Mechanical modeling method for thin shell of densely-distributed pre-supporting structure

Abstract

The invention provides a dense pre-support structure thin shell mechanical modeling method, and relates to the technical field of tunnel engineering soft stratum pre-support structure mechanical modeling, and the method comprises the steps: calculating the equivalent stiffness of a pipe shed-jet grouting pile composite layer based on a Voigt theory; establishing a continuous thin shell model taking the control equation as a core; constructing a plastic / elastic disturbance partition in front of the tunnel face and a four-section type boundary condition of a supporting structure through a Pasternak foundation model; and solving the constructed continuous thin shell mechanical model through a finite difference method to obtain radial displacement, and completing mechanical modeling of the tunnel engineering soft stratum pre-supporting structure. The continuous thin shell model designed by the invention can provide high-reliability theoretical support for tunnel pre-support design.

Description

Technical Field

[0001] This application relates to the field of mechanical modeling technology for pre-supported structures in soft soil strata of tunnel engineering, and in particular to a mechanical modeling method for thin-shell structures with dense pre-supported structures. Background Technology

[0002] Tunnel pre-support technologies such as pipe roofs, horizontal jet grouting piles, and curtain grouting are widely used in tunnel engineering in soft soil strata. Structurally, grouting pipe roofs, horizontal jet grouting piles, and combinations of grouting pipe roofs and horizontal jet grouting piles can be viewed as thin shells composed of densely arranged and bonded columns or piles with a certain longitudinal length, a certain transverse span, and a relatively small radial thickness. For such structures, a mechanical model is needed to analyze the most dangerous locations in the tunnel and the deformation at those locations after using this technology.

[0003] Currently, the mechanical models for grouting pipe roofs and horizontal jet grouting piles are mainly based on elastic foundation beam models, with limited research on spatial mechanical models. While mechanical models that discretize grouting pipe roofs and horizontal jet grouting piles into independent elastic beams in the longitudinal direction can characterize their stress characteristics to some extent, the discretization assumption weakens the explicit coupling between the spatial synergy of the structural system and key mechanical processes (stress concentration, shear slip), leading to certain biases in the prediction of hazardous areas.

[0004] Secondly, traditional analytical solution methods are insufficient for solving high-order nondifferential equations with varying coefficients. Finally, mechanical models combining densely pre-supported structures with thin-shell mechanics have received relatively little attention. Summary of the Invention

[0005] The purpose of this invention is to provide a mechanical modeling method for thin-shell structures with dense pre-support, addressing the problems of insufficient accuracy and oversimplification of boundary conditions in existing tunnel pre-support mechanical models.

[0006] The above-mentioned objective of this application is achieved through the following technical solution: S1: Establish a continuous thin-shell mechanical model of the pipe roof-jet grouting pile composite dense pre-supported structure; S2: The Pasternak foundation model is adopted, combined with the continuous thin shell mechanical model, and the spatial variation of foundation reaction force and overburden load is quantified by the difference of seven-segment boundary conditions. S3: The continuous thin-shell mechanical model is solved by the finite difference method to obtain the radial displacement, thus completing the mechanical modeling of the pre-support structure of the soft strata in the tunnel engineering.

[0007] Optionally, step S1 includes: The continuous thin-shell mechanical model includes: calculating the equivalent elastic modulus of the composite layer based on Voigt's equivalent theory. And assume equivalent elastic modulus It can be used to calculate the equivalent bending stiffness of a structure. ; The thin-shell mechanical model satisfies the governing equations:

[0008] in: The equivalent bending stiffness of the densely pre-supported structure; For the Laplace operator thin shell, only the α and β directions are considered, i.e., the longitudinal and circumferential directions; This is the normal deformation amount; The equivalent elastic modulus of the densely pre-supported structure; The thickness of the densely pre-supported structure; The radius of the tunnel excavation; Let be a displacement function, representing the radial displacement on the cylindrical surface. external underlying pressure To pre-support the lower support force; assume that the force is uniform in the ring direction.

