Structural optimization method, device, electronic equipment and medium for tunnel primary support steel frame

Abstract

The present application provides a structural optimization method, device, electronic device and medium for a tunnel initial support steel frame. The method includes establishing a target support model for an initial support steel frame used for initial support in a target tunnel to determine a target load applied by the surrounding rock to the target initial support steel frame; taking the target initial support steel frame as an initial design area, decomposing the initial design area into multiple sub-design areas, assigning a relative density to each sub-design area as a variable during optimization of the sub-design area, and establishing a topological optimization objective function of the strain energy of the structural flexibility of the design area under volume constraints; inputting the target load into the topological optimization objective function, determining a topological optimization result, and determining a target support scheme for the target initial support steel frame, so as to use steel sections to perform initial support on a target position of the target tunnel based on the target support scheme, so that the strength of the initial support steel frame can meet the surrounding rock load and avoid waste of steel.

Description

Technical Field

[0001] The present application relates to the field of tunnel technology, and in particular to a method, device, electronic equipment and medium for optimizing the structure of a tunnel primary support steel frame. Background Art

[0002] In soft rock tunnels or tunnels with large deformation after excavation, the surrounding rock has poor self-stabilization ability and a long self-stabilization time. At the same time, since support types such as shotcrete lining and anchors cannot provide sufficient support resistance in time to limit the deformation of the surrounding rock, in order to maintain the stability of the surrounding rock and ensure the continuation of the excavation operation, it is necessary to immediately provide strong support for the surrounding rock, and at this time, it is often necessary to use a steel arch frame with greater rigidity.

[0003] At present, the design of steel frames in the primary support of large-section tunnels generally adopts equal strength design, which will lead to unreasonable use of steel. In small and medium-section tunnels, equal strength design is relatively conservative, resulting in waste of steel. In super-large sections, when the size of steel is limited, the large surrounding rock load generated during excavation may cause instability and damage of the primary support. Summary of the invention

[0004] In view of this, the purpose of the present application is to provide a structural optimization method, device, electronic equipment and medium for the primary support steel frame of a tunnel, which can optimize the design of the primary support steel frame of a large-section tunnel, and the strength can meet the surrounding rock load and avoid waste of steel.

[0005] The present application provides a method for optimizing the structure of a tunnel primary support steel frame, the method comprising the following steps:

[0006] For the initial support steel frame used for initial support in the target tunnel, a target support model of the target position where the target initial support steel frame is located is established, and the steel material performance parameters of the target initial support steel frame and the surrounding rock material performance parameters of the target position where the target initial support steel frame is located in the target support model are configured to obtain a constructed target support model; the cross-section of the target initial support steel frame and the target position of the target tunnel are matched;

[0007] Based on the constructed target support model, determine the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame;

[0008] Based on the topology optimization method, the target primary support steel frame is taken as the initial design area, the initial design area is decomposed into multiple sub-design areas, a relative density is assigned to each sub-design area as a variable during the optimization of the sub-design area, and under the volume constraint, a topology optimization objective function of the strain energy of the structural flexibility of the design area is established;

[0009] The target load is input into the topology optimization objective function, and the strain energy of the topology optimization objective function under the target load meets the structural strength requirement and has the smallest volume as the optimization goal, the initial design area is optimized, and the topology optimization result of each sub-design area in the initial design area is determined; the topology optimization result includes whether there is a steel section in the sub-design area, and the structural properties of the steel section when there is a steel section in the sub-design area; the structural properties of the steel section include size and shape;

[0010] Based on the topology optimization results of each sub-design area in the initial design area, a target support scheme of the target primary support steel frame is determined, so as to use steel sections to perform initial support on the target position of the target tunnel based on the target support scheme.

[0011] In some embodiments, in the structural optimization method of the tunnel primary support steel frame, for the primary support steel frame used for initial support in the target tunnel, a target support model for the target position of the target primary support steel frame is established, and the steel material performance parameters of the target primary support steel frame and the surrounding rock material performance parameters of the target position of the target primary support steel frame in the target support model are configured to obtain a constructed target support model; including:

[0012] According to the buried depth of the target primary support steel frame of the target tunnel, determine the surrounding rock size of the target position of the target tunnel in the target support model;

[0013] Determine the size of the target primary support steel frame in the target support model;

[0014] A target support model is established based on the surrounding rock size of the target position of the target tunnel and the size of the target primary support steel frame in the target support model; the target support model includes a surrounding rock structure and a steel structure;

[0015] According to the size of the surrounding rock and the size of the target primary support steel frame, the grid size of the surrounding rock structure and the grid size of the steel structure are determined respectively, and the surrounding rock structure and the steel structure are divided by using the free meshing technology to obtain the target support model with the meshing completed;

[0016] The steel material performance parameters of the target primary support steel frame and the surrounding rock material performance parameters of the target position where the target primary support steel frame is located in the target support model are configured to obtain a constructed target support model.

[0017] In some embodiments, in the structural optimization method of the tunnel primary support steel frame, based on the constructed target support model, determining the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame includes:

[0018] Determining the stress of the surrounding rock grid unit of the surrounding rock structure in the constructed target support model according to the yield criterion;

[0019] According to the buried depth of the target primary support steel frame of the target tunnel, the lateral pressure coefficient and the model boundary conditions in the target support model are determined; in the model boundary conditions, the axial displacement of the surrounding rock and the target primary support steel frame in the tunnel is zero, the bottom of the surrounding rock is fixed, and the horizontal displacement of the side limit is zero;

[0020] Based on the stress, lateral pressure coefficient and model boundary conditions of the surrounding rock grid unit in the target support model, the structure of the target support model is discretized into a finite number of structural units using ABQUS calculation software; the structural units are connected through nodes, and the force and deformation of the structural units are transmitted through the nodes;

[0021] According to the equilibrium conditions of each node and the deformation coordination conditions of adjacent structural units at the common nodes, the discrete body composed of various structural units is used to represent the continuum of the target support model. Under the constraints of the equilibrium conditions and deformation coordination conditions, the unit structure analysis is carried out to determine the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame.

[0022] In some embodiments, in the structural optimization method of the tunnel primary support steel frame, determining the stress of the surrounding rock grid unit of the surrounding rock structure in the constructed target support model according to the yield criterion includes:

[0023] Based on the control equation of the yield criterion described in the following formula (1), the stress of the surrounding rock grid unit of the surrounding rock structure in the constructed target support model is determined:

[0024]

[0025] Wherein, σ1 represents the first principal stress of the surrounding rock grid unit, σ2 represents the second principal stress of the surrounding rock grid unit, σ3 represents the third principal stress of the surrounding rock grid unit, and c represents the cohesion of the surrounding rock grid unit. Characterizes the internal friction angle of the surrounding rock grid unit.

[0026] In some embodiments, in the structural optimization method of the tunnel primary support steel frame, the topology optimization objective function is as shown in the following formula (2):

[0027]

[0028] The constraint condition of the topology optimization objective function is shown in the following formula (3):

[0029]

[0030] KU=F,

[0031] k i =(ρ i ) p k0,

[0032] 0≤ρ min ≤ρ i ≤ρ max , (3);

[0033] Where C is the strain energy of the structural flexibility, in MJ; U represents the displacement vector; F represents the force vector, corresponding to the target load; K represents the structural stiffness matrix; N is the total number of sub-design areas; u i is the displacement vector of the ith sub-design area; k0 is the initial stiffness matrix of the unit, k i is the optimized stiffness matrix; v i is the optimized unit volume; V is the optimized volume; V0 is the previous volume; f is the optimized volume ratio; ρ i is the relative density of the ith sub-design region; ρ min is the lower limit of unit density; ρ max is the upper limit of unit density; p is the penalty factor.

[0034] In some embodiments, in the structural optimization method of the tunnel primary support steel frame, the target load is input into the topology optimization objective function, the strain energy of the topology optimization objective function under the target load meets the structural strength requirements and the volume is minimized as the optimization goal, the initial design area is optimized, and the topology optimization result of each sub-design area in the design area is determined; including:

[0035] Design the variables of each sub-design area in the topology optimization objective function and determine the strain energy and volume corresponding to the variables;

[0036] Determine the relationship between volume and strain energy;

[0037] Based on the relationship between the volume and strain energy, the variables of each sub-design area when the strain energy meets the structural strength requirements and the volume is minimized are determined to determine the topology optimization result of each sub-design area in the initial design area.

