CN107330272A - The determination method of tunnel vault three-dimensional gushing water destruction critical hydraulic pressure and critical thickness - Google Patents
The determination method of tunnel vault three-dimensional gushing water destruction critical hydraulic pressure and critical thickness Download PDFInfo
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Abstract
The invention discloses a kind of three-dimensional gushing water destruction critical hydraulic pressure of tunnel vault and the determination method of critical thickness.When the present invention is based on the destruction of tunnel vault critical water inrush, water pressure working power is equal to the interior energy dissipated power at Three-Dimensional fracture face with water barrier gravity acting power sum, water pressure external force power, water barrier gravity external force power and interior energy dissipated power are calculated respectively, construct the functional containing hydraulic pressure external force power, water barrier gravity external force power and interior energy dissipated power；The condition of extreme value, and combination displacement, stress boundary condition and law of conservation of energy are asked according to the calculus of variations, it is determined that in known impermeable layer thickness, critical hydraulic pressure when vault gushing water is destroyed；Or determine in known aqueous layer water pressure, the critical thickness of water barrier；Simultaneously according to the rupture surface function tried to achieve, Three-Dimensional fracture face shape graph during gushing water can be drawn.The present invention may determine that whether whether gushing water, impermeable layer thickness meet requirement to tunnel vault, and provide foundation for the decompression that sluices.
Description
Technical field
The invention belongs to tunnel gushing water destruction field, and in particular to a kind of three-dimensional gushing water destruction critical hydraulic pressure of tunnel vault with
The determination method of critical thickness.
Background technology
With quickly propelling for China's strategy to develop western regions, the infrastructure such as west area traffic, energy is significantly opened up
Open, major long tunnel is built more and more.In major long tunnel construction process, the geology calamities such as gushing water prominent mud, rock burst, gas are frequently encountered
The prominent mud of evil, wherein gushing water is particularly acute.Gushing water dash forward mud disaster gently then destroy by rush of water equipment, affect adversely the duration, it is heavy then cause casualties with
The heavy losses of property.Therefore, carrying out the research of tunnel gushing water has highly important engineering significance and scientific value.At present for such as
What determines that the critical thickness of tunnel gushing water uses numerical simulation either empirical equation or use plate theory and beam theory mostly
Analyzed, and the critical hydraulic pressure research for gushing water is less；It is prominent with the face of Karst Tunnel to study the mostly of gushing water simultaneously
Based on water, study less for tunnel vault gushing water.
The content of the invention
It is an object of the invention to provide the determination of a kind of three-dimensional gushing water destruction critical hydraulic pressure of tunnel vault and critical thickness
Method.The inventive method may determine that whether whether gushing water, impermeable layer thickness meet requirement to tunnel vault, and be carried for sluicing decompression
For foundation, under such as high hydraulic pressure, hydraulic pressure is reduced to below critical hydraulic pressure, then it is possible to prevente effectively from the generation of gushing water；While this hair
Bright method can determine that three-dimensional is caved in shape during the destruction of tunnel top gushing water.
The determination method of the three-dimensional gushing water destruction critical hydraulic pressure of the tunnel vault of the present invention and critical thickness, including order below
The step of：
(1) the interior energy dissipated power of the plane of fracture is calculated by following formula：
In formula：EDFor interior energy dissipated power；L1The half of scope is ruptured for water barrier top surface；L2Ruptured for water barrier bottom surface
The half of the half of scope, i.e. vault bay；σciFor complete country rock uniaxial compressive strength；σtmFor the tensile strength of country rock；A、B
For Analysis of Field Geotechnical Parameters；F (x) is plane of fracture shape bus function, f'(x) tangent slope that is f (x), i.e. first derivative；X is rupture
X coordinate value in face shape bus function f (x)；V is the discontinuous velocity on the plane of fracture；
(2) piezometric head external force power is calculated by following formula：
Wp=p π L1 2v；
In formula：WpFor piezometric head external force power；P is piezometric head；
(3) the external force power that water barrier gravity load is done is：
In formula：WrThe external force power done by water barrier gravity load；γ is country rock severe；
(4) in the external force power and the plane of fracture that piezometric head external force power, water barrier gravity load are done
The functional that energy dissipated power is built is as follows：
In formula：ξ is the difference of interior energy dissipated power and water pressure external force power and water barrier deadweight power；Referred to as functional；
(5) when the functional in step (4) has extreme value, then by the variation principle of functional, its corresponding Eulerian equation can be obtained
