CN116341086A - Method, system and storage medium for calculating internal force of tunnel structure crossing active fault - Google Patents

Method, system and storage medium for calculating internal force of tunnel structure crossing active fault Download PDF

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CN116341086A
CN116341086A CN202310526302.1A CN202310526302A CN116341086A CN 116341086 A CN116341086 A CN 116341086A CN 202310526302 A CN202310526302 A CN 202310526302A CN 116341086 A CN116341086 A CN 116341086A
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CN116341086B (en
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王明年
罗勋
张霄
于丽
杨恒洪
王玉锁
刘大刚
唐浪洲
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Southwest Jiaotong University
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Abstract

The invention relates to the technical field of earthquake resistance of a tunnel structure passing through a movable fault, in particular to a method, a system and a storage medium for calculating internal force of the tunnel structure passing through the movable fault, which comprise the following steps: 1. acquiring an active fault dislocation curve; 2. establishing an internal force calculation model of a tunnel structure crossing the movable fault; 3. based on finite difference method and Euler-Bernoulli beam theory, calculating longitudinal deformation of tunnel structureu y The method comprises the steps of carrying out a first treatment on the surface of the 4. Based on finite difference method and Euler-Bernoulli beam theory, calculating horizontal deformation of tunnel structureu x Vertical deformationu z The method comprises the steps of carrying out a first treatment on the surface of the 5. Based on the finite difference method and the Euler-Bernoulli beam theory, the forces within the tunnel structure are calculated. The invention can better calculate the internal force of the tunnel structure crossing the movable fault.

Description

Method, system and storage medium for calculating internal force of tunnel structure crossing active fault
Technical Field
The invention relates to the technical field of earthquake resistance of a tunnel passing through an active fault, in particular to a method, a system and a storage medium for calculating internal force of a tunnel passing through an active fault.
Background
Fault dislocation deformation and earthquake energy are generated in the process of moving fault dislocation. Therefore, the tunnel damage across the movable fault can be basically divided into two main categories, namely structural vibration damage caused by earthquake and cleavage damage caused by fault dislocation. Vibration damage refers to the phenomenon that after an earthquake propagates to a structure, the structure is damaged due to interaction caused by the dynamic characteristic of the structure and the mass rigidity difference between the structure and surrounding rock; the fault dislocation damage refers to the phenomenon that when faults are dislocated, tunnels penetrating through faults are driven to move together, so that the tunnels are deformed and damaged. Therefore, a reasonable mechanical analysis model for the tunnel structure of the crossing movable fracture zone is provided, and the method is particularly important for the tunnel structure design of the crossing movable fracture zone.
Various calculation models are proposed by students at home and abroad aiming at crossing the movable fault tunnel and the underground pipeline. The Newmark and Hall firstly provide an underground pipeline internal force calculation model under fault dislocation, but the bending rigidity and the transverse soil pressure effect of the underground pipeline are not considered in the calculation model, so that the internal force calculation result is smaller. In order to overcome the above drawbacks, kennedy et al have proposed a computational model that considers the flexural rigidity of the pipeline, taking into account the effects of lateral earth pressure on this basis, wang and Yeh, but are mainly applicable to walk-slip faults. Then, a large number of scholars further improve the calculation accuracy of the model on the basis of the calculation accuracy, and the application range of the calculation model is widened. The above computational model is typically only for a single fault type (forward, reverse, and walk faults), and the faults are considered to be evenly staggered. In actual engineering, the faults are usually oblique faults, and have oblique sliding and sliding properties, and the oblique sliding faults have obvious spatial non-uniformity, so that horizontal, vertical and longitudinal three-way deformation occurs when the tunnel passes through the oblique sliding faults. Therefore, the application range of the currently proposed calculation model is limited, and the method is difficult to be suitable for mechanical response analysis of the tunnel crossing the active fault under different fault types.
Disclosure of Invention
The invention provides a method, a system and a storage medium for calculating internal force of a tunnel structure crossing an active fault, which can calculate the internal force of the tunnel structure better.
