CN111274639B - Method for judging minimum safe thickness of water-resisting layer damaged by water outburst of tunnel face crack - Google Patents
Method for judging minimum safe thickness of water-resisting layer damaged by water outburst of tunnel face crack Download PDFInfo
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Abstract
The invention discloses a recognition method for minimum safe thickness of a water-resisting layer of a tunnel face crack water bursting damage, which simplifies the tunnel face outline into a circle, regards the water-resisting layer as a rock beam structure and establishes a mechanical model; and calculating the total potential energy of the mechanical model system through a standard expression based on the cusp type mutation model, establishing a model potential function expression, and judging the minimum safe thickness through the model potential function expression. The invention provides an identification method for the water burst damage of the karst tunnel face crack, so that whether the construction is safe or not can be evaluated, and whether the thickness of a water-resisting layer meets the requirement or not can be evaluated.
Description
Technical Field
The invention belongs to the technical field of tunnel engineering, and particularly relates to a method for judging the minimum safe thickness of a waterproof layer of a tunnel face crack damaged by water protrusion.
Background
The development of the karst in China is widely distributed, particularly, the karst in the southwest area is extremely developed, with the further implementation of the western large development and the rapid development of national economy, underground projects in the karst area are increased day by day, and the construction is often disturbed by karst fissure water disasters, so that underground karst water burst and mud burst, surrounding rock instability and collapse, supporting structures are deformed and cracked and the like are caused, the safety of personnel is endangered, the construction progress is influenced, the ecological environment is also badly influenced, and even the tunnel is abandoned or the line is changed and the site is shifted. The problem of karst fissure water outburst is a common main geological disaster in karst tunnel construction, and a water diversion pressure tunnel and surrounding rocks of an underground cavern of a hydropower station can also generate fissure rock mass hydraulic fracture to cause engineering accidents.
The key of the tunnel outburst prevention is how to determine the minimum safe thickness of a tunnel face water-resisting layer so as to guide the design and construction of the tunnel. At present, the tunnel engineering design with the minimum safe thickness of a water-resisting layer is often semi-empirical and is based on the past engineering experience and provides larger safe reserve; in theory analysis, the safe thickness numerical simulation calculation is mostly carried out on the basis of plastic region penetration, the process is troublesome, and the result reasonableness is not to be questioned.
Disclosure of Invention
Therefore, in order to ensure the safety of the tunnel in the karst region, reduce the construction cost and improve the design level and the construction technology of the tunnel in the karst region, it is necessary to provide a method for judging the safe thickness of the water-resisting layer of the tunnel face crack water outburst damage of the karst tunnel.
The invention aims to provide a method for judging the minimum safe thickness of a water-resisting layer of tunnel face crack water bursting damage, which is used for judging whether the tunnel face of a karst tunnel bursts water or not and providing a calculation method, so that whether tunnel construction is safe or not and whether the thickness of the water-resisting layer meets the requirement or not can be evaluated.
In order to achieve the purpose, the invention is realized by adopting the following technical scheme:
the invention discloses a minimum safe thickness identification method of a water-resisting layer when water burst of a crack of a tunnel face is damaged, which is characterized in that the outline of the tunnel face is simplified into a circle, the water-resisting layer is regarded as a rock beam structure, and a mechanical model is established; and solving the total potential energy of the mechanical model system through a standard expression based on the cusp type mutation model, establishing a model potential function expression, and identifying the minimum safe thickness through the model potential function expression.
Preferably, the total potential energy consists of bending deformation potential energy of the rock beam body under the action of the filling materials and the karst water in the karst cavity, system potential energy and work done by the pressure at two sides of the rock beam body in the deformation process; determined by equation (1):
V＝U+ΔE-W (1)
in the formula (1), V is the total potential energy of the system; u is the bending deformation potential energy of the rock beam, Delta E is the potential energy added by the system, and W is the work done by the pressure at the two sides of the rock beam body.