For：
Solution can be obtained：
In formula：ψ is ψ [f (x), f'(x), x]；c2Be Eulerian equation is solved and is integrated obtained by constant coefficient；
(6) coefficient c in step (5)2Determined by following steps：
(a) at the top of water barrier, it is 0 that it, which is sheared, i.e.,：
τxy(x=L1The σ of)=0.5n sin2θ-τnCos2 θ=0；
In formula：τxyFor shear stress；τnFor cutting at the country rock plane of fracture
Stress, i.e. shearing strength；σnFor the direct stress at the country rock plane of fracture, i.e. normal stress；θ is plane of fracture shape bus function f (x)
The inclination angle of slope；
Can be in the hope of：c2=0；
So as to：
In formula：c3For function f'(x) coefficient obtained by integration；
(b) by geometrical condition：
It can obtain,
In formula：H is vault impermeable layer thickness；c3For function f'(x) coefficient obtained by integration；
(c) by conservation of energy principle, i.e., external force power is equal with interior energy dissipated power, can obtain：
Formula in (b) and (c) in simultaneous step (6), can be in the hope of vault in the case of known to impermeable layer thickness H
Critical piezometric head p when gushing water is destroyed；Or in the case of known to piezometric head p, can be in the hope of vault gushing water
Critical vault impermeable layer thickness H during destruction；
(d) plane of fracture shape bus function f (x) rotates about the z axis, you can obtain Three-Dimensional fracture surface function：
The critical hydraulic pressure when present invention is determines that the three-dimensional gushing water of tunnel vault is destroyed provides computational methods with critical thickness；
It may determine that whether whether gushing water, impermeable layer thickness meet requirement to tunnel vault accordingly, and foundation, such as water provided for the decompression that sluices
Pressure is high, hydraulic pressure is reduced to below critical hydraulic pressure, then it is possible to prevente effectively from the generation of gushing water；The method of the present invention can be true simultaneously
Three-dimensional is caved in shape when determining the destruction of tunnel top gushing water.The method of the present invention, can also be applied to mining tunnel, hydraulic tunnel
Deng hypogee structure vault or top plate whether the judgement of gushing water, critical hydraulic pressure and the determination of critical impermeable layer thickness etc..
Brief description of the drawings
Fig. 1 is the principle schematic of the inventive method.
In figure：F (x) is plane of fracture shape bus function；L1The half of scope is ruptured for water barrier top surface；L2For water barrier
The half of the half, i.e. vault bay of bottom surface rupture scope；τnFor the shear stress at the country rock plane of fracture, i.e. shearing strength；σnTo enclose
Direct stress at the rock plane of fracture, i.e. normal stress；θ is the inclination angle of plane of fracture shape bus function f (x) slopes；P aquifer water pressures
Power, can be the water pressure of solution cavity/molten chamber in Karst area；H is vault impermeable layer thickness.
Embodiment
The invention will be further described below in conjunction with the accompanying drawings.
It is the original of the three-dimensional gushing water destruction critical hydraulic pressure of tunnel vault of the present invention and the determination method of critical thickness referring to Fig. 1
Manage schematic diagram.
First, according to Tunnel Engineering overview and country rock level condition, obtain the related mechanics parameter of country rock, as described above in enclose
Rock parameter A, B, the half L of tunnel vault span2, complete country rock uniaxial compressive strength σci, country rock tensile strength sigmatm, country rock weight
Spend γ, and the parameter such as piezometric head p or impermeable layer thickness H.
Specific calculation procedure is as follows：
(1) the interior energy dissipated power of the plane of fracture is calculated by following formula：
In formula：EDFor interior energy dissipated power；L1The half of scope is ruptured for water barrier top surface；L2Ruptured for water barrier bottom surface
The half of the half of scope, i.e. vault bay；σciFor the compression strength of complete country rock rock；σtmFor the tensile strength of country rock；A、
B is Analysis of Field Geotechnical Parameters；F (x) is plane of fracture shape bus function, f'(x) tangent slope that is f (x), i.e. first derivative；X is rupture
X coordinate value in face shape bus function f (x)；V is the discontinuous velocity on the plane of fracture；
(2) piezometric head external force power is calculated by following formula：
Wp=p π L1 2v；
In formula：WpFor piezometric head external force power；P is piezometric head；
(3) the external force power that water barrier gravity load is done is：
In formula：WrThe external force power done by water barrier gravity load；γ is country rock severe；
(4) in the external force power and the plane of fracture that piezometric head external force power, water barrier gravity load are done
The functional that energy dissipated power is built is as follows：
In formula：ξ is the difference of interior energy dissipated power and water pressure external force power and water barrier deadweight power；Referred to as functional；
(5) when the functional in step (4) has extreme value, then by the variation principle of functional, its corresponding Eulerian equation can be obtained
For：
Solution can be obtained：
In formula：ψ is ψ [f (x), f'(x), x]；；c2Be Eulerian equation is solved and is integrated obtained by constant coefficient；
(6) coefficient c in step (5)2Determined by following steps：
