CN112632655A - Finite element unit model for simulating shield tunnel circumferential weld - Google Patents
Finite element unit model for simulating shield tunnel circumferential weld Download PDFInfo
- Publication number
- CN112632655A CN112632655A CN202011304713.9A CN202011304713A CN112632655A CN 112632655 A CN112632655 A CN 112632655A CN 202011304713 A CN202011304713 A CN 202011304713A CN 112632655 A CN112632655 A CN 112632655A
- Authority
- CN
- China
- Prior art keywords
- seam
- stiffness
- deformation
- dislocation
- tunnel
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Geometry (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Architecture (AREA)
- Civil Engineering (AREA)
- Structural Engineering (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Lining And Supports For Tunnels (AREA)
Abstract
The invention discloses a finite element model for simulating a shield tunnel circumferential weld, which is a one-dimensional two-node unit, wherein a unit stiffness matrix changes along with the development of discontinuous deformation of a circumferential weld joint and is divided into three stages. The elements of the unit stiffness matrix of each stage directly correspond to the axial tension-compression stiffness, the shear stiffness and the bending stiffness of the circular seam joint, and have definite physical significance. The finite element unit model provided by the invention can well simulate the discontinuous deformation of the circumferential seam position of the shield tunnel, so that the tunnel longitudinal deformation mode obtained by calculation is close to the actual longitudinal deformation mode of the tunnel, and the level of practical application is achieved.
Description
Technical Field
The invention belongs to the technical field of building structures, and relates to a finite element unit model for simulating the stress performance of a shield tunnel circumferential seam and an algorithm thereof.
Background
Engineering practice shows that discontinuous deformation at the circumferential seam joint of the shield tunnel is a main component of longitudinal deformation of the shield tunnel. In order to simulate the stress deformation characteristics of the shield tunnel circumferential seams, scholars at home and abroad propose finite element unit models of various types.
The force bearing performance of the circular seam is simulated by adopting a spring unit from Xiye Jian III, Xiaoquan Chun and the like. The axial tension-compression stiffness, the shear stiffness and the bending stiffness of the spring unit are determined by the axial tension-compression stiffness, the shear stiffness and the bending stiffness of the annular seam joint. The cell models proposed by the later scholars are mostly improved from spring cell models. For example, Liu Chong et al teach that a spring element essentially expresses the relationship between node force and node displacement for the node to which it is attached. Therefore, the relation between the node force and the node displacement can be directly expressed in a matrix mode, and the matrix unit is adopted to replace the spring unit. For another example, julienhua et al propose that the discontinuous deformation of the position of the circular seam joint cannot be reflected by simulating the circular seam joint by using a spring unit. The modeling idea of a Goodman unit in discontinuous medium mechanics is used by Zhu Heihua and the like, and a two-node joint unit with discontinuous circular seam position displacement is established for simulating the stress deformation characteristic of the circular seam.
At present, various spring unit models and improved spring unit models have two defects.
First, various types of spring element models and improved spring element models lack reliable calculation parameters. The current spring unit model and the improved spring unit model have the calculation parameters basically derived from the full-scale test of the circumferential seam joint. In the existing full-scale test of the circular seam joint, a duct piece with a certain width is cut out from a duct piece ring to be used as a test component. Therefore, only local stress performance parameters of the circular seam can be obtained actually. The parameter is directly applied to a spring unit model for simulating the stress performance of the whole circular seam surface, and a certain mismatching problem still exists.
Secondly, the rigidity matrix form of various spring unit models and improved spring unit models does not change along with the deformation development of the circumferential seam joint, and the characteristic that the stress performance of the circumferential seam joint of the shield tunnel changes in stages along with the deformation development of the circumferential seam joint cannot be reflected.
Disclosure of Invention
The invention aims to provide a finite element model for simulating a shield tunnel circumferential weld, which can reflect the stress deformation characteristics of a circumferential weld joint and can easily obtain calculation parameters.
In order to achieve the purpose, the invention adopts the following technical scheme:
a finite element unit model for simulating a shield tunnel circumferential weld is a one-dimensional two-node unit, and a unit stiffness matrix changes along with the development of discontinuous deformation of a circumferential weld joint and is divided into three stages.
Further, elements of the unit stiffness matrix of each stage directly correspond to axial tension-compression stiffness, shear stiffness and bending stiffness of the circumferential seam joint.
If i is the number of the stage, and i is 1, 2, 3, the unit stiffness matrix K corresponding to the i-th stageiThe following were used:
wherein, Kn(Δu)、KS(Δv)、KθThe (delta theta) is a bounded function, and the physical significance of the (delta theta) is the axial tension and compression stiffness, the shear stiffness and the bending stiffness of the annular seam joint, which are respectively functions of axial tension and compression deformation, shear deformation (dislocation) and bending deformation (opening) of the annular seam joint.
This is further explained below in conjunction with the drawings.
The joint unit to be established is a two-node unit as shown in fig. 1.