[0038] In some embodiments, in the structural optimization method of the tunnel primary support steel frame, based on the relationship between the volume and strain energy, determining the variables of each sub-design area when the strain energy meets the structural strength requirements and the volume is minimized includes:

[0039] Based on the relationship between the volume and the strain energy, a curve graph of the volume optimization rate and the strain energy is generated by taking the volume optimization rate as the abscissa and the strain energy as the ordinate;

[0040] Based on the curve graph of the volume optimization rate and the strain energy, determining a target point in the curve graph where the rate of change of the strain energy is greater than a preset rate threshold;

[0041] The volume and strain energy corresponding to the target point are determined as the optimization objectives, and the variables of each sub-design area are determined.

[0042] In some embodiments, a structural optimization device for a tunnel primary support steel frame is also provided, the device comprising:

[0043] The first establishment module is used to establish a target support model for the target position of the target initial support steel frame used for initial support in the target tunnel, and configure the steel material performance parameters of the target initial support steel frame and the surrounding rock material performance parameters of the target position of the target initial support steel frame in the target support model to obtain a constructed target support model; the cross-section of the target initial support steel frame and the target position of the target tunnel are matched;

[0044] A first determination module is used to determine the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame based on the constructed target support model;

[0045] The second establishment module is used to take the target primary support steel frame as the initial design area based on the topology optimization method, decompose the initial design area into multiple sub-design areas, assign a relative density to each sub-design area as a variable when optimizing the sub-design area, and establish a topology optimization objective function of the strain energy of the structural flexibility of the design area under the volume constraint;

[0046] An optimization module is used to input the target load into the topology optimization objective function, optimize the initial design area with the strain energy of the topology optimization objective function under the target load meeting the structural strength requirement and minimizing the volume as the optimization goal, and determine the topology optimization result of each sub-design area in the initial design area; the topology optimization result includes whether there is a steel section in the sub-design area, and the structural properties of the steel section when there is a steel section in the sub-design area; the structural properties of the steel section include size and shape;

[0047] The second determination module is used to determine a target support scheme for a target initial support steel frame based on the topology optimization results of each sub-design area in the initial design area, so as to use steel sections to perform initial support on a target position of a target tunnel based on the target support scheme.

[0048] In some embodiments, an electronic device is also provided, including: a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is running, the processor and the memory communicate through the bus, and when the machine-readable instructions are executed by the processor, the steps of the structural optimization method of the tunnel primary support steel frame are executed.

[0049] In some embodiments, a computer-readable storage medium is also provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the structural optimization method of the tunnel primary support steel frame are executed.

[0050] Based on this, in an embodiment of the present application, a method, device, electronic device and medium for optimizing the structure of a tunnel primary support steel frame are provided. For a primary support steel frame used for initial support in a target tunnel, a target support model for the target position of the target primary support steel frame is established, and the steel material performance parameters of the target primary support steel frame and the surrounding rock material performance parameters of the target position of the target primary support steel frame in the target support model are configured to obtain a constructed target support model; the cross-sections of the target primary support steel frame and the target position of the target tunnel are matched; based on the constructed target support model, the target load applied to the target primary support steel frame by the surrounding rock of the target tunnel is determined; based on a topological optimization method, the target primary support steel frame is used as an initial design area, the initial design area is decomposed into multiple sub-design areas, a relative density is assigned to each sub-design area as a variable during the optimization of the sub-design area, and the structural flexibility of the design area is established under volume constraints. The target load is input into the topology optimization objective function, and the strain energy of the topology optimization objective function under the target load is taken as the optimization target to meet the structural strength requirements and minimize the volume, optimize the initial design area, and determine the topology optimization result of each sub-design area in the initial design area; the topology optimization result includes whether there is a steel section in the sub-design area, and the structural properties of the steel section when there is a steel section in the sub-design area; the structural properties of the steel section include size and shape; based on the topology optimization result of each sub-design area in the initial design area, determine the target support scheme of the target initial support steel frame, so as to use the steel section to perform initial support on the target position of the target tunnel based on the target support scheme, thereby optimizing the structure of the initial support steel frame in the tunnel, and strengthening the steel frame at the local position of the section under the principle of saving steel materials to meet the stiffness requirements of the support. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0052] Figure 1 A flow chart showing the structural optimization method of the tunnel primary support steel frame according to the embodiment of the present application is shown;

[0053] Figure 2A flow chart of a method for establishing a target support model at a target position of a target primary support steel frame according to an embodiment of the application is shown;

[0054] Figure 3 A schematic diagram of the target support model described in the embodiment of the present application is shown;

[0055] Figure 4 The present application embodiment is shown Figure 3 An enlarged schematic diagram of the primary support steel frame in the target support model shown;

[0056] Figure 5 A flow chart of a method for determining a topology optimization result of each sub-design area in the initial design area according to an embodiment of the present application is shown;

[0057] Figure 6 The steel model diagram described in the embodiment of the present application is shown;

[0058] Figure 7 The graph shows the relationship between the volume optimization rate and the strain energy of the steel model structure when the vertical-to-horizontal load ratio is 1:1 according to the embodiment of the present application;

[0059] Figure 8 The figure shows the optimal result of topological optimization of the steel model structure when the vertical and horizontal loads are 1:1 as described in the embodiment of the present application;

[0060] Fig. 9 The graph shows the relationship between the volume optimization rate and the strain energy of the steel model structure when the vertical-to-horizontal load ratio is 1:2 according to the embodiment of the present application;

[0061] Fig.10 The optimal result diagram of the topological optimization of the steel model structure when the vertical and horizontal loads are 1:2 as described in the embodiment of the present application is shown;

[0062] Fig.11 The graph shows the relationship between the volume optimization rate and the strain energy of the steel model structure when the vertical-to-horizontal load ratio is 1:3 according to the embodiment of the present application;

[0063] Fig.12 The figure shows the optimal result of topological optimization of the steel model structure when the vertical and horizontal loads are 1:3 as described in the embodiment of the present application;

[0064] Fig.13 The graph shows the relationship between the volume optimization rate and the strain energy of the steel model structure when the vertical-to-horizontal load ratio is 1:4 according to the embodiment of the present application;

[0065] Fig.14 The optimal result diagram of the topological optimization of the steel model structure when the vertical and horizontal loads are 1:4 as described in the embodiment of the present application is shown;

[0066] Fig.15 Shows Figure 3 The relationship curve between volume optimization rate and strain energy of the target support model shown;

[0067] Fig.16 In the embodiment of the present application, Figure 3 The optimal result diagram of the structural topology optimization of the target support model shown;

[0068] Fig.17 A schematic diagram of the structure of the structural optimization device for the tunnel primary support steel frame according to an embodiment of the present application is shown;

[0069] Fig.18 A schematic structural diagram of an electronic device described in an embodiment of the present application is shown. DETAILED DESCRIPTION

[0070] To make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. It should be understood that the drawings in the present application only serve the purpose of explanation and description and are not used to limit the scope of protection of the present application. In addition, it should be understood that the schematic drawings are not drawn in real proportion. The flowchart used in this application shows the operations implemented according to some embodiments of the present application. It should be understood that the operations of the flowchart can be implemented out of sequence, and the steps without logical context can be reversed in order or implemented simultaneously. In addition, those skilled in the art can add one or more other operations to the flowchart under the guidance of the content of the present application, or remove one or more operations from the flowchart.

[0071] In addition, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings here can be arranged and designed in various configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the application claimed for protection, but merely represents the selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without making creative work belong to the scope of protection of the present application.

[0072] It should be noted that the term "comprising" will be used in the embodiments of the present application to indicate the existence of the features declared thereafter, but does not exclude the addition of other features.

[0073] In soft rock tunnels or tunnels with large deformation after excavation, the surrounding rock has poor self-stabilization ability and a long self-stabilization time. At the same time, since support types such as shotcrete lining and anchors cannot provide sufficient support resistance in time to limit the deformation of the surrounding rock, in order to maintain the stability of the surrounding rock and ensure the continuation of the excavation operation, it is necessary to immediately provide strong support for the surrounding rock, and at this time, it is often necessary to use a steel arch frame with greater rigidity.

