CN112784335A - Tunnel mechanical behavior analysis method based on tunnel secondary lining surface strain - Google Patents
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Abstract
The invention discloses a tunnel mechanical behavior analysis method based on tunnel secondary lining surface strain, which is characterized by comprising the steps of using a homogeneous circular ring tunnel model in an elastic mechanics theory, utilizing secondary lining surface strain at the positions of a tunnel vault, an arch shoulder, an arch waist and an arch foot, deducing a pressure equation set of a simplified double-layer circular ring based on a geometric equation, a compatibility equation and a stress balance equation, writing an MATLAB solving program, and solving a stress numerical value in the double-layer circular ring so as to deduce the axial force and the bending moment of the tunnel secondary lining. And (3) establishing an entity unit load-structure model of the tunnel by using finite element software ANSYS, carrying out numerical calculation under an elastic constitutive structure, and determining a structure correction coefficient by comparing with an actual project. The invention solves the problems that the traditional sensor has higher loss rate in the long-term operation process of the tunnel and can not be used for mechanical detection of the whole service life of the tunnel. The method has important significance for reflecting the long-term mechanical property of the tunnel by using the surface strain of the secondary lining and fully exerting the advantages of the fiber bragg grating sensor.
Description
Technical Field
The invention relates to the technical field of tunnel engineering monitoring, in particular to a tunnel mechanical behavior analysis method based on tunnel secondary lining surface strain.
Background
Although with the continuous development of computer performance and numerical simulation methods, various complex actual conditions can be calculated and results with reference significance can be obtained. From the existing theoretical research results at home and abroad, most theoretical deductions still mainly research the distribution and stress variation of plastic areas in rock and soil mass around the tunnel, and less research is carried out on the distribution of stress in the supporting structure capable of directly reflecting the safety performance of the tunnel; the action of the supporting structure of the tunnel on the rock mass is simplified into uniformly distributed supporting force, and the actual condition of tunnel lining is difficult to reflect; many researches simplify a tunnel supporting structure into a single-layer homogeneous circular ring structure, in actual engineering, mountain tunnels and shield tunnels partially located in a complex geological environment or having special requirements on water resistance and the like widely use secondary linings as important components of the supporting structure, the secondary linings are usually molded reinforced concrete, primary supports are formed by obvious difference of physical and mechanical parameters such as elastic modulus and the like of steel arch frames and sprayed concrete, and certain error exists in simulation by using the single-layer homogeneous circular ring.
In addition, the existing research mainly analyzes the internal mechanical behavior of the supporting structure based on the external load borne by the supporting structure, in engineering practice, the pressure of surrounding rocks is difficult to measure accurately, a vibrating string type soil pressure cell sensor buried between the surrounding rocks and primary support is easy to damage, and an actual measurement value cannot be obtained. Theoretical calculations based on the external pressure of the structure will not reflect the mechanical properties of the lining.
Disclosure of Invention
The invention aims to overcome the defect that the mechanical property of a lining cannot be reflected based on the theoretical calculation result of the external pressure of a structure in the prior art, and provides a tunnel mechanical behavior analysis method based on the surface strain of a tunnel secondary lining.
In order to achieve the purpose, the invention is implemented according to the following technical scheme:
a tunnel mechanical behavior analysis method based on tunnel secondary lining surface strain comprises the following steps:
s1, simplifying and assuming the tunnel model, and establishing a circular tunnel form of the double-layer circular ring bearing load of the tunnel and a stress form of a differential unit under a cylindrical coordinate system in an elastic mechanics system: simplifying the primary support and the secondary lining of the tunnel into double-layer homogeneous elastic rings with different material properties; the circular tunnel is infinitely long in the longitudinal direction, and the influence of the length direction is not counted; neglecting the gravity action of the double-layer homogeneous ring; assuming that the tunnel is located in a homogeneous rock-soil mass, the tunnel is under the action of uniformly distributed horizontal and vertical soil pressures; the shear force between the rock-soil body and the tunnel lining is ignored, the shear force between the primary support and the secondary lining is ignored, and the deformation of the rock-soil body and the secondary lining meets a deformation compatibility equation; the inner layer and outer layer supporting structures of the tunnel are always in an elastic state, and the external pressure applied to the tunnel is kept unchanged;
s2, carrying out mapping formula derivation according to the assumption of the step S1;
s3, establishing the solution of the mapping relation by using MATLAB: the secondary lining surface strain epsilon obtained by the displacement continuous condition between layers, the radial stress continuous condition between layers, the tunnel inner side load condition and the tunnel inner side surface-mounted strain gaugeθSolving a linear equation set containing 9 unknowns as a known condition, and writing a solving equation set solving equation in Matlab software;
s4, performing modeling calculation on the circular tunnel by using ANSYS software, and verifying the consistency of the numerical simulation calculation result and the theoretical calculation result when calculating the pressure coefficients of different sides of the tunnel respectively;
s5, performing modeling calculation on the monitored section of the mountain tunnel by using FLAC3D software, and comparing calculation results of numerical simulation and theoretical deduction to obtain correction coefficients of axial force and bending moment of the arch crown, arch shoulder, arch waist and arch foot of the monitored section.
