Submarine shield tunnel lining internal force analysis method based on matrix displacement method

Abstract

The invention discloses a seabed shield tunnel lining internal force analysis method based on a matrix displacement method, and belongs to the field of seabed shield tunnel analys.The seabed shield tunnel lining internal force is calculated through the matrix displacement method in structural mechanics, safety early warning is given out in time, and compared with a traditional theoretical calculation and simulation prediction method, the method has the advantages that the method is simple and convenient to operate. The scheme shows remarkable advantages in the field of internal force solution and structural damage prediction of the lining of the shield tunnel crossing the deep sea high-water-pressure seepage area, tedious experiment and modeling processes are omitted during practice, the goal of low-carbon early warning can be achieved while cost reduction and efficiency improvement are achieved, meanwhile, accurate prediction can be achieved, and the method is suitable for large-scale popularization and application. And a solid technical support is provided for effective protection of safe construction of tunnel engineering.

Description

Technical Field

[0001] This invention belongs to the field of submarine shield tunnel analysis, specifically relating to a method for analyzing the internal forces of submarine shield tunnel lining based on the matrix displacement method. Background Technology

[0002] As a crucial component of urban infrastructure, tunnel construction is experiencing continuous growth in both scale and number. During tunnel construction, excavation disrupts the structural balance of the original soil, causing deformation of the surrounding soil. Once this deformation stabilizes, stress is fed back to the lining, resulting in changes in the lining's stress state and making it extremely complex. Furthermore, in the construction of undersea tunnels, in addition to the pressure from the surrounding rock and overburden, there is also the pressure of deep water. When traversing weak subsurface layers, risks such as slippage, lining misalignment, and cracking occur.

[0003] In existing technologies, the calculation of internal forces in tunnel linings often employs the state-space method. For example, the invention patent with publication number CN113177288A discloses an analysis and calculation method for the internal forces and relative deformations of circular shield tunnel linings based on measured data and the state-space method. The loads on the circular shield tunnel include two cases: a) commonly used design loads, namely, ground loads and soil reaction forces. The ground loads are the vertical soil pressure at the top and bottom of the tunnel and the horizontal soil pressure on both sides of the tunnel. The soil reaction forces are the forces applied to the lining by the ground springs after being stressed; b) test conditions, where the loads are applied by jacks. The calculation yields state vectors for each location of the entire lining, including internal forces and displacements. However, this method does not consider the overall shape of the shield tunnel and ignores the influence of inter-segment interactions. Furthermore, when collecting measured data, the complex geological environment surrounding the lining is not specific enough, and the complex situation is unclear. The testing requires a large investment of manpower and equipment on the construction site, resulting in high testing costs. Moreover, due to the complex underground environment, the accuracy of monitoring results is difficult to guarantee, reducing work efficiency and the precision of the decomposition results. In addition, considering that in addition to the pressure of the surrounding rock and soil, there is also deep water pressure in the undersea tunnel, the traditional method is not applicable.

[0004] Therefore, it is necessary to further study and develop new methods for calculating the internal forces of shield tunnel linings in deep-buried seabed soft strata, in order to improve work efficiency, reduce testing costs, and ensure the quality of analysis results. Summary of the Invention

[0005] To address the shortcomings of traditional analysis methods, such as insufficient detail regarding the complex geological environment surrounding the lining, unclear complexities, the need for significant manpower and equipment investment at the construction site during testing, and long testing and analysis cycles, this invention provides a matrix displacement method for analyzing the internal forces of the lining of a submarine shield tunnel. By establishing a discretized lining model, introducing a joint stiffness matrix, additional water pressure, and inter-ring resistance of the lining, the calculation and analysis results are made stable and reliable.

