CN116341086B - 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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CN116341086B
CN116341086B CN202310526302.1A CN202310526302A CN116341086B CN 116341086 B CN116341086 B CN 116341086B CN 202310526302 A CN202310526302 A CN 202310526302A CN 116341086 B CN116341086 B CN 116341086B
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deformation
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fault
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CN116341086A (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 dislocation curve delta f of horizontal direction of active fault x Longitudinal dislocationCurve Δf y Vertical dislocation curve Δf 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 u of tunnel structure y ；
4. Based on finite difference method and Euler-Bernoulli beam theory, calculating horizontal deformation u of tunnel structure x Vertical deformation u 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 condition of movable fault dislocation, the tunnel structure is deformed in a horizontal direction, a vertical direction and a longitudinal direction, wherein the horizontal direction is the x-axis direction, the vertical direction is the z-axis direction, the longitudinal direction is the y-axis direction, the burial depth of the tunnel structure is C, the thickness of the lining is t, the equivalent diameter of the tunnel structure is D, the fault inclination angle is alpha, and the intersection angle of the tunnel structure and the fault is beta;
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 delta f in fault x ，Δf y ，Δf z Under the action of the three-way load q of the tunnel structure x ，q y ，q z Acting to generate three-way deformation u 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 pressure q x ，q y ，q z The calculation formula is as follows:
q x ＝k x Δu x (1)
q y ＝k y Δu y (2)
q z ＝k z Δu z (3)
wherein Deltau x ，Δu y ，Δu z The horizontal tunnel structure and the vertical tunnel structure are respectively deformed relative to surrounding rocks; k (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 coefficient k x ，k y ，k z The calculation formula is as follows:
k y ＝ξk z ＝ξk x (5)
wherein E is t And I is the tunnel structure elastic modulus and moment of inertia, respectively; e and v are the stratum elastic modulus and Poisson's ratio, respectively; ζ is the coefficient ratio of the longitudinal surrounding rock bed;
horizontal, vertical and longitudinal tunnel structure-surrounding rock relative deformation deltau x ，Δu y ，Δu z The calculation formulas are respectively as follows:
Δu x ＝Δf x -u x (7)
Δu y ＝Δf y -u y (8)
Δu z ＝Δf z -u z (9)
according to Euler-Bernoulli beam theory, the horizontal, vertical and longitudinal deformation differential equations of the tunnel structure are respectively:
wherein A is the cross-sectional area of the tunnel structure;
preferably, in step three, the tunnel structure is deformed longitudinally by u y The calculation method of (1) is as follows:
the tunnel structure passing through the movable fracture zone is divided into n+5 parts, wherein the tunnel structure comprises two virtual nodes at two ends, the unit length is delta=l/n, and L is the length of the tunnel structure.
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:
wherein k is yi ，u yi ，Δf yi The method comprises the steps of respectively obtaining the longitudinal surrounding rock bed coefficient of an i node, the deformation of a tunnel structure and the deformation of a fracture zone;
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, namely when i=0 or i=n, the axial force N=0; the method is based on finite difference equation and Euler-Bernoulli beam theory:
u y-1 ＝u y1 (14)
u yn+1 ＝u yn-1 (15)
the longitudinal deformation u passing through the movable fault tunnel structure is obtained by the combined type (13) to the formula (15) y The calculation formula is as follows:
[B] (n+1)×(n+1) [u y ] (n+1)×1 ＝[Δf y ] (n+1)×1 (16)
in the middle of
[B] (n+1)×(n+1) ＝[B 1 ] (n+1)×(n+1) +[B 2 ] (n+1)×(n+1) (17)
Preferably, in the fourth step, the tunnel structure is deformed horizontally u x Vertical deformation u of tunnel structure 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:
wherein k is zi ，u zi ，Δf zi The vertical surrounding rock bed coefficients of the i nodes, 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 i=0 or i=n, the vertical bending moment M z =0, vertical shear V z =0; based on the finite difference formula, the difference form of the boundary condition is obtained as follows:
u z-1 ＝2u z0 -u z1 (23)
u z-2 ＝4u z0 -4u z1 +u z2 (24)
u zn+1 ＝2u zn -u zn-1 (25)
u zn+2 ＝4u zn -4u zn-1 +u zn-2 (26)
the vertical deformation u of the tunnel structure passing through the movable fault is obtained by the combined type (22) to the formula (26) z The calculation formula is as follows:
[A] (n+1)×(n+1) [u z ] (n+1)×1 ＝[Δf z ] (n+1)×1 (27)
in the middle of
[A] (n+1)×(n+1) ＝[A 1 ] (n+1)×(n+1) +[A 2 ] (n+1)×(n+1) (28)
Δf in formula (27) z ，k z By Δf x ，k x Replacing to obtain horizontal deformation u of tunnel structure x And (5) calculating a formula.
