Fine numerical simulation method for crack width of subway shield tunnel under surface loading

Abstract

The invention discloses a metro shield tunnel crack width refined numerical simulation method under surface loading, and the method comprises the following specific steps: describing the overall stress deformation characteristics of a soil body-shield tunnel structure based on a stratum-structure method, and simulating a macroscopic equivalent model by adopting a continuous medium model, and the equivalent stiffness reduction effect caused by the influence of longitudinal seams and circular seams is fully considered, the most unfavorable section position along the shield tunnel is determined, so that the key section is replaced with a refined model considering local hand hole weakening, multi-contact and built-in steel bars, and the shield tunnel crack evolution characteristics are described by adopting a total strain crack model. And obtaining the millimeter-scale crack width of the target tunnel structure based on a load-structure method. According to the analysis method, the millimeter-scale crack width of the shield tunnel under the action of ground surface loading can be accurately obtained, the structure safety state can be rapidly evaluated in combination with current specifications, and an important basis is provided for operation and maintenance of the subway shield tunnel.

Description

Technical Field

[0001] The present invention relates to the technical field of subway shield tunnel safety assessment, in particular to a refined numerical simulation method for crack width in a subway shield tunnel under surface loading. Background Art

[0002] Due to the shortage of urban surface resources, my country has become a major country in the development and utilization of underground space. As of the end of 2023, a total of 61 cities in China have opened 11,034 kilometers of urban rail transit lines and 8,008.17 kilometers of subway operating lines, ranking first in the world, accounting for 25% of the world, of which shield tunnels account for about 80%, and their structural safety is crucial.

[0003] Shield tunnels located in typical soft soil usually face weak and complex geology. The large-scale distribution of underconsolidated soil layers induces the continuous aggravation of uneven settlement of the shield tunnel structure. In addition, the surface loading makes the tunnel structure prone to frequent diseases, rapid deterioration, and short lifespan. Structural degradation often shows the characteristics of gradual development.

[0004] Shield tunnels are often constructed using circular segments assembled with bolted connections. They are stressed using a multi-hinged, discontinuous circular arch structure, exhibiting a degree of flexibility both longitudinally and transversely. This allows the tunnel structure to withstand certain loads and coordinate deformation when the surrounding soil deforms. However, when subjected to external construction loads, the surrounding soil is disturbed, causing changes in the stress state within a certain range around the excavation. This induces additional stress in the tunnel structure, and in severe cases, the lining structure can be subjected to large nonlinear deformations, resulting in deformation, cracking, and water leakage in the tunnel segments. This reduces the tunnel's serviceability and, in turn, impacts subway safety. Failure to promptly reinforce existing defects can lead to deep damage to the segmental lining, ultimately leading to overall structural instability and failure, resulting in significant loss of life and property.

[0005] In a shield tunnel in operation, only the cracking and crushing of the inner side surface above the roadbed can be observed, while the outer side of the tunnel cannot be directly observed. In actual engineering, the stress characteristics and cracking conditions of each side of the shield tunnel cannot be obtained like in indoor tests. In-depth numerical simulation analysis is required to evaluate the actual stress state of the shield tunnel and the effects of reinforcement measures after implementation, so as to present the damage and cracking conditions of the tunnel parts that cannot be directly observed, and evaluate the safety of the shield tunnel under different deformation and cracking states, and take reinforcement measures according to different safety conditions.

[0006] Therefore, the research on the evolution of crack damage in shield tunnels under surface loading has important scientific significance and engineering application value. However, to date, there is still a lack of a refined numerical simulation method for the crack width of shield tunnel segments that can reflect the weakening of local handholes, multiple contacts and the influence of built-in steel bars, while ensuring high calculation accuracy and high computational efficiency. Summary of the Invention

[0007] The purpose of the present invention is to address the defects of the above-mentioned prior art and provide a refined numerical simulation method for the crack width of subway shield tunnels under surface loads. This method can accurately obtain the crack width of the shield tunnel at the millimeter scale. Combined with the current specifications, it can quickly evaluate the structural safety status and provide an important basis for the operation and maintenance of the shield tunnel.

