CN114707382A - Bending rigidity calculation method for duct piece joint containing elastic liner - Google Patents
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Abstract
The invention discloses a method for calculating the bending rigidity of a segment joint with an elastic liner, which comprises the following steps: 1) calculating the axial force level of the joint part of the segment lining; 2) dividing each functional area of the tube sheet joint; 3) simulating each functional area by adopting a spring or a cylindrical material; 4) obtaining the stress-strain relation of the materials of each functional area; 5) dividing the columnar material area into a plurality of micro-element blocks; 6) initializing a bending moment value of the segment joint; 7) establishing a pipe piece joint displacement coordination equation, an axial force balance equation and a bending moment balance equation; 8) solving an equation set, and calculating a segment joint corner; 9) and 7) returning to the step 7) to be repeatedly executed in sequence to obtain a joint bending moment-corner relation curve so as to obtain the bending rigidity of the joint. The invention can fully consider the combined force transfer action of the elastic liner and the concrete in the segment joint, and can more accurately calculate the bending rigidity of the segment joint, thereby being applied to the structural design of the segment lining of the auxiliary shield tunnel.
Description
Technical Field
The invention belongs to the technical field of civil and hydraulic engineering, and particularly relates to a method for calculating the bending rigidity of a segment joint with an elastic liner, which is suitable for the structural design of the segment joint of a shield tunnel in the fields of civil engineering, water conservancy and the like.
Background
Along with the large-scale development of subways, highways and hydraulic engineering, the application of the shield method in tunnel engineering is more and more extensive. The segment lining is used as an important composition structure of the shield tunnel, and the bending rigidity of a joint of the segment lining is a key factor to be considered in the design process of the segment lining structure. The existing method for calculating the bending rigidity of the segment joint is mostly suitable for the segment joint without an elastic liner, namely, the force transmission action of a joint bolt and concrete is mainly considered. For the segment joint containing the elastic liner, the elastic liner is generally assumed to be a flexible material, and the concrete is assumed to be a rigid material, so that the force transfer effect of the elastic liner is only considered, and the combined force transfer effect of the elastic liner and the concrete is neglected. The method can cause the theoretical calculation value of the bending rigidity of the segment joint to be larger than the actual value due to the insufficient and reasonable consideration of the softening effect of the elastic liner on the segment joint, thereby causing the design condition of the segment lining to be dangerous. Therefore, how to fully consider the joint force transfer action of the joint bolt, the elastic liner and the concrete according to the structural characteristics of the segment joint, and reasonably and accurately calculating the bending rigidity of the joint is a key factor for ensuring the reliable structural design of the shield tunnel segment lining.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a method for calculating the bending rigidity of a segment joint with an elastic liner, so that the joint force transfer effect of the elastic liner and concrete can be fully considered, the bending rigidity of the segment joint can be more accurately calculated, and a basis is provided for the structural design of a segment lining.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention discloses a method for calculating bending rigidity of a duct piece joint with an elastic liner, which is characterized by comprising the following steps of:
firstly, preliminarily estimating the axial force level N of a lining formed by a whole ring of pipe pieces at each pipe piece joint by adopting an inertial method or a finite element method;
secondly, according to the contact positions of the elastic liner, the water-stopping liner, the bolt and the concrete, the pipe joint is sequentially divided into a separation area, a water-stopping liner force transmission area, an elastic liner force transmission area, a bolt force transmission area and a separation area from top to bottom along the thickness direction;
thirdly, the height of the bolt spring is set to be hbSimulating the bolt force transmission area by adopting the bolt spring according to the position of the bolt;
let the thickness of the composite material column of 'concrete-elastic liner-concrete' be l and the width be lcAnd the distances from the upper edge and the lower edge of the duct piece are respectively ha、hcSimulating the elastic liner force transmission area by using the composite material column;
fourthly, according to the stress sigma of the boltb(εb) Strain epsilonbRelationship of (c) and stress of concrete (σ)c(εc) Strain epsiloncRelationship (c), stress σ of elastic cushion materiale(ε) -Strain εeUsing the equations (1) and (2) to calculate the spring force F of the bolt springb-a displacement ΔbThe relationship of (1):
