CN108090283A - The finite element method of tunnel-vehicle coupled vibrations under a kind of DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES - Google Patents
The finite element method of tunnel-vehicle coupled vibrations under a kind of DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES Download PDFInfo
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Abstract
The present invention proposes a kind of finite element method of tunnel under DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES-vehicle coupled vibrations, is related to automation Computer Aided Design field.Comprise the following steps：(1) static analysis is carried out to full basement rock three-dimensional finite element model before tunnel excavation；(2) basement rock-lining cutting-bedding coupled system three-dimensional finite element model is established based on speed and coupled wave theory；(3) coupled system initial displacement is eliminated using initial stress method；(4) automatization simulation train operation time-histories load；(5) apply train operation time-histories load automatically to coupled system and calculate.The present invention uses software Program formatter, and based on speed and Coupled with Finite Element principle, automation applies dynamic load of the train with change in time and space, simplifies modeling program, reduce amount of calculation, problem is identified suitable for the security performance of the shield tunnel in the case where DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES acts on.
Description
Technical field
The present invention relates to automation Computer Aided Design fields, are related specifically to a kind of tunnel under DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES-vehicle coupling
The finite element method of vibration.
Background technology
With the sustained and rapid development of Chinese national economy, the size of population constantly expanded and worsening traffic shape
Contradiction between condition becomes increasingly conspicuous.Under huge traffic pressure, the rail lines such as subway, inter-city train increase severely.Train
The dynamic load with spatial variations at any time can be generated during being walked in tunnel, and passes through bedding and is transferred to tunnel-liner.Train
Influence of the dynamic load to basement rock-lining cutting-bedding coupled system is the important indicator for evaluating tunnel safety performance.
The common feature of such Tunnel Engineering is that the long scale of construction of circuit is big, and uncertain factor is more, is obtained by field test
The cycle of structural response is longer, and data discrete is big.Finite element time history analysis method be the such time-histories data problem of analysis most just
Prompt method.Its primary operational method is, based on basement rock-lining cutting-bedding coupling model, import Train induced load function with compared with
The dither effect of accurate simulation train, carries out Dynamic time history analysis, extracts the stress and anamorphic effect of coupled system.
Since tunnel structure circuit is long, model is big, need to determine model meshes size with reference to train running speed, and pass through
Coupling technique reduces scale of model；And the time-histories of train load loading is long, spatial variations are fast, by user interface manual loading
Can not simulating load with space-time variation.At present, though there is document to be directed to the track irregularity mould with reference to British Rail technique center
The train load exciting force function that type determines is introduced, but is not had under finite element analysis environment, is established to being based on the function
Coupling system model specific method and train time-histories load automate systematically discussing for application technology.
The content of the invention
Present invention solves the technical problem that it is：The present invention proposes a kind of tunnel under DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES-vehicle coupled vibrations
Finite element method, rely on ANSYS software APDL language program composition function, solve coupling technique under model build
Vertical and automation applies the problem of train time-histories load.
The technical scheme is that：
The finite element method of tunnel-vehicle coupled vibrations, comprises the following steps under a kind of DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES：
Step 1：By basement rock layering and material, determine model unit type and shape, material properties etc., establish tunnel and open
Full basement rock three-dimensional finite element model 1 before digging, and carry out the static analysis under gravity, with iswrite orders by full model section
Point stress and deformation result deposit file 1；
This analysis purpose is that initial stress and first displacement under the outer casing gravity of extraction lining cutting pass through initial stress
Balancing method, eliminates the gravity initial displacement of basement rock-lining cutting-bedding coupled system in subsequent step 3, and retains outside lining cutting
The primary stress of casing.During modeling, the corresponding excavation position in hollow tunnel in annular lining cutting and lining cutting need to be filled original
Rock stratum, and carry out entity and grid cutting.