[0008] To achieve the above object, the present invention provides the following technical solution: a method for fine-grained numerical simulation of crack width in a subway shield tunnel under surface load, comprising the following steps: Step S1: numerically simulate the engineering geology and surrounding environment of the subway shield tunnel and establish an initial model. In the model, the shield tunnel is simplified longitudinally into a three-dimensional shell unit of a continuous homogeneous cylinder, and the soil adopts a solid unit. Constitutive relations are introduced into the analysis model to describe the mechanical behavior of the soil and the shield tunnel: the shield tunnel adopts a linear elastic constitutive model, and the soil adopts a Mohr-Coulomb model. The Coulom interface friction constitutive relation is introduced to describe the interaction between the soil and the tunnel structure.

[0009] Step S2: According to the grouping of the tunnels in the modeling, the numerical model is subjected to ground stress balance and then the soil is excavated. After the excavation reaches the length of the shield machine body, the shield tunnel segments are activated at the tail of the shield machine.

[0010] Step S3: applying a surface load based on the numerical model, performing numerical simulation analysis on the adverse effects of the shield tunnel, and obtaining the most unfavorable cross-sectional position of the tunnel deformation.

[0011] Step S4: Establish a refined analysis model of the shield tunnel, in which three-dimensional solid elements are used for bolts and segments, and embedded rod elements are used for steel bars. In the analysis model, a constitutive relationship is introduced to describe the nonlinear mechanical behavior of the shield tunnel structure: the shield tunnel adopts a total strain crack model, and the steel bars and bolts adopt a double broken line constitutive model. The Coulom interface friction constitutive relationship is introduced to describe the nonlinear mechanical behavior of segment joint contact and segment-bolt contact.

[0012] Step S5: The soil pressure around the segment lining at the most unfavorable cross-sectional location is extracted using the cross-sectional integral principle. The load-structure method is used to apply a load to the refined shield tunnel model. The hoop force of the soil on the tunnel structure is simulated by a soil spring, which is a three-way nonlinear spring that is only compressed but not tensile, and consists of two tangential springs and one normal spring.

[0013] Step S6: Output the stress and displacement cloud map of the shield tunnel structure based on the calculation results, use the combined line function to extract the internal force distribution curve of the segment, and obtain the crack width index of the shield tunnel under the influence of surface load.

[0014] Furthermore, in step S1, DIANA finite element software is used to establish a geometric model of soil and shield tunnel, wherein in the soil geometric model, the X direction is the cross-sectional direction, the Z direction is the longitudinal excavation direction of the tunnel, and the Y direction is the tunnel burial depth direction.

[0015] Furthermore, in step S2, the initial boundary condition constraints are set for the soil geometric model using DIANA software, and the initial stress balance is performed on the soil geometric model using geotechnical mechanics staged construction commands.

[0016] Furthermore, in step S3, the surface load converted to overburden pressure is calculated by the following formula: ; Where, Indicates the natural density of the soil. h Indicates the thickness of the soil layer.

[0017] Furthermore, in step S4, the segment lining concrete is simulated using the total strain crack model. The main idea of the model is to convert the cracking strain and elastic strain Considered uniformly, the magnitude of the stress is calculated by the crack direction, and the unit strain vector In the coordinate system xyz The expression in is: ; Based on the strain transformation matrix T , calculate the strain vector The expression is: ; The total strain crack model can be divided into a fixed crack model and a rotating crack model according to the relationship between the crack direction and the principal stress direction. In the rotating crack model, the principal stress direction of the unit determines the strain conversion matrix. T , the expression is: ; In the fixed crack model, the stress vector in the crack coordinate system is for: ; Where, Indicates the angle threshold of different cracks; Finally, the stress vector expression in the unit coordinate system is calculated as follows: .