As shown in fig. 1, the node seats of the joint unitsThe mark is obtained by taking a node i as an origin, pointing the node i to a node j in the positive direction of the X axis, and rotating the X axis by 90 degrees anticlockwise in the positive direction of the Y axis. Let node i displace as u in the X-axis directioniDisplacement in the Y-axis direction of viAngle of rotation thetaiLet node j displace as u in the X-axis directionjDisplacement in the Y-axis direction of vjAngle of rotation thetaj. The positive direction of the linear displacement of each node is the same as the positive direction of the coordinate system of the node, and the positive direction of the angular displacement of each node is rotated from the X axis to the Y axis according to the right-hand rule. The node relative displacement vector Δ is represented by the following equations (1) and (2):
wherein:
as shown in fig. 2, assuming that the bending moment of the node i is M, the shearing force of the node i is Q, and the axial force of the node i is N, the positive direction thereof coincides with the positive direction of the unit coordinate system. Because the joint unit is not affected by any external load, the bending moment, the shearing force, the axial force and the node i of the node j are equal and opposite to each other according to the balance condition of the joint unit. The node force vector F is shown in equation (3) below:
traditionally, the cell stiffness matrix reflects the relationship of cell nodal forces and nodal displacements. However, for the novel joint unit, in order to give the actual physical meaning to each element of the stiffness matrix (each element corresponds to a certain stiffness of the circular seam), the stiffness matrix described below represents the relationship between the node force and the node relative displacement. For convenience of description, this stiffness matrix is referred to as a generalized cell stiffness matrix, which is converted to the form of a traditional cell stiffness matrix at the time of specific programming calculations.
The generalized element stiffness matrix K of the joint element reflects the relationship between the node force vector F and the node relative displacement vector Δ, as shown in equation (4) below:
F＝K·Δ (4)
as the deformation characteristics and the stress performance of each stage of the stress deformation of the tunnel are different, the forms of the joint generalized unit stiffness matrix K of each stage are different. Engineering practice shows that a certain longitudinal pressure acts on the circumferential seam interface of the shield tunnel. When the non-uniform settlement of the tunnel is small, the establishment generated at the circular seam joint is smaller than the maximum static friction force of the circular seam interface, and the maximum tensile stress caused by the bending moment generated at the circular seam joint on the circular seam interface is smaller than the compressive stress acting on the circular seam interface, the circular seam joint is in the 1 st stage of stress deformation. At the moment, the tunnel circular seam is not opened or staggered, so that the displacement components of the node i and the node j are basically the same, and the relative displacement matrix delta is approximate to a zero matrix no matter how the node force matrix F changes. At this time, the relationship between the node force and the node relative displacement of the tunnel is shown in the following equation (5):
where μ denotes the coefficient of friction at the circumferential seam face, I denotes the moment of inertia of the tunnel cross-section, and r denotes the radius of the segment ring.
According to the formula, the flexibility matrix of the joint unit in the stage is a 3-order 0 matrix, and the generalized stiffness matrix of the joint unit in the stage is 0 except that the diagonal elements are infinite. The physical significance of the generalized rigidity matrix of the circumferential seam unit at the stage is that the bending rigidity, the shearing rigidity and the axial tension and compression rigidity of the tunnel circumferential seam joint at the stage 1 are infinite.
As the uneven settlement of the tunnel increases, discontinuous deformation occurs at the circumferential seam joint. At the moment, the axial tension and compression stiffness, the bending stiffness and the shear stiffness of the circular seam joint are bounded functions respectively taking the axial tension and compression deformation, the bending deformation and the shear deformation of the circular seam joint as independent variables.
Therefore, the generalized stiffness matrix of the circumferential seam joint unit at stage 2 can be written as the following equation (6):
where ρ represents the curvature radius of the longitudinal deformation curve of the tunnel, ρ0Representing the critical radius of curvature of the tunnel longitudinal deformation curve.
In the above formula, KnThe axial tension and compression stiffness of the circular seam is represented, and the value of the axial tension and compression stiffness is the compression stiffness of concrete in the jurisdiction range of the joint unit when the circular seam is compressed and is close to infinity; the value of the tensile strength is the total tensile rigidity of all the bolts of the circular seam when the tensile strength is tensile, and when all the bolts on the section of the circular seam are in tensile yield, KnThe value is zero, as shown in the following formula (7), wherein E represents the elastic modulus of the bolt steel, a represents the cross-sectional area of the bolt, EA represents the section tensile stiffness of a single bolt, L represents the length of the single bolt, and n represents the number of bolts on the circumferential seam section. KSThe shearing rigidity of the annular seam is shown, and the magnitude of the shearing rigidity of the annular seam is changed along with the development of the dislocation. KθThe bending rigidity of the circular seam is shown, and the magnitude of the bending rigidity changes along with the development of the circular seam.
Wherein f isyIndicating the yield strength of the girth bolts; and A represents the cross-sectional area of the bolt.
