Nonlinear spring pretreatment method in load structure method

Abstract

The invention discloses a method for preprocessing a nonlinear spring in a load structure method. The method comprises the following steps: S1, inputting a refined shield segment structure model; s2, extracting segment peripheral node information meeting constraint conditions, calculating spring end point coordinates and establishing a nonlinear spring set; s3, executing the following operations on each segment peripheral node obtained in the S2: traversing all units, and judging whether the traversed units contain the current peripheral node or not; if so, searching and recording all peripheral node coordinates of the unit; calculating the peripheral surface area of each unit based on the recorded unit node coordinates, and calculating the rigidity of a nonlinear spring at the current peripheral node according to the peripheral surface area of each unit; s4, updating the original calculation analysis file according to the nonlinear spring set established in S2 and the rigidity, calculated in S3, of the nonlinear springs at the peripheral nodes; according to the method, the rapid application preprocessing of the segment load is realized, and the calculation efficiency and the simulation precision of actual engineering geological conditions are improved.

Description

Technical Field

[0001] This application relates to the technical field of shield tunneling, and particularly to a method for preprocessing non-linear springs in the load structure method. Background Art

[0002] In the traditional finite element analysis method, the lining segments are simulated by structural elements, while the bolts between the segment blocks are represented by linear rotational springs or non-linear interface models. To perform a stress analysis on the shield tunnel segments and then evaluate and predict the long-term and short-term stability of the surrounding rock of the shield tunnel, it is often necessary to construct a refined three-dimensional segment structure model. However, the irregular geometric characteristics may lead to stress concentration, local failure, or even overall collapse. Therefore, the refinement degree of the segment block model provides a basic model for accurate analysis results and design suggestions. Commonly used analysis methods include the load structure method and the stratum structure method. The load structure method is widely used in complex mechanized tunnel engineering because a large number of interactions between interfaces may consume a lot of time, and it is economically unfeasible and inefficient. In this method, the interaction effect between the segment blocks and the surrounding rock is represented by setting non-linear springs at the numerical nodes, and the accuracy of simulating the interaction effect largely depends on the accuracy of spring stiffness calculation and application. For irregular geometric blocks, the distribution of numerical nodes is non-uniform, and the rules and quantities of mesh division are not unified, which restricts the efficiency of numerical analysis preprocessing and also brings great obstacles to the scenario deduction of the segment structure disasters of shield tunnels under multiple working conditions and multiple scenarios.

[0003] Therefore, there is an urgent need to propose an automatic preprocessing framework for irregular segment blocks to provide technical support for the accurate prediction of the disaster risk of the shield tunnel support structure and the stability evaluation of construction risks. Summary of the Invention

[0004] To solve the above problems, this application provides a method for preprocessing non-linear springs in the load structure method, which can achieve rapid preprocessing of segment loads, improve both the calculation efficiency of numerical simulation analysis and the simulation accuracy of actual engineering geological conditions. The technical solutions are as follows:

[0005] This application provides a method for preprocessing non-linear springs in the load structure method, including the following steps:

[0006] S1 Input a refined shield segment structure model to obtain the original calculation and analysis file;

[0007] S2 Extract the peripheral node information of the segments that meet the constraint conditions, calculate the spring endpoint coordinates, and establish a non-linear spring set;

[0008] S3 extracts the outermost unit information of each specific block unit type of the segment in the original calculation and analysis file, and performs the following operations on each segment peripheral node obtained in S2: traverse all units to determine whether the traversed unit contains the current peripheral node; if it contains, search for and record the coordinates of all peripheral nodes of the unit; calculate the area of each unit's peripheral surface based on the recorded unit node coordinates, and calculate the stiffness of the nonlinear spring at the current peripheral node according to the area of each unit's peripheral surface.

[0009] S4 updates the original calculation and analysis file according to the set of nonlinear springs established in S2 and the stiffness of the nonlinear springs at the peripheral nodes calculated in S3.

[0010] For example, in the method for preprocessing nonlinear springs in the load structure method provided in an embodiment, in S1, the refined shield segment model is meshed, and it is ensured that the outermost mesh unit type of the segment is a hexahedron unit.

[0011] For example, in the method for preprocessing nonlinear springs in the load structure method provided in an embodiment, in S2, the segment peripheral node information that meets the following constraint conditions is extracted:

[0012] d > 0.5×(D - T)

[0013] where d is the distance from the node to the center of the tunnel segment, D is the outer diameter of the segment, and T is the thickness of the outermost hexahedron mesh unit.