[0009] Optionally, step S2 includes: The foundation reaction force is determined using the Pasternak foundation model, and the specific expression is as follows:

[0010] in for The subgrade coefficient at the point, for The shear modulus of the foundation at a point; The tunnel's support structure consists of three parts: a densely distributed pre-supported shell structure, the primary support, and the secondary lining section. The secondary lining section is simplified to a fixed end, the closed section of the initial support is simplified to a constant foundation reaction coefficient, and the unclosed section of the initial support is simplified to a linearly decreasing foundation reaction coefficient. The specific expressions are as follows:

[0011] in This represents the variation function of the machine tool coefficient along the longitudinal direction α. The equivalent subgrade coefficient of the initial support. Let be the cycle number of the initial closed segment. Let be the cycle number of the unclosed segment in the initial branch. For the excavation advance, Represents the length of the initial closed segment. This represents the length of the unclosed section of the initial support; The unsupported section has no supporting force; The area in front of the tunnel face is divided into a plastic disturbance section and an elastic disturbance section. In the plastic disturbance section, the supporting force increases linearly with the foundation reaction coefficient, and its specific expression is as follows:

[0012] in The subgrade coefficient of the surrounding rock; The ground reaction coefficient is constant in the elastically disturbed section; there is no bending moment, shear force, rotation, or displacement in the undisturbed section.

[0013] Optionally, step S2 may further include: Quantification of overburden load base It is determined by the following formula:

[0014] in The excavation width is less than the tunnel burial depth. It is a shallow-buried tunnel; The critical depth for deep burial is greater than the tunnel burial depth. For deep-buried tunnels; , and for The coefficient is determined by the following formula:

[0015] in The overlying soil is heavy. For tunnel burial depth, For the cohesion of the surrounding rock, The internal friction angle of the surrounding rock. The width is calculated based on the overlying load. This refers to the excavation height; Considering factors such as the stress release effect of the surrounding rock and the excavation disturbance effect, the magnitude of the overburden load is segmented in the longitudinal direction, and the following simplification is made: The overlying load on the initially closed section is constant. The load on the unsupported section decreases linearly until it reaches a minimum value at the edge of the unsupported section, which is 0.6 times the base value. The unsupported segment increases uniformly to the elastic disturbance segment, reaching its maximum value at the edge of the plastic disturbance segment, which is 1.2 times the base value; the plastic disturbance segment decreases linearly to 0 in the undisturbed segment.

[0016] Optionally, step S3 includes: The OE segment includes: the initial support closed segment OA, the initial support unclosed segment AB, the unsupported segment BC, the plastic disturbance segment CD, and the elastic disturbance segment DE; Add three virtual nodes to the left end of the OE segment, labeled as follows: ; Add three virtual nodes to the right end of the OE segment, labeled as follows: ; The node labels in the OE segment are as follows ; The distance between the two nodes is ; Represents a node Radial displacement at the location; Based on continuity and boundary conditions, the differential equation is derived piecewise using Taylor expansion, and the first six terms of the Taylor expansion are used to represent any node on the OE segment. If the displacement is such that the governing equations are finite, then the specific form after finite difference is as follows:

[0017] in express The equivalent bending stiffness of the thin shell at the point; Represents a node Radial displacement at the location; express The subgrade coefficient of the surrounding rock; express The shear modulus of the surrounding rock.

[0018] Optionally, step S3 may also include: Boundary conditions are set as follows: Point O is considered a fixed end, and the displacement, rotation, bending moment, and shear force at point E are all zero. The following is obtained:

[0019] Measure the displacement at point B and the displacement during the previous excavation cycle, and let the displacements at these two points be . , , ; Substitute the boundary conditions at point B into the equations and calculate the values ​​of each node in segment BE. ,as follows

[0020] Assuming the ring is subjected to uniform force in the upward direction, the displacements of each node in the longitudinal direction can be expressed by matrix multiplication as follows:

[0021] radial displacement for:

[0022] External loads for:

[0023] in , and This represents the coefficient matrix.

[0024] An electronic device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to enable the electronic device to perform a mechanical modeling method for a densely pre-supported thin-shell structure.

[0025] A computer-readable storage medium storing instructions that, when executed, perform a method for mechanical modeling of a densely pre-supported thin-shell structure.

