CN107315880A - The localization method of tunnel straight flange wall three-dimensional failure mode under action of horizontal seismic - Google Patents
The localization method of tunnel straight flange wall three-dimensional failure mode under action of horizontal seismic Download PDFInfo
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Abstract
The invention discloses a kind of localization method of tunnel straight flange wall three-dimensional failure mode under action of horizontal seismic.The present invention is mainly：According to tunnel location seismic fortification intensity, tunnel horizontal earthquake action acceleration is obtained；According to country rock level condition, the related mechanics parameter of country rock is obtained；Calculate the interior energy dissipated power at straight flange wall Three-Dimensional fracture face；Straight flange wall three-dimensional is calculated to cave in the external force power that internal earthquake load done；Build the functional containing earthquake external force power and interior energy dissipated power；The condition of extreme value is sought according to the calculus of variations, Three-Dimensional fracture face shape function is determined；According to displacement, stress boundary condition and the conservation of energy, the coefficient value of Three-Dimensional fracture face shape function is determined；According to plane of fracture shape function and its coefficient value, drawing three-dimensional plane of fracture shape graph.The present invention provides computational methods for the three-dimensional failure mode of tunnel straight flange wall under varying level geological process；According to failure mode, reference can be provided for earthquake territory tunnel reinforcement scope.
Description
Technical field
The invention belongs to the determination technology of tunnel damage envelope under earthquake, and in particular to tunnel under a kind of action of horizontal seismic
The localization method of the three-dimensional failure mode of road straight flange wall.
Background technology
China is one of many earthquake countries in the world, has many big and medium-sized cities to meet with the attack of violent earthquake, earthquake
The frequency of generation is high, intensity is big, and the disaster caused is serious, such as Tangshan Earthquake, Wenchuan earthquake.Abroad such as Japan, equally
Occurred multiple violent earthquake.In earthquake, structure is built by heavy damage in the underground such as some tunnels, subway, most of to need again
Repair and reinforce.As can be seen here, seismic force can not be ignored for the influence of tunnel structure.For subway station, servant
Row of channels, underground vehicle driving channel, subterranean commercial area etc., frequently with the form of straight flange wall, therefore how tunnel is straight under Study of Seismic
The security of abutment wall seems extremely important.It is mainly research its dynamic response characteristics, antidetonation to the seismic study in tunnel at present to subtract
Shake measure etc., and when occurring for earthquake, whether country rock caves in and collapse range has the research such as much seldom, this direct shadow
Ring the formulation of maintenance and reinforcement scope and rational approach after the escape safety and calamity of personnel under earthquake.
The content of the invention
It is an object of the invention to provide a kind of positioning of tunnel straight flange wall three-dimensional failure mode under action of horizontal seismic
Method.The present invention can provide reference according to failure mode for earthquake territory Tunnel Repair reinforcing scope；It also can determine whether earthquake in addition
Whether lower abutment wall is safe；And calculate the volume of abutment wall destruction landslide under earthquake.
The localization method of the three-dimensional failure mode of tunnel straight flange wall, mainly includes as follows under the action of horizontal seismic of the present invention
The step of order：
(1) according to tunnel location seismic fortification intensity, tunnel horizontal earthquake action acceleration is obtained；
(2) according to country rock level condition, the related mechanics parameter of country rock is obtained；
(3) the interior energy dissipated power at straight flange wall Three-Dimensional fracture face is calculated；
(4) straight flange wall three-dimensional is calculated to cave in the external force power that internal earthquake load done；
(5) functional containing earthquake external force power and interior energy dissipated power is built；
(6) condition of extreme value is sought according to the calculus of variations, Three-Dimensional fracture face shape function is determined；
(7) according to displacement, stress boundary condition and conservation of energy principle, the coefficient of Three-Dimensional fracture face shape function is determined
Value；
(8) according to plane of fracture shape function and its coefficient value, drawing three-dimensional plane of fracture shape graph.
