Railway tunnel lining shock damage calculation method and system based on near-field dynamics

Abstract

The invention relates to a railway tunnel lining shock damage calculation method and system based on near-field dynamics. The method comprises the following steps: establishing finite element models of tunnel surrounding rock, lining support and fault; physical and mechanical parameters are given, boundary conditions are set, then initial balance is carried out, and tunnel excavation rebalance is carried out; first deformation and stress of the finite element model are obtained through quasi-static calculation; the finite element unit is used for judging that the fault area and the crossed tunnel area are damaged; dispersing the damaged finite element units into near-field dynamics material point units; on the basis of initial balance, tunnel excavation rebalance is conducted again, and second deformation and stress are obtained through quasi-static calculation; and calculating the damage of the inter-unit bond of the material point. According to the method, the finite element and the near-field dynamics calculation method are combined, the defect that the problems of discontinuous deformation and damage cannot be handled by only adopting the finite element method is overcome, near-field dynamics calculation is only carried out on the damaged finite element unit, and calculation is more efficient and more accurate.

Description

Technical Field

[0001] The invention relates to the technical field of railway tunnel lining safety maintenance, and in particular to a method and system for calculating seismic damage of railway tunnel lining based on peri-field dynamics. Background Art

[0002] If a long tunnel project passes through a fault zone in a high-intensity earthquake zone, when the fault moves, the ground deformation will cause the tunnel support structure to deform. The tunnel support structure will deform unevenly and may change continuously. When the deformation accumulates to a certain extent, it will have a serious impact on the safety of the railway tunnel lining.

[0003] In order to timely grasp the deformation of tunnel lining, the finite element numerical calculation method can be used to calculate the seismic damage of cross-fault tunnels. However, the finite element numerical calculation method is based on the assumption of continuous deformation, but the deformation of the tunnel crossing the fault zone is essentially discontinuous, and there is a fundamental contradiction between the two. Therefore, the calculation of the seismic damage of cross-fault tunnels by the finite element numerical calculation method will inevitably lead to inaccurate and unreliable results.

[0004] Therefore, it is necessary to propose new measures to overcome the above-mentioned defects. Summary of the invention

[0005] The purpose of the present invention is to provide a method and system for calculating the seismic damage of railway tunnel lining based on peridynamics, so as to solve the problems of inaccuracy and unreliability in the current calculation of seismic damage of tunnel lining based on finite element numerical calculation method.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] A method for calculating seismic damage of railway tunnel lining based on peridynamics, the method comprising:

[0008] Establish finite element models of tunnel surrounding rock, lining support, and faults;

[0009] Assign physical and mechanical parameters to the finite element model and set boundary conditions, then perform initial balance, excavate the tunnel and rebalance;

[0010] The first deformation and stress of the finite element model are obtained through pseudo-static calculation;

[0011] Finite element elements for determining damage in fault areas and cross-tunnel areas;

[0012] Discretize the damaged finite element into material point elements of peridynamics;

[0013] On the basis of the initial balance, the excavated tunnel is rebalanced again, and the second deformation and stress are obtained through pseudo-static calculation;

[0014] Computes the damage to the bonds between material point elements.

[0015] Furthermore, the finite element model is given physical and mechanical parameters, including:

[0016] Physical and mechanical parameters of the surrounding rock are assigned to the tunnel surrounding rock, and the physical and mechanical parameters of the surrounding rock include surrounding rock stratum, elastic modulus, Poisson's ratio, cohesion, internal friction angle, and density.

[0017] Furthermore, boundary conditions are set for the finite element model, including:

[0018] Apply vertical ground stress σ1 in both the upper and lower directions of the finite element model;

[0019] Apply lateral pressure σ2 on the left and right sides of the finite element model;

[0020] σ2=λσ1

[0021] in:

[0022] λ is the Poisson's ratio of the surrounding rock.

[0023] Further, the initial balance includes:

[0024] The vertical and horizontal geostresses are converted into stress-strain conditions in the calculation area, and the constraints are converted into displacement boundary conditions. The adaptive dynamic relaxation algorithm is used to iteratively calculate and finally reach the initial equilibrium.

[0025] Further, the tunnel excavation was rebalanced, including:

[0026] Set the tunnel excavation area and set the grid in the excavation area to dormant state to simulate tunnel excavation and perform balance calculations.

