CN115186324A - Method for evaluating influence of shallow tunnel overexcavation on collapse of arch - Google Patents
Method for evaluating influence of shallow tunnel overexcavation on collapse of arch Download PDFInfo
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Abstract
The invention discloses a method for evaluating the influence of shallow tunnel overexcavation on arch collapse. The method mainly comprises the following steps: determining an overexcavation shape and an overexcavation area according to the overexcavation condition of the shallow tunnel; calculating the collapse body weight doing work of the shallow tunnel; calculating internal energy dissipation of a shallow tunnel collapse body; solving the collapse range and the collapse amount according to the minimum energy consumption principle and the boundary conditions; and (4) changing different over excavation angles, over excavation heights and over excavation areas, and evaluating the influence of the over excavation angles, the over excavation heights and the over excavation areas on the collapse range and the collapse size of the shallow tunnel. The method can be applied to analysis of the influence of the overbreak of the arch part on the collapse in shallow underground engineering, can consider the influence of factors such as an overbreak angle, an overbreak height and an overbreak area, and provides theoretical method guidance for evaluating the overbreak influence and the reinforcement and prevention of the collapse.
Description
Technical Field
The invention belongs to the technical field of tunnel construction, and particularly relates to a method for evaluating influence of shallow tunnel overexcavation on arch collapse.
Background
As more and more tunnels are built, as in the current chuhai line, the tunnels account for a large proportion. Due to the influences of geological conditions of surrounding rocks, drilling and blasting construction parameters and the like, the phenomenon of overbreak is common in a tunnel construction site. At present, related research documents are basically used for researching the deformation stress of the surrounding rock caused by overexcavation, and the like, and most of the related patents are detection and control devices, such as the following patents: an interval medicine loading tool (CN 201922381532.5) for railway tunnel linear overexcavation control and the like. Tunnel collapse is a common accident, and overbreak is also a main cause of tunnel collapse, and particularly for shallow tunnels, overbreak and collapse can be caused when overbreak is too large. However, no literature exists for theoretically analyzing the influence of overbreak on collapse of the shallow tunnel, and a corresponding evaluation method is also lacked.
Disclosure of Invention
The invention aims to solve the technical problems in the prior art and provide a method for evaluating the influence of shallow tunnel overexcavation on collapse of an arch.
The object of the present invention is achieved by the following technical means.
The method for evaluating the influence of the overbreak of the shallow tunnel on the collapse of the arch part comprises the following steps.
(1) Determining an overexcavation shape and an overexcavation area according to the overexcavation condition of the shallow tunnel; the overexcavation shape is simplified into a triangle, and the overexcavation area is determined by the following formula.
In the formula, S c The area of the overbreak area; r is the radius of the arch part of the tunnel; theta is an overexcavation angle; h is the overbreak height; and pi is the circumferential ratio.
(2) And calculating the gravity work of the shallow tunnel collapse body, which is determined by the following formula.
In the formula, P γ Is shallowBurying collapse body weight work of the tunnel; l is 1 Is half of the width of a surface collapse area of the shallow tunnel, L 2 The width of the collapse area in the shallow tunnel is half of that of the collapse area in the shallow tunnel; gamma is the surrounding rock gravity; g (x) is a tunnel arch profile function; 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.
The tunnel arch contour function g (x) is specifically determined by the following equation.
In the formula, H is the buried depth of the shallow buried tunnel.
(3) And calculating the internal energy dissipation of the shallow tunnel collapse body, which is determined by the following formula.
In the formula, P D Internal energy dissipation of the shallow tunnel collapse body is achieved;
compressive strength of the complete surrounding rock; A. b is a surrounding rock parameter;
is the tangent slope of f (x), i.e., the first derivative;
the tensile strength of the surrounding rock.
(4) And solving the collapse range and the collapse quantity according to the minimum energy consumption principle and the boundary conditions, wherein the method comprises the following steps.
And (I) performing work by the gravity of a shallow tunnel collapse body and dissipating internal energy to construct the following function.
In the formula:
the difference between the internal energy dissipation of the shallow tunnel collapse 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.
Combining with the boundary conditions, the solution can be obtained:
。
in the formula, c 1 Are coefficients.
(III) is known from the geometrical conditions.
The following formula can be obtained.
(IV) according to the law of conservation of energy, namely that the gravity work of the shallow tunnel collapse body is equal to the internal energy dissipation, so that the shallow tunnel collapse body can be obtained.
(V) combining the formulas of the steps (III) and (IV) to form an equation system, so that the width of the surface collapse area of the shallow tunnel is 2L 1 And the width of the collapse area in the hole is 2L 2 The value of (2) and the slump value, i.e., the slump area, can be obtained by the following equation.