The method for calculating the internal force of the tunnel structure crossing the movable fault comprises the following steps:
1. acquisition of active fault horizontal dislocation curveΔf x Longitudinal dislocation curveΔf y Vertical dislocation curveΔf z ；
2. Establishing an internal force calculation model of a tunnel structure crossing the movable fault;
3. based on finite difference method and Euler-Bernoulli beam theory, calculating longitudinal deformation of tunnel structureu y ；
4. Based on finite difference method and Euler-Bernoulli beam theory, calculating horizontal deformation of tunnel structureu x Vertical deformationu z ；
5. Based on the finite difference method and the Euler-Bernoulli beam theory, the forces within the tunnel structure are calculated.
Preferably, in the second step, the method for establishing the calculation model of the tunnel structure crossing the active fault comprises the following steps:
1) Under the dislocation of the movable fault, the tunnel structure is deformed in the horizontal direction, the vertical direction and the longitudinal direction, and the horizontal direction isxThe axial direction and the vertical direction arezIn the axial direction and the longitudinal direction ofyIn the axial direction, the buried depth of the tunnel structure isCThe lining thickness istThe equivalent diameter of the tunnel structure isDFault inclination angle ofαThe intersection angle of the tunnel structure and the fault isβ；
2) The tunnel structure crossing the movable fracture zone is simplified into an Euler-Bernoulli beam, and the surrounding is realizedThe rock is simplified into a three-way spring, and the fracture zone dislocation is simplified into three-way dislocation deformation acting on the three-way spring; dislocation in three directions of faultΔf x ，Δf y ，Δf z Under the action of (a), the tunnel structure receives three-way loadq x ，q y ，q z Acting to generate three-way deformationu x ，u y ，u z ；
3) Dividing an internal force calculation model of a tunnel structure crossing the movable fault into a horizontal direction, a vertical direction and an axial direction;
horizontal, vertical and longitudinal surrounding rock pressureq x ，q y ，q z The calculation formula is as follows:
Figure SMS_1
；
in the method, in the process of the invention,Δu x ，Δu y ，Δu z the horizontal tunnel structure and the vertical tunnel structure are respectively deformed relative to surrounding rocks;k x ，k y ，k z the reaction coefficients of the surrounding rock foundation are respectively horizontal, vertical and longitudinal;
horizontal, vertical and longitudinal surrounding rock foundation reaction coefficientk x ，k y ，k z The calculation formula is as follows:
Figure SMS_2
；
Figure SMS_3
；
in the method, in the process of the invention,E t andI the tunnel structure elastic modulus and the inertia moment are respectively;Eandνthe stratum elastic modulus and poisson ratio are respectively;ξis the coefficient ratio of the longitudinal surrounding rock bed;
horizontal, verticalLongitudinal tunnel structure-surrounding rock relative deformationΔu x ，Δu y ，Δu z The calculation formulas are respectively as follows:
Figure SMS_4
；
according to Euler-Bernoulli beam theory, the horizontal, vertical and longitudinal deformation differential equations of the tunnel structure are respectively:
Figure SMS_5
；
in the method, in the process of the invention,Ais the cross-sectional area of the tunnel structure;
preferably, in step three, the tunnel structure is deformed longitudinallyu y The calculation method of (1) is as follows:
dividing tunnel structure crossing movable fracture zone inton+5 parts including two virtual nodes at each end, the unit length isΔ=L/n，LIs the tunnel structure length.