[0018] Furthermore, in step S4, the Coulom interface friction constitutive relation is used for the segment joint contact and segment-bolt contact, which is expressed as: ; ; Where, t s and t t is the shear force acting on the interface plane, u s and u t represents the relative shear displacement on the interface plane, t n and u n They represent the traction and relative displacement perpendicular to the plane respectively. In the elastic state, the expression is: ; ; Through the yield function f The effective shear stress that controls friction slip is expressed as: ; ; Where, represents the effective shear stress, c Indicates cohesion, represents the friction angle; When friction slip occurs on the interface, the criterion for shear traction behavior is: ; .

[0019] Furthermore, in step S4, the steel bars and bolts adopt a bifold line constitutive model, which is expressed as: ; Where, is the material stress; E s is the elastic modulus of the material; fy,r is the material yield stress; ε y is the yield strain of the material; ε u is the ultimate strain of the material; k is the slope of the material hardening section, ; f st,r is the ultimate stress of the material.

[0020] Furthermore, in step S5, the tangential spring stiffness of the soil spring is 0.3 times the normal stiffness, and the normal stiffness expression is: ; Where, E is the Young's modulus of soil; v is Poisson's ratio; R is the outer radius of the tunnel.

[0021] Compared with the prior art, the present invention has the following beneficial effects: 1. It can accurately simulate the nonlinear mechanical response of shield tunnel structures under surface loads and accurately obtain the millimeter-scale crack width of the structure; 2. By comparing with the on-site monitoring results, the feasibility and accuracy of the method of the present invention were verified; 3. Combined with the current specifications, the structural safety status of operating shield tunnels can be quickly assessed, providing an important basis for shield tunnel operation and maintenance.

[0022] Specifically, the present invention provides a refined numerical simulation method for crack widths in shield tunnel segments under surface loading. This method combines the stratum-structure method with the load-structure method. By establishing a refined numerical analysis model, it not only accurately measures the crack width of shield tunnels under surface loading, but also reflects the nonlinear mechanical behavior of shield tunnels. The accuracy and applicability of the present method have been verified by comparison with on-site monitoring results. The present analysis method can accurately measure the crack width of shield tunnels under surface loading at the millimeter scale. Combined with current specifications, it can rapidly assess the structural safety status, providing an important basis for shield tunnel operation and maintenance. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0024] Figure 1 Flowchart of the numerical simulation analysis method according to an embodiment of the present invention.

[0025] Figure 2 This is a schematic diagram of the tunnel stratigraphic structure; Figure 3 Model mesh division and load influence range; Figure 4 This is the vertical deformation diagram of the tunnel under the influence of surface load; Figure 5 The most unfavorable cross-sectional position diagram of tunnel deformation; Figure 6 This is a diagram of the ground spring and load distribution; Figure 7 This is the block structure diagram of the shield tunnel segment; Figure 8 A detailed model diagram of the shield tunnel; Figure 9 This is a diagram showing the evolution of crack width in a shield tunnel under the influence of surface load; Figure 10 This is the stress diagram of the internal reinforcement of the shield tunnel under the influence of surface load; Figure 11 This is the internal force distribution curve of the shield tunnel under the influence of surface load; Figure 12 This is a diagram of internal cracks in the segment vault monitored on-site under the influence of surface loading. DETAILED DESCRIPTION

[0026] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0027] The refined numerical simulation method for crack width of subway shield tunnel under surface load includes the following steps: Step S1: Numerical simulation is performed based on the engineering geology and surrounding environment of the subway shield tunnel to establish an initial model. In this model, the shield tunnel is simplified longitudinally as a continuous homogeneous cylindrical three-dimensional shell element, and the soil is represented by a solid element. Constitutive relations are introduced into the analysis model to describe the mechanical behavior of the soil and shield tunnel: the shield tunnel adopts a linear elastic constitutive model, and the soil adopts the Mohr-Coulomb model. DIANA finite element software is used to establish geometric models of the soil and shield tunnel. In the soil geometric model, the X direction is the cross-sectional direction, the Z direction is the longitudinal excavation direction of the tunnel, and the Y direction is the tunnel depth direction. The Coulom interface friction constitutive relation is introduced to describe the interaction between the soil and the tunnel structure.

