A calculation method for determining influence of overbreak on collapse of deep-buried rectangular tunnel roof

Abstract

The application discloses a kind of calculation methods for determining the influence of overbreak on collapse of deep-buried rectangular tunnel roof.It mainly includes the following steps: according to the overbreak of deep-buried rectangular tunnel roof, determine the shape and area of overbreak;calculate the work done by gravity of deep-buried rectangular tunnel collapse body;calculate the energy dissipation inside deep-buried rectangular tunnel collapse body;according to the principle of minimum energy consumption and boundary conditions, solve the collapse range and the size of collapse;change different overbreak height, overbreak width, overbreak area, calculate its influence on the collapse range and the size of collapse.The application can be applied to the influence analysis of overbreak on collapse in deep-buried rectangular section form underground engineering, provides a calculation method for determining the influence of overbreak on collapse of deep-buried rectangular tunnel roof, and can consider the influence of overbreak width, overbreak height and overbreak area, provides theoretical method guidance for determining overbreak influence and collapse reinforcement and prevention, is conducive to safe construction.

Description

Technical Field

[0001] This invention belongs to the field of tunnel construction technology, specifically relating to a calculation method for determining the impact of over-excavation of the roof slab of a deeply buried rectangular tunnel on collapse. Background Technology

[0002] With the ongoing "Belt and Road" initiative and the development of a "transportation powerhouse," along with the expansion of urban underground space, numerous tunnels and underground engineering projects will be constructed, gradually trending towards deeper burial depths. In underground energy extraction, after the development of shallow resources, the focus is now shifting towards deeper resources, with mining depths continuously expanding underground, inevitably involving many deeply buried underground engineering projects. Due to the presence of rock joints and fissures, over-excavation and under-excavation are unavoidable even with controlled blasting. Over-excavation is even more severe when smooth blasting is not used or when increased explosive charges are used to expedite progress. Excessive over-excavation can induce landslides. Existing regulations, whether for water conservancy and hydropower or highway / railway tunnel construction, only specify permissible over-excavation amounts, without addressing the impact of over-excavation on surrounding rock collapses. Existing patents and literature primarily concern the impact of over-excavation on surrounding rock and support systems, or control devices. Reports on how to assess the impact of over-excavation on landslides are scarce. Summary of the Invention

[0003] The purpose of this invention is to address the aforementioned technical problems in the prior art by providing a calculation method for determining the impact of over-excavation of the roof slab of a deeply buried rectangular tunnel on collapse.

[0004] The objective of this invention is achieved through the following technical solution.

[0005] The calculation method for determining the impact of over-excavation of the roof slab of a deeply buried rectangular tunnel on landslides includes the following steps.

[0006] (1) Determine the over-excavation shape and over-excavation area based on the over-excavation situation of the top plate of the deep-buried rectangular tunnel; the over-excavation shape is simplified to a triangle, and its over-excavation area is determined by the following formula.

[0007] .

[0008] In the formula, S c The area of ​​the over-excavated zone; h This is the over-excavation height. t This refers to the over-excavation width.

[0009] (2) Calculate the work done by gravity in the collapse of a deep-buried rectangular tunnel, which is determined by the following formula.

[0010] .

[0011] In the formula, P γThe work done by gravity in the collapse of a deeply buried rectangular tunnel; L It is half the width of the collapse zone; γ is the unit weight of the surrounding rock; f ( x ) is the shape function of the collapse; v For the permissible speed field for maneuver; x In a rectangular coordinate system x Axis coordinate values.

[0012] (3) Calculate the energy dissipation in the collapse body of a deep-buried rectangular tunnel, which is determined by the following formula.

[0013] .

[0014] In the formula, P D This is for energy dissipation within the collapsed body of a deeply buried rectangular tunnel; The compressive strength of the intact surrounding rock; A , B These are the parameters of the surrounding rock. for f(x) The slope of the tangent line, i.e., the first derivative; This represents the tensile strength of the surrounding rock.

[0015] (4) Based on the principle of minimum energy consumption and boundary conditions, solve the collapse range and collapse volume of the deep-buried rectangular tunnel, which includes the following steps.

[0016] (I) Construct the following function based on the work done by gravity and the dissipation of internal energy in the collapse of a deeply buried rectangular tunnel.

[0017] .

[0018] In the formula: The difference between the energy dissipation within the collapsed section of a deeply buried rectangular tunnel and the work done by the weight of the collapsed section. , is a generic function.

[0019] (II) By the variational principle of the functional, the corresponding Euler equation can be obtained.

[0020] ...

[0021] By combining the boundary conditions, the solution can be obtained as follows: .

[0022] In the formula, H This refers to the height of the collapse zone in the roof of a deeply buried rectangular tunnel. .