Preferably, in the fifth step, the internal force calculating method includes:
solving three-way deformation u of tunnel structure crossing movable fault x 、u y And u z Then, based on the finite difference method and Euler-Bernoulli beam theory, the axial force N and the bending moment M of the i node are calculated x 、M z Shear V x 、V z ：
Wherein N is i For the i-node axial force, M xi 、M zi Respectively i node horizontal bending moment and vertical bending moment, V xi 、V zi Respectively i node horizontal and vertical shearing forces, u yi+1 、u yi-1 Longitudinal displacement of i+1 and i-1 nodes, u zi 、u zi-1 、u zi+1 Vertical displacement of i, i+1 and i-1 nodes, u xi+2 、u xi+1 、u xi-1 、u xi-2 The nodes i+2, i+1, i-1 and i-2 are respectively horizontally displaced, u zi+2 、u zi+1 、u zi-1 、u zi-2 The vertical displacement of the nodes i+2, i+1, i-1 and i-2 is respectively shown.
The invention provides an internal force calculation system for a crossing active fault tunnel structure, which adopts the internal force calculation method for 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 u based on a finite difference method and an Euler-Bernoulli beam theory y ；
The tunnel structure horizontal and vertical deformation calculation module is used for calculating the tunnel structure horizontal based on a finite difference method and an Euler-Bernoulli beam theoryTo deformation u x Vertical deformation u of tunnel structure 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 scholars Okada, the dislocation curve delta f of the horizontal dislocation of the active fault is obtained x Longitudinal dislocation curve Δf y Vertical dislocation curve Δf 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 u of tunnel structure y ；
4. Based on finite difference method and Euler-Bernoulli beam theory, calculating horizontal deformation u of tunnel structure x Vertical deformation u 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 u based on a finite difference method and an Euler-Bernoulli beam theory y ；
The tunnel structure horizontal deformation and vertical deformation calculation module is used for calculating the tunnel structure horizontal deformation u based on a finite difference method and an Euler-Bernoulli beam theory x Vertical deformation u of tunnel structure 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) With the movable fault dislocation, the tunnel structure is deformed in three directions of horizontal direction (x-axis direction), vertical direction (z-axis direction) and longitudinal direction (y-axis direction), the burial depth of the tunnel structure is C, the lining thickness is t, the equivalent diameter of the tunnel structure is D (D= (W+H)/2, W is the span of the tunnel structure, H is the height of the tunnel structure), the fault inclination angle is alpha, and the tunnel structure-fault intersection angle is beta, as 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 dislocation delta f (delta f x ，Δf y ，Δf z ) Under the influence of the three-way load q (q x ，q y ，q z ) Three-way deformation u (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 pressure q x ，q y ，q z The calculation formula is as follows:
q x ＝k x Δu x (1)
q y ＝k y Δu y (2)
q z ＝k z Δu z (3)
wherein Deltau x ，Δu y ，Δu z The horizontal tunnel structure and the vertical tunnel structure are respectively deformed relative to surrounding rocks; k (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 coefficient k x ，k y ，k z The calculation formula is as follows:
k y ＝ξk z ＝ξk x (5)
wherein E is t And I is the tunnel structure elastic modulus and moment of inertia, respectively, i=pi [ D ] 4 -(D-2t) 4 ]4; e and v are the stratum elastic modulus and Poisson's ratio, respectively; ζ is the longitudinal surrounding rock bed coefficient ratio, which can be taken to be 0.5 according to the related study.
Horizontal, vertical and longitudinal tunnel structure-surrounding rock relative deformation deltau x ，Δu y ，Δu z The calculation formulas are respectively as follows:
Δu x ＝Δf x -u x (7)
Δu y ＝Δf y -u y (8)
Δu z ＝Δf z -u z (9)
according to Euler-Bernoulli beam theory, the horizontal, vertical and longitudinal deformation differential equations of the tunnel structure are respectively:
wherein a is the cross-sectional area of the tunnel structure, a=pi D 2 /4-π(D-2t) 2 /4。
Since the tomographic shifts have significant unevenness, it is difficult to obtain the analytical solutions of the formulas (10) to (12), and thus the numerical solutions of the formulas (10) to (12) are obtained by the finite difference method. The tunnel structure passing through the movable fracture zone is divided into n+5 parts, wherein the tunnel structure comprises two virtual nodes at two ends, the unit length is delta=l/n, and L is the length of the tunnel structure, as shown in fig. 5.
