CN106599346A - Method for calculating triangular resistance load of shield tunnel in compound stratum - Google Patents
Method for calculating triangular resistance load of shield tunnel in compound stratum Download PDFInfo
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Abstract
The invention provides a method for calculating triangular resistance load of a shield tunnel in a compound stratum. Triangular resistance deformation delta is regarded as superposition of horizontal deformation U<x>(q<1>, q<G>, e<1>, e<2>, g, q<w>) caused by load, except triangular resistance, and horizontal deformation U<x>(kdelta) caused by triangular resistance load PP; taylor expansion of the horizontal deformation U<x>(kdelta) caused by triangular resistance load PP is carried out; furthermore, an expression of the horizontal deformation U<x>(kdelta) obtained by ignoring the higher order term is substituted into a superposition horizontal deformation expression; with the help of numerical values locally, a semi-analytical formula of triangular resistance deformation is solved; and thus, a formula of the triangular resistance deformation delta is obtained. The problem that the traditional shield tunnel triangular resistance displacement calculation formula is not suitable for the compound stratum is really solved; a relatively universal calculation method is provided; and simultaneously, the basis is provided for precisely solving the internal force of a segment of the shield tunnel.
Description
Technical field
The present invention relates to the Calculation Methods for Internal Force technical field of shield tunnel chip architecture, relates in particular to a kind of compound
Stratum shield tunnel triangle drag load computational methods.
Background technology
At present, domestic shield tunnel tunnel segment structure internal force is calculated and adopts modified routine method mostly.Modified routine method assumes
Structure is elastic uniform plastid, it is considered to which girth joint is present, and the overall bending stiffness of annulus is reduced, and takes annulus bending rigidity for η EI.
The load that tunnel structure is subject in modified routine method is as shown in figure 1, including top vertical earth pressure q1, hogback soil pressure qG, top bottom
Portion's level is to soil pressure e1And e2, lining cutting deadweight g, hydrostatic pressure qw, vertical counter-force q in bottom2, level is to triangle drag PP.On
State in load level and belong to tunnel structure to triangle drag PP and produced by the soil body by being deformed under other active load actions
It is raw by power, have relation with other active loads.Impact of the triangle drag to shield tunnel structural internal force is very big,
Therefore determination of the accurate calculating of triangle drag load to shield tunnel segment inner force has important meaning.（In Fig. 1,
H0Level of ground water height is represented, H represents tunnel thickness of earth-fill cover, H1For H and H0Difference）
Triangle drag PP assumes to be in isosceles triangle, in the range from the upper and lower angle α of tunnel horizontal axis within 45 °,
Power is calculated as follows：
Wherein, k is the resistance coefficient of Tunnel Passing soil layer（kN/m3）, δ is to deform at tunnel annulus horizontal diameter（m）.
The calculating for deforming δ at tunnel annulus horizontal diameter is most important.Existing specification and the δ for being given of document calculates public
Formula is as follows：
Wherein：
q0For overcharge on ground standard value（kPa）, γiFor the severe standard value of each layer soil in tunnel top
（kN/m3）, level of ground water above soil layer takes natural density, and level of ground water following soil layer water and soil point takes buoyant weight degree, h when calculatingiFor tunnel
Push up the thickness of each layer soil（m）；
γ′tFor the weighted average buoyant weight degree of more than horizontal axis in Tunnel Passing soil layer each layer soil（kN/m3）；
R0For tunnel radius（m）；
γcFor section of jurisdiction material severe（kN/m3）；T is section of jurisdiction thickness（m）；
e1=q1tg2(45 ° of-φ/2) -2Ctg (45 ° of-φ/2), e2=e1+2γ′t1RHtg2(45 ° of-φ/2), γ 't1For tunnel
Road passes through the weighted average severe standard value of soil layer（kN/m3）, level of ground water above soil layer takes natural density, level of ground water with
Lower soil layer takes buoyant weight degree；C, φ are passed through the weighted average cohesive strength standard value of soil layer by tunnel（kPa）, weighted average internal friction
Angle standard value（°）；
γwFor the severe of water（kN/m3）；
η is section of jurisdiction bending rigidity reduction coefficient；E is the elastic modelling quantity of section of jurisdiction material（kPa）；I is the inertia of tunnel cross-section
Square（m4）；
K is the resistance coefficient of Tunnel Passing soil layer（kN/m3）.