[0074] At present, the design of steel frames in the primary support of large-section tunnels generally adopts equal strength design, which will lead to unreasonable use of steel. In small and medium-section tunnels, equal strength design is relatively conservative, resulting in waste of steel. In super-large sections, when the size of steel is limited, the large surrounding rock load generated during excavation may cause instability and damage of the primary support.

[0075] Specifically, when the steel frame is designed with equal strength, the thickness of the steel frame at different positions in the tunnel primary support is the same, for example, the thickness of the top steel frame and the side steel frame is the same; however, when analyzing the stress of the steel frame, the stress on the top is greater than the stress on the side, and the steel frame is designed to have the same thickness, resulting in a waste of steel. In the super-large section, the stress on the top is very large, and the thickness of the steel is very high when the equal strength design is used, which may exceed the restrictions on the size and weight of the steel section; and if the strength is not enough, the large surrounding rock load generated during excavation may cause the primary support to become unstable and damaged.

[0076] Based on this, in an embodiment of the present application, a method, device, electronic device and medium for optimizing the structure of a tunnel primary support steel frame are provided. For a primary support steel frame used for initial support in a target tunnel, a target support model for the target position of the target primary support steel frame is established, and the steel material performance parameters of the target primary support steel frame and the surrounding rock material performance parameters of the target position of the target primary support steel frame in the target support model are configured to obtain a constructed target support model; the cross-sections of the target primary support steel frame and the target position of the target tunnel are matched; based on the constructed target support model, the target load applied to the target primary support steel frame by the surrounding rock of the target tunnel is determined; based on a topological optimization method, the target primary support steel frame is used as an initial design area, the initial design area is decomposed into multiple sub-design areas, a relative density is assigned to each sub-design area as a variable during the optimization of the sub-design area, and the structural flexibility of the design area is established under volume constraints. The target load is input into the topology optimization objective function, and the strain energy of the topology optimization objective function under the target load is taken as the optimization target to meet the structural strength requirements and minimize the volume, optimize the initial design area, and determine the topology optimization result of each sub-design area in the initial design area; the topology optimization result includes whether there is a steel section in the sub-design area, and the structural properties of the steel section when there is a steel section in the sub-design area; the structural properties of the steel section include size and shape; based on the topology optimization result of each sub-design area in the initial design area, determine the target support scheme of the target initial support steel frame, so as to use the steel section to perform initial support on the target position of the target tunnel based on the target support scheme, thereby optimizing the structure of the initial support steel frame in the tunnel, and strengthening the steel frame at the local position of the section under the principle of saving steel materials to meet the stiffness requirements of the support.

[0077] Please refer to Figure 1 , Figure 1 A flow chart showing the structural optimization method of the tunnel primary support steel frame according to the embodiment of the present application is shown; Figure 1 As shown, the structural optimization method of the tunnel primary support steel frame includes the following steps S101-S105:

[0078] S101. For a primary support steel frame used for initial support in a target tunnel, a target support model for a target position of the target primary support steel frame is established, and performance parameters of the steel material of the target primary support steel frame and performance parameters of the surrounding rock material at the target position of the target primary support steel frame are configured in the target support model to obtain a constructed target support model; the cross-section of the target primary support steel frame and the target position of the target tunnel are matched;

[0079] S102, based on the constructed target support model, determining the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame;

[0080] S103, based on the topology optimization method, taking the target primary support steel frame as the initial design area, decomposing the initial design area into multiple sub-design areas, assigning a relative density to each sub-design area as a variable during the optimization of the sub-design area, and establishing a topology optimization objective function of the strain energy of the structural flexibility of the design area under the volume constraint;

[0081] S104, inputting the target load into the topology optimization objective function, taking the strain energy of the topology optimization objective function under the target load to meet the structural strength requirement and minimize the volume as the optimization goal, optimizing the initial design area, and determining the topology optimization result of each sub-design area in the initial design area; the topology optimization result includes whether there is a steel section in the sub-design area, and the structural properties of the steel section when there is a steel section in the sub-design area; the structural properties of the steel section include size and shape;

[0082] S105. Determine a target support scheme for a target primary support steel frame based on the topology optimization result of each sub-design area in the initial design area, so as to perform initial support on a target position of a target tunnel using steel sections based on the target support scheme.

[0083] The structural optimization method of the tunnel primary support steel frame described in the embodiment of the present application is used to perform topological optimization on the primary support steel frame in the tunnel.

[0084] Topological optimization can be divided into two categories: topological optimization of discrete structures (such as steel frames, trusses, stiffened plates and other structures and their combinations) and topological optimization of continuum structures (such as two-dimensional plates and shells, three-dimensional solids, etc.).

[0085] Continuum structure optimization design can be divided into size optimization, shape optimization and topology optimization.

[0086] Size optimization: Under the condition that the structural shape and combination remain unchanged, calculate the optimal cross-sectional dimensions of the structural components, optimize the cross-sectional area (such as discrete bodies such as trusses), select the optimal thickness of the plate, etc.

[0087] Shape optimization: Under certain conditions of optimizing the topological relationship of the structure, the shape and boundary of the design domain are used as design variables, and the optimal shape and boundary of the structure are sought through calculation. In discrete body structures, shape optimization is to optimize the position of nodes, while in solid structures, the variable to be optimized is the boundary shape of the structure.

[0088] Topological optimization: In a certain structural area, we seek the best configuration of optimization variables such as shape, position, area, and quantity of non-solid areas that can be realized within the structure. When the structure satisfies the constraints of displacement and stress, the load is transferred to the support of the structure, and the performance index of a certain structure is achieved. This is to select a subset Ωm on the continuum Ω under the premise of satisfying the constraints and the objective function. The topological optimization of discrete structures is to determine the optimal connection relationship between nodes when the node positions are given; for the topological optimization of continuum structures, not only the shape of the structure boundary is optimized, but also the shape and position of the holes in the structure.

[0089] The three levels of structural optimization play different roles and tasks in the optimization process and play an important role in the design and development process of the product.

[0090] Topological optimization is a simple method, which is to seek the best force transmission path of the structure under certain external forces and constraints.

[0091] In the embodiment of the present application, the structure of the primary support steel frame of the tunnel is optimized based on topological optimization theory.

[0092] In the step S101, a target support model of the target position of the target primary support steel frame is established for the primary support steel frame used for initial support in the target tunnel, and the steel material performance parameters of the target primary support steel frame and the surrounding rock material performance parameters of the target position of the target primary support steel frame in the target support model are configured to obtain a constructed target support model; the cross-sections of the target primary support steel frame and the target position of the target tunnel are matched.

[0093] For details, please refer to Figure 2 , for the initial support steel frame used for initial support in the target tunnel, a target support model for the target position of the target initial support steel frame is established, and the steel material performance parameters of the target initial support steel frame and the surrounding rock material performance parameters of the target position of the target initial support steel frame in the target support model are configured to obtain a constructed target support model; comprising the following steps S201-S205:

[0094] S201, determining the surrounding rock size of the target position of the target tunnel in the target support model according to the buried depth of the target primary support steel frame of the target tunnel;

[0095] S202, determining the size of the target primary support steel frame in the target support model;

[0096] S203, establishing a target support model based on the surrounding rock size of the target position of the target tunnel and the size of the target primary support steel frame in the target support model; the target support model includes a surrounding rock structure and a steel structure;

[0097] S204, according to the size of the surrounding rock and the size of the target primary support steel frame, determine the grid size of the surrounding rock structure and the grid size of the steel structure respectively, divide the surrounding rock structure and the steel structure by using a free meshing technology, and obtain a target support model with meshing completed;

[0098] S205. Configure the steel material performance parameters of the target primary support steel frame and the surrounding rock material performance parameters of the target position where the target primary support steel frame is located in the target support model to obtain a constructed target support model.

[0099] According to the burial depth of the target primary support steel frame of the target tunnel, the surrounding rock size of the target position of the target tunnel in the target support model is determined. The surrounding rock range of the primary support steel frame load in the tunnel is different for surrounding rocks of different burial depths. The smaller the burial depth, the smaller the surrounding rock range. Correspondingly, the larger the burial depth, the larger the surrounding rock range.