(VI) according to the above, combining the actual over-excavation condition to obtain the collapse range of the shallow tunnel caused by over-excavation, including the collapse area, the collapse height, the collapse width and the like; and (3) changing relevant parameters such as the overexcavation height, the overexcavation angle and the like to obtain the influence of the overexcavation height, the overexcavation angle and the overexcavation area on the collapse of the arch part of the shallow tunnel, thereby providing theoretical method guidance for evaluating the overexcavation influence and reinforcing and preventing the collapse of the shallow tunnel.
Compared with the prior art and the research method, the invention has the following advantages:
the prior literature technology mainly aims at the influence of overexcavation on surrounding rocks and supports; the prior patent technology is only used for checking the overbreak or controlling the device and the like. The influence of over excavation on collapse of the shallow tunnel is lacked, the collapse range of the shallow tunnel after over excavation is large, and the collapse height and width are large, so that the follow-up treatment and reinforcement on collapse are directly influenced.
The invention provides a theoretical calculation method for evaluating the influence of shallow tunnel overexcavation on arch collapse; and the influence of the over-cut height and the over-cut angle on the collapse of the shallow tunnel can be obtained by changing relevant parameters such as the over-cut height and the over-cut angle, so that reference is provided for the collapse treatment under the influence of the over-cut. The method can be applied to traffic tunnels, mining tunnels, hydraulic tunnels, subway interval tunnels and other underground projects, and can be used for analyzing the influence of over excavation on collapse, so that theoretical method guidance is provided for evaluating the influence of over excavation and reinforcing and preventing 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,Hburying depth for the tunnel;L 1 is half of the width of the collapse area of the shallow tunnel surface,L 2 the width of the collapse area in the shallow tunnel is half of that of the collapse area in the shallow tunnel; (ii) aRFor tunnel arch halvesDiameter;θan overbreak angle;hthe height of the overbreak is set;f(x)is a function of the shape of the collapse;g(x) Is a tunnel arch profile 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 angles on the collapse height, the collapse width and the 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 the overbreak heighthWhen the influence of (2) is given, the values of other parameters are respectively as follows:A=0.15，B=0.6，σ c =0.5MPa，σ t =σ c /100，R=11m，γ=20kN/m 3 ，θover cut height of =6 °hSix cases, i.e., 0m,0.2m,0.4m,0.6m,0.8m and 1.0m, were selected for calculation.
Study of the over cut angleθWhen the influence of (2) is given, the values of other parameters are respectively as follows:A=0.15，B=0.6，σ c =0.5MPa，σ t =σ c /100，R=11m，γ=20kN/m 3 ，h=0.6m, over-cut angleθSix conditions of 0 degrees, 2 degrees, 4 degrees, 6 degrees, 8 degrees and 10 degrees are respectively selected for calculation.
Referring to fig. 1, the method for evaluating the influence of overbreak of the shallow tunnel on collapse of the arch portion is as follows.
(1) Determining an overexcavation shape and an overexcavation area according to the overexcavation condition of the shallow tunnel; the overexcavation shape is simplified into a triangle, and the overexcavation area is determined by the following formula.
In the formula, S c The area of the overbreak area; r is the radius of the arch part of the tunnel; theta is an overexcavation angle; h is the overbreak height; and pi is the circumferential ratio.
(2) And calculating the gravity work of the shallow tunnel collapse body, which is determined by the following formula.
In the formula, P γ Acting for the gravity of the shallow tunnel collapse body; l is a radical of an alcohol 1 Is half of the width of a surface collapse area of the shallow tunnel, L 2 The width of the collapse area in the shallow tunnel is half of that of the collapse area in the shallow tunnel; gamma is the surrounding rock gravity; g (x) is a tunnel arch contour function; f (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.
The tunnel arch contour function g (x) is specifically determined by the following equation.
In the formula, H is the buried depth of the shallow buried tunnel.
(3) And calculating the internal energy dissipation of the shallow tunnel collapse body, which is determined by the following formula.
In the formula, P D Internal energy dissipation of the collapsed body of the shallow tunnel;
compressive strength of the complete surrounding rock; A. b is a surrounding rock parameter;
is the tangent slope of f (x), i.e., the first derivative;
the tensile strength of the surrounding rock.
(4) And solving the collapse range and the collapse amount according to the minimum energy consumption principle and the boundary conditions, wherein the method comprises the following steps.
And (I) performing work by the gravity of a shallow tunnel collapse body and dissipating internal energy to construct the following function.
In the formula:
the difference between internal energy dissipation of a shallow tunnel collapse body and collapse body weight work;
is a general function.