Step 2：The full basement rock threedimensional model 1 that step 1 is established separately deposits generation new model, excavates the soil body successively, establishes lining
Block and bedding establish visco-elastic artificial boundary, form basement rock-lining cutting-bedding coupled system three-dimensional finite element model 2, loading
APDL language self-compiling programs based on node coupled wave theory, realize that tunnel-liner is connected with bedding；
Step 3：For basement rock-lining cutting-bedding coupled system three-dimensional finite element model 2, using initial stress balancing method,
Call in the stress and deformation result of lining cutting layer periphery basement rock node in file 1 using isfile orders, eliminate basement rock-lining cutting-
Accumulated deformation under bedding coupled system gravity, and introduce rock stratum and the primary stress on lining cutting contact surface；
Step 4：APDL language self-compiling programs are loaded, based on track irregularity exciting force function, simulate train operation time-histories
Load；
Step 5：APDL language self-compiling programs are loaded, apply train operation time-histories load to coupled system and are calculated.
Further, in the step 2, train load impetus is on bedding node.To ensure Ground Induced by Train Moving edge
The accurate application of tunnel vertical axis is no more than υ Δ t along tunnel lengthwise to control bedding size of mesh opening, and υ transports for train in formula
Scanning frequency degree, Δ t are load time step-length.But coupled system covers structure-rich, and circuit is long, if by lining cutting and the fine and closely woven list of bedding
Member implements conode processing, and modeling and calculating cost increase severely, therefore lining cutting grid can be more extensive.Load APDL language self-programmings
Sequence based on node coupled wave theory, realizes that tunnel-liner is connected with thick, refined net between bedding, specific method is：
(1) all node definitions of lining cutting are selected as array cq, it is fixed to obtain node total number cqnum, dim order by get orders
Adopted array cqcount；
(2) the minimum node of number is found in cq arrays, and ndnext orders are embedded in being cycled by do, is found one by one
Adjacent node is numbered, is sequentially stored into array cqcount；
(3) it is array jc to select on bedding with all node definitions in lining cutting contact surface, and it is total to obtain node by get orders
Number jcnum, dim command definition arrays jccount；
(4) the minimum node of number is found in jc arrays, ndnext orders are embedded in being cycled by do, finds compile one by one
Number adjacent node, is sequentially stored into array jccount；
(5) all nodes of cqcount arrays are selected, nnear orders are embedded in being cycled by do, found from 1 to jcnum and
Node similar in each node of jccount arrays, and one cqcount node of a corresponding exclusion；
(6) cq coupling commands are embedded in being cycled by do, realize the coupling of bedding node and lining cutting node one by one from 1 to jcnum
It closes.
Further, in the step 4, consider that track irregularity exciting force function is：
P (t)=P0+P1sinω1t+P2sinω2t+P3sinω3t (1)
P1、P2、P3To press the oscillatory load under driving stationarity, circuit additional load and corrugation control condition, meter
Formula is：
ωiFor vehicle circular frequency, calculating formula is：
ωi=2 π υ/li(i=1,2,3) (3)
In formula (1), P0For vehicle static load；In formula (2), M0For train unsprung mass, aiFor typical rise；In formula (3), υ
For train running speed, liFor Geometric irregularity curve typical wavelengths；By driving stationarity, work as li=50m, ai=16mm, when
li=20m, ai=9mm, works as li=10m, ai=5mm by circuit additional load situation, works as li=5m, ai=2.5mm, works as li=
2m,ai=0.6mm, works as li=1m, ai=1.3mm by corrugation situation, works as li=0.5m, ai=0.1mm, works as li=
0.02m,ai=0.005mm；
APDL language self-compiling programs are loaded, based on track irregularity exciting force function, simulate train operation time-histories load,
Specific method is：
(1) DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES parameter is defined, including distance between axles d, train running speed υ, vehicle before and after tunnel overall length s, train
Total time ttime, load time step-length time, loading total step number ti, loading step i are run in tunnel, wherein
(2) define arrays force1, implements cycling of do from step 1 to ti is loaded, and it is any to define train by formula (1)-(3)
The exciting force that front-wheel changes over time is：
Force1 (i)=P0+P1sinω1(i·time)+P2sinω2(i·time)+P3sinω3(itime), and
It adds and works as (itime-s/ υ) ＞ 0, then force1 (i)=0；
(3) define arrays force2, implements cycling of do from step 1 to ti is loaded, and it is any to define train by formula (1)-(3)
The exciting force that trailing wheel changes over time is：
Force2 (i)=P0+P1sinω1(i·time-d/υ)+P2sinω2(i·time-d/υ)+P3sinω3(i·
Time-d/ υ),
And additional as (itime-d/ υ) ＜ 0, then force2 (i)=0.