With the development of the longitudinal uneven settlement of the tunnel, when the curvature of the longitudinal deformation curve of the tunnel is smaller than the critical curvature (the curvature of the longitudinal deformation curve when the edgemost girth bolt enters the yielding state), the structural characteristics of the girth joint determine that the girth joint cannot be continuously opened. At this time, the forced deformation of the circular seam joint enters a stage 3, one item of bending stiffness in the generalized stiffness matrix of the circular seam unit in the stage is close to infinity, and the axial tension and compression stiffness and the shear stiffness are still bounded functions of corresponding deformation, as shown in the following formula (8):
one of the purposes of the invention is to seek a value taking method for the calculation parameters of the circular seam joint unit. Three calculation parameters are required to be input into the circular seam joint unit: axial tension and compression rigidity of the circular seam, bending rigidity of the circular seam and shearing rigidity of the circular seam. The solution process of the axial tension-compression stiffness of the circumferential seam has been described above, and the bending stiffness K of the circumferential seam is described belowθ(Delta theta) and Ring gap shear stiffness KS(Δ v) is a value.
The bending stiffness of the circumferential seam joint is solved first. In the process of bending the annular seam, tensile stress is borne by the bolts, and compressive stress is borne by the segment ring body, as shown in fig. 3.
The position of the neutral axis can be known from the deformation coordination condition and the balance condition
Satisfies the following requirement (9):
wherein, Kj1The rigidity of tensile lines of all bolts on the section of the circular seam is shown, l represents the length of the circular seam bolt, ECACDenotes the compressive stiffness of the concrete of the torus, where ECDenotes the modulus of elasticity, A, of the concreteCRepresents the cross-sectional area of the annulus;
the central angle corresponding to the neutral axis is shown.
The equivalent stiffness of the joint unit can be calculated according to the position of the neutral axis as shown in the following formula (10):
wherein E isCDenotes the modulus of elasticity, I, of the concreteCRepresenting the moment of inertia of the tunnel cross section.
Therefore, the bending stiffness K of the circumferential seamθAs shown in the following formula (11):
wherein, L represents a single bolt length.
The shear stiffness of the circumferential seam joint is solved below. The existing research can provide the shear rigidity change rule of the annular seam local member consisting of a single bolt and the nearby concrete, and the research develops the shear rigidity change rule to the whole annular seam surface. As shown in FIG. 4, the central angle is set to
The shear force F of the bolt and the circumferential seam local member formed by the nearby concreteiAnd dislocation station DiThe relationship satisfies the following formula (12):
Fi＝fi(Di) (12)
set up wrong platform D of ith bolt position departmentiThe relation between the circular seam surface total dislocation D and the circular seam surface total dislocation D satisfies the following formula (13):
Di＝gi(D) (13)
assuming that F is the total shearing force of the circular seam surface, summing all the i formulas (12) and substituting the formula (13), the relationship between the total shearing force of the circular seam surface and the total dislocation of the circular seam surface can be obtained as shown in the following formula (14):
the relation between the total shearing force of the annular seam surface and the total dislocation of the annular seam surface is described by the formula (14), and the change rule of the shearing rigidity of the annular seam joint is substantially. The local shear stiffness variation law of the circumferential seam joints of various structures is given by a method of a full-scale test, and therefore, a specific form of the formula (12) is known. The following discusses mainly the specific form of formula (13).
The total dislocation of the annular seam surfaces is a result of a combined effect of the amount of settlement of a certain annular tube piece relative to the adjacent annular tube piece and the amount of convergence relative to the adjacent annular tube piece. In order to more clearly clarify the relationship between the total dislocation of the circular seam and each dislocation of the bolts, the total dislocation of the circular seam surface is not decomposed into relative settlement and relative convergence, the relationship between the displacement of the two parts and each dislocation of the bolts is respectively analyzed, and then the summation is carried out to obtain the relationship between the total dislocation of the circular seam surface and each dislocation of the bolts. Firstly, the relation between relative settlement and dislocation of bolts at various positions is researched.
The relative settlement of the segment rings represents the rigid displacement of the segment rings, so that the shape of the segment rings is not changed before and after the relative settlement, and the segment rings are all perfect circles, as shown in fig. 4:
as can be seen from FIG. 4, let d be the relative settlement between the centers of two adjacent circular tube pieces, and let d be the angle between the horizontal direction and the line connecting the ith bolt and the center of the circle
Then the ith bolt radial dislocation caused by the overall relative settlement of the circumferential seam surface is
Induced tangential dislocation of
The relationship between relative convergence and dislocation of bolts at each site is discussed below.