Further, the step S2 specifically includes: according to the assumption of S1, simplifying a stress-strain relational expression, a geometric equation of a simplified model, a balance equation and a deformation coordination equation under an elastic mechanics cylindrical coordinate system; according to the principle of elastomechanics superposition, boundary conditions in the horizontal direction and the vertical direction are converted into an expression form under a polar coordinate system, vertical loads and horizontal loads acting on the boundary of the tunnel supporting structure are converted into a normal load and a tangential load, and the normal load is divided into a voltage-sharing load and a load which continuously changes along with the angle; for the centrosymmetric pressure-equalized ring, the internal stress is irrelevant to the numerical value of an angle, a stress boundary and a displacement boundary condition of the double-layer homogeneous ring are established, an equation set is established through the boundary condition, and the equation set is solved; for normal and tangential stresses that vary with angle, the stress function is written as cos2 θ, since both shear and shear stresses are related to
In the form of the method, the stress function meets a deformation coordination equation, and a double-layer homogeneous ring stress boundary condition and a displacement boundary condition are established to obtain the determined equation set.
Further, the S3 includes a linear equation system with 9 unknowns, which is written as the following formula:
writing a solving equation set in Matlab software, wherein A.B ═ C, A is a coefficient matrix, B is an unknown matrix, C is a result matrix, and solving the unknown B by using an equation (1):
B＝CA-1 (1)
substituting the material parameters and the tunnel inner side test strain value, calculating and solving an unknown number of an equation set, substituting the unknown number into the equation set, and solving the magnitude of the P external force corresponding to the theta angle, or sequentially solving the magnitude of the stress strain at each position of the tunnel, and further calculating to obtain the axial force bending moment value.
Compared with the prior art, the method uses a homogeneous circular ring tunnel model in the theory of elastic mechanics, utilizes the secondary lining surface strain at the arch crown, arch shoulder, arch waist and arch foot positions of the tunnel, derives the compression equation set of the simplified double-layer circular ring through a geometric equation, a compatibility equation and a stress balance equation, writes an MATLAB solution program to solve the stress numerical value in the double-layer circular ring, and further derives the axial force and the bending moment of the secondary lining of the tunnel. And (3) establishing an entity unit load-structure model of the tunnel by using finite element software ANSYS, carrying out numerical calculation under an elastic constitutive structure, and determining a structure correction coefficient by comparing with an actual project. The invention solves the problems that the traditional sensor has higher loss rate in the long-term operation process of the tunnel and can not be used for mechanical detection of the whole service life of the tunnel. The method has important significance for reflecting the long-term mechanical property of the tunnel by using the surface strain of the secondary lining and fully exerting the advantages of the fiber bragg grating sensor.
Drawings
Fig. 1 is a flow chart of tunnel mechanical behavior deduction based on the surface strain of a tunnel secondary lining.
FIG. 2 is a schematic diagram of a theoretical derivation model: (a) a layered pressure-equalizing homogeneous circular ring; (b) and (5) a stress schematic diagram of the object under the polar coordinate system.
Fig. 3 is a schematic diagram of vertical symmetrical load decomposition.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. The specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
As shown in fig. 1, the present embodiment provides a tunnel mechanical behavior analysis method based on surface strain of a tunnel secondary lining, and the specific analysis steps are as follows:
1) as shown in fig. 2, (a) layered pressure-equalized homogeneous circular rings; (b) according to the stress schematic diagram of the object under the polar coordinate system, firstly, a tunnel model is simplified and assumed, and a circular tunnel form of a tunnel double-layer circular ring bearing load and a stress form of a differential unit under a cylindrical coordinate system in an elastic mechanics system are established.
