Three-center circle fitting method for inner contour of anchor section in railway tunnel

Abstract

The present invention relates to a three-center circle fitting method for the inner contour of a railway tunnel anchor section. The method comprises: establishing a Cartesian coordinate system based on the structural centerline and the horizontal inner rail surface line; determining the coordinates of key control points of the inner contour based on the top-down and left-to-right fitting principle; and finally fitting the inner contours of the arch, sidewall, and invert of the catenary anchor section of a single-track railway tunnel. The method of the present invention can be used for the three-center circle fitting method for the inner contour of a 160km / h single-track railway tunnel anchor section. The method introduces the analytical method of the multi-circle intersecting plane equation group to achieve arc co-tangent transition and area optimization, avoiding the large amount of trial design work caused by frequent changes in the height of the catenary anchor section. The method forms a universal method for fitting the inner contour of the tunnel anchor section lining when different heights are raised under two different track laying methods: ballasted and ballastless.

Description

Technical Field

[0001] The invention relates to the field of tunnel construction design, and in particular to a three-center circle fitting method for the inner contour of an anchor section of a railway tunnel. Background Art

[0002] During railway tunnel design, the catenary anchor section often requires a higher cross-section than normal. This can be achieved by using a three-center arc to fit the inner contour of the tunnel anchor section lining. This ensures optimal structural stress, minimizes excavation and support work, and optimizes the cross-sectional spatial layout.

[0003] Traditional inner contour fitting methods often pre-determine the radii of the arch and sidewall arcs, resulting in non-co-tangent intersections and stress concentration at the arc transitions. Furthermore, when the required height of the tunnel vault changes due to changes in the catenary power supply method, the sidewall arc radius must be re-assumed and re-determined, requiring repeated trial calculations, which is computationally intensive. Summary of the Invention

[0004] The present application provides a three-center circle fitting method for the inner contour of a railway tunnel anchor section, which solves the problem of repeated trial calculations caused by frequent changes in the height of the contact network anchor section in railway tunnel design.

[0005] In order to achieve the above object, the technical solution of the present invention is as follows:

[0006] A three-center circle fitting method for the inner contour of the anchor section of a railway tunnel is proposed. A Cartesian coordinate system is established based on the structural centerline and the horizontal inner rail surface line. Based on the top-down and left-to-right fitting principle, the coordinates of the key control points of the inner contour are determined analytically using a set of multi-circle intersecting plane equations. Ultimately, the inner contours of the arch, side walls, and invert arch of the catenary anchor section of a single-track railway tunnel are fitted.

[0007] Furthermore, the inner contour arcs of the arch and the side wall ensure cotangency and smooth transition, and the inner contour arc of the inverted arch ensures that the rise-to-span ratio meets 1 / 6 to 1 / 8.

[0008] Furthermore, the arch inner contour fitting specifically includes the following steps:

[0009] By giving the inner arc radius r1 and the center angle α of the arch, the inner contour arc of the arch is made with the radius r1 and the center angle α, and the center O1 is determined, the starting point of the arc is point C, and the end point of the arc is point D.

[0010] Furthermore, the side wall inner contour fitting specifically includes the following steps:

[0011] Draw line segment O1O downward from the center of the circle O1; draw a horizontal line from point O, and intercept line segments OA and OB in the horizontal left and right directions respectively. Then establish a Cartesian coordinate system with O1O as the vertical axis, AB as the horizontal axis, and point O as the origin; line segment AB is the horizontal rail surface line, and O1O is the center line of the inner contour, which is controlled by the basic limit of the entire tunnel.

[0012] Let OA = OB = a + b

[0013] Among them, a is the width of the roadbed; b is the width of the top surface of the ditch cover.

[0014] Connect the starting point C of the arch arc and point A on the horizontal axis, draw the perpendicular bisector l1 of the line segment CA, and extend it in the opposite direction. Intersect the perpendicular bisector l1 at O2; with O2 as the center of the side wall arc, draw an arc with CO2 as the radius through points C and A, that is, is the arc of the left wall, and the corresponding central angle is β1;

[0015] Repeat the above steps to determine the arc of the right wall

[0016] Furthermore, when ballastless track is laid, the track bed width a is 190 cm, and when ballasted track is laid, the track bed width a is 220 cm;

[0017] When laying ballastless track, the width b of the top surface of the ditch cover is 125cm, and when laying ballasted track, the width b of the top surface of the ditch cover is 115cm.