[0028] Step S2: Based on the grouping of tunnels in the modeling, the numerical model is subjected to ground stress balance before excavation. After the excavation reaches the length of the shield machine body, the shield tunnel segments are activated at the tail of the shield machine. The initial boundary condition constraints of the soil geometric model are set using the DIANA software, and the initial stress balance of the soil geometric model is performed using the geotechnical mechanics staged construction command.

[0029] Step S3: Apply surface load based on the numerical model. The surface load is converted into overburden pressure using the following formula: ; Where, Indicates the natural density of the soil. h Indicates the thickness of the soil layer.

[0030] By numerically simulating the adverse effects of shield tunneling, the most unfavorable cross-sectional position of tunnel deformation is obtained.

[0031] Step S4: Establishing a refined analysis model of the shield tunnel, wherein the bolts and segments in the model use three-dimensional solid elements, and the steel bars use embedded rod elements; introducing a constitutive relationship in the analysis model to describe the nonlinear mechanical behavior of the shield tunnel structure: the shield tunnel uses a total strain crack model, and the steel bars and bolts use a double-broken line constitutive model; The total strain crack model is used to simulate the segment lining concrete. The main idea of the model is to convert the cracking strain and elastic strain Considered uniformly, the magnitude of the stress is calculated by the crack direction, and the unit strain vector In the coordinate system xyz The expression in is: ; Based on the strain transformation matrix T , calculate the strain vector The expression is: ; The total strain crack model can be divided into a fixed crack model and a rotating crack model according to the relationship between the crack direction and the principal stress direction. In the rotating crack model, the principal stress direction of the unit determines the strain conversion matrix. T , the expression is: ; In the fixed crack model, the stress vector in the crack coordinate system is for: ; Where, Indicates the angle threshold of different cracks; Finally, the stress vector expression in the unit coordinate system is calculated as follows: .

[0032] The Coulom interface friction constitutive relation is introduced to describe the nonlinear mechanical behavior of segment joint contact and segment-bolt contact. The Coulom interface friction constitutive relationship is used for the segment joint contact and segment-bolt contact, which can be expressed as: ; ; Where, t s and t t is the shear force acting on the interface plane, u s and u t represents the relative shear displacement on the interface plane, t n and u n They represent the traction and relative displacement perpendicular to the plane respectively. In the elastic state, the expression is: ; ; Through the yield function f The effective shear stress that controls friction slip is expressed as: ; ; Where, represents the effective shear stress, c Indicates cohesion, represents the friction angle; When friction slip occurs on the interface, the criterion for shear traction behavior is: ; .

[0033] The steel bars and bolts adopt a double-broken line constitutive model, which can be expressed as: ; Where, is the material stress; E s is the elastic modulus of the material; f y,r is the material yield stress; ε y is the yield strain of the material; ε uis the ultimate strain of the material; k is the slope of the material hardening section, ; f st,r is the ultimate stress of the material.

[0034] Step S5: The soil pressure around the segment lining at the most unfavorable cross-sectional location is extracted using the cross-sectional integral principle. The load-structure method is used to apply a load to the refined shield tunnel model. The hoop force of the soil on the tunnel structure is simulated by a soil spring, which is a three-way nonlinear spring that is only compressed but not tensile, and consists of two tangential springs and one normal spring.

[0035] The tangential spring stiffness of the soil spring is 0.3 times the normal stiffness. The normal stiffness expression is: ; Where, E is the Young's modulus of soil; v is Poisson's ratio; R is the outer radius of the tunnel.

[0036] Step S6: Output the stress and displacement cloud map of the shield tunnel structure based on the calculation results, use the combined line function to extract the internal force distribution curve of the segment, and obtain the crack width index of the shield tunnel under the influence of surface load.