[0026] The beneficial effects of the technical solution provided in this application are: This application establishes a continuous thin-shell mechanical model for a composite densely distributed pre-supported structure of pipe roof and jet grouting piles. Using the Pasternak foundation model, the spatial variation of foundation reaction force and overlying load is quantified through differential segmentation of seven boundary conditions. The radial displacement is obtained by solving the constructed continuous thin-shell mechanical model using the finite difference method, thus completing the mechanical modeling of the pre-supported structure in soft soil strata of tunnel engineering. Combining the composite thin-shell structure formed by jet grouting piles and large pipe roofs, a mechanical model is established using thin-shell theory, and verified through numerical solutions and engineering measurements. This method overcomes the limitations of traditional elastic foundation beam theory, improves the ability to express the mechanical behavior of complex support systems, and provides a theoretical basis for the refined design and safety assessment of pre-supported structures. Attached Figure Description

[0027] The present application will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings: Figure 1 This is a structural diagram of the model construction steps in an embodiment of the present invention; Figure 2 This is a simplified schematic diagram of the bed coefficient segments in an embodiment of the present invention; Figure 3 This is a simplified schematic diagram of the segmentation and boundary conditions of each segment in an embodiment of the present invention; Figure 4 This is a schematic diagram of discrete analysis in an embodiment of the present invention; Figure 5 This is a simplified process diagram of the densely pre-supported structure in an embodiment of the present invention; Figure 6 This is a comparison chart of the results obtained using the analytical method and the finite difference method when the linear differential equations degenerate into constant coefficients in this invention embodiment; Figure 7 This is a comparison chart of the solution results using this model, the displacement calculation results of other models, and the monitoring data used in this embodiment of the invention; Figure 8 This is a comparison chart of the solution results of this model used in the embodiments of the present invention, the bending moment calculation results of other models, and the monitoring data; Figure 9 This is a schematic diagram of the electronic device structure in an embodiment of the present invention. Detailed Implementation

[0028] To provide a clearer understanding of the technical features, objectives, and effects of this application, the specific embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0029] The embodiments of this application provide a method for mechanical modeling of thin-shell structures with dense pre-supported structures.

[0030] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating the steps of a method for mechanical modeling a densely pre-supported thin-shell structure according to an embodiment of this application, including: S1: Establish a continuous thin-shell mechanical model of the pipe roof-jet grouting pile composite dense pre-supported structure; S2: The Pasternak foundation model is adopted, combined with the continuous thin shell mechanical model, and the spatial variation of foundation reaction force and overburden load is quantified by the difference of seven-segment boundary conditions. S3: The continuous thin-shell mechanical model is solved by the finite difference method to obtain the radial displacement, thus completing the mechanical modeling of the pre-support structure of the soft strata in the tunnel engineering.

[0031] This application provides an embodiment as follows, which, when compared with the traditional formula solution, verifies the correctness of the finite difference decomposition method; the calculation results of the model verified by the traditional formula method are compared with real-world cases to further verify the engineering reliability of the model, such as... Figure 5 and Figure 6 As shown, the results indicate that the model's prediction of displacement at the most dangerous location has a relative error of less than 14%, and its prediction of longitudinal bending moment is in good agreement with the actual trend.

[0032] Step S1 includes: The continuous thin-shell mechanical model includes: calculating the equivalent elastic modulus of the composite layer based on Voigt's equivalent theory. And assume equivalent elastic modulus It can be used to calculate the equivalent bending stiffness of a structure. ; The thin-shell mechanical model satisfies the governing equations:

[0033] in: The equivalent bending stiffness of the densely pre-supported structure; For the Laplace operator thin shell, only the α and β directions are considered, i.e., the longitudinal and circumferential directions; This is the normal deformation amount; The equivalent elastic modulus of the densely pre-supported structure; The thickness of the densely pre-supported structure; The radius of the tunnel excavation; Let be a displacement function, representing the radial displacement on the cylindrical surface. external underlying pressure To pre-support the lower support force; assume that the force is uniform in the ring direction.

[0034] This implementation first equates the densely arranged jet grouting piles and pipe roof structure system to a continuous thin-shell structure with uniform mechanical properties. The thin-shell mechanical model is constructed based on the following assumptions: Assumption (1) Shell continuity assumption: The pipe roof and jet grouting piles form a continuous composite through dense arrangement and grouting, which is regarded as a thin shell that is continuous and smooth in the longitudinal and circumferential directions.