According to the finite difference method, the differential form of the longitudinal deformation differential equation (11) of the tunnel structure crossing the movable fault is as follows:
Figure SMS_6
；
in the method, in the process of the invention,k yi ，u yi ，Δf yi respectively isiThe longitudinal surrounding rock bed coefficient of the node, the tunnel structure deformation and the fracture zone deformation;
according to the stress characteristics of the tunnel structure penetrating through the movable fracture zone, the axial force at the two ends of the tunnel structure is 0, namelyi=0 ori=nAxial forceN=0; the method is based on finite difference equation and Euler-Bernoulli beam theory:
Figure SMS_7
；
combined type (13) to (15) to obtain a tunnel junction crossing the movable faultLongitudinal deformation of structureu y The calculation formula is as follows:
Figure SMS_8
；
in the middle of
Figure SMS_9
Figure SMS_10
；
Preferably, in the fourth step, the tunnel structure is deformed horizontallyu x Vertical deformation of tunnel structureu z The calculation method of (1) is as follows:
according to the finite difference theory, the finite difference form of the tunnel structure vertical deformation differential equation (12) is as follows:
Figure SMS_11
；
in the method, in the process of the invention,k zi ，u zi ，Δf zi respectively isiThe vertical surrounding rock bed coefficient of the node, the tunnel structure deformation and the fracture zone deformation;
according to the stress characteristics of the tunnel structure crossing the movable fracture zone, the boundary conditions at the two ends are as follows: when (when)i=0 ori=nVertical bending momentM z =0, vertical shear forceV z =0; based on the finite difference formula, the difference form of the boundary condition is obtained as follows:
Figure SMS_12
；
the vertical deformation of the tunnel structure passing through the movable fault is obtained by the combined type (22) to (26)u z The calculation formula is as follows:
Figure SMS_13
；
in the middle of
Figure SMS_14
；
Figure SMS_15
；
In the formula (27)Δf z ，k z By usingΔf x ，k x Replacing to obtain horizontal deformation of the tunnel structureu x And (5) calculating a formula.
Preferably, in the fifth step, the internal force calculating method includes:
solving three-way deformation of tunnel structure passing through movable faultu x 、u y Andu z then, based on the finite difference method and Euler-Bernoulli beam theory, the method is to calculateiAxial force of nodeNBending momentM x 、M z Shear forceV x 、V z ：
Figure SMS_16
；
In the method, in the process of the invention,N i is thatiThe axial force of the node is calculated,M xi 、M zi respectively isiThe node is provided with a horizontal bending moment and a vertical bending moment,V xi 、V zi respectively isiThe node is in horizontal and vertical shearing force,u yi+1 、u yi-1 respectively isi+1、i-1 a longitudinal displacement of the node,u zi 、u zi-1 、u zi+1 respectively isi、i+1、i-1 a vertical displacement of the node,u xi+2 、u xi+1 、u xi-1 、u xi-2 respectively isi+2、i+1、i-1、i-2 nodeThe horizontal direction of displacement is carried out,u zi+2 、u zi+1 、u zi-1 、u zi-2 respectively isi+2、i+1、i-1、i-2 node vertical displacement.
The invention provides a system for calculating internal force of a crossing movable fault tunnel structure, which adopts the crossing embodiment, and also provides a system for calculating internal force of a crossing movable fault tunnel structure, which adopts a method for calculating internal force of a movable fault tunnel structure and comprises the following steps:
the model building module is used for building an internal force calculation model of the tunnel structure crossing the movable fault;
the tunnel structure longitudinal deformation calculation module is used for calculating the tunnel structure longitudinal deformation based on a finite difference method and an Eulter-Bernoulli beam theoryu y ；
The tunnel structure horizontal deformation and vertical deformation calculation module is used for calculating the tunnel structure horizontal deformation based on a finite difference method and an Euler-Bernoulli beam theoryu x Vertical deformation of tunnel structureu z ；
And the internal force module is used for calculating the internal force of the tunnel structure based on a finite difference method and an Eulter-Bernoulli beam theory.
The invention provides a storage medium for calculating internal force of a crossing active fault tunnel structure, which stores a computer program, and the computer program is executed by a computer to realize the method for calculating the internal force of the crossing active fault tunnel structure.
The invention fully considers the uneven dislocation characteristic of the movable fault, adopts the Euler-Bernoulli beam theory and the finite difference method to obtain the internal force and deformation calculation method of the tunnel structure under the uneven dislocation of the movable fault, establishes the calculation model of the tunnel structure under the uneven dislocation of the movable fault, and compares the theoretical calculation result with the numerical simulation result.