[0037] In a specific implementation, this embodiment selects a shield tunnel in a certain subway section in a soft soil area affected by surface loads, and performs simulation with the help of the finite element software DIANA.

[0038] like Figure 1 As shown, the refined numerical simulation method of the crack width of shield tunnel segments under the action of surface load in this embodiment includes the following steps: The model was built using DIANA (Displacement Analyzer), which accurately simulates the entire process of a reinforced concrete structure, from its initial state to the development of cracks, their continuous expansion, and eventual collapse. This simulation accurately accounts for the actual structure geometry, the concrete's material properties (crack constitutive model), the individual simulation of the rebar, and the bond and slip characteristics between the two. DIANA software is command-driven, allowing the model to be controlled and modified by inputting commands, ultimately achieving the desired numerical model. DIANA numerical simulation primarily involves four steps: establishing the finite element model, assigning material parameters, defining initial and boundary conditions, and solving the problem.

[0039] The model soil layer of this embodiment is divided into five layers. The soil layers are respectively as follows: ②1 sandy silt, ③2 sandy silt, ③5 sandy silt, ③6 silty silt clay with clay silt and ⑥2 silty clay. The soil mechanical parameters are shown in Table 1. The tunnel stratum structure is shown in Table 1. Figure 2 shown.

[0040] Table 1: Soil mechanical parameters In the subway project selected in this embodiment, relevant departments discovered through monitoring that a large area of soil was piled above a certain section of the line. Through on-site observation of the shield tunnel segments in this section, it was found that large areas of longitudinal cracks appeared on the inner side of the arch of some segments.

[0041] According to the actual subway shield tunnel project, the shield tunnel excavation and loading were numerically simulated to establish an initial model.

[0042] The corresponding geometric model was established using DIANA. The inner and outer diameters of the shield tunnel in the overburden area are 5.5 m and 6.2 m, respectively, with a burial depth of 7.5 m. Considering the distribution of the overburden and the influence of tunnel excavation, the length, width, and height of the soil model are 100 m, 75 m, and 40 m, respectively. The X direction is the cross-sectional direction of the geometric model; the Z direction is the longitudinal excavation direction of the tunnel; and the Y direction is the tunnel burial depth.

[0043] The boundary conditions involved in the soil geometric model are as follows: the upper part is a free boundary of the ground surface, the lower boundary is subject to Y-direction constraints, the front and rear boundaries are subject to Z-direction constraints, and the left and right boundaries are subject to X-direction constraints.

[0044] The shield tunnel is simplified into a three-dimensional shell unit of a continuous homogeneous cylinder in the longitudinal direction. The circumferential equivalent stiffness coefficient is taken as 0.7, the longitudinal equivalent stiffness reduction coefficient is taken as 0.01, and the soil adopts solid units according to the designed unit grid size (the unit grid is divided into 1 meter).

[0045] The contact relationship between the tunnel and the soil is considered in the model, and the Coulom interface friction constitutive relation is introduced to describe the interaction between the tunnel and the soil. The sum of the tangential stiffness and the normal stiffness is 1×10 8 N / m 3 With 2×10 12 N / m 3 .

[0046] DIANA software includes built-in constitutive relationships for many materials to accommodate simulation requirements for different materials or research areas. Considering the engineering geological conditions selected for this example, where the soil layer is located in a soft soil area and the majority of the soil is in an elastoplastic state, the Mohr-Coulomb model was ultimately selected as the constitutive model for this example, and a linear elastic constitutive model was used for the shield tunnel.

[0047] Shield tunnel excavation and load analysis were performed using the geotechnical mechanics tool in DIANA in a phased construction process, as shown in Table 2. In phase 1, all geotechnical elements were activated for in-situ stress equilibrium. In phase 2, soil elements within the tunnel were removed for tunnel excavation. In phase 3, the segments, internal reinforcement, and connecting bolts were activated. In phase 4, surface loads were applied in four steps. Load factors were set to 0.25, 0.5, 0.75, and 1.0 to account for the staged on-site load conditions.