Fb＝F0+mAbσb (1)
in formulae (1) and (2): fbIs the tension of the bolt; m is the number of bolts contained in the segment joint; a. thebThe sectional area of a single bolt; epsilonbIs the strain of the bolt material; deltabIs the elongation of the bolt; l isbIs the length of the bolt;
calculating the relation of the equivalent stress sigma (epsilon) -strain epsilon of the composite material column by using the formula (3) and the formula (4):
σ(ε)＝σc(εc)＝σe(εe) (3)
in formulae (3) and (4): σ (ε) is the stress of the composite column under any strain ε condition; sigmac(εc) For concrete at any strain epsiloncStress under conditions; sigmae(εe) For elastic inserts at any strain epsiloneStress under conditions; t is the thickness of the elastic pad;
fifthly, equally dividing the composite material column into n micro-element blocks along the thickness direction of the tube piece; assuming that the strains at the upper and lower edges of the composite column are respectively εe1And εe2Then, the stress σ at the center position of the arbitrary ith infinitesimal block in the middle is calculated by using the equations (5) and (6)iAnd strain epsiloni：
In formulae (5) and (6): σ (ε)i) For the ith infinitesimal block at any strain epsiloniStress under conditions;
defining and initializing the bending moment applied to the segment joint as M;
and seventhly, obtaining a deformation coordination equation of the segment joint by using an equation (7) according to the deformation coordination relationship between the bolt spring and the composite material column in the expansion deformation process of the segment joint:
according to the balance condition of the axial force of the segment joint, an axial force balance equation of the segment joint is obtained by using the formula (8):
in the formula (8), B represents the width of the segment;
according to the balance condition of the bending moment of the segment joint, obtaining a bending moment balance equation of the segment joint by using a formula (9):
in formula (9): h is the thickness of the pipe piece;
eighth step, solving the equations (8) and (9) to obtain the strain epsilon of the upper and lower edges of the composite material columne1And εe2Thereby obtaining the rotation angle θ of the segment joint by using equation (10):
and ninthly, setting the bending moment M to be different values, and then respectively returning to the seventh step for sequential execution to obtain a joint bending moment M-corner theta relation curve of the segment joint under a certain axial force level N, so that the bending rigidity of the segment joint is obtained according to the slope of the curve.
The method for calculating the bending rigidity of the duct piece joint with the elastic liner is also characterized in that: and in the second step, the influence of the water-stopping pad on the bending rigidity of the pipe sheet joint is neglected, so that the force transfer area of the water-stopping pad is merged into the adjacent separation area.
Further: in the third step, when the bolt spring simulates the force transfer area of the bolt, the force of the bolt spring under pressure is zero.
Further: in the third step, the width l of the composite material columncThe value of (a) is determined according to the Saint-Venn principle, or let lcIs equal to l.
Further: in the third step, when the composite material column is adopted to simulate the force transfer area of the elastic liner, the segment joint without the elastic liner is simulated by using the thickness t of the elastic liner as 0.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the invention, when the bending rigidity of the segment joint is calculated, the force transmission effect of the bolt is considered through the spring, and the combined force transmission effect of the elastic liner and the concrete is fully considered through the concrete-elastic liner-concrete composite material column, so that the calculation result is more in line with the actual bearing characteristic of the segment joint.
2. The invention adopts the one-way tension spring and the composite material column which is only pressed and not tensioned, and can simulate the opening deformation rule of the segment joint in the gradual opening process of the segment joint under the action of the bending moment, thereby accurately calculating the bending rigidity of the segment joint under different load actions.
3. The invention is not only suitable for the segment joint with the elastic liner, but also suitable for the segment joint without the elastic liner, and the structure optimization design can be carried out on the segment joint in the design stage based on the invention.
Drawings
FIG. 1 is a functional area division diagram of a segment structure according to the present invention;
FIG. 1a is a schematic view of a segment structure calculation model according to the present invention;
FIG. 2 is a graph of the stress and deformation of the segment joint according to the present invention;
FIG. 3 is a schematic view of the segment joint location of the present invention;
FIG. 4a is a graph showing the calculated results of the positive bending moment-corner relationship curve of the joint according to the present invention;
FIG. 4b is a graph showing the calculated negative bending moment-rotation angle relationship curve of the joint according to the present invention.
