A method for evaluating the influence of over-excavation of shallow tunnels on crown collapse

Abstract

The present invention discloses a method for evaluating the influence of over-excavation of shallow tunnels on the collapse of the arch part. It mainly includes the following steps: determining the over-excavation shape and over-excavation area according to the over-excavation situation of the shallow tunnel; calculating the work done by the gravity of the collapsed body of the shallow tunnel; calculating the energy dissipation in the collapsed body of the shallow tunnel; solving the collapse range and the magnitude of the collapse volume according to the principle of minimum energy dissipation and boundary conditions; changing different over-excavation angles, over-excavation heights, and over-excavation areas to evaluate their influence on the collapse range and collapse magnitude of the shallow tunnel. The present invention can be applied to the analysis of the influence of over-excavation of the arch part on collapse in shallow underground engineering, and can consider the influence of factors such as over-excavation angle, over-excavation height, and over-excavation area, providing theoretical method guidance for evaluating the influence of over-excavation and the reinforcement and prevention of collapse.

Description

Technical Field

[0001] The present invention belongs to the technical field of tunnel construction, and particularly relates to a method for evaluating the influence of over-excavation of shallow tunnels on crown collapse. Background Art

[0002] With the construction of more and more tunnels, such as a large proportion of tunnels in the current Sichuan-Tibet line. Affected by the geological conditions of the surrounding rock itself and drilling and blasting construction parameters, over-excavation is a common phenomenon at tunnel construction sites. Currently, the relevant research literature mainly focuses on the influence of over-excavation on the deformation and stress of the surrounding rock, and most of the existing patents are some detection and control devices, such as the patent: a spaced charging tool for linear over-excavation control of railway tunnels (CN201922381532.5), etc. Tunnel collapse is a common accident, and over-excavation is also the main inducement for tunnel collapse. Especially for shallow tunnels, when the over-excavation is too large, roof collapse will occur. However, there is no literature analyzing the influence of over-excavation on the collapse of shallow tunnels theoretically, nor is there a corresponding evaluation method. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for evaluating the influence of over-excavation of shallow tunnels on crown collapse in view of the above technical problems existing in the prior art.

[0004] The purpose of the present invention is achieved by the following technical solutions.

[0005] The method for evaluating the influence of over-excavation of shallow tunnels on crown collapse includes the following steps.

[0006] A method for evaluating the influence of over-excavation of shallow tunnels on crown collapse, characterized by including the following steps:

[0007] (1) According to the over-excavation situation of the shallow tunnel, determine the over-excavation shape and over-excavation area; the over-excavation shape is simplified to a triangle, and its over-excavation area is determined by the following formula.

[0008] .

[0009] In the formula, S c is the over-excavation area; R is the radius of the tunnel crown; θ is the over-excavation angle; h is the over-excavation height; π is the pi.

[0010] (2) Calculate the work done by the gravity of the shallow tunnel collapse body, which is determined by the following formula.

[0011] .

[0012] In the formula, P γis the work done by the gravity of the shallow-buried tunnel collapse body; L 1 is half of the width of the ground collapse area of the shallow-buried tunnel, L 2 is half of the width of the in-tunnel collapse area of the shallow-buried tunnel; γ is the unit weight of the surrounding rock; g ( x ) is the tunnel arch contour function; f ( x ) is the collapse shape function; v is the kinematically admissible velocity field; x in the rectangular coordinate system x axis coordinate value;

[0013] Among them, the tunnel arch contour function g( x ) is specifically determined by the following formula.

[0014] .

[0015] In the formula, H is the burial depth of the shallow-buried tunnel.

[0016] (3)Calculate the energy dissipation in the shallow-buried tunnel collapse body, which is determined by the following formula.

[0017] .

[0018] In the formula, P D is the energy dissipation in the shallow-buried tunnel collapse body; is the uniaxial compressive strength of the intact surrounding rock; A 、 B are the surrounding rock parameters; is f(x) tangent slope of, that is, the first derivative; is the tensile strength of the surrounding rock.

[0019] (4)According to the principle of minimum energy dissipation and boundary conditions, solve the collapse range and the size of the collapse volume, which includes the following steps.