Drawings
FIG. 1 is a flow chart of a method of calculating internal forces across an active fault tunnel structure in an embodiment;
FIG. 2 (a) is a schematic diagram of a tunnel structure crossing an active fault before dislocation in an embodiment;
FIG. 2 (b) is a schematic diagram of a tunnel structure crossing an active fault after dislocation in an embodiment;
FIG. 3 is a schematic diagram of a calculation model of a tunnel structure crossing an active fault in an embodiment;
FIG. 4 (a) is a schematic diagram illustrating horizontal decomposition of a computational model of a tunnel structure traversing an active fault in an embodiment;
FIG. 4 (b) is a schematic view showing a longitudinal decomposition of a calculation model of a tunnel structure crossing an active fault in the embodiment;
FIG. 4 (c) is a schematic view showing a vertical decomposition of a calculation model of a tunnel structure crossing an active fault in the embodiment;
FIG. 5 is a discretized schematic diagram of a tunnel structure in an embodiment;
FIG. 6 is a schematic diagram of a finite element computation model in an embodiment;
FIG. 7 (a) is a graph showing the comparison of the results of horizontal deformation of the theoretical model and the numerical model in the example;
FIG. 7 (b) is a graph showing the comparison of the longitudinal deformation results of the theoretical model and the numerical model in the example;
FIG. 7 (c) is a graph showing the comparison of the results of vertical deformation of the theoretical model and the numerical model in the example;
FIG. 7 (d) is a graph showing the comparison of the results of horizontal bending moment between the theoretical model and the numerical model in the example;
FIG. 7 (e) is a graph showing the comparison of the results of the vertical bending moment of the theoretical model and the numerical model in the example;
FIG. 7 (f) is a graph showing the comparison of the horizontal shear results of the theoretical model and the numerical model in the examples;
FIG. 7 (g) is a graph comparing the results of the vertical shear of the theoretical model and the numerical model in the examples;
FIG. 7 (h) is a graph showing the results of axial force of the theoretical model and the numerical model in the example.
Detailed Description
For a further understanding of the present invention, the present invention will be described in detail with reference to the drawings and examples. It is to be understood that the examples are illustrative of the present invention and are not intended to be limiting.
Examples
As shown in fig. 1, the present embodiment provides a method for calculating an internal force of a tunnel structure crossing an active fault, which includes the following steps:
1. based on the calculation method proposed by Japanese student Okada, the dislocation curve of the horizontal dislocation of the active fault is obtainedΔf x Longitudinal dislocation curveΔf y Vertical dislocation curveΔf z ；
2. Establishing an internal force calculation model of a tunnel structure crossing the movable fault;
3. based on finite difference method and Euler-Bernoulli beam theory, calculating longitudinal deformation of tunnel structureu y ；
4. Based on finite difference method and Euler-Bernoulli beam theory, calculating horizontal deformation of tunnel structureu x Vertical deformationu z ；
5. Based on the finite difference method and the Euler-Bernoulli beam theory, the forces within the tunnel structure are calculated.
The embodiment also provides a system for calculating the internal force of the crossing active fault tunnel structure, which adopts the method for calculating the internal force of the crossing active fault tunnel structure and comprises the following steps:
the model building module is used for building an internal force calculation model of the tunnel structure crossing the movable fault;
the tunnel structure longitudinal deformation calculation module is used for calculating the tunnel structure longitudinal deformation based on a finite difference method and an Eulter-Bernoulli beam theoryu y ；
The tunnel structure horizontal deformation and vertical deformation calculation module is used for calculating the tunnel structure horizontal deformation based on a finite difference method and an Euler-Bernoulli beam theoryu x Vertical deformation of tunnel structureu z ；
And the internal force module is used for calculating the internal force of the tunnel structure based on a finite difference method and an Eulter-Bernoulli beam theory.
The embodiment also provides a storage medium for calculating the internal force of the crossing active fault tunnel structure, which stores a computer program, and the computer program is executed by a computer to realize the method for calculating the internal force of the crossing active fault tunnel structure.
