions, the installation angle of the orifice pipe is easily disturbed, resulting in a decrease in the stability of the sleeve structure and affecting the support effect of the pipe shed.

Method used

By introducing components such as adjustment racks, adjustment discs and drive plates into the arch structure, it is allowed to adjust its installation angle after the orifice tube is installed, ensuring installation accuracy and enhancing structural stability.

Benefits of technology

It effectively reduces the installation error of orifice pipes, improves the stability and support effect of the arch and pipe shed, and ensures safety and efficiency during construction.

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Abstract

The utility model relates to the field of cover arches and pipe sheds, in particular to a cover arch and pipe shed structure of a crushed rock-soil body mountain tunnel portal, which comprises I-shaped steel, an orifice pipe, a square sleeve, an adjusting rack, an adjusting disc and a driving plate, and one end of the orifice pipe is hinged in a notch of the I-shaped steel; one end of the square sleeve is fixedly connected to the I-shaped steel and located in the same notch with the orifice pipe, the adjusting rack is slidably arranged in the square sleeve, the other end of the orifice pipe abuts against the end, away from the I-shaped steel, of the adjusting rack, the adjusting disc is rotationally arranged outside the square sleeve, and a containing groove is formed in the surface of the adjusting disc. A circular plate is rotatably arranged in the containing groove, the circular plate and the adjusting disc are concentrically arranged, the driving plate is arranged on the plate surface of the circular plate, a mounting groove is formed in the side wall of the square sleeve, and the driving plate is engaged in a tooth groove of the adjusting rack through the mounting groove, so that angle adjustment can be performed after the orifice pipe is mounted; and the possibility of generating errors is reduced.
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Description

Technical Field

[0001] The present application relates to the field of casing arches and pipe roofs, and particularly to a casing arch and pipe roof structure for the entrance of a mountain tunnel in fractured rock and soil mass. Background Art

[0002] Currently, the casing arch and the pipe roof are two commonly used support structures in tunnel construction. The casing arch is an arched structure that uses a pipe roof for advanced support during the construction of the entrance section to fix or support the end of the pipe roof. The pipe roof is a steel pipe structure arranged circumferentially at a certain interval along a part or all of the cross-section of an underground project. The main purpose is to provide a temporary support method for enhancing the bearing capacity of the formation for safe excavation under special conditions.

[0003] The existing method is to use the combination connection of I-beams and connecting plates and cooperate with concrete pouring to build the casing arch structure. The orifice pipe is installed at a certain angle on the casing arch according to the measured data at the construction site, and holes are drilled through the orifice pipe, and seamless steel pipes meeting the specifications are inserted into the drilled holes to build the pipe roof structure.

[0004] The above existing technical solutions have the following defects: After the pipe roof is built, due to the complex and changeable geological conditions at the construction site, such as the inclination of the rock stratum and uneven settlement, etc., it will interfere with the installation angle of the orifice pipe and reduce the stability of the entire casing arch structure. As the installation foundation of the pipe roof steel pipe, the orifice pipe with an angular deviation will reduce the stability of the pipe roof steel pipe and deteriorate the support effect. Content of the Utility Model

[0005] In order to be able to adjust the angle after the installation of the orifice pipe, reduce the possibility of generating errors, and enhance the stability of the casing arch and the subsequent built pipe roof, the present application provides a casing arch and pipe roof structure for the entrance of a mountain tunnel in fractured rock and soil mass.

[0006] The above technical objectives of the present application are achieved through the following technical solutions:

[0007] A casing arch and pipe roof structure for the entrance of a mountain tunnel in fractured rock and soil mass, including an I-beam, an orifice pipe, a square sleeve, an adjusting rack, an adjusting disc, and a driving plate. One end of the orifice pipe is hinged in the groove of the I-beam;

[0008] One end of the square sleeve is fixedly connected to the I-beam and is located in the same groove as the orifice pipe. The adjusting rack is slidably arranged in the square sleeve. The other end of the orifice pipe abuts against the end of the adjusting rack away from the I-beam. The adjusting disc is rotatably arranged outside the square sleeve. A receiving groove is formed on the surface of the adjusting disc. A circular plate is rotatably arranged in the receiving groove. The circular plate is concentric with the adjusting disc. The driving plate is arranged on the surface of the circular plate. An installation groove is formed on the side wall of the square sleeve. The driving plate is engaged in the tooth groove of the adjusting rack through the installation groove.