Its detailed process is as follows：
(1) the interior energy dissipated power in straight flange wall Three-Dimensional fracture face is calculated by below equation：
In formula：EDFor interior energy dissipated power；L is the half of plane of fracture projected length on abutment wall；σciIt is anti-for complete country rock
Compressive Strength；σtmFor the tensile strength of country rock；A, B are Analysis of Field Geotechnical Parameters, can be obtained according to related form is consulted in step (2)；f
(x) it 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 bus letter
X coordinate value in number f (x)；V is the discontinuous velocity on the plane of fracture；
(2) the external force power that earthquake load is done is：
In formula：ηcFor comprehensive effect coefficient, the open cut tunnel of rock foundation uses 0.2, other to use 0.25；A is horizontal earthquake
Acceleration is acted on, is determined by step (1)；G is acceleration of gravity；γ is country rock severe；It is convenient to derive, order
(3) functional by earthquake external force power and interior energy dissipated power structure is as follows：
In formula：ξ is the difference of earthquake external force power and interior energy dissipated power；
Referred to as functional；
(4) when the functional in step (3) has extreme value, then by the variation principle of functional, its corresponding Euler's square can be obtained
Cheng Wei：
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；
(5) coefficient c in step (4)2Determined by following steps：
(a) from symmetry, at the top of the plane of fracture, its slope is 0, i.e. f'(x)=0,
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 the depth of abutment wall damage envelope；c3For function f'(x) obtained by integration in coefficient, with step (5) (a)
C3Unanimously；
(c) by conservation of energy principle, i.e., external force power is equal with interior energy dissipated power, can obtain：
Formula can be tried to achieve in (b) and (c) in simultaneous step (5)：
So as to：
(d) plane of fracture shape bus function f (x) rotates about the z axis, you can obtain Three-Dimensional fracture surface function：
Further, with reference to the Three-Dimensional fracture surface function z=f (x, y) tried to achieve, and country rock relevant parameter and tunnel place are combined
The horizontal ground motion acceleration in area, you can draw the plane of fracture shape, so that it is determined that under earthquake abutment wall reinforcing scope；And root
According to scope 2L of the plane of fracture on abutment wall, height, width with the actual abutment wall in tunnel are compared, if peripheral wall height, width>
2L, then under earthquake, abutment wall will not be destroyed；Otherwise abutment wall can be destroyed, so as to assess the security of abutment wall under earthquake；Further
By integration, then the volume destroyed under earthquake can be obtained.
The inventive method is determines under different earthquake grade, i.e., the three-dimensional destruction shape of tunnel straight flange wall under varying level earthquake
Shape provides computational methods；According to failure mode, reference can be provided for Tunnel Repair reinforcing scope after the calamity of earthquake territory；In addition
It can determine whether whether abutment wall is safe under earthquake；And calculate the volume that abutment wall collapses under earthquake.The method of the present invention, can also be applied to
Subway station under geological process, servant's row or vehicle driving passage, subterranean commercial area etc. there is the hypogee structure of straight flange wall
Three-dimensional damage envelope determination, reinforcing scope determination, abutment wall security evaluation 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；L is the half of plane of fracture projected length on abutment wall；τnTo enclose
Shear stress at the rock plane of fracture, 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
The inclination angle of shape bus function f (x) slopes；A is horizontal earthquake action acceleration；H is the depth of abutment wall damage envelope.
Embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings.
It is the original of the localization method of the three-dimensional failure mode of tunnel straight flange wall under action of horizontal seismic of the present invention referring to Fig. 1
Manage schematic diagram.The inventive method is mainly included following steps in sequence：
(1) according to tunnel location seismic fortification intensity, tunnel horizontal earthquake action acceleration is obtained；
(2) according to country rock level condition, the related mechanics parameter of country rock is obtained；
(3) the interior energy dissipated power at straight flange wall Three-Dimensional fracture face is calculated；
(4) straight flange wall three-dimensional is calculated to cave in the external force power that internal earthquake load done；
(5) functional containing earthquake external force power and interior energy dissipated power is built；
(6) condition of extreme value is sought according to the calculus of variations, Three-Dimensional fracture face shape function is determined；
(7) according to displacement, stress boundary condition and conservation of energy principle, the coefficient of Three-Dimensional fracture face shape function is determined
Value；
(8) according to plane of fracture shape function and its coefficient value, drawing three-dimensional plane of fracture shape graph.