Above-mentioned load computing formula is all based on uniform stratum and is derived by, it can be seen that level is to soil pressure e1And e2In ladder
Distribution of shapes.But actual shield tunnel may pass through non-homogeneous compound stratum.Compound stratum canonic form is as shown in Fig. 2 table
Existing form is usually soft lower hard, and stratum 1 is soft layer, and stratum 2 is competent bed（In Fig. 2, D represents tunnel external diameter, H1
Represent the height of tunnel cross-section middle and lower part hard rock）.Severe γ on stratum 1 and 2, cohesive strength C, internalfrictionangleφ differ greatly, because
, when the diversity of strict consideration compound stratum, level to geostatic shield is in no longer simple trapezoidal profile, on two kinds of stratum for this
Mutation is produced at separating surface.
Deform the computing formula of δ at tunnel annulus horizontal diameter based on the load form in Fig. 1, for compound stratum level
Essential change is there occurs to soil pressure form, the computing formula of above-mentioned triangle drag deformation δ is also no longer suitable for.
The content of the invention
In view of the foregoing, the present invention provides a kind of compound stratum shield tunnel triangle drag load computational methods, leads to
The semi analytic formula that the deformation of triangle drag is solved by numerical computations is crossed, the shield tunnel suitable for non-homogeneous compound stratum is obtained
Soil layer construction is assumed to elasticity by the structure computation method of road section of jurisdiction, the structure computation method for solving existing duct pieces of shield tunnel
Homogeneous body causes the inaccurate technical problem of result of calculation.
For achieving the above object, the present invention adopts the technical scheme that a kind of compound stratum shield tunnel triangle of offer resists
Power load computational methods, including：
Step S1：It is related to tunnel deformation determination to be calculated according to tunnel method for determining load in conventional load structure method
Stratum drag load numerical value, the load numerical value include top vertical earth pressure q1, hogback soil pressure qG, top/bottom part level to
Soil pressure e1And e2, lining cutting deadweight g and hydrostatic pressure qw, level is to triangle drag PP；
Step S2：Try to achieve the horizontal distortion U that the load in addition to triangle drag PP causesx(q1,qG,e1,e2,g,qw) and
The horizontal distortion U that triangle drag load PP causesx(kδ)；
Step S3：Deformation at tunnel annulus horizontal diameter is considered as into what the load in addition to triangle drag PP caused
Horizontal distortion Ux(q1,qG,e1,e2,g,qw) and the horizontal distortion U that cause of triangle drag load PPxThe superposition of (k δ), obtains three
Angular drag deforms the expression formula of δ：
δ=Ux(q1,qG,e1,e2,g,qw)-Ux(kδ)
Step S4：The horizontal distortion U that triangle drag load PP is causedx(k δ) does Taylor expansion and ignores higher order term,
To obtain horizontal distortion UxThe expression formula of (k δ)：
Ux(k δ)=f × δ；
Wherein, f is undetermined constant, unrelated with triangle drag deformation δ；
Step S5：The expression formula that step S4 is obtained is substituted in the expression formula that step S3 is obtained, and tries to achieve the change of triangle drag
The formula of shape δ：
Further, the top vertical earth pressure q in step S11, hogback soil pressure qG, top/bottom part level is to soil pressure
Power e1And e2, lining cutting deadweight g and hydrostatic pressure qwFor exact figures value when, can be solved by numerical analysis software.
Further, the load numerical value further includes vertical counter-force q in bottom2。
Further, in step S4, f is to deform the unrelated undetermined constants of δ with triangle drag, can be expressed as below
Formula：
Wherein, the desirable arbitrary little values of triangle drag deformation δ are substituted into and calculated；Ux(k δ) is acted on to determine triangular load
Deform at lower tunnel horizontal diameter, can be tried to achieve by numerical computations mode, the expression formula of f is obtained then.
Further, the desirable little value scope of the triangle drag deformation δ is the value less than or equal to 0.001.
Further, in step S1, the tunnel method for determining load is modified routine method.
The present invention is as a result of above technical scheme so as to have the advantages that：
（1）The present invention is considered as the level change that the load in addition to triangle drag causes by the way that triangle drag is deformed into δ
Shape Ux(q1,qG,e1,e2,g,qw) and the horizontal distortion U that cause of triangle drag load PPxThe superposition of (k δ), such that it is able to local
The semi analytic formula of triangle drag deformation is solved by numerical computations, traditional shield tunnel triangle drag position is solved really
The problem that computing formula is not suitable for compound stratum is moved, is reached and is proposed a kind of more generally applicable computational methods.
（2）By preceding solution, the present invention provides the foundation for the accurate duct pieces of shield tunnel internal force that solves.