Construction of calculation model of tunnel structure crossing movable fault
1) Under the fault movement of the movable fault, the tunnel structure generates horizontal directionxAxial direction and vertical directionzAxial direction and longitudinal directionyAxial direction) three-way deformation, the buried depth of the tunnel structure isCThe lining thickness istThe equivalent diameter of the tunnel structure isD（D=(W+H)/2，WFor the span of the tunnel structure,Htunnel structure height), fault inclination angle isαThe intersection angle of the tunnel structure and the fault isβAs shown in fig. 2 (a) and 2 (b).
2) The tunnel structure penetrating through the movable fracture zone is simplified into an Euler-Bernoulli beam, surrounding rock is simplified into a three-way spring, and fracture zone dislocation is simplified into three-way dislocation deformation acting on the three-way spring; in fault three-way dislocationΔf（Δf x ，Δf y ，Δf z ) Under the action of (a), the tunnel structure receives three-way loadq（q x ，q y ，q z ) Three-way deformation occursu（u x ，u y ，u z ) As shown in fig. 3.
3) Dividing a calculation model of a tunnel structure crossing the movable fault into a horizontal direction, a vertical direction and an axial direction, as shown in fig. 4 (a), 4 (b) and 4 (c);
horizontal, vertical and longitudinal surrounding rock pressureq x ，q y ，q z The calculation formula is as follows:
Figure SMS_17
；
in the method, in the process of the invention,Δu x ，Δu y ，Δu z the horizontal tunnel structure and the vertical tunnel structure are respectively deformed relative to surrounding rocks;k x ，k y ，k z respectively are provided withIs the counterforce coefficient of the horizontal, vertical and longitudinal surrounding rock foundations.
Horizontal, vertical and longitudinal surrounding rock foundation reaction coefficientk x ，k y ，k z The calculation formula is as follows:
Figure SMS_18
；
Figure SMS_19
；
in the method, in the process of the invention,E t andI the elastic modulus and the moment of inertia of the tunnel structure are respectively,I=π[D 4 -(D-2t) 4 ]/4；Eandνthe stratum elastic modulus and poisson ratio are respectively;ξfor the longitudinal surrounding rock bed coefficient ratio, 0.5 was assumed according to the related study.
Horizontal, vertical and longitudinal tunnel structure-surrounding rock relative deformationΔu x ，Δu y ，Δu z The calculation formulas are respectively as follows:
Figure SMS_20
；
according to Euler-Bernoulli beam theory, the horizontal, vertical and longitudinal deformation differential equations of the tunnel structure are respectively:
Figure SMS_21
；
in the method, in the process of the invention,Ais the cross-sectional area of the tunnel structure,A=πD 2 /4-π(D-2t) 2 /4。
since the tomographic movement has significant unevenness, it is difficult to obtain the analytical solutions of the formulae (10) to (12), the numerical solutions of the formulae (10) to (12) are obtained by a finite difference method. Dividing tunnel structure crossing movable fracture zone inton+5 parts including two virtual nodes at each end, unit lengthDegree ofΔ=L/n，LIs the tunnel structure length, as shown in fig. 5.
(1) Longitudinal deformation of tunnel structureu y Calculation method
According to the finite difference method, the differential form of the longitudinal deformation differential equation (11) of the tunnel structure crossing the movable fault is as follows:
Figure SMS_22
；
in the method, in the process of the invention,k yi ，u yi ，Δf yi respectively isiThe longitudinal surrounding rock bed coefficient of the node, the tunnel structure deformation and the fracture zone deformation;
according to the stress characteristics of the tunnel structure penetrating through the movable fracture zone, the axial force at the two ends of the tunnel structure is 0, namelyi=0 ori=nAxial forceN=0. The method is based on finite difference equation and Euler-Bernoulli beam theory:
Figure SMS_23
；
and (3) the combined type (13) to (15) to obtain a longitudinal deformation calculation formula of the tunnel structure crossing the movable fault, wherein the calculation formula is as follows:
Figure SMS_24
；
in the middle of
Figure SMS_25
；
(2) Horizontal deformation of tunnel structureu x Vertical deformationu z Calculation method
And as the deformation differential equation forms of the vertical tunnel structure and the horizontal tunnel structure are consistent, the solving process is the same. Here, a vertical modification will be described as an example. According to the finite difference theory, the finite difference form of the tunnel structure vertical deformation differential equation (12) is as follows:
Figure SMS_26
；
in the method, in the process of the invention,k zi ，u zi ，Δf zi the vertical surrounding rock bed coefficient of the i node, the tunnel structure deformation and the fracture zone deformation are respectively.