[0014] For example, in the method for preprocessing nonlinear springs in the load structure method provided in an embodiment, in S2, the spring endpoint coordinates are calculated according to the segment peripheral node information and the following formula:

[0015]

[0016] where R is the outer radius of the segment.

[0017] For example, in the method for preprocessing nonlinear springs in the load structure method provided in an embodiment, in S3, the following operations are performed: outer loop: traverse each segment peripheral node recorded in S2 as the current node; inner loop: for each current node, traverse all units to determine whether the node numbers of all nodes of the traversed unit contain the node number of the current node; if it contains, search for and record the coordinates of all peripheral nodes of the unit; loop until all units are traversed, and store the coordinates of all nodes of each unit containing the current node for calculating the peripheral surface area.

[0018] For example, in the method for preprocessing nonlinear springs in the load structure method provided in an embodiment, in S3, the area of each unit's peripheral surface is calculated using the following formula:

[0019]

[0020] Among them, x ij , y ij , z ij respectively represent the x, y, and z coordinate values of the j-th node of the i-th unit, and S i represents the area of the peripheral surface of the i-th unit.

[0021] For example, in the method for preprocessing non-linear springs in the load structure method provided in an embodiment, in S3, the stiffness calculation formula of the non-linear spring at each peripheral node is:

[0022]

[0023] Among them, k represents the elastic stiffness of the spring, K represents the resistance coefficient of the surrounding rock, and n is the number of units sharing the peripheral node.

[0024] For example, in the method for preprocessing non-linear springs in the load structure method provided in an embodiment, the exposed surface of the unit is a quadrilateral surface, and each peripheral node is shared by four such quadrilateral surfaces. The stiffness of the non-linear spring at the node is the arithmetic mean of the areas of the four quadrilateral surfaces.

[0025] For example, in the method for preprocessing non-linear springs in the load structure method provided in an embodiment, the interaction between the segment structure and the surrounding rock is simulated by two-point non-linear springs. When the spring is in tension, the surrounding rock and the shield segment are separated, and the spring stiffness is infinitesimal; when the spring is in compression, the spring stiffness is the spring stiffness value calculated in S3.

[0026] The beneficial effects brought by a method for preprocessing non-linear springs in a load structure method provided in some embodiments of the present application are as follows: The automatic preprocessing method for irregular segment blocks in the present application can ignore the influence of the mesh regularity degree, automatically calculate the stiffness of the non-linear spring at each numerical node according to the formation information, automatically generate the spring end points and create a set of non-linear spring elements. The present application can realize the rapid application of preprocessing for segment loads, which not only improves the calculation efficiency of numerical simulation analysis but also improves the simulation accuracy of the actual engineering geological conditions. Description of the Drawings

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present specification or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0028] Figure 1It is the flowchart of the method for preprocessing non-linear springs in the load structure method of this application;

[0029] Figure 2 It is the structural model of the shield segment ring;

[0030] Figure 3 (a) is the side view of the standard segment structure at an angle;

[0031] Figure 3 (b) is the side view of the standard segment structure at another angle;

[0032] Figure 3 (c) is the side view of the standard segment structure at yet another angle;

[0033] Figure 4 It is Figure 3 The enlarged view of part A of (c);

[0034] Figure 5 (a) is the schematic diagram of simulating the left cavity of the surrounding rock of the shield tunnel segment;

[0035] Figure 5 (b) is the schematic diagram of simulating the right cavity of the surrounding rock of the shield tunnel segment;

[0036] Figure 5 (c) is the schematic diagram of simulating the cavities on both sides of the surrounding rock of the shield tunnel segment;

[0037] Figure 6 (a) is the deformation nephogram of the shield tunnel segment with a left cavity;

[0038] Figure 6 (b) is the deformation nephogram of the shield tunnel segment with a right cavity;

[0039] Figure 6 (c) is the deformation nephogram of the shield tunnel segment with cavities on both sides;

[0040] Figure 7 (a) is the damage nephogram of the segment with a 0° formation dip angle;

[0041] Figure 7 (b) is the damage nephogram of the segment with a 21° formation dip angle;

[0042] Figure 7 (c) is the damage nephogram of the segment with a 90° formation dip angle.

[0043] Reference numerals: 1 - standard segment, 2 - closure segment, 3 - adjacent segment, 4 - non-linear spring, 5 - bolt hole, 6 - manhole, 7 - tetrahedral mesh, 8 - hexahedral mesh. Detailed implementation manners

[0044] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present application.

