Method for calculating surrounding rock pressure of shallow-buried unequal-span bifurcated tunnel

Abstract

The invention discloses a method for calculating surrounding rock pressure of a shallow-buried unequal-span bifurcated tunnel. The method mainly comprises the following steps: establishing a mechanical model of the shallow-buried unequal-span bifurcated tunnel; calculating the slip surface side resistance of the wedge block on the outer side of the large-span hole; the horizontal lateral pressure coefficient of the outer side of the large-span hole is calculated; calculating the side resistance of the trapezoidal block on the inner side of the large-span hole; calculating a horizontal lateral pressure coefficient of the inner side of the large-span hole; calculating the vertical surrounding rock pressure and the horizontal surrounding rock pressure of the large-span hole; and calculating the vertical surrounding rock pressure and the horizontal surrounding rock pressure of the small-span hole. The calculation method is provided for determining the surrounding rock pressure of the shallow-buried unequal-span bifurcated tunnel, the condition that the fracture surface is inclined can be considered, and the influence of the relative size and the relative position of the two bifurcated tunnels can be considered.

Description

Technical Field

[0001] The present invention relates to the field of tunnel design and construction, and in particular to a method for calculating the surrounding rock pressure of a shallow-buried unequal-span bifurcated tunnel. Background Art

[0002] A bifurcated tunnel is a tunnel project where two lines intersect or diverge. The intersection of a bifurcated tunnel includes both small-span sections and large-span sections. The cross-section and orientation of the two branch lines can be adjusted as needed, allowing the cross-section to increase in size as traffic volume increases. Furthermore, bifurcated tunnels can effectively reduce ground occupation, conserving land resources.

[0003] Unequal span bifurcated tunnels are more complex than separated equal span double-hole tunnels and equal span small clear distance tunnels. The surrounding rock pressure is not only affected by the clear distance between the two holes, but also by factors such as the relative vertical position of the two holes and the relative size of different spans. There is no content on the calculation of the surrounding rock pressure of bifurcated tunnels in the existing "Highway Tunnel Design Code" and "Railway Tunnel Design Code". There are existing literature on the surrounding rock pressure of unequal span tunnels, but the calculated failure surface is a straight line, which is not consistent with the actual non-linear failure. The present invention mainly proposes a model and method for calculating the surrounding rock pressure of shallow buried unequal span bifurcated tunnels based on the establishment of an oblique failure model. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for calculating the surrounding rock pressure of a shallow buried unequal span bifurcated tunnel in order to solve the above technical problems existing in the prior art.

[0005] The above-mentioned object of the present invention is achieved through the following technical solutions.

[0006] The method for calculating the surrounding rock pressure of a shallow-buried unequal-span bifurcated tunnel of the present invention comprises the following steps in sequence.

[0007] (1) Establish a mechanical model of a shallow-buried bifurcated tunnel with unequal spans.

[0008] (2) Calculate the side resistance of the sliding surface of the wedge block on the outside of the large-span tunnel using the following formula.

[0009] .

[0010] Where, T a1 is the lateral resistance on the sliding surface BK of the large-span tunnel; h a The distance from the ground surface to the bottom of the large-span tunnel arch; β a1 is the fracture angle on the fracture surface AK on the left side of the large-span tunnel; f Calculate friction angle for surrounding rock; α a1is the slip angle on the large-span tunnel slip surface BK; γ is the weight of the surrounding rock; i 1 is the friction angle on the sliding surface BK of the large-span tunnel.

[0011] in, β a1 It can be expressed by the following formula.

[0012] .

[0013] Where, represents the length of KR, which is expressed by the following formula.

[0014] .

[0015] Where, k 1. k 2. k 3. k 4 are all intermediate variables, , , , .

[0016] Furthermore, combined with the side resistance boundary condition d T a1 | y=0 =0, the slip angle can be obtained α a1 and rupture angle β a1 .

[0017] Among them, d T a1 It is expressed by the following formula.

[0018] .