[0018] Furthermore, the inverted arch inner contour fitting specifically includes the following steps:

[0019] Draw a line segment OE downward from the origin O of the coordinate axis, OE is the vector height, satisfying

[0020] Take point E as the base point, take the line segment EO3 upwards, and draw a circle with O3 as the center and EO3 as the radius, which is connected to the arc of the side wall. and The extension line intersects at points F and G; connecting points F and G forms an inverted arc with EO3 The corresponding central angle is γ; The corresponding central angle is β2.

[0021] Furthermore, according to the fitting principle from top to bottom and from left to right, the control parameters of the inner contour of the tunnel anchor section are obtained:

[0022]

[0023] Where H is the height from the rail surface to the arch top; r1, r2, r3 are the radii of circles O1, O2, O3; r1, r3 and O1O are pre-given dimensions; h is the vertical distance from the arch foot to the arch top; α is the central angle of circle O1; β1 is the arc The central angle of the circle; β2 is the arc The central angle of the circle; γ is the central angle of the circle O3; θ is the angle between the chord CA and the vertical line; x F and y2 are the horizontal coordinates of point F and O2 respectively, which can be obtained by calculating the coordinates of the control points.

[0024] Furthermore, the coordinates of the key control points A, B, C, D, T, and P of the inner contour are:

[0025]

[0026] Furthermore, according to the circle equations of O2 and O3, the coordinates of the intersection F and G of the side wall arc and the inverted arch arc are fitted:

[0027]

[0028] Among them, OE is a preset length; the coordinates of points F and G are a pair of valid solutions to the equation group.

[0029] An electronic device for three-center circle fitting of the inner contour of an anchor section in a railway tunnel, comprising:

[0030] At least one processor; and at least one memory in communication with the processor, wherein: the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the above-mentioned fitting method.

[0031] The beneficial effects of the present invention are as follows:

[0032] 1. This invention's three-center circle fitting method for the inner contour of a railway tunnel anchor section focuses on adapting to varying track laying methods and contact heights within the anchor section. By establishing a Cartesian coordinate system based on the horizontal axis of the track surface and the vertical axis of the structural centerline, the method dynamically adjusts the vertical distance between the arch center and the track surface, achieving adaptive tangency between the arch and the sidewall arc. By establishing an analytical equation for the multi-circle intersecting plane, the method rapidly locates the key intersection point between the sidewall arc and the inverted arch arc, extrapolates key control points of the entire inner contour, and establishes a coordinate system for these control points.

[0033] 2. The method of the present invention saves a lot of trial design work caused by the prior assumption of the arc radius of the side wall. The proposed analytical method can quickly and accurately calculate the coordinates of the key control points of the inner contour without the need for mapping. The corresponding mapping method is universal at the application level and scientific at the theoretical level.

[0034] 3. The method of the present invention can adapt to different heightening requirements of the contact network at the anchor section, and is also suitable for inner contour fitting under both ballasted and ballastless track laying conditions. While improving design accuracy and rigor, it has a strong promotion prospect. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0036] Figure 1 This is a schematic diagram of the inner contour fitting of a general anchor section arch portion of a single-track tunnel according to an embodiment of the present invention;

[0037] Figure 2 This is a schematic diagram of the inner contour fitting of a side wall of a general anchor section of a single-track tunnel according to an embodiment of the present invention;

[0038] Figure 3 This is a schematic diagram of the inner contour fitting of a general anchor section invert of a single-track tunnel according to an embodiment of the present invention;

[0039] Figure 4 This is a schematic diagram of estimating key parameters of the inner profile of a general anchor section of a single-track tunnel according to an embodiment of the present invention;

[0040] Figure 5 It is a schematic diagram of the physical structure of an electronic device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0041] The present invention will be further described in detail below by means of specific embodiments in conjunction with the accompanying drawings. Similar elements in different embodiments are numbered with associated similar elements. In the following embodiments, many detailed descriptions are provided to enable the present application to be better understood. However, those skilled in the art will readily appreciate that some of the features may be omitted in different circumstances, or may be replaced by other elements, materials, or methods. In some cases, some operations related to the present application are not shown or described in the specification. This is to avoid the core portion of the present application being overwhelmed by excessive descriptions, and for those skilled in the art, it is not necessary to describe these related operations in detail. They will fully understand the related operations based on the description in the specification and the general technical knowledge in the art.