Detailed Description
In this embodiment, the shield tunnel has a structure with an elastic liner segment joint as shown in fig. 1. A bending rigidity calculation method for a segment joint containing an elastic liner comprises the following steps:
firstly, preliminarily estimating the axial force level N of a lining formed by a whole ring of pipe pieces at each pipe piece joint by adopting an inertial method or a finite element method;
and secondly, as shown in fig. 1, according to the contact position of the elastic liner, the water-stopping liner, the bolt and the concrete, the pipe joint is sequentially divided into a separation area, a water-stopping liner force transmission area, an elastic liner force transmission area, a bolt force transmission area and a separation area from top to bottom along the thickness direction. Since the compression stiffness of the water stop pad is much less than that of concrete, the water stop pad has negligible effect on the bending stiffness of the pipe joint, thereby incorporating the force transfer zone of the water stop pad into its adjacent separation zone, as shown in fig. 1 a.
Thirdly, the height of the bolt spring is set to be hbAccording to the position of the bolt, simulating a bolt force transmission area by using a bolt spring;
let the thickness of the composite material column of 'concrete-elastic liner-concrete' be l and the width be lcWherein lcEqual to l, the distance between the composite material column and the upper edge and the lower edge of the duct piece is ha、hcSimulating a force transmission area of the elastic liner by adopting a composite material column;
the bolt spring and composite post are shown in fig. 1a, where: h is the thickness of the pipe piece;
a top separation zone gap;
is the bottom separation region gap.
Fourthly, according to the stress sigma of the boltb(εb) Strain epsilonbRelation of (d), stress of concrete (σ)c(εc) Strain epsiloncRelationship between, playStress sigma of liner materiale(ε) -Strain εeUsing the equations (1) and (2) to calculate the spring force F of the bolt springb-a displacement ΔbThe relationship of (1):
Fb＝F0+mAbσb (1)
in formulae (1) and (2): fbFor bolt tension, when the bolt spring is compressed, let F b0; m is the number of bolts contained in the segment joint; a. thebThe sectional area of a single bolt; epsilonbIs the strain of the bolt material; deltabIs the elongation of the bolt; l isbIs the length of the bolt;
calculating the relation of the equivalent stress sigma (epsilon) -strain epsilon of the composite material column by using the formula (3) and the formula (4):
σ(ε)＝σc(εc)＝σe(εe) (3)
in formulae (3) and (4): sigma (epsilon) is the stress of the composite material column under any strain epsilon condition; sigmac(εc) For concrete at any strain epsiloncStress under conditions; sigmae(εe) For elastic cushioning at any strain epsiloneStress under conditions; t is the thickness of the elastic pad;
when the segment joint does not contain an elastic liner, it can be considered as a special case, namely, when the thickness t of the elastic liner is 0, namely, the stress sigma (epsilon) -strain epsilon relation of the composite material column and the concrete stress sigma (epsilon)c(εc) Strain epsiloncThe relationship is consistent.