[0020] (Ⅰ)Construct the following function from the work done by the gravity of the shallow-buried tunnel collapse body and the internal energy dissipation.

[0021] .

[0022] In the formula: is the difference between the energy dissipation in the shallow-buried tunnel collapse body and the work done by the gravity of the collapse body; , is the functional.

[0023] (Ⅱ)From the variational principle of the functional, the corresponding Euler equation can be obtained as follows.

[0024] .

[0025] Combined with the boundary conditions, the solution is as follows: .

[0026] In the formula, c 1 is the coefficient.

[0027] (III) It can be known from the geometric conditions.

[0028] .

[0029] From this, the following formula can be obtained.

[0030] .

[0031] (IV) According to the law of conservation of energy, that is, the work done by the gravity of the collapsed soil mass in a shallow-buried tunnel is equal to the internal energy dissipation, it can be obtained.

[0032] .

[0033] (V) Combining the formulas in steps (III) and (IV) can form a system of equations, so that the width 2 of the surface collapse area of the shallow-buried tunnel L 1 and the width 2 of the in-tunnel collapse area L 2 can be solved, and the size of the collapse, that is, the collapse area, can be obtained from the following formula.

[0034] .

[0035] In the formula, S is the collapse area.

[0036] (VI) According to the above, combined with the actual over-excavation situation, the collapse range of the shallow-buried tunnel caused by over-excavation can be obtained, including the collapse area, collapse height and collapse width; by changing the relevant parameters of the over-excavation height, over-excavation angle and over-excavation area, the influence of the over-excavation height, over-excavation angle and over-excavation area on the arch collapse of the shallow-buried tunnel can be obtained, so as to provide a theoretical method guidance for evaluating the influence of over-excavation and the reinforcement and prevention of the collapse of the shallow-buried tunnel.

[0037] Compared with the existing technologies and research methods, the present invention has the following advantages.

[0038] The existing literature technology research mainly focuses on the influence of over-excavation on the surrounding rock and support; the existing patent technologies only focus on the inspection or control devices of over-excavation, etc. There is a lack of research on the influence of over-excavation on the collapse of shallow-buried tunnels, as well as how large the collapse range of shallow-buried tunnels is after over-excavation, what the collapse height and width are, which directly affect the subsequent treatment and reinforcement of the collapse.

[0039] The present invention provides a theoretical calculation method for evaluating the influence of over-excavation of shallow tunnels on arch collapse. By changing relevant parameters such as the over-excavation height and over-excavation angle, the influence of the over-excavation height and over-excavation angle on the collapse of shallow tunnels can be obtained, thereby providing a reference for the treatment of collapses under the influence of over-excavation. The method of the present invention can not only be applied to traffic tunnels, but also to the analysis of the influence of over-excavation on collapses in underground projects such as mining roadways, hydraulic tunnels, and subway interval tunnels, thereby providing theoretical method guidance for evaluating the influence of over-excavation and the reinforcement and prevention of collapses. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic diagram of tunnel collapse under over-excavation in an embodiment of the present invention.

[0041] Figure 1 In H is the tunnel burial depth; L 1 is half of the width of the ground collapse area of the shallow tunnel, L 2 is half of the width of the in-tunnel collapse area of the shallow tunnel;; R is the radius of the tunnel arch; θ is the over-excavation angle; h is the over-excavation height; f(x) is the collapse shape function; g ( x ) is the tunnel arch contour function; v is the kinematically admissible velocity field; x in the rectangular coordinate system x axis coordinate value.

[0042] Figure 2 is the influence of different over-excavation heights on the collapse height, collapse width, and collapse area.

[0043] Figure 3 is the influence of different over-excavation angles on the collapse height, collapse width, and collapse area.

[0044] The present invention will be further described below in conjunction with the drawings and embodiments.

[0045] The specific data of this embodiment project are as follows: When studying the influence of the over-excavation height h , the other parameter values are respectively: A =0.15, B =0.6, σ c =0.5MPa, σ t = σ c / 100, R =11m, γ = 20kN / m 3 , θ= 6°, overexcavation height h Six cases of 0 m, 0.2 m, 0.4 m, 0.6 m, 0.8 m, and 1.0 m are selected for calculation respectively.