[0042] In addition, the features, operations, or characteristics described in the specification may be combined in any appropriate manner to form various embodiments. Furthermore, the steps or actions in the method description may be reordered or adjusted in a manner readily apparent to those skilled in the art. Therefore, the various sequences in the specification and drawings are provided solely for the purpose of clearly describing a particular embodiment and are not intended to be mandatory, unless otherwise specified.

[0043] The serial numbers assigned to components herein, such as "first," "second," etc., are used solely to distinguish the objects being described and do not convey any sequential or technical meaning. References to "connection" and "coupling" herein, unless otherwise specified, include both direct and indirect connections (couplings).

[0044] The basic idea of ​​the present invention is to simply and directly increase the height of the vertical axis by establishing a Cartesian coordinate system based on the horizontal axis of the rail surface and the vertical axis of the structure centerline, thereby meeting the height increase requirement of the contact network anchor section and ensuring cross-section optimization and smooth transition.

[0045] Example 1:

[0046] This embodiment relates to a three-center circle fitting method for the inner contour of the anchor section of a single-track railway tunnel, specifically including the fitting of the inner contours of the arch, side walls and invert of the anchor section of the tunnel.

[0047] This embodiment uses a tunnel design speed target of 160 km / h as an example. Of course, in other embodiments, this method can also be applied to tunnel designs with other speed targets. Therefore, the arch center radius and angle, as well as the distance from the arch center to the top of the inner rail, can be determined based on the tunnel design speed target and the construction clearance.

[0048] At the same time, the inner contour fitting method of the method of the present invention is applicable to two types of track laying conditions: ballasted trackbed and ballastless trackbed. In this embodiment, the ballasted trackbed is taken as an example for introduction.

[0049] Figure 1-Figure 4 This is a fitting diagram of the method of this embodiment. The meanings of the letters involved in the figure are introduced as follows:

[0050] A, B, C, D, F, G - key control points of inner contour, r1 - arch arc radius, r2 - side wall arc radius; r3 - inverted arch arc radius, O - Cartesian coordinate origin, O1 - arch center, O2 - variable wall center, O3 - inverted arch center, α - arch center angle, β1 - side wall arc center angle above rail surface, β2 - entire side wall arc center angle, γ - inverted arch arc center angle, AB - horizontal axis of coordinate, O3E - vertical axis of coordinate, O1O - distance from center O1 to the top surface of inner rail, OE - inverted arch sag, θ is the angle between chord CA and vertical line.

[0051] The specific process of inner contour fitting in this embodiment is as follows:

[0052] First, the inner contour fitting of the tunnel arch.

[0053] See also Figure 1 , specifically including the following steps:

[0054] By giving the inner arc radius r1 and the center angle α of the arch, the inner contour arc of the arch is made with the radius r1 and the center angle α, and the center O1 is determined, the starting point of the arc is point C, and the end point of the arc is point D.

[0055] Second, the inner contour fitting of the tunnel side wall.

[0056] See also Figure 2 , specifically including the following steps:

[0057] Step S1: Draw a line segment O1O downward from the center of the circle O1; draw a horizontal line from point O, and intercept line segments OA and OB along the horizontal left and horizontal right directions respectively, and then establish a Cartesian coordinate system with O1O as the vertical axis, AB as the horizontal axis and point O as the origin; line segment AB is the horizontal rail surface line, and O1O is the center line of the inner contour, which is controlled by the basic limit of the entire tunnel.

[0058] Let OA=OB=a+b.

[0059] Among them, a is the width of the track bed. When laying ballasted track bed, large-scale machinery maintenance needs to be considered and 220 cm is taken; b is the top surface width of the ditch cover. When laying ballasted track, 115 cm is taken.