The relative convergence of the tube sheet rings represents deformation of the tube sheet rings, and therefore the centroid positions of the tube sheet rings before and after the relative convergence are unchanged, as shown in fig. 5:
the shape of the deformed shield tunnel is not necessarily regular, but in actual engineering, the long axis length and the short axis length of the deformed shield tunnel can be measured. In order to make the present study more suitable for practical engineering, the shape of the deformed shield tunnel is not assumed to be an ellipse. The polar equation of a deformed annular segment can be expressed by the following formula (15):
wherein: rho' represents the polar distance in a polar coordinate equation, wherein a is the half-long axial length of the deformed tunnel, and b is the half-short axial length of the deformed tunnel. Considering that under the condition of symmetrical load applied to the tunnel, the elongation of the transverse axis is equal to the shortening of the short axis, so that a + b is 2r, wherein r is the radius of the tunnel before deformation. The derivation assumes that points on the tunnel are in one-to-one correspondence before and after deformation, and as shown in the above figure, the coordinates before deformation of the ith bolt are set to
Then its deformed coordinate is
The displacement of the ith bolt during deformation is shown by the following equation (16):
similarly, let the half-length axial length of the adjacent ring segment of the ring segment after deformation be a0Half minor axis length of b0Then, the displacement of the ith bolt in the process of convergence and deformation of the adjacent ring segments is shown as the following formula (17):
therefore, the relative displacement of the adjacent two ring segments at the ith bolt is shown as the following formula (18):
decomposing the delta d along the radial direction and the tangential direction of the deformed tunnel, and obtaining the radial dislocation and the tangential dislocation of the ith bolt under the relative convergence action of the annular seam surfaces of the two adjacent annular pipe pieces as shown in the figure as follows (19):
by adopting the technical scheme, the finite element model provided by the invention can well simulate the discontinuous deformation of the circumferential seam position of the shield tunnel, so that the tunnel longitudinal deformation mode obtained by calculation is close to the actual longitudinal deformation mode of the tunnel, and the level of practical application is achieved.
Drawings
FIG. 1 is a schematic diagram of a node coordinate system and node displacement.
FIG. 2 is a force diagram of a node.
FIG. 3 is a schematic diagram of the calculation of bending stiffness.
FIG. 4 is a schematic diagram showing the displacement relationship of bolts at different positions under the relative settlement condition.
FIG. 5 is a schematic diagram of the displacement relationship of bolts at different positions under the condition of relative convergence.
FIG. 6 is a schematic view of a lining ring design.
Fig. 7 is a schematic diagram of a simulation object.
Fig. 8 is a schematic diagram of a computing unit.
FIG. 9 is a schematic diagram of the variation law of stiffness of an example circular seam.
FIG. 10 is a schematic view showing the relationship between bending moment and corner of two types of models.
FIG. 11 is a schematic diagram of the shear-slip relationship between two types of models.
FIG. 12 is a schematic view of the design of the lining ring of example two.
FIG. 13 is a schematic diagram of the shear stiffness variation law of the circular seam of the second embodiment.
FIG. 14 is a schematic view showing the relationship between bending moment and corner of two types of models.
FIG. 15 is a schematic diagram of the shear-slip relationship between two types of models.
Detailed Description
The present invention is specifically described below with reference to the flow charts and examples of the present invention.
Example one
Overview of the engineering:
the shield segment length of a certain cross-river tunnel is 2442.5 m. The shield constructs the section of jurisdiction design for two-sided wedge general ring, and the external diameter is 11800mm, internal diameter 10800mm, and the ring width is 2m, section of jurisdiction thickness 500mm, and the wedge volume is 40 mm. The duct piece assembly adopts a 5+2+1 form assembly, namely 5 standard blocks, 2 adjacent blocks and 1 capping block (K block), and the duct piece assembly rotates (determines the position of the K block) according to the line shape and the tunneling posture of a tunnel and is assembled by staggered joints. The pipe pieces are connected by adopting oblique bolts, longitudinal joints are connected by adopting 16M 36 bolts, circumferential joints are connected by adopting 46M 30 bolts, the strength grade of lining concrete is C60, and the impermeability grade is P12. As shown in fig. 6.
Calculating parameters:
calculating the inertia moment I of the section of the tunnel according to the section size of the tunnel for the novel joint unitCTunnel section area ACCircular seam bolt line rigidity Kj1. The length l of the tunnel circumferential seam bolt and the elastic modulus E of the concrete are obtainedC. The bending rigidity of the circular seam in the 2 nd stage and the 3 rd stage is 5.239 multiplied by 10 by substituting the parameters into the formula (9) and the formula (11)14N.mm/rad. And calculating the shearing force staggered platform relation of the single bolt according to the sizes of the circular seam bolt and the bolt hole. The law of change of the shear stiffness of the circumferential seams is calculated according to the arrangement of the bolts on the ring surface, and is shown in fig. 9.