[0100] Therefore, it is necessary to determine the surrounding rock size in the target support model based on the buried depth of the target primary support steel frame.

[0101] When modeling the tunnel surrounding rock and initial support, it is considered that the main function of the initial support is to provide resistance to partial deformation and stress of the surrounding rock before the second lining is poured. Since the research is mainly on the topological optimization of steel, the relationship between steel and concrete and surrounding rock can be simplified to a model in which steel is the research subject and concrete and surrounding rock are the load transfer media.

[0102] For example, the surrounding rock size is determined to be 120m×1m×100m (length×width×height), the cross-sectional size of the primary support steel frame is 1m×0.5m, of which 0.5m is the thickness, and the target support model is established.

[0103] Please refer to Figure 3 , Figure 3 A schematic diagram of the target support model described in the embodiment of the present application is shown; Figure 4 An enlarged schematic diagram of the primary support steel frame in the target support model is shown.

[0104] Here, the surrounding rock may also be referred to as the bottom layer.

[0105] According to the size of the surrounding rock and the size of the target primary support steel frame, the grid size of the surrounding rock structure and the grid size of the steel structure are determined respectively. The target support model after meshing is as follows: Figure 3 shown.

[0106] For example, in some embodiments, since the surrounding rock range is relatively large, the mesh division length of the surrounding rock structure is 2 meters, and the size of the steel section is relatively small, the units are appropriately encrypted in the mesh division, the mesh division length is 0.05 meters, and the default unit type C3D8R (8-node hexahedral linear reduced integration unit) of the free mesh division technology is used for mesh division.

[0107] When performing finite element numerical analysis and calculation on the structure, whether the performance parameters of the material are reasonable will directly affect the accuracy of the optimization simulation. The target support model described in the embodiment of the present application is divided into two parts: surrounding rock and steel. For example, V-grade surrounding rock is used, and the performance parameters of the surrounding rock material are: density: 2.0×10 3 kg / m3, elastic modulus 1.5Gpa, Poisson's ratio 0.35, as shown in Table 1 below; the performance parameters of the steel material are: density 7.8×10 3 kg / m3, elastic modulus 210GPa, Poisson's ratio 0.3, as shown in Table 2 below.

[0108] Table 1: Performance parameters of surrounding rock materials.

[0109]

[0110] Table 2: Relevant parameters of steel sections.

[0111]

[0112] In step S102, based on the constructed target support model, the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame is determined.

[0113] In the embodiment of the present application, based on the constructed target support model, determining the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame includes:

[0114] Determining the stress of the surrounding rock grid unit of the surrounding rock structure in the constructed target support model according to the yield criterion;

[0115] According to the buried depth of the target primary support steel frame of the target tunnel, the lateral pressure coefficient and the model boundary conditions in the target support model are determined; in the model boundary conditions, the axial displacement of the surrounding rock and the target primary support steel frame in the tunnel is zero, the bottom of the surrounding rock is fixed, and the horizontal displacement of the side limit is zero;

[0116] Based on the stress, lateral pressure coefficient and model boundary conditions of the surrounding rock grid unit in the target support model, the structure of the target support model is discretized into a finite number of structural units using ABQUS calculation software; the structural units are connected through nodes, and the force and deformation of the structural units are transmitted through the nodes;

[0117] According to the equilibrium conditions of each node and the deformation coordination conditions of adjacent structural units at the common nodes, the discrete body composed of various structural units is used to represent the continuum of the target support model. Under the constraints of the equilibrium conditions and deformation coordination conditions, the unit structure analysis is carried out to determine the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame.

[0118] Specifically, in the embodiment of the present application, in the structural optimization method of the tunnel primary support steel frame, the stress of the surrounding rock grid unit of the surrounding rock structure in the constructed target support model is determined according to the yield criterion, including:

[0119] Based on the control equation of the yield criterion described in the following formula (1), the stress of the surrounding rock grid unit of the surrounding rock structure in the constructed target support model is determined:

[0120]

[0121] Wherein, σ1 represents the first principal stress of the surrounding rock grid unit, σ2 represents the second principal stress of the surrounding rock grid unit, σ3 represents the third principal stress of the surrounding rock grid unit, and c represents the cohesion of the surrounding rock grid unit. Characterizes the internal friction angle of the surrounding rock grid unit.

[0122] Specifically, in the embodiment of the present application, the surrounding rock material adopts the Mohr-Coulomb yield criterion to analyze the stress and deformation properties of the soil unit in the structural model.

[0123] In tunnel construction, shotcrete is applied immediately after tunnel excavation, fitting closely with the surrounding rock behind it. The shrinkage of the material itself is small, and there is no obvious relative sliding. The deformation of the support is consistent with the deformation of the surrounding rock of the tunnel chamber. Therefore, the contact separation between the surrounding rock and the initial support is not considered in the model.

[0124] For different burial depths, the stress state of the strata around the tunnel and the stress conditions of the initial support are different, and the lateral pressure coefficient λ is different. For example, the lateral pressure coefficient λ is selected as 1.84 according to the geological survey report.

[0125] In the step S103, based on the topology optimization method, the target primary support steel frame is taken as the initial design area, and the initial design area is decomposed into multiple sub-design areas. A relative density is assigned to each sub-design area as a variable during the optimization of the sub-design area, and under the volume constraint, a topology optimization objective function of the strain energy of the structural flexibility of the design area is established.

[0126] The topology optimization objective function is shown in the following formula (2):

[0127]

[0128] The constraint condition of the topology optimization objective function is shown in the following formula (3):

[0129]

[0130] KU=F,

[0131] ki =(ρ i ) p k0,

[0132] 0≤ρ min ≤ρ i ≤ρ max , (3);

[0133] Where C is the strain energy of the structural flexibility, in MJ; U represents the displacement vector; F represents the force vector, corresponding to the target load; K represents the structural stiffness matrix; N is the total number of sub-design areas; u i is the displacement vector of the ith sub-design area; k0 is the initial stiffness matrix of the unit, k i is the optimized stiffness matrix; v i is the optimized unit volume; V is the optimized volume; V0 is the previous volume; f is the optimized volume ratio; ρ i is the relative density of the ith sub-design region; ρ min is the lower limit of unit density; ρ max is the upper limit of unit density; p is the penalty factor.

[0134] The design principle of the topology optimization objective function is explained below.

[0135] When performing topological optimization design on a structure, no matter whether the engineering structure is a discrete body or a continuous body, the initial optimization design area must be selected first. Usually, the base structure method is used to describe it. The so-called base structure method is to first discretize the initial optimization design area, thereby dividing the initial optimization design area into multiple design areas. For example, the initial design area is first discretized using the finite element method, and each finite element individual is a sub-design area. After discretization, a base structure composed of sub-optimized design areas will be formed. On this basis, the appropriate optimization criteria and methods are selected to delete some redundant and useless units from the base structure, and finally form an optimal topological form.

[0136] In actual engineering, the steel frame is an elastic structure of a continuum. When the continuum is subjected to topological optimization design of stiffness, the optimization goal is generally to maximize the structural stiffness or minimize the flexibility. In the embodiment of the present application, when the steel section is subjected to topological optimization, the minimum flexibility is selected as the condition. When the external load is given, the strain energy of the system structure can be used to represent the size of the overall structural stiffness of the system. The greater the strain energy of the system structure, the greater the structural stiffness. Therefore, the mathematical model of the topological optimization rigidity design of the continuum structure is expressed as the following formula (4):

[0137] minC

[0138] sta E (u, v) = C

[0139] u∈U

[0140] |σ|≤[σ]

[0141] |u|≤[u]

[0142] V≤V0, (4);

[0143] Among them, U represents the allowable displacement field; σ represents the stress field; V represents the volume, V0 represents the front volume, among which, a E (u, v) represents the virtual work of the internal force of the elastic body; u represents the real displacement; v represents the virtual displacement; C is the strain energy of the structural flexibility.

