A semi-analytical method and system for deep-buried tunnels based on excavation compensation

Abstract

This application provides a semi-analytical method, system, medium, equipment, and computer program product for deep-buried tunnels based on excavation compensation, belonging to the field of tunnel engineering technology. For the coordinated deformation stage of the stratum response, the finite difference method is used to divide the tunnel excavation process into m unloading stages. A calculation model considering the unloading path and the coordinated deformation of NPR anchors / cables and surrounding rock is constructed. Combining surrounding rock mechanical parameters, initial boundary conditions, and NPR anchor / cable parameters, the stratum response at each stage is solved, and then an excavation compensation scheme for deep-buried tunnels is designed based on the solution results. This method considers the unloading path and studies the influence of NPR anchors / cables on the stratum response through the semi-analytical ECM calculation method of the interaction between NPR anchors / cables and surrounding rock. By analyzing the interaction mechanism between NPR anchors / cables and surrounding rock, guidance is provided for the application of ECM in deep-buried tunnels.

Description

Technical Field

[0001] This application relates to the field of tunnel engineering technology, and in particular to a semi-analytical method, system, medium, equipment and computer program product for deep buried tunnels based on excavation compensation. Background Technology

[0002] As underground engineering projects gradually extend deeper into the strata, problems such as large deformation of soft rock and rock bursts caused by deep rock excavation become more prominent, posing more challenges to the construction of deep-buried tunnels.

[0003] Considering the effects of tunnel excavation, some scholars have proposed the Excavation Compensation Method (ECM) for deep-buried tunnels, and it has been successfully applied to disaster control during the construction of several deep-buried tunnels. ECM posits that tunnel failure is caused by excavation, with two main excavation effects: stress redistribution and surrounding rock degradation. After excavation, the radial stress of the surrounding rock rapidly decreases to zero, while tangential stress concentrates, transforming the stress state from a true triaxial stress state to a biaxial / uniaxial stress state, leading to rock degradation and the formation of a plastic zone. The purpose of ECM is to provide high-prestress compensation before surrounding rock failure. Therefore, the Excavation Compensation Method (ECM), using high-strength, high-toughness NPR anchors / cables as the core material, plays a positive role in disaster control for deep-buried tunnels.

[0004] However, the interaction mechanism between NPR anchors / cables and the surrounding rock under ECM is still unclear. Therefore, an improved technical solution is needed to address the shortcomings of the existing technology. Summary of the Invention

[0005] The purpose of this application is to provide a semi-analytical method, system, medium, equipment, and computer program product for deep buried tunnels based on excavation compensation, so as to solve or alleviate the problems existing in the prior art.

[0006] To achieve the above objectives, this application provides the following technical solution:

[0007] Firstly, this application provides a semi-analytical method for deep-buried tunnels based on excavation compensation, including:

[0008] Step S1: Obtain the surrounding rock mechanical parameters, initial boundary conditions, and NPR anchor / cable parameters for the deep-buried tunnel;

[0009] Step S2: For the collaborative deformation stage of the stratum response, the tunnel excavation process is divided into m unloading stages to obtain a calculation model of the collaborative deformation of NPR anchors / cables and surrounding rock considering the unloading path.

[0010] The collaborative deformation stage is the stage in which the surrounding rock and the NPR anchor / cable jointly cause formation deformation after the NPR anchor / cable is installed. The calculation model for the collaborative deformation of the NPR anchor / cable and the surrounding rock includes: dividing the surrounding rock in each unloading stage into n toroidal surfaces of equal thickness, each toroidal surface being enclosed by nodes with inner and outer radii of r(i) and r(i+1) respectively; using variables with two dimensions to characterize the mechanical state of the surrounding rock at each node; the two dimensions include a first dimension and a second dimension, the first dimension being the radius and the second dimension being the unloading stage; m and n are positive integers, and i is the node number, with a value range of 1, 2, ..., n;

[0011] Step S3: Based on the calculation model of the coordinated deformation of NPR anchors / cables and surrounding rock, and combined with the mechanical parameters of surrounding rock, initial boundary conditions, and NPR anchors / cables, the finite difference method is used to solve the ground response of each unloading stage, and the solution results of the ground response of the tunnel under the action of NPR anchors / cables are obtained.

[0012] Step S4: Based on the solution results of the ground response of the tunnel under the action of NPR anchors / cables, determine the excavation compensation scheme for the deep-buried tunnel.

[0013] In conjunction with the first aspect, among some possible implementation methods, based on the calculation model of the coordinated deformation of NPR anchors / cables and surrounding rock, and combining the surrounding rock mechanical parameters, initial boundary conditions, and NPR anchor / cable parameters, the finite difference method is used to solve for the ground response at each unloading stage, obtaining the solution results of the tunnel's ground response under the action of NPR anchors / cables, including:

[0014] Based on incremental theory, the change in virtual support pressure of the tunnel wall, Δpi, is calculated at each unloading stage.

[0015] Based on the change in virtual support pressure Δpi in the tunnel wall, combined with the surrounding rock mechanics parameters and NPR anchor / cable parameters, the boundary conditions for each unloading stage are updated.

[0016] Based on the equilibrium equation and yield equation of the surrounding rock, the stress distribution at each unloading stage is solved using the Runge-Kutta method.

[0017] Calculate the displacement distribution at each unloading stage;

[0018] Update the surrounding rock mechanics parameters and NPR anchor / cable parameters for each unloading stage.

[0019] In conjunction with the first aspect, in some possible implementations, based on the equilibrium equations and yield equations of the surrounding rock, the Runge-Kutta method is used to solve for the stress distribution at each unloading stage, including:

[0020] In each unloading stage, it is first assumed that the surrounding rock is in a plastic state. Based on the preset initial conditions, the radial stress of each node is solved using the Runge-kutta method.

[0021] If the radial stress at each node is greater than the radial stress at the boundary of the elasto-plastic region, then the radius R of the plastic region is determined. p The value is 0, and the stress state at all nodes and the displacement of all nodes are updated according to the tunnel radius R0;

[0022] If the radial stress at each node is less than or equal to the radial stress at the boundary of the elastoplastic region, then the radius R of the plastic region is determined. p Greater than 0, and based on the radius R of the plastic zone p Update the stress state and displacement of the elastic and plastic regions respectively.

[0023] In conjunction with the first aspect, the surrounding rock mechanical parameters for each unloading stage are updated as follows:

[0024] When the radius of the plastic zone R p If the value is greater than 0, the plastic shear strain of the surrounding rock is updated based on the elastic strain increment and plastic strain increment of the surrounding rock.

[0025] In conjunction with the first aspect, among some possible implementations, the NPR anchor / cable parameters are updated, including:

[0026] When the deformation of the NPR anchor / cable exceeds the maximum deformation, the axial force p of the NPR anchor / cable will be... s Set to 0; otherwise, update the axial force of the NPR anchor / cable based on the displacement difference of the NPR anchor / cable.