[0027] Furthermore, the first deformation and stress of the finite element model are obtained through pseudo-static calculation, including:

[0028] Seismic shear deformation is gradually applied to the left boundary of the tunnel, and the deformation and stress in the model area are calculated.

[0029] Furthermore, the finite element unit for determining the damage in the fault area and the cross tunnel area includes:

[0030] The finite element units that are damaged in the fault area and the cross tunnel area are determined according to the yield criterion, and the yield judgment criterion is the maximum shear stress criterion and the Mohr-Coulomb criterion.

[0031] Furthermore, the damaged finite element units are discretized into material point units of peridynamics, and the material parameters of the material point units are consistent with the original finite element model.

[0032] Furthermore, the damage of the bonds between material point elements is calculated, including:

[0033] The damage D of the bond between material point units is:

[0034]

[0035] in:

[0036] ε is strain;

[0037] ε c0 is the compressive strain corresponding to the compressive strength;

[0038] r is the post-peak strain softening index;

[0039] ε cr is the residual compressive strain corresponding to the residual compressive strength;

[0040] γ c is the residual compressive strength coefficient, γ c =σ cr / σ c0 ;

[0041] σ cr is the residual compressive strength under uniaxial stress state;

[0042] σ c0 It is the uniaxial compressive strength of the material when it is not damaged;

[0043] ε cu is the final compressive strain corresponding to the complete damage state.

[0044] On the other hand, a system for calculating seismic damage of railway tunnel lining based on peridynamics is provided, wherein the system is used to implement the method described, and comprises:

[0045] Finite element model building module, used to build finite element models of tunnel surrounding rock, lining support and faults;

[0046] The balancing module is used to assign physical and mechanical parameters to the finite element model and set boundary conditions, and then perform initial balancing and rebalancing of the excavated tunnel;

[0047] A first quasi-static calculation module, used for obtaining a first deformation and stress of a finite element model through quasi-static calculation;

[0048] A damage determination module is used to determine the finite element units that have been damaged in the fault area and the cross tunnel area;

[0049] Peridynamics discretization module, which discretizes the damaged finite element elements into peridynamic material point elements;

[0050] The second quasi-static calculation module is used to rebalance the excavated tunnel based on the initial balance, and obtain the second deformation and stress through quasi-static calculation;

[0051] The damage calculation module is used to calculate the damage of the bonds between material point elements.

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] The present invention provides a method and system for calculating seismic damage of railway tunnel lining based on peridynamics, which combines the finite element numerical calculation method with the peridynamic calculation method to overcome the defect that the single finite element numerical calculation method cannot handle non-continuous deformation and damage problems, and performs peridynamic calculation only on the finite element units that are damaged in the fault area and the cross-tunnel area, so the calculation is more efficient and accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, drawings of other embodiments can be obtained based on these drawings without paying creative work.

[0055] Figure 1 It is a flow chart of the method of the present invention.

[0056] Figure 2 It is a schematic diagram of the numerical calculation model of the present invention.

[0057] Figure 3 It is a schematic diagram of damage calculation results of the present invention. DETAILED DESCRIPTION

[0058] In order to facilitate the understanding of the present invention, the present invention will be described more fully below with reference to the relevant drawings. The preferred embodiments of the present invention are given in the drawings. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present invention more thoroughly understood.

[0059] It should be noted that similar reference numerals and letters represent similar items, and therefore, once an item is defined in one embodiment, it does not need to be further defined and explained in subsequent embodiments. In addition, the term "comprising" and the like and any variation thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0060] It should also be noted that although the order of steps is mentioned in the method description, in some cases, they may be performed in an order different from that shown here, and this should not be construed as a limitation on the order of the steps.

[0061] Meanwhile, in the description of the present invention, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance. Of course, such objects can be interchanged where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than that illustrated or described herein.

[0062] The existing finite element numerical calculation method is based on the assumption of continuous deformation, which is not suitable for analyzing and calculating discontinuous deformation problems such as tunnels crossing fault zones. In view of such defects and limitations, the present invention provides a railway tunnel lining seismic damage calculation method based on peridynamics. On the basis of the finite element numerical calculation method, peridynamics means are introduced to obtain a tunnel lining seismic damage calculation method coupled with peridynamics and finite elements. The finite element numerical calculation method cannot handle the problem of discontinuous deformation and damage, while the peridynamic method can handle the problem of discontinuous deformation and damage. The organic combination of the two is more accurate and efficient when analyzing and calculating the deformation problem of tunnels crossing fault zones.