[0006] This invention is achieved using the following technical solution: a method for analyzing the internal forces of the lining of a submarine shield tunnel based on the matrix displacement method, comprising the following steps: Step A: Establish a discretized model of the lining: Divide the single-ring lining into multiple beam elements and simplify the lining joints into elastic hinge nodes with rotational stiffness. Step B: Solve for the external pressures on the lining: including the inter-ring resistance of the lining, the water pressure on the lining, and the pressure of the surrounding rock, specifically including: Step B1: Calculate the impact of shield attitude on the inter-ring resistance of the lining; During shield tunneling, an overall displacement occurs when crossing adverse geological conditions, and calculate the impact of this situation on the internal forces; Step B2: Calculate the water pressure in the lining; Considering the water pressure during the construction of the undersea tunnel, an axisymmetric radial seepage model is used, and the pressure is calculated separately using the continuity equation and Darcy's law. Step B3: Calculate the surrounding rock pressure of the lining: The active and passive surrounding rock pressures on the lining are calculated using structural mechanics methods. In the calculation of the passive surrounding rock pressure, the influence of the water pressure on the lining is considered in addition to the active surrounding rock pressure. Step C: Calculate the internal forces of the lining based on the matrix displacement method, perform targeted processing on the stiffness matrix and transformation matrix of the lining components, and consider the shield offset displacement in the structural displacement. Specifically: Step C1: Construct the element stiffness matrix: Based on the lining body stiffness matrix, curvature correction stiffness matrix, and joint stiffness matrix, construct the element stiffness matrix; Step C2: Integrate the global stiffness matrix: Use the coordinate transformation method to convert the stiffness matrix of the lining unit in the local coordinate system into the global stiffness matrix in the global coordinate system; Step C3: Solve for nodal displacement vectors: Solve the overall stiffness matrix equation to obtain nodal displacement vectors, and correct the obtained displacements based on the tunnel boring machine slippage. Step C4: Finally, calculate the internal force vectors at the ends of each element and summarize them to obtain the overall force on the lining, i.e., the internal force of the lining.

[0007] Compared with the prior art, the advantages and positive effects of the present invention are as follows: This scheme addresses the stress mode of submarine tunnel lining by combining surrounding rock pressure and seawater pressure, and calculates the stress using the matrix displacement method. This includes establishing a discretized lining model, incorporating curved beam stiffness correction, introducing a joint stiffness matrix, considering additional seawater pressure and inter-ring resistance of the lining, making the damage analysis of the structure more convenient and the results more accurate. Because it adopts the introduction of a lining joint stiffness matrix, considers deep water pressure and the slippage of the tunnel boring machine under a weak bottom layer, and takes into account the inconsistency of local coordinate systems at both ends during matrix transformation, it ensures the stability and reliability of the assessment and analysis results. This approach effectively simplifies the operational process and improves the efficiency and quality of analysis. Simultaneously, it meets the reliability standards for surface structures during underground and subsea engineering construction, ensuring the normal progress of underground construction and the safe use of completed facilities. It holds significant importance in subway tunnel construction and renovation, and has broad application prospects and economic benefits. Attached Figure Description

[0008] Figure 1 This is a schematic diagram of the analysis method flow described in an embodiment of the present invention; Figure 2 This is a diagram of the discretized lining model according to an embodiment of the present invention; Figure 3 This is a stress diagram of a tunnel under normal conditions according to an embodiment of the present invention; Figure 4 This is an overall offset diagram of the tunnel boring machine-lining according to an embodiment of the present invention; Figure 5 The offset diagram is simplified for an embodiment of the present invention; Figure 6 This is a diagram of the water pressure calculation model according to an embodiment of the present invention; Figure 7 This is the original stress diagram of the lining in an embodiment of the present invention; Figure 8 This is a diagram illustrating the calculation of passive pressure on surrounding rock in an embodiment of the present invention; Figure 9 This is a schematic diagram of a partial coordinate system for a bent member according to an embodiment of the present invention; Figure 10 This is a diagram showing the stiffness matrix relationship of an embodiment of the present invention; Figure 11 This is a schematic diagram of the overall stress on the lining in an embodiment of the present invention. Detailed Implementation