[0027] Secondly, this application provides a semi-analytical system for deep-buried tunnels based on excavation compensation, comprising:

[0028] The parameter acquisition module is used to acquire the surrounding rock mechanical parameters, initial boundary conditions, and NPR anchor / cable parameters of the deep-buried tunnel.

[0029] The model building module is used to divide the tunnel excavation process into m unloading stages for the collaborative deformation stage of the stratum response using the finite difference method, and obtains a calculation model of the collaborative deformation of NPR anchors / cables and surrounding rock considering the unloading path.

[0030] The collaborative deformation stage is the stage in which the surrounding rock and the NPR anchor / cable jointly cause formation deformation after the NPR anchor / cable is installed. The calculation model for the collaborative deformation of the NPR anchor / cable and the surrounding rock includes: dividing the surrounding rock in each unloading stage into n toroidal surfaces of equal thickness, each toroidal surface being enclosed by nodes with inner and outer radii of r(i) and r(i+1) respectively; using variables with two dimensions to characterize the mechanical state of the surrounding rock at each node; the two dimensions include a first dimension and a second dimension, the first dimension being the radius and the second dimension being the unloading stage; m and n are positive integers, and i is the node number, with a value range of 1, 2, ..., n;

[0031] The solution module is used to calculate the formation response at each stage based on the calculation model of NPR anchor / cable and surrounding rock co-deformation, combined with surrounding rock mechanical parameters, initial boundary conditions, and NPR anchor / cable parameters, to obtain the solution results of the formation response of the tunnel under the action of NPR anchor / cable.

[0032] The design module is used to determine the excavation compensation scheme for deep-buried tunnels based on the solution results of the ground response of the tunnel under NPR anchor / cable action.

[0033] Thirdly, embodiments of this application provide a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the steps of the semi-analytical method for deep-buried tunnels based on excavation compensation described in any of the above embodiments.

[0034] Fourthly, embodiments of this application provide an electronic device, including: a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the semi-analytical method for deep-buried tunnels based on excavation compensation described in any of the above embodiments.

[0035] Fifthly, this embodiment provides a computer program product containing computer-executable instructions, which are used to cause a computer to perform the steps of the semi-analytical method for deep-buried tunnels based on excavation compensation described in any of the above embodiments.

[0036] The technical solution of this application embodiment has the following beneficial effects:

[0037] In this embodiment, for the cooperative deformation stage of the stratum response, the finite difference method is used to divide the tunnel excavation process into m unloading stages. A calculation model considering the unloading path and the cooperative deformation of NPR anchors / cables and surrounding rock is constructed. Combining the surrounding rock mechanical parameters, initial boundary conditions, and NPR anchor / cable parameters, the stratum response of each stage is solved, and then the excavation compensation scheme for deep-buried tunnels is designed based on the solution results. This method considers the unloading path and, based on the finite difference method, proposes a semi-analytical ECM method for the interaction between NPR anchors / cables and surrounding rock to study the influence of NPR anchors / cables on stratum reaction forces. By analyzing the interaction mechanism between NPR anchors / cables and surrounding rock, guidance is provided for the application of ECM in deep-buried tunnels. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of an electronic device provided according to some embodiments of this application.

[0039] Figure 2 This is a flowchart illustrating a semi-analytical method for deep-buried tunnels based on excavation compensation, provided according to some embodiments of this application.

[0040] Figure 3 This is a schematic diagram of a deep circular tunnel model provided according to some embodiments of this application.

[0041] Figure 3a Force-displacement curves for ordinary anchor bolts / cables, prestressed NPR anchor bolts / cables, and unprestressed NPR anchor bolts / cables.

[0042] Figure 4 This is a schematic diagram of a calculation model for the coordinated deformation of NPR anchor bolts / cables and surrounding rock according to some embodiments of this application.

[0043] Figure 4a This is a schematic diagram of the technical steps of the ECM semi-analysis method provided according to some embodiments of this application.

[0044] Figure 5 This is a two-dimensional simulation model created in FLAC3D.

[0045] Figure 6 This is a schematic diagram comparing stress and displacement without the application of NPR anchors / cables.

[0046] Figure 7 This is a schematic diagram of the stress distribution when using NPR anchors / cables.

[0047] Figure 8 This is a schematic diagram comparing stress and displacement when NPR anchors / cables are used. Detailed Implementation

[0048] The embodiments of this application will now be described with reference to the accompanying drawings.

[0049] The embodiments of this application can be applied to Figure 1 Among the electronic devices shown, the electronic devices may be, but are not limited to, mobile terminals such as mobile phones, tablets, handheld computers, and personal digital assistants (PDAs), smart home devices such as smart TVs and smart cameras, wearable devices such as smart bracelets, smartwatches, and smart glasses, or other computer devices such as desktop, laptop, notebook, ultra-mobile personal computer (UMPC), netbook, and smart screen.

[0050] like Figure 1 As shown, the electronic device 200 may include one or more of the following components: a processor 201, a memory 203, a communication interface 202, and a communication bus 204. The memory 203 can be connected to the processor 201 via the bus 204. The bus can transfer data between the processor 201 and the memory 203. The bus can be divided into an address bus, a data bus, a control bus, etc.

[0051] Processor 201 may include one or more processing cores. Processor 201 can connect to various parts within the electronic device 200 using various interfaces and lines. It performs various functions and processes data by running or executing instructions, programs, code sets, or instruction sets stored in memory 203, and by calling data stored in memory 203. For example, processor 201 may include an application processor (AP), a modem processor, a CPU, a graphics processing unit (GPU), an image signal processor (ISP), a controller, a video codec, a digital signal processor (DSP), a field-programmable gate array (FPGA), a programmable logic array (PLA), and / or a neural network processing unit (NPU). The CPU primarily handles the operating system, user interface, and applications; the GPU is responsible for rendering and drawing the content to be displayed; the NPU implements artificial intelligence (AI) functions; and the modem handles wireless communication. Different processing units can be independent devices or integrated into one or more processors. For example, the multiple processing units shown above are all integrated into a single SoC, or the AP is a separate semiconductor chip, while other processing units are integrated into a single SoC. This application does not limit this to any particular type.

[0052] The memory 203 may include random access memory (RAM), read-only memory (ROM), or non-transitory computer-readable storage medium. The memory 203 can be used to store instructions, programs, code, code sets, or instruction sets. The memory 203 may include a program storage area and a data storage area. The program storage area may store instructions for implementing an operating system or instructions for at least one function, such as a semi-analytical method for deep-buried tunnels based on excavation compensation. The data storage area may store data created based on the use of the electronic device 200, such as input data related to deep-buried tunnels.

[0053] In addition, those skilled in the art will understand that the structure of the electronic device 200 shown in the above figures does not constitute a limitation on the electronic device 200. The electronic device may include more or fewer components than shown, or combine certain components, or have different component arrangements. For example, the electronic device 200 may also include components such as a microphone, speaker, radio frequency circuit, sensor, audio circuit, power supply, and Bluetooth module, which will not be described in detail here.