For the traditional spring unit model, the influence of longitudinal pressure between rings is not considered when the bending spring stiffness is calculated, so the whole process bending stiffness is equal to the bending stiffness of the 2 nd and 3 rd stages of the joint unit model. The shear rigidity of the shear-resistant steel bar does not count the influence of static friction on the section, and is directly taken as the pure shear rigidity of all the inclined bolts on the section of the circular seam, as shown in formula (20):
the calculated annular gap shear stiffness of the traditional spring unit model is 4.4 multiplied by 106kN/m。
Novel joint unit and traditional spring unit atress performance contrast:
in order to fully show the difference of the stress performance of the two models, the following loading paths are adopted: firstly, loading the axial pressure N to 18040kN, temporarily considering no bending shear coupling effect of a circular seam, and respectively investigating the difference of the stress performance of the two models under the independent action of the bending moment M and the shearing force Q. Firstly, the shearing force Q is made to be 0, 3000kNm is loaded on each stage of the bending moment M until 123000kNm is obtained, and the relation between the bending moment and the corner of the two models is obtained by solving the relation as shown in figure 10. And then, the bending moment M is set to be 0, each stage of the shearing force Q is loaded with 500kN until 20500kN, and the shearing force dislocation relation of the two models is obtained by solving as shown in the figure 11.
As can be seen from fig. 10, the joint unit model has a large stage 1 rigidity under the action of bending moment, which is mainly because the stage 1 circular seam is not opened for the joint unit, and the displacements of the cross section of the circular seam are continuous, so the bending rigidity of the system is practically equivalent to that of the two ring pipe piece bodies. In stage 2, the rigidity of the joint unit model is greatly reduced, which is mainly caused by the fact that the annular seams in stage 2 are opened, so that the system generates extra corners. In phase 3, the stiffness of the joint unit model is increased again, mainly due to the change in longitudinal deformation mode of the whole tunnel. In fact, in practical engineering, when the circumferential seam bending moment reaches the dividing point between the 2 nd stage and the 3 rd stage, the stress mode of the whole tunnel is changed, and the increment of the circumferential seam bending moment in the 3 rd stage is small. Compared with a novel joint unit model, the bending rigidity of the circular seam is considered to be kept unchanged in the whole stress deformation process by the traditional beam spring model, and the bending rigidity of the circular seam is equivalent to the bending rigidity of the circular seam in the 2 nd and 3 rd stages. The view ignores the influence of axial pressure acting on the circular seam section on the bending rigidity of the circular seam, also ignores the influence of longitudinal deformation mode adjustment of the tunnel in a large deformation stage on the bending rigidity of the circular seam, actually exaggerates the corner of a system, and underestimates the bending rigidity of the circular seam.
As can be seen from FIG. 11, under the action of shearing force, the rigidity of the novel joint unit model in the 1 st stage is close to infinity, which is mainly because relative dislocation of the circular seam can not occur when the shearing force of the circular seam does not exceed the static friction force of the circular seam. And (3) the increment of the annular seam shearing force in the 2 nd stage is borne by the annular seam bolt group, microscopically, part of the bolts are pulled, and part of the bolts are bent, so that the shearing rigidity of the system is smaller. Compared with a novel joint unit model, the traditional beam spring model considers that the shear rigidity of the system is kept unchanged in the whole process of stress deformation and is the pure shear rigidity of the circumferential seam bolt group. In the stage 1, the traditional spring unit model neglects the effect of static friction force on the section of the circular seam, and underestimates the shearing rigidity of the circular seam. In the stage 2, the traditional spring unit model regards the shear stiffness of the circular seam as the pure shear stiffness of the bolt group, and ignores that the microscopic circular seam bolt is not in the pure shear stress state, but in the tension or bending stress state. The phase 2 conventional spring element model actually overestimates the shear stiffness of the circumferential seam.
Example two
Overview of the engineering:
the external diameter of a certain tunnel is 7000mm, the internal diameter is 6300mm, the ring width is 1.5m, and the thickness of the pipe piece is 350 mm. The segment assembly adopts a 3+2+1 form assembly, namely 3 standard blocks, 2 adjacent blocks and 1 capping block (K block), and the segment assembly rotates (determines the position of the K block) according to the line shape and the tunneling posture of the tunnel and is assembled by staggered joints. The circumferential seams are connected by 16M 30 bolts, the strength grade of the lining concrete is C60, and the impermeability grade is P12. As shown in fig. 12.
Calculating parameters:
calculating the inertia moment I of the section of the tunnel according to the section size of the tunnel for the novel joint unitCTunnel section area ACCircular seam bolt line rigidity Kj1. The length l of the tunnel circumferential seam bolt and the elastic modulus E of the concrete are obtainedC. The bending rigidity of the circular seam in the 2 nd stage and the 3 rd stage is 6.3 multiplied by 10 calculated by substituting the parameters into the formula (9) and the formula (11)13N.mm/rad. And calculating the shearing force staggered platform relation of the single bolt according to the sizes of the circular seam bolt and the bolt hole. The calculated shear stiffness variation law of the annular gap according to the arrangement mode of the bolts on the annular surface is shown in FIG. 13.