[0023] (III) From the geometric conditions, we can know that

[0024] .

[0025] thereby: .

[0026] (IV) According to the law of conservation of energy, that is, the work done by gravity in the collapse of a deep rectangular tunnel is equal to the dissipation of internal energy, we can obtain the following.

[0027] .

[0028] (V) Combining the formulas from steps (III) and (IV), a system of equations can be formed, from which the collapse height can be obtained. H and the width of the landslide 2 L The size of the landslide, i.e. the area of ​​the landslide, can be obtained by the following formula.

[0029] .

[0030] (VI) Based on the above, and combined with the actual over-excavation situation, the collapse range caused by over-excavation of the roof of the deep-buried rectangular tunnel can be obtained, including the collapse area, collapse height and collapse width; by changing the relevant parameters of over-excavation height, over-excavation width and over-excavation area, the impact of over-excavation height, over-excavation width and over-excavation area on the collapse of the deep-buried rectangular tunnel can be obtained, thus providing theoretical and methodological guidance for determining the impact of over-excavation and the reinforcement and prevention of collapse.

[0031] Compared with existing technologies and research methods, the present invention has the following advantages.

[0032] Existing literature and technical research mainly focus on the impact of over-excavation on the surrounding rock and support; existing patented technologies only address over-excavation inspection or control devices. There is a lack of information on the impact of over-excavation on the collapse of deeply buried rectangular tunnels, and on the extent, height, and width of the tunnel collapse after over-excavation. These factors directly affect subsequent remediation and reinforcement.

[0033] This invention provides a theoretical calculation method for assessing the impact of over-excavation on collapses in deeply buried rectangular tunnels. By changing relevant parameters such as over-excavation height and width, the influence of over-excavation height and width on collapses in deeply buried rectangular tunnels can be determined, thus providing a reference for collapse management under the influence of over-excavation. This method can be applied not only to underground deeply buried rectangular traffic tunnels, but also to the analysis of the impact of over-excavation on collapses in other forms of underground engineering with deeply buried rectangular cross-sections, such as deeply buried rectangular hydraulic tunnels and deeply buried rectangular roadways, thereby providing theoretical and methodological guidance for determining the impact of over-excavation and for the reinforcement and prevention of collapses. Detailed Implementation

[0034] The present invention will be further described below with reference to embodiments.

[0035] The specific data for this embodiment of the project are as follows: Study of over-excavation height. h When the influence of the other parameters is considered, the values ​​of the other parameters are as follows: A =0.3,B =0.7, s c =5MPa, s t = s c / 100, γ=20kN / m 3 , t =1.5m, b=10m, H=5m. Over-excavation height. h The calculations were performed for six different values: 0m, 0.2m, 0.4m, 0.6m, 0.8m, and 1.0m.

[0036] Study over-excavation width t When the influence, A =0.3, B =0.7, s c =5MPa, s t = s c / 100, γ=20kN / m 3 , h =0.6m, b=10m, H=5m. Over-excavation angle. t The calculations were performed for six different values: 0m, 0.5m, 1m, 1.5m, 2m, and 2.5m.

[0037] The calculation method for the impact of over-excavation on the roof of a deeply buried rectangular tunnel on landslides is as follows in this embodiment.

[0038] (1) Determine the over-excavation shape and over-excavation area based on the over-excavation situation of the top plate of the deep-buried rectangular tunnel; the over-excavation shape is simplified to a triangle, and its over-excavation area is determined by the following formula.

[0039] .

[0040] In the formula, S c The area of ​​the over-excavated zone; h This is the over-excavation height. t This refers to the over-excavation width.

[0041] (2) Calculate the work done by gravity in the collapse of a deep-buried rectangular tunnel, which is determined by the following formula.

[0042] .

[0043] In the formula, P γ The work done by gravity in the collapse of a deeply buried rectangular tunnel; L It is half the width of the collapse zone; γ is the unit weight of the surrounding rock; f ( x ) is the shape function of the collapse; vFor the permissible speed field for maneuver; x In a rectangular coordinate system x Axis coordinate values.

[0044] (3) Calculate the energy dissipation in the collapse body of a deep-buried rectangular tunnel, which is determined by the following formula.

[0045] .

[0046] In the formula, P D This is for energy dissipation within the collapsed body of a deeply buried rectangular tunnel; The compressive strength of the intact surrounding rock; A , B These are the parameters of the surrounding rock. for f(x) The slope of the tangent line, i.e., the first derivative; This represents the tensile strength of the surrounding rock.

[0047] (4) Based on the principle of minimum energy consumption and boundary conditions, solve the collapse range and collapse volume of the deep-buried rectangular tunnel, which includes the following steps.

[0048] (I) Construct the following function based on the work done by gravity and the dissipation of internal energy in the collapse of a deeply buried rectangular tunnel.

[0049] .

[0050] In the formula: The difference between the energy dissipation within the collapsed section of a deeply buried rectangular tunnel and the work done by the weight of the collapsed section. , is a generic function.

[0051] (II) By the variational principle of the functional, the corresponding Euler equation can be obtained.

[0052] .

[0053] By combining the boundary conditions, the solution can be obtained as follows: .

[0054] In the formula, H This refers to the height of the collapse zone in the roof of a deeply buried rectangular tunnel. .

[0055] (III) From the geometric conditions, we can know that

[0056] .

[0057] thereby: .

[0058] (IV) According to the law of conservation of energy, that is, the work done by gravity in the collapse of a deep rectangular tunnel is equal to the dissipation of internal energy, we can obtain the following.

[0059] .

[0060] (V) Combining the formulas from steps (III) and (IV), a system of equations can be formed, from which the collapse height can be obtained. H and the width of the landslide 2 L The size of the landslide, i.e. the area of ​​the landslide, can be obtained by the following formula.

[0061] .

[0062] (VI) Based on the above, and combined with the actual over-excavation situation, the collapse range caused by over-excavation of the roof of the deep-buried rectangular tunnel can be obtained, including the collapse area, collapse height and collapse width; by changing the relevant parameters of over-excavation height, over-excavation width and over-excavation area, the impact of over-excavation height, over-excavation width and over-excavation area on the collapse of the deep-buried rectangular tunnel can be obtained, thus providing theoretical and methodological guidance for determining the impact of over-excavation and the reinforcement and prevention of collapse.

[0063] Based on the above method and steps, the effects of different over-excavation heights and widths on the collapse height, collapse width, and collapse area can be obtained. As the over-excavation height increases... h With over-excavation width t As the collapse surface increases, its shape expands, its width and height gradually increase, resulting in an increasing area of ​​the collapse surface.

Claims

1. A calculation method for determining the impact of over-excavation of the roof slab of a deeply buried rectangular tunnel on landslides, characterized in that... Includes the following steps: (1) Based on the over-excavation situation of the roof slab of the deeply buried rectangular 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: ； In the formula, S c The area of ​​the over-excavated zone; h This is the over-excavation height. t This refers to the over-excavation width; (2) The work done by gravity in the collapse of a deeply buried rectangular tunnel is calculated using the following formula: ； In the formula, P γ The work done by gravity in the collapse of a deeply buried rectangular tunnel; L It is half the width of the collapse zone; γ is the unit weight of the surrounding rock; f ( x ) is the shape function of the collapse; v For the permissible speed field for maneuver; x In a rectangular coordinate system x Axis coordinate values; (3) Calculate the energy dissipation within the collapsed body of a deeply buried rectangular tunnel, which is determined by the following formula: ； In the formula, P D This is for energy dissipation within the collapsed body of a deeply buried rectangular tunnel; The compressive strength of the intact surrounding rock; A , B These are the parameters of the surrounding rock. for f(x) The slope of the tangent line, i.e., the first derivative; The tensile strength of the surrounding rock; (4) Based on the principle of minimum energy consumption and boundary conditions, the collapse range and collapse volume of the deeply buried rectangular tunnel are determined, which includes the following steps: (I) Based on the work done by gravity and the dissipation of internal energy during the collapse of a deeply buried rectangular tunnel, the following function is constructed: ； In the formula: The difference between the energy dissipation within the collapsed section of a deeply buried rectangular tunnel and the work done by the weight of the collapsed section. , is a generalized function; (II) By the variational principle of functional theory, the corresponding Euler equation can be obtained as follows: ； By combining the boundary conditions, the solution can be obtained as follows: ; In the formula, H This refers to the height of the collapse zone in the roof of a deeply buried rectangular tunnel. ; (III) From the geometric conditions, we know that: ； thereby: ; (IV) According to the law of conservation of energy, that is, the work done by gravity in the collapse of a deeply buried rectangular tunnel is equal to the dissipation of internal energy, we can obtain: ； (V) Combining the formulas from steps (III) and (IV), a system of equations can be formed, from which the collapse height can be obtained. H and the width of the landslide 2 L The size of the landslide, i.e., the area of ​​the landslide, can be obtained by the following formula: ； (VI) Based on the above, and combined with the actual over-excavation situation, the collapse range caused by over-excavation of the roof of the deep-buried rectangular tunnel can be obtained, including the collapse area, collapse height and collapse width; by changing the relevant parameters of over-excavation height, over-excavation width and over-excavation area, the impact of over-excavation height, over-excavation width and over-excavation area on the collapse of the deep-buried rectangular tunnel can be obtained, thus providing theoretical and methodological guidance for determining the impact of over-excavation and the reinforcement and prevention of collapse.

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