[0009] To better understand the above-mentioned objectives, features, and advantages of the present invention, the invention will be further described below in conjunction with the accompanying drawings and embodiments. Many specific details are set forth in the following description to provide a thorough understanding of the invention. However, the invention can also be implemented in other ways different from those described herein. While maintaining the core concepts of the invention, those skilled in the art can make corresponding adjustments and optimizations, for example, using tools such as MATLAB or structural mechanics solvers may yield better results. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0010] This embodiment demonstrates that this solution is applicable to the refined mechanical analysis and design of shield tunnel lining structures under complex geological conditions of deep burial and high water pressure. It aims to ensure reliable calculation of internal forces during shield tunnel construction in complex seabed environments, accurately analyze structural stability, and combine... Figure 1 As shown, it includes the following steps: Step A: Establish a discretized model of the lining. As an arched solid structure, the mechanical properties of tunnel lining are mainly affected by the combined effects of bending moment and axial force. The entire lining is discretized and decomposed, and the joint nodes are optimized to become elastic nodes with a certain strength. The remaining parts are supported by elastic bracing to simulate the surrounding rock. The arched components (bent beams) are further transformed into elastic beams suitable for the matrix displacement method. Specifically, in the structural discretization process, beam elements capable of simultaneously withstanding bending moment and axial force are used for simulation, with each element connected by nodes. To simplify the calculation model, it is assumed that each element has a uniform thickness, and the calculated thickness is the arithmetic mean of the thicknesses at both ends of the element. Furthermore, since the thickness of each element is equal, and the thickness within a single element is also equal, the beam elements with thickness are simplified to rods for easier calculation.

[0011] Simultaneously, a balance must be struck between computational accuracy and efficiency when considering the number of elements. Based on engineering experience, it is recommended to divide the lining into 30-60 elements. Fewer than 30 elements may affect the accuracy of the calculation results; while more than 60 elements, although theoretically improving accuracy, will significantly increase computational costs, and the improvement in accuracy will be limited. This embodiment uses a 30-element division and simplifies the establishment of the lining discretization model, such as... Figure 2 As shown in the figure, the elastic support is arranged radially, where the dots represent rigid hinges, the numbers 1, 2, 3... are element nodes, and ①, ②, ③... are the divided rod elements. This partitioning method can meet both engineering accuracy requirements and ensure computational efficiency.

[0012] For ease of calculation, some elastic supports are used to replace the rock pillars, and they are hinged to the nodes between the support structure units so that they do not bear bending moments, but only axial forces. The direction of the elastic supports should be consistent with the direction of the elastic reaction force, which is radial. For the sake of drawing convenience, the diagram has been uniformly treated, and the friction between the support structure and the surrounding rock is ignored. Only axial pressure is transmitted (due to the adhesion between the surrounding rock and the support structure, a small amount of axial tension may also be transmitted).

[0013] Step B: Calculate the external pressure on the lining, including the inter-ring resistance of the lining, the water pressure of the lining, and the pressure of the surrounding rock of the lining; Step B1: Calculate the influence of shield attitude on the inter-ring resistance of the lining. Under normal conditions, the overall stress of a tunnel when excavated in a straight line is as follows: Figure 3 As shown. When the tunnel boring machine (TBM) reaches soft strata, such as clay, silt, and soft soil composite strata, due to the poor stability of the geological environment, there is a possibility of overall displacement of the TBM and its lining. Figure 4 As shown, 1 represents the planned tunneling route; 2 represents the slippage route of the weak subgrade; 3 represents the tunnel boring machine (TBM); 4 represents the lining; 5 represents the inter-ring resistance of the lining; α represents the angle between the forward direction after slippage and the planned forward direction. If the TBM does not adjust its excavation direction in time, it will briefly deviate downward (or upward), and there will also be a tendency for inter-ring drag, resulting in inter-ring resistance. The tunnel is simplified as a mechanical member. Based on force balance, the total external force is balanced with its own weight. Therefore, the influence of gravity is not considered. A member length of 5 times the tunnel cross-sectional dimension is selected. The inter-ring resistance is then calculated by combining the slippage distance ∆ detected by the tunnel shield. The simplified solution diagram is shown below. Figure 5 As shown. The graphical method is used to solve for the end shear force. Where EI represents the bending stiffness, the value of which is determined by the material strength, and D represents the diameter of the tunnel section. This indicates the amount of displacement caused by the overall offset of the tunnel ring, i.e., the magnitude of the inter-ring resistance. Determine that (inter-ring resistance and end shear force are equal), and calculate the magnitude of the end shear force as described above. The loads are applied to each element in step A to obtain the nodal load matrix. .