[0054] This application provides a semi-analytical method for deep-buried tunnels based on excavation compensation, which describes the interaction mechanism between NPR anchors / cables and surrounding rock during the excavation of deep-buried tunnels, accurately reflects the influence of NPR anchors / cables on the stratum response, and provides guidance for the application of ECM in deep-buried tunnels.

[0055] Figure 2 This is a flowchart illustrating a semi-analytical method for deep-buried tunnels based on excavation compensation, provided according to some embodiments of this application.

[0056] like Figure 2 As shown, the semi-analytical method for deep-buried tunnels based on excavation compensation includes:

[0057] Step S1: Obtain the surrounding rock mechanical parameters, initial boundary conditions, and NPR anchor / cable parameters for the deep-buried tunnel.

[0058] Among them, the surrounding rock mechanical parameters include at least: plastic shear strain; the NPR anchor / cable parameters include: support time, prestress magnitude and constant resistance value; and the initial boundary conditions include: initial original rock stress p0.

[0059] Furthermore, the surrounding rock mechanical parameters may also include: compressive strength, shear strength, elasticity model, Poisson's ratio, etc.; NPR anchor / cable parameters may also include: number of NPR anchors / cables, location, etc.

[0060] Understandably, the above parameters can be obtained through indoor tests (such as uniaxial tests or triaxial tests) after rock mass sampling, or through in-situ tests.

[0061] The research object of this embodiment is a deep-buried circular tunnel (hereinafter referred to as a deep circular tunnel). The geological response during the excavation of a deep-buried circular tunnel can be simplified as a "thick-walled cylinder" model.

[0062] Figure 3 This is a schematic diagram of a deep circular tunnel model provided according to some embodiments of this application. (a) is a schematic diagram of the tunnel model, and (b) is a schematic diagram of the interaction between the NPR anchor / cable and the surrounding rock.

[0063] like Figure 3As shown, a deeply buried circular tunnel with radius R0 is assumed to be located in a homogeneous, continuous, and isotropic rock mass, subjected to hydrostatic pressure p0. The surrounding rock mass exhibits strain softening behavior, including plastic, elastic, and elasto-plastic (EP) zones. A constitutive model reflecting the mechanical properties of ideal elasto-plastic or strain-softened rock mass is employed. Considering the three-dimensional spatial effects during tunnel construction, a uniform radial support pressure p is assumed on the tunnel wall. i As the working face advances, p i The displacement u of the tunnel wall gradually decreases. r0 Gradually increase, once p i If the support pressure is less than the critical support pressure, a radius of R will appear. p The plastic zone. L is the length of the NPR anchor / cable.

[0064] Suppose when p i Reduce to p a At that time, end anchor NPR anchor bolts / cables are used for support. Figure 3 Figure (b) shows the interaction model between the NPR anchor / cable and the surrounding rock. The force exerted by the NPR anchor / cable on the tunnel wall (i.e., the axial force of the NPR anchor / cable) can be simplified to a radially uniform support pressure p. s Because NPR anchors / cables elongate with the deformation of the surrounding rock, p s It can be calculated using the following formula:

[0065]

[0066] In the formula, p s For radially uniform support pressure, S a and S b These refer to the circumferential and longitudinal spacing of the NPR anchor bolts / cables, respectively.

[0067] Step S2: For the collaborative deformation stage of the stratum response, the tunnel excavation process is divided into m unloading stages using the finite difference method, resulting in a calculation model of the collaborative deformation of NPR anchors / cables and surrounding rock considering the unloading path.

[0068] The synergistic deformation stage is the stage after the NPR anchor / cable is installed, where the surrounding rock and the NPR anchor together cause stratum deformation.

[0069] It should be noted that, based on the installation time of the NPR anchor / cable, the ground response can be divided into three stages: i) Initial deformation stage: This stage occurs before the installation of the NPR anchor / cable, and the surrounding rock is the only bearing medium. ii) Prestressing stage: At the end of this stage, the displacements of the inner and outer anchoring ends of the NPR anchor / cable are u... in-i and u ex-iiii) Co-deformation stage: This stage occurs after the NPR anchor / cable is installed. The surrounding rock and the NPR anchor / cable deform together. At the end of the co-deformation stage, the displacements of the inner and outer anchoring ends of the NPR anchor / cable are u, respectively. in-f and u ex-f .

[0070] Considering the initial deformation Δu generated when prestress F0 is applied p The deformation of the NPR anchor / cable during the coordinated deformation stage and the resulting axial force F of the NPR anchor / cable are calculated using the following formula:

[0071] Δu2=(u ex-f -u ex-i )-(u in-f -u in-i (2)

[0072] F = E b Δu=E b (Δu2+Δu1) (3)

[0073] In the formula, Δu2 is the deformation of the NPR anchor / cable during the coordinated deformation stage, i.e., the displacement difference between the two ends of the NPR anchor / cable; Δu1 is the initial deformation generated when the prestress F0 is applied; and the total elongation Δu = Δu2 + Δu1. in-i u ex-i These are the displacements of the inner and outer anchoring ends of the NPR anchor / cable during the prestressing stage, u ex-f u in-f These represent the displacements of the inner and outer anchoring ends of the NPR anchor bolt / cable during the coordinated deformation stage, respectively; F is the axial force of the NPR anchor bolt / cable; and E... b It refers to the stiffness of the NPR anchor bolt / cable.

[0074] The purpose of this embodiment is to study the interaction mechanism between NPR anchors / cables and the surrounding rock, and to propose a semi-analytical solution for ECM stratum response considering the unloading path, namely, a semi-analytical method for deep-buried tunnels based on excavation compensation. Therefore, for the collaborative deformation stage of the stratum response, a calculation model for the collaborative deformation of NPR anchors / cables and the surrounding rock considering the unloading path is constructed using the finite difference method. This calculation model divides the tunnel excavation process into m unloading stages, calculates the boundary conditions, surrounding rock stress and displacement, and updates parameters for each stage to reflect the influence of the unloading path on the collaborative deformation of NPR anchors / cables and the surrounding rock.

[0075] In other words, the proposed semi-analytical method for deep-buried tunnels based on excavation compensation consists of a total of m unloading stages, each stage including four steps: updating boundary conditions, calculating the stress and displacement distribution of the surrounding rock, and updating parameters.