(1) Longitudinal deformation u of tunnel structure 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:
wherein k is yi ，u yi ，Δf yi The method comprises the steps of respectively obtaining the longitudinal surrounding rock bed coefficient of an i node, the deformation of a tunnel structure and the deformation of a fracture zone;
according to the stress characteristic of the tunnel structure crossing the movable fracture zone, the axial force at two ends of the tunnel structure is 0, namely when i=0 or i=n, the axial force n=0. The method is based on finite difference equation and Euler-Bernoulli beam theory:
u y-1 ＝u y1 (2)
u yn+1 ＝u yn-1 (3)
the longitudinal deformation calculation formulas of the tunnel structure crossing the movable fault are obtained by the combined formulas (13) to (15):
[B] (n+1)×(n+1) [u y ] (n+1)×1 ＝[Δf y ] (n+1)×1 (4)
in the middle of
[B] (n+1)×(n+1) ＝[B 1 ] (n+1)×(n+1) +[B 2 ] (n+1)×(n+1) (5)
(2) Horizontal deformation u of tunnel structure x Vertical deformation u 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:
wherein k is 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 i=0 or n, the vertical bending moment M z =0, vertical shear V z =0. Based on the finite difference formula, the difference form of the boundary condition is obtained as follows:
u z-1 ＝2u z0 -u z1 (23)
u z-2 ＝4u z0 -4u z1 +u z2 (24)
u zn+1 ＝2u zn -u zn-1 (25)
u zn+2 ＝4u zn -4u zn-1 +u zn-2 (26)
the vertical deformation u of the tunnel structure passing through the movable fault is obtained by the combined type (22) to the formula (26) z The calculation formula is as follows:
[A] (n+1)×(n+1) [u z ] (n+1)×1 ＝[Δf z ] (n+1)×1 (27)
in the middle of
[A] (n+1)×(n+1) ＝[A 1 ] (n+1)×(n+1) +[A 2 ] (n+1)×(n+1) (28)
Δf in formula (27) z ，k z By Δf 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 u of tunnel structure crossing movable fault x 、u y And u z Then, based on the finite difference method and Euler-Bernoulli beam theory, the axial force N and the bending moment M of the i node are calculated x 、M z Shear V x 、V z ：
Wherein N is i For the i-node axial force, M xi 、M zi Respectively i node horizontal bending moment and vertical bending moment, V xi 、V zi Respectively i node horizontal and vertical shearing forces, u yi+1 、u yi-1 Longitudinal displacement of i+1 and i-1 nodes, u zi 、u zi-1 、u zi+1 Vertical displacement of i, i+1 and i-1 nodes, u xi+2 、u xi+1 、u xi-1 、u xi-2 The nodes i+2, i+1, i-1 and i-2 are respectively horizontally displaced, u zi+2 、u zi+1 、u zi-1 、u zi-2 The vertical displacement of the nodes i+2, i+1, i-1 and i-2 is respectively shown.
(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
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 (6)

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 dislocation curve delta f of horizontal direction of active fault x Longitudinal dislocation curve Δf y Vertical dislocation curve Δf 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 u of tunnel structure y ；
4. Based on finite difference method and Euler-Bernoulli beam theory, calculating horizontal deformation u of tunnel structure x Vertical deformation u z ；
5. Calculating the internal force of the tunnel structure based on a finite difference method and an Euler-Bernoulli beam theory;
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 condition of movable fault dislocation, the tunnel structure is deformed in a horizontal direction, a vertical direction and a longitudinal direction, wherein the horizontal direction is the x-axis direction, the vertical direction is the z-axis direction, the longitudinal direction is the y-axis direction, the burial depth of the tunnel structure is C, the thickness of the lining is t, the equivalent diameter of the tunnel structure is D, the fault inclination angle is alpha, and the intersection angle of the tunnel structure and the fault is beta;
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 delta f in fault x ，Δf y ，Δf z Under the action of the three-way load q of the tunnel structure x ，q y ，q z Acting to generate three-way deformation u 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 pressure q x ，q y ，q z The calculation formula is as follows:
q x ＝k x Δu x (1)
q y ＝k y Δu y (2)
q z ＝k z Δu z (3)
wherein Deltau x ，Δu y ，Δu z The horizontal tunnel structure and the vertical tunnel structure are respectively deformed relative to surrounding rocks; k (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 coefficient k x ，k y ，k z The calculation formula is as follows:
k y ＝ξk z ＝ξk x (5)
wherein E is t And I is the tunnel structure elastic modulus and moment of inertia, respectively; e and v are the stratum elastic modulus and Poisson's ratio, respectively; ζ is the coefficient ratio of the longitudinal surrounding rock bed;
horizontal, vertical and longitudinal tunnel structure-surrounding rock relative deformation deltau x ，Δu y ，Δu z The calculation formulas are respectively as follows:
Δu x ＝Δf x -u x (7)
Δu y ＝Δf y -u y (8)
Δu z ＝Δf z -u z (9)
according to Euler-Bernoulli beam theory, the horizontal, vertical and longitudinal deformation differential equations of the tunnel structure are respectively:
wherein A is the cross-sectional area of the tunnel structure.