[0035] Assumption (2) Elastic homogeneity assumption: The equivalent elastic modulus E, Poisson's ratio ν and bending stiffness D are calculated by the Voigt volume average method, and the shell is simplified to a homogeneous isotropic thin shell.

[0036] Assumption (3) Mid-surface assumption: All deformations unfold along the mid-surface of the shell, applicable to small deformation theory; structural instability is analyzed using geometric linear analysis.

[0037] Assumption (4) Circumferential uniformity: The external load and foundation reaction force in the radial direction are uniformly distributed on the surface of the thin shell and do not change along the circumferential direction.

[0038] Assumption (5) Linear variation: It is assumed that the overburden load and the foundation reaction force vary linearly in the longitudinal direction.

[0039] Step S2 includes: The foundation reaction force is determined using the Pasternak foundation model, and the specific expression is as follows:

[0040] in for The subgrade coefficient at the point, for The shear modulus of the foundation at a point; In a specific embodiment of this application, taking into account both GRC and SCC curves, the SCC curve is segmented, as shown in Figure 2: the tunnel support structure consists of three parts: a densely distributed pre-supported shell structure, an initial support, and a secondary lining section.

[0041] The seven-segment boundary condition simplifies and quantifies the spatial variation of foundation reaction force and overburden load: Secondary lining section (JO section): The furthest from the working face, it is supported by the pre-supported shell, primary support and secondary lining. The secondary lining is strong enough and the deformation is relatively small. Therefore, the small displacement of the JO section is ignored and point O is regarded as the fixed end. Initial support closed section (OA section): The support force of this section is provided by the densely distributed pre-supported shell structure and the initial support. The initial support is completely closed, and the equivalent subgrade coefficient of the initial support is constant. Section AB (Unclosed Initial Support): The support conditions for this section are similar to those for section OA, but the initial support is not closed. The equivalent subgrade coefficient of the initial support decreases linearly from point A (closed state) to point B (initial support installation end) to 0. ; Unsupported section (BC section): This section has neither primary support nor secondary lining, and the upper load is entirely borne by the densely distributed pre-supported shell structure.

[0042] Plastic disturbance section (CD section): This section is supported by a dense network of pre-reinforced structures and the underlying plastic disturbance soil, which provides support to the overlying rock. Plastic deformation of the surrounding rock dominates, and the subgrade coefficient increases from point C to point D. ; Elastic disturbance section (DE section): This section is supported by a densely distributed pre-reinforced structure and the elastic disturbance soil below it, which provides support for the overlying surrounding rock. Elastic deformation of the surrounding rock dominates, and the subgrade coefficient is constant. Undisturbed section (EK section): This section is not affected by excavation disturbance and has no structural deformation. The densely distributed pre-supported shell structure in this section has no displacement, rotation, bending moment and shear force. When the initial support is first installed, its strength has not yet taken effect and the initial support is not closed. The equivalent subgrade coefficient of the initial support at point B is 0. It gradually strengthens from point B to point A. According to assumption (5), this segment increases linearly, as shown in Figure 2(b). When it reaches point A, the initial support is closed, and the equivalent subgrade coefficient reaches a constant value. The OA segment is the same as point A; at point O, the extremely high strength of the secondary lining allows the structure to reach equilibrium with only minor deformation, and increases the slope of the SCC to the right of point O; point L represents the maximum displacement that the support structure can withstand and the maximum pressure that will cause failure. For GRC: at point E, the surrounding soil is undisturbed and does not deform; the DE segment only undergoes elastic deformation, and the surrounding rock subgrade coefficient is a constant value. Irreversible plastic deformation occurred in the surrounding rock of section CD, and the subgrade coefficient gradually decreased from point D to point C (according to assumption (5), this section decreases linearly, as shown in Figure 2(c)), reaching its minimum value at point C (upper bench tunnel face). The GRC and SCC intersect at points O and M. Point O is the new equilibrium point of the system, and point M represents the case with the largest radial displacement without initial support and secondary lining.