[0076] Figure 3aForce-displacement curves are shown for ordinary anchor bolts / cables, prestressed NPR anchor bolts / cables, and unprestressed NPR anchor bolts / cables. Figure 3a As shown in the figure, the red dashed line represents prestressed active support, and the black solid line represents passive support. It can be seen from the figure that as the deformation of the anchor bolt / cable increases, the axial force of both ordinary NPR anchor bolts / cables and NPR anchor bolts / cables increases from 0 to a maximum value F. C The corresponding deformation is Δu c Assuming the prestress applied to the NPR anchor / cable is F0, and at the end of the prestressing stage, the deformation (displacement) of the NPR anchor / cable is Δu1. The axial force of the NPR anchor / cable will increase from F0 to its maximum value F. C As deformation increases further, ordinary anchor bolts / cables will break quickly due to their smaller elongation. However, the axial force of NPR anchor bolts / cables will remain constant, i.e., the set constant resistance value F. C Once the deformation of the NPR anchor / cable exceeds the set maximum deformation Δu... f The NPR anchor / cable will break, F=0, and when F is reached... C The deformation of NPR anchors / cables with and without prestress is the same. Therefore, when studying the interaction between NPR anchors / cables and the surrounding rock, the tensile fracture process of the NPR anchors / cables should be considered to improve the accuracy of the calculations.

[0077] The following is a more detailed description of the calculation model for the coordinated deformation of NPR anchors / cables and surrounding rock. The calculation model is as follows: the surrounding rock is divided into n toroidal surfaces of equal thickness, and each toroidal surface is surrounded by nodes with inner and outer radii of r(i) and r(i+1) respectively; variables with two dimensions are used to characterize the mechanical state of the surrounding rock at each node; the two dimensions include a first dimension and a second dimension, the first dimension being the radius and the second dimension being the unloading stage.

[0078] Where m and n are both positive integers greater than 1, and i is the node number, which takes values ​​from 1 to 2 to m.

[0079] Figure 4 This is a schematic diagram of a calculation model for the coordinated deformation of NPR anchor bolts / cables and surrounding rock according to some embodiments of this application.

[0080] like Figure 4 As shown, assume the surrounding rock consists of n small toroidal surfaces of equal thickness, where the i-th toroidal surface is enclosed by two computational nodes with radii r(i-1) and r(i). Each node corresponds to a mechanical state of the surrounding rock, such as radial stress σ. rAll variables representing the surrounding rock mechanical state at each node contain two dimensions. The first dimension represents a stage of stress release, i.e., the unloading stage, and the second dimension represents a location at a radius r, i.e., the radius of the calculation node. For example, the first dimension might be k, representing the k-th unloading stage, and the second dimension might be r(i), representing the radius at the i-th node.

[0081] The variables of the surrounding rock mechanical state at each node all contain two dimensions, for example, σ. r To represent radial stress, σ r (k,r) represents the radial stress at radius r in the k-th stage of stress release, which is the radial stress at radius r in the k-th unloading stage. For each unloading stage, the finite difference method is used to solve the formation response.

[0082] Step S3: Based on the calculation model of the coordinated deformation of NPR anchors / cables and surrounding rock, and combined with the mechanical parameters of the surrounding rock, initial boundary conditions, and NPR anchors / cables, the ground response at each stage is solved to obtain the solution results of the ground response of the tunnel under the action of NPR anchors / cables.

[0083] Specifically, based on the calculation model of the coordinated deformation of NPR anchors / cables and surrounding rock, and combining the surrounding rock mechanical parameters, boundary conditions, and NPR anchor / cable parameters, the ground response at each stage is solved to obtain the solution results of the tunnel's ground response under the action of NPR anchors / cables, including:

[0084] Step S31: Based on incremental theory, calculate the change Δp of the virtual support pressure on the tunnel wall at each unloading stage. i ;

[0085] Step S32: Based on the change in virtual support pressure Δp of the tunnel wall i By combining the surrounding rock mechanical parameters and NPR anchor / cable parameters, the boundary conditions for each unloading stage are updated;

[0086] Step S33: Based on the equilibrium equation and yield equation of the surrounding rock, use the Runge-kutta method to solve for the stress distribution at each unloading stage;

[0087] Step S34: Calculate the displacement distribution at each unloading stage;

[0088] Step S35: Update the surrounding rock mechanical parameters and NPR bolt / cable parameters for each unloading stage.

[0089] The above steps will be explained in detail below with specific implementation examples.

[0090] In step S31, based on the calculation model of the coordinated deformation of NPR anchors / cables and surrounding rock, considering the unloading path, and using incremental theory, the excavation process of the deep-buried tunnel is simplified as the virtual support pressure of the tunnel wall gradually decreases along the unloading path. Therefore, the initial original rock stress (hydrostatic pressure p0) is uniformly divided into m equal parts. Then, based on the surrounding rock mechanical parameters, initial boundary conditions, NPR anchor / cable parameters, etc., the stratum response of each unloading stage is solved one by one to obtain the solution result of the stratum response of the tunnel under the action of NPR anchors / cables.

[0091] The change in virtual support pressure of the tunnel wall at each unloading stage Δp i It can be calculated using the following formula:

[0092]

[0093] In other words, the calculation model of NPR anchor / cable and surrounding rock co-deformation divides stress release into m unloading stages, and the virtual support pressure of the tunnel wall in adjacent stages is calculated according to Δp. i By gradually decreasing the force, the finite difference method is used to solve for the ground response of the tunnel under the action of NPR anchors / cables at each stage, including stress distribution, deformation distribution and surrounding rock convergence constraint curve, and to study the influence of NPR anchors / cables on the ground reaction force.

[0094] In step S32, assume that when p i Press Δp i The change gradually decreases to p a When end anchor NPR bolt / cable support is used, the corresponding unloading stage is the j-th unloading stage. The boundary conditions for the entire stress release process can be calculated as follows:

[0095]

[0096] In the formula, p bk The boundary conditions for the k-th unloading stage during stress release are: p0, pk, and pk. s It provides radially uniform support pressure.

[0097] It should be noted that after using NPR anchors / cables, the axial force of the NPR anchors / cables will affect the boundary conditions. Therefore, during the prestressing and coordinated deformation stages after using NPR anchors / cables, it is necessary to first calculate the radial uniform support pressure p according to formula (1). s Then, it is combined with the initial original rock stress p0 and the total change in virtual support pressure of the tunnel wall kΔp during the k unloading stages. i Summation is performed to update the boundary conditions.

[0098] It should also be noted that in this embodiment, the stress relief factor method is used to simulate the unloading and deformation process of the NPR anchor / cable with the surrounding rock. That is, it is assumed that when the stress relief coefficient α = α0, p i Reduce to p a Use NPR anchor bolts / cables. That is, the critical value p for using NPR anchor bolts / cables. a The stress relief coefficient α can be simulated by taking different values. By changing the value α0 of the stress relief coefficient α, the timing of the use of NPR anchor bolts / cables can be changed, thereby simulating the interaction between NPR anchor bolts / cables and surrounding rock under different unloading processes.

[0099] The purpose of step S33 is to perform stress redistribution calculations. A detailed description follows:

[0100] First, determine the basic equations of the surrounding rock, including: equilibrium equation, yield equation, and geometric equation.

[0101] Considering the infinitesimal elements in polar coordinates, the equilibrium equations of the surrounding rock can be written in the following form:

[0102]

[0103] In the formula, σ r and σ θ These represent radial stress and tangential stress, respectively; r represents the radial distance, i.e., the radius, ω represents the azimuth angle, and L... z The axial thickness of the tunnel is represented by dω, dr, and dσ. r These are the differentials of the azimuth angle, radius, and radial stress, respectively.