For the traditional spring unit model, the influence of longitudinal pressure between rings is not considered when the bending spring stiffness is calculated, so the whole process bending stiffness is equal to the bending stiffness of the 2 nd and 3 rd stages of the joint unit model. The shear rigidity of the bolt is directly taken as the pure shear rigidity of all the inclined bolts on the section of the circular seam without counting the influence of static friction on the section, and the pure shear rigidity is shown as the following formula (20):
the calculated annular seam shear stiffness of the traditional spring unit model is 1.53 multiplied by 106kN/m。
Novel joint unit and traditional spring unit atress performance contrast:
in order to fully show the difference of the stress performance of the two models, the following loading paths are adopted: firstly, loading the axial pressure N to 18040kN, temporarily considering no bending shear coupling effect of a circular seam, and respectively investigating the difference of the stress performance of the two models under the independent action of the bending moment M and the shearing force Q. Firstly, the shearing force Q is made to be 0, 3000kNm is loaded on each stage of the bending moment M until 77100kNm is reached, and the relation between the bending moment and the corner of the two models is obtained by solving the relation as shown in FIG. 14. And then, the bending moment M is set to be 0, each stage of the shearing force Q is loaded with 500kN till 14300kN, and the shearing force dislocation relation of the two models is obtained by solving as shown in the figure 15.
As can be seen from fig. 14, the joint unit model has a large stage 1 rigidity under the action of bending moment, which is mainly because the stage 1 circular seam is not opened for the joint unit, and the displacements of the cross section of the circular seam are continuous, so the bending rigidity of the system is practically equivalent to that of the two ring pipe piece bodies. In stage 2, the rigidity of the joint unit model is greatly reduced, which is mainly caused by the fact that the annular seams in stage 2 are opened, so that the system generates extra corners. In phase 3, the stiffness of the joint unit model is increased again, mainly due to the change in longitudinal deformation mode of the whole tunnel. In fact, in practical engineering, when the circumferential seam bending moment reaches the dividing point between the 2 nd stage and the 3 rd stage, the stress mode of the whole tunnel is changed, and the increment of the circumferential seam bending moment in the 3 rd stage is small. Compared with a novel joint unit model, the bending rigidity of the circular seam is considered to be kept unchanged in the whole stress deformation process by the traditional beam spring model, and the bending rigidity of the circular seam is equivalent to the bending rigidity of the circular seam in the 2 nd and 3 rd stages. The view ignores the influence of axial pressure acting on the circular seam section on the bending rigidity of the circular seam, also ignores the influence of longitudinal deformation mode adjustment of the tunnel in a large deformation stage on the bending rigidity of the circular seam, actually exaggerates the corner of a system, and underestimates the bending rigidity of the circular seam.
As can be seen from fig. 15, under the action of shear force, the stiffness of the novel joint unit model in the 1 st stage is close to infinity, which is mainly because relative dislocation of the circular seam does not occur when the shearing force of the circular seam does not exceed the static friction force of the circular seam. And (3) the increment of the annular seam shearing force in the 2 nd stage is borne by the annular seam bolt group, microscopically, part of the bolts are pulled, and part of the bolts are bent, so that the shearing rigidity of the system is smaller. Compared with a novel joint unit model, the traditional beam spring model considers that the shear rigidity of the system is kept unchanged in the whole process of stress deformation and is the pure shear rigidity of the circumferential seam bolt group. In the stage 1, the traditional spring unit model neglects the effect of static friction force on the section of the circular seam, and underestimates the shearing rigidity of the circular seam. In the stage 2, the traditional spring unit model regards the shear stiffness of the circular seam as the pure shear stiffness of the bolt group, and ignores that the microscopic circular seam bolt is not in the pure shear stress state, but in the tension or bending stress state. The phase 2 conventional spring element model actually overestimates the shear stiffness of the circumferential seam.
The foregoing description and description of the embodiments are provided to facilitate understanding and application of the invention by those skilled in the art. It will be readily apparent to those skilled in the art that various modifications can be made to these teachings and the generic principles described herein may be applied to other embodiments without the use of the inventive faculty. Therefore, the present invention is not limited to the above description and the description of the embodiments, and those skilled in the art should make improvements and modifications within the scope of the present invention based on the disclosure of the present invention.
Claims (8)
1. The utility model provides a finite element unit model of simulation shield tunnel circumferential weld, this unit is two node units of one-dimensional, its characterized in that: the unit rigidity matrix changes along with the development of the discontinuous deformation of the circular seam joint and is divided into three stages.
2. The finite element model for simulating the circumferential seam of the shield tunnel according to claim 1, wherein: the elements of the unit stiffness matrix of each stage directly correspond to the axial tension-compression stiffness, the shear stiffness and the bending stiffness of the circular seam joint.
3. The finite element model for simulating the circumferential seam of the shield tunnel according to claim 1, wherein if i is the serial number of the stage, i is 1, 2, 3, the element stiffness matrix K corresponding to the i-th stageiThe following were used:
wherein, Kn(Δu)、KS(Δv)、KθThe (delta theta) is a bounded function, and the physical significance of the (delta theta) is the axial tension-compression stiffness, the shear stiffness and the bending stiffness of the annular seam joint, which are respectively functions of axial tension-compression deformation, shear deformation or dislocation and bending deformation or opening of the annular seam joint.