(1) Simplifying the primary support and secondary lining of the tunnel into a double-layer homogeneous elastic ring with different material properties, wherein the radius of the inner ring is a, the radius of the outer ring is b, the material parameter of the inner ring is the same as that of the secondary lining of the tunnel, and the thickness of the inner ring is h1The parameters of the outer ring material are the same as those of the primary support material of the tunnel, and the thickness is h2. Establishing a polar coordinate system by taking the circle center of the circular ring as an origin, wherein the z direction is a longitudinal direction vertical to the plane of the circular ring;
(2) assuming that the circular tunnel is infinitely long in the longitudinal direction (z direction), the problem is reduced to the plane strain problem of epsilon without considering the influence of the length directionz＝0、εθz＝0、εrz＝0；
(3) Neglecting the gravity action borne by the double-layer homogeneous circular ring;
(4) assuming that the tunnel is located in a homogeneous rock-soil mass, it is acted on by uniformly distributed horizontal and vertical soil pressures, where the horizontal side pressure has a value of the vertical side pressure multiplied by a side pressure coefficient lambda.
(5) The shear force between the rock-soil body and the tunnel lining is ignored, the shear force between the primary support and the secondary lining is ignored, and the deformation of the rock-soil body and the secondary lining meets the deformation compatibility equation.
(6) The inner layer and the outer layer of the tunnel supporting structure are always in an elastic state, and the external pressure applied to the tunnel is kept unchanged.
2) Performing mapping relation formula derivation
(1) Since the tunnel is assumed to be in a plane strain state, and the double-layer homogeneous circular ring has an axisymmetric characteristic, the stress-strain relationship can be simplified as shown in formula (2):
the plane strain is simplified:
εθz＝0，εrz＝0，τrz＝0 (2)
in the formula: epsilonθz-tangential plane strain; epsilonrz-radial plane strain; tau isrz-radial shear stress; theta- (theta) -phiA tangential direction; r-radial direction; z-longitudinal direction.
(2) Simplifying a geometric equation, a balance equation and a deformation coordination equation of a double-layer homogeneous circular ring compression model under an elastic mechanics cylindrical coordinate system, wherein the equations are respectively shown as formulas (3), (4) and (5)
As a function of stress.
The geometric equation is as follows:
the equilibrium equation:
compatibility equations:
in the formula: epsilonr-a positive radial strain; epsilonθ-tangential positive strain; gamma rayrθ-radial shear strain; u. ofr-a radial displacement; u. ofθ-a tangential displacement; r-radial coordinate; theta-tangential coordinate; tau isrθ-tangential loading;
-a stress function.
(3) The load borne by the tunnel supporting structure is bidirectional axisymmetric load, and the stress boundary condition of the tunnel primary support is sigma of the load in the vertical direction according to the principle of elastomechanics superpositionyFor horizontal loads, the stress boundary condition of the tunnel primary support is σx- λ P. Respectively converting the boundary conditions in the horizontal direction and the vertical direction into expression forms under a polar coordinate system to obtainFormula (6):
in the formula: sigmar-a normal load; sigmaθ-tangential positive stress; tau isrθ-tangential loading; p-vertical load; λ -lateral pressure coefficient; theta-angle.
From the above formula, the vertical and horizontal loads acting on the boundary of the tunnel supporting structure can be converted into a normal load sigmarAnd a tangential load τrθThe boundary load of the supporting structure is shown in figure 3.
For the convenience of formula derivation, the normal load can be decomposed into a voltage-sharing load
And a load varying with the angle theta
In order to obtain the stress value inside the tunnel, two groups of stress functions are introduced respectively aiming at two load modes.
(4) For a centrosymmetrically stressed ring, the internal stress is independent of the value of the angle θ, and therefore the stress function is
According to
The stress value obtained by the solution is shown as the formula (7):
the boundary conditions of the double-layer homogeneous ring are as follows:
stress boundary:
displacement boundary:
from this boundary condition, four sets of equations can be listed, corresponding to A1、C1、A2、C2Four sets of unknowns:
in the formula: a-radial coordinate coefficient; c is a constant coefficient; a-the inner diameter of the ring; b-the outside diameter of the ring; r is the radius; h is1-secondary lining thickness; h is2-preliminary support thickness; d is the radial coordinate of the junction position of the inner ring and the outer ring; v is1-secondary lining poisson's ratio; v is1-preliminary bracing poisson's ratio; e1-secondary lining tensile compression modulus of elasticity; e1-primary support tensile and compressive modulus of elasticity; the other symbols have the same meanings as above.