[0043] The tunnel's support structure consists of three parts: a densely distributed pre-supported shell structure, the primary support, and the secondary lining section. The secondary lining section is simplified to a fixed end, the closed section of the initial support is simplified to a constant foundation reaction coefficient, and the unclosed section of the initial support is simplified to a linearly decreasing foundation reaction coefficient. The specific expressions are as follows:

[0044] in This represents the variation function of the machine tool coefficient along the longitudinal direction α. The equivalent subgrade coefficient of the initial support. Let be the cycle number of the initial closed segment. Let be the cycle number of the unclosed segment in the initial branch. For the excavation advance, Represents the length of the initial closed segment. This represents the length of the unclosed section of the initial support; The unsupported section has no supporting force; The area in front of the tunnel face is divided into a plastic disturbance section and an elastic disturbance section. In the plastic disturbance section, the supporting force increases linearly with the foundation reaction coefficient, and its specific expression is as follows:

[0045] in The subgrade coefficient of the surrounding rock; The ground reaction coefficient is constant in the elastically disturbed section; there is no bending moment, shear force, rotation, or displacement in the undisturbed section.

[0046] Step S2 also includes: Quantification of overburden load base It is determined by the following formula:

[0047] in The excavation width is less than the tunnel burial depth. It is a shallow-buried tunnel; The critical depth for deep burial is greater than the tunnel burial depth. For deep-buried tunnels; , and for The coefficient is determined by the following formula:

[0048] in The overlying soil is heavy. For tunnel burial depth, For the cohesion of the surrounding rock, The internal friction angle of the surrounding rock. The width is calculated based on the overlying load. This refers to the excavation height; Considering factors such as the stress release effect of the surrounding rock and the excavation disturbance effect, the magnitude of the overburden load is segmented in the longitudinal direction, and the following simplification is made: The overlying load on the initially closed section is constant; The load on the unsupported section decreases linearly until it reaches a minimum value at the edge of the unsupported section, which is 0.6 times the base value. The unsupported segment increases uniformly to the elastic disturbance segment, reaching its maximum value at the edge of the plastic disturbance segment, which is 1.2 times the base value; the plastic disturbance segment decreases linearly to 0 in the undisturbed segment.

[0049] In one specific embodiment of this application, the simplification process may be achieved by... Figure 3 This indicates that segment OA is the initial support closed segment, segment AB is the support unclosed segment, segment BC is the unsupported segment, segment CD is the plastic disturbance segment, and segment DE is the elastic disturbance segment.

[0050] Step S3 includes: In one specific embodiment of this application, such as Figure 4 The finite difference decomposition method shown adds three virtual nodes at both ends, labeled as... .

[0051] The OE segment includes: the initial support closed segment OA, the initial support unclosed segment AB, the unsupported segment BC, the plastic disturbance segment CD, and the elastic disturbance segment DE; Add three virtual nodes to the left end of the OE segment, labeled as follows: ; Add three virtual nodes to the right end of the OE segment, labeled as follows: ; The node labels in the OE segment are as follows ; The distance between the two nodes is ; Represents a node Radial displacement at the location; Based on continuity and boundary conditions, the differential equation is derived piecewise using Taylor expansion, and the first six terms of the Taylor expansion are used to represent any node on the OE segment. If the displacement is such that the governing equations are finite, then the specific form after finite difference is as follows:

[0052] in express The equivalent bending stiffness of the thin shell at the point; Represents a node Radial displacement at the location; express The subgrade coefficient of the surrounding rock; express The shear modulus of the surrounding rock.

[0053] Step S3 also includes: Boundary conditions are set as follows: Point O is considered a fixed end, and the displacement, rotation, bending moment, and shear force at point E are all zero. The following is obtained:

[0054] Measure the displacement at point B and the displacement during the previous excavation cycle, and let the displacements at these two points be . , , ; Substitute the boundary conditions at point B into the equations and calculate the values ​​of each node in segment BE. ,as follows

[0055] Assuming the ring is subjected to uniform force in the upward direction, the displacements of each node in the longitudinal direction can be expressed by matrix multiplication as follows:

[0056] radial displacement for:

[0057] External loads for:

[0058] in , and This represents the coefficient matrix.

[0059] In one specific embodiment of this application, when When the value is large enough, the error of the difference solution can be ignored and the radial displacement of each point in the longitudinal direction can be solved.