4. The finite element model for simulating a shield tunnel circumferential seam of claim 3, wherein:
axial tension and compression stiffness K of circular seamnWhen the concrete is compressed, the value of the compressed concrete is the compression rigidity of the concrete in the jurisdiction range of the joint unit and is close to infinity; the value of the tensile strength is the total tensile rigidity of all the bolts of the circular seam when the tensile strength is tensile, and when all the bolts on the section of the circular seam are in tensile yield, KnIs zero, as follows:
Kn＝∞(N≥0)
Kn＝0(N≤-nfyA)
wherein EA represents the section tensile stiffness of a single bolt, L represents the length of the single bolt, n represents the number of bolts on the circular seam section, and fyIndicating the yield strength of the girth bolts.
5. The finite element model for simulating a shield tunnel circumferential seam of claim 3,
flexural rigidity K of the circumferential weldθAs shown in the following formula:
wherein the content of the first and second substances,
indicating the central angle corresponding to the position of the neutral axis.
6. The finite element model for simulating a shield tunnel circumferential seam of claim 3,
the change rule of the shear rigidity of the annular seam joint is embodied by the following relation between the total shear force F of the annular seam surface and the total dislocation of the annular seam:
wherein, the central angle is set as
The shear force F of the bolt and the circumferential seam local member formed by the nearby concreteiAnd dislocation station DiRelationships betweenSatisfies the following formula:
Fi＝fi(Di)
set up wrong platform D of ith bolt position departmentiAnd the relation with the circular seam surface total dislocation D satisfies the following formula:
Di＝gi(D)。
7. the finite element model for simulating a shield tunnel circumferential seam of claim 6, wherein:
the total dislocation of the annular seam surfaces is the result of the comprehensive effect of the settlement of a certain annular pipe piece relative to the adjacent annular pipe piece and the convergence relative to the adjacent annular pipe piece; and decomposing the total dislocation of the circular seam surface into relative settlement and relative convergence, respectively analyzing the relationship between the displacement of the two parts and the dislocation of the bolts at each point, and summing to obtain the relationship between the total dislocation of the circular seam surface and the dislocation of the bolts at each point.
8. The finite element model for simulating a shield tunnel circumferential seam of claim 7, wherein:
setting the relative settlement of the circle centers of two adjacent ring pipe pieces as d, and setting the included angle between the connecting line of the ith bolt and the circle center and the horizontal direction as
Then the ith bolt radial dislocation caused by the overall relative settlement of the circumferential seam surface is
Induced tangential dislocation of
Setting a as the half-long axial length of the deformed tunnel, b as the half-short axial length of the deformed tunnel, and a + b as 2r, wherein r is the radius of the tunnel before deformation; assuming that points on the tunnel are in one-to-one correspondence before and after deformation, and setting the coordinate before deformation of the ith bolt as
Then its deformed coordinate is
The displacement d of the ith bolt during deformation is given by:
the half-length axial length of the adjacent ring segment after deformation is a0Half minor axis length of b0Then the displacement d of the ith bolt in the convergence and deformation process of the adjacent ring segments0As shown in the following formula:
the radial dislocation and the tangential dislocation of the ith bolt of two adjacent ring segments under the relative convergence action of the ring seam surfaces are respectively shown as follows:
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202011304713.9A CN112632655B (en) | 2020-11-19 | 2020-11-19 | Finite element unit model for simulating shield tunnel circumferential weld |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202011304713.9A CN112632655B (en) | 2020-11-19 | 2020-11-19 | Finite element unit model for simulating shield tunnel circumferential weld |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112632655A true CN112632655A (en) | 2021-04-09 |
| CN112632655B CN112632655B (en) | 2022-03-04 |
Family
ID=75303514
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202011304713.9A Active CN112632655B (en) | 2020-11-19 | 2020-11-19 | Finite element unit model for simulating shield tunnel circumferential weld |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112632655B (en) |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101586463A (en) * | 2009-06-18 | 2009-11-25 | 苏州市交通设计研究院有限责任公司 | Lining design method of shield tunnel |
| CN101667220A (en) * | 2009-09-22 | 2010-03-10 | 同济大学 | Simulation method of shield tunnel joint structure |
| CN104537162A (en) * | 2014-12-16 | 2015-04-22 | 上海交通大学 | Method for determining capability of resisting slab staggering and expanding deformation of joints between shield tunnel lining rings |