Description of the drawings
Fig. 1 is computation model schematic diagram of the existing duct pieces of shield tunnel structural internal force calculation using modified routine method.
Fig. 2 is the sectional schematic diagram on exemplary complex stratum.
Fig. 3 is that compound stratum calculates load schematic diagram in the inventive method.
Specific embodiment
For the benefit of to the understanding of the present invention, illustrate below in conjunction with drawings and Examples.
Fig. 3 is referred to, the present invention provides a kind of compound stratum shield tunnel triangle drag load computational methods.
Because compound stratum level is no longer simple trapezoidal to soil pressure load, when there is qualitative change in shape, triangle drag
The calculating of deformation δ is more difficult.In order to solve this problem, the present invention solves triangle drag and becomes by local by numerical computations
The semi analytic formula of shape, more accurately to reflect segment deformation and force-bearing situation.Wherein, methods described step includes：
Step S1：It is related to tunnel deformation determination to be calculated according to tunnel method for determining load in conventional load structure method
Stratum drag load numerical value, the load numerical value include top vertical earth pressure q1, hogback soil pressure qG, top/bottom part level to
Soil pressure e1And e2, lining cutting deadweight g and hydrostatic pressure qw, level is to triangle drag PP.In the present invention, the load numerical value
It is to calculate to determine by modified routine method.
Step S2：Try to achieve the horizontal distortion U that the load in addition to triangle drag PP causesx(q1,qG,e1,e2,g,qw) and
The horizontal distortion U that triangle drag load PP causesx(kδ)；
Step S3：Because tunnel belongs to Linear Elastic Structure, deformation at tunnel annulus horizontal diameter is considered as described except three
The horizontal distortion U that load outside angular drag PP causesx(q1,qG,e1,e2,g,qw) and the water that causes of triangle drag load PP
Flat deformation UxThe superposition of (k δ), obtains the expression formula that triangle drag deforms δ：
δ=Ux(q1,qG,e1,e2,g,qw)-Ux(kδ)；
Wherein, δ is variable to be solved in above-mentioned equation, Ux(q1,qG,e1,e2,g,qw) it is in addition to triangle drag
The horizontal distortion that load causes, because each load is determination numerical value, therefore can be solved by numerical analysis software.
Step S4：Due to UxLoad itself contains known variables δ undetermined in (k δ), therefore cannot be straight by numerical computations software
Connect solution；Therefore on the basis of elastic small deformation problem is considered, the horizontal distortion U that triangle drag load PP is causedx(k
δ) do Taylor expansion and ignore higher order term, to obtain horizontal distortion UxThe expression formula of (k δ)：
Ux(k δ)=f × δ；
Wherein, f is undetermined constant, unrelated with triangle drag deformation δ.
Further, f can obtain following expression：
Wherein, the desirable arbitrary little values of triangle drag deformation δ are substituted into and calculated, such as during δ=0.001, can obtain following formula：
Then U in above-mentioned formulax(0.001k) deform at the lower tunnel horizontal diameter of triangular load effect to determine, can be by numerical value
Calculation is tried to achieve, and the expression formula of f is obtained then.Specifically, in the present invention, the triangle drag deformation δ's is desirable
Little value scope is the value less than or equal to 0.001；More specifically, the present invention mentions " ignoring higher order term " in step S4, in before this
Carry be δ be mathematically infinitely small, when actually meeting the precision of engineering design, δ can use the value less than or equal to 0.001 and be counted
Calculate.
Step S5：The expression formula that step S4 is obtained is substituted in the expression formula that step S3 is obtained, and is calculated as follows：
δ=Ux(q1,qG,e1,e2,g,qw)-Ux(kδ)
=Ux(q1,qG,e1,e2,g,qw)-f×δ
δ+f × δ=Ux(q1,qG,e1,e2,g,qw)
δ (1+f)=Ux(q1,qG,e1,e2,g,qw)
Finally try to achieve the formula that triangle drag deforms δ：
Separately, in Fig. 3, H0Level of ground water height is represented, H represents tunnel thickness of earth-fill cover, H1For H and H0Difference.
The present invention is described in detail above in association with drawings and Examples, those skilled in the art can basis
Described above makes many variations example to the present invention.Thus, some of embodiment details should not constitute limitation of the invention,
The present invention is by the scope defined using appended claims as protection scope of the present invention.