[0048] Table 2: Construction steps The surface load can be simplified as a uniformly distributed load applied to the surface. By calculating the relevant parameters of the loaded soil, it can be known that the equivalent simplified load value is 110 kPa. The load impact range is 30 m in width and 40 m in length. Figure 3 shown.

[0049] The surface load is calculated by the following formula: Where, Indicates the natural density of the soil. h Indicates the thickness of the soil layer.

[0050] According to the calculation results, the vertical deformation of the tunnel under the influence of surface load and the most unfavorable cross-sectional position of the tunnel deformation are obtained as follows: Figure 4 、 Figure 5 As shown in the figure, the soil pressure around the segment lining at the most unfavorable cross-section position is extracted using the cross-section integral principle, and the load size is shown in Table 3. P v1 is the overlying vertical soil pressure; P y1 is the soil pressure at the bottom of the tunnel; P x1 is the lateral earth pressure on the vault, P x2 is the lateral earth pressure on the vault.

[0051] Table 3: Load size The effect of soil on the tunnel is simulated by soil springs. The soil springs are three-dimensional nonlinear springs that are only compressed but not tensile. They include a normal spring perpendicular to the contact surface and two tangential springs along the contact surface. The distribution of the stratum springs and loads is shown in the figure. Figure 6 The tangential spring stiffness of the soil spring is 0.3 times the normal stiffness, and the normal stiffness expression is: Where, E is the Young's modulus of soil; v is Poisson's ratio; R is the outer radius of the tunnel.

[0052] Based on the actual project, a detailed analysis model of the shield tunnel was established. The outer diameter of the tunnel segment is 6.2 m, the inner diameter is 5.5 m, the thickness is 0.35 m, and the width is 1.2 m. The segment lining block pattern is composed of 1 capping block (16°), 2 adjacent blocks (65°), 2 standard blocks (65°), and 1 arch bottom block (84°). The joints are connected by 12 5.8-grade circumferential and 10 longitudinal M30 bent bolts. The segment structure is as follows: Figure 7 The segments are made of HRB335 steel bars, with inner and outer main steel bar diameters of 22 mm and 16 mm respectively, stirrup diameter of 10 mm, concrete cover thickness of 50 mm, and concrete grade of C50.

[0053] According to the above model parameters, DIANA is used to model the segments and bolts, and the steel bars are simulated by embedded rod elements. The refined model is as follows: Figure 8 shown.

[0054] The constitutive relationship is introduced into the refined model to describe the nonlinear mechanical behavior of the shield tunnel structure: the total strain crack model is adopted for the shield tunnel, and the double-broken line constitutive model is adopted for the steel bars and bolts. The material parameters are shown in Table 3. The Coulom interface friction constitutive relationship is introduced to describe the nonlinear mechanical behavior of the segment joint contact and segment-bolt contact. The sum of the joint tangential stiffness and normal stiffness is 5×10 11 N / m 3 With 8×10 8 N / m 3 Since the segments are connected by solid bolts, the interface opening behavior is set to compression only without tension, with a cohesion of 0 MPa, a friction angle of 30°, and an opening strength of 0 N / m. 2 .

[0055] Table 4: Material parameters The relevant parameters calculated by the above method are input into DIANA software for calculation, and the evolution process of shield tunnel crack width under surface load is output as follows: Figure 9 As shown, the output built-in reinforcement stress is as follows Figure 10 As shown in the figure, the internal force distribution curve of the segment is drawn according to the calculation results. Figure 11 shown.

[0056] Depend on Figure 9 It can be seen that after the first load application, cracks in the segment initiated, and the initial cracks appeared at locations with relatively low segment ring stiffness, namely the longitudinal seam joints and handholes in the tension zone, with a maximum crack width of 0.22 mm. After the second load application, the cracks gradually extended to the inner side of the arch bottom and the outer side of the right arch waist, and showed a trend of continuing to develop through, with a maximum crack width of 0.53 mm. No cracks appeared at the left arch waist due to uneven force. After the fourth load application, the cracks in the longitudinal seam joints and the tension zone of the segment extended and penetrated, forming a large-area network of cracks, and the tunnel structure failed and was damaged. The maximum crack width was 2.05 mm.