[0014] Step B2: Calculate the water pressure in the lining. The water pressure calculation employs an axisymmetric radial seepage model, combined with the continuity equation and Darcy's law. The model diagram is shown below. Figure 6 As shown, 6 represents the horizontal plane; 7 represents the seabed; h0 is the far-field head height at the tunnel center; r h r is the distance between the tunnel center and the seabed; r1 is the inner diameter of the tunnel lining; r2 is the outer diameter of the tunnel lining; r g The radius of the tunnel grouting ring; The fluid continuity equation is: The shield tunnel lining is axisymmetric, and the water head h is at an angle. Irrelevant; and considering that the pressurized water flow is only radial and independent of z, the simplified equation is: Integrating twice yields: Where C and D are constants, and D is a boundary condition.

[0015] Using Darcy's law, the flow rate Q at radius r is calculated as follows: The model consists of three regions: the surrounding rock (with radius r). h r g ), Grouting ring (radius divided into r) g The lining (with radii divided into r1 and r2) has a permeability coefficient of k for each region. r k g k f The flow rate Q is the same at each cross-section, and the head is continuous at the junction, h(r) h Given h(r1) = h0 and h(r2) = 0, the flow expressions for each zone are: Solve the water head behind the lining for: External water pressure formula , bring in have to: Will The loads are applied to each element in step A to obtain the nodal load matrix. .

[0016] Step B3: Calculate the pressure of the surrounding rock lining. The active load + passive load mode of the lining under the pressure of the surrounding rock was calculated using structural mechanics methods. The specific stress situation is as follows: Figure 7 As shown, 8 represents the vertical active pressure of the surrounding rock; 9 represents the lateral active pressure of the surrounding rock; 10 represents the excavation outline of the surrounding rock; 11 represents the lining deformation curve; 12 represents the passive pressure of elastic reaction force; 13 represents the surface line (sea level line); and 14 represents the stratigraphic boundary line.

[0017] (1) Calculate the active pressure of the surrounding rock. First, determine the active pressure on the surrounding rock, including the vertical active pressure and the lateral active pressure. The vertical active pressure is calculated using the following formula: In the formula, The vertical active pressure of the surrounding rock (kM / m). The unit weight of the surrounding rock (kN / ), Where S is the equivalent load height (m), and S is the surrounding rock grade. The formula for calculating the width influence coefficient is as follows: Where B is the tunnel width (m), and i is the rate of increase or decrease of the surrounding rock pressure when B increases by 1m. When B < 5m, i = 0.2; when B > 5m, i = 0.1.

[0018] Lateral surrounding rock pressure According to empirical formulas, for shield tunnels, a smaller load value should be selected.

[0019] Table 1 Calculation Table of Active Pressure on Lateral Surrounding Rock income , To distribute the load uniformly, , The loads are applied to each element in step A to obtain the nodal load matrix. .

[0020] (2) Calculate the passive pressure of the surrounding rock The passive pressure on the surrounding rock is calculated using the method of assuming the range of the resistance zone and the law of resistance distribution. The calculation diagram is shown below. Figure 8 This method assumes that the passive pressure on the surrounding rock on both sides of the arch follows a quadratic parabolic distribution, with the main control point being the zero point of the passive pressure, b. This point is typically located at a symmetrical centerline offset ψ. b At, ψ b The angle is 40°~60°, and the precise location is determined by successive approximation method; the zero point a of passive pressure is at the arch foot; the maximum point h of passive pressure is at the maximum lining span, close to the center point of the tunnel. For circular shield tunnels, h is located at the center of the passive pressure zone.