[0104] In infinitesimal elements, Then formula (6) can be rewritten as follows:

[0105]

[0106] Within the elastic region, σ r and σ θ The sum is 2p0, therefore, formula (7) can be written as follows:

[0107]

[0108] In the plastic zone, the stress state of the surrounding rock should also satisfy the yield equation f(σ). r Formula (7) can be expressed as follows:

[0109]

[0110] The geometric equations of the surrounding rock are as follows:

[0111]

[0112] In the formula, ε r and ε θ These are radial and tangential displacements, respectively.

[0113] Based on the established fundamental equations of the surrounding rock, the stress distribution of the surrounding rock can be obtained using the Runge-Kutta method to solve for the stress distribution at each unloading stage. This process further includes the following specific steps:

[0114] Step S331: In each unloading stage, it is first assumed that the surrounding rock is in a plastic state. Based on the preset initial conditions, the radial stress of each node is solved using the Runge-Kutta method (i.e., the Runge-Kutta solution method).

[0115] Step S332: If the radial stress at each node is greater than the radial stress at the boundary of the elastoplastic region, then determine the radius R of the plastic region. p The value is 0, and the stress state at all nodes and the displacement of all nodes are updated according to the tunnel radius R0;

[0116] Step S333: If the radial stress at each node is less than or equal to the radial stress at the boundary of the elastoplastic region, then determine the radius R of the plastic region. p Greater than 0, and based on the radius R of the plastic zone p Update the stress state and displacement of the elastic and plastic regions respectively.

[0117] In step S331, the expression for the iteration step size function of the Runge-kutta solution method is as follows:

[0118]

[0119] In the formula, H is the step size function in the Runge-Kutta solution method, and σ ci σ3 is the uniaxial compressive strength, σ3 is the minimum principal stress, and m is the uniaxial compressive strength. b s are both Hoek-Brown parameters.

[0120] In each unloading stage, it is first assumed that the surrounding rock is in a plastic state, and then the initial condition p is applied. s =0, calculate the radial stress at each node during this unloading stage, as shown in the following expression:

[0121]

[0122] h = r(i+1) - r(i) (14)

[0123] k1=H(r(i),σ r(k,r(i)) (15)

[0124]

[0125] In the formula, k is the sequence number of the unloading stage, indicating the kth unloading stage, r(i) and r(i+1) are the radii of nodes i and i+1 respectively, h is the iteration step size, which can be calculated according to formula (14), and k1, k2, k3 and k4 are the slope estimates for each iteration, which can be calculated according to formulas (15) to (18).

[0126] Referring to the calculation methods of existing research (see Xiao et al. (2023)), the radial stress σ at the boundary EP of the elastoplastic region is calculated. rp .

[0127] Furthermore, due to the radial stress σ at the boundary EP of the elastoplastic region... rp It is a constant, therefore, the true plastic zone radius R p Corresponding to σ r Less than σ rp Therefore, it can be determined whether the radial stress at each node is less than the radial stress σ at the boundary EP of the elasto-plastic region. rp To determine whether a plastic zone has been generated.

[0128] If the radial stress at each node is greater than the radial stress σ at the boundary of the elastoplastic region rp If no plastic region is generated, then it is determined that R is not generated. p If the value is 0, then the stress state of all calculated nodes needs to be updated:

[0129]

[0130] If the radial stress at each node is less than or equal to the radial stress σ at the boundary of the elastoplastic region rp If so, it is determined that a plastic region has been formed, R p >r0 (r0 is the tunnel radius, r0 = R0), based on the radius R of the plastic zone p Update the stress state and displacement of the elastic and plastic regions respectively.

[0131] The stress state update steps are as follows:

[0132] The radial stress σ at node i within the plastic zone r(k,r(i)) Substituting into the yield equation, the tangential stress σ at that node can be calculated. θ(k,r(i)) .

[0133] The stress state in the elastic zone needs to be updated using the following formula:

[0134]

[0135] In step S34, displacement redistribution calculation is performed to update the displacement. Depending on whether a plastic zone is generated, the displacement redistribution calculation includes the following steps:

[0136] When R p =0, the displacement distribution can be calculated using the following formula:

[0137]

[0138] When R p >r0, the solution within the elastic zone can be calculated using the following formula:

[0139]

[0140] In the formula, u r Let σ be the displacement at radius r. rp G represents the critical support pressure when the surrounding rock exhibits a plastic zone, and G is the rock mass shear modulus.

[0141] The displacement distribution in the plastic zone is related to the degree of unloading in the plastic zone. Therefore, all mechanical variables can be written in incremental form. The total strain increment of the surrounding rock can be divided into elastic strain increment and plastic strain increment, and the calculation formula is as follows:

[0142]

[0143] In the formula, and These are the elastic radial strain increment and elastic tangential strain increment at node i in the unloading stage k, respectively; and These are the plastic radial strain increment and plastic tangential strain increment at node i in the unloading stage k, respectively; Δε θ(k,r(i)) and Δε r(k,r(i)) These are the total radial strain increment and the total tangential strain increment at node i in the unloading stage k, respectively.

[0144] According to Hooke's Law, the elastic strain increment between two adjacent unloading stages can be calculated using the following formula:

[0145]

[0146] In the formula, G is the rock mass shear modulus, and v is Poisson's ratio.

[0147] The relationship between the increments of plastic strain can be expressed as follows:

[0148]

[0149] In the formula, For the increment of plastic radial strain, Let N be the plastic tangential strain increment, g be the plastic potential function, and N be the plastic strain increment. ψ = (1+sinψ) / (1-sinψ), where ψ is the shear dilatation angle.

[0150] The incremental form of the geometric equation is:

[0151]

[0152] Substituting equations (25) to (28) and (30) to (31) into equation (29), the displacement compatibility equation of the plastic zone can be expressed as follows:

[0153]

[0154] According to formula (32), the stress increment of each calculation node in the current unloading stage k in the plastic zone relative to the previous unloading stage (k-1) needs to be calculated first:

[0155]

[0156] According to the Runge-Kutta equations, considering the initial conditions, the displacement increment can be calculated. Then, the displacement distribution in the plastic zone can be obtained:

[0157]

[0158] The displacement is updated through the steps above. The following describes the parameter update steps, including updating the surrounding rock mechanical parameters and NPR anchor / cable parameters.

[0159] Update the surrounding rock mechanical parameters, including: when the radius R of the plastic zone p If the value is greater than 0, the plastic shear strain of the surrounding rock is updated based on the elastic strain increment and plastic strain increment of the surrounding rock.