[0009] By adopting the above technical solution, a circular plate is set to drive a driving plate to drive the adjusting rack, so that the adjusting rack can move along the length direction of the square sleeve, and one end of the orifice pipe is hinged at the end of the adjusting rack. The angle of the orifice pipe is adjusted by the movement of the adjusting rack. After the orifice pipe is installed, the installation angle of the orifice pipe can be adjusted according to the data measured at the construction site, which can reduce the possibility of errors in the installation of the orifice pipe and enhance the stability of the sleeve arch and the subsequently constructed pipe shed.

[0010] Optionally, the arch and pipe roof structure also includes a fixed seat, a first hinged column and a second hinged column, the ends of the first hinged column and the second hinged column are fixedly connected to the peripheral wall of the orifice pipe, and the first hinged column and the second hinged column are coaxially arranged, the fixed seat is fixedly arranged in the groove of the I-beam, the first hinged column and the second hinged column are hinged on the fixed seat, and a locking nut is threadedly connected to the second hinged column, and the locking nut can lock the orifice pipe on the fixed seat.

[0011] By adopting the above technical solution, the end of the orifice pipe hinged on the fixed seat can cooperate with the adjusting rack to adjust the installation angle of the orifice pipe, and the fixed seat provides a firm support for the orifice pipe and the subsequent pipe shed structure, avoiding the orifice pipe to be compressed and moved when the sleeve arch and the pipe shed structure are in use, avoiding the efficiency of subsequent pipe shed construction, and improving the reliability of the sleeve arch and the pipe shed structure.

[0012] Optionally, the arch and pipe rack structure also includes a friction gear, which is coaxially fixed to the circumferential wall of the first hinged column at one end away from the orifice pipe, and has teeth formed on the side wall of the friction gear and on the outer surface of the fixed seat, and the teeth on the friction gear are meshed with the teeth on the fixed seat.

[0013] By adopting the above technical solution, the friction gear is against the outer surface of the fixed seat, and the teeth of the friction gear are meshed with the teeth of the fixed seat. The friction gear can increase the friction between the clamping friction gear and the fixed seat, so that the orifice pipe will not rotate at will, reducing the error of the subsequent construction of the pipe rack structure.

[0014] Optionally, the ends of the teeth on the side wall of the friction gear and the ends of the teeth on the outer surface of the fixed seat are processed to form chamfers with arcs.

[0015] By adopting the above technical solution, the chamfer can make the friction gear rotate against the outer surface of the fixed seat, while increasing the friction between the friction gear and the fixed seat, so that the orifice pipe will not rotate at will, reducing the error of the subsequent construction of the pipe rack structure.

[0016] Optionally, the arch and pipe roof structure also includes a trapezoidal plate and a fastening rod, the trapezoidal plate is hinged on the side wall of the square sleeve and fixed to the adjusting disc, the hinge between the trapezoidal plate and the square sleeve and the adjusting disc are both located on the same side wall of the square sleeve, one end of the fastening rod is processed into an eccentric end, the eccentric end is hinged on the trapezoidal plate, the square sleeve is located between the eccentric end and the adjusting disc, and the hinge between the eccentric end and the trapezoidal plate is on the end face of the eccentric end and deviates from the center of the end face.

[0017] By adopting the above technical solution, the drive plate can be always inserted in the tooth groove of the adjustment rack through the fastening rod and the trapezoidal plate, thereby preventing the adjustment rack from separating from the drive plate and causing the installation angle of the orifice tube to be offset.

[0018] Optionally, the sleeve arch and pipe roof structure also includes a third hinged column and a rotating handle, the third hinged column rotates to penetrate the adjustment disk and is coaxially fixed to the circular plate, and the rotating handle is L-shaped and one end is fixed to the end face of the third hinged column away from the adjustment disk.

[0019] By adopting the above technical solution and providing a rotating handle and a third hinged column, the position of the adjustment rack can be adjusted more easily.