[0060] In one specific embodiment of this application, if the subgrade coefficient and external load of each segment are uniform and constant within the segment, it is transformed into a set of fourth-order linear differential equations with constant coefficients, and the value of the characteristic equation is less than zero when substituted into the actual numerical range. Therefore, it can be expressed as follows:

[0061] in These are undetermined coefficients (constants). and The coefficient of α,

[0062]

[0063] By substituting the boundary conditions and the continuity condition that the displacement, rotation angle, bending moment, and shear force at the connection points of each segment are equal, the longitudinal displacement curve can be solved.

[0064] In the description of this invention, it should be understood that in the accompanying drawings, "α" represents the longitudinal direction, with its positive direction representing the right and its negative direction representing the left; "α", "β", and "γ" conform to the left-hand rule, and the orientation or positional relationship indicated by the terms "α", "β", and "γ" is based on the orientation or positional relationship shown in the accompanying drawings and is only for the convenience of describing the invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the specific features, structures, materials, or characteristics described can be combined in any suitable manner in one or more embodiments or examples. The calculation results under simplified conditions are as follows... Figure 6 The results are completely consistent, verifying the accuracy of the model solution.

[0065] Figure 6 and Figure 7 The comparison between this model and existing engineering case monitoring data and existing research calculation results shows that the displacement prediction error of the calculation model proposed in this invention is <14%. In the bending moment verification case, several monitoring points were set up in different geological sections. Based on the on-site measured values, the bed coefficient of the surrounding rock was calculated to be distributed between 5 and 20 kN / m. After calculation, it was found that the model calculation results and the monitoring data showed good agreement on the longitudinal trend of bending moment, which verified the engineering reliability of the model of this invention.

[0066] This application also discloses an electronic device. (See reference...) Figure 9 , Figure 9 This is a schematic diagram of the structure of an electronic device disclosed in an embodiment of this application. The electronic device 500 may include: at least one processor 501, at least one network interface 504, a user interface 503, a memory 505, and at least one communication bus 502.

[0067] The communication bus 502 is used to enable communication between these components.

[0068] The user interface 503 may include a display screen, and optionally, the user interface 503 may also include a standard wired interface or a wireless interface.

[0069] The network interface 504 may optionally include a standard wired interface or a wireless interface (such as a Wi-Fi interface).

[0070] This application also discloses a computer-readable storage medium storing multiple instructions adapted for loading by a processor to execute the above-described method for mechanical modeling of a densely pre-supported thin-shell structure.

[0071] The above are merely exemplary embodiments of this disclosure and should not be construed as limiting the scope of this disclosure. Any equivalent changes and modifications made in accordance with the teachings of this disclosure shall still fall within the scope of this disclosure.

[0072] This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not described in this disclosure. The specification and embodiments are to be considered exemplary only, and the scope and spirit of this disclosure are defined by the claims.

Claims

1. A method for mechanical modeling of a densely pre-supported thin-shell structure, characterized in that, The method includes the following steps: S1: Establish a continuous thin-shell mechanical model of the pipe roof-jet grouting pile composite dense pre-supported structure; S2: The Pasternak foundation model is adopted, combined with the continuous thin shell mechanical model, and the spatial variation of foundation reaction force and overburden load is quantified by the difference segmentation of seven boundary conditions. S3: The radial displacement is obtained by solving the continuous thin-shell mechanical model constructed by the finite difference method, and the mechanical modeling of the pre-support structure of the soft stratum in the tunnel project is completed.

2. The method for mechanical modeling of a densely pre-supported thin-shell structure as described in claim 1, characterized in that, Step S1 includes: The continuous thin-shell mechanical model includes: calculating the equivalent elastic modulus of the composite layer based on Voigt's equivalent theory. And assume equivalent elastic modulus It can be used to calculate the equivalent bending stiffness of a structure. ; The thin-shell mechanical model satisfies the governing equations: in: The equivalent bending stiffness of the densely pre-supported structure; For the Laplace operator thin shell, only the α and β directions are considered, i.e., the longitudinal and circumferential directions; This is the normal deformation amount; The equivalent elastic modulus of the densely pre-supported structure; The thickness of the densely pre-supported structure; The radius of the tunnel excavation; Let be a displacement function, representing the radial displacement on the cylindrical surface. external underlying pressure To pre-support the lower support force; assume that the force is uniform in the ring direction.

3. The method for mechanical modeling of a densely pre-supported thin-shell structure as described in claim 2, characterized in that, Step S2 includes: The foundation reaction force is determined using the Pasternak foundation model, and the specific expression is as follows: in for The subgrade coefficient at the point, for The shear modulus of the foundation at a point; The tunnel's support structure consists of three parts: a densely distributed pre-supported shell structure, the primary support, and the secondary lining section. The secondary lining section is simplified to a fixed end, the closed section of the initial support is simplified to a constant foundation reaction coefficient, and the unclosed section of the initial support is simplified to a linearly decreasing foundation reaction coefficient. The specific expressions are as follows: in This represents the variation function of the machine tool coefficient along the longitudinal direction α. The equivalent subgrade coefficient of the initial support. Let be the cycle number of the initial closed segment. Let be the cycle number of the unclosed segment in the initial branch. For the excavation advance, Represents the length of the initial closed segment. This represents the length of the unclosed section of the initial support; The unsupported section has no supporting force; The area in front of the tunnel face is divided into a plastic disturbance section and an elastic disturbance section. In the plastic disturbance section, the supporting force increases linearly with the soil reaction coefficient, and its specific expression is as follows: in The subgrade coefficient of the surrounding rock; The ground reaction coefficient is constant in the elastically disturbed section; there is no bending moment, shear force, rotation, or displacement in the undisturbed section.

4. The method for mechanical modeling of a densely pre-supported thin-shell structure as described in claim 3, characterized in that, Step S2 also includes: Quantification of overburden load base It is determined by the following formula: in The excavation width is less than the tunnel burial depth. It is a shallow-buried tunnel; The critical depth for deep burial is greater than the tunnel burial depth. For deep-buried tunnels; , and for The coefficient is determined by the following formula: in The overlying soil is heavy. For tunnel burial depth, For the cohesion of the surrounding rock, The internal friction angle of the surrounding rock. The width is calculated based on the overlying load. This refers to the excavation height; Considering factors such as the stress release effect of the surrounding rock and the excavation disturbance effect, the magnitude of the overburden load is segmented in the longitudinal direction, and the following simplification is made: The overlying load on the initially closed section is constant; The load on the unsupported section decreases linearly until it reaches a minimum value at the edge of the unsupported section, which is 0.6 times the base value. The value increases uniformly from the unsupported segment to the elastic disturbance segment, reaching its maximum value at the edge of the plastic disturbance segment, which is 1.2 times the base value; the plastic disturbance segment decreases linearly until the undisturbed segment is 0.

5. The method for mechanical modeling of a densely pre-supported thin-shell structure as described in claim 4, characterized in that, Step S3 includes: The OE segment includes: the initial support closed segment OA, the initial support unclosed segment AB, the unsupported segment BC, the plastic disturbance segment CD, and the elastic disturbance segment DE; Add three virtual nodes to the left end of the OE segment, labeled as follows: ; Add three virtual nodes to the right end of the OE segment, labeled as follows: ; The node labels in the OE segment are as follows ; The distance between the two nodes is ; Represents a node Radial displacement at the location; Based on continuity and boundary conditions, the differential equation is derived piecewise using Taylor expansion, and the first six terms of the Taylor expansion are used to represent any node on the OE segment. If the displacement is such that the governing equations are finite, then the specific form after finite difference is as follows: in express The equivalent bending stiffness of the thin shell at the point; Represents a node Radial displacement at the location; express The subgrade coefficient of the surrounding rock; express The shear modulus of the surrounding rock.

6. The method for mechanical modeling of a densely pre-supported thin-shell structure as described in claim 4, characterized in that, Step S3 also includes: Boundary conditions are set as follows: Point O is considered a fixed end, and the displacement, rotation, bending moment, and shear force at point E are all zero. The following is obtained: Measure the displacement at point B and the displacement during the previous excavation cycle, and let the displacements at these two points be . , , ; Substitute the boundary conditions at point B into the equations and calculate the values ​​of each node in segment BE. ,as follows Assuming the ring is subjected to uniform force in the upward direction, the displacements of each node in the longitudinal direction can be expressed by matrix multiplication as follows: radial displacement for: External loads for: in , and This represents the coefficient matrix.

7. An electronic device, characterized in that, The device includes a processor, a memory, a user interface, and a network interface. The memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory to cause the electronic device to perform the method as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores instructions that, when executed by a computer, perform the method as described in any one of claims 1-6.

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