Because the mechanical properties of the inner lining and the outer lining are the same, the unknown coefficient of the stress function in the inner ring in the formula is represented by subscript 1, and the stress function in the outer ring is represented by subscript 2; d represents the radial coordinate of the junction position of the inner circular ring and the outer circular ring, and the four groups of equations are solved simultaneously to obtain:
A1＝-2C1a2 (11)
in the formula: k is the bulk modulus of elasticity; g-modulus of elasticity in shear; epsilon'θThe tangential strain of the double-layer circular ring model is only under the action of uniformly distributed normal loads; the other symbols have the same meanings as above.
(5) For normal stress varying with angle theta
And tangential stress
Since both shear and shear stresses are related to cos2 θ, the stress function can be written as
In the form of (1), the stress function is required to satisfy the deformation coordination equation (18):
solving the available stress function
The expression of (a) is:
the partial derivatives of the stress function are respectively solved to obtain the stress component as follows:
in the formula: f (r) -a radius function; A. b, C, D-coefficient; the rest symbols are as before.
For the double-layer homogeneous circle, the stress boundary condition and the displacement boundary condition are respectively shown as (21) and (22):
stress boundary conditions:
displacement boundary conditions:
according to the boundary conditions, for the double-layer circular ring model subjected to normal and tangential stresses changing along with the angle theta, 8 unknowns in the stress functions of the inner circular ring and the outer circular ring can be solved by eight sets of equations shown in formulas (23) to (30):
in addition to the above 8 equations determined by the stress boundary and displacement boundary conditions, the secondary lining surface strain epsilon caused by the angle-varying load according to the principle of elastomechanics superpositionθCan be expressed as the total strain εTheta totalAnd surface strain ε 'of the previously calculated uniform normal loading'θThus, equation (31) of set 9 can be derived:
3) solving for establishing mapping relationships using MATLAB
The secondary lining surface strain epsilon obtained by the displacement continuous condition between layers, the radial stress continuous condition between layers, the tunnel inner side load condition and the tunnel inner side surface-mounted strain gaugeθSolving a system of linear equations containing 9 unknowns as known conditions, written as equation (32)
Writing a solving equation set in Matlab software, wherein the equation set can be written as A.B ═ C, A is a coefficient matrix, B is an unknown matrix, C is a result matrix, and solving the unknown B through an equation (33):
B＝CA-1 (33)
substituting the material parameters and the tunnel inner side test strain value, and calculating and solving the unknown number of the equation set. Substituting the equation into the equation set, the magnitude of the external force P corresponding to the angle theta can be obtained, the magnitude of the stress strain at each position of the tunnel can be sequentially solved, and then the axial force and bending moment value can be obtained through calculation.
4) Determining a correction factor
In the numerical simulation process by using the FLAC3D, the construction method and the support measure are comprehensively considered, and a corresponding calculation model is established.
And (2) establishing a plane graph through CAD, transversely taking 50m from the two sides of the tunnel by taking the center line of the tunnel as a reference during modeling, taking the longitudinal boundary from the bottom of the inverted arch by 46m to 42m from the top of the arch, carrying out grid division in ANSYS, and assigning different material parameters to the upper step, the lower step, the reserved core soil, the primary support, the secondary lining and the like of the tunnel, so that the calculation models introduced into the FLAC3D are divided into different groups, and the excavation and support calculation are facilitated.
According to the tunnel section information, the buried depth of the tunnel supporting structure is 478m, the surrounding rock grade is IV grade, the lithology is mainly slate and phyllite, and the physical and mechanical parameters of the rock mass at the periphery of the tunnel are determined as shown in the table 1.
TABLE 1 physical and mechanical parameters of phyllite mass around tunnel
The combined supporting action of the steel arch and the primary support is usually considered by a method of equivalent rigidity, and the concrete is sprayed according to the conversion of the formula (34).
In the formula: e is the converted elastic modulus of the concrete; ecThe elastic modulus of the original concrete; sgThe sectional area of the steel arch frame; egThe elastic modulus of steel; scIs the cross-sectional area of the concrete; and S is the total area of the concrete and the steel arch frame. The tunnel support parameters were determined as shown in table 2.
Table 2 physical and mechanical parameters of tunnel supporting structure
The theoretical solution of the internal force of the secondary lining of the tunnel section obtained by numerical model calculation is shown in table 3.