[0021] First, determine the internal force M at each cross-section inside the lining under the action of active pressure and water pressure seepage. i0 N i0 And calculate the displacement δ at the point of maximum resistance. h0 Then calculate σ. h When =1, M at each section of the lining structure i1 N i1and the displacement δ of point h h1 Using the superposition principle, the total displacement of point h is obtained. : In this formula, This represents the actual stress. Furthermore, according to the local deformation theory, the stress calculation formula at point h is: K is the elastic resistance coefficient of the surrounding rock.

[0022] Combining the two equations, we get: The values ​​and locations of points a, b, and the point of maximum resistance h were then obtained. A coordinate system was established to solve a quadratic function. Substituting the values ​​of the three points, the passive pressure on the surrounding rock was determined. .Will The loads are applied to each element in step A to obtain the nodal load matrix. .

[0023] Step C: Calculate the internal forces of the lining using the matrix displacement method. In this embodiment, the matrix displacement method is used to calculate the internal force of the lining. The basic principle is as follows: (1) First, the element stiffness matrix of the local coordinate system is formed; (2) After transformation matrix, the stiffness matrix of the global coordinate system is formed, and then the global stiffness matrix is ​​integrated; (3) The nodal load vector is obtained; (4) The nodal displacement vector is obtained; (5) The end force vector of the rod is calculated. The end force vector of each element is obtained and summarized to form the overall force of the lining, that is, the overall internal force of the lining is obtained. The internal force of the lining is compared with the strength of the lining material to make a timely damage warning. At the same time, according to the "Technical Specification for Monitoring of Urban Rail Transit Engineering", the total displacement of the shield tunnel in the soft stratum shall not exceed 30mm. When the monitored value exceeds 2 / 3 of the specified value, an early warning should be sent in time. Specifically: Step C1: Construct the element stiffness matrix First, determine the stiffness matrix of the reinforced concrete lining material, which can be determined based on the material strength, denoted as [Material]. The matrix originates from the basic element stiffness matrix of beams and bars in structural mechanics; then, a curvature-corrected stiffness matrix is ​​introduced. The matrix is ​​calculated and corrected based on the radius R (the distance from the tunnel center to the lining axis); finally, the joint stiffness matrix is ​​determined. Considering the stiffness of the joint material, including , The θ direction. The stiffness matrix will eventually be corrected. and joint stiffness matrix Combined lining element stiffness matrix .

[0024] In structural mechanics, this can be viewed as the internal forces at the ends of the member caused by a displacement of 1 in each direction. This method is also used for members with bending characteristics, and the effect is as follows: Figure 9 As shown, 15 represents a straight beam member, and the obtained internal forces at the beam ends are incorporated into... The curvature correction stiffness matrix is ​​obtained from .

[0025] In the formula, abcdef are the modification coefficients of the arched member calculated according to the straight beam calculation method.

[0026] = In the formula They are x, y, Stiffness in direction and rotation.

[0027] Step C2: Integrate the overall stiffness matrix The element stiffness matrix obtained in step C1 is transformed into the global stiffness matrix using the following formula: Among them, for the unit coordinate transformation matrix In a straight beam, the two endpoints are located on the same straight line, and the direction of the two sides is consistent with the angle between the two sides and the global coordinate system. Therefore, there is only one angle α. However, in an arched member, the two sides are inconsistent and should be treated separately.

[0028] Determined based on the rotation angle of each local coordinate system. For curved members, the local coordinate systems are as follows: Figure 10 As shown, the transformation matrix for the bending beam is obtained by performing transformations at both ends. .

[0029] T= The overall stiffness matrix is ​​then formed using the element integration method. .

[0030] Step C3: Calculate the nodal displacement vectors The nodal displacement vector is obtained by the following formula.

[0031] In addition to the traditional active and passive loads, the construction of submarine shield tunnels also involves significant seawater pressure and the inter-ring resistance mentioned in the previous steps. The overall force diagram is as follows: Figure 11 As shown, 16 represents the water pressure in each direction, and 17 represents the inter-ring resistance.