Further, APDL language self-compiling programs are loaded in step 5, coupled system is applied at any time and spatial variations
Train operation time-histories load, specific method is：
(1) the longitudinal node of two row that selection bedding upper limb biserial wheel rolls, it is array to define front-wheel running position
Dist1, trailing wheel running position are array dist2；
(2) from 1 to ti implementation cycling of do of step is loaded, corresponding i-th loading step, front-wheel running position is dist1 (i)=υ
I, trailing wheel running position are dist2 (i)=υ i-d, find the node nearest apart from front and rear wheel position respectively by node orders
Number, back to array n1 (i) and n2 (i), choose node n1 (i) and n2 (i), loaded respectively by F orders force1 (i) with
force2(i)；
(3) loading of train time-histories load in all time steps is sequentially completed, time-histories point is carried out to the Coupled Vibration System
Analysis.
Compared on going result, the beneficial effects of the invention are as follows：The present invention is realized establishes tunnel system using coupled wave theory
The technology that system finite element model and automatization simulation train exciting force influence.Based on Coupled with Finite Element technology, create bedding with
The nested procedure of lining cutting node coupling, substantially reduces model calculation scale；Based on time-history analysis principle, create with space-time
The nested procedure that the train exciting force automation of variation applies, can realize the quick addition of Train induced load.It is of the present invention
Method is the secondary development that ANSYS softwares are directed to tunnel structure dynamic Property Analysis problem, by automating input medium, is controlled
Simulation scale reduces and calculates cost.The technology can be directed to the kinematic analysis problem of all kinds of train transportation routes, for engineering skill
Art personnel directly use.
Description of the drawings
Fig. 1 is tunnel under DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES-vehicle coupled vibrations finite element analysis flow chart.
Fig. 2 is basement rock-lining cutting-bedding coupled system FEM model schematic diagram.
Fig. 3 is that lining cutting-bedding is of coupled connections FEM model schematic diagram.
Fig. 4 is train front-wheel exciting force time-histories schematic diagram.
Fig. 5 is t=10s basement rock-lining cutting-bedding coupled system vertical displacement cloud atlas.
Specific embodiment
The present invention will be further described below in conjunction with the accompanying drawings.
As shown in Figure 1, realize that the flow of the present invention is as follows using ANSYS softwares：
Step 1：Full basement rock three-dimensional finite element model before tunnel excavation is established, and carries out static analysis：By basement rock layering and
Material determines model unit type and shape, material properties etc., establishes basement rock three-dimensional finite element model 1, and carries out gravity work
Full model node stress and deformation result are stored in file 1 by the static analysis under with iswrite orders.
Step 2：Basement rock-lining cutting-bedding coupled system three-dimensional finite element model is established, it is real based on node coupled wave theory
Existing tunnel-liner is connected with bedding：Generation new model is separately deposited by basement rock threedimensional model 1, the soil body is excavated successively, establishes lining cutting and base
Bed establishes visco-elastic artificial boundary, forms basement rock-lining cutting-bedding coupled system three-dimensional finite element model 2, as shown in Figure 2；
Bedding is controlled to be no more than υ Δ t along tunnel lengthwise to size of mesh opening, υ is train running speed in formula, and Δ t walks for the load time
It is long；APDL language self-compiling programs are loaded, define bedding and the set of node in lining cutting contact surface respectively, cq is embedded in being cycled by do
The extensive lining cutting node of the fine and closely woven bedding node of grid and grid is realized coupling processing, as shown in Figure 3 by coupling command.
Step 3：Using initial stress balancing method, basement model Static Calculation is called in as a result, eliminating basement rock-lining cutting-bedding
Initial displacement under coupled system gravity：For basement rock-lining cutting-bedding coupled system three-dimensional finite element model 2, make
The stress and deformation result of lining cutting layer periphery basement rock node in file 1 are called in isfile orders, is eliminated under the gravity of rock stratum
Accumulated deformation, and introduce the primary stress on rock stratum and lining cutting contact surface.