[0144] For the steel in the primary support of the tunnel, considering the lightest weight, that is, the lowest cost requirement, a given area Q is set, and the area is discretized using n microstructures with holes. For the convenience of studying the problem, the unit area rectangle (1×1) is taken as the microstructure, and the hole size is a×a. The weight of the design area is the following formula (5)

[0145]

[0146] Among them, W represents the weight of the design area, a m represents the size of the mth microstructure hole; γ represents the heaviness of the structure, and n represents the number of microstructures with holes.

[0147] The design variable is taken as the size of the microstructure hole a m , the objective function is the weight W of the design area, then the mathematical model of topology optimization can be expressed as:

[0148]

[0149] The constraints of the weight W are considered at the same time, and the constraints of the weight W include stress constraints and stability constraints.

[0150] Structural topology optimization is to obtain the optimal design goal by continuously modifying the unit material properties of the specified optimization area in the initial model during the analysis process, effectively removing or adding or subtracting units from the analysis model. Commonly used topological expressions and material interpolation model methods include: homogenization method, density method and topological function description method. Among them, the homogenization method and density method are the most widely used structural topology optimization methods. The former is rarely used for macroscopic structural topology optimization due to its complex design and solution, and is generally used for composite material topology optimization. Therefore, the model method used in the embodiment of the present application is the density method.

[0151] The basic idea of ​​the density method is to introduce a hypothetical material with a variable relative density between 0 and 1, and assume a nonlinear relationship between the macroscopic elastic modulus of the design material and its density. Among them, the most widely used model is the solid isotropie material with penalization model (SIMP) method. In this method, after decomposing the design material into a finite element mesh, SIMP assigns a relative density ρi to each unit as a variable during optimization, so that the structural topology optimization problem is converted into an optimal material distribution problem. The range of ρi is 0≤ρi≤1. When ρi=1, it means that the material is retained; when ρi=0, it means that the material is removed. Then, under the volume constraint, when the objective function is strain energy, the continuum structure topology optimization model based on the SIMP method is the following formulas (2) and (3):

[0152]

[0153] The constraint condition of the topology optimization objective function is shown in the following formula (3):

[0154]

[0155] KU=F,

[0156] k i =(ρ i ) p k0,

[0157] 0≤ρ min ≤ρ i ≤ρ max , (3);

[0158] Where C is the strain energy of the structural flexibility, in MJ; U represents the displacement vector; F represents the force vector, corresponding to the target load; K represents the structural stiffness matrix; N is the total number of sub-design areas; u i is the displacement vector of the ith sub-design area; k0 is the initial stiffness matrix of the unit, k i is the optimized stiffness matrix; v i is the optimized unit volume; V is the optimized volume; V0 is the previous volume; f is the optimized volume ratio; ρ i is the relative density of the ith sub-design region; ρ min is the lower limit of unit density; ρ max is the upper limit of unit density; p is the penalty factor.

[0159] Among them, ρ minis the lower limit of the cell density, which is used to prevent the occurrence of ill-conditioned matrices. When calculating, a very small positive number close to 0 can be taken, such as 0.00001; ρmax is the upper limit of the cell density, which is a positive number close to 1; p is a penalty factor, which is used to reduce the number of cells with intermediate cell density and make the result close to the 0 / 1 distribution. Generally, p is considered to be 3 during optimization.

[0160] In the step S104, the target load is input into the topology optimization objective function, and the initial design area is optimized with the minimum strain energy and the minimum volume of the topology optimization objective function under the target load as the optimization goal, and the topology optimization result of each sub-design area in the initial design area is determined.

[0161] Please refer to Figure 5 , inputting the target load into the topology optimization objective function, taking the strain energy of the topology optimization objective function under the target load to meet the structural strength requirements and minimize the volume as the optimization goal, optimizing the initial design area, and determining the topology optimization result of each sub-design area in the design area; comprising the following steps S501-S503:

[0162] S501, designing a variable of each sub-design region in the topology optimization objective function, and determining the strain energy and volume corresponding to the variable;

[0163] S502, determining the relationship between volume and strain energy;

[0164] S503. Based on the relationship between the volume and strain energy, determine the variables of each sub-design area when the strain energy meets the structural strength requirement and the volume is minimized, so as to determine the topology optimization result of each sub-design area in the initial design area.

[0165] Based on the relationship between the volume and the strain energy, determining the variables of each sub-design region when the strain energy meets the structural strength requirements and the volume is minimized includes the following steps:

[0166] Based on the relationship between the volume and the strain energy, a curve graph of the volume optimization rate and the strain energy is generated by taking the volume optimization rate as the abscissa and the strain energy as the ordinate;

[0167] Based on the curve graph of the volume optimization rate and the strain energy, determining a target point in the curve graph where the rate of change of the strain energy is greater than a preset rate threshold;

[0168] S503: Determine the volume and strain energy corresponding to the target point as the optimization target, and determine the variables of each sub-design area.

[0169] Exemplarily, in an embodiment of the present application, a ring-shaped steel section is selected, and based on the above-mentioned topology optimization objective function with the strain energy of the steel section as the optimization target, the topology optimization of the steel section under different lateral pressure coefficients is simulated according to different ratios of horizontal and vertical loads.

[0170] In order to facilitate modeling and ensure the accuracy of the results, a quarter of a circle is used instead of a circle. The two endpoints are only allowed to have radial displacement to constrain their rotation, such as Figure 6 As shown, Figure 6 The steel model diagram described in the embodiment of the present application is shown; the optimization area is a circular ring with a radius of 5m and a cross-section of 0.3m×0.3m, and the material is Q235 steel. The specific material property parameters are shown in Table 3.

[0171] Table 3 Material characteristic parameters of steel

[0172] Material Model <![CDATA[Heavy (KN / m 3 )]]> Deformation modulus (GPa) Poisson's ratio Tensile strength(MPa) Q235 78 210 0.3 375

[0173] A vertical uniformly distributed load of 30 KPa is applied to the model, and the topological optimization results of the steel frame by ABAQUS are solved under the conditions that the ratio of the vertical uniformly distributed load to the horizontal uniformly distributed load is 1:1, 1:2, 1:3 and 1:5, respectively. Thus, the horizontal load is changed while the vertical load remains unchanged, so as to achieve the effect of simulating the topological optimization of the circular steel under different lateral pressure coefficients.

[0174] When the vertical to horizontal load ratio is 1:1, the relationship between the volume optimization rate and strain energy of the structure is as follows: Figure 7 shown.

[0175] Depend on Figure 7 It can be seen that when the volume optimization rate is less than 40%, the structural strain energy is proportional to the structural volume optimization rate. For every 10% decrease in the structural volume, the strain energy increases by about 1.5MJ. When the volume optimization rate exceeds 40%, as the optimization rate increases, the strain energy generated by the structure increases. This shows that due to the increase in the hole space, the stress path of the structure begins to gradually deteriorate. Under the premise of ensuring volume optimization and structural strength, 40% is the optimal volume optimization rate of the structure under this load combination. At this time, the optimization result is the most reasonable form of topology optimization. The results are as follows: Figure 8 shown.

[0176] analyze Figure 8 Since the horizontal load is the same as the vertical load, the optimization result is a symmetrical structure. It can be clearly seen from the figure that the two free ends of the structure have a larger stiffness, while the stiffness is smaller in the middle. The overall stiffness shows the characteristics of "large at both ends and small in the middle". This design principle is usually adopted in the design of many bridges to ensure structural stability.

[0177] When the vertical and horizontal loads are 1:2, the relationship between the volume optimization rate and the strain energy of the structure is as follows: Fig. 9 Compared with the volume optimization rate and strain energy relationship curve when the vertical and horizontal loads are 1:1, when the vertical and horizontal loads are 1:2, although the structural strain increases significantly due to the increase in horizontal loads and the curve has certain fluctuations, the curve as a whole also shows that the structural strain energy increases steadily in the first half, and then the growth rate increases. It can be seen from the curve that the change node of this curve appears at about 45%, and the structure with an optimization rate of 43.98% is taken as the optimal solution for topology optimization.