[0020] Optionally, the arch and pipe rack structure also includes an arch foundation frame, which includes a first connecting plate and a second connecting plate. The arch foundation frame is divided into two layers of upper and lower arch structures. The lower layer is formed by splicing and fixing multiple pieces of the first connecting plates, and the upper layer is formed by splicing and fixing the second connecting plates and the I-beams alternately in sequence. The orifice pipe is suspended in the groove of the I-beam away from the first connecting plate.

[0021] By adopting the above technical solution, the sleeve arch can provide advance support for the pipe shed, fix and support the pipe shed, and facilitate subsequent construction.

[0022] Optionally, the sleeve arch and pipe-roof structure further includes a pipe-roof steel pipe, which is adapted to the orifice pipe and inserted in the orifice pipe.

[0023] By adopting the above technical solution, the pipe-roof structure is constructed with pipe-roof steel pipes, which can further support the excavated mountain and ensure construction safety.

[0024] In summary, this application has the following technical effects:

[0025] 1. By setting up I-beams, orifice pipes, square sleeves, adjustment racks, adjustment discs and drive plates, after the orifice pipes are installed, the installation angle of the orifice pipes can be adjusted according to the data measured on the construction site, which can reduce the possibility of errors in the installation of the orifice pipes and enhance the stability of the sleeve arch and the subsequent pipe shed;

[0026] 2. By providing a fixed seat, a first hinge post, and a second hinge post, the compression movement of the orifice pipe during the use of the sleeve arch and the pipe shed structure is avoided, the efficiency of subsequent pipe shed erection is prevented, and the reliability of the sleeve arch and the pipe shed structure is improved;

[0027] 3. By providing a trapezoidal plate and a fastening rod, the driving plate can always be inserted into the tooth groove of the adjusting rack, preventing the separation of the adjusting rack and the driving plate and avoiding the deviation of the installation angle of the orifice pipe. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is the external shape structure diagram of the present application;

[0029] Figure 2 is the external shape structure diagram of the present application from another angle;

[0030] Figure 3 is the prominent structure diagram of the adjustable component of the present application;

[0031] Figure 4 is the prominent structure diagram of the adjustable component of the present application.

[0032] Description of the reference numerals: 1, sleeve arch foundation frame; 11, first connecting plate; 12, second connecting plate; 13, I-beam; 14, fixed reinforcement; 15, bolt; 16, nut; 2, adjustable component; 21, orifice pipe; 22, fixed seat; 221, first hinge post; 222, second hinge post; 223, locking nut; 23, friction gear; 24, adjusting seat; 241, square sleeve; 242, installation groove; 25, adjusting rack; 26, trapezoidal plate; 261, installation notch; 27, adjusting disc; 271, driving plate; 272, disc body; 273, third hinge post; 274, rotating handle; 28, fastening rod; 281, eccentric end; 3, pipe shed steel pipe. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0033] The following further details the present application with reference to the accompanying drawings.

[0034] The embodiment of the present application discloses a sleeve arch and a pipe shed structure for the entrance of a mountain tunnel in a broken rock mass. Referring to Figure 1 , the sleeve arch and the pipe shed structure include a sleeve arch foundation frame 1, an adjustable component 2, and a pipe shed steel pipe 3. The sleeve arch and the pipe shed structure can adjust the installation angle of the orifice pipe 21 after its installation is completed, reducing the possibility of generating errors and enhancing the stability of the sleeve arch and the subsequent erected pipe shed.