[0032] Simultaneously, due to the overall slippage of the shield tunnel, which involves the simultaneous displacement of the ground foundation and the lining, the required... The total structural displacement is obtained by superimposing the overall slip on the basis. max, max= +δ.

[0033] Step C4: Calculation of Lining Internal Forces The internal force equations can be solved using the matrix displacement method in structural mechanics as follows: in, The vector of internal forces at the rod end; The element stiffness matrix; This is the element coordinate transformation matrix; The element displacement matrix; This is the nodal load vector, which is opposite to the external pressure P; Finally, the matrix displacement method formula was modified for bending members before calculation. This method reduces the error caused by directly using the matrix displacement method for bending members. On the other hand, it simplifies the complex stress characteristics of current undersea tunnels and provides a comprehensive stress mode, which provides a reference for the internal force calculation of current undersea tunnels. Furthermore, this method, after targeted processing, is also applicable to non-undersea tunnels.

[0034] This invention, while ensuring prediction accuracy, can accurately calculate the internal forces of the lining using structural mechanics methods combined with the structural strength rheology theory under high water pressure seepage, and provide timely warnings based on the obtained internal force relationships in accordance with national construction standards. The application of this invention not only avoids unnecessary resource waste caused by over-analysis but also effectively prevents structural safety hazards that may arise from insufficient calculation accuracy.

[0035] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments for application in other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for analyzing the internal forces of the lining of a submarine shield tunnel based on the matrix displacement method, characterized in that, Includes the following steps: Step A: Establish a discretized model of the lining: Divide the single-ring lining into multiple beam elements and simplify the lining joints into elastic hinge nodes with rotational stiffness. Step B: Solve for the external pressures on the lining: including the inter-ring resistance of the lining, the water pressure on the lining, and the pressure of the surrounding rock of the lining; Step C: Calculate the internal forces of the lining based on the matrix displacement method, perform targeted processing on the stiffness matrix and transformation matrix of the lining components, and consider the shield offset displacement in the structural displacement. Specifically: Step C1: Construct the element stiffness matrix: Based on the lining body stiffness matrix, curvature correction stiffness matrix, and joint stiffness matrix, construct the element stiffness matrix; Step C2: Integrate the global stiffness matrix: Use the coordinate transformation method to convert the stiffness matrix of the lining unit in the local coordinate system into the global stiffness matrix in the global coordinate system; Step C3: Solve for nodal displacement vectors: Solve the overall stiffness matrix equation to obtain nodal displacement vectors, and correct the obtained displacements based on the tunnel boring machine slippage. Step C4: Finally, calculate the internal force vectors at the ends of each element and summarize them to obtain the overall force on the lining, i.e., the internal force of the lining.

2. The method for analyzing the internal forces of the lining of a submarine shield tunnel based on the matrix displacement method according to claim 1, characterized in that: In step A, the entire lining is discretized and decomposed. At the same time, the nodes at the lining connection are optimized and transformed into elastic nodes with a certain strength. The remaining parts are supported by elastic supports to mimic the surrounding rock protection. In addition, the single-ring lining is simplified into an arched component and then transformed into an elastic beam.

3. The method for analyzing the internal forces of the lining of a submarine shield tunnel based on the matrix displacement method according to claim 1, characterized in that: Step B specifically includes the following steps: Step B1: Calculate the impact of shield attitude on the inter-ring resistance of the lining; During shield tunneling, an overall displacement occurs when crossing adverse geological conditions, and calculate the impact of this situation on the internal forces; Step B2: Calculate the water pressure in the lining; Considering the water pressure during the construction of the undersea tunnel, an axisymmetric radial seepage model is used, and the pressure is calculated separately using the continuity equation and Darcy's law. Step B3: Calculate the surrounding rock pressure of the lining: The active and passive surrounding rock pressures on the lining are calculated using structural mechanics methods. In the calculation of the passive surrounding rock pressure, the influence of the water pressure on the lining is considered in addition to the active surrounding rock pressure.