According to the stress characteristics of the tunnel structure crossing the movable fracture zone, the boundary conditions at the two ends are as follows: when (when)i=0 or n, vertical bending momentM z =0, vertical shear forceV z =0. Based on the finite difference formula, the difference form of the boundary condition is obtained as follows:
Figure SMS_27
；
the vertical deformation of the tunnel structure passing through the movable fault is obtained by the combined type (22) to (26)u z The calculation formula is as follows:
Figure SMS_28
；
in the middle of
Figure SMS_29
；
In the formula (27)Δf z ，k z By usingΔf x ，k x And (5) replacing to obtain a calculation formula of horizontal deformation ux of the tunnel structure.
(3) Tunnel structure internal force calculation method
Solving three-way deformation of tunnel structure passing through movable faultu x 、u y Andu z then, based on the finite difference method and Euler-Bernoulli beam theory, the method is to calculateiAxial force of nodeNBending momentM x 、M z Shear forceV x 、V z ：
Figure SMS_30
；
In the method, in the process of the invention,N i is thatiThe axial force of the node is calculated,M xi 、M zi respectively isiThe node is provided with a horizontal bending moment and a vertical bending moment,V xi 、V zi respectively isiThe node is in horizontal and vertical shearing force,u yi+1 、u yi-1 respectively isi+1、i-1 a longitudinal displacement of the node,u zi 、u zi-1 、u zi+1 respectively isi、i+1、i-1 a vertical displacement of the node,u xi+2 、u xi+1 、u xi-1 、u xi-2 respectively isi+2、i+1、i-1、iThe-2 node is displaced horizontally,u zi+2 、u zi+1 、u zi-1 、u zi-2 respectively isi+2、i+1、i-1、i-2 node vertical displacement.
(4) Model verification
To verify the rationality of the calculation model, a finite element model is established to verify the calculation model, and a model of a tunnel structure crossing the active fault is established by adopting Midas GTS NX 2022. Wherein, the beam unit is adopted to simulate the tunnel structure, the unit length is 0.1m, the three-way spring unit is adopted to simulate surrounding rock, the Okada model is adopted to calculate the uneven deformation of the surrounding rock at the position of the tunnel structure, and the uneven deformation is applied to the boundary nodes of the springs, as shown in fig. 6.
The tunnel structure, faults and surrounding rock calculation parameters are shown in table 1.
Table 1 calculation parameters
Figure SMS_31
The theoretical model calculation results and the finite element model calculation results under the condition of different fault displacement are shown in fig. 7 (a), 7 (b), 7 (c), 7 (d), 7 (e), 7 (f), 7 (g) and 7 (h), the tunnel structure is deformed in three directions under the action fault displacement to generate three-direction internal force, the internal force and the deformation are increased along with the increase of the displacement, and the theoretical calculation results are well matched with the numerical simulation results.
According to the method, the uneven dislocation characteristics of the movable faults are fully considered, the Euler-Bernoulli beam theory and the finite difference method are adopted, the internal force and deformation calculation method of the tunnel structure under the uneven dislocation of the movable faults are obtained, the calculation model of the tunnel structure under the uneven dislocation of the movable faults is built, and the theoretical calculation result and the numerical simulation result are compared, so that the method has good accuracy and rationality.
The invention and its embodiments have been described above by way of illustration and not limitation, and the invention is illustrated in the accompanying drawings and described in the drawings in which the actual structure is not limited thereto. Therefore, if one of ordinary skill in the art is informed by this disclosure, the structural mode and the embodiments similar to the technical scheme are not creatively designed without departing from the gist of the present invention.