(a) at the top of water barrier, it is 0 that it, which is sheared, i.e.,：
τxy(x=L1The σ of)=0.5n sin2θ-τnCos2 θ=0；
In formula：τxyFor shear stress；τnShould for cutting at the country rock plane of fracture
Power, i.e. shearing strength；σnFor the direct stress at the country rock plane of fracture, i.e. normal stress；θ is plane of fracture shape bus function f (x) oblique
The inclination angle of rate；
Can be in the hope of：c2=0；
So as to：
In formula：c3For function f'(x) coefficient obtained by integration；
(b) by geometrical condition：
It can obtain,
In formula：H is vault impermeable layer thickness；c3For function f'(x) coefficient obtained by integration；
(c) by conservation of energy principle, i.e., external force power is equal with interior energy dissipated power, can obtain：
Formula in (b) and (c) in simultaneous step (6), can be in the hope of vault in the case of known to impermeable layer thickness H
Critical piezometric head p when gushing water is destroyed；Or in the case of known to piezometric head p, can be in the hope of vault gushing water
Critical vault impermeable layer thickness H during destruction；
(d) plane of fracture shape bus function f (x) rotates about the z axis, you can obtain Three-Dimensional fracture surface function：
Claims (1)
1. the determination method of a kind of three-dimensional gushing water destruction critical hydraulic pressure of tunnel vault and critical thickness, it is characterised in that including as follows
The step of order：
(1) the interior energy dissipated power of the plane of fracture is calculated by following formula：
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In formula：EDFor interior energy dissipated power；L1The half of scope is ruptured for water barrier top surface；L2Scope is ruptured for water barrier bottom surface
Half, i.e. vault bay half；σciFor complete country rock uniaxial compressive strength；σtmFor the tensile strength of country rock；A, B are to enclose
Rock parameter；F (x) is plane of fracture shape bus function, f'(x) tangent slope that is f (x), i.e. first derivative；X is plane of fracture shape
X coordinate value in shape bus function f (x)；V is the discontinuous velocity on the plane of fracture；
(2) piezometric head external force power is calculated by following formula：
Wp=p π L1 2v；
In formula：WpFor piezometric head external force power；P is piezometric head；
(3) the external force power that water barrier gravity load is done is：
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In formula：WrThe external force power done by water barrier gravity load；γ is country rock severe；
(4) the external force power and the interior energy consumption of the plane of fracture done by piezometric head external force power, water barrier gravity load
The functional for dissipating power structure is as follows：
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In formula：ψ is ψ [f (x), f'(x), x]；c2Be Eulerian equation is solved and is integrated obtained by constant coefficient；
(6) coefficient c in step (5)2Determined by following steps：
(a) at the top of water barrier, it is 0 that it, which is sheared, i.e.,：
τxy(x=L1The σ of)=0.5n sin2θ-τnCos2 θ=0；
In formula：τxyFor shear stress；τnFor the shear stress at the country rock plane of fracture,
That is shearing strength；σnFor the direct stress at the country rock plane of fracture, i.e. normal stress；θ is plane of fracture shape bus function f (x) slopes
Inclination angle；
Can be in the hope of：c2=0；
So as to：
In formula：c3For function f'(x) coefficient obtained by integration；
(b) by geometrical condition：
It can obtain,
In formula：H is vault impermeable layer thickness；c3For function f'(x) coefficient obtained by integration；
(c) by conservation of energy principle, i.e., external force power is equal with interior energy dissipated power, can obtain：
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Formula in (b) and (c) in simultaneous step (6), can be in the hope of vault gushing water in the case of known to impermeable layer thickness H
Critical piezometric head p during destruction；Or in the case of known to piezometric head p, can be destroyed in the hope of vault gushing water
When critical vault impermeable layer thickness H；
(d) plane of fracture shape bus function f (x) rotates about the z axis, you can obtain Three-Dimensional fracture surface function：
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Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710520089.8A CN107330272B (en) | 2017-06-30 | 2017-06-30 | Method for determining critical water pressure and critical thickness of tunnel vault in three-dimensional water inrush damage |
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| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710520089.8A CN107330272B (en) | 2017-06-30 | 2017-06-30 | Method for determining critical water pressure and critical thickness of tunnel vault in three-dimensional water inrush damage |
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| Publication Number | Publication Date |
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| CN107330272A true CN107330272A (en) | 2017-11-07 |
| CN107330272B CN107330272B (en) | 2020-06-26 |
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| CN201710520089.8A Active CN107330272B (en) | 2017-06-30 | 2017-06-30 | Method for determining critical water pressure and critical thickness of tunnel vault in three-dimensional water inrush damage |
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| CN112131628A (en) * | 2020-07-29 | 2020-12-25 | 北京工业大学 | Method for calculating minimum water inrush prevention safety thickness by comprehensively considering inclination angle and trend of tunnel crossing water-rich fault |
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