CN107330272B - Method for determining critical water pressure and critical thickness of tunnel vault in three-dimensional water inrush damage - Google Patents

Method for determining critical water pressure and critical thickness of tunnel vault in three-dimensional water inrush damage Download PDF

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CN107330272B
CN107330272B CN201710520089.8A CN201710520089A CN107330272B CN 107330272 B CN107330272 B CN 107330272B CN 201710520089 A CN201710520089 A CN 201710520089A CN 107330272 B CN107330272 B CN 107330272B
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安永林
胡文轩
岳健
欧阳鹏博
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Hunan University of Science and Technology
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Abstract

The invention discloses a method for determining critical water pressure and critical thickness of tunnel vault three-dimensional water inrush damage. According to the method, based on the fact that when the critical water burst of the tunnel vault is damaged, the sum of the water pressure acting power and the water-resisting layer gravity acting power is equal to the internal energy dissipation power at the three-dimensional fracture surface, the water pressure external force power, the water-resisting layer gravity external force power and the internal energy dissipation power are calculated respectively, and a functional containing the water pressure external force power, the water-resisting layer gravity external force power and the internal energy dissipation power is constructed; determining the condition of an extreme value according to a variational method, and determining the critical water pressure when the vault water inrush is damaged when the thickness of the water barrier is known by combining displacement, stress boundary conditions and an energy conservation law; or determining the critical thickness of the water-resisting layer when the water pressure of the water-bearing layer is known; and meanwhile, according to the obtained fracture surface function, a three-dimensional fracture surface shape graph during water bursting can be drawn. The method can judge whether the vault of the tunnel has water inrush and whether the thickness of the waterproof layer meets the requirements, and provides a basis for draining and reducing pressure.