[0057] Internal cracks in the segment vault at the site Figure 12 As shown in the figure, the accuracy and applicability of the method of the present invention were verified by comparing with the on-site monitoring results.

[0058] Depend on Figure 10 It can be seen that the inner side of the arch bottom and the outer sides of the left and right arch waists of the built-in steel bars in the pipe segment are subject to tensile stress. The maximum tensile stress of the steel bar is at the same location as the crack in the pipe segment. The maximum steel bar stress reaches 173 MPa, which does not reach the yield strength of the steel bar.

[0059] Figure 11 The diagram below shows the changes in bending moment and axial force of the segmental lining under the action of surface load. The axial force is positive when the section is compressed, and the bending moment is positive when the inner side of the section is tensile. Figure 11 It can be seen that the axial force distribution of the segmental lining is full-circle compression, while the bending moment distribution is tension at the inner sides of the crown and arch base and the outer sides of the left and right arch haunches. Ground loading significantly increases the internal forces of the segment, further compressing the crown and arch base and exerting tension on the arch haunches. As the loading increases, the joint stiffness decreases, causing the bending moment to further concentrate on the segment. The axial force changes in a similar manner to the bending moment, with the axial force increasing most significantly at the crown, arch base, and arch haunches.

[0060] The present invention provides a refined numerical simulation method for crack width in shield tunnel segments under surface loading. This method combines the stratum-structure method with the load-structure method. By establishing a refined numerical analysis model, it not only accurately measures crack width in shield tunnels under surface loading but also reflects the nonlinear mechanical behavior of shield tunnels. Comparison with field monitoring results verifies the accuracy and applicability of the present method. The present analysis method can accurately measure millimeter-scale crack width in shield tunnels under surface loading. Combined with current standards, it can rapidly assess the structural safety status, providing an important basis for shield tunnel operation and maintenance.

[0061] Throughout this specification, references to terms such as "one embodiment," "example," or "specific example" indicate that the specific features, structures, materials, or characteristics described in conjunction with that embodiment or example are included in at least one embodiment or example of the present invention. In this specification, schematic representations of these terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0062] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, many modifications and variations are possible based on the content of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, thereby enabling those skilled in the art to better understand and utilize the present invention. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A refined numerical simulation method for crack width of shield tunnel segments under surface loads, characterized by: The steps include: S1: Numerical simulations were performed based on the engineering geology and surrounding environment of the subway shield tunnel to establish an initial model. In this initial model, the shield tunnel was simplified longitudinally into a three-dimensional shell element consisting of a continuous homogeneous cylinder. Constitutive relations were introduced into the analysis model to describe the mechanical behavior of the soil and the shield tunnel. The shield tunnel adopted a linear elastic constitutive model, and the soil adopted the Mohr-Coulomb model; the interaction between the soil and the tunnel structure was described. S2: Based on the tunnel grouping in the modeling, the numerical model is subjected to ground stress balance and then the soil is excavated. After the excavation reaches the length of the shield machine body, the shield tunnel segments are activated at the tail of the shield machine. S3: Based on the numerical model, the surface load is applied to convert the overburden pressure. Through numerical simulation analysis of the adverse effects of the shield tunnel, the most unfavorable cross-sectional position of the tunnel deformation is obtained; S4: Establish a refined analysis model for shield tunnels, in which bolts and segments are represented by three-dimensional solid elements, and steel bars are represented by embedded rod elements. A constitutive relationship is introduced into the analysis model to describe the nonlinear mechanical behavior of the shield tunnel structure. The shield tunnel adopts a total strain crack model, and a bifold line constitutive model is adopted for steel bars and bolts. The nonlinear mechanical behavior of segment joint contact and segment-bolt contact is described. S5: The earth pressure around the segmental lining at the most unfavorable cross-sectional location is extracted using the cross-sectional integral principle, and the load-structure method is used to apply loads to the refined shield tunnel model. S6: Output the stress and displacement cloud map of the shield tunnel structure based on the calculation results, use the combined line function to extract the internal force distribution curve of the segment, and obtain the crack width index of the shield tunnel under the influence of surface load.