Claims (7)

1. The method for calculating the internal force of the tunnel structure crossing the movable fault is characterized by comprising the following steps of: the method comprises the following steps:
1. acquisition of active fault horizontal dislocation curveΔf x Longitudinal dislocation curveΔf y Vertical dislocation curveΔf z ；
2. Establishing an internal force calculation model of a tunnel structure crossing the movable fault;
3. based on finite difference method and Euler-Bernoulli beam theory, calculating longitudinal deformation of tunnel structureu y ；
4. Based on finite difference method and Euler-Bernoulli beam theory, calculating horizontal deformation of tunnel structureu x Vertical deformationu z ；
5. Based on the finite difference method and the Euler-Bernoulli beam theory, the forces within the tunnel structure are calculated.
2. The method for calculating internal force of crossing active fault tunnel structure according to claim 1, wherein: in the second step, the method for establishing the calculation model of the tunnel structure crossing the movable fault comprises the following steps:
1) Under the dislocation of the movable fault, the tunnel structure is deformed in the horizontal direction, the vertical direction and the longitudinal direction, and the horizontal direction isxThe axial direction and the vertical direction arezIn the axial direction and the longitudinal direction ofyIn the axial direction, the buried depth of the tunnel structure isCThe lining thickness istThe equivalent diameter of the tunnel structure isDFault inclination angle ofαThe intersection angle of the tunnel structure and the fault isβ；
2) The tunnel structure penetrating through the movable fracture zone is simplified into an Euler-Bernoulli beam, surrounding rock is simplified into a three-way spring, and fracture zone dislocation is simplified into three-way dislocation deformation acting on the three-way spring; dislocation in three directions of faultΔf x ，Δf y ，Δf z Under the action of (a), the tunnel structure receives three-way loadq x ，q y ，q z Acting to generate three-way deformationu x ，u y ，u z ；
3) Dividing an internal force calculation model of a tunnel structure crossing the movable fault into a horizontal direction, a vertical direction and an axial direction;
horizontal, vertical and longitudinal surrounding rock pressureq x ，q y ，q z The calculation formula is as follows:
Figure QLYQS_1
；
in the method, in the process of the invention,Δu x ，Δu y ，Δu z the horizontal tunnel structure and the vertical tunnel structure are respectively deformed relative to surrounding rocks;k x ，k y ，k z the reaction coefficients of the surrounding rock foundation are respectively horizontal, vertical and longitudinal;
horizontal, vertical and longitudinal surrounding rock foundation reaction coefficientk x ，k y ，k z The calculation formula is as follows:
Figure QLYQS_2
；
Figure QLYQS_3
；
in the method, in the process of the invention,E t and I the tunnel structure elastic modulus and the inertia moment are respectively;Eandνthe stratum elastic modulus and poisson ratio are respectively;ξis the coefficient ratio of the longitudinal surrounding rock bed;
horizontal, vertical and longitudinal tunnel structure-surrounding rock relative deformationΔu x ，Δu y ，Δu z The calculation formulas are respectively as follows:
Figure QLYQS_4
；
according to Euler-Bernoulli beam theory, the horizontal, vertical and longitudinal deformation differential equations of the tunnel structure are respectively:
Figure QLYQS_5
；
in the method, in the process of the invention,Ais the cross-sectional area of the tunnel structure.