[0160] In this embodiment, the evolution of the surrounding rock mechanical parameters and the plastic shear strain γ p(k,r(i)) Calculate using the following formula:

[0161] γ p(k,r(i)) =γ p(k-1,r(i)) +Δγ p(k,r(i)) (35)

[0162]

[0163] In the formula, γ p(k-1,r(i)) γ p(k,r(i)) Let Δγ be the plastic shear strain of node i in the (k-1)th and kth unloading stages. p(k,r(i)) This represents the change in plastic shear strain at node i of the two adjacent unloading stages, k-1 and k-th.

[0164] Update NPR anchor / cable parameters, including: when the NPR anchor / cable deformation is greater than the maximum deformation Δu. fWhen the condition is met, the axial force of the NPR anchor rod / cable is set to 0; otherwise, the axial force of the NPR anchor rod / cable is updated according to the displacement difference between the two ends of the NPR anchor rod / cable, i.e., formula (3), and its value is equal to the radial uniform support pressure p. s .

[0165] Specifically, based on formulas (27) and (31), the following can be calculated: and Δε θ Substituting into formula (25) yields the result. The deformation Δu2 of the NPR anchor / cable during the coordinated deformation stage, i.e. the elongation of the NPR anchor / cable, can be obtained according to formula (2).

[0166] Step S4: Based on the solution results of the ground response of the tunnel under the action of NPR anchors / cables, determine the excavation compensation scheme for the deep-buried tunnel.

[0167] After obtaining the solution results for the stratum response, the excavation compensation support scheme for tunnel engineering can be designed or adjusted based on the interaction mechanism between the surrounding rock and NPR anchors / cables reflected in the solution results. For example, parameters such as the number, spacing, support time, prestress magnitude, and constant resistance value of NPR anchors / cables can be adjusted to obtain better excavation compensation support effects.

[0168] To further understand the scheme of this embodiment, as an example, the semi-analytical method for deep-buried tunnels based on excavation compensation can be described as follows: Figure 4a The implementation of technical steps, such as Figure 4a As shown, in this method:

[0169] Step 1: Input material parameters, boundary conditions, NPR anchor / cable parameters, unloading steps, and the number of surrounding rock rings n. Here, material parameters refer to the surrounding rock mechanical parameters. The boundary conditions input in the initial step are the initial boundary conditions. Combined with the NPR anchor / cable parameters, the total number of unloading stages m, and the total number of surrounding rock rings n, these are used as input parameters for the semi-analytical solution, and the calculation process is started.

[0170] Step 2: Divide the surrounding rock into n rings and n+1 nodes, and calculate the virtual support force increment.

[0171] Step 3: Calculate the radial stress σ at the elastoplastic interface based on existing research. rp .

[0172] Step 4: Determine whether to apply anchor bolts. If no anchor bolts are applied, apply radially uniform support pressure p. s Set to 0, then proceed to the step of calculating the boundary conditions according to (5). If anchor bolts have been applied, calculate the total elongation Δu of the anchor bolts according to formula (2), and then determine whether the anchor bolts have failed: compare Δu with the maximum deformation Δu f If Δu > Δuf This indicates that the anchor bolt has failed, and the radial uniform support pressure p will be reduced. s Set to 0, then proceed to the step of calculating the boundary conditions according to (5); if the anchor bolt has not failed, i.e., Δu≤Δu f Then, the radial uniform support pressure p is calculated according to formula (1). s Simultaneously, calculate the NPR anchor bolt / cable axial force according to formula (3); then calculate the boundary condition p according to formula (5). bk The steps.

[0173] Step 5: If the radial stress σ at all nodes r >σ rp If no plastic region is generated, then it is determined that no plastic region has been generated: Let R p =0, calculate and update σ at all nodes according to formulas (19) and (20). r and σ θ The displacement distribution u is calculated according to formula (23). r .

[0174] Step 6: If the radial stress σ is not at all nodes r >σ rp It can be determined that R p >r0, a plastic region is generated: record R p The position is calculated and updated according to formulas (21) and (22) for the elastic zone σ. r and σ θ The stress increment is calculated according to formula (33), and the displacement distribution in the plastic zone is calculated using the Runge-Kutta method according to formulas (32) and (34). The displacement distribution in the elastic zone is calculated according to formula (24). The plastic shear strain is calculated according to formulas (35) and (36), and the mechanical parameters are updated.

[0175] Step 7: Calculate the NPR anchor / cable elongation according to formula (2); then return to step 4 and repeat the steps of determining whether to apply the anchor and the subsequent steps. After repeating m times, end the loop and output the formation response and axial force evolution of the model.

[0176] Furthermore, to verify the effectiveness of the method provided in this embodiment, the solution results of the formation response calculated in this embodiment are compared with the semi-analytical solution provided in existing literature (hereinafter referred to as Literature 1) and the simulation results of FLAC3D, under both cases of not using NPR anchors / cables and using NPR anchors / cables. Specifically, as shown in... Figure 5As shown, a 100m×100m two-dimensional simulation model was established in FLAC3D. A circular tunnel with a radius of 5 meters was excavated at the center of the model. The main rock was the red bed soft rock widely distributed in the Dianzhong Water Diversion Project. Based on the stress-strain curve obtained from the red bed soft rock at a depth of 220 meters, a constitutive model of strain-softened rock mass mechanical properties was used to consider the characteristics of strain softening. As an example, the rock mass parameters are shown in Table 1. According to the engineering geological survey, the hydrostatic pressure of the model was set to the maximum horizontal stress of 8.008 MPa. After calibrating the model parameters, numerical simulation was performed to obtain the stress distribution and displacement distribution of the surrounding rock.

[0177] Table 1 Rock Mass Parameters

[0178]

[0179] Figure 6 The paper demonstrates a comparative verification of the formation response using the semi-analytical solution provided in this embodiment, the semi-analytical solution provided in reference 1, and the FLAC3D numerical simulation results without the use of NPR anchors / cables. (a) shows the surrounding rock stress distribution, and (b) shows the displacement distribution. The results show that, without the use of NPR anchors / cables, the semi-analytical solution provided in this embodiment, the semi-analytical solution in reference 1, and the numerical simulation results are all in good agreement. It should also be noted that the types and values ​​of the rock mass parameters may differ depending on the selected constitutive model, and the simulation results of the strain-softening constitutive model may also vary; however, they all generally agree with the analytical solution results provided in this embodiment.