Claims (6)
1. a kind of compound stratum shield tunnel triangle drag load computational methods, it is characterised in that include：
Step S1：Calculate according to tunnel method for determining load in conventional load structure method and determine the ground related to tunnel deformation
Layer drag load numerical value, the load numerical value includes top vertical earth pressure q1, hogback soil pressure qG, top/bottom part level is to soil pressure
Power e1And e2, lining cutting deadweight g and hydrostatic pressure qw, level is to triangle drag PP；
Step S2：Try to achieve the horizontal distortion U that the load in addition to triangle drag PP causesx(q1,qG,e1,e2,g,qw) and triangle
The horizontal distortion U that shape drag load PP causesx(kδ)；
Step S3：Deformation at tunnel annulus horizontal diameter is considered as into the level that the load in addition to triangle drag PP causes
Deformation Ux(q1,qG,e1,e2,g,qw) and the horizontal distortion U that cause of triangle drag load PPxThe superposition of (k δ), obtains triangle
Drag deforms the expression formula of δ：
δ=Ux(q1,qG,e1,e2,g,qw)-Ux(kδ)；
Step S4：The horizontal distortion U that triangle drag load PP is causedx(k δ) does Taylor expansion and ignores higher order term, to obtain
Horizontal distortion UxThe expression formula of (k δ)：
Ux(k δ)=f × δ；
Wherein, f is undetermined constant, unrelated with triangle drag deformation δ；
Step S5：The expression formula that step S4 is obtained is substituted in the expression formula that step S3 is obtained, and tries to achieve triangle drag deformation δ's
Formula：
2. compound stratum shield tunnel triangle drag load computational methods according to claim 1, it is characterised in that：Institute
State the top vertical earth pressure q in step S11, hogback soil pressure qG, top/bottom part level is to soil pressure e1And e2, lining cutting deadweight g and
Hydrostatic pressure qwFor exact figures value when, can be solved by numerical analysis software.
3. compound stratum shield tunnel triangle drag load computational methods according to claim 2, it is characterised in that：Institute
State load numerical value and further include vertical counter-force q in bottom2。
4. compound stratum shield tunnel triangle drag load computational methods according to claim 1, it is characterised in that：Institute
In stating step S4, f is to deform the unrelated undetermined constants of δ with triangle drag, can obtain following expression：
Wherein, the desirable arbitrary little values of triangle drag deformation δ are substituted into and calculated；Ux(k δ) acts on lower tunnel to determine triangular load
Deform at road horizontal diameter, can be tried to achieve by numerical computations mode, the expression formula of f is obtained then.
5. compound stratum shield tunnel triangle drag load computational methods according to claim 4, it is characterised in that：Institute
The desirable little value scope for stating triangle drag deformation δ is the value less than or equal to 0.001.
6. compound stratum shield tunnel triangle drag load computational methods according to claim 1, it is characterised in that：Institute
In stating step S1, the tunnel method for determining load is modified routine method.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107178392A (en) * | 2017-06-28 | 2017-09-19 | 中铁第四勘察设计院集团有限公司 | A kind of method for controlling Tunneling by mining method secondary lining water pressure |
| CN107194136A (en) * | 2017-07-31 | 2017-09-22 | 中国水利水电第七工程局成都水电建设工程有限公司 | A kind of pressure from surrounding rock computational methods suitable for many stratum shallow tunnels |
| CN110552716A (en) * | 2019-09-19 | 2019-12-10 | 西南交通大学 | Assembling method of circular shield tunnel lining structure |
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| CN105787193A (en) * | 2016-03-16 | 2016-07-20 | 上海市城市建设设计研究总院 | Method for calculating triangular resistance loads of shield tunnel model structure |
| CN105971614A (en) * | 2016-06-17 | 2016-09-28 | 上海隧道工程有限公司 | Shield tunneling machine and shield construction method applied to composite stratum with upper soft portion and lower hard portion |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107178392A (en) * | 2017-06-28 | 2017-09-19 | 中铁第四勘察设计院集团有限公司 | A kind of method for controlling Tunneling by mining method secondary lining water pressure |
| CN107194136A (en) * | 2017-07-31 | 2017-09-22 | 中国水利水电第七工程局成都水电建设工程有限公司 | A kind of pressure from surrounding rock computational methods suitable for many stratum shallow tunnels |
| CN110552716A (en) * | 2019-09-19 | 2019-12-10 | 西南交通大学 | Assembling method of circular shield tunnel lining structure |
| CN110552716B (en) * | 2019-09-19 | 2020-05-26 | 西南交通大学 | Assembling method of circular shield tunnel lining structure |
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Application publication date: 20170426 |