[0035] Combined with Figure 1 and Figure 2, the casing arch foundation frame 1 is an arched structure assembled by combining and connecting a first connecting plate 11, a second connecting plate 12 and an I-beam 13. Both the first connecting plate 11 and the second connecting plate 12 are steel plates. The casing arch foundation frame 1 is divided into an upper and a lower layer structure. The lower layer structure is assembled by splicing several first connecting plates 11 into an arched structure. The first connecting plate 11 is a strip-shaped plate. The length directions of two first connecting plates 11 are parallel to each other, and the two first connecting plates 11 are connected by a fixing bar 14. The fixing bar 14 is a steel bar. The two ends of the fixing bar 14 are bent and the ends penetrate into the surfaces of the adjacent two first connecting plates 11 and are welded to the first connecting plates 11, thereby connecting and fixing the two first connecting plates 11. The upper layer is assembled by splicing the second connecting plate 12 and the I-beam 13. The second connecting plate 12 and the I-beam 13 are arranged alternately in sequence. The second connecting plate 12 is arranged at an interval from the first connecting plate 11. The I-beam 13 and the first connecting plate 11 are fixedly connected by bolts 15 and nuts 16. The length direction of the I-beam 13 is parallel to the length direction of the first connecting plate 11, and the I-beam 13 and the first connecting plate 11 are connected by bolts 15.

[0036] Refer to Figure 3 , the adjustable assembly 2 includes an orifice tube 21, a fixed seat 22 and a friction gear 23. Two notches are formed in the length direction of the I-beam 13. The orifice tube 21 is suspended in the notch of the I-beam 13 facing away from the first connecting plate 11. The length direction of the orifice tube 21 is parallel to the length direction of the I-beam 13. The fixed seat 22 is U-shaped. The U-shaped opening of the fixed seat 22 faces away from the first connecting plate 11 and is consistent with the notch orientation. The bottom of the fixed seat 22 is connected to the web surface of the I-beam 13 at one end of its length direction by bolts 15. A first hinge column 221 and a second hinge column 222 are respectively arranged at the two ends of the fixed seat 22. The axes of the first hinge column 221 and the second hinge column 222 are on the same straight line and are both perpendicular to the end plate surface of the fixed seat 22. Both the first hinge column 221 and the second hinge column 222 are hinged to the fixed seat 22. The opposite end parts of the first hinge column 221 and the second hinge column 222 are respectively fixedly connected to the peripheral wall of one end of the orifice tube 21.

[0037] Refer to Figure 3, the friction gear 23 is fixedly connected to the end of the first hinge column 221 away from the orifice pipe 21. The friction gear 23 is coaxially arranged with the first hinge column 221. The side wall of the friction gear 23 abuts against the outer plate surface of one end of the fixed seat 22. Circular teeth are formed on the side wall of the friction gear 23 that abuts against the plate surface of the fixed seat 22, and circular teeth are formed on the outer plate surface of the fixed seat 22. The teeth on the friction gear 23 mesh with the teeth on the outer plate surface of the end of the fixed seat 22. The protruding ends of the teeth on the end plate surface of the fixed seat 22 and the teeth on the friction gear 23 are all processed into chamfers with arcs. The friction gear 23 can increase the friction between the first hinge column 221 and the fixed seat 22, preventing the orifice pipe 21 from rotating randomly and reducing the error in subsequent construction of the pipe shed structure. Threads are formed on the peripheral wall of the second hinge column 222 away from the friction gear 23. A locking nut 223 is threadedly connected to the second hinge column 222. The locking nut 223 can lock the orifice pipe 21 on the fixed seat 22. When the orifice pipe 21 rotates, the rotation of the friction gear 23 on the end of the fixed seat 22 does not affect the threaded connection between the end of the second hinge column 222 and the locking nut 223.

[0038] Combined with Figure 3 and Figure 4 , the adjustable assembly 2 further includes an adjusting seat 24, an adjusting rack 25, a trapezoidal plate 26, an adjusting disc 27, and a fastening rod 28. The adjusting seat 24 includes a square sleeve 241. The adjusting seat 24 is fixedly arranged between the orifice pipe 21 and the web of the I-beam 13 and is located at the end away from the fixed seat 22. One end of the square sleeve 241 is welded to the surface of the web of the I-beam 13. The adjusting rack 25 is adapted to the square sleeve 241 and is slidably inserted into the square sleeve 241. Teeth are formed on the side wall of the adjusting rack 25 along the length direction. The peripheral wall of the end of the orifice pipe 21 away from the fixed seat 22 abuts against the end of the adjusting rack 25 away from the I-beam 13.