2. The refined numerical simulation method for shield tunnel segment crack width under surface load according to claim 1 is characterized in that: In step S1, considering the equivalent stiffness reduction effect caused by the influence of longitudinal joints and circumferential joints, the soil body adopts solid elements.

3. The refined numerical simulation method for crack width of shield tunnel segments under surface load according to claim 2 is characterized in that: In step S1, the DIANA finite element software is used to establish the soil and shield tunnel geometric models, the initial boundary conditions of the soil geometric model are constrained by the DIANA software, and the initial stress balance of the soil geometric model is performed by the geotechnical mechanics staged construction command.

4. The refined numerical simulation method for crack width of shield tunnel segments under surface load according to claim 3 is characterized in that: In step S3, the surface load converted to overburden pressure is calculated by the following formula: ； Where, It represents the natural density of soil, and h represents the thickness of soil layer.

5. The refined numerical simulation method for crack width of shield tunnel segments under surface load according to claim 4 is characterized in that: In step S4, the segment lining concrete is simulated using the total strain crack model, and the cracking strain and elastic strain Substitute uniformly, and the stress magnitude is calculated by the crack direction, and the unit strain vector The expression in the coordinate system xyz is: ； Based on the strain transformation matrix T, calculate the strain vector The expression is: ； The total strain crack model can be divided into a fixed crack model and a rotating crack model based on the relationship between the crack direction and the principal stress direction. In the rotating crack model, the principal stress direction of the unit determines the strain transformation matrix T, which is expressed as: ； In the fixed crack model, the stress vector in the crack coordinate system is for: ； Where, Indicates the angle threshold of different cracks; Finally, the stress vector expression in the unit coordinate system is calculated as follows: 。 6. The refined numerical simulation method for crack width of shield tunnel segments under surface load according to claim 5 is characterized in that: In step S4, the Coulom interface friction constitutive relation is used for the segment joint contact and segment-bolt contact, which is expressed as: ； ； Where, t s and t t is the shear force acting on the interface plane, u s and u t represents the relative shear displacement on the interface plane, t n and u n They represent the traction and relative displacement perpendicular to the plane respectively. In the elastic state, the expression is: ； ； The effective shear stress of friction slip is controlled by the yield function f, which is expressed as: ； ； Where, represents the effective shear stress, c represents the cohesion, represents the friction angle; When friction slip occurs on the interface, the criterion for shear traction behavior is: ； 。 7. The refined numerical simulation method for crack width of shield tunnel segments under surface load according to claim 5 is characterized in that: In step S4, the steel bars and bolts adopt a bifold line constitutive model, which is expressed as: ； Where, is the material stress, E s is the elastic modulus of the material, f y,r is the material yield stress, ε y is the yield strain of the material, ε u is the ultimate strain of the material, k is the slope of the hardening section of the material, ;f st,r is the ultimate stress of the material.

8. The refined numerical simulation method for crack width of shield tunnel segments under surface load according to claim 5 is characterized in that: In step S5, the hoop force of the soil on the tunnel structure is simulated by a soil spring, which is a three-way nonlinear spring that is only compressed but not tensile, and consists of two tangential springs and one normal spring.

9. The refined numerical simulation method for crack width of shield tunnel segments under surface load according to claim 8 is characterized in that: In step S5, the tangential spring stiffness of the soil spring is 0.3 times the normal stiffness, and the normal stiffness expression is: ； Where E is the Young's modulus of the soil; v is the Poisson's ratio; and R is the outer radius of the tunnel.

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