[0178] Please refer to Fig.10 , Fig.10 The figure shows the optimal result of the structural topology optimization of the steel model when the vertical and horizontal loads are 1:2; Fig.10 It can be seen that when the horizontal load is twice the vertical load, the result of topological optimization is no longer symmetrical. Since the left half mainly bears horizontal loads in the axial direction and vertical loads in the radial direction, the axial force is greater than that of the right half, while the bending moment is smaller than that of the right half. Therefore, the volume subtracted by topological optimization of the left half is smaller. We know that under the conditions of certain length and material of the component, the ability of the component to resist axial load is proportional to the cross-sectional area. Therefore, in the left half with a larger axial force, in order to maintain the compressive stiffness of the structure, the volume subtracted by topological optimization is smaller than that of the right half with a smaller axial force. The deformation of the right half with a larger bending moment is too large, so a certain degree of flexibility is required to ensure the safety of the structure.

[0179] Please refer to Fig.11 , Fig.11 The relationship between the volume optimization rate and strain energy of the structure when the vertical-horizontal load is 1:3 is shown in the embodiment of the present application. Fig.12 It can be seen that when the volume optimization rate is less than 40%, the structural strain energy increases relatively steadily. Then, with the increase of the topology optimization volume, the growth rate of the structural strain accelerates. Therefore, the structure with a volume optimization rate of 38.33% is taken as the optimal topology optimization result.

[0180] Please refer to Fig.12 , Fig.12 The optimal result diagram of the structural topology optimization of the steel model when the vertical-horizontal load ratio is 1:3. Similar to the result when the vertical-horizontal load ratio is 1:2, the topology optimization result is also asymmetric when the vertical-horizontal load ratio is 1:3. The topology optimization volume of the left half subjected to the larger axial force is small, while the topology optimization volume of the right half subjected to the larger bending moment is large.

[0181] Please refer to Fig.13 , Fig.13 The relationship between the volume optimization rate and strain energy of the structure when the vertical and horizontal loads are 1:5 is shown. Fig.13It can be seen that the curve change process is mainly divided into three stages: in the first stage, the volume optimization rate is linearly related to the strain energy; in the second stage, as the volume optimization rate increases, the strain energy increases parabolically; in the third stage, when the volume optimization rate continues to increase, at the 62% node, the strain energy has a sudden increase, indicating that the steel frame can no longer withstand the applied load and the deformation is too large. The maximum volume optimization rate in the stage of linear increase of strain energy is the optimal solution for steel frame optimization. The optimal volume optimization rate of this model is 38.66%.

[0182] Please refer to Fig.14 , Fig.14 The optimal result diagram of the structural topology optimization of the steel model when the vertical and horizontal loads are 1:5 as described in the embodiment of the present application is shown.

[0183] It can be seen that when performing topological optimization on steel frames, ABAQUS topological optimization follows such a rule: at locations where the axial force is large and the bending moment is small, the volume removed by topological optimization is small, while at locations where the axial force is small and the bending moment is large, the volume removed by topological optimization is large. It can be seen from the optimal result diagrams in the three cases that as the horizontal load ratio increases, the volume difference between the left and right parts becomes more and more obvious.

[0184] By comparing the optimization results of circular steel sections under different lateral pressure coefficients, the following conclusions can be drawn:

[0185] When topological optimization is performed on a circular steel section with a radius of 5m and a cross-section of 0.3m×0.3m, under different horizontal and vertical load ratios, the optimal topological optimization volume is around 40%. The study believes that this value is not accidental. When the shape and material of the topological optimization object are constant, the final optimal topological optimization volume will not increase or decrease significantly due to changes in load.

[0186] Under the condition of symmetric load, the optimal structural solution of topology optimization is also symmetric; under the condition of asymmetric load, the optimal solution of topology optimization is asymmetric.

[0187] Under different vertical and horizontal load conditions, the optimal topology optimization solutions all show the characteristics of stiffness being "large at both ends and small in the middle".

[0188] Under asymmetric load conditions, if the quarter-circular ring steel is divided into left and right halves, structural mechanics calculations show that the axial force in the left half is larger than that in the right half, while the positive and negative bending moments are almost the same. Therefore, the stress in the left half is greater than that in the right half. In the topology optimization results, the optimized volume ratio of the left half is smaller than that of the right half. This shows that the volume removed by topology optimization is smaller at locations with large stress.

[0189] Based on the curve graph of the volume optimization rate and strain energy, determine the target point in the curve graph where the rate of change of strain energy is greater than a preset rate threshold; that is, based on the volume-strain energy relationship, find the slope mutation point as the optimal point for selecting the optimization result.

[0190] For example, by Figure 3 The topological optimization of the medium-shaped steel in the initial support of the tunnel shown in Figure 1 shows the volume optimization rate and structural strain energy curves according to different load and lateral pressure coefficient combinations. Fig.15 As shown. Fig.15 From the volume-strain energy curve in , we can see that as the volume decreases during the optimization process, the strain energy of the steel gradually increases, the flexibility increases, and the rate of change increases. Therefore, in order to ensure the rationality and stability of the structure, it is more reasonable to select the point of sudden change as the optimization result. Fig.15 It can be seen that when the optimized volume is about 0.5, the strain energy is about to increase significantly, and the optimization result at this time is the most reasonable form of topology optimization.

[0191] Please refer to Fig.16 , Fig.16 In the embodiment of the present application, Figure 3 Optimal results of structural topology optimization for the target support model of the example.

[0192] In step S105, based on the topology optimization results of each sub-design area in the initial design area, a target support scheme of the target initial support steel frame is determined, so as to use steel sections to perform initial support on the target position of the target tunnel based on the target support scheme.

[0193] Through the topological optimization of large-span steel sections, the following conclusions can be drawn:

[0194] The topological optimization results show that the volume of the steel frame at the invert is smaller after optimization, and the stress value is smaller, which is mainly affected by axial force. Therefore, a steel frame with a smaller cross-sectional area can be set at the invert, and the compressive strength of the concrete itself can be used more.

[0195] The topological optimization results show that the volume of the steel frame retained at the arch is small after optimization, and the closer to the middle, the thinner the steel frame is. Therefore, the arch can use small-section steel or steel grilles (steel grilles were used in actual construction). The volume removed by optimization at the arch waist and arch foot is small, and stress concentration will occur at the arch foot. Therefore, the stiffness is expected to be relatively large. The situation at the arch waist is the same as that of the circular steel. This is because the axial force here is too large, so sufficient stiffness is needed to resist the pressure from above. During the construction process, the cross-sectional area of ​​the steel at the arch waist and arch foot can be increased.

[0196] Based on the same inventive concept, the embodiment of the present application also provides a structural optimization device for the tunnel primary support steel frame corresponding to the structural optimization method for the tunnel primary support steel frame. Since the principle of solving the problem by the device in the embodiment of the present application is similar to the structural optimization method for the tunnel primary support steel frame described above in the embodiment of the present application, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be repeated.

[0197] Please refer to Fig.17 , Fig.17 The schematic diagram of the structure of the structural optimization device for the tunnel primary support steel frame according to the embodiment of the present application is shown; Fig.17 As shown, the device comprises:

[0198] The first establishing module 1701 is used to establish a target support model for the target position of the target initial support steel frame for initial support in the target tunnel, and configure the steel material performance parameters of the target initial support steel frame and the surrounding rock material performance parameters of the target position of the target initial support steel frame in the target support model to obtain a constructed target support model; the cross-section of the target initial support steel frame and the target position of the target tunnel are matched;

[0199] The first determination module 1702 is used to determine the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame based on the constructed target support model;

[0200] The second establishment module 1703 is used to use the target primary support steel frame as an initial design area based on a topology optimization method, decompose the initial design area into multiple sub-design areas, assign a relative density to each sub-design area as a variable when optimizing the sub-design area, and establish a topology optimization objective function of the strain energy of the structural flexibility of the design area under a volume constraint;

[0201] The optimization module 1704 is used to input the target load into the topology optimization objective function, optimize the initial design area with the strain energy of the topology optimization objective function under the target load meeting the structural strength requirement and minimizing the volume as the optimization goal, and determine the topology optimization result of each sub-design area in the initial design area; the topology optimization result includes whether there is a steel section in the sub-design area, and the structural properties of the steel section when there is a steel section in the sub-design area; the structural properties of the steel section include size and shape;

[0202] The second determination module 1705 is used to determine a target support scheme for a target initial support steel frame based on the topology optimization results of each sub-design area in the initial design area, so as to use steel sections to perform initial support on a target position of a target tunnel based on the target support scheme.