A fifth step of equally dividing the composite material column into n micro element blocks in the thickness direction of the tube sheet as shown in fig. 2 (a); assuming that the strains at the upper and lower edges of the composite column are respectively εe1And εe2Then, the stress σ at the center position of the arbitrary ith infinitesimal block in the middle is calculated by using the equations (5) and (6)iAnd strain epsiloni：
In formulae (5) and (6): sigma (. epsilon.)i) For the ith infinitesimal block at any strain epsiloniStress under conditions;
defining and initializing the bending moment applied to the segment joint as M;
seventhly, as shown in (b) of fig. 2, obtaining a segment joint deformation coordination equation by using an equation (7) according to the deformation coordination relationship between the bolt spring and the composite material column in the expansion deformation process of the segment joint:
as shown in fig. 2 (c), the axial force balance equation of the segment joint is obtained by using equation (8) according to the balance condition of the axial force of the segment joint:
in the formula (8), B represents the width of the segment;
as shown in fig. 2 (c), the bending moment equilibrium equation of the segment joint is obtained by using equation (9) according to the equilibrium condition of the bending moment of the segment joint:
in formula (9): h is the thickness of the pipe piece;
and eighthly, obtaining a nonlinear equation set by combining the vertical equation (8) and the equation (9). According to formula (1), formula (2) and formula (7), FbCan be used bye1And εe2And (4) expressing. Therefore, when N is a fixed value and any bending moment M value is input, the equation set only contains epsilone1And εe2Two unknowns. Thus, equations (8) and (9) are solved to obtain the strain ε of the upper and lower edges of the composite columne1And εe2From (d) in fig. 2, the rotation angle θ of the segment joint is obtained by equation (10):
since the concrete on the outer edge of the segment joint does not normally contact under normal load, the joint deformation needs to be checked so as to satisfy the following formula (11) and formula (12):
in formulae (11) and (12): deltaeCalculating a value for the deformation of the outer edge of the joint; deltaiA value is calculated for the amount of deformation of the joint inner edge.
And ninthly, after the bending moment M is set to be different values, the step is repeated for seven times and is sequentially executed, a joint bending moment M-corner theta relation curve of the segment joint under a certain axial force level N is obtained, and therefore the bending rigidity of the segment joint is obtained according to the slope of the curve.
Example (b): the assembly condition of the whole ring segments of a shield tunnel is shown in figure 3. The duct piece joint has the following size parameters: 1600mm for B, 400mm for H, Ha＝104mm，hb＝150mm，hc＝25mm，l＝271mm，
The concrete strength was C50. BoltThe parameters are as follows: m is 4, Eb＝210GPa，Lb＝600mm，Ab＝706.5mm2，F0＝100kN，fb480 MPa. The elastic pad parameters were: t is 1.5mm, and the stress-strain relationship is σe＝378.39εe 3.0892MPa。
Calculating the whole ring duct piece by adopting the first step, wherein the fourth step is that the joint is acted by positive bending moment, and the axial force is about 3000 kN; seventhly, the axial force of the joint is about 3200kN under the action of negative bending moment, and the axial force of the joint is about 3500kN under the action of negative bending moment.
And (4) calculating the rotation angle of each joint under the action of corresponding axial force and different bending moments by adopting the second step to the ninth step, and obtaining the bending rigidity of each joint according to the slope of the bending moment-rotation angle relation curve of each joint as shown in fig. 4a and 4 b.
In conclusion, the method can consider the size and structure characteristics of the segment joint and the combined force transmission effect of the joint bolt, the elastic liner and the concrete, so that the bending rigidity of the segment joint in the process of gradually opening each stage under the action of axial force and bending moment can be more accurately calculated, and the calculation result can be used for assisting the structural design of the segment lining of the shield tunnel.