[0180] Since existing technologies lack analytical solutions for excavation compensation, numerical simulations are used to compare the interaction between the NPR anchor / cable and the surrounding rock with the method provided in this embodiment. In both the FLAC3D numerical simulation and the scheme of this embodiment, NPR anchors / cables with a length of 5.0 meters are used, and the stress release coefficient of the NPR anchor / cable is 0.5. Other parameters are shown in Table 2. Table 2 is as follows:

[0181] Table 2. Relevant parameters for numerical simulation

[0182]

[0183] Figure 7 This is a schematic diagram of stress distribution when using NPR anchors / cables. Figure 7As shown, an axial force curve (axial growth curve) is plotted based on the semi-analytical solution of this embodiment, and an axial force cloud map is plotted based on the FLAC3D numerical simulation results. It can be seen from the figure that in the numerical solution obtained by the FLAC3D simulation, the axial force range of the NPR anchor / cable is 150kN to 172.72kN. In the solution provided by this embodiment, the axial force of the NPR anchor / cable is 165.49kN, indicating that the solution provided by this embodiment has good performance, achieving computational accuracy comparable to numerical simulation, while avoiding the large amount of computation required by numerical simulation, thus improving efficiency. Observing the axial growth curve plotted in this embodiment, the axial force of the NPR anchor / cable exhibits a two-stage growth as the stress release coefficient α increases. When α is between 0.5 and 0.81, the surrounding rock is in an elastic state, and the axial force growth curve is linear. When α = 0.81, the tunnel wall surrounding rock enters a plastic state, and thereafter, the axial force growth curve exhibits a non-linearity.

[0184] Figure 8 This diagram illustrates the stress and displacement comparison when using NPR anchor bolts / cables. (a) shows the stress distribution, and (b) shows the displacement distribution. The red circles represent the results of FLAC3D numerical simulation, and the black curves represent the stress and displacement distribution curves calculated by the method provided in this application's embodiments. Figure 8 As shown, the calculation results of the method provided in this embodiment are in excellent agreement with the FLAC3D numerical simulation results, indicating that the method provided in this embodiment can well describe the interaction mechanism between NPR anchors / cables and the surrounding rock. Considering the supporting effect of NPR anchors / cables, the radial stress of the tunnel inner wall is slightly greater than 0.0.

[0185] In summary, the method provided in this embodiment, considering the unloading effect during excavation, adopts the finite difference method and proposes a semi-analytical solution method for the formation response suitable for ECM. This method is used to study the interaction mechanism between NPR anchors / cables and the surrounding rock, and to design excavation compensation based on the solution results. This technical solution considers three deformation stages for the surrounding rock and NPR anchors / cables: the initial deformation stage, the prestressing stage, and the synergistic deformation stage. When the deformation of the NPR anchor / cable exceeds the set maximum deformation, the NPR anchor / cable will break. The formation reaction force calculated by the method provided in this application is in excellent agreement with the results of reference 1 and FLAC3D numerical simulation.

[0186] Comparing the ground reaction forces at locations with and without NPR anchors / cables, with ordinary anchors / cables, and with NPR anchors / cables, both radial and tangential stresses in the tunnel wall increase under NPR anchors / cables, indicating that NPR anchors / cables can improve the bearing capacity of the surrounding rock. The size of the plastic zone decreases. The surrounding rock enters the plastic zone with delayed acceleration. Under the action of NPR anchors / cables, the displacement of the tunnel wall decreases.

[0187] Furthermore, the semi-analytical solution provided in this embodiment was used to perform parametric analysis on timed support, prestress magnitude, and constant resistance value. The results show that as the timed support is delayed, the support effect of the NPR anchor / cable cannot be fully realized. The displacement of the tunnel wall gradually increases. With the increase of prestress, the displacement of the tunnel wall gradually decreases. Increasing the constant resistance value is another important factor in reducing tunnel wall deformation. Therefore, the method provided in this embodiment can provide guidance for the application of ECM in deeply buried tunnels.

[0188] In summary, this embodiment proposes a semi-analytical ECM method based on the finite difference method to study the influence of NPR anchors / cables on the ground reaction force. Then, the design or adjustment of excavation compensation support is based on the calculation results of the ECM semi-analytical method. In the ECM semi-analytical method, the stress release factor method is used to simulate the unloading and deformation processes of the NPR anchors / cables and the surrounding rock. Once the deformation of the NPR anchors / cables exceeds the preset maximum deformation, fracture will occur. This method can solve for the ground response of the tunnel under the action of NPR anchors / cables, including stress distribution, deformation distribution, and the surrounding rock convergence constraint curve. The proposed solution is verified by comparing it with the semi-analytical and numerical solutions proposed in existing literature 1. The results show that ordinary anchors / cables will fracture when the deformation is large. However, NPR anchors / cables can deform together with the surrounding rock, improving the bearing capacity of the surrounding rock. The corresponding support measures are adjusted based on the influence of NPR anchor / cable parameters (including support time, prestress magnitude, and constant resistance value) on the ground reaction force. Early use of NPR anchors / cables with higher prestress and increasing the constant resistance of NPR anchors / cables can better control the deformation of the surrounding rock.

[0189] Based on the same inventive concept, this embodiment provides a semi-analytical system for deep-buried tunnels based on excavation compensation, the system comprising:

[0190] The parameter acquisition module is used to acquire the surrounding rock mechanical parameters, initial boundary conditions, and NPR anchor / cable parameters of the deep-buried tunnel.

[0191] The model building module is used to divide the tunnel excavation process into m unloading stages for the collaborative deformation stage of the stratum response using the finite difference method, and obtains a calculation model of the collaborative deformation of NPR anchors / cables and surrounding rock considering the unloading path.

[0192] The synergistic deformation stage is the stage in which the surrounding rock and the NPR anchor / cable jointly cause stratum deformation after the NPR anchor / cable is installed.

[0193] The solution module is used to calculate the formation response at each stage based on the calculation model of NPR anchor / cable and surrounding rock co-deformation, combined with surrounding rock mechanical parameters, initial boundary conditions, and NPR anchor / cable parameters, to obtain the solution results of the formation response of the tunnel under the action of NPR anchor / cable.

[0194] The design module is used to determine the excavation compensation scheme for deep-buried tunnels based on the solution results of the ground response of the tunnel under NPR anchor / cable action.

[0195] The deep-buried tunnel semi-analytical system based on excavation compensation provided in this embodiment can realize the steps and processes of the deep-buried tunnel semi-analytical method based on excavation compensation provided in any of the above embodiments, and achieve the same technical effect, which will not be described in detail here.

[0196] This application also provides a computer program product comprising computer-executable instructions. In one embodiment, the computer-executable instructions are used to cause a computer to perform the functions described in the method embodiments above.

[0197] Computer-executable instructions can be stored in a computer-readable storage medium. This application also provides a computer-readable storage medium storing executable instructions. In one embodiment, the computer-executable instructions are used to cause a computer to perform the functions described in the method embodiments above.

[0198] The computer-readable storage medium provided in the embodiments of this application may be random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), register, hard disk, portable hard disk, CD-ROM, or any other form of computer-readable storage medium known in the art.

[0199] Computer-executable instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another. For example, the computer program or instructions can be transferred from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means. The computer-readable storage medium can be any available medium that a computer can access, or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium, such as a floppy disk, hard disk, or magnetic tape; it can also be an optical medium, such as a digital video disc (DVD); or it can be a semiconductor medium, such as a solid-state drive.