TABLE 3 theoretical solution of inner force of secondary lining of tunnel section
The calculation results of numerical simulation and theoretical deduction are compared to find that the correction coefficient of the vault axial force bending moment at the tunnel monitoring section position is shown in table 4.
TABLE 4 correction factor of tunnel monitoring section
5) Engineering example
After the tunnel is in service for a certain period, if the tunnel is cracked or the embedded vibrating wire type monitoring element is damaged, a surface-mounted optical fiber sensor can be selected for monitoring the surface strain of the lining, and other optical fiber grating strain sensors can be installed as supplements as required. The surface-mounted optical fiber sensor for monitoring the secondary lining surface of the tunnel comprises a surface-mounted optical fiber grating concrete strain gauge, a surface-mounted optical fiber grating accelerometer and an optical fiber grating crack meter, and is used for monitoring the surface stress state, the vibration condition and the surface crack of the secondary lining respectively.
The calculation formula of the surface strain is shown as follows:
ε＝K(λ1-λ10)-B(λt1-λt0) (35)
B＝C(αA-αB)×106+K (36)
in the formula: ε -surface strain, unit: mu epsilon;
k-strain coefficient of strain gauge, unit: mu epsilon/nm;
b-temperature compensated strain coefficient, unit: mu epsilon/nm;
c-temperature coefficient of temperature compensation sensor, unit: DEG C/nm;
λ1-current wavelength of the strain fiber grating, unit: nm;
λ10-initial wavelength of the strain fiber grating, unit: nm;
λt1temperature compensation fiber grating current wavelength, unit: nm;
λt0temperature compensation fiber grating initial wavelength, unit: nm;
αA-coefficient of thermal expansion of the measured body, in units: μ m/m.times.DEG C, where the concrete is 10X 10-6/℃；
αBThe coefficient of thermal expansion of the sensor, in units: μ m/m.times.DEG C, where the stainless steel is 16.6X 10-6/℃。
The surface strain of the tunnel lining is calculated in the fiber bragg grating monitoring data in the formulas (35) and (36), the final surface strain result is substituted into an elastic mechanics mapping relation model and multiplied by a correction coefficient, and the axial force and the bending moment of the section position can be calculated and are shown in the table 5.
As can be seen from Table 5, the average relative error between the theoretical calculation result of the axial force and the field actual measurement result is 15.94%, and the average relative error between the theoretical calculation result of the bending moment and the field actual measurement result is 22.67%, so that the elastic mechanics mapping model corrected by the FLAC3D static calculation can be used for deducing the mechanical characteristics of the tunnel secondary lining.
TABLE 5 tunnel ZK187+000 section secondary lining internal force
The technical solution of the present invention is not limited to the limitations of the above specific embodiments, and all technical modifications made according to the technical solution of the present invention fall within the protection scope of the present invention.
Claims (3)
1. A tunnel mechanical behavior analysis method based on tunnel secondary lining surface strain is characterized by comprising the following steps:
s1, simplifying and assuming the tunnel model, and establishing a circular tunnel form of the double-layer circular ring bearing load of the tunnel and a stress form of a differential unit under a cylindrical coordinate system in an elastic mechanics system: simplifying the primary support and the secondary lining of the tunnel into double-layer homogeneous elastic rings with different material properties; the circular tunnel is infinitely long in the longitudinal direction, and the influence of the length direction is not counted; neglecting the gravity action of the double-layer homogeneous ring; assuming that the tunnel is located in a homogeneous rock-soil mass, the tunnel is under the action of uniformly distributed horizontal and vertical soil pressures; the shear force between the rock-soil body and the tunnel lining is ignored, the shear force between the primary support and the secondary lining is ignored, and the deformation of the rock-soil body and the secondary lining meets a deformation compatibility equation; the inner layer and outer layer supporting structures of the tunnel are always in an elastic state, and the external pressure applied to the tunnel is kept unchanged;
s2, carrying out mapping formula derivation according to the assumption of the step S1;
s3, establishing the solution of the mapping relation by using MATLAB: the secondary lining surface strain epsilon obtained by the displacement continuous condition between layers, the radial stress continuous condition between layers, the tunnel inner side load condition and the tunnel inner side surface-mounted strain gaugeθSolving a linear equation set containing 9 unknowns as a known condition, and writing a solving equation set solving equation in Matlab software;
s4, performing modeling calculation on the circular tunnel by using ANSYS software, and verifying the consistency of the numerical simulation calculation result and the theoretical calculation result when calculating the pressure coefficients of different sides of the tunnel respectively;
s5, performing modeling calculation on the monitored section of the mountain tunnel by using FLAC3D software, and comparing calculation results of numerical simulation and theoretical deduction to obtain correction coefficients of axial force and bending moment of the arch crown, arch shoulder, arch waist and arch foot of the monitored section.