Claims (5)
1. A bending rigidity calculation method of a segment joint containing an elastic gasket is characterized by comprising the following steps:
firstly, preliminarily estimating the axial force level N of a lining formed by a whole ring of pipe pieces at each pipe piece joint by adopting an inertial method or a finite element method;
secondly, according to the contact positions of the elastic liner, the water-stopping liner, the bolt and the concrete, the pipe joint is sequentially divided into a separation area, a water-stopping liner force transmission area, an elastic liner force transmission area, a bolt force transmission area and a separation area from top to bottom along the thickness direction;
thirdly, the height of the bolt spring is set to be hbSimulating the bolt force transmission area by adopting the bolt spring according to the position of the bolt;
the thickness of the composite material column of' concrete-elastic liner-concreteIs l, width is lcAnd the distances from the upper edge and the lower edge of the duct piece are respectively ha、hcSimulating the elastic liner force transmission area by using the composite material column;
fourthly, according to the stress sigma of the boltb(εb) Strain epsilonbRelationship of (c) and stress of concrete (σ)c(εc) Strain epsiloncRelationship (c), stress σ of elastic cushion materiale(ε) -Strain εeUsing the equations (1) and (2) to calculate the spring force F of the bolt springb-a displacement ΔbThe relationship of (1):
Fb＝F0+mAbσb (1)
in formulae (1) and (2): fbIs the tension of the bolt; m is the number of bolts contained in the segment joint; a. thebThe sectional area of a single bolt; epsilonbIs the strain of the bolt material; deltabIs the elongation of the bolt; l isbIs the length of the bolt;
calculating the relation of the equivalent stress sigma (epsilon) -strain epsilon of the composite material column by using the formula (3) and the formula (4):
σ(ε)＝σc(εc)＝σe(εe) (3)
in formulae (3) and (4): σ (ε) is the stress of the composite column under any strain ε condition; sigmac(εc) For concrete at any strain epsiloncStress under conditions; sigmae(εe) For elastic cushioning at any strain epsiloneStress under conditions; t is the thickness of the elastic pad;
fifthly, equally dividing the composite material column into n micro-element blocks along the thickness direction of the tube piece;assuming that the strains at the upper and lower edges of the composite column are respectively εe1And εe2Then, the stress σ at the center position of the arbitrary ith infinitesimal block in the middle is calculated by using the equations (5) and (6)iAnd strain epsiloni：
In formulae (5) and (6): sigma (. epsilon.)i) For the ith infinitesimal block at any strain epsiloniStress under conditions;
defining and initializing the bending moment applied to the segment joint as M;
and seventhly, obtaining a deformation coordination equation of the segment joint by using an equation (7) according to the deformation coordination relationship between the bolt spring and the composite material column in the expansion deformation process of the segment joint:
according to the balance condition of the axial force of the segment joint, an axial force balance equation of the segment joint is obtained by using the formula (8):
in the formula (8), B represents the width of the segment;
according to the balance condition of the bending moment of the segment joint, obtaining a bending moment balance equation of the segment joint by using a formula (9):
in formula (9): h is the thickness of the pipe piece;
eighth step, solving the equations (8) and (9) to obtain the strain epsilon of the upper and lower edges of the composite material columne1And εe2Thereby obtaining the rotation angle θ of the segment joint by using equation (10):
and ninthly, setting the bending moment M to be different values, and then respectively returning to the seventh step for sequential execution to obtain a joint bending moment M-corner theta relation curve of the segment joint under a certain axial force level N, so that the bending rigidity of the segment joint is obtained according to the slope of the curve.
2. The method of claim 1, wherein the method comprises the steps of: and in the second step, the influence of the water-stopping pad on the bending rigidity of the pipe sheet joint is neglected, so that the force transfer area of the water-stopping pad is merged into the adjacent separation area.
3. The method of claim 1, wherein the method comprises the steps of: in the third step, when the bolt spring simulates the force transfer area of the bolt, the force of the bolt spring under pressure is zero.
4. The method of claim 1, wherein the method comprises the steps of: in the third step, the width l of the composite material columncThe value of (a) is determined according to the Saint-Venn principle, or let lcIs equal to l.
5. The method of claim 1, wherein the method comprises the steps of: in the third step, when the composite material column is adopted to simulate the force transfer area of the elastic liner, the segment joint without the elastic liner is simulated by using the thickness t of the elastic liner as 0.
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| CN117454485A (en) * | 2023-10-31 | 2024-01-26 | 江汉大学 | Method for calculating bending-resistant bearing capacity of transverse joint of shield tunnel |
| CN117454485B (en) * | 2023-10-31 | 2024-04-19 | 江汉大学 | Method for calculating bending-resistant bearing capacity of transverse joint of shield tunnel |
| CN117198138A (en) * | 2023-11-01 | 2023-12-08 | 湖南大学 | Shield constructs section of jurisdiction micro aggregate concrete scale model and pouring mould thereof |
| CN117216862A (en) * | 2023-11-09 | 2023-12-12 | 湖南大学 | Three-dimensional shield tunnel dynamic analysis model based on fiber beam unit |
| CN117216862B (en) * | 2023-11-09 | 2024-02-02 | 湖南大学 | Three-dimensional shield tunnel dynamic analysis model based on fiber beam unit |
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