A method for evaluating the influence of overexcavation of deep-buried tunnels on arch collapse

Abstract

The present invention discloses a method for evaluating the influence of overexcavation of deep-buried tunnels on arch collapse. It mainly includes the following steps: determining the overexcavation shape and overexcavation area according to the overexcavation situation of deep-buried tunnels; calculating the work done by the gravity of the tunnel collapse body; calculating the energy dissipation in the tunnel collapse body; solving the collapse range and the magnitude of the collapse volume according to the principle of minimum energy dissipation and boundary conditions; changing different overexcavation heights, overexcavation angles, and overexcavation areas to evaluate their influence on the potential collapse range and collapse magnitude. The present invention provides a calculation method for evaluating the influence of overexcavation of deep-buried tunnels on arch collapse, and can consider the influence of overexcavation angle, overexcavation height, and overexcavation area, so as to provide a reference for the collapse treatment under the influence of overexcavation. The present invention can be applied to the analysis of the influence of arch overexcavation on collapse in deep-buried underground engineering, and provides a theoretical method guidance for evaluating the influence of overexcavation 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 deep-buried tunnels on arch collapse. Background Technique

[0002] Limited by factors such as construction technology level, topographic and geological conditions, measurement and setting-out accuracy, and organizational management ability, over-excavation will occur during the construction process of the drill-and-blast method; some over-excavations are also important factors inducing collapse. Existing patents and literature are basically about the control or device of over-excavation technology, such as the patent: A device and detection method for tunnel over-excavation and under-excavation detection (CN202110504803.0), etc. However, how to evaluate the influence of over-excavation on collapse has not been reported theoretically in the literature. The existing highway tunnel construction technical specifications only stipulate the allowable over-excavation amount, and do not involve the relevant regulations on the influence of over-excavation on surrounding rock collapse. Summary of the Invention

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

[0004] The purpose of the present invention is realized through the following technical solutions: The method for evaluating the influence of over-excavation of deep-buried tunnels on arch collapse includes the following steps.

[0005] (1) According to the over-excavation situation of the deep-buried 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.

[0006] .

[0007] In the formula, S c is the over-excavation area; R is the radius of the tunnel arch; θ is the over-excavation angle; h is the over-excavation height; π is the pi.

[0008] (2) Calculate the work done by the gravity of the deep-buried tunnel collapse body, which is determined by the following formula.

[0009] .

[0010] In the formula, P γ is the work done by the gravity of the deep-buried tunnel collapse body; L is half of the width of the collapse area; γ is the unit weight of the surrounding rock; f(x) is the collapse shape function; g ( x ) is the tunnel arch contour function; v is the kinematically admissible velocity field;x in a rectangular coordinate system x the x-axis coordinate value

[0011] Among them, the tunnel arch contour function g(x) is specifically determined by the following formula

[0012] .

[0013] (3) Calculate the energy dissipation in the deep-buried tunnel collapse body, which is determined by the following formula

[0014] .

[0015] In the formula P D is the energy dissipation in the deep-buried tunnel collapse body is the compressive strength of the intact surrounding rock A , B are the surrounding rock parameters is f ( x ) the tangent slope, that is, the first derivative is the tensile strength of the surrounding rock

[0016] (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

[0017] (I) Construct the following function from the work done by the gravity of the deep-buried tunnel collapse body and the internal energy dissipation

[0018] .

[0019] In the formula is the difference between the energy dissipation in the deep-buried tunnel collapse body and the work done by the gravity of the collapse body , is a functional

[0020] (II) From the variational principle of the functional, the corresponding Euler equation can be obtained as

[0021] .

[0022] Combined with the boundary conditions, the solution is .

[0023] In the formula H is the height of the tunnel collapse area .

[0024] (III) From the geometric conditions, it can be known that

[0025] .

[0026] Thus .

[0027] (IV) According to the law of conservation of energy, that is, the work done by the gravity of the collapsed body in the deeply buried tunnel is equal to the internal energy dissipation, we can obtain:

[0028] .

[0029] (V) Combining the formulas in steps (III) and (IV) can form a system of equations, from which the collapse height H and the collapse width 2 L can be solved. The size of the collapse, that is, the collapse area, can be obtained by the following formula:

[0030] .