Description

Method for determining critical water pressure and critical thickness of tunnel vault in three-dimensional water inrush damage
Technical Field
The invention belongs to the field of tunnel water inrush damage, and particularly relates to a method for determining critical water pressure and critical thickness of tunnel vault three-dimensional water inrush damage.
Background
With the rapid promotion of the western major development strategy in China, the infrastructure of traffic, energy and the like in western regions is greatly expanded, and the construction of long and large tunnels is more and more. During the construction of the long and large tunnel, water inrush and mud inrush, rock burst, gas and other geological disasters are frequently encountered, wherein the water inrush and mud inrush are particularly serious. The water and mud burst disaster can destroy machines and tools, delay construction period and cause personal casualties and major property loss. Therefore, the development of the research on water inrush of the tunnel has very important engineering significance and scientific value. At present, numerical simulation or empirical formula is mostly adopted for determining the critical thickness of tunnel water inrush, or the analysis is carried out by adopting the theory of thin plates and the theory of beams, and the research on the critical water pressure of water inrush is less; meanwhile, most of researches on water inrush are mainly on water inrush of a tunnel face of the karst tunnel, and the researches on water inrush of a tunnel vault are less.
Disclosure of Invention
The invention aims to provide a method for determining the critical water pressure and the critical thickness of the three-dimensional water inrush damage of a tunnel vault. The method can judge whether the vault of the tunnel has water inrush and whether the thickness of the waterproof layer meets the requirements, and provides a basis for draining and reducing pressure, and if the water pressure is reduced below the critical water pressure under high water pressure, the water inrush can be effectively avoided; meanwhile, the method can determine the shape of the three-dimensional collapsed body when the tunnel top is damaged by water inrush.
The method for determining the critical water pressure and critical thickness of the three-dimensional water inrush damage of the tunnel vault comprises the following steps in sequence:
(1) the internal energy dissipated power at the fracture surface is calculated from:
Figure GDA0002413717070000021
in the formula: eDPower is dissipated for internal energy; l is1Is half of the fracture range of the top surface of the water-resisting layer; l is2The crack is half of the crack range of the bottom surface of the waterproof layer, namely half of the arch crown span; sigmaciThe uniaxial compressive strength of the complete surrounding rock; sigmatmTensile strength of the surrounding rock; A. b is a surrounding rock parameter; f (x) is the fracture surface shape generatrix function, and f' (x) is the tangent slope of f (x), i.e. the first derivative; x is the x coordinate value in the fracture surface shape bus function f (x); v is the discontinuity velocity at the fracture plane;
(2) the aquifer water pressure external force power is calculated by the following formula:
Wp＝pπL1 2v；
in the formula: wpThe external force power is the water pressure of the aquifer; p is the aquifer water pressure;
(3) the external force power of the dead weight load of the waterproof layer is as follows:
Figure GDA0002413717070000022
in the formula: wrExternal force power for dead weight load of the waterproof layer; gamma is the surrounding rock gravity;
(4) the functional constructed by the external force power of the water pressure of the aquifer, the external force power of the self-weight load of the waterproof layer and the internal energy dissipation power at the fracture surface is as follows:
Figure GDA0002413717070000023
ξ is the difference between the internal energy dissipation power and the external force power of the water pressure and the dead weight power of the water-resisting layer;
Figure GDA0002413717070000024
referred to as a generic function;
(5) when the functional in the step (4) has an extreme value, the euler equation corresponding to the functional is obtained according to the variational principle of the functional:
Figure GDA0002413717070000031
solving to obtain:
Figure GDA0002413717070000032
in the formula: psi is psi [ f (x), f' (x), x]；c2Is a constant coefficient obtained by solving the Euler equation and integrating;
(6) coefficient c in step (5)2Is determined by the following steps:
(a) on top of the water barrier, its shear is 0, i.e.:
τxy(x＝L1)＝0.5σnsin 2θ-τncos 2θ＝0；
in the formula: tau isxyIs a shear stress;
Figure GDA0002413717070000033
τnshear stress at the fracture surface of the surrounding rock, namely shear strength; sigmanThe normal stress at the fracture surface of the surrounding rock, namely the normal stress; theta is broken(x) dip of slope of the fracture shape generatrix function f;
the following can be obtained: c. C2＝0；
So that:
Figure GDA0002413717070000034
in the formula: c. C3A coefficient integrated for the function f' (x);
(b) from the geometrical conditions:
Figure GDA0002413717070000035
it is possible to obtain,
Figure GDA0002413717070000036
in the formula: h is the thickness of the vault water-proof layer; c. C3A coefficient integrated for the function f' (x);
(c) by the energy conservation principle, that is, the external force power is equal to the internal energy dissipation power, the following can be obtained:
Figure GDA0002413717070000037
the formulas in (b) and (c) in the simultaneous step (6) can obtain the critical aquifer water pressure p when the vault water burst is destroyed under the condition that the thickness H of the waterproof layer is known; or under the condition that the water pressure p of the aquifer is known, the critical vault waterproof layer thickness H when the vault is broken by water burst can be obtained;
(d) and (3) rotating the fracture surface shape bus function f (x) around the Z axis to obtain a three-dimensional fracture surface function:
Figure GDA0002413717070000041
wherein y is the y-axis coordinate of the three-dimensional fracture surface.