[0063] like Figure 1 , the method comprising:

[0064] S1: Establish finite element models of tunnel surrounding rock, lining support and faults.

[0065] S2: Assign physical and mechanical parameters to the finite element model and set boundary conditions, then perform initial balance, excavate the tunnel and then rebalance.

[0066] in:

[0067] S201: assigning physical and mechanical parameters to the finite element model, including: assigning physical and mechanical parameters of surrounding rock to the tunnel surrounding rock, wherein the surrounding rock physical and mechanical parameters include surrounding rock stratum, elastic modulus, Poisson's ratio, cohesion, internal friction angle, and density.

[0068] S202: Set boundary conditions for the finite element model, including:

[0069] Apply vertical ground stress σ1 in both the upper and lower directions of the finite element model;

[0070] Apply lateral pressure σ2 on the left and right sides of the finite element model;

[0071] σ2=λσ1

[0072] in:

[0073] λ is the Poisson's ratio of the surrounding rock.

[0074] S203: Initial balance, including:

[0075] The vertical and horizontal geostresses are converted into stress-strain conditions in the calculation area, and the constraints are converted into displacement boundary conditions. The adaptive dynamic relaxation algorithm is used to iteratively calculate and finally reach the initial equilibrium.

[0076] S204: Tunnel excavation rebalancing, including:

[0077] A tunnel excavation area is set, and the grids in the excavation area are set to a dormant state for simulating tunnel excavation, and the balance method in step S203 is used to perform balance calculation.

[0078] S3: Obtain the first deformation and stress of the finite element model through pseudo-static calculation. Including:

[0079] Seismic shear deformation is gradually applied to the left boundary of the tunnel, and the deformation and stress of the model area are further calculated using finite element calculation software.

[0080] S4: Finite element unit for determining damage in fault area and cross tunnel area. Includes:

[0081] The finite element units that are damaged in the fault area and the cross tunnel area are determined according to the yield criterion. The yield judgment criteria are the maximum shear stress criterion and the Mohr-Coulomb criterion. The maximum shear stress criterion is that when the shear stress reaches the maximum shear stress of tensile failure or compressive yield failure, the failure occurs. The Mohr-Coulomb criterion is that when the ratio of the shear stress to the normal stress on the shear plane reaches the maximum, the material yields and fails.

[0082] S5: Discretize the damaged finite element into material point elements of peridynamics. The material parameters of the material point elements are consistent with the original finite element model.

[0083] S6: Based on the initial balance, the excavated tunnel is rebalanced again, and the second deformation and stress are obtained through pseudo-static calculation.

[0084] S7: Calculate the damage of the bonds between material point elements.

[0085] Calculates damage to bonds between material point elements, including:

[0086] The damage D of the bond between material point units is:

[0087]

[0088] ε is strain;

[0089] ε c0 is the compressive strain corresponding to the compressive strength;

[0090] r is the post-peak strain softening index;

[0091] ε cr is the residual compressive strain corresponding to the residual compressive strength;

[0092] γ c is the residual compressive strength coefficient, γ c =σ cr / σ c0 ;

[0093] σ cr is the residual compressive strength under uniaxial stress state;

[0094] σ c0 It is the uniaxial compressive strength of the material when it is not damaged;

[0095] ε cu is the final compressive strain corresponding to the complete damage state.

[0096] The method of the present invention, after obtaining the finite element units of the fault area and the cross tunnel area that are damaged, only discretizes the finite element units of this part into material point units of peridynamics, and performs peridynamic calculations on this part instead of the entire model, thereby overcoming the problem of consuming a large amount of computing resources when all peridynamic calculations are used, and significantly improving the computing efficiency.

[0097] Example:

[0098] This embodiment compares the computational efficiency through a specific two-dimensional example.

[0099] Condition 1: The surrounding rock of the tunnel is discretized in advance, and the numerical model is discretized into 500×500 material points. The tunnel surrounding rock and lining support adopt solid units.

[0100] Working condition 2: using the coupling calculation method proposed in the present invention, only the plastic region (i.e. the finite element unit where damage occurs) is discretized by using peridynamic material points and then the calculation is performed.

[0101] (1) The finite element model is established as follows Figure 2 The blank space inside the model is the tunnel.

[0102] (2) The physical and mechanical parameters of the surrounding rock are shown in Table 1.

[0103] Table 1 Physical and mechanical parameters of surrounding rock

[0104]

[0105] (3) Set boundary conditions. Apply vertical ground stress σ1 in the upper and lower directions of the finite element model, and apply lateral pressure σ2 on the left and right sides of the finite element model.

[0106] σ2=λσ1

[0107] in:

[0108] λ is the Poisson's ratio of the surrounding rock.

[0109] (4) Initial equilibrium, that is, the displacement and force of the established finite element model reach a state of equilibrium under the ground stress boundary conditions.

[0110] (5) Tunnel excavation: Here, a relatively mature unit life and death is used for tunnel excavation. A tunnel excavation area is set, and the grids in the excavation area are set to dormant state to simulate tunnel excavation.

[0111] (6) Perform quasi-static calculations to obtain the damage characteristics around the tunnel, such as Figure 3 shown.

[0112] The calculation is performed using a 16-core CPU, 32G memory, and 3.7Hz AMD Ryzen 4th generation processor. The calculation efficiency comparison is shown in Table 2.

[0113] Table 2 Comparison of calculation efficiency

[0114] Working conditions time Condition 1 621s Condition 2 512s

[0115] It can be seen from Table 2 that the coupling calculation method proposed in the present invention can not only objectively calculate the discontinuous deformation problem, but also significantly shorten the calculation time and make the calculation more efficient.

[0116] In addition, the present invention also provides a railway tunnel lining seismic damage calculation system based on peridynamics, which is used to implement the above method, including:

[0117] The finite element model building module is used to build the finite element model of the tunnel surrounding rock, lining support and fault, corresponding to S1 of the above method;

[0118] The balancing module is used to assign physical and mechanical parameters to the finite element model and set boundary conditions, and then perform initial balancing and rebalancing of the excavated tunnel, which corresponds to S2 of the above method;

[0119] A first quasi-static calculation module, used for obtaining a first deformation and stress of the finite element model through quasi-static calculation, corresponding to S3 of the above method;

[0120] A damage determination module, used to determine the finite element units that are damaged in the fault area and the cross tunnel area, corresponding to S4 of the above method;

[0121] The peridynamic discretization module is used to discretize the damaged finite element units into peridynamic material point units, which corresponds to S5 of the above method;

[0122] The second quasi-static calculation module is used to rebalance the excavated tunnel based on the initial balance, and obtain the second deformation and stress through quasi-static calculation, which corresponds to S6 of the above method;

[0123] The damage calculation module is used to calculate the damage of the bonds between material point elements, corresponding to S7 of the above method.

[0124] Those skilled in the art will appreciate that all or part of the functions of the embodiments of the present invention may be implemented by hardware or by computer programs. When all or part of the functions in the above-mentioned embodiments are implemented by computer programs, the program may be stored in a computer-readable storage medium, and the storage medium may include: a read-only memory, a random access memory, a disk, an optical disk, a hard disk, etc., and the program is executed by a computer to implement the above-mentioned functions. For example, the program is stored in the memory of the device, and when the program in the memory is executed by the processor, all or part of the above-mentioned functions can be implemented. In addition, when all or part of the functions in the above-mentioned embodiments are implemented by computer programs, the program may also be stored in a storage medium such as a server, another computer, a disk, an optical disk, a flash disk or a mobile hard disk, and is downloaded or copied and saved in the memory of the local device, or the system of the local device is updated, and when the program in the memory is executed by the processor, all or part of the functions in the above-mentioned embodiments can be implemented.

[0125] The above specific examples are used to illustrate the present invention, which is only used to help understand the present invention and is not intended to limit the present invention. For those skilled in the art, according to the concept of the present invention, some simple deductions, modifications or substitutions can be made.

Claims

1. A method for calculating seismic damage of railway tunnel lining based on peridynamics, characterized by: The method comprises: Establish finite element models of tunnel surrounding rock, lining support, and faults; Assign physical and mechanical parameters to the finite element model and set boundary conditions, then perform initial balance, excavate the tunnel and rebalance; The first deformation and stress of the finite element model are obtained through pseudo-static calculation; Finite element elements for determining damage in fault areas and cross-tunnel areas; Discretize the damaged finite element into material point elements of peridynamics; On the basis of the initial balance, the excavated tunnel is rebalanced again, and the second deformation and stress are obtained through pseudo-static calculation; Computes the damage to the bonds between material point elements.

2. The method for calculating seismic damage of railway tunnel lining based on peridynamics according to claim 1 is characterized by: Assign physical and mechanical parameters to the finite element model, including: Physical and mechanical parameters of the surrounding rock are assigned to the tunnel surrounding rock, and the physical and mechanical parameters of the surrounding rock include surrounding rock stratum, elastic modulus, Poisson's ratio, cohesion, internal friction angle, and density.

3. The method for calculating seismic damage of railway tunnel lining based on peridynamics according to claim 2 is characterized by: Set boundary conditions for the finite element model, including: Apply vertical ground stress σ1 in both the upper and lower directions of the finite element model; Apply lateral pressure σ2 on the left and right sides of the finite element model; σ2=λσ1 in: λ is the Poisson's ratio of the surrounding rock.

4. The method for calculating seismic damage of railway tunnel lining based on peridynamics according to claim 3 is characterized by: Initial balancing, including: The vertical and horizontal geostresses are converted into stress-strain conditions in the calculation area, and the constraints are converted into displacement boundary conditions. The adaptive dynamic relaxation algorithm is used to iteratively calculate and finally reach the initial equilibrium.

5. The method for calculating seismic damage of railway tunnel lining based on peridynamics according to claim 4 is characterized by: Tunnel excavation rebalancing, including: Set the tunnel excavation area and set the grid in the excavation area to dormant state to simulate tunnel excavation and perform balance calculations.

6. The method for calculating seismic damage of railway tunnel lining based on peridynamics according to claim 5 is characterized by: The first deformation and stress of the finite element model are obtained through pseudo-static calculation, including: Seismic shear deformation is gradually applied to the left boundary of the tunnel, and the deformation and stress in the model area are calculated.

7. The method for calculating seismic damage of railway tunnel lining based on peridynamics according to claim 6 is characterized by: Finite element units for determining damage in fault areas and cross-tunnel areas include: The finite element units that are damaged in the fault area and the cross tunnel area are determined according to the yield criterion, and the yield judgment criterion is the maximum shear stress criterion and the Mohr-Coulomb criterion.

8. The method for calculating seismic damage of railway tunnel lining based on peridynamics according to claim 7 is characterized by: The damaged finite element units are discretized into material point units of peridynamics, and the material parameters of the material point units are consistent with the original finite element model.

9. The method for calculating seismic damage of railway tunnel lining based on peridynamics according to claim 8 is characterized by: Calculates damage to bonds between material point elements, including: The damage D of the bond between material point units is: in: ε is strain; ε c0 is the compressive strain corresponding to the compressive strength; r is the post-peak strain softening index; ε cr is the residual compressive strain corresponding to the residual compressive strength; γ c is the residual compressive strength coefficient, γ c =σ cr / σ c0 ; σ cr is the residual compressive strength under uniaxial stress state; σ c0 It is the uniaxial compressive strength of the material when it is not damaged; ε cu is the final compressive strain corresponding to the complete damage state.

10. A railway tunnel lining seismic damage calculation system based on peridynamics, characterized by: The system is used to implement the method according to claim 1, comprising: Finite element model building module, used to build finite element models of tunnel surrounding rock, lining support and faults; The balancing module is used to assign physical and mechanical parameters to the finite element model and set boundary conditions, and then perform initial balancing and rebalancing of the excavated tunnel; A first quasi-static calculation module, used for obtaining a first deformation and stress of a finite element model through quasi-static calculation; A damage determination module is used to determine the finite element units that have been damaged in the fault area and the cross tunnel area; Peridynamics discretization module, which discretizes the damaged finite element elements into peridynamic material point elements; The second quasi-static calculation module is used to rebalance the excavated tunnel based on the initial balance, and obtain the second deformation and stress through quasi-static calculation; The damage calculation module is used to calculate the damage of the bonds between material point elements.

Images