Its detailed process is as follows：
(1) the interior energy dissipated power in straight flange wall Three-Dimensional fracture face is calculated by below equation：
In formula：EDFor interior energy dissipated power；L is the half of plane of fracture projected length on abutment wall；σciFor complete country rock rock
The compression strength of stone；σtmFor the tensile strength of country rock；A, B are Analysis of Field Geotechnical Parameters, can be obtained according to related form is consulted in step (2)
；F (x) is plane of fracture shape bus function, f'(x) tangent slope that is f (x), i.e. first derivative；X is that plane of fracture shape is female
X coordinate value in line function f (x)；V is the discontinuous velocity on the plane of fracture；
(2) the external force power that earthquake load is done is：
In formula：ηcFor comprehensive effect coefficient, the open cut tunnel of rock foundation uses 0.2, other to use 0.25；A is horizontal earthquake
Acceleration is acted on, is determined by step (1)；G is acceleration of gravity；γ is country rock severe；It is convenient to derive, order
(3) functional by earthquake external force power and interior energy dissipated power structure is as follows：
In formula：ξ is the difference of earthquake external force power and interior energy dissipated power；
Referred to as functional；
(4) when the functional in step (3) has extreme value, then by the variation principle of functional, its corresponding Euler's square can be obtained
Cheng Wei：
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 (4)2Determined by following steps：
(a) from symmetry, at the top of the plane of fracture, its slope is 0, i.e. f'(x)=0,
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 the depth of abutment wall damage envelope；c3For function f'(x) obtained by integration in coefficient, with step (5) (a)
C3Unanimously；
(c) by conservation of energy principle, i.e., external force power is equal with interior energy dissipated power, can obtain：
Formula can be tried to achieve in (b) and (c) in simultaneous step (5)：
So as to：
(d) plane of fracture shape bus function f (x) rotates about the z axis, you can obtain Three-Dimensional fracture surface function：
Further, with reference to the Three-Dimensional fracture surface function z=f (x, y) tried to achieve, and country rock relevant parameter and tunnel place are combined
The horizontal ground motion acceleration in area, you can draw the plane of fracture shape, so that it is determined that under earthquake abutment wall reinforcing scope；And root
According to scope 2L of the plane of fracture on abutment wall, height, width with the actual abutment wall in tunnel are compared, if peripheral wall height, width>
2L, then under earthquake, abutment wall will not be destroyed；Otherwise abutment wall can be destroyed, so as to assess the security of abutment wall under earthquake；Further
By integration, then the volume destroyed under earthquake can be obtained.
In case history, according to the computational methods more than present invention, actual numerical value is substituted into, you can obtain straight flange wall three-dimensional
The coefficient value of plane of fracture shape function and Three-Dimensional fracture face shape function, according to plane of fracture shape function and its coefficient value, can be painted
Straight flange wall plane of fracture 3D shape figure processed.
Claims (3)
1. the localization method of tunnel straight flange wall three-dimensional failure mode under a kind of action of horizontal seismic, it is characterised in that including as follows
The step of order：
(1) according to tunnel location seismic fortification intensity, tunnel horizontal earthquake action acceleration is obtained；
(2) according to country rock level condition, the related mechanics parameter of country rock is obtained；
(3) the interior energy dissipated power at straight flange wall Three-Dimensional fracture face is calculated；
(4) straight flange wall three-dimensional is calculated to cave in the external force power that internal earthquake load done；
(5) functional containing earthquake external force power and interior energy dissipated power is built；
(6) condition of extreme value is sought according to the calculus of variations, Three-Dimensional fracture face shape function is determined；
(7) according to displacement, stress boundary condition and conservation of energy principle, the coefficient value of Three-Dimensional fracture face shape function is determined；
(8) according to plane of fracture shape function and its coefficient value, drawing three-dimensional plane of fracture shape graph.