[0203] In some embodiments, in the structural optimization device for the tunnel primary support steel frame, the first establishment module establishes a target support model for the target position of the target primary support steel frame for the primary support steel frame used for initial support in the target tunnel, and configures the steel material performance parameters of the target primary support steel frame and the surrounding rock material performance parameters of the target position of the target primary support steel frame in the target support model, and when the constructed target support model is obtained, it is specifically used to:

[0204] According to the buried depth of the target primary support steel frame of the target tunnel, determine the surrounding rock size of the target position of the target tunnel in the target support model;

[0205] Determine the size of the target primary support steel frame in the target support model;

[0206] A target support model is established based on the surrounding rock size of the target position of the target tunnel and the size of the target primary support steel frame in the target support model; the target support model includes a surrounding rock structure and a steel structure;

[0207] According to the size of the surrounding rock and the size of the target primary support steel frame, the grid size of the surrounding rock structure and the grid size of the steel structure are determined respectively, and the surrounding rock structure and the steel structure are divided by using the free meshing technology to obtain the target support model with the meshing completed;

[0208] The steel material performance parameters of the target primary support steel frame and the surrounding rock material performance parameters of the target position where the target primary support steel frame is located in the target support model are configured to obtain a constructed target support model.

[0209] In some embodiments, in the structural optimization device for the tunnel primary support steel frame, the first determination module, when determining the target load applied to the target primary support steel frame by the surrounding rock of the target tunnel based on the constructed target support model, is specifically used to:

[0210] Determining the stress of the surrounding rock grid unit of the surrounding rock structure in the constructed target support model according to the yield criterion;

[0211] According to the buried depth of the target primary support steel frame of the target tunnel, the lateral pressure coefficient and the model boundary conditions in the target support model are determined; in the model boundary conditions, the axial displacement of the surrounding rock and the target primary support steel frame in the tunnel is zero, the bottom of the surrounding rock is fixed, and the horizontal displacement of the side limit is zero;

[0212] Based on the stress, lateral pressure coefficient and model boundary conditions of the surrounding rock grid unit in the target support model, the structure of the target support model is discretized into a finite number of structural units using ABQUS calculation software; the structural units are connected through nodes, and the force and deformation of the structural units are transmitted through the nodes;

[0213] According to the equilibrium conditions of each node and the deformation coordination conditions of adjacent structural units at the common nodes, the discrete body composed of various structural units is used to represent the continuum of the target support model. Under the constraints of the equilibrium conditions and deformation coordination conditions, the unit structure analysis is carried out to determine the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame.

[0214] In some embodiments, in the structural optimization device for the tunnel primary support steel frame, the first determination module, when determining the stress of the surrounding rock grid unit of the surrounding rock structure in the constructed target support model according to the yield criterion, is specifically used to:

[0215] Based on the control equation of the yield criterion described in the following formula (1), the stress of the surrounding rock grid unit of the surrounding rock structure in the constructed target support model is determined:

[0216]

[0217] Wherein, σ1 represents the first principal stress of the surrounding rock grid unit, σ2 represents the second principal stress of the surrounding rock grid unit, σ3 represents the third principal stress of the surrounding rock grid unit, and c represents the cohesion of the surrounding rock grid unit. Characterizes the internal friction angle of the surrounding rock grid unit.

[0218] In some embodiments, in the structural optimization device for the tunnel primary support steel frame, the topology optimization objective function is as shown in the following formula (2):

[0219]

[0220] The constraint condition of the topology optimization objective function is shown in the following formula (3):

[0221]

[0222] KU=F,

[0223] k i =(ρ i ) p k0,

[0224] 0≤ρ min ≤ρ i ≤ρ max , (3);

[0225] Where C is the strain energy of the structural flexibility, in MJ; U represents the displacement vector; F represents the force vector, corresponding to the target load; K represents the structural stiffness matrix; N is the total number of sub-design areas; u i is the displacement vector of the ith sub-design area; k0 is the initial stiffness matrix of the unit, k i is the optimized stiffness matrix; v iis the optimized unit volume; V is the optimized volume; V0 is the previous volume; f is the optimized volume ratio; ρ i is the relative density of the ith sub-design region; ρ min is the lower limit of unit density; ρ max is the upper limit of unit density; p is the penalty factor.

[0226] In some embodiments, in the structural optimization device for the tunnel primary support steel frame, the second determination module, when inputting the target load into the topology optimization objective function, takes the strain energy of the topology optimization objective function under the target load to meet the structural strength requirements and minimize the volume as the optimization goal, optimizes the initial design area, and determines the topology optimization results of each sub-design area in the design area, is specifically used to:

[0227] Design the variables of each sub-design area in the topology optimization objective function and determine the strain energy and volume corresponding to the variables;

[0228] Determine the relationship between volume and strain energy;

[0229] Based on the relationship between the volume and strain energy, the variables of each sub-design area when the strain energy meets the structural strength requirements and the volume is minimized are determined to determine the topology optimization result of each sub-design area in the initial design area.

[0230] In some embodiments, in the structural optimization device for the tunnel primary support steel frame, the second determination module, when determining the variables of each sub-design area when the strain energy meets the structural strength requirements and the volume is minimum based on the relationship between the volume and the strain energy, is specifically used to:

[0231] Based on the relationship between the volume and the strain energy, a curve graph of the volume optimization rate and the strain energy is generated by taking the volume optimization rate as the abscissa and the strain energy as the ordinate;

[0232] Based on the curve graph of the volume optimization rate and the strain energy, determining a target point in the curve graph where the rate of change of the strain energy is greater than a preset rate threshold;

[0233] The volume and strain energy corresponding to the target point are determined as the optimization objectives, and the variables of each sub-design area are determined.

[0234] Based on the same inventive concept, an electronic device corresponding to the structural optimization method of the tunnel primary support steel frame is also provided in the embodiment of the present application. Since the principle of solving the problem by the electronic device in the embodiment of the present application is similar to the structural optimization method of the tunnel primary support steel frame described above in the embodiment of the present application, the implementation of the electronic device can refer to the implementation of the method, and the repeated parts will not be repeated.

[0235] Please refer to Fig.18 , Fig.18 A schematic diagram of the structure of the electronic device described in an embodiment of the present application is shown; the electronic device 1800 includes: a processor 1802, a memory 1801 and a bus, the memory 1801 stores machine-readable instructions executable by the processor 1802, and when the electronic device 1800 is running, the processor 1802 communicates with the memory 1801 through the bus, and when the machine-readable instructions are executed by the processor 1802, the steps of the structural optimization method of the tunnel primary support steel frame are executed.

[0236] Based on the same inventive concept, a computer-readable storage medium corresponding to the structural optimization method of the tunnel primary support steel frame is also provided in the embodiment of the present application. Since the principle of solving the problem by the computer-readable storage medium in the embodiment of the present application is similar to the structural optimization method of the tunnel primary support steel frame described above in the embodiment of the present application, the implementation of the computer-readable storage medium can refer to the implementation of the method, and the repeated parts will not be repeated.

[0237] An embodiment of the present application provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps of the structural optimization method of the tunnel primary support steel frame are executed.

[0238] Those skilled in the art can clearly understand that, for the convenience and simplicity of description, the specific working process of the system and device described above can refer to the corresponding process in the method embodiment, and will not be repeated in this application. In the several embodiments provided in this application, it should be understood that the disclosed system, device and method can be implemented in other ways. The device embodiments described above are merely schematic. For example, the division of the modules is only a logical function division. There may be other division methods in actual implementation. For example, multiple modules or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some communication interfaces, indirect coupling or communication connection of devices or modules, which can be electrical, mechanical or other forms.

[0239] The modules described as separate components may or may not be physically separated, and the components shown as modules may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0240] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0241] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a non-volatile computer-readable storage medium that is executable by a processor. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for a computer device (which can be a personal computer, a platform server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard drives, ROM, RAM, magnetic disks, or optical disks.

