CN114922686A - Calculation method for determining influence of over excavation of top plate of deep-buried rectangular tunnel on collapse - Google Patents
Calculation method for determining influence of over excavation of top plate of deep-buried rectangular tunnel on collapse Download PDFInfo
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Abstract
The invention discloses a method for calculating the influence of over excavation of a top plate of a deep-buried rectangular tunnel on collapse. The method mainly comprises the following steps: determining an overexcavation shape and an overexcavation area according to the overexcavation condition of the top plate of the deep-buried rectangular tunnel; calculating collapse body weight doing work of the deep-buried rectangular tunnel; calculating internal energy dissipation of the collapsed body of the deeply buried rectangular tunnel; solving the collapse range and the collapse amount according to the minimum energy consumption principle and the boundary conditions; and (4) changing different overbreak heights, overbreak widths and overbreak areas, and calculating the influence of the overbreak heights, the overbreak widths and the overbreak areas on the collapse range and the collapse size. The method can be applied to analysis of the influence of the over excavation on the collapse in the underground engineering with the form of the deep-buried rectangular section, provides a calculation method for determining the influence of the over excavation on the collapse of the top plate of the deep-buried rectangular tunnel, can consider the influence of the over excavation width, the over excavation height and the over excavation area, provides theoretical method guidance for determining the over excavation influence and reinforcing and preventing the collapse, and is favorable for safe construction.
Description
Technical Field
The invention belongs to the technical field of tunnel construction, and particularly relates to a calculation method for determining the influence of over excavation of a top plate of a deep-buried rectangular tunnel on collapse.
Background
Along with the development of urban underground space, a plurality of tunnels and underground engineering can be built, and the tunnel gradually develops towards the trend of deeper and deeper burial depth; in underground mining of energy such as mining and the like, after shallow resources are developed, development is gradually carried out towards deep resources, the mining depth is continuously expanded towards underground deep parts, and a plurality of deeply buried underground projects are necessarily involved. Due to the existence of the rock mass joint crack, even if controlled blasting is adopted, overbreak and undermining are inevitable; if smooth blasting is not adopted or the loading amount is increased for the purpose of achieving the scheduled speed, the overbreak phenomenon is more serious. If some of the overbreaks are too large, collapse will be induced. The existing specification, whether the part of water conservancy and hydropower, or the technical specification of highway/railway tunnel construction, only provides the regulation on the allowable excessive excavation amount, and does not relate to the relevant regulation on the influence of the excessive excavation on the collapse of the surrounding rocks. The prior patents and documents are basically about the influence of the overexcavation on the surrounding rock and the timbering, the control device, and the like. There are few reports on how overbreak can be assessed for the effect of landslide.
Disclosure of Invention
The invention aims to provide a calculation method for determining the influence of the overbreak of a top plate of a deep-buried rectangular tunnel on collapse, aiming at the technical problems in the prior art.
The object of the present invention is achieved by the following technical means.
The method for determining the influence of the overexcavation of the top plate of the deep-buried rectangular tunnel on the collapse comprises the following steps.
(1) Determining an overexcavation shape and an overexcavation area according to the overexcavation condition of the top plate of the deep-buried rectangular tunnel; the overbreak shape is simplified to a triangle, and the overbreak area is determined by the following formula.
In the formula, Sc is the area of the overexcavation region; h is the overbreak height and t is the overbreak width.
(2) And calculating the gravity work of the collapsed body of the deeply buried rectangular tunnel, which is determined by the following formula.
In the formula, P γ Acting for the gravity of the deeply buried rectangular tunnel collapse body; l is half of the width of the collapse area; gamma is the surrounding rock gravity; f (x) is a collapsed shape function; v is the maneuvering allowable speed field; and x is the coordinate value of the x axis in the rectangular coordinate system.
(3) And calculating the internal energy dissipation of the deep-buried rectangular tunnel in the collapsed body, wherein the internal energy dissipation is determined by the following formula.
In the formula, P D Internal energy dissipation of a collapsed square body of the deeply-buried rectangular tunnel is achieved;compressive strength of the complete surrounding rock; A. b is a surrounding rock parameter;the tangent slope of f (x), i.e., the first derivative;the tensile strength of the surrounding rock.
(4) According to the minimum energy consumption principle and the boundary conditions, the collapse range and the collapse quantity of the deep-buried rectangular tunnel are solved, and the method comprises the following steps.
And (I) constructing the following function by the gravity work and internal energy dissipation of the deeply buried rectangular tunnel collapse body.
In the formula:the difference between internal energy dissipation of a collapsed rectangular tunnel body and collapse body weight work is calculated;it is a general function.
And (II) according to the variation principle of the general function, obtaining a corresponding Euler equation as follows.
in the formula, H is the height of a collapse area of a top plate of the deeply-buried rectangular tunnel;。
(III) according to the geometric conditions.