2. according to claim 1 under action of horizontal seismic tunnel straight flange wall three-dimensional failure mode localization method, it is special
Levy and be that detailed process is as follows：
(1) the interior energy dissipated power in straight flange wall Three-Dimensional fracture face is calculated by below equation：
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In formula：EDFor interior energy dissipated power；L is the half of plane of fracture projected length on abutment wall；σciFor complete country rock pressure resistance
Degree；σtmFor the tensile strength of country rock；A, B are Analysis of Field Geotechnical Parameters, can be obtained according to related form is consulted in step (2)；F (x) is
Plane of fracture shape bus function, f'(x) be f (x) tangent slope, i.e. first derivative；X is plane of fracture shape bus function f (x)
In x coordinate value；V is the discontinuous velocity on the plane of fracture；
(2) the external force power that earthquake load is done is：
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In formula：ηcFor comprehensive effect coefficient, the open cut tunnel of rock foundation uses 0.2, other to use 0.25；A adds for horizontal earthquake action
Speed, is determined by step (1)；G is acceleration of gravity；γ is country rock severe；It is convenient to derive, order
(3) functional by earthquake external force power and interior energy dissipated power structure is as follows：
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In formula：ξ is the difference of earthquake external force power and interior energy dissipated power；
Referred to as functional；
(4) when the functional in step (3) has extreme value, then by the variation principle of functional, can obtain its corresponding Eulerian equation is：
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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；
(5) coefficient c in step (4)2Determined by following steps：
(a) from symmetry, at the top of the plane of fracture, its slope is 0, i.e. f'(x)=0,
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 the depth of abutment wall damage envelope；c3For function f'(x) obtained by integration in coefficient, with step (5) (a) c3
Unanimously；
(c) by conservation of energy principle, i.e., external force power is equal with interior energy dissipated power, can obtain：
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<mo>)</mo>
</mrow>
<mi>B</mi>
</msup>
<msup>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>c</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>1</mn>
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<mi>B</mi>
<mo>)</mo>
</mrow>
</msup>
<msub>
<mi>&sigma;</mi>
<mrow>
<mi>t</mi>
<mi>m</mi>
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</msub>
<mo>;</mo>
</mrow>
<mrow>
<mi>h</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mn>2</mn>
<mi>B</mi>
</mrow>
<mrow>
<mi>&omega;</mi>
<mi>B</mi>
</mrow>
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<msub>
<mi>&sigma;</mi>
<mrow>
<mi>t</mi>
<mi>m</mi>
</mrow>
</msub>
<mo>;</mo>
</mrow>
So as to：
<mrow>
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<mrow>
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<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
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<mn>1</mn>
<mo>/</mo>
<mi>B</mi>
</mrow>
</msup>
<msup>
<mrow>
<mo>(</mo>
<mfrac>
<mi>&omega;</mi>
<mrow>
<mn>2</mn>
<msub>
<mi>&sigma;</mi>
<mrow>
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<mo>)</mo>
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<mfrac>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mi>B</mi>
</mrow>
<mi>B</mi>
</mfrac>
</msup>
<msup>
<mi>x</mi>
<mrow>
<mn>1</mn>
<mo>/</mo>
<mi>B</mi>
</mrow>
</msup>
<mo>-</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mn>2</mn>
<mi>B</mi>
</mrow>
<mrow>
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<mi>B</mi>
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<mrow>
<mi>t</mi>
<mi>m</mi>
</mrow>
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(d) plane of fracture shape bus function f (x) rotates about the z axis, you can obtain Three-Dimensional fracture surface function：
<mrow>
<mi>z</mi>
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<mi>f</mi>
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<mi>x</mi>
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<mi>B</mi>
</mrow>
<mi>B</mi>
</mfrac>
</msup>
<msup>
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<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
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<msup>
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</mrow>
<mrow>
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</mrow>
</msup>
<mo>-</mo>
<mfrac>
<mrow>
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<mn>2</mn>
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<mi>&omega;</mi>
<mi>B</mi>
</mrow>
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<mo>.</mo>
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3. according to claim 2 under action of horizontal seismic tunnel straight flange wall three-dimensional failure mode localization method, it is special
Levy and be：With reference to the Three-Dimensional fracture surface function z=f (x, y) tried to achieve, and combine the level of country rock relevant parameter and tunnel location
Earthquake ground motion acceleration, you can draw the plane of fracture shape, so that it is determined that under earthquake abutment wall reinforcing scope；And according to the plane of fracture
Scope 2L on abutment wall, height, width with the actual abutment wall in tunnel are compared, if peripheral wall height, width>2L, then
Under shake, abutment wall will not be destroyed；Otherwise abutment wall can be destroyed, so as to assess the security of abutment wall under earthquake；Further pass through product
Point, then it can obtain the volume destroyed under earthquake.
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