Step 4：Based on track irregularity exciting force function, train operation time-histories load is simulated：According to formula (1)-(3),
By vehicle static load, train unsprung mass, train running speed, typical rise and Geometric irregularity curve typical wavelengths, structure row
Vehicle exciting force function；APDL language self-compiling programs are loaded, parametrization inputs distance between axles, train operation before and after tunnel overall length, train
Speed, vehicle run total time, load time step-length, loading total step number in tunnel, implement cycling of do for all time steps
Program defines the forward and backward wheel exciting force of each time step, as shown in Figure 4.
Step 5：Apply train operation time-histories load to coupled system and calculate：APDL language self-compiling programs are loaded, for
All time steps implement do cyclic programs, determine front and rear wheel load(ing) point present position during each time step, and in wheel loading most
Apply front and rear wheel exciting force at neighboring node；The loading of train time-histories load in all time steps is sequentially completed, to the coupling
Vibrational system carries out time-history analysis, obtains time-history analysis as a result, as shown in Figure 5.
Example：Tunnel-vehicle Coupled Vibration System automation modeling and calculating
Step 1：Full basement rock three-dimensional finite element model before tunnel excavation is established, and carries out static analysis.With 550m long undergrounds
Tunnel is analysis object, and edpth of tunnel 23m, diameter 6.1m, basement rock is respectively from top to bottom argillic horizon and middle layer of sand, determines mould
Type cell type is solid45, and tunneling material is concrete C50.Material properties are assigned, establish basement rock three-dimensional finite element model
1, and the static analysis under gravity is carried out, full model node stress and deformation result are stored in by file with iswrite orders
1。
Step 2：Basement rock-lining cutting-bedding coupled system three-dimensional finite element model is established, it is real based on node coupled wave theory
Existing tunnel-liner is connected with bedding.Generation new model is separately deposited by basement rock threedimensional model 1, the soil body is excavated successively, establishes lining cutting and base
Bed establishes the visco-elastic artificial boundary of combin14 unit simulations, forms basement rock-lining cutting-bedding coupled system Three-D limited
Meta-model 2；By train running speed υ=200km/h, load time step delta t=0.01s, control bedding along tunnel lengthwise to
Size of mesh opening is no more than υ Δs t=0.56m；APDL language self-compiling programs are loaded, are defined respectively in bedding and lining cutting contact surface
Set of node jc and cq, cq coupling commands are embedded in being cycled by do, by the fine and closely woven bedding node of grid and the extensive lining cutting of grid
Node realizes coupling processing.
Step 3：Using initial stress balancing method, basement model Static Calculation is called in as a result, eliminating basement rock-lining cutting-bedding
Initial displacement under coupled system gravity.For basement rock-lining cutting-bedding coupled system three-dimensional finite element model 2, make
The stress and deformation result of remaining basement rock after the excavation of lining cutting layer periphery in file 1 are called in isfile orders, eliminates rock stratum weight
Accumulated deformation under power effect, and introduce rock stratum and the primary stress on lining cutting contact surface.
Step 4：Based on track irregularity exciting force function, train operation time-histories load is simulated.According to formula (1)-(3),
Vehicle static load P0=80kN, train unsprung mass M0=750kg, train running speed υ=200km/h, Geometric irregularity curve
Typical wavelengths and typical rise take l1=10m, a1=5mm, l2=2m, a2=0.6mm, l3=0.5m, a3=0.1mm, structure row
Vehicle exciting force function；APDL language self-compiling programs are loaded, parametrization inputs distance between axles before and after tunnel overall length 550m, train
17.5m, train running speed 200km/h, vehicle run total time about 10s, load time step-length 10s, loading always in tunnel
Step number 1000 implements do cyclic programs for all time steps, defines the forward and backward wheel exciting force array force1 of each time step
(i) and force2 (i).
Step 5：Apply train operation time-histories load to coupled system and calculate.APDL language self-compiling programs are loaded, for
All time steps implement do cyclic programs, determine front and rear wheel load(ing) point present position dist1 (i) and dist2 during each time step
(i), most neighboring node is found by node orders, front and rear wheel exciting force is applied by F orders respectively；It is sequentially completed all time steps
The loading of interior train time-histories load carries out time-history analysis to the Coupled Vibration System.