The invention provides a calculation method for determining the critical water pressure and critical thickness when the three-dimensional water inrush of the tunnel vault is damaged; therefore, whether the vault of the tunnel has water inrush and whether the thickness of the waterproof layer meets the requirements can be judged, and a basis is provided for draining and reducing pressure, if the water pressure is high and is reduced below the critical water pressure, the water inrush can be effectively avoided; meanwhile, the method can determine the shape of the three-dimensional collapsed body when the tunnel top is damaged by water inrush. The method can also be applied to the judgment of whether the vault or the top plate of the underground building structure such as a mining roadway, a hydraulic tunnel and the like has water inrush, the determination of the critical water pressure and the critical water-resisting layer thickness and the like.
Drawings
FIG. 1 is a schematic diagram of the method of the present invention.
In the figure: (x) is the fracture surface shape generatrix function; l is1Is half of the fracture range of the top surface of the water-resisting layer; l is2The crack is half of the crack range of the bottom surface of the waterproof layer, namely half of the arch crown span; tau isnShear stress at the fracture surface of the surrounding rock, namely shear strength; sigmanThe normal stress at the fracture surface of the surrounding rock, namely the normal stress; θ is the slope of the fracture surface shape generatrix function f (x); p water-bearing stratum water pressure, in karst section, can be the water pressure of karst cave/cavity; h is the vault water barrier thickness.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 1, a schematic diagram of the principle of the method for determining the critical water pressure and critical thickness of the tunnel vault in the three-dimensional water inrush destruction mode is shown.
Firstly, according to the tunnel engineering outline and the surrounding rock grade condition, the related mechanical parameters of the surrounding rock are obtained, such as the surrounding rock parameter A, B in the above, and the L is half of the span of the vault of the tunnel2Uniaxial compressive strength sigma of complete surrounding rockciTensile strength sigma of surrounding rocktmThe weight gamma of the surrounding rock, the water pressure p of an aquifer or the thickness H of a water-resisting layer and other parameters.
The specific calculation steps are as follows:
(1) the internal energy dissipated power at the fracture surface is calculated from:
Figure GDA0002413717070000051
in the formula: eDPower is dissipated for internal energy; l is1Is half of the fracture range of the top surface of the water-resisting layer; l is2The crack is half of the crack range of the bottom surface of the waterproof layer, namely half of the arch crown span; sigmaciCompressive strength of the complete surrounding rock; sigmatmTensile strength of the surrounding rock; A. b is a surrounding rock parameter; f (x) is the fracture surface shape generatrix function, and f' (x) is the tangent slope of f (x), i.e. the first derivative; x is the x coordinate value in the fracture surface shape bus function f (x); v is the discontinuity velocity at the fracture plane;
(2) the aquifer water pressure external force power is calculated by the following formula:
Wp＝pπL1 2v；
in the formula: wpThe external force power is the water pressure of the aquifer; p is the aquifer water pressure;
(3) the external force power of the dead weight load of the waterproof layer is as follows:
Figure GDA0002413717070000052
in the formula: wrExternal force power for dead weight load of the waterproof layer; gamma is the surrounding rock gravity;
(4) the functional constructed by the external force power of the water pressure of the aquifer, the external force power of the self-weight load of the waterproof layer and the internal energy dissipation power at the fracture surface is as follows:
Figure GDA0002413717070000053
ξ is the difference between the internal energy dissipation power and the external force power of the water pressure and the dead weight power of the water-resisting layer;
Figure GDA0002413717070000061
(5) when the functional in the step (4) has an extreme value, the euler equation corresponding to the functional is obtained according to the variational principle of the functional:
Figure GDA0002413717070000062
solving to obtain:
Figure GDA0002413717070000063
in the formula: psi is psi [ f (x), f' (x), x]；；c2Is a constant coefficient obtained by solving the Euler equation and integrating;
(6) coefficient c in step (5)2Is determined by the following steps:
(a) on top of the water barrier, its shear is 0, i.e.:
τxy(x＝L1)＝0.5σnsin 2θ-τncos 2θ＝0；
in the formula: tau isxyIs a shear stress;
Figure GDA0002413717070000064
τnshear stress at the fracture surface of the surrounding rock, namely shear strength; sigmanThe normal stress at the fracture surface of the surrounding rock, namely the normal stress; θ is the slope of the fracture surface shape generatrix function f (x);
the following can be obtained: c. C2＝0；
So that:
Figure GDA0002413717070000065
in the formula: c. C3A coefficient integrated for the function f' (x);
(b) from the geometrical conditions:
Figure GDA0002413717070000066
it is possible to obtain,
Figure GDA0002413717070000067
in the formula: h is the thickness of the vault water-proof layer; c. C3A coefficient integrated for the function f' (x);
(c) by the energy conservation principle, that is, the external force power is equal to the internal energy dissipation power, the following can be obtained:
Figure GDA0002413717070000071
the formulas in (b) and (c) in the simultaneous step (6) can obtain the critical aquifer water pressure p when the vault water burst is destroyed under the condition that the thickness H of the waterproof layer is known; or under the condition that the water pressure p of the aquifer is known, the critical vault waterproof layer thickness H when the vault is broken by water burst can be obtained;
(d) and (3) rotating the fracture surface shape bus function f (x) around the Z axis to obtain a three-dimensional fracture surface function:
Figure GDA0002413717070000072
wherein y is the y-axis coordinate of the three-dimensional fracture surface.