[0200] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A semi-analytical method for deep-buried tunnel based on excavation compensation, characterized in that, include: Step S1: Obtain the surrounding rock mechanical parameters, initial boundary conditions, and NPR anchor / cable parameters for the deep-buried tunnel; Step S2: For the collaborative deformation stage of the stratum response, the tunnel excavation process is divided into m unloading stages to obtain a calculation model of the collaborative deformation of NPR anchors / cables and surrounding rock considering the unloading path. The cooperative deformation stage is a stage in which the surrounding rock and the NPR anchor / cable jointly cause stratum deformation after the NPR anchor / cable is installed. The calculation model of the cooperative deformation of the NPR anchor / cable and the surrounding rock comprises: dividing the surrounding rock in each unloading stage into n annuli with the same thickness, each annulus being surrounded by nodes with inner and outer radii of and respectively; adopting variables containing two dimensions to represent the mechanical state of the surrounding rock at each node; the two dimensions comprise a first dimension and a second dimension, the first dimension being a radius, and the second dimension being an unloading stage; m and n are positive integers, and i is a node serial number, and the value range of i is 1, 2, … n. Step S3: Based on the calculation model of the coordinated deformation of NPR anchors / cables and surrounding rock, and combined with the mechanical parameters of surrounding rock, initial boundary conditions, and NPR anchors / cables, the finite difference method is used to solve the ground response of each unloading stage, and the solution results of the ground response of the tunnel under the action of NPR anchors / cables are obtained. Step S4: Based on the solution results of the ground response of the tunnel under the action of NPR anchors / cables, determine the excavation compensation scheme for the deep-buried tunnel; Step S3 includes: Step S31: Based on incremental theory, calculate the change in virtual support pressure on the tunnel wall at each unloading stage. ; Step S32: Based on the change in virtual support pressure on the tunnel wall By combining the surrounding rock mechanical parameters and NPR anchor / cable parameters, the boundary conditions for each unloading stage are updated; Step S33: Based on the equilibrium equation and yield equation of the surrounding rock, use the Runge-kutta method to solve for the stress distribution at each unloading stage; Step S34: Calculate the displacement distribution at each unloading stage; Step S35: Update the surrounding rock mechanical parameters and NPR anchor / cable parameters for each unloading stage; Update NPR anchor / cable parameters, including: When the NPR anchor bolt / cable deformation is greater than the maximum deformation When the condition is met, set the axial force of the NPR anchor / cable to 0; otherwise, update the axial force of the NPR anchor / cable based on the displacement difference between the two ends of the NPR anchor / cable. ； In the formula, It refers to the deformation of the NPR anchor / cable during the coordinated deformation stage, i.e., the displacement difference between the two ends of the NPR anchor / cable. Applying prestress The initial deformation generated at that time, F is the axial force of the NPR anchor rod / cable. It refers to the stiffness of the NPR anchor bolt / cable.

2. The method according to claim 1, characterized in that, Based on the equilibrium and yield equations of the surrounding rock, the Runge-Kutta method is used to solve for the stress distribution at each unloading stage, including: In each unloading stage, it is first assumed that the surrounding rock is in a plastic state. Based on the preset initial conditions, the radial stress of each node is solved using the Runge-kutta method. If the radial stress at each node is greater than the radial stress at the boundary of the elastoplastic region, then determine the radius of the plastic region. The value is 0, and the stress state at all nodes and the displacement of all nodes are updated according to the tunnel radius R0; If the radial stress at each node is less than or equal to the radial stress at the boundary of the elastoplastic region, then the radius of the plastic region is determined. Greater than 0, and based on the radius of the plastic zone Update the stress state and displacement of the elastic and plastic regions respectively.

3. The method according to claim 2, characterized in that, Update the surrounding rock mechanical parameters for each unloading stage, specifically as follows: When the radius of the plastic zone If the value is greater than 0, the plastic shear strain of the surrounding rock is updated based on the elastic strain increment and plastic strain increment of the surrounding rock.

4. A semi-analytical system for deep-buried tunnels based on excavation compensation, characterized in that, include: The parameter acquisition module is used to acquire the surrounding rock mechanical parameters, initial boundary conditions, and NPR anchor / cable parameters of the deep-buried tunnel. The model building module is used to divide the tunnel excavation process into m unloading stages for the collaborative deformation stage of the stratum response using the finite difference method, and obtains a calculation model of the collaborative deformation of NPR anchors / cables and surrounding rock considering the unloading path. The coordinated deformation stage refers to the stage after the NPR anchor / cable is installed, where the surrounding rock and the NPR anchor / cable jointly cause formation deformation. The calculation model for the coordinated deformation of the NPR anchor / cable and the surrounding rock includes: dividing the surrounding rock in each unloading stage into n annular surfaces of equal thickness, each annular surface consisting of inner and outer radii of... and The nodes form a boundary; a variable with two dimensions is used to characterize the mechanical state of the surrounding rock at each node; the two dimensions include a first dimension and a second dimension, the first dimension being the radius and the second dimension being the unloading stage; m and n are positive integers, and i is the node number, with a value range of 1, 2, ... n; The solution module is used to calculate the ground response at each stage based on the computational model of the coordinated deformation of NPR anchors / cables and surrounding rock, combining surrounding rock mechanical parameters, initial boundary conditions, and NPR anchor / cable parameters, to obtain the solution results of the tunnel's ground response under the action of NPR anchors / cables; including: Based on incremental theory, the change in virtual support pressure on the tunnel wall during each unloading stage is calculated. ; Based on the change in virtual support pressure of the tunnel wall By combining the surrounding rock mechanical parameters and NPR anchor / cable parameters, the boundary conditions for each unloading stage are updated; Based on the equilibrium equation and yield equation of the surrounding rock, the stress distribution at each unloading stage is solved using the Runge-kutta method. Calculate the displacement distribution at each unloading stage; Update the surrounding rock mechanics parameters and NPR anchor / cable parameters for each unloading stage; Update NPR anchor / cable parameters, including: When the NPR anchor bolt / cable deformation is greater than the maximum deformation When the condition is met, set the axial force of the NPR anchor / cable to 0; otherwise, update the axial force of the NPR anchor / cable based on the displacement difference between the two ends of the NPR anchor / cable. ； In the formula, It refers to the deformation of the NPR anchor / cable during the coordinated deformation stage, i.e., the displacement difference between the two ends of the NPR anchor / cable. Applying prestress The initial deformation generated at that time, F is the axial force of the NPR anchor rod / cable. It refers to the stiffness of the NPR anchor bolt / cable; The design module is used to determine the excavation compensation scheme for deep-buried tunnels based on the solution results of the ground response of the tunnel under NPR anchor / cable action.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the semi-analytical method for deep-buried tunnels based on excavation compensation as described in any one of claims 1 to 3.

6. An electronic device, characterized in that, include: The memory, the processor, and the program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the steps of the semi-analytical method for deep-buried tunnels based on excavation compensation as described in any one of claims 1 to 3.

7. A computer program product, characterized in that, It includes computer-executable instructions for causing a computer to perform the steps of the semi-analytical method for deep-buried tunnels based on excavation compensation as described in any one of claims 1 to 3.

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