And (II) according to the variation principle of the general function, obtaining a corresponding Euler equation as follows.
Combining with the boundary conditions, the solution can be obtained:
。
in the formula, c 1 Are coefficients.
(III) is known from the geometrical conditions.
The following formula can be obtained.
(IV) the energy conservation law, namely that the gravity work of the shallow tunnel collapse body is equal to the internal energy dissipation, is adopted to obtain the energy conservation method.
(V) combining the formulas of the steps (III) and (IV) to form an equation system, so that the width of the surface collapse area of the shallow tunnel is 2L 1 And the width of the collapse area in the hole is 2L 2 The value of (2) and the collapse size, i.e., the collapse area, can be obtained by the following equation.
(VI) according to the above, combining the actual over-excavation condition to obtain the collapse range of the shallow tunnel caused by over-excavation, including the collapse area, the collapse height, the collapse width and the like; and (3) changing relevant parameters such as the overexcavation height, the overexcavation angle and the like to obtain the influence of the overexcavation height, the overexcavation angle and the overexcavation area on the collapse of the arch part of the shallow tunnel, thereby providing theoretical method guidance for evaluating the overexcavation influence and reinforcing and preventing the collapse of the shallow tunnel.
According to the above method steps, the influence of different overbreak heights and overbreak angles on the collapse height, the collapse width and the collapse area can be obtained, as shown in fig. 2 and 3. As can be seen from the figure, as the overbreak height is reachedhAngle with respect to overexcavationθThe area of the collapsed surface is increased due to the fact that the collapsed surface is enlarged in shape, the collapsed width is gradually increased, and the collapsed height is also gradually increased.
Claims (1)
1. A method for evaluating the influence of over excavation of a shallow tunnel on collapse of an arch part is characterized by comprising the following steps:
(1) Determining an overexcavation shape and an overexcavation area according to the overexcavation condition of the shallow tunnel; the overexcavation shape is simplified into a triangle, and the overexcavation area is determined by the following formula:
in the formula, S c The area of the overbreak area; r is the radius of the arch part of the tunnel; theta is the overetch angleDegree; h is the overbreak height; pi is the circumference ratio;
(2) Calculating the gravity of the shallow tunnel collapse body to do work, which is determined by the following formula,
in the formula, P γ Acting for the gravity of the shallow tunnel collapse body; l is a radical of an alcohol 1 Is half of the width of a surface collapse area of the shallow tunnel, L 2 The width of the collapse area in the shallow tunnel is half of that of the collapse area in the shallow tunnel; gamma is the surrounding rock gravity; g (x) is a tunnel arch contour function; f (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;
the tunnel arch contour function g (x) is specifically determined by the following formula:
in the formula, H is the buried depth of the shallow tunnel;
(3) Calculating the internal energy dissipation of the shallow tunnel collapse body, which is determined by the following formula:
in the formula, P D Internal energy dissipation of the shallow tunnel collapse body is achieved;
compressive strength of the complete surrounding rock; A. b is a surrounding rock parameter;
is the tangent slope of f (x), i.e., the first derivative;
tensile strength of the surrounding rock;
(4) Solving the collapse range and the collapse amount according to the minimum energy consumption principle and the boundary conditions, wherein the method comprises the following steps of:
the method comprises the following steps that (I) the shallow tunnel collapse body gravity does work and internal energy is dissipated, and the following function is constructed:
in the formula:
the difference between the internal energy dissipation of the shallow tunnel collapse body and the collapse body weight is worked;
is a general function;
(II) according to the variation principle of the general function, the corresponding Euler equation is obtained as follows:
combining with the boundary conditions, the solution can be obtained:
；
in the formula, c 1 Is a coefficient;
(III) the geometrical conditions show that:
the following formula can thus be obtained:
(IV) according to the law of conservation of energy, namely that the gravity work of the shallow tunnel collapse body is equal to the internal energy dissipation, obtaining:
(V) combining the formulas of the steps (III) and (IV) to form an equation system, so that the width of the surface collapse area of the shallow tunnel is 2L 1 And the width of the cave-in collapse area is 2L 2 The value of (2), the collapse size, i.e., 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 of the shallow tunnel caused by the over excavation, including the collapse area, the collapse height, the collapse width and the like; and (3) changing relevant parameters such as the overexcavation height, the overexcavation angle and the like to obtain the influence of the overexcavation height, the overexcavation angle and the overexcavation area on the collapse of the arch part of the shallow tunnel, thereby providing theoretical method guidance for evaluating the overexcavation influence and reinforcing and preventing the collapse of the shallow tunnel.
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