[0039] Combined with Figure 3 and Figure 4 , there are two trapezoidal plates 26. The two trapezoidal plates 26 are arranged in parallel and at intervals. The two trapezoidal plates 26 are located on opposite sides of the square sleeve 241. The plate surface of the trapezoidal plate 26 is a right trapezoid. Installation notches 261 are formed on the side walls of the long bottom edges of the two trapezoidal plates 26. The trapezoidal plate 26 is provided with an installation notch 261 and is hinged to the side wall of the square sleeve 241 on one side of the installation notch 261.

[0040] Combined with Figure 3 and Figure 4, the adjusting disc 27 includes a driving plate 271, a disc body 272, a circular plate (not shown in the figure), a third hinge column 273 and a rotating handle 274. A circular accommodating groove is formed on one side surface of the disc body 272. The circular plate is adapted to the accommodating groove and rotatably arranged in the accommodating groove, and the circular plate is concentric with the disc body 272. The driving plate 271 is integrally formed on the surface of the circular plate facing away from the disc body 272, and the surface of the driving plate 271 is perpendicular to the surface of the disc body 272. The third hinge column 273 is rotatably arranged on the disc body 272 coaxially and fixedly connected to the circular plate. The trapezoidal plate 26 is located on the other side of the opening of the installation notch 261 and fixedly connected to the surface of the disc body 272. The trapezoidal plate 26 and the driving plate 271 are located on the same side of the disc body 272.

[0041] Combined with Figure 3 and Figure 4 , one end of the rotating handle 274 is fixedly connected to the end of the third hinge column 273 away from the circular plate. An installation groove 242 is formed on the side wall of the square sleeve 241 close to the disc body 272. The installation groove 242 communicates with the inside and outside of the square sleeve 241. The driving plate 271 is located in the installation groove 242. The side wall of the driving plate 271 facing away from the circular plate is inserted into the tooth groove of the adjusting rack 25. When the circular plate is rotated by the rotating handle 274, the driving plate 271 can drive the adjusting rack 25 to move up and down along the length direction of the square sleeve 241, so as to adjust the installation angle of the orifice pipe 21.

[0042] Combined with Figure 3 and Figure 4 , the fastening rod 28 is arranged on the side of the square sleeve 241 away from the disc body 272. The length direction of the fastening rod 28 is always perpendicular to the length direction of the orifice pipe 21. One end of the fastening rod 28 is processed into an eccentric end 281. The axis of the eccentric end 281 is perpendicular to the length direction of the fastening rod 28. The two end faces of the eccentric end 281 are respectively hinged to the opposite side surfaces of the two trapezoidal plates 26. The hinged position is located at the edge of the trapezoidal plate 26 away from the installation notch 261. The hinged position on the end face of the eccentric end 281 deviates from the center of the end face. The fastening rod 28 can make the driving plate 271 always inserted into the tooth groove of the adjusting rack 25.

[0043] Combined with Figures 1 to 4 , the pipe shed steel pipe 3 is adapted to the orifice pipe 21 and inserted into the orifice pipe 21. Each orifice pipe 21 is provided with a pipe shed steel pipe 3. The pipe shed steel pipe 3 is a seamless steel pipe. The pipe shed steel pipe 3 is coaxially arranged with the orifice pipe 21. Multiple pipe shed steel pipes 3 form a pipe shed structure.

[0044] This specific embodiment is only an explanation of the present application, and it is not a limitation of the present application. Those skilled in the art can make modifications to this embodiment without creative contributions according to needs after reading this specification, but as long as it is within the scope of the claims of the present application, it is protected by the patent law.

Claims

1. The tunnel portal arch and pipe shed structure of broken rock and soil mountain tunnel is characterized by: The sleeve arch and pipe shed structure comprises an I-beam (13), an orifice pipe (21), a square sleeve (241), an adjustment rack (25), an adjustment disc (27) and a driving plate (271), wherein one end of the orifice pipe (21) is hinged in a notch of the I-beam (13); One end of the square sleeve (241) is fixedly connected to the I-beam (13) and is located in the same notch as the orifice tube (21); the adjusting rack (25) is slidably arranged in the square sleeve (241); the other end of the orifice tube (21) abuts against the end of the adjusting rack (25) away from the I-beam (13); the adjusting disc (27) is rotatably arranged outside the square sleeve (241); a receiving groove is provided on the surface of the adjusting disc (27); a circular plate is rotatably arranged in the receiving groove; the circular plate and the adjusting disc (27) are arranged concentrically; the driving plate (271) is arranged on the surface of the circular plate; a mounting groove (242) is provided on the side wall of the square sleeve (241); the driving plate (271) is meshed in the tooth groove of the adjusting rack (25) through the mounting groove (242).

2. The broken rock and soil mountain tunnel portal sleeve arch and pipe shed structure according to claim 1 is characterized by: The sleeve arch and pipe shed structure also includes a fixing seat (22), a first hinge column (221) and a second hinge column (222), the ends of the first hinge column (221) and the second hinge column (222) are both fixedly connected to the peripheral wall of the orifice pipe (21), and the first hinge column (221) and the second hinge column (222) are coaxially arranged, the fixing seat (22) is fixedly arranged in the notch of the I-beam (13), the first hinge column (221) and the second hinge column (222) are both hinged on the fixing seat (22), and a locking nut is threadedly connected to the second hinge column (222), and the locking nut can lock the orifice pipe (21) on the fixing seat (22).

3. The broken rock and soil mountain tunnel portal sleeve arch and pipe shed structure according to claim 2 is characterized by: The sleeve arch and pipe shed structure also includes a friction gear (23), which is coaxially fixed to the peripheral wall of the first hinge column (221) at one end away from the orifice pipe (21), and teeth are formed on the side wall of the friction gear (23), and teeth are formed on the outer surface of the fixed seat (22), and the teeth on the friction gear (23) are meshed with the teeth on the fixed seat (22).

4. The broken rock and soil mountain tunnel portal sleeve arch and pipe shed structure according to claim 3 is characterized by: The ends of the teeth on the side wall of the friction gear (23) and the ends of the teeth on the outer surface of the fixing seat (22) are both processed to form chamfers with arcs.

5. The broken rock and soil mountain tunnel portal sleeve arch and pipe shed structure according to claim 1 is characterized by: The sleeve arch and pipe shed structure also includes a trapezoidal plate (26) and a fastening rod (28). The trapezoidal plate (26) is hinged on the side wall of the square sleeve (241) and fixedly connected to the adjusting disc (27). The hinge between the trapezoidal plate (26) and the square sleeve (241) and the adjusting disc (27) are both located on the same side wall of the square sleeve (241). One end of the fastening rod (28) is processed into an eccentric end (281). The eccentric end (281) is hinged on the trapezoidal plate (26). The square sleeve (241) is located between the eccentric end (281) and the adjusting disc (27). The hinge between the eccentric end (281) and the trapezoidal plate (26) is deviated from the end face center on the end face of the eccentric end (281).

6. The broken rock and soil mountain tunnel portal sleeve arch and pipe shed structure according to claim 5 is characterized by: The sleeve arch and pipe shed structure also includes a third hinged column (273) and a rotating handle (274). The third hinged column (273) rotates to penetrate into the adjusting disc (27) and is coaxially fixed to the circular plate. The rotating handle (274) is L-shaped and one end is fixed to the end surface of the third hinged column (273) away from the adjusting disc (27).

7. The broken rock and soil mountain tunnel portal sleeve arch and pipe shed structure according to claim 2 is characterized by: The sleeve arch and pipe shed structure also includes an sleeve arch foundation frame (1), the sleeve arch foundation frame (1) includes a first connecting plate (11) and a second connecting plate (12), the sleeve arch foundation frame (1) is divided into an upper and lower arch structure, the lower layer is formed by splicing and fixing a plurality of the first connecting plates (11), and the upper layer is formed by splicing and fixing the second connecting plates (12) and the I-beams (13) in sequence, and the orifice pipe (21) is suspended in a groove of the I-beam (13) away from the first connecting plate (11).

8. The broken rock and soil mountain tunnel portal sleeve arch and pipe shed structure according to claim 1, characterized in that: The sleeve arch and pipe-roof structure also includes a pipe-roof steel pipe (3), wherein the pipe-roof steel pipe (3) is adapted to the orifice pipe (21) and inserted into the orifice pipe (21).