Based on the present invention, the numerical analysis to tunnel safety performance under the influence of DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES can be realized, illustrated by
It is that other analysis methods do not have to be considered Coupling method based on speed and automated application with the method for change in time and space DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES
Have.Example described above only row example to clearly illustrate, and the restriction not to implementation.The present invention is not being departed from
Several improvement can be made on the premise of principle, these improvement also should be regarded as protection scope of the present invention, there is no need and unable to right
All implementations are exhaustive.
Claims (5)
1. a kind of finite element method of tunnel-vehicle coupled vibrations under DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES, it is characterised in that：Including following step
Suddenly：
Step 1：By basement rock layering and material, model unit type and shape, material properties etc. are determined, establish before tunnel excavation entirely
Basement rock three-dimensional finite element model 1, and carry out the static analysis under gravity, with iswrite orders by full model node stress
File 1 is stored in deformation result；
Step 2：The full basement rock threedimensional model 1 that step 1 is established separately deposits generation new model, excavates the soil body successively, establish lining cutting and
Bedding establishes visco-elastic artificial boundary, forms basement rock-lining cutting-bedding coupled system three-dimensional finite element model 2, loads APDL
Language self-compiling program based on node coupled wave theory, realizes that tunnel-liner is connected with bedding；
Step 3：Using initial stress balancing method, the stress of lining cutting layer periphery basement rock node in file 1 is called in using isfile orders
And deformation result, the accumulated deformation under basement rock-lining cutting-bedding coupled system gravity is eliminated, and introduces rock stratum and lining cutting
Primary stress on contact surface；
Step 4：APDL language self-compiling programs are loaded, based on track irregularity exciting force function, simulate train operation time-histories load；
Step 5：APDL language self-compiling programs are loaded, apply train operation time-histories load to coupled system and are calculated.
2. the finite element method of tunnel-vehicle coupled vibrations under a kind of DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES according to claim 1,
It is characterized in that：In the step 2, to ensure accurate application of the Ground Induced by Train Moving along tunnel vertical axis, along tunnel lengthwise to control
Bedding size of mesh opening processed is no more than υ Δ t, and υ is train running speed in formula, and Δ t is load time step-length, loads APDL language
Self-compiling program based on node coupled wave theory, realizes that tunnel-liner is connected with thick, refined net between bedding, specific method is：
(1) all node definitions of lining cutting are selected as array cq, node total number cqnum, dim command definition number is obtained by get orders
Group cqcount；
(2) the minimum node of number is found in cq arrays, and ndnext orders are embedded in being cycled by do, finds number phase one by one
Adjacent node, is sequentially stored into array cqcount；
(3) it is array jc to select on bedding with all node definitions in lining cutting contact surface, and node total number is obtained by get orders
Jcnum, dim command definition array jccount；
(4) the minimum node of number is found in jc arrays, ndnext orders are embedded in being cycled by do, it is adjacent to find number one by one
Node, be sequentially stored into array jccount；
(5) all nodes of cqcount arrays are selected, nnear orders are embedded in being cycled by do, found from 1 to jcnum and
Node similar in each node of jccount arrays, and one cqcount node of a corresponding exclusion；
(6) cq coupling commands are embedded in being cycled by do, realize the coupling of bedding node and lining cutting node one by one from 1 to jcnum.