[0242] The above are only specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for optimizing the structure of a tunnel primary support steel frame, characterized in that: The method comprises the following steps: For the initial support steel frame used for initial support in the target tunnel, a target support model of the target position where the target initial support steel frame is located is established, and the steel material performance parameters of the target initial support steel frame and the surrounding rock material performance parameters of the target position where the target initial support steel frame is located in the target support model are configured to obtain a constructed target support model; the cross-section of the target initial support steel frame and the target position of the target tunnel are matched; Based on the constructed target support model, determine the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame; Based on the topology optimization method, the target primary support steel frame is taken as the initial design area, the initial design area is decomposed into multiple sub-design areas, a relative density is assigned to each sub-design area as a variable during the optimization of the sub-design area, and under the volume constraint, a topology optimization objective function of the strain energy of the structural flexibility of the design area is established; The target load is input into the topology optimization objective function, and the strain energy of the topology optimization objective function under the target load meets the structural strength requirement and has the smallest volume as the optimization goal, the initial design area is optimized, and the topology optimization result of each sub-design area in the design area is determined; the topology optimization result includes whether there is a steel section in the sub-design area, and the structural properties of the steel section when there is a steel section in the sub-design area; the structural properties of the steel section include size and shape; Based on the topology optimization results of each sub-design area in the design area, a target support scheme of the target initial support steel frame is determined, so as to use steel sections to perform initial support on the target position of the target tunnel based on the target support scheme.

2. The structural optimization method of the tunnel primary support steel frame according to claim 1 is characterized in that: For the initial support steel frame used for initial support in the target tunnel, a target support model for the target position of the target initial support steel frame is established, and the steel material performance parameters of the target initial support steel frame and the surrounding rock material performance parameters of the target position of the target initial support steel frame in the target support model are configured to obtain a constructed target support model; including: According to the buried depth of the target primary support steel frame of the target tunnel, determine the surrounding rock size of the target position of the target tunnel in the target support model; Determine the size of the target primary support steel frame in the target support model; A target support model is established based on the surrounding rock size of the target position of the target tunnel and the size of the target primary support steel frame in the target support model; the target support model includes a surrounding rock structure and a steel structure; According to the size of the surrounding rock and the size of the target primary support steel frame, the grid size of the surrounding rock structure and the grid size of the steel structure are determined respectively, and the surrounding rock structure and the steel structure are divided by using the free meshing technology to obtain the target support model with the meshing completed; The steel material performance parameters of the target primary support steel frame and the surrounding rock material performance parameters of the target position where the target primary support steel frame is located in the target support model are configured to obtain a constructed target support model.

3. The structural optimization method of the tunnel primary support steel frame according to claim 2 is characterized in that: Based on the constructed target support model, the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame is determined, including: Determining the stress of the surrounding rock grid unit of the surrounding rock structure in the constructed target support model according to the yield criterion; According to the buried depth of the target primary support steel frame of the target tunnel, the lateral pressure coefficient and the model boundary conditions in the target support model are determined; in the model boundary conditions, the axial displacement of the surrounding rock and the target primary support steel frame in the tunnel is zero, the bottom of the surrounding rock is fixed, and the horizontal displacement of the side limit is zero; Based on the stress, lateral pressure coefficient and model boundary conditions of the surrounding rock grid unit in the target support model, the structure of the target support model is discretized into a finite number of structural units using ABQUS calculation software; the structural units are connected through nodes, and the force and deformation of the structural units are transmitted through the nodes; According to the equilibrium conditions of each node and the deformation coordination conditions of adjacent structural units at the common nodes, the discrete body composed of various structural units is used to represent the continuum of the target support model. Under the constraints of the equilibrium conditions and deformation coordination conditions, the unit structure analysis is carried out to determine the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame.

4. The structural optimization method of the tunnel primary support steel frame according to claim 3 is characterized in that: Determining the stress of the surrounding rock grid unit of the surrounding rock structure in the constructed target support model according to the yield criterion includes: Based on the control equation of the yield criterion described in the following formula (1), the stress of the surrounding rock grid unit of the surrounding rock structure in the constructed target support model is determined: Wherein, σ1 represents the first principal stress of the surrounding rock grid unit, σ2 represents the second principal stress of the surrounding rock grid unit, σ3 represents the third principal stress of the surrounding rock grid unit, and c represents the cohesion of the surrounding rock grid unit. Characterizes the internal friction angle of the surrounding rock grid unit.

5. The structural optimization method of the tunnel primary support steel frame according to claim 1 is characterized in that: The topology optimization objective function is shown in the following formula (2): The constraint condition of the topology optimization objective function is shown in the following formula (3): KU=F, k i =(ρ i ) p k0, 0≤ρ min ≤ρ i ≤ρ max ,(3); Where C is the strain energy of the structural flexibility, in MJ; U represents the displacement vector; F represents the force vector, corresponding to the target load; K represents the structural stiffness matrix; N is the total number of sub-design areas; u i is the displacement vector of the ith sub-design area; k0 is the initial stiffness matrix of the unit, k i is the optimized stiffness matrix; v i is the optimized unit volume; V is the optimized volume; V0 is the previous volume; f is the optimized volume ratio; ρ i is the relative density of the ith sub-design region; ρ min is the lower limit of unit density; ρ max is the upper limit of unit density; p is the penalty factor.

6. The structural optimization method of the tunnel primary support steel frame according to claim 1 or 5, characterized in that: The target load is input into the topology optimization objective function, and the strain energy of the topology optimization objective function under the target load meets the structural strength requirement and the volume is minimized as the optimization goal, the initial design area is optimized, and the topology optimization result of each sub-design area in the design area is determined, including: Design the variables of each sub-design area in the topology optimization objective function and determine the strain energy and volume corresponding to the variables; Determine the relationship between volume and strain energy; Based on the relationship between the volume and strain energy, the variables of each sub-design area when the strain energy meets the structural strength requirements and the volume is minimized are determined to determine the topology optimization result of each sub-design area in the initial design area.

7. The structural optimization method of the tunnel primary support steel frame according to claim 6 is characterized in that: Based on the relationship between volume and strain energy, the variables of each sub-design area are determined when the strain energy meets the structural strength requirements and the volume is minimized, including: Based on the relationship between the volume and the strain energy, a curve graph of the volume optimization rate and the strain energy is generated by taking the volume optimization rate as the abscissa and the strain energy as the ordinate; Based on the curve graph of the volume optimization rate and the strain energy, determining a target point in the curve graph where the rate of change of the strain energy is greater than a preset rate threshold; The volume and strain energy corresponding to the target point are determined as the optimization objectives, and the variables of each sub-design area are determined.

8. The structural optimization device of the tunnel primary support steel frame is characterized by: The device comprises: The first establishment module is used to establish a target support model for the target position of the target initial support steel frame used for initial support in the target tunnel, and configure the steel material performance parameters of the target initial support steel frame and the surrounding rock material performance parameters of the target position of the target initial support steel frame in the target support model to obtain a constructed target support model; the cross-section of the target initial support steel frame and the target position of the target tunnel are matched; A first determination module is used to determine the target load applied by the surrounding rock of the target tunnel to the target primary support steel frame based on the constructed target support model; The second establishment module is used to take the target primary support steel frame as the initial design area based on the topology optimization method, decompose the initial design area into multiple sub-design areas, assign a relative density to each sub-design area as a variable when optimizing the sub-design area, and establish a topology optimization objective function of the strain energy of the structural flexibility of the design area under the volume constraint; An optimization module is used to input the target load into the topology optimization objective function, optimize the initial design area with the strain energy of the topology optimization objective function under the target load meeting the structural strength requirement and minimizing the volume as the optimization goal, and determine the topology optimization result of each sub-design area in the initial design area; the topology optimization result includes whether there is a steel section in the sub-design area, and the structural properties of the steel section when there is a steel section in the sub-design area; the structural properties of the steel section include size and shape; The second determination module is used to determine a target support scheme for a target initial support steel frame based on the topology optimization results of each sub-design area in the initial design area, so as to use steel sections to perform initial support on a target position of a target tunnel based on the target support scheme.

9. An electronic device, characterized in that include: A processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is running, the processor and the memory communicate via the bus, and when the machine-readable instructions are executed by the processor, the steps of the structural optimization method for the primary support steel frame of a tunnel are performed as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, which, when executed by a processor, executes the steps of the structural optimization method for the tunnel primary support steel frame as described in any one of claims 1 to 7.

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