3. The method for calculating the internal force of the tunnel structure crossing the active fault according to claim 2, wherein: in the third step, the tunnel structure is deformed longitudinallyu y The calculation method of (1) is as follows:
dividing tunnel structure crossing movable fracture zone inton+5 parts including two virtual nodes at each end, the unit length isΔ=L/n，LThe length of the tunnel structure is as follows:
according to the finite difference method, the differential form of the longitudinal deformation differential equation (11) of the tunnel structure crossing the movable fault is as follows:
Figure QLYQS_6
；
in the method, in the process of the invention,k yi ，u yi ，Δf yi respectively isiThe longitudinal surrounding rock bed coefficient of the node, the tunnel structure deformation and the fracture zone deformation;
according to the stress characteristics of the tunnel structure penetrating through the movable fracture zone, the axial force at the two ends of the tunnel structure is 0, namelyi=0 ori=nAxial forceN=0; the method is based on finite difference equation and Euler-Bernoulli beam theory:
Figure QLYQS_7
；
the combined type (13) to (15) obtains the longitudinal deformation passing through the movable fault tunnel structureu y The calculation formula is as follows:
Figure QLYQS_8
。
4. a method of calculating internal forces across an active fault tunnel structure according to claim 3, wherein: in the fourth step, the tunnel structure is deformed horizontallyu x Vertical deformation of tunnel structureu z The calculation method of (1) is as follows:
according to the finite difference theory, the finite difference form of the tunnel structure vertical deformation differential equation (12) is as follows:
Figure QLYQS_9
；
in the method, in the process of the invention,k zi ，u zi ，Δf zi respectively isiThe vertical surrounding rock bed coefficient of the node, the tunnel structure deformation and the fracture zone deformation;
according to the stress characteristics of the tunnel structure crossing the movable fracture zone, the boundary conditions at the two ends are as follows: when (when)i=0 ori=nVertical bending momentM z =0, vertical shear forceV z =0; based on the finite difference formula, the difference form of the boundary condition is obtained as follows:
Figure QLYQS_10
；
the vertical deformation of the tunnel structure passing through the movable fault is obtained by the combined type (22) to (26)u z The calculation formula is as follows:
Figure QLYQS_11
；
in the middle of
Figure QLYQS_12
；
Figure QLYQS_13
；
In the formula (27)Δf z ，k z By usingΔf x ，k x Replacing to obtain horizontal deformation of the tunnel structureu x And (5) calculating a formula.
5. The method for calculating the internal force of the tunnel structure crossing the active fault according to claim 4, wherein: in the fifth step, the internal force calculation method comprises the following steps:
solving three-way deformation of tunnel structure passing through movable faultu x 、u y Andu z then, based on the finite difference method and Euler-Bernoulli beam theory, the method is to calculateiShaft of nodeForce of forceNBending momentM x 、M z Shear forceV x 、V z ：
Figure QLYQS_14
；
In the method, in the process of the invention,N i is thatiThe axial force of the node is calculated,M xi 、M zi respectively isiThe node is provided with a horizontal bending moment and a vertical bending moment,V xi 、V zi respectively isiThe node is in horizontal and vertical shearing force,u yi+1 、u yi-1 respectively isi+1、i-1 a longitudinal displacement of the node,u zi 、u zi-1 、u zi+1 respectively isi、i+1、i-1 a vertical displacement of the node,u xi+2 、u xi+1 、u xi-1 、u xi-2 respectively isi+2、i+1、i-1、iThe-2 node is displaced horizontally,u zi+2 、u zi+1 、u zi-1 、u zi-2 respectively isi+2、i+1、i-1、i-2 node vertical displacement.
6. The internal force calculation system for crossing the movable fault tunnel structure is characterized in that: a method for calculating internal force of a tunnel structure crossing active fault according to any one of claims 1 to 5, comprising:
the model building module is used for building an internal force calculation model of the tunnel structure crossing the movable fault;
the tunnel structure longitudinal deformation calculation module is used for calculating the tunnel structure longitudinal deformation based on a finite difference method and an Eulter-Bernoulli beam theoryu y ；
The horizontal deformation and vertical deformation calculation module of the tunnel structure is used for calculating based on a finite difference method and an Euler-Bernoulli beam theoryCalculating horizontal deformation of tunnel structureu x Vertical deformation of tunnel structureu z ；
And the internal force module is used for calculating the internal force of the tunnel structure based on a finite difference method and an Eulter-Bernoulli beam theory.
7. A storage medium for force computation in a traversing active fault tunnel structure, characterized by: which stores a computer program that is executed by a computer to implement the method for calculating internal force across an active fault tunnel structure according to any one of claims 1 to 5.
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