3. the finite element method of tunnel-vehicle coupled vibrations under a kind of DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES according to claim 1,
It is characterized in that：In the step 4, consider that track irregularity exciting force function is：
P (t)=P0+P1sinω1t+P2sinω2t+P3sinω3t (1)
P1、P2、P3To press the oscillatory load under driving stationarity, circuit additional load and corrugation control condition, calculating formula
For：
ωiFor vehicle circular frequency, calculating formula is：
ωi=2 π υ/li(i=1,2,3) (3)
In formula (1), P0For vehicle static load；In formula (2), M0For train unsprung mass, aiFor typical rise；In formula (3), υ is train
The speed of service, liFor Geometric irregularity curve typical wavelengths；By driving stationarity, work as li=50m, ai=16mm, works as li=20m,
ai=9mm, works as li=10m, ai=5mm by circuit additional load situation, works as li=5m, ai=2.5mm, works as li=2m, ai=
0.6mm works as li=1m, ai=1.3mm by corrugation situation, works as li=0.5m, ai=0.1mm, works as li=0.02m, ai=
0.005mm；
APDL language self-compiling programs are loaded, based on track irregularity exciting force function, simulate train operation time-histories load, specific side
Method is：
(1) DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES parameter is defined, including distance between axles d, train running speed υ, vehicle before and after tunnel overall length s, train in tunnel
Total time ttime, load time step-length time, loading total step number ti, loading step i are run in road, wherein
(2) define arrays force1, from load step 1 to ti implement cycling of do, by formula (1)-(3) define any front-wheel of train with
The exciting force of time change is：
Force1 (i)=P0+P1sinω1(i·time)+P2sinω2(i·time)+P3sinω3(itime), and additional work as
(itime-s/ υ) ＞ 0, then force1 (i)=0；
(3) define arrays force2, from load step 1 to ti implement cycling of do, by formula (1)-(3) define any trailing wheel of train with
The exciting force of time change is：
Force2 (i)=P0+P1sinω1(i·time-d/υ)+P2sinω2(i·time-d/υ)+P3sinω3(i·time-
D/ υ), and additional as (itime-d/ υ) ＜ 0, then force2 (i)=0.
4. the finite element method of tunnel-vehicle coupled vibrations under a kind of DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES according to claim 1,
It is characterized in that：APDL language self-compiling programs are loaded in step 5, the train operation with spatial variations at any time is applied to coupled system
Time-histories load, specific method are：
(1) the longitudinal node of two row that selection bedding upper limb biserial wheel rolls, it is array dist1 to define front-wheel running position, after
Wheel running position is array dist2；
(2) from 1 to ti implementation cycling of do of step is loaded, corresponding i-th loading step, front-wheel running position is dist1 (i)=υ i, after
Wheel running position is dist2 (i)=υ i-d, finds the node serial number nearest apart from front and rear wheel position respectively by node orders,
Back to array n1 (i) and n2 (i), node n1 (i) and n2 (i) are chosen, force1 (i) and force2 is loaded by F orders respectively
(i)；
(3) loading of train time-histories load in all time steps is sequentially completed, time-history analysis is carried out to the Coupled Vibration System.
5. the finite element method of tunnel-vehicle coupled vibrations under a kind of DYNAMIC LOADING OF DRIVING TRAIN ON BRIDGES according to claim 1,
It is characterized in that：For basement rock-lining cutting-bedding coupled system three-dimensional finite element model 2 in step 3, using initial stress balancing method,
The stress and deformation result of lining cutting layer periphery basement rock node in file 1 are called in using isfile orders, eliminates rock stratum gravity
Under accumulated deformation, and introduce the primary stress on rock stratum and lining cutting contact surface.
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| CN111079323A (en) * | 2019-11-12 | 2020-04-28 | 湖南大学 | Power response prediction method and system based on human-vehicle-road coupling vibration model |
| CN111488641A (en) * | 2020-04-13 | 2020-08-04 | 中原工学院 | Tunnel engineering numerical simulation display method based on virtual reality |
| CN111597617A (en) * | 2020-05-18 | 2020-08-28 | 中铁第六勘察设计院集团有限公司 | Method for predicting fatigue life of shield tunnel |
| CN112199872A (en) * | 2020-10-09 | 2021-01-08 | 浙江大学 | Tunnel modal identification method |
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| CN111488641A (en) * | 2020-04-13 | 2020-08-04 | 中原工学院 | Tunnel engineering numerical simulation display method based on virtual reality |
| CN111597617A (en) * | 2020-05-18 | 2020-08-28 | 中铁第六勘察设计院集团有限公司 | Method for predicting fatigue life of shield tunnel |
| CN111597617B (en) * | 2020-05-18 | 2022-05-27 | 中铁第六勘察设计院集团有限公司 | Method for predicting fatigue life of shield tunnel |
| CN112199872A (en) * | 2020-10-09 | 2021-01-08 | 浙江大学 | Tunnel modal identification method |
| CN112199872B (en) * | 2020-10-09 | 2022-08-12 | 浙江大学 | Tunnel modal identification method |
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