[0046] Study the influence of overexcavation angle θ When, the other parameter values are as follows: A = 0.15, B = 0.6, σ c = 0.5 MPa, σ t = σ c / 100, R = 11 m, γ = 20 kN / m 3 , h = 0.6 m, overexcavation angle θ Six cases of 0°, 2°, 4°, 6°, 8°, and 10° are selected for calculation respectively.

[0047] See Figure 1 , the method for evaluating the influence of overexcavation of shallow - buried tunnel on arch collapse in this embodiment is as follows.

[0048] (1) According to the overexcavation situation of the shallow - buried tunnel, determine the overexcavation shape and overexcavation area; the overexcavation shape is simplified to a triangle, and its overexcavation area is determined by the following formula.

[0049] .

[0050] In the formula, S c is the overexcavation area; R is the radius of the tunnel arch; θ is the overexcavation angle; h is the overexcavation height; π is the pi.

[0051] (2) Calculate the work done by the gravity of the shallow - buried tunnel collapse body, which is determined by the following formula.

[0052] .

[0053] In the formula, P γ is the work done by the gravity of the shallow - buried tunnel collapse body; L 1 is half of the width of the ground collapse area of the shallow - buried tunnel, L 2 is half of the width of the in - tunnel collapse area of the shallow - buried tunnel; γ is the unit weight of the surrounding rock; g ( x ) is the tunnel arch contour function; f ( x ) is the collapse shape function; v is the kinematically admissible velocity field; xIn the rectangular coordinate system x The coordinate value on the

[0054] Among them, the tunnel arch profile function g( x ) is specifically determined by the following formula.

[0055] .

[0056] In the formula, H is the buried depth of the shallow-buried tunnel.

[0057] (3) Calculate the energy dissipation in the collapse body of the shallow-buried tunnel, which is determined by the following formula.

[0058] .

[0059] In the formula, P D is the energy dissipation in the collapse body of the shallow-buried tunnel; is the compressive strength of the intact surrounding rock; A , B are the surrounding rock parameters; is f(x) The tangent slope of, that is, the first derivative; is the tensile strength of the surrounding rock.

[0060] (4) According to the principle of minimum energy consumption and boundary conditions, solve the collapse range and the size of the collapse volume, which includes the following steps.

[0061] (Ⅰ) From the work done by the gravity of the collapse body of the shallow-buried tunnel and the internal energy dissipation, construct the following function.

[0062] .

[0063] In the formula: is the difference between the energy dissipation in the collapse body of the shallow-buried tunnel and the work done by the gravity of the collapse body; , is a functional.

[0064] (Ⅱ) From the variational principle of the functional, the corresponding Euler equation can be obtained as.

[0065] .

[0066] Combined with the boundary conditions, the solution is: .

[0067] In the formula, c 1 is a coefficient.

[0068] (Ⅲ) From the geometric conditions, it can be known that.

[0069] .

[0070] The following formula can be obtained therefrom.

[0071] .

[0072] (IV) According to the law of conservation of energy, that is, the work done by the gravity of the collapsed body of the shallow-buried tunnel is equal to the internal energy dissipation, it can be obtained that

[0073] .

[0074] (V) Combining the formulas in steps (III) and (IV) can form a system of equations, so that the width 2 L 1 of the surface collapse area of the shallow-buried tunnel and the width 2 L 2 of the in-tunnel collapse area can be solved, and the size of the collapse, that is, the collapse area, can be obtained from the following formula.

[0075] .

[0076] In the formula, S is the collapse area.

[0077] (VI) According to the above, combined with the actual over-excavation situation, the collapse range of the shallow-buried tunnel caused by over-excavation can be obtained, including the collapse area, collapse height and collapse width; by changing the relevant parameters of the over-excavation height, over-excavation angle and over-excavation area, the influence of the over-excavation height, over-excavation angle and over-excavation area on the arch collapse of the shallow-buried tunnel can be obtained, so as to provide theoretical method guidance for evaluating the influence of over-excavation and the reinforcement and prevention of the collapse of the shallow-buried tunnel.