[0060] Step S2: Connect the starting point C of the arch and point A on the horizontal axis, draw the perpendicular bisector l1 of the line segment CA, and extend it in the opposite direction. Intersect the perpendicular bisector l1 at O2; with O2 as the center of the side wall arc, draw an arc with CO2 as the radius through points C and A, that is, is the arc of the left wall, and the corresponding central angle is β1.

[0061] Step S3: Repeat step S2 to determine the arc of the right wall

[0062] Third, the inner contour fitting of the tunnel invert.

[0063] See also Figure 3 , specifically including the following steps:

[0064] Step P1: Draw a line segment OE downward from the origin O of the coordinate axis, OE is the vector height, satisfying

[0065] Step P2: Take point E as the base point, take line segment EO3 upwards, and draw a circle with O3 as the center and EO3 as the radius, which is connected to the arc of the side wall. and The extension line intersects at points F and G; connecting points F and G forms an inverted arc with EO3 The corresponding central angle is γ; The corresponding central angle is β2.

[0066] See also Figure 4 , the control parameters of the tunnel anchor section profile are as follows:

[0067]

[0068] Where H is the height from the rail surface to the arch top; r1, r2, r3 are the radii of circles O1, O2, O3; r1, r3 and O1O are pre-given dimensions; h is the vertical distance from the arch foot to the arch top; α is the central angle of circle O1; β1 is the arc The central angle of the circle; β2 is the arc The central angle of the circle; γ is the central angle of the circle O3; θ is the angle between the chord CA and the vertical line; x F and y2 are the horizontal coordinates of point F and O2 respectively, which can be obtained by calculating the coordinates of the control points.

[0069] The coordinates of the key control points A, B, C, D, T, and P of the inner contour are:

[0070]

[0071]

[0072] According to the circle equations of O2 and O3, the coordinates of the intersection F and G of the side wall arc and the inverted arch arc are fitted:

[0073]

[0074] Among them, OE is a preset length; the coordinates of points F and G are a pair of valid solutions to the equation group.

[0075] Example 2:

[0076] Different from Example 1, in this embodiment, the contour fitting method is applied to the tunnel design under ballastless track conditions. When the ballastless track is laid, the track bed width a is 190 cm, and when the ballastless track is laid, the ditch cover top surface width b is 125 cm.

[0077] The fitting method of the present invention is used for the three-center circle fitting method of the inner contour of the anchor section of a single-track railway tunnel. The method introduces the analytical means of a multi-circle intersecting plane equation group to achieve arc co-tangent transition and area optimization, avoiding a large amount of trial design work caused by frequent changes in the height of the catenary anchor section. The method forms a universal method for fitting the inner contour of the tunnel anchor section lining when the height is different under two different ballasted and ballastless track laying methods.

[0078] Example 3:

[0079] This embodiment relates to an electronic device for fitting three-center circles of the inner contour of an anchor section in a railway tunnel. Figure 5 The present invention provides a schematic diagram of the physical structure of an electronic device provided in an embodiment of the present invention. The electronic device may include: a processor 301, a communications interface 302, a memory 303, and a bus 304. The processor 301, the communications interface 302, and the memory 303 communicate with each other via the bus 304. The processor 301 may call a computer program stored in the memory 303 and executable on the processor 301 to execute the fitting method provided in the above-mentioned embodiment 1. For example, the method includes: establishing a Cartesian coordinate system based on the structural centerline and the horizontal inner rail surface line, and according to the principle of fitting from top to bottom and from left to right, using the analytical method of a multi-circle intersecting plane equation system to determine the coordinates of the key control points of the inner contour, and finally fitting the inner contours of the arch, side wall, and invert of the catenary anchor section of a single-track railway tunnel.

[0080] In addition, the logic instructions in the above-mentioned memory 303 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on this understanding, the technical solution of the embodiment of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0081] The above examples are used to illustrate the present invention, which are only used to help understand the present invention and are not intended to limit the present invention. Those skilled in the art can make several simple deductions, modifications or substitutions based on the concept of the present invention.

Claims

1. A three-center circle fitting method for the inner contour of an anchor section of a railway tunnel, characterized in that: A Cartesian coordinate system based on the structural centerline and the horizontal inner rail surface line was established. Based on the top-down, left-to-right fitting principle, the coordinates of the key control points of the inner contour were determined using a multi-circle intersecting plane equation system. Ultimately, the inner contours of the arch, sidewalls, and invert of the catenary anchor section of a single-track railway tunnel were fitted. The inner contour arc of the arch and the side wall ensures cotangency and smooth transition, and the inner contour arc of the inverted arch ensures that the rise-to-span ratio meets 1 / 6 to 1 / 8; The arch inner contour fitting specifically includes the following steps: By giving the inner arc radius r1 and the center angle α of the arch, the inner contour arc of the arch is made with the radius r1 and the center angle α, and the center O1 is determined. The starting point of the arc is point C and the end point of the arc is point D. The inner contour fitting of the side wall specifically includes the following steps: Draw line segment O1O downward from the center of the circle O1; draw a horizontal line from point O, and intercept line segments OA and OB in the horizontal left and right directions respectively. Then establish a Cartesian coordinate system with O1O as the vertical axis, AB as the horizontal axis, and point O as the origin; line segment AB is the horizontal rail surface line, and O1O is the center line of the inner contour, which is controlled by the basic limit of the entire tunnel. Let OA = OB = a + b Among them, a is the width of the roadbed; b is the width of the top surface of the ditch cover; Connect the starting point C of the arch arc and point A on the horizontal axis, draw the perpendicular bisector l1 of the line segment CA, and extend it in the opposite direction. Intersect the perpendicular bisector l1 at O2; with O2 as the center of the side wall arc, draw an arc with CO2 as the radius through points C and A, that is, is the arc of the left wall, and the corresponding central angle is β1; Repeat the above steps to determine the arc of the right wall 2. The three-center circle fitting method for the inner contour of the anchor section of a railway tunnel according to claim 1 is characterized by: When laying ballastless track, the track bed width a is 190cm, and when laying ballasted track, the track bed width a is 220cm; When laying ballastless track, the width b of the top surface of the ditch cover is 125cm, and when laying ballasted track, the width b of the top surface of the ditch cover is 115cm.

3. The three-center circle fitting method for the inner contour of the anchor section of a railway tunnel according to claim 1 is characterized by: The inverted arch inner contour fitting specifically includes the following steps: Draw a line segment OE downward from the origin O of the coordinate axis, OE is the vector height, satisfying Take point E as the base point, take the line segment EO3 upwards, and draw a circle with O3 as the center and EO3 as the radius, which is connected to the arc of the side wall. and The extension line intersects at points F and G; connecting points F and G forms an inverted arc with EO3 The corresponding central angle is γ; The corresponding central angle is β2.

4. The three-center circle fitting method for the inner contour of the anchor section of a railway tunnel according to claim 3 is characterized by: According to the fitting principle from top to bottom and from left to right, the control parameters of the inner contour of the tunnel anchor section are obtained: Where H is the height from the rail surface to the arch top; r1, r2, r3 are the radii of circle 1, circle 2, and circle 3; r1, r3, and O1O are pre-given dimensions; h is the vertical distance from the arch foot to the arch top; α is the central angle of circle 1; β1 is the arc The central angle of the circle; β2 is the arc The central angle of circle 3; γ is the central angle of circle 3; θ is the angle between chord CA and the vertical line; x F and y2 are the horizontal coordinate of point F and the vertical coordinate of O2 respectively, which can be obtained by calculating the coordinates of the control points.

5. The three-center circle fitting method for the inner contour of the anchor section of a railway tunnel according to claim 4 is characterized in that: The coordinates of the key control points A, B, C, D, T, and P of the inner contour are:

6. The method for fitting the inner contour of the anchor section of a railway tunnel according to claim 5, characterized in that: According to the equations of circles 2 and 3, fit the coordinates of the intersection point F and G of the side wall arc and the inverted arch arc: Among them, OE is a preset length; the coordinates of points F and G are a pair of rational number solutions to the equation group, and x2 is the horizontal coordinate of O2.

7. An electronic device for fitting the inner contour of a railway tunnel anchor section with three center circles, characterized in that: include: at least one processor; and at least one memory communicatively connected to the processor, wherein: the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the fitting method according to any one of claims 1 to 6.

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