[0045] Unless otherwise defined, the technical terms or scientific terms used in this disclosure should have the ordinary meaning understood by those of ordinary skill in the field to which this disclosure belongs. The "first", "second" and similar terms used in this disclosure do not denote any order, quantity or importance, but are only used to distinguish different components. The terms such as "including" or "comprising" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. The terms such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left", "right" are only used to represent relative position relationships. When the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0046] For the segment structure with irregular geometric shapes, it is difficult to evenly divide the mesh in numerical simulation analysis, resulting in disadvantages such as low calculation and application efficiency of the nonlinear spring stiffness for simulating the interaction between the structure and the surrounding rock. The present application provides a method for preprocessing the nonlinear spring in the load structure method, which belongs to the fast analysis method and technology in the field of segment structure analysis of shield tunnels. Specifically, it is a method and technology for quickly applying loads in segment stability analysis, which can achieve accurate and rapid calculation and application of the interaction force between the refined shield tunnel segment model and the surrounding rock and soil mass, as Figure 1 shown, including the following steps:

[0047] S1 Input the refined shield segment structure model to obtain the original calculation and analysis file;

[0048] The shield segment ring structure model is as Figure 2 shown. Among them, when meshing based on the refined segment structure model, due to the complex and irregular geometric shape of the segment, it is difficult to achieve uniform meshing in ABAQUS, and it is impossible to ensure the uniform distribution of the nodes on the periphery of the segment, nor can it ensure that the area of the elements on the periphery of the segment is equal. Therefore, there are no special requirements for the element type when meshing the segment, and it only needs to ensure that the element type within a certain thickness range on the periphery of the segment is a hexahedron element, as Figure 3 (a), Figure 3 (b), Figure 3 (c) shown.

[0049] S2 extracts the segment peripheral node information that meets the constraint conditions, calculates the spring end point coordinates, and establishes a set of non-linear springs;

[0050] Among them, extract the segment peripheral node information that meets the following constraint conditions:

[0051] d > 0.5×(D - T)

[0052] Among them, d is the distance from the node to the center of the tunnel segment, D is the outer diameter of the segment, and T is the thickness of the outer hexahedron mesh element.

[0053] Record the node numbers and coordinates that meet the requirements, and create a folder for storage. For example, save the peripheral node information of the segment in the Node.inp file.

[0054] Set the spring length to 1m. According to the above-extracted segment peripheral node information, calculate the coordinates of the other end point of the spring according to the following formula:

[0055]

[0056] Among them, R is the outer radius of the segment.

[0057] Define a set of non-linear springs, and then define a set of non-linear spring end points for subsequent application of boundary conditions.

[0058] S3 extracts the outermost unit information of each segment's specific block element type from the original calculation and analysis file, and performs the following operations on each segment peripheral node obtained in S2: traverse all units, and determine whether the traversed unit contains the current peripheral node; if it contains, search for and record the coordinates of all peripheral nodes of the unit; calculate the area of each unit's peripheral surface based on the recorded unit node coordinates, and calculate the stiffness of the non-linear spring at the current peripheral node according to the area of each unit's peripheral surface.

[0059] Specifically, in S3, perform the following operations:

[0060] Outer loop: Traverse each segment peripheral node recorded in S2 as the current node;

[0061] Inner loop: For each current node, traverse all units, and determine whether the node numbers of the traversed unit contain the node number of the current node;

[0062] If it contains, search for and record the coordinates of all peripheral nodes of the unit; loop until all units are traversed, and store the coordinates of all peripheral nodes of each unit containing the current node for calculating the peripheral surface area.

[0063] Specifically, extract the element information of the specific block element type C3D8R (i.e., 8-node hexahedron linear reduced integration element) in each segment (including standard block, closure block, and adjacent block) from the original calculation analysis file, save and store it, for example, store it as Element.inp file; perform a loop search to determine the number of elements to which the nodes in the Node.inp file belong, denoted as N; loop through each node in the Node.inp file to search for each element, and the number of elements is the number of elements recorded in the Element.inp file. Determine whether each node of each element is the node recorded in the Node.inp file. If so, assign the node coordinates to new variables, denoted as a1, b1, c1, d1, and store the node number, node x, y, z coordinate values respectively; loop through the search until all nodes in the element are searched, and store the coordinates of the peripheral nodes of each element to which the node belongs. For example, each peripheral node belongs to four elements, and the node coordinates of the four elements to which the node belongs need to be stored. As Figure 4 shown Figure 4 the P node in belongs to four elements S1, S2, S3, and S4.

[0064] Calculate the area of each peripheral face of the element using the following formula:

[0065]

[0066] where x ij , y ij , z ij represent the x, y, z coordinate values of the j-th node of the i-th element respectively, and S i represents the area of the peripheral face of the i-th element.