2. The method for analyzing mechanical behavior of a tunnel based on surface strain of a secondary tunnel lining according to claim 1, wherein the step S2 specifically includes: according to the assumption of S1, simplifying a stress-strain relational expression, a geometric equation of a simplified model, a balance equation and a deformation coordination equation under an elastic mechanics cylindrical coordinate system; according to the principle of elastomechanics superposition, boundary conditions in the horizontal direction and the vertical direction are converted into an expression form under a polar coordinate system, vertical loads and horizontal loads acting on the boundary of the tunnel supporting structure are converted into a normal load and a tangential load, and the normal load is divided into a voltage-sharing load and a load which continuously changes along with the angle; for the centrosymmetric pressure-equalized ring, the internal stress is irrelevant to the numerical value of an angle, a stress boundary and a displacement boundary condition of the double-layer homogeneous ring are established, an equation set is established through the boundary condition, and the equation set is solved; for normal and tangential stresses that vary with angle, the stress function is written as cos2 θ, since both shear and shear stresses are related to
In the form of the method, the stress function meets a deformation coordination equation, and a double-layer homogeneous ring stress boundary condition and a displacement boundary condition are established to obtain the determined equation set.
3. The method for analyzing mechanical behavior of a tunnel based on surface strain of a tunnel secondary lining according to claim 1, wherein the S3 contains a linear equation system of 9 unknowns, which is written as a formula:
writing a solving equation set in Matlab software, wherein A.B ═ C, A is a coefficient matrix, B is an unknown matrix, C is a result matrix, and solving the unknown B by using an equation (1):
B＝CA-1 (1)
substituting the material parameters and the tunnel inner side test strain value, calculating and solving an unknown number of an equation set, substituting the unknown number into the equation set, and solving the magnitude of the P external force corresponding to the theta angle, or sequentially solving the magnitude of the stress strain at each position of the tunnel, and further calculating to obtain the axial force bending moment value.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
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| CN113361169A (en) * | 2021-06-10 | 2021-09-07 | 安徽省建筑科学研究设计院 | Efficient prediction method for longitudinal deformation of shield tunnel caused by surface burst loading |
| CN113836620A (en) * | 2021-09-09 | 2021-12-24 | 武汉理工大学 | Method and device for rapidly calculating tunnel crack width based on parametric modeling |
| CN113836620B (en) * | 2021-09-09 | 2023-09-15 | 武汉理工大学 | Tunnel crack width rapid calculation method and device based on parametric modeling |
| CN114112174B (en) * | 2021-12-02 | 2023-07-21 | 华设设计集团股份有限公司 | Tunnel water and soil pressure monitoring method based on strain measurement |
| CN114112174A (en) * | 2021-12-02 | 2022-03-01 | 华设设计集团股份有限公司 | Tunnel water and soil pressure monitoring method based on strain measurement |
| CN114357572A (en) * | 2021-12-14 | 2022-04-15 | 中铁隧道局集团路桥工程有限公司 | Transverse pipe curtain deformation prediction method, device and equipment and readable storage medium |
| CN114894109A (en) * | 2022-02-09 | 2022-08-12 | 重庆交通大学 | Tunnel strain information acquisition method and related device |
| CN114894109B (en) * | 2022-02-09 | 2023-10-17 | 重庆交通大学 | Tunnel strain information acquisition method and related device |
| CN117574670B (en) * | 2023-12-05 | 2024-11-08 | 宁波大学 | Numerical simulation evaluation method for mechanical properties of liquefiable soil tunnel secondary lining under earthquake action |
| CN117993089A (en) * | 2024-04-07 | 2024-05-07 | 华东交通大学 | Tunnel lining displacement calculation method and system based on shell model |
| CN117993089B (en) * | 2024-04-07 | 2024-06-07 | 华东交通大学 | Tunnel lining displacement calculation method and system based on shell model |
| CN118171377A (en) * | 2024-05-14 | 2024-06-11 | 西南交通大学 | Soil tunnel lining stress numerical simulation method based on multi-solver coupling |
| CN118171377B (en) * | 2024-05-14 | 2024-07-12 | 西南交通大学 | Soil tunnel lining stress numerical simulation method based on multi-solver coupling |
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