[0031] In the formula: S is the collapse area.

[0032] (VI) According to the above, combined with the actual over-excavation situation, the collapse range caused by over-excavation can be obtained, including the collapse area, the collapse height and the collapse width; by changing the relevant parameters of the over-excavation height, the over-excavation angle and the over-excavation area, the influence of the over-excavation height, the over-excavation angle and the over-excavation area on the collapse of the deeply buried tunnel can be obtained, thus providing a theoretical method guidance for evaluating the influence of over-excavation and the reinforcement and prevention of collapse.

[0033] Compared with the existing technologies and research methods, the present invention has the following advantages.

[0034] The existing literature technology research mainly focuses on the influence of over-excavation on the surrounding rock and support; the existing patent technology only focuses on the inspection or control device of over-excavation, etc. There is a lack of research on the influence of over-excavation on the tunnel collapse, as well as the size of the tunnel collapse range after over-excavation, the collapse height and the collapse width, which directly affect the subsequent treatment and reinforcement.

[0035] The present invention provides a theoretical calculation method for evaluating the influence of over-excavation on the arch collapse of deeply buried tunnels; by changing the relevant parameters of the over-excavation height and the over-excavation angle, the influence of the over-excavation height and the over-excavation angle on the collapse of the deeply buried tunnel can be obtained, thus providing a reference for the collapse treatment 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 collapse in underground projects such as mining roadways, hydraulic tunnels, and subway interval tunnels, thus providing a theoretical method guidance for evaluating the influence of over-excavation and the reinforcement and prevention of collapse. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a schematic diagram of tunnel collapse under over-excavation in an embodiment of the present invention.

[0037] Figure 1 In, H is the height of the tunnel collapse area; L is half of the width of the collapse area; Ris the radius of the tunnel arch; θ is the over-excavation angle; h is the over-excavation height; h 1 is the collapse height at the crown; f(x) is the collapse shape function. g ( x ) is the contour function of the tunnel arch; v is the allowable velocity field of the vehicle; x in the rectangular coordinate system x axis coordinate value.

[0038] Figure 2 is the influence of different over-excavation heights on the collapse height, collapse width, and collapse area.

[0039] Figure 3 is the influence of different over-excavation angles on the collapse height, collapse width, and collapse area. Specific implementation mode

[0040] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0041] 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 = 0.3, B = 0.7, σ c = 5 MPa, σ t = σ c / 100, R = 11 m, γ = 20 kN / m 3 , θ = 30°, the over-excavation height h is respectively selected as six cases of 0 m, 0.2 m, 0.4 m, 0.6 m, 0.8 m, and 1.0 m for calculation.

[0042] When studying the influence of the over-excavation angle θ , the other parameter values are respectively: A = 0.3, B = 0.7, σ c = 5 MPa, σ t = σ c / 100, R = 11 m, γ = 20 kN / m 3 , h = 0.6 m, the over-excavation angle θ is respectively selected as six cases of 0°, 10°, 20°, 30°, 40°, and 50° for calculation.

[0043] See Figure 1 , the method for evaluating the influence of over-excavation of deep-buried tunnels on arch collapse in this embodiment is as follows:

[0044] (1) Determine the over-excavation shape and over-excavation area according to the over-excavation condition of the deep-buried tunnel; the over-excavation shape is simplified to a triangle, and its over-excavation area is determined by the following formula.

[0045] .

[0046] In the formula, S c is the over-excavation area; R is the radius of the tunnel arch; θ is the over-excavation angle; h is the over-excavation height; π is the pi.

[0047] (2) Calculate the work done by the gravity of the deep-buried tunnel collapse body, which is determined by the following formula.

[0048] .

[0049] In the formula, P γ is the work done by the gravity of the deep-buried tunnel collapse body; L is half of the width of the collapse area; γ is the unit weight of the surrounding rock; f(x) is the collapse shape function; g ( x ) is the tunnel arch profile function; v is the kinematically admissible velocity field; x is the x axis coordinate value in the rectangular coordinate system.

[0050] Among them, the tunnel arch profile function g(x) is specifically determined by the following formula.

[0051] .

[0052] (3) Calculate the energy dissipation in the deep-buried tunnel collapse body, which is determined by the following formula.

[0053] .