4. The method for analyzing the internal forces of the lining of a submarine shield tunnel based on the matrix displacement method according to claim 3, characterized in that: In step B1, the inter-ring resistance P of the lining rings 阻 = Where EI represents the bending stiffness and D represents the tunnel cross-sectional radius. This indicates the offset of this tunnel ring due to the overall displacement.

5. The method for analyzing the internal forces of the lining of a submarine shield tunnel based on the matrix displacement method according to claim 3, characterized in that: In step B2, the lining water pressure is determined using an axisymmetric radial seepage model, combined with the continuity equation and Darcy's law. The lining water pressure is: , , The unit weight of water is represented by h0, and the far-field head height is represented by r at the tunnel center. h r is the distance between the tunnel center and the seabed; r1 is the inner diameter of the tunnel lining; r2 is the outer diameter of the tunnel lining; r g Let k be the radius of the tunnel grouting ring. r k g k f The value represents the permeability coefficient for each region.

6. The method for analyzing the internal forces of the lining of a submarine shield tunnel based on the matrix displacement method according to claim 3, characterized in that: In step B3, the calculation method for the lining surrounding rock pressure is as follows: (1) Active pressure of surrounding rock: Vertical surrounding rock active pressure: ,in, , This refers to the active pressure on the vertical surrounding rock. The density of the surrounding rock is [value missing]. The height is the equivalent load, and S is the surrounding rock grade. This is the width influence coefficient; Vertical active pressure of surrounding rock: When the surrounding rock level is I~II, III, IV, V and VI, the corresponding lateral active pressure of surrounding rock is 0, <0.15, respectively. (0.15~0.3) (0.3~0.5) and (0.5~1.0) ; (2) Passive pressure of surrounding rock: The passive pressure of surrounding rock is calculated by assuming the range of resistance zone and the law of resistance distribution.

7. The method for analyzing the internal forces of the lining of a submarine shield tunnel based on the matrix displacement method according to claim 1, characterized in that: In step C1, the element stiffness matrix is ​​constructed using the following method: First, determine the body stiffness matrix of the reinforced concrete lining based on the material strength, denoted as . Then, a curvature correction stiffness matrix is ​​introduced based on the body stiffness matrix. The calculation was corrected based on the distance from the tunnel center to the lining axis; finally, the joint stiffness matrix was determined. Finally, the stiffness matrices of the above elements are combined to obtain the stiffness matrix of the lining element. , .

8. The method for analyzing the internal forces of the lining of a submarine shield tunnel based on the matrix displacement method according to claim 7, characterized in that: In step C2, the element stiffness matrix obtained in step C1 is transformed into the global stiffness matrix. The specific formula is as follows: ,in, The element coordinate transformation matrix is ​​then used to form the global stiffness matrix through the element integration method. .

9. The method for analyzing the internal forces of the lining of a submarine shield tunnel based on the matrix displacement method according to claim 8, characterized in that: In step C3, considering the resistance between the lining rings, special treatment is given to the slippage phenomenon in the weak sublayer. Specifically, the nodal displacement vector is obtained through matrix operations using the following formula. : Where P represents the external force acting on the lining. Indicates the active pressure of the surrounding rock. Indicates the passive pressure on the surrounding rock. Indicates the water pressure in the lining. Indicates the resistance between the lining rings; Simultaneously, due to the overall slippage of the shield tunnel, which involves the simultaneous displacement of both the foundation and the lining, the required... Based on the overall slip, max, that is max= +δ, max represents the total displacement of the structure. This indicates the offset of this tunnel ring due to the overall displacement.

10. The method for analyzing the internal forces of the lining of a submarine shield tunnel based on the matrix displacement method according to claim 1, characterized in that: In step C4, when calculating the internal forces of the lining, the internal force equations are solved using the matrix displacement method in structural mechanics as follows: in, The vector of internal forces at the rod end; The element stiffness matrix; This is the element coordinate transformation matrix; The element displacement matrix; The nodal load vector is opposite to the external pressure P; finally, the matrix displacement method formula is modified for bending members before calculation. When lining slippage occurs, the total displacement used to solve for internal forces also includes the overall offset caused by slippage.

Images