[0067] For peripheral nodes, each node is shared by four quadrilateral faces. Therefore, consider the area of the element to which the node belongs as the average value of the areas of these four quadrilateral faces. Then, the stiffness calculation formula of the nonlinear spring at each node is:

[0068]

[0069] where k represents the elastic stiffness of the spring, K represents the resistance coefficient of the surrounding rock, and n is the number of elements sharing the peripheral node.

[0070] Update the original calculation analysis file according to the nonlinear spring set established based on the S2 and the stiffness of the nonlinear spring at the peripheral nodes calculated by the S3.

[0071] The interaction between the segment structure and the surrounding rock is simulated by a two-point nonlinear spring. When the spring is in tension, the surrounding rock and the shield segment are separated, and the spring does not work, that is, the spring stiffness when the spring is in tension is set to be infinitesimal. When the spring is in compression, the spring stiffness is given the spring stiffness value calculated in S3.

[0072] The method for preprocessing the nonlinear spring in the load structure method of this application is applicable to the accurate calculation of the nonlinear spring stiffness of a non-uniform grid structure, realizes the automatic construction and application of nonlinear spring elements without being restricted by the grid element type, and realizes the efficient and rapid calculation of the nonlinear spring stiffness at each numerical node.

[0073] Based on the method for preprocessing the nonlinear spring in the load structure method of this application, a nonlinear spring preprocessing program can be compiled. This program can realize the automatic calculation of the nonlinear spring stiffness, and can realize the automatic construction and application of spring elements. This program is encapsulated as a.f90 format file based on the Fortran language and named Pretreatment.f90. In the Pretreatment.f90 program, various parameters in the shield segment are set and modified, such as the segment outer diameter D, the thickness T of the peripheral hexahedron grid, the rock mass resistance coefficient K, etc. Based on the drive of the secondary development program, efficient and rapid load structure analysis can be realized. The specific algorithm flow is as follows:

[0074] Input: Refined shield tunnel structure model, original calculation analysis file Calculation_o.inp

[0075] Output: Return the updated calculation analysis file Calculation_n.inp

[0076] ***n is the number of grid nodes of the shield segment structure

[0077] ***d is the distance from the node to the center of the circle, D is the segment outer diameter, and T is the thickness of the peripheral hexahedron grid

[0078] ***M is the number of peripheral layer elements

[0079] 1. Obtain the information of the peripheral nodes of the segment

[0080] for i = 1 to n:

[0081] if d > 0.5×(D - T):

[0082] (1) Record the node number and coordinates

[0083] (2) Record the number of nodes that meet the conditions, denoted as m

[0084] (3) Calculate the spring end point coordinates (x', y', z')

[0085]

[0086] (4) Establish a set of non - linear springs

[0087] 2. Calculate the area of the quadrilateral around the segment

[0088] for t = 1 to m:

[0089] for j = 1 to M:

[0090] if a certain node number of the element = the node number:

[0091] (1) Record the information of this node

[0092] (2) Calculate the area Si of the quadrilateral around the segment:

[0093]

[0094] 3. Assign the stiffness of the non - linear spring at the segment node

[0095] (1) Calculate the spring stiffness k at this node

[0096]

[0097] (2) Set the spring stiffness. The spring stiffness in the tensile state is infinitesimal, and the spring stiffness in the compressive state is the calculated value.

[0098] 4. Update the original calculation and analysis file Calculation_o.inp.

[0099] By running the non - linear spring pre - processing algorithm in the load - structure method of this application, the spring endpoint information and the set of non - linear springs can be generated. According to the relevant format of the calculation and analysis file in ABAQUS, the statements for setting the spring stiffness are generated and stored as AddNode.inp, AddElement.inp, and AddStiffness.inp files respectively.

[0100] Based on the method of non - linear spring pre - processing in the load - structure method of this application, numerical analysis tests on the geological conditions with stratum cavities in the surrounding rock of the shield tunnel segments can be carried out to study the influence of the existence of stratum cavities on the deformation and failure of the segment structure. The research results are as shown in Figure 5 (a) - 5(c) and Figure 6 (a) - 6(c);

[0101] In addition, based on the method for preprocessing the nonlinear spring in the load structure method of the present application, it is also possible to quickly study the deformation and failure characteristics of shield tunnel segments under different occurrence geological conditions, such as the internal force, deformation distribution characteristics, and damage evolution law of shield tunnel segments in hard-soft interbedded rock masses with different formation thickness ratios, strength ratios, and formation dips. The research results are as shown in Figure 7 (a)-7(c).