(IV) according to the law of conservation of energy, namely that the gravity work of the deeply buried rectangular tunnel collapse body is equal to the internal energy dissipation, so that the method can be obtained.
And (V) combining the formulas of the steps (III) and (IV) to form an equation system, so that the collapse height H and the collapse width 2L can be solved, and the collapse size, namely the collapse area, can be obtained by the following formula.
(VI) according to the above, combining the actual over-excavation condition to obtain the collapse range caused by the over-excavation of the top plate of the deep-buried rectangular tunnel, including the collapse area, the collapse height, the collapse width and the like; and (3) changing relevant parameters such as the over-excavation height, the over-excavation width and the like to obtain the influence of the over-excavation height, the over-excavation width and the over-excavation area on the collapse of the deeply-buried rectangular tunnel, thereby providing theoretical method guidance for determining the over-excavation influence and the reinforcement and prevention of the collapse.
Compared with the prior art and the research method, the invention has the following advantages:
the prior literature technical research mainly aims at the influence on surrounding rocks and supports after overexcavation; the prior patent technology is only used for checking the overbreak or controlling the device and the like. The influence of over excavation on the collapse of the deeply-buried rectangular tunnel is lacked, the collapse range of the over-excavated tunnel is large, and the collapse height and width are large, so that the subsequent treatment and reinforcement are directly influenced.
The invention provides a theoretical calculation method for evaluating the influence of the overexcavation of the deep-buried rectangular tunnel on collapse; and the influence of the over-excavation height and the over-excavation width on the collapse of the deeply-buried rectangular tunnel can be obtained by changing relevant parameters such as the over-excavation height and the over-excavation width, so that reference is provided for the collapse treatment under the influence of the over-excavation. The method can be applied to underground deep-buried rectangular traffic tunnels, and can also be applied to analysis on the influence of the over excavation on the collapse in other forms of underground engineering of deep-buried rectangular sections, such as deep-buried rectangular hydraulic tunnels, deep-buried rectangular roadways and the like, so that theoretical method guidance is provided for determining the over excavation influence and reinforcing and preventing the collapse.
Drawings
Fig. 1 is a schematic view of collapse of an overbreak tunnel according to an embodiment of the present invention.
In the context of figure 1 of the drawings,Hthe height of the collapse area of the tunnel;Lhalf the width of the collapse zone;bthe width of the rectangular tunnel is general;hin order to achieve the over-digging height,tthe width of the overbreak is adopted;f(x)is in a collapsed shapeA shape function;va maneuvering allowable speed field;xin a rectangular coordinate systemxThe axis coordinate values.
FIG. 2 is a graph showing the effect of different overbreak heights on slump height, slump width, and slump area.
FIG. 3 is a graph showing the effect of different overbreak widths on collapse height, collapse width and collapse area.
Detailed Description
The invention is further described below with reference to the figures and examples.
The specific data of the project of the embodiment are as follows: study of overbreak heighthWhen the influence is given, the values of other parameters are respectively as follows:A=0.3,B=0.7,σ c =5MPa,σ t =σ c /100,γ=20kN/m 3 ,t=1.5m, b =10m, H =5 m. Height of overbreakhSix conditions of 0m, 0.2m, 0.4m, 0.6m, 0.8m and 1.0m are respectively selected for calculation.
Study of overbreak widthtIn the event of (2) the effect of (c),A=0.3,B=0.7,σ c =5MPa,σ t =σ c /100,γ=20kN/m 3 ,h=0.6m, b =10m, H =5 m. Over-cut angletSix conditions of 0m, 0.5m, 1m, 1.5m, 2m and 2.5m are respectively selected for calculation.
Referring to fig. 1, the method for calculating the influence of the overbreak of the top plate of the deep-buried rectangular tunnel on the collapse according to the embodiment is as follows:
(1) determining an overexcavation shape and an overexcavation area according to the overexcavation condition of the top plate of the deep-buried rectangular tunnel; the overbreak shape is simplified to a triangle, and the overbreak area is determined by the following formula.
In the formula, Sc is the area of the overexcavation region; h is the overbreak height, and t is the overbreak width.
(2) And calculating the gravity work of the collapsed body of the deeply buried rectangular tunnel, which is determined by the following formula.
In the formula, P γ Acting for the gravity of the deeply buried rectangular tunnel collapse body; l is half of the width of the collapse area; gamma is the surrounding rock gravity; (x) is a collapsed shape function; v is the maneuver allowable velocity field; and x is the coordinate value of the x axis in the rectangular coordinate system.
(3) And calculating the internal energy dissipation of the deep-buried rectangular tunnel collapse body, which is determined by the following formula.
In the formula, P D Internal energy dissipation of the collapsed body of the deeply buried rectangular tunnel;compressive strength of the complete surrounding rock; A. b is a surrounding rock parameter;the tangent slope of f (x), i.e., the first derivative;the tensile strength of the surrounding rock.
(4) According to the minimum energy consumption principle and the boundary conditions, the collapse range and the collapse quantity of the deep-buried rectangular tunnel are solved, and the method comprises the following steps.
And (I) constructing a function by gravity work and internal energy dissipation of a deeply buried rectangular tunnel collapse body.
In the formula:the difference between the internal energy dissipation of the collapsed rectangular tunnel body and the collapse body weight is worked;is a general function.
And (II) according to the variation principle of the general function, obtaining a corresponding Euler equation as follows.
in the formula, H is the height of a collapse area of a top plate of the deeply-buried rectangular tunnel;。
(III) from the geometric conditions.
(IV) according to the law of conservation of energy, namely the gravity work of the collapsed body of the deeply buried rectangular tunnel is equal to the dissipation of internal energy, so that the energy-saving tunnel can be obtained.
And (V) combining the formulas in the steps (III) and (IV) to form an equation system, so that the collapse height H and the collapse width 2L can be obtained, and the collapse size, namely the collapse area, can be obtained according to the following formula.
(VI) according to the above, combining the actual over-excavation condition to obtain the collapse range caused by the over-excavation of the top plate of the deep-buried rectangular tunnel, including the collapse area, the collapse height, the collapse width and the like; and (3) changing relevant parameters such as the over-excavation height, the over-excavation width and the like to obtain the influence of the over-excavation height, the over-excavation width and the over-excavation area on the collapse of the deeply-buried rectangular tunnel, thereby providing theoretical method guidance for determining the over-excavation influence and the reinforcement and prevention of the collapse.
According to the above method steps, the influence of different overbreak heights and overbreak widths on the collapse height, the collapse width and the collapse area can be obtained, as shown in fig. 2 and fig. 3. As can be seen from the figure, with overbreak heighthAnd width of overbreaktThe collapsed surface is enlarged in shape, the collapsed width is gradually increased, and the collapsed height is also gradually increased, so that the area of the collapsed surface is increased.
Claims (1)
1. A calculation method for determining the influence of the overexcavation of a top plate of a deep-buried rectangular tunnel on collapse is characterized by comprising the following steps:
(1) determining an overexcavation shape and an overexcavation area according to the overexcavation condition of the top plate of the deep-buried rectangular tunnel; the overbreak shape is simplified into a triangle, and the overbreak area is determined by the following formula:
in the formula, Sc is the area of the overexcavation region; h is the overbreak height, and t is the overbreak width;
(2) calculating the gravity of the collapsed square body of the deeply-buried rectangular tunnel to do work, wherein the gravity is determined by the following formula:
in the formula, P γ Doing work for the gravity of the collapsed square body of the deeply-buried rectangular tunnel; l is half of the width of the collapse area; gamma is the surrounding rock gravity; (x) is a collapsed shape function; v is the maneuver allowable velocity field; x is an x-axis coordinate value in a rectangular coordinate system;
(3) calculating the internal energy dissipation of the deep-buried rectangular tunnel collapse body, which is determined by the following formula:
in the formula, P D Internal energy dissipation of the collapsed body of the deeply buried rectangular tunnel;compressive strength of the complete surrounding rock; A. b is a surrounding rock parameter;the tangent slope of f (x), i.e., the first derivative;tensile strength of the surrounding rock;
(4) according to the minimum energy consumption principle and boundary conditions, the collapse range and the collapse amount of the deeply buried rectangular tunnel are solved, and the method comprises the following steps of:
the method comprises the following steps that (I) the following functions are constructed by the gravity work and internal energy dissipation of a deeply buried rectangular tunnel collapse body:
in the formula:the difference between internal energy dissipation of a collapsed rectangular tunnel body and collapse body weight work is calculated;is a general function;
(II) according to the variation principle of the general function, the corresponding Euler equation is obtained as follows:
in the formula, H is the height of a collapse area of a top plate of the deeply-buried rectangular tunnel; ;
(III) from the geometric conditions, it is known that:
(IV) according to the law of conservation of energy, namely the gravity work of the collapsed body of the deeply buried rectangular tunnel is equal to the dissipation of internal energy, the method can be obtained as follows:
(V) combining the formulas of the steps (III) and (IV) to form an equation system, so that the collapse height H and the collapse width 2L can be solved, and the collapse size, namely the collapse area, can be obtained by the following formula:
(VI) according to the above, combining the actual over-excavation condition to obtain the collapse range caused by the over-excavation of the top plate of the deep-buried rectangular tunnel, including the collapse area, the collapse height, the collapse width and the like; and (3) changing relevant parameters such as the over-excavation height, the over-excavation width and the like to obtain the influence of the over-excavation height, the over-excavation width and the over-excavation area on the collapse of the deeply-buried rectangular tunnel, thereby providing theoretical method guidance for determining the over-excavation influence and the reinforcement and prevention of the collapse.
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