2. The method for calculating internal force of crossing active fault tunnel structure according to claim 1, wherein: in step three, the tunnel structure is deformed longitudinally u y The calculation method of (1) is as follows:
dividing a tunnel structure crossing the movable fracture zone into n+5 parts, wherein the tunnel structure comprises two virtual nodes at two ends, the unit length is delta=l/n, and L is the length of the tunnel structure;
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:
wherein k is yi ，u yi ，Δf yi The method comprises the steps of respectively obtaining the longitudinal surrounding rock bed coefficient of an i node, the deformation of a tunnel structure and the deformation of a fracture zone;
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, namely when i=0 or i=n, the axial force N=0; the method is based on finite difference equation and Euler-Bernoulli beam theory:
u y-1 ＝u y1 (14)
u yn+1 ＝u yn-1 (15)
the longitudinal deformation u passing through the movable fault tunnel structure is obtained by the combined type (13) to the formula (15) y The calculation formula is as follows:
[B] (n+1)×(n+1) [u y ] (n+1)×1 ＝[Δf y ] (n+1)×1 (16)
in the middle of
[B] (n+1)×(n+1) ＝[B 1 ] (n+1)×(n+1) +[B 2 ] (n+1)×(n+1) (17)
3. The method for calculating the internal force of the tunnel structure crossing the active fault according to claim 2, wherein: in the fourth step, the tunnel structure is deformed in the horizontal direction u x Vertical deformation u of tunnel structure 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:
wherein k is zi ，u zi ，Δf zi The vertical surrounding rock bed coefficients of the i nodes, 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 i=0 or i=n, the vertical bending moment M z =0, vertical shear V z =0; based on the finite difference formula, the difference form of the boundary condition is obtained as follows:
u z-1 ＝2u z0 -u z1 (23)
u z-2 ＝4u z0 -4u z1 +u z2 (24)
u zn+1 ＝2u zn -u zn-1 (25)
u zn+2 ＝4u zn -4u zn-1 +u zn-2 (26)
the vertical deformation u of the tunnel structure passing through the movable fault is obtained by the combined type (22) to the formula (26) z The calculation formula is as follows:
[A] (n+1)×(n+1) [u z ] (n+1)×1 ＝[Δf z ] (n+1)×1 (27)
in the middle of
[A] (n+1)×(n+1) ＝[A 1 ] (n+1)×(n+1) +[A 2 ] (n+1)×(n+1) (28)
Δf in formula (27) z ，k z By Δf x ，k x Replacing to obtain horizontal deformation u of tunnel structure x And (5) calculating a formula.
4. A method of calculating internal forces across an active fault tunnel structure according to claim 3, wherein: in the fifth step, the internal force calculation method comprises the following steps:
solving three-way deformation u of tunnel structure crossing movable fault x 、u y And u z Then, based on the finite difference method and Euler-Bernoulli beam theory, the axial force N and the bending moment M of the i node are calculated x 、M z Shear V x 、V z ：
Wherein N is i For the i-node axial force, M xi 、M zi Respectively i node horizontal bending moment and vertical bending moment, V xi 、V zi Respectively i node horizontal and vertical shearing forces, u yi+1 、u yi-1 Longitudinal displacement of i+1 and i-1 nodes, u zi 、u zi-1 、u zi+1 Vertical displacement of i, i+1 and i-1 nodes, u xi+2 、u xi+1 、u xi-1 、u xi-2 The nodes i+2, i+1, i-1 and i-2 are respectively horizontally displaced, u zi+2 、u zi+1 、u zi-1 、u zi-2 The vertical displacement of the nodes i+2, i+1, i-1 and i-2 is respectively shown.
5. 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 4, 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 u based on a finite difference method and an Euler-Bernoulli beam theory y ；
The tunnel structure horizontal deformation and vertical deformation calculation module is used for calculating the tunnel structure horizontal deformation u based on a finite difference method and an Euler-Bernoulli beam theory x Vertical deformation u of tunnel structure 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.
6. 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 as claimed in any one of claims 1 to 4.
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