Preferably, the flexural equation of the body of the rock beam is:
in formula (2): omega m Is the deflection of the central axis of the water-resisting layer,r is the distance from any point of the waterproof layer to the central axis, and R is the radius of the tunnel face;
the bending deformation potential energy U generated by the deformation of the waterproof layer in front of the tunnel face is determined by the formula (3):
in formula (3): EI is the bending stiffness of the body of the beam,
d is the thickness of the water-resisting layer, and ν is Poisson's ratio.
Preferably, the system potential energy comprises the potential energy when the fracture in front of the tunnel face is not expanded and the system added potential energy delta E when the fractured rock mass reaches a fracture damage water bursting state:
in formula (4): q is the pressure difference between two sides of the water-resisting layer;
obtaining the following energy equation according to Bernoulli:
in formula (5): Δ h is the on-way head loss; z is a radical of 1 、p 1 、v 1 Respectively the elevation of the water level of the dissolution cavity in front of the palm surface, the water pressure and the water flow speed; z is a radical of 2 、p 2 、v 2 Respectively the elevation, the water pressure and the water flow speed of the water inrush hole. Wherein z is 1 ＝z 2 ，v 1 ＝v 2 0. When the crack expands to the critical water inrush opening,
it is possible to obtain,
q＝γΔh＝p 1 -p 2 (8)。
preferably, the work done by the pressure on both sides of the rock beam body is determined by the formula W (9):
the model potential function is of formula (10):
preferably, the model potential function is expanded by taylor series at r ═ 0, and the simplified potential function expression obtained after the third term and the following high-order terms are ignored is as follows:
solving a system potential function based on a standard expression of a cusp mutation model, namely the system meets the relation when reaching a critical state:
the minimum thickness D of the water-resisting layer is obtained as follows:
compared with the existing research method, the invention has the advantages that: the shape function of the water bursting fracture surface is not artificially assumed, but a potential energy function relation is obtained according to a sharp point mutation model, and a state critical mutation value is obtained by combining a Taylor series numerical method.
The method provides an identification method for the water outburst damage of the karst tunnel face crack, and accordingly whether construction is safe or not and whether the thickness of a water-resisting layer meets requirements or not can be evaluated.
The method can also be applied to the evaluation of whether the tunnel face of underground structures such as a deeply-buried water diversion pressure tunnel, a hydropower station underground cavern, a mining roadway and the like is damaged by water inrush under the condition of water enrichment, and the determination of the minimum safe thickness of a water-resisting layer when the water inrush damage occurs.
Drawings
FIG. 1 is a simplified model diagram of a tunnel face;
FIG. 2 is a mechanical model of a water-barrier layer of a tunnel face;
FIG. 3 is a partial enlarged view of a water-barrier palm-face crack.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings.
As shown in fig. 1, fig. 2 and fig. 3, the method for identifying the minimum safe thickness of the water-resisting layer of the tunnel face crack water bursting damage disclosed by the invention comprises the following steps:
1. simplifying the outline of the tunnel face of the karst tunnel into a circle, taking the water-resisting layer as a rock beam structure, and establishing a mechanical model; calculating the total potential energy of the mechanical model system based on a standard expression of a cusp type mutation model, and establishing a model potential function expression;
2. the total potential energy of the system consists of bending deformation potential energy of the rock beam body under the action of the filling materials and the karst water in the karst cavity, system potential energy and work done by the pressure at two sides of the rock beam body in the deformation process, and the potential function expression is as follows:
V＝U+ΔE-W (1)
in the formula: v is the total potential energy of the system; u is the bending deformation potential energy of the rock beam, Delta E is the potential energy added by the system, and W is the work done by the pressure at the two sides of the rock beam body;
3. let the flexural equation of the rock beam structure be:
in the formula: omega m The deflection of the central axis of the waterproof layer is shown, R is the distance from any point of the waterproof layer to the central axis, and R is the radius of the tunnel face;
4. bending deformation potential energy U generated by deformation of the waterproof layer in front of the tunnel face:
in the formula: the EI is the bending rigidity of the rock beam body,
d is the thickness of the water-resisting layer, v is the Poisson's ratio,