| CN107060816A (en) * | 2017-05-23 | 2017-08-18 | 中铁第四勘察设计院集团有限公司 | A kind of attachment structure suitable for tunnel duct piece longitudinal joint |
| CN108241783A (en) * | 2018-01-05 | 2018-07-03 | 浙江大学城市学院 | The shield tunnel Method for Calculating Deformation of section of jurisdiction faulting of slab ends and rotation is considered under a kind of ground preloading simultaneously |
| CN108571328A (en) * | 2018-06-29 | 2018-09-25 | 西南交通大学 | A kind of stratum interface segment shield tunnel segment lining structure and design method |
| CN208502789U (en) * | 2018-07-23 | 2019-02-15 | 中铁四院集团西南勘察设计有限公司 | Connector and duct pieces of shield tunnel connection structure between duct pieces of shield tunnel |
-
2020
- 2020-11-19 CN CN202011304713.9A patent/CN112632655B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101586463A (en) * | 2009-06-18 | 2009-11-25 | 苏州市交通设计研究院有限责任公司 | Lining design method of shield tunnel |
| CN101667220A (en) * | 2009-09-22 | 2010-03-10 | 同济大学 | Simulation method of shield tunnel joint structure |
| CN104537162A (en) * | 2014-12-16 | 2015-04-22 | 上海交通大学 | Method for determining capability of resisting slab staggering and expanding deformation of joints between shield tunnel lining rings |
| CN107060816A (en) * | 2017-05-23 | 2017-08-18 | 中铁第四勘察设计院集团有限公司 | A kind of attachment structure suitable for tunnel duct piece longitudinal joint |
| CN108241783A (en) * | 2018-01-05 | 2018-07-03 | 浙江大学城市学院 | The shield tunnel Method for Calculating Deformation of section of jurisdiction faulting of slab ends and rotation is considered under a kind of ground preloading simultaneously |
| CN108571328A (en) * | 2018-06-29 | 2018-09-25 | 西南交通大学 | A kind of stratum interface segment shield tunnel segment lining structure and design method |
| CN208502789U (en) * | 2018-07-23 | 2019-02-15 | 中铁四院集团西南勘察设计有限公司 | Connector and duct pieces of shield tunnel connection structure between duct pieces of shield tunnel |
Non-Patent Citations (2)
| Title |
|---|
| ZHAO HUILING等: "《Simplified nonlinear simulation of shield tunnel lining reinforced by epoxy bonded steel plates》", 《ELSEVIER》 * |
| 柳献等: "《快速接头盾构隧道衬砌结构设计参数研究》", 《现代隧道技术》 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112632655B (en) | 2022-03-04 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN101667220B (en) | Simulation method of shield tunnel joint structure | |
| CN106096211B (en) | A kind of underground engineering confined concrete support system design method | |
| Zhang et al. | ‘Standing’full-scale loading tests on the mechanical behavior of a special-shape shield lining under shallowly-buried conditions | |
| CN110909429B (en) | Corrugated steel plate lining reinforcement parameter optimization design method and structure based on tunnel lining defect detection | |
| Chen et al. | Experimental study on ultimate bending performance of grouted connections in offshore wind turbine support structures | |
| Jusoh et al. | Segment’ s Joint In Precast Tunnel Lining Design | |
| Afshan et al. | Ultimate capacity of a segmental grey cast iron tunnel lining ring subjected to large deformations | |
| CN112632655B (en) | Finite element unit model for simulating shield tunnel circumferential weld | |
| Seidel et al. | Full-scale validation of FE models for geometrically imperfect flange connections | |
| CN113360985A (en) | High-precision prediction method for longitudinal deformation of existing shield tunnel caused by penetration of newly-built tunnel | |
| CN114662180A (en) | Shield tunnel longitudinal mechanical response calculation method based on inter-ring weak connection effect | |
| Ren et al. | Compressive behavior of stiffened steel tubes for wind turbine towers | |
| Chen et al. | Flexural behavior and resistance of uni-planar KK and X tubular joints | |
| CN109388870B (en) | Method for calculating minimum backfilling length of oil and gas pipeline by using strong group | |
| Cao et al. | Design of tension circular flange joints in tubular structures | |
| Ma et al. | Numerical study and design method of a single-layer spherical reticulated dome with hollow ball-tube bolted joints | |
| CN112052616A (en) | Method for calculating external pressure critical elastoplasticity buckling pressure of steel pipeline with random corrosion defects | |
| Zhu et al. | Study on parameter influence of new composite lining of water conveyance tunnel under high internal water pressure | |
| Liu et al. | Experimental and numerical study on the ultimate bearing capacity of a K-type tube-gusset plate joint of a steel transmission tower | |
| Orynyak et al. | Assessment of stress-displacement state of cable suspended pipeline bridge during inspection pig motion | |
| Nie et al. | Ultimate capacity of bulge formed T-joints under brace axial compressive loading | |
| CN116244809A (en) | Determination method and system for longitudinal equivalent bending stiffness and deformation of double-round shield tunnel | |
| Bardakjian et al. | Design Guidelines for the Steel Pipelines of a Major Project in San Antonio, Texas | |
| Liang et al. | Optimization calculation method and weighing test of static friction coefficient of RPC spherical joint based on half space contact model | |
| Zhao | Calculation of Internal Force and Deformation of Overlying Soil Corrugated Arch Bridge Based on Plate and Shell Theory |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |