A catenary-based super-long-span tunnel structure and a drawing method thereof

Abstract

The application belongs to the technical field of tunnel construction, and provides a catenary-based super-long-span tunnel structure and a drawing method thereof. The catenary arch crown and catenary inverted arch are adopted, so that the stress balance problem of the large-span tunnel under the action of uniform load is solved. Under the action of uniform load, the catenary can well conduct stress, greatly improves the stability of the tunnel structure, and solves the problems of high tunnel arch crown excavation and high engineering cost caused by the original single or three heart circles. The catenary arch crown is arranged, so that the arch crown height is reduced, and the engineering cost is reduced. The catenary-based super-long-span tunnel drawing method is a new method for tunnel contour drawing which is more in line with engineering practice and more effective. The catenary equation is introduced into the contour drawing of the super-long-span tunnel arch crown and inverted arch, which has guiding significance for the design of the super-long-span tunnel structure.

Description

Technical Field

[0001] This invention relates to the field of tunnel construction technology, and in particular to a super-large span tunnel structure based on a catenary and its drawing method. Background Technology

[0002] Under uniformly distributed loads, catenary lines can transmit force well and act as ideal axes under certain load conditions. The principle of catenary lines is used in suspension bridges, hyperbolic arch bridges, overhead cables, and hyperbolic arch dams. However, due to the small span of existing tunnels, catenary lines have not yet been used to draw the inner contour of tunnels.

[0003] Currently, tunnel arch structures are typically single-centered or triple-centered circular structures. These structures effectively convert the vertical load on the tunnel arch crown into axial force on the arch walls, resulting in better stress distribution. However, with the increasing excavation spans of underground engineering projects, tunnels with spans exceeding 20m are becoming more common, and ultra-large span underground space structures ranging from 30m to 60m are gradually emerging. This places stricter demands on the stress balance of the arch. Using single-centered or triple-centered circular structures would lead to excessively high excavation of the tunnel arch crown, resulting in excessively high engineering costs, and would not meet the stress balance requirements under load. The load on the tunnel arch crown is generally a uniformly distributed load in tunnel structure calculations. This invention introduces the catenary equation into the drawing of the inner contour of the arch crown and invert of ultra-large span tunnels, and provides a method for drawing ultra-large span tunnel structures. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a super-large span tunnel structure based on a catenary and its drawing method, which solves the problems of excessively high arch excavation, high engineering costs, and failure to meet the stress balance under uniformly distributed loads in existing technologies.

[0005] According to an embodiment of the present invention, a super-large span tunnel structure based on a catenary includes: a catenary arch, wherein the curve formed by the catenary arch is a catenary; an arc-shaped sidewall, wherein the arc-shaped sidewall is disposed at the bottom of the catenary arch; an arc-shaped arch foot, wherein the arc-shaped arch foot is disposed at the bottom of the arc-shaped sidewall; and a catenary invert, wherein the top of the catenary invert is disposed at the bottom position of the arc-shaped arch foot.

[0006] Preferably, the circular arc sidewalls and circular arc arch feet are mirrored on the central axis of the catenary arch top and the catenary invert, and another set of circular arc sidewalls and circular arc arch feet are provided, and the catenary arch top, circular arc sidewalls, circular arc arch feet and catenary invert form the tunnel outline.

[0007] Preferably, it also includes: anchor bolts, wherein there are several anchor bolts, one end of which is fixed sequentially to the catenary arch and the arc side wall, and the other end is sequentially installed in the outer wall.

[0008] Preferably, it further includes: anchor cables, wherein there are several anchor cables arranged sequentially and at intervals with the anchor rods, one end of each anchor cable is fixed sequentially to the catenary arch and the arc side wall, and the other end is sequentially installed in the outer wall.

[0009] Preferably, the catenary arch and the catenary invert are located on the same axis, and the distance between them is the tunnel construction clearance height.

[0010] Preferably, it further includes: an initial support structure, which is disposed on the inner side forming the tunnel profile; and a secondary lining structure, which is disposed on the inner side of the initial support structure.

[0011] A method for drawing ultra-long span tunnels based on catenary lines includes the following steps:

[0012] S1. Determine the width and height of the construction clearance for Tunnel 01 according to the specifications;

[0013] S2. First, draw the inner contour of the catenary of the 02 arch. Import the formula from Excel into CAD. Edit the catenary formula in Excel and use an arithmetic progression to edit the corresponding data relationship between the span and the height. The span should be appropriately larger than the tunnel construction clearance width. Adjust the constant a so that the ratio of the catenary sag to the height of the arch catenary f1 / L1 is not less than 1:10. Import the data into CAD to generate the catenary at the top of the arch.

[0014] S3. Similarly, generate the catenary line of the 03 inverted arch and mirror it. Place the catenary line of the 02 arch top and the catenary line of the 03 inverted arch on the same axis. The distance between them can be taken as the building clearance height of 01.

[0015] S4. Draw the auxiliary large circle arc RO intersecting with the 02 / 03 catenary. Use the fillet command to draw the 04R1 large circle arc and connect it smoothly with the 02 catenary. R0 > R1, fillet command radius = R1. Similarly, use the fillet command to draw the 05 small circle arc radius and connect it smoothly with the 03 inverted arch catenary.

[0016] S5. After the inner contour of the tunnel is drawn, check whether the inner contour meets the building clearance requirements and verify the catenary height ratio of the 02 arch on the contour. If it does not meet the requirements, adjust the constant a value or R1 value and recalculate and draw.

[0017] Preferably, the catenary formula is as follows: Where a is a constant, y is the Y-axis coordinate, and x is the X-axis coordinate.

[0018] Preferably, in step S5, after the tunnel inner contour is drawn, the fitting error between the large circular arc and the 02 catenary line can be analyzed by drawing a large circular arc and fitting it with the 02 catenary line.

[0019] Preferably, in step S2, f1 is the height of the catenary of the arch, and L1 is the span of the catenary segment of the arch.

[0020] Compared with existing technologies, this invention has the following advantages: By adopting a catenary arch and a catenary invert, it solves the problem of force balance required for large-span tunnels under uniformly distributed loads. Because the catenary can transmit force well under uniformly distributed loads, it greatly improves the stability of the tunnel structure. At the same time, it solves the problem that the original use of single-centered or three-centered circles would lead to excessively high tunnel arch excavation and high project costs. By setting a catenary arch, the arch height is reduced, and the project cost is also reduced.

[0021] The proposed method for drawing ultra-large span tunnels based on catenary curves has formed a new method for drawing tunnel outlines that is more in line with engineering practice and more effective. This invention introduces the catenary curve equation into the drawing of the inner outline of the arch and invert of ultra-large span tunnels, which has guiding significance for the design of ultra-large span tunnel structures in the later stage. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the tunnel outline structure of the present invention.

[0023] Figure 2 This is a schematic diagram of the tunnel drawing method of the present invention.

[0024] Figure 3 for Figure 2 A schematic diagram of the tunnel outline.

[0025] In the above attached figures: 1. Catenary arch; 2. Circular sidewall; 3. Circular arch foot; 4. Catenary invert; 5. Anchor bolt; 6. Anchor cable; 7. Initial support structure; 8. Secondary lining structure. Detailed Implementation

[0026] The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0027] like Figure 1 As shown, this embodiment of the invention proposes a super-large span tunnel structure based on a catenary, comprising:

[0028] Catenary arch 1, the curve formed by catenary arch 1 is a catenary;

[0029] Arc-shaped sidewall 2 is located at the bottom of the catenary arch 1;

[0030] The circular arch foot 3 is located at the bottom of the circular arch side wall 2;

[0031] The top of the catenary inverted arch 4 is located at the bottom of the circular arch foot 3.

[0032] In this embodiment, by setting a catenary arch 1, wherein the curved catenary of the catenary arch 1 is set, the force can be well transmitted under uniform load, which greatly improves the stability of the tunnel structure. By setting arc sidewalls 2 on both sides of the bottom of the catenary arch 1, the stability of the tunnel sidewall structure is increased. By setting arc arch feet 3 on both sides of the bottom of the arc sidewalls 2, the stability of the tunnel arch foot structure is increased. By setting a catenary invert arch 4, wherein the curve of the catenary invert arch 4 is also set as a catenary, the force at the bottom of the tunnel can be well transmitted, thus improving the overall structural stability of the tunnel.

[0033] The circular arc sidewall 2 and the circular arc arch foot 3 are mirrored on the central axis of the catenary arch 1 and the catenary inverted arch 4. Another set of circular arc sidewall 2 and circular arc arch foot 3 are set there, and the catenary arch 1, the circular arc sidewall 2, the circular arc arch foot 3 and the catenary inverted arch 4 form the tunnel outline.

[0034] In this embodiment, the circular arc sidewalls 2 and the circular arc arch feet 3 are mirror images of the catenary arch top 1 and the catenary invert arch 4 on both sides, and the supports are smoothly connected to form a closed tunnel profile, which improves the overall stability of the tunnel profile.

[0035] Furthermore, a super-large span tunnel structure based on a catenary also includes:

[0036] Anchor bolts 5, there are several anchor bolts 5, one end of the anchor bolts 5 is fixed to the tunnel outline in sequence, and the other end is installed in the outer wall in sequence.

[0037] In this embodiment, by setting a number of anchor bolts 5, the upper support of the tunnel outline is reinforced together with the outer surrounding rock. The number of anchor bolts 5 forms a system anchor bolt, which reinforces the main body of the tunnel and improves the stability support of the tunnel outline.

[0038] In addition, a super-large span tunnel structure based on a catenary also includes:

[0039] Anchor cables 6, there are several anchor cables 6, and they are arranged alternately with anchor rods 5. One end of the anchor cables 6 is fixed to the tunnel outline 2 in sequence, and the other end is installed in the outer wall in sequence.

[0040] In this embodiment, by providing a plurality of anchor cables 6, which are then combined with a plurality of anchor rods 5, the stability of the tunnel profile support is further improved.

[0041] In addition, the catenary arch 1 and the catenary invert arch 4 are set in mirror image on the same axis, and the distance between them is the tunnel construction clearance height.

[0042] In this embodiment, the catenary arch 1 and the catenary invert 4 are located on the same axis, ensuring that the force at the bottom and top of the tunnel can be well transmitted, thereby improving the overall structural stability of the tunnel.

[0043] It should be noted that a type of super-large span tunnel structure based on catenary also includes:

[0044] Initial support structure 7 is located on the inner side of the tunnel profile.

[0045] The secondary lining structure 8 is located inside the initial support structure 7.

[0046] In this embodiment, by setting the initial support structure 7, it is convenient to form a tunnel structure system with sufficient safety together with the surrounding rock, which can withstand various possible loads; maintain the usable clearance of the tunnel cross section, and enhance the stability of the tunnel body by setting the secondary lining structure 8, ensuring the safety of later operation.

[0047] On the other hand, as attached Figure 2 and attached Figure 3 As shown, this embodiment of the invention also provides a method for drawing ultra-long span tunnels based on catenary lines, which includes the following steps:

[0048] S1. Determine the width and height of the construction clearance for Tunnel 01 according to the specifications;

[0049] S2. First, draw the inner contour of the catenary of the 02 arch. Import the formula from Excel into CAD. Edit the catenary formula in Excel and use an arithmetic progression to edit the corresponding data relationship between the span and the height. The span should be appropriately larger than the tunnel construction clearance width. Adjust the constant a so that the ratio of the catenary sag to the height of the arch catenary f1 / L1 is not less than 1:10. Import the data into CAD to generate the catenary at the top of the arch.

[0050] S3. Similarly, generate the catenary line of the 03 inverted arch and mirror it. Place the catenary line of the 02 arch top and the catenary line of the 03 inverted arch on the same axis. The distance between them can be taken as the building clearance height of 01.

[0051] S4. Draw the auxiliary large circle arc RO intersecting with the 02 / 03 catenary. Use the fillet command to draw the 04R1 large circle arc and connect it smoothly with the 02 catenary. R0 > R1, fillet command radius = R1. Similarly, use the fillet command to draw the 05 small circle arc radius and connect it smoothly with the 03 inverted arch catenary.

[0052] S5. After the inner contour of the tunnel is drawn, check whether the inner contour meets the building clearance requirements and verify the catenary height ratio of the 02 arch on the contour. If it does not meet the requirements, adjust the constant a value or R1 value and recalculate and draw.

[0053] The formula for the catenary is: Where a is a constant, y is the Y-axis coordinate, and x is the X-axis coordinate.

[0054] In this embodiment, based on the catenary formula, when the constant a is determined, the corresponding X-axis coordinate or y-axis coordinate can be derived from the y-axis coordinate or X-axis coordinate of the catenary.

[0055] In step S5, after the tunnel inner contour is drawn, the fitting error between the large circular arc and the 02 catenary line can be analyzed by drawing the large circular arc and fitting it with the 02 catenary line.

[0056] In this embodiment, the fitting error between the great circular arc and the 02 catenary is analyzed by drawing a diagram showing the seamless connection between the great circular arc and the catenary. Since the fitting error is within 0.01m, the catenary segment can be approximately replaced by the great circular arc segment, facilitating engineering construction.

[0057] In step S2, f1 is the height of the catenary of the arch, and L1 is the span of the catenary segment of the arch.

[0058] Example 1:

[0059] According to the specifications, the clearance width and height of a tunnel are determined through step S1, the catenary arch height f1 = 5.894m is determined, the span of the catenary segment in the arch is 30m, and the constant a = 0.05 is set. Therefore, the abscissa of the catenary is determined to be between -15 and 15. By taking the coordinate nodes on the abscissa, the Y-axis coordinate is derived using the catenary equation. The catenary formula is then edited in Excel to generate the vertical coordinates of the catenary corresponding to the abscissa of each node. See the table below (unit: m):

[0060]

[0061]

[0062]

[0063] Import the composite coordinate data from the table above into CAD to generate the catenary curve of the arch.

[0064] In step S3, the generated arch catenary line is mirrored to generate the inverted arch catenary line, where the two are located on the same axis and the distance between them is the building clearance height.

[0065] In step S4, draw a large arc R0 in CAD that intersects with the catenary of the arch top and the catenary of the invert arch generated above. Use the fillet command to draw the large arc 04R1 and connect it smoothly with the catenary of 02. R0 > R1, and the radius of the fillet command = R1. Similarly, use the fillet command to draw the small arc 05 with the radius that connects smoothly with the catenary of 03 invert arch.

[0066] After the tunnel inner contour is drawn in step S5, check that the inner contour meets the building clearance requirements and verify the catenary height ratio of the 02 arch on the contour. The catenary height ratio of the arch is 5.894 / 30≈0.196456, which meets the 1 / 10 requirement. There is no need to adjust the constant value a or R1 value and recalculate and draw.

[0067] Next, by plotting large circular arcs, the arcs with radii between 20 and 22 showed the best fit with the catenary. Then, radii between 20.0 and 22.0 were input into Excel, maximizing the arc radius of the fit between the catenary and the circular arc. Finally, the fitted arc with a radius of 20.5m showed a fitting error of less than 0.01m with the catenary at a = 0.05 within the node range of 19 to 45. See the table below (unit: m) (Catalogue - Circle = Difference in vertical coordinates between catenary and circular arc):

[0068]

[0069]

[0070]

[0071] Example 2:

[0072] According to the specifications, the clearance width and height of a tunnel are determined through step S1, the catenary arch height f1 = 2.324m is determined, the span of the catenary segment in the arch is 22m, and the constant a = 0.03786 is set. Therefore, the abscissa of the catenary is determined to be between -11 and 11. By taking the coordinate nodes on the abscissa, the Y-axis coordinate is derived using the catenary equation. The catenary formula is then edited in Excel to generate the vertical coordinates of the catenary corresponding to the abscissa of each node. See the table below (unit: m):

[0073]

[0074]

[0075]

[0076] Import the composite coordinate data from the table above into CAD to generate the catenary curve of the arch.

[0077] In step S3, the generated arch catenary line is mirrored to generate the inverted arch catenary line, where the two are located on the same axis and the distance between them is the building clearance height.

[0078] In step S4, draw a large arc R0 in CAD that intersects with the catenary of the arch top and the catenary of the invert arch generated above. Use the fillet command to draw the large arc 04R1 and connect it smoothly with the catenary of 02. R0 > R1, and the radius of the fillet command = R1. Similarly, use the fillet command to draw the small arc 05 with the radius that connects smoothly with the catenary of 03 invert arch.

[0079] After completing the tunnel inner contour drawing in step S5, check that the inner contour meets the building clearance requirements and verify the catenary elevation ratio of the 02 arch on the contour. The catenary elevation ratio of the arch is 2.324 / 22≈0.105629, which meets the 1 / 10 requirement. There is no need to adjust the constant value a or R1 value and recalculate and draw.

[0080] Next, by plotting large circular arcs, the arcs with radii between 27 and 28 m showed the best fit with the catenary. Then, radii between 27.0 and 28.0 m were input into Excel, maximizing the arc radius of the fit between the catenary and the circular arc. Finally, the fitted arc with a radius of 27.0 m showed a fitting error of less than 0.01 m with the catenary at a = 0.05 within the node range of 3 to 79. See the table below (unit: m) (Catalogue - Circle = Difference in vertical coordinates between catenary and circular arc):

[0081]

[0082]

[0083]

[0084] Example 3:

[0085] According to the specifications, the width and height of a tunnel's structural clearance are determined through step S1, and the catenary arch height f1 = 4.597m is determined. The span of the catenary segment in the arch is 40m. A constant a = 0.0226 is set, and the span of the catenary segment in the arch is 40m. Therefore, the abscissa of the catenary is determined to be between -20 and 20. By taking the coordinate nodes on the abscissa, the Y-axis coordinate is derived using the catenary equation. The catenary formula is then edited in Excel to generate the vertical coordinates of the catenary corresponding to the abscissa of each node. See the table below (unit: m):

[0086]

[0087]

[0088]

[0089] Import the composite coordinate data from the table above into CAD to generate the catenary curve of the arch.

[0090] In step S3, the generated arch catenary line is mirrored to generate the inverted arch catenary line, where the two are located on the same axis and the distance between them is the building clearance height.

[0091] In step S4, draw a large arc R0 in CAD that intersects with the catenary of the arch top and the catenary of the invert arch generated above. Use the fillet command to draw the large arc 04R1 and connect it smoothly with the catenary of 02. R0 > R1, and the radius of the fillet command = R1. Similarly, use the fillet command to draw the small arc 05 with the radius that connects smoothly with the catenary of 03 invert arch.

[0092] After the tunnel inner contour is drawn in step S5, check that the inner contour meets the building clearance requirements and verify the catenary sag ratio of the 02 arch on the contour. The catenary sag ratio of the arch is 4.597 / 40≈0.114937, which meets the 1 / 10 requirement. There is no need to adjust the constant value a or R1 value and recalculate and draw.

[0093] Next, by plotting large circular arcs, the arcs with radii between 45 and 46 mm fit the catenary best. Then, radii between 45.0 and 46.0 mm were entered into Excel to maximize the arc range of the catenary-arc fit. Finally, the fitted arc with a radius of 45.0 m had a fitting error of less than 0.01 m with the catenary at a = 0.05 within the node range of 11 to 59. See the table below (unit: m) (Catalogue - Circle = Difference in vertical coordinates between catenary and arc):

[0094]

[0095]

[0096]

[0097] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A super-large span tunnel structure based on a catenary, characterized in that, include: The catenary arch (1) forms a curve called a catenary. Arc-shaped sidewall (2), which is located at the bottom of the catenary arch (1); A circular arch foot (3) is provided at the bottom of the circular arch sidewall (2); The top of the catenary arch (4) is located at the bottom of the circular arch foot (3); The circular arc sidewall (2) and circular arc arch foot (3) are mirror images of the central axis of the catenary arch top (1) and the catenary inverted arch (4) and another set of circular arc sidewall (2) and circular arc arch foot (3) are provided, and the catenary arch top (1), circular arc sidewall (2), circular arc arch foot (3) and catenary inverted arch (4) form the tunnel outline; The catenary arch (1) and the catenary invert (4) are located on the same axis and are mirror images of each other, with the distance between them being the tunnel construction clearance height.

2. The super-large span tunnel structure based on a catenary as described in claim 1, characterized in that: Also includes: Anchor bolts (5), the number of anchor bolts (5) is several, one end of the anchor bolts (5) is fixed on the tunnel outline in sequence, and the other end is installed in the outer wall in sequence.

3. The super-large span tunnel structure based on a catenary as described in claim 2, characterized in that: Also includes: Anchor cables (6) are a number of cables and are arranged in sequence with the anchor rods (5). One end of each anchor cable (6) is fixed to the tunnel outline and the other end is installed in the outer wall.

4. The super-large span tunnel structure based on a catenary as described in claim 1, characterized in that: Also includes: Initial support structure (7), the initial support structure (7) is located on the inside of the tunnel profile; Secondary lining structure (8) is located inside the initial support structure (7).

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