5. potential energy when the fracture in front of the face is not expanded and potential energy delta E added by the system when the fractured rock mass reaches a fracture damage water inrush state are as follows:
in the formula: q is the pressure difference between two sides of the water barrier
Obtaining the following energy equation according to Bernoulli:
in the formula: Δ h is the on-way head loss; z is a radical of formula 1 、p 1 、v 1 Respectively the elevation of the water level of the dissolution cavity in front of the palm surface, the water pressure and the water flow speed; z is a radical of 2 、p 2 、v 2 Respectively the elevation, the water pressure and the water flow speed of the water inrush hole. Wherein z is 1 ＝z 2 ，v 1 ＝v 2 0. When the crack expands to the critical water inrush opening,
it is possible to obtain,
q＝γΔh＝p 1 -p 2 (8)。
6. in the whole bending deformation process of the beam body, the work W of the pressure on the two sides:
7. in summary, the potential function of the model system is:
and expanding the above expression at a position where r is 0 by using a Taylor series, and simplifying the third term and the subsequent high-order terms after omitting to obtain a potential function expression as follows:
8. solving a system potential function based on a standard expression of a cusp mutation model, namely the system meets the relation when reaching a critical state:
therefore, the minimum thickness of the water barrier layer can be found as:
therefore, the minimum safe thickness of the waterproof layer is related to the radius of the tunnel face and the water pressure in the solution cavity.
The present invention is capable of other embodiments, and various changes and modifications may be made by one skilled in the art without departing from the spirit and scope of the invention.
Claims (2)
1. The method for judging the minimum safe thickness of the water-resisting layer damaged by water bursting of the tunnel face crack is characterized by comprising the following steps of: simplifying the profile of the tunnel face into a circle, regarding the water-resisting layer as a rock beam structure, and establishing a mechanical model; calculating the total potential energy of the mechanical model through a standard expression based on a cusp type mutation model, establishing a model potential function expression, and judging the minimum safe thickness through the model potential function expression;
the total potential energy consists of bending deformation potential energy of the rock beam body under the action of the filling materials and the karst water in the dissolving cavity, system potential energy and work done by the pressure at two sides of the rock beam body in the deformation process; determined by equation (1):
V＝U+ΔE-W (1)
in the formula (1), V is the total potential energy of the system; u is the bending deformation potential energy of the rock beam, Delta E is the potential energy added by the system, and W is the work done by the pressure at both sides of the rock beam body;
wherein: the flexural equation for the body of the beam is:
in formula (2): omega m The deflection of the central axis of the waterproof layer is shown, R is the distance from any point of the waterproof layer to the central axis, and R is the radius of the tunnel face;
the bending deformation potential energy U generated by the deformation of the waterproof layer in front of the tunnel face is determined by the formula (3):
in formula (3):EI is the bending stiffness of the body of the beam,
d is the thickness of the water-resisting layer, and ν is Poisson's ratio;
wherein: the system potential energy comprises potential energy when a fracture in the front of a tunnel face is not expanded and potential energy delta E increased by the system when fractured rock mass reaches a fracture damage water bursting state:
in formula (4): q is the pressure difference between two sides of the water-resisting layer;
obtaining the following energy equation according to Bernoulli:
in formula (5): Δ h is the on-way head loss; z is a radical of formula 1 、p 1 、v 1 Respectively the elevation of the water level of the dissolution cavity in front of the palm surface, the water pressure and the water flow speed; z is a radical of 2 、p 2 、v 2 Respectively the elevation, the water pressure and the water flow speed of the water inrush hole. Wherein z is 1 ＝z 2 ，v 1 ＝v 2 0; when the crack expands to the critical water inrush opening,
it is possible to obtain,
q＝γΔh＝p 1 -p 2 (8)；
wherein: the work done by the pressure on the two sides of the rock beam body is determined by the formula W (9):
the model potential function is of formula (10):
2. the recognition method according to claim 1, characterized in that: and expanding the model potential function at the position where r is 0 by adopting a Taylor series, and obtaining a simplified potential function expression by neglecting a third term and a later high-order term as follows:
solving a system potential function based on a standard expression of a cusp mutation model, namely the system meets the relation when reaching a critical state:
the minimum thickness D of the water-resisting layer is obtained as follows:
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