[0078] According to the above method steps, the influence of different over-excavation heights and over-excavation angles on the collapse height, collapse width and collapse area can be obtained, as shown in Figure 2 and Figure 3 . It can be seen from the figure that with the increase of the over-excavation height h and the over-excavation angle θ , the shape of the collapse surface expands, the collapse width gradually increases, and the collapse height also gradually increases, resulting in an increasing trend of the area of the collapse surface.

Claims

1. A method for evaluating the influence of over-excavation of shallow tunnels on arch collapse, characterized in that It includes the following steps: (1) Determine the over-excavation shape and over-excavation area according to the over-excavation condition of the shallow-buried tunnel. The over-excavation shape is simplified to a triangle, and its over-excavation area is determined by the following formula: ； Wherein, S c is the area of the over-excavated area; R is the radius of the tunnel crown; θ is the over-excavation angle; h is the over-excavation height; π is the pi; (2) Calculate the work done by the gravity of the collapsed mass of the shallow-buried tunnel, which is determined by the following formula: ； Where P γ is the work done by the gravity of the collapsed body in the shallow-buried tunnel; L 1 is half of the width of the surface collapse area of the shallow-buried tunnel, L 2 is half of the width of the in-tunnel collapse area of the shallow-buried tunnel; γ is the unit weight of the surrounding rock; g ( x ) is the contour function of the tunnel arch; f ( x ) is the collapse shape function; v is the kinematically admissible velocity field; x in the rectangular coordinate system x is the coordinate value of the x-axis; Among them, the tunnel arch profile function g( x ) is specifically determined by the following formula: ； In the formula, H is the buried depth of the shallow-buried tunnel; (3) Calculate the energy dissipation in the collapsed mass of the shallow-buried tunnel, which is determined by the following formula: ； where P D is the energy dissipation in the collapse body of the shallow-buried tunnel; is the uniaxial compressive strength of the intact surrounding rock; A , B are the surrounding rock parameters; is f(x) 's tangent slope, i.e., the first derivative; is the tensile strength of the surrounding rock; (4) According to the principle of minimum energy dissipation and boundary conditions, solve the collapse range and the magnitude of the collapsed volume, which includes the following steps: (Ⅰ) Construct the following function from the work done by the gravity of the collapsed mass of the shallow-buried tunnel and the energy dissipation: ； In the formula: is the difference between the energy dissipation in the collapse body of the shallow-buried tunnel and the work done by the gravity of the collapse body; , is a generic function; (Ⅱ) According to the variational principle of the functional, the corresponding Euler equation can be obtained as follows: ； Combined with the boundary conditions, the solution can be obtained as follows: ; In the formula, c 1 is a coefficient; (Ⅲ) From the geometric conditions, it can be known that: ； Thus, the following formula can be obtained: ； (Ⅳ) According to the law of conservation of energy, that is, the work done by the gravity of the collapsed mass of the shallow-buried tunnel is equal to the energy dissipation, it can be obtained that: ； (V) Combining the formulas in steps (III) and (IV) can form a system of equations, from which the width \(b_1\) of the ground collapse area of the shallow-buried tunnel and the width \(b_2\) of the in-tunnel collapse area can be solved. L The value of \(b_1\) and \(b_2\), and the size of the collapse, i.e., the collapse area, can be obtained by the following formula: L The value of \(b_2\), and the size of the collapse, i.e., the collapse area, can be obtained by the following formula: ； In the formula, S is the collapsed area; (Ⅵ) According to the above, combined with the actual over-excavation condition, the collapse range of the shallow-buried tunnel caused by over-excavation can be obtained, including the collapsed area, the collapsed height and the collapsed width. By changing the relevant parameters of the over-excavation height, over-excavation angle and over-excavation area, the influence of the over-excavation height, over-excavation angle and over-excavation area on the collapse of the arch of the shallow-buried tunnel can be obtained, so as to provide a theoretical method guidance for evaluating the influence of over-excavation and the reinforcement and prevention of the collapse of the shallow-buried tunnel.

Images