[0054] In the formula, P D is the energy dissipation in the deep-buried tunnel collapse body; is the uniaxial compressive strength of the intact surrounding rock; A , B are the surrounding rock parameters; is the f ( x ) tangent slope, that is, the first derivative; is the tensile strength of the surrounding rock.

[0055] (4) According to the principle of minimum energy consumption and boundary conditions, solve the collapse range and the amount of collapse, which includes the following steps.

[0056] (I) Construct the following function from the internal energy dissipation and the work done by the gravity of the collapse body in a deep-buried tunnel.

[0057] .

[0058] In the formula: is the difference between the internal energy dissipation in the collapse body of the deep-buried tunnel and the work done by the gravity of the collapse body; , is a functional.

[0059] (II) According to the variational principle of the functional, the corresponding Euler equation can be obtained as follows.

[0060] .

[0061] Combining the boundary conditions, the solution is: .

[0062] In the formula, H is the height of the tunnel collapse area; .

[0063] (III) From the geometric conditions, it can be known that.

[0064] .

[0065] Thus: .

[0066] (IV) According to the law of conservation of energy, that is, the work done by the gravity of the collapse body in the deep-buried tunnel is equal to the internal energy dissipation, it can be obtained that.

[0067] .

[0068] (V) Combining the formulas in steps (III) and (IV) can form a system of equations, so that the collapse height H and the collapse width 2 L can be solved. The size of the collapse, that is, the collapse area, can be obtained from the following formula:

[0069] .

[0070] In the formula: S is the collapse area.

[0071] (Ⅵ) According to the above, combined with the actual over-excavation situation, the collapse range 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 collapse of deep-buried tunnels can be obtained, thus providing theoretical method guidance for evaluating the influence of over-excavation and the reinforcement and prevention of collapse.

[0072] 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 Figure 2 and Figure 3 shown. It can be seen from the figure that as the over-excavation height h and the over-excavation angle θ increase, the shape of the collapse surface expands, the collapse width gradually increases, and the collapse height also gradually increases, resulting in an increasing trend in the area of the collapse surface.

Claims

1. A method for evaluating the influence of over-excavation of a deeply buried tunnel on the collapse of the arch part, 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 deep-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-excavation area; R is the radius of the tunnel arch; 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 body of the deep-buried tunnel, which is determined by the following formula: ； In the formula, P γ is the work done by the gravity of the collapse body of the deep-buried tunnel; L is half of the width of the collapse area; γ is the unit weight of the surrounding rock; f(x) is the collapse shape function; g ( x ) is the contour function of the tunnel arch; v is the kinematically admissible velocity field; x in the rectangular coordinate system x is the coordinate value of the Wherein, the tunnel arch contour function g(x) is specifically determined by the following formula: ； (3) Calculate the internal energy dissipation in the collapsed body of the deep-buried tunnel, which is determined by the following formula: ； In the formula, P D is the energy dissipation in the collapse body of the deep 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, that is, the first derivative; is the tensile strength of the surrounding rock; (4) According to the principle of minimum energy consumption and boundary conditions, solve the collapse range and the magnitude of the collapse volume, which includes the following steps: (Ⅰ) Construct the following function from the work done by the gravity of the collapsed body of the deep-buried tunnel and the internal energy dissipation: ； Wherein: is the difference between the energy dissipation in the collapse body of the deep-buried tunnel and the work done by the gravity of the collapse body; , is a functional; (Ⅱ) According to the variational principle of the functional, the corresponding Euler equation can be obtained as: ； Combined with the boundary conditions, the solution can be obtained as follows: ; In the formula, H is the height of the tunnel collapse area; ; (Ⅲ) From the geometric conditions, it can be known that: ； Thus: ; (Ⅳ) According to the law of conservation of energy, that is, the work done by the gravity of the collapsed body of the deep-buried tunnel is equal to the internal 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 collapse height can be solved. H and the collapse width 2 L , and the collapse size, i.e., the collapse area, can be obtained by the following formula: ； In the formula: S is the collapse area; (Ⅵ) According to the above, combined with the actual over-excavation condition, the collapse range 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 collapse of the deep-buried tunnel can be obtained, so as to provide a theoretical method guidance for evaluating the over-excavation influence and the reinforcement and prevention of the collapse.

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