[0102] For the segment structure with irregular geometric shape, it is difficult to evenly divide the grid in numerical simulation analysis, resulting in disadvantages such as low calculation and application efficiency of the nonlinear spring stiffness for simulating the interaction between the structure and the surrounding rock. The present application proposes a method for quickly calculating the nonlinear spring stiffness at each numerical node according to the characteristics of the existing grid division, and proposes a technology for automatic construction and application of spring elements. Compared with the prior art, the present application can realize the rapid preprocessing of segment loads, which not only improves the calculation efficiency of numerical simulation analysis but also improves the simulation accuracy of actual engineering geological conditions.

[0103] Although the implementation schemes of the present application have been disclosed as above, they are not limited to the applications listed in the specification and the implementation manners. It can be fully applied to various fields suitable for the present application. For those familiar with the field, additional modifications can be easily made. Therefore, without departing from the general concept defined by the claims and the equivalent scope, the present application is not limited to the specific details and the illustrated examples here.

Claims

1. A method for preprocessing nonlinear springs in a load structure method, characterized in that: The following steps are involved: S1 inputs the refined shield segment structure model and obtains the original calculation and analysis file; S2 extracts the segment peripheral node information that meets the constraint conditions, calculates the spring endpoint coordinates and establishes a nonlinear spring set; S3 extracts the outermost unit information of the specific block unit type of each segment in the original calculation and analysis file, and performs the following operations on each segment peripheral node obtained in S2: traverses all units to determine whether the traversed unit contains the current peripheral node; if it contains, searches and records the coordinates of all peripheral nodes of the unit; calculates the peripheral surface area of ​​each unit based on the recorded unit node coordinates, and calculates the stiffness of the nonlinear spring at the current peripheral node according to the peripheral surface area of ​​each unit; S4 updates the original calculation and analysis file according to the nonlinear spring set established in S2 and the stiffness of the nonlinear springs at the peripheral nodes calculated in S3.

2. The method for preprocessing nonlinear springs in the load structure method according to claim 1, characterized in that: In S1, the refined shield segment model is meshed, and the outermost mesh unit type of the segment is ensured to be a hexahedral unit.

3. The method for preprocessing nonlinear springs in the load structure method according to claim 2, characterized in that: In S2, the segment peripheral node information satisfying the following constraints is extracted: d>0.5×(DT) Among them, d is the distance between the node and the center of the tunnel segment, D is the outer diameter of the segment, and T is the thickness of the outer hexahedral grid unit.

4. The method for preprocessing nonlinear springs in the load structure method according to claim 3, characterized in that: In S2, the spring endpoint coordinates are calculated based on the segment peripheral node information and the following formula: Where R is the outer radius of the segment.

5. The method for preprocessing nonlinear springs in the load structure method according to claim 3, characterized in that: In S3, the following operations are performed: Outer loop: traverse each peripheral node of the segment recorded in S2 as the current node; Inner loop: traverse all units for each current node, and determine whether the node number of the traversed units contains the node number of the current node; If it is included, search and record all peripheral node coordinates of the unit; loop processing until all units are traversed, store all peripheral node coordinates of each unit including the current node for calculating the peripheral surface area.

6. The method for preprocessing nonlinear springs in the load structure method according to claim 3, characterized in that: In S3, the peripheral surface area of ​​each unit is calculated using the following formula: Among them, x ij ,y ij ,z ij Respectively represent the x, y, and z coordinate values ​​of the jth node of the ith unit, S i Represents the area of ​​the outer surface of the i-th unit.

7. The method for preprocessing nonlinear springs in the load structure method according to claim 6, characterized in that: In S3, the stiffness calculation formula of the nonlinear spring at each peripheral node is: Among them, k represents the elastic stiffness of the spring, K represents the resistance coefficient of the surrounding rock, and n is the number of units sharing the peripheral node.

8. The method for preprocessing nonlinear springs in the load structure method according to claim 7, characterized in that: The exposed surface of the unit is a quadrilateral surface, each peripheral node is shared by four of the quadrilateral surfaces, and the stiffness of the nonlinear spring at the node is the arithmetic mean of the areas of the four quadrilateral surfaces.

9. The method for preprocessing nonlinear springs in the load structure method according to claim 7, characterized in that: A two-point nonlinear spring is used to simulate the interaction between the segment structure and the surrounding rock. When the spring is under tension, the surrounding rock and the shield segment are separated, and the spring stiffness is infinitely small; when the spring is under compression, the spring stiffness is the spring stiffness value calculated in S3.

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