[0019] Where, t 1. t 2. t 3. t 4. t 5. t 6 is the intermediate variable, , , , , , .

[0020] (3) Calculate the horizontal side pressure coefficient outside the large-span tunnel using the following formula.

[0021] .

[0022] Where λ a1is the horizontal side pressure coefficient outside the large-span tunnel.

[0023] (4) Calculate the side resistance of the trapezoidal blocks inside the large-span tunnel, which is determined by the following formula.

[0024] . .

[0025] Where, T a2 is the lateral resistance on the sliding surface CJ of the large-span tunnel; l a The intersection point between the inner edge of the large-span tunnel and the fracture surface N Horizontal distance; i 2 is the friction angle on the sliding surface CJ of the large-span tunnel; β a2 is the rupture angle on the rupture surface NJ on the right side of the large-span tunnel.

[0026] in, β a2 It can be determined by the following formula.

[0027] .

[0028] (5) Calculate the horizontal side pressure coefficient inside the large-span tunnel, which is determined by the following formula.

[0029] .

[0030] Where λ a2 is the horizontal side pressure coefficient inside the large-span tunnel.

[0031] (6) Calculate the vertical and horizontal surrounding rock pressures of large-span tunnels, which are determined by the following formula.

[0032] .

[0033] .

[0034] .

[0035] .

[0036] .

[0037] Where, q a1 is the vertical surrounding rock pressure outside the large-span tunnel; q a2 is the vertical surrounding rock pressure inside the large-span tunnel; q a is the average vertical pressure of the large-span tunnel; b a It is a large tunnel span;h a1 is the distance from the large-span cave vault to the ground surface; e a1i is the horizontal surrounding rock pressure outside the large-span tunnel; e a2i is the horizontal surrounding rock pressure inside the large-span tunnel; h ai It is the vertical distance from the calculation point to the vault of the large-span cave.

[0038] (7) Similarly, the small-span tunnel can be derived similarly to the large-span tunnel, and the vertical and horizontal surrounding rock pressures of the small-span tunnel can be calculated, which are determined by the following formula.

[0039] .

[0040] .

[0041] .

[0042] .

[0043] .

[0044] Where, q b1 is the vertical surrounding rock pressure outside the small span tunnel; q b2 is the vertical surrounding rock pressure inside the small span tunnel; q b is the average vertical pressure of the small span tunnel; b b It is the span of a small tunnel; h b1 is the distance from the small span arch to the ground surface; l b1 is the horizontal side pressure coefficient outside the small span tunnel; l b2 is the horizontal side pressure coefficient inside the small span tunnel; α b1 is the slip angle on the small span tunnel slip surface FK; e b1i is the horizontal surrounding rock pressure outside the small span tunnel; e b2i is the horizontal surrounding rock pressure inside the small span tunnel; h bi is the vertical distance from the calculation point to the small span arch top; l b2 is the horizontal side pressure coefficient inside the small span tunnel; l b1 is the horizontal side pressure coefficient outside the small span tunnel.

[0045] Compared with the existing technology and research methods, the present invention has the following advantages: The existing technical research objects are mainly focused on the analysis of surrounding rock pressure of equal-span tunnels with small clearance, and there is little research on unequal-span bifurcated tunnels.

[0046] This invention provides a theoretical calculation method for determining the surrounding rock pressure of shallow, unequal-span bifurcated tunnels. By varying the depth, relative position, and relative size of the two tunnels in the bifurcated tunnel, the surrounding rock pressure under varying depths, relative positions, and relative sizes can be determined, providing a theoretical basis for the design and construction of shallow, unequal-span bifurcated tunnels. This method can be applied to the calculation and safety assessment of surrounding rock pressure in shallow underground projects with unequal spans and small spacing, such as those involved in the construction of adjacent mining tunnels, hydraulic tunnels, and subway tunnels. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 This is the calculation diagram of the surrounding rock pressure of the shallow buried unequal span tunnel of the present invention.

[0048] In the figure, b a For the large hole span; b b is the span of the small hole; h a is the distance from the ground surface to the bottom of the large hole ( h a1 For burial depth, h a2 is height); h b is the distance from the ground surface to the bottom of the small hole ( h b1 For burial depth, h b2 is height); l is the tunnel clearance ( l a and l b The intersection point between the inner edge of the double holes and the fracture surface N horizontal distance); W a1 、 W a 、 W a2 is the weight of the large hole block; W b1 、 W b 、 W b2 is the weight of the small hole block; T a1 、 T a2、T b1 and T b1 is the side resistance of the slip surface; F a1 、F a2 、F b1 and F b2 is the fracture surface supporting force; f Calculate the friction angle for the fracture surface; i 1 is the friction angle of the outer sliding surface; i 2 is the friction angle of the inner sliding surface; i 1 and i 2 According to the specification f The value is reduced; β a1 、 β a2 、 β b1 and β b2 is the rupture angle on the rupture surface; α a1 、 α b1 is the slip angle on the slip surface of the large hole and the small hole.

[0049] Figure 2 This is the surrounding rock pressure distribution diagram of the shallow buried unequal span bifurcated tunnel of the present invention.

[0050] In the figure, q a1 is the vertical surrounding rock pressure outside the large-span tunnel; q a2 is the vertical surrounding rock pressure inside the large-span tunnel; e b1i is the horizontal surrounding rock pressure outside the small span tunnel; e b2i is the horizontal surrounding rock pressure inside the small span tunnel; e a1i is the horizontal surrounding rock pressure outside the large-span tunnel; e a2i It is the horizontal surrounding rock pressure inside the large-span tunnel.

[0051] Figure 3 This is the calculation diagram of the wedge block outside the large span hole of the shallow buried unequal span bifurcated tunnel of the present invention.

[0052] Figure 4 This is the microelement bar diagram of the wedge-shaped block outside the large-span tunnel of the shallow-buried unequal-span bifurcated tunnel of the present invention.

[0053] Figure 5 The outer rupture angle of the large span tunnel of the shallow buried unequal span bifurcated tunnel of the present inventionβ a1 Graphical diagram of the method.

[0054] Figure 6 This paper implements the calculation example of the present invention to study the influence of the buried depth on the vertical surrounding rock pressure of a shallow bifurcated tunnel. DETAILED DESCRIPTION

[0055] The present invention will be further described below with reference to the accompanying drawings and examples.

[0056] The specific data of this embodiment project are as follows: h a1 =15m, height of the large hole h a2 =9.55m, large hole span b a =11.9m, height of the small hole h b2 =9.2m, the span of the small hole is b b =10.7m, tunnel spacing l =10m, the surrounding rock grade is V, the bulk density c =19.5 kN / m³, calculated friction angle of fracture surface f =48°, i 1=31.2°, i 2=28.8°.

[0057] See also Figure 1~Figure 5 The calculation method of the surrounding rock pressure of the shallow-buried unequal-span bifurcated tunnel in this embodiment is as follows.

[0058] A method for calculating surrounding rock pressure of a shallow-buried bifurcated tunnel with unequal spans is characterized by comprising the following steps in sequence.

[0059] (1) Establish a mechanical model of a shallow-buried bifurcated tunnel with unequal spans.

[0060] (2) Calculate the side resistance of the sliding surface of the wedge block on the outside of the large-span tunnel using the following formula.

[0061] .

[0062] Where, T a1 is the lateral resistance on the sliding surface BK of the large-span tunnel; h a The distance from the ground surface to the bottom of the large-span tunnel arch; β a1 is the fracture angle on the fracture surface AK on the left side of the large-span tunnel; f Calculate friction angle for surrounding rock; α a1 is the slip angle on the large-span tunnel slip surface BK; γ is the weight of the surrounding rock; i 1 is the friction angle on the sliding surface BK of the large-span tunnel.

[0063] in, β a1 It can be expressed by the following formula.

[0064] .

[0065] Where, represents the length of KR, which is expressed by the following formula.

[0066] .

[0067] Where, k 1. k 2. k 3. k 4 are all intermediate variables, , , , .

[0068] Furthermore, combined with the side resistance boundary condition d T a1 | y=0 =0, the slip angle can be obtained α a1 and rupture angle β a1 .

[0069] Among them, d T a1 It is expressed by the following formula.

[0070] .

[0071] Where, t 1. t 2. t 3. t 4. t 5. t 6 is the intermediate variable, , , , , , .

[0072] (3) Calculate the horizontal side pressure coefficient outside the large-span tunnel using the following formula.

[0073] .

[0074] Where λ a1 is the horizontal side pressure coefficient outside the large-span tunnel.

[0075] (4) Calculate the side resistance of the trapezoidal blocks inside the large-span tunnel, which is determined by the following formula.

[0076] . .

[0077] Where, T a2 is the lateral resistance on the sliding surface CJ of the large-span tunnel; l a The intersection point between the inner edge of the large-span tunnel and the fracture surface N Horizontal distance; i 2 is the friction angle on the sliding surface CJ of the large-span tunnel; β a2 is the rupture angle on the rupture surface NJ on the right side of the large-span tunnel.

[0078] in, β a2 It can be determined by the following formula.

[0079] .

[0080] (5) Calculate the horizontal side pressure coefficient inside the large-span tunnel, which is determined by the following formula.

[0081] .

[0082] Where λ a2 is the horizontal side pressure coefficient inside the large-span tunnel.

[0083] (6) Calculate the vertical and horizontal surrounding rock pressures of large-span tunnels, which are determined by the following formula.

[0084] .

[0085] .

[0086] .

[0087] .

[0088] .

[0089] Where, q a1 is the vertical surrounding rock pressure outside the large-span tunnel; q a2 is the vertical surrounding rock pressure inside the large-span tunnel; q a is the average vertical pressure of the large-span tunnel; b a It is a large tunnel span; h a1 is the distance from the large-span cave vault to the ground surface;e a1i is the horizontal surrounding rock pressure outside the large-span tunnel; e a2i is the horizontal surrounding rock pressure inside the large-span tunnel; h ai It is the vertical distance from the calculation point to the vault of the large-span cave.

[0090] (7) Similarly, the small-span tunnel can be derived similarly to the large-span tunnel, and the vertical and horizontal surrounding rock pressures of the small-span tunnel can be calculated, which are determined by the following formula.

[0091] .

[0092] .

[0093] .

[0094] .

[0095] .

[0096] Where, q b1 is the vertical surrounding rock pressure outside the small span tunnel; q b2 is the vertical surrounding rock pressure inside the small span tunnel; q b is the average vertical pressure of the small span tunnel; b b It is the span of a small tunnel; h b1 is the distance from the small span arch to the ground surface; l b1 is the horizontal side pressure coefficient outside the small span tunnel; l b2 is the horizontal side pressure coefficient inside the small span tunnel; α b1 is the slip angle on the small span tunnel slip surface FK; e b1i is the horizontal surrounding rock pressure outside the small span tunnel; e b2i is the horizontal surrounding rock pressure inside the small span tunnel; h bi is the vertical distance from the calculation point to the small span arch top; l b2 is the horizontal side pressure coefficient inside the small span tunnel; l b1 is the horizontal side pressure coefficient outside the small span tunnel.

[0097] According to the above method and steps, by changing the tunnel burial depth, the influence of the burial depth on the vertical surrounding rock pressure of shallow unequal span bifurcated tunnels can be obtained. Figure 6 As shown in the figure, with the increase of burial depth, the surrounding rock pressure of both holes of the unequal-span bifurcated tunnel increases; under shallow burial, the surrounding rock pressure of the small-span hole is greater than that of the large-span hole, because in this calculation condition, the burial depth of the small-span tunnel is greater than that of the large-span tunnel, that is, under shallow burial, the burial depth is a very important factor affecting the size of the surrounding rock pressure. Compared with the span, the burial depth is decisive.

Claims

1. A method for calculating surrounding rock pressure of shallow buried unequal span bifurcated tunnels, characterized in that The steps include the following sequence: (1) Establish a mechanical model for shallow-buried unequal-span bifurcated tunnels; (2) Calculate the side resistance of the sliding surface of the wedge block outside the large-span tunnel using the following formula: ； Where, T a1 is the lateral resistance on the sliding surface BK of the large-span tunnel; h a The distance from the ground surface to the bottom of the large-span tunnel arch; β a1 is the fracture angle on the fracture surface AK on the left side of the large-span tunnel; φ Calculate friction angle for surrounding rock; α a1 is the slip angle on the large-span tunnel slip surface BK; γ is the weight of the surrounding rock; θ 1 is the friction angle on the sliding surface BK of the large-span tunnel; in, β a1 It can be expressed by the following formula: ； Where, represents the length of KR, which is expressed by the following formula, ； Where, k 1. k 2. k 3. k 4 are all intermediate variables, , , , ; Furthermore, combined with the side resistance boundary condition d T a1 | y=0 =0, the slip angle can be obtained α a1 and rupture angle β a1 ; Among them, d T a1 It is expressed by the following formula: ； Where, t 1. t 2. t 3. t 4. t 5. t 6 is the intermediate variable, , , , , , ; (3) Calculate the horizontal pressure coefficient outside the large-span tunnel using the following formula: ； Where λ a1 is the horizontal side pressure coefficient outside the large-span tunnel; (4) Calculate the side resistance of the trapezoidal block inside the large-span tunnel, which is determined by the following formula: ； Where, T a2 is the lateral resistance on the sliding surface CJ of the large-span tunnel; l a The intersection point between the inner edge of the large-span tunnel and the fracture surface N Horizontal distance; θ 2 is the friction angle on the sliding surface CJ of the large-span tunnel; β a2 is the rupture angle on the rupture surface NJ on the right side of the large-span tunnel; in, β a2 It can be determined by the following formula: ； (5) Calculate the horizontal pressure coefficient inside the large-span tunnel, which is determined by the following formula: ； Where λ a2 is the horizontal side pressure coefficient inside the large-span tunnel; (6) Calculate the vertical and horizontal surrounding rock pressures of large-span tunnels, which are determined by the following formula: ； ； ； ； ； Where, q a1 is the vertical surrounding rock pressure outside the large-span tunnel; q a2 is the vertical surrounding rock pressure inside the large-span tunnel; q a is the average vertical pressure of the large-span tunnel; b a It is a large tunnel span; h a1 is the distance from the large-span cave vault to the ground surface; e a1i is the horizontal surrounding rock pressure outside the large-span tunnel; e a2i is the horizontal surrounding rock pressure inside the large-span tunnel; h ai is the vertical distance from the calculation point to the vault of the large-span cave; (7) Similarly, the small-span tunnel can be derived similarly to the large-span tunnel. The vertical and horizontal surrounding rock pressures of the small-span tunnel can be calculated and determined by the following formula: ； ； ； ； ； Where, q b1 is the vertical surrounding rock pressure outside the small span tunnel; q b2 is the vertical surrounding rock pressure inside the small span tunnel; q b is the average vertical pressure of the small span tunnel; b b It is the span of a small tunnel; h b1 is the distance from the small span arch to the ground surface; λ b1 is the horizontal side pressure coefficient outside the small span tunnel; λ b2 is the horizontal side pressure coefficient inside the small span tunnel; α b1 is the slip angle on the small span tunnel slip surface FK; e b1i is the horizontal surrounding rock pressure outside the small span tunnel; e b2i is the horizontal surrounding rock pressure inside the small span tunnel; h bi is the vertical distance from the calculation point to the small span arch top; λ b2 is the horizontal side pressure coefficient inside the small span tunnel; λ b1 is the horizontal side pressure coefficient outside the small span tunnel.

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