Claims (1)

1. A method for determining the critical water pressure and critical thickness of tunnel vault three-dimensional water inrush destruction is characterized by comprising the following steps in sequence:
(1) the internal energy dissipated power at the fracture surface is calculated from:
Figure FDA0002413717060000011
in the formula: eDPower is dissipated for internal energy; l is1Is half of the fracture range of the top surface of the water-resisting layer; l is2The crack is half of the crack range of the bottom surface of the waterproof layer, namely half of the arch crown span; sigmaciThe uniaxial compressive strength of the complete surrounding rock; sigmatmTensile strength of the surrounding rock; A. b is a surrounding rock parameter; f (x) is the fracture surface shape generatrix function, and f' (x) is the tangent slope of f (x), i.e. the first derivative; x is the x coordinate value in the fracture surface shape bus function f (x); v is the discontinuity velocity at the fracture plane;
(2) the aquifer water pressure external force power is calculated by the following formula:
Wp＝pπL1 2v；
in the formula: wpIs an aquiferWater pressure external force power; p is the aquifer water pressure;
(3) the external force power of the dead weight load of the waterproof layer is as follows:
Figure FDA0002413717060000012
in the formula: wrExternal force power for dead weight load of the waterproof layer; gamma is the surrounding rock gravity;
(4) the functional constructed by the external force power of the water pressure of the aquifer, the external force power of the self-weight load of the waterproof layer and the internal energy dissipation power at the fracture surface is as follows:
Figure FDA0002413717060000013
ξ is the difference between the internal energy dissipation power and the external force power of the water pressure and the dead weight power of the water-resisting layer;
Figure FDA0002413717060000014
referred to as a generic function;
(5) when the functional in the step (4) has an extreme value, the euler equation corresponding to the functional is obtained according to the variational principle of the functional:
Figure FDA0002413717060000021
solving to obtain:
Figure FDA0002413717060000022
in the formula: psi is psi [ f (x), f' (x), x]；c2Is a constant coefficient obtained by solving the Euler equation and integrating;
(6) coefficient c in step (5)2Is determined by the following steps:
(a) on top of the water barrier, its shear is 0, i.e.:
τxy(x＝L1)＝0.5σnsin2θ-τncos2θ＝0；
in the formula: tau isxyIs a shear stress;
Figure FDA0002413717060000023
τnshear stress at the fracture surface of the surrounding rock, namely shear strength; sigmanThe normal stress at the fracture surface of the surrounding rock, namely the normal stress; θ is the slope of the fracture surface shape generatrix function f (x);
the following can be obtained: c. C2＝0；
So that:
Figure FDA0002413717060000024
in the formula: c. C3A coefficient integrated for the function f' (x);
(b) from the geometrical conditions:
Figure FDA0002413717060000025
it is possible to obtain,
Figure FDA0002413717060000026
in the formula: h is the thickness of the vault water-proof layer; c. C3A coefficient integrated for the function f' (x);
(c) by the energy conservation principle, that is, the external force power is equal to the internal energy dissipation power, the following can be obtained:
Figure FDA0002413717060000031
the formulas in (b) and (c) in the simultaneous step (6) can obtain the critical aquifer water pressure p when the vault water burst is destroyed under the condition that the thickness H of the waterproof layer is known; or under the condition that the water pressure p of the aquifer is known, the critical vault waterproof layer thickness H when the vault is broken by water burst can be obtained;
(d) and (3) rotating the fracture surface shape bus function f (x) around the Z axis to obtain a three-dimensional fracture surface function:
Figure FDA0002413717060000032
wherein y is the y